The coldest temperature recorded in a city in Texas was −22.3°F. The coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold. What equation can be used to represent the coldest temperature recorded at Vostok Station in °F?

Answers

Answer 1

The equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given that the coldest temperature recorded in a city in Texas was −22.3°F and the coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold.

This means that the coldest temperature recorded at Vostok Station in Antarctica was

4*(−22.3)°F = 89.2°F

Hence, the equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

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Related Questions

Suppose you roll the number cube 199 more times would you expect the experimental probability of rolling a 3 or 4 the same as your answer in exercise 5

Answers

Not really because the 5 wouldn’t be divisible by 3 or 4 or 199 so no

Alexia used three reams of paper in her first semester of school. Each ream has the same number of sheets. She used another 40 sheets after that. Write an expression to represents the number of sheets Alexia used

Answers

An expression to represent the number of sheets Alexia used is y = 3x + 40.

In math, expressions are mathematical statements with a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

The mathematical operators can be any of addition, subtraction, multiplication, or division. For example, p + q is an expression where p and q are terms having an addition operator in between.

There are two types of expressions, numerical expressions - which contain only numbers, and algebraic expressions- which contain both numbers and variables.

let

x = the number of sheets per ream

y = the total number of sheets

Alexia used three reams of paper, so the total number of sheets per ream will be 3x since each ream has the same number of sheets.

After that, she used another 40 sheets. Therefore the expression will become as

y = 3x + 40 represents the total number of sheets Alexia used.

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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.

PLSSSSS HELPPP!!!!!

Answers

The surface area of the rectangular prism is 112 square metes.

What is surface area?

The sum of all area of each surface that make up an object is referred to as its surface area.

So that in the given question,

Area of a rectangle = length x width

i. area of its base = length x width

                            = 8 x 2

                            = 16 sq. m

ii. area of its front surface = length x width

                                      = 4 x 8

                                      = 32 sq. m

iii. area of it one of its sides = length x width

                                    = 4 x 2

                                    = 8 sq. m

Therefore,

surface area of the rectangular prism = (2 x 16) + (2 x 32) + (2 x 8)

                                       = 32 + 64 + 16

                                       = 112

The surface area of the rectangular prism is 112 square meters.

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The 5th graders are going to paint miniature self portraits in art class. Each student has a canvas that is 5. 3 cm wide and 8. 5 cm tall.


The art teacher has 6 bottles of white paint for the background. Each bottle covers 220. 8 square cm of canvas.


There are 30 students in the class.


Does he have enough paint for all the canvases? If not, how much more does he need?

Answers

There is not enough paint for all the canvases. 26.7 cm² of more white paint is required.

Area of each canvas = Length × width

Area of each canvas = 5.3 × 8.5

Performing multiplication

Area of each canvas = 45.05 cm²

Total area of canvas in the class = 45.05 × 30

Performing multiplication

Total area of canvas in the class = 1351.5 cm²

Available amount of white paint = 6 × 220.8

Performing multiplication

Available amount of white paint = 1324.8 cm²

The available amount is less than canvas area in the class.

Amount of paint required = 1351.5 - 1324.8

Performing subtraction

Amount of paint required = 26.7 cm²

Thus, 26.7 cm² of white paint is required.

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A three-column table is given. Part A C D Part 14 28 63 Whole 50 B 90 What is the value of B in the table? 64 50 40 12

Answers

Using the constant of proportionality the value for B in the table is obtained as option C: B = 40.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

The table contains three columns A, C, D.

The first row contains all the part values - 14, 28, 63

The second row contains all the whole values - 20, B, 90

It is necessary to calculate the constant of proportionality.

In this case, for A, we have 14 part and 20 whole, the constant will be -

COP = Whole / Part

COP = 20 / 14

COP = 1.42857

In this case, for C, we have 63 part and 90 whole, the constant will be -

COP = Whole / Part

COP = 90 / 63

COP = 1.42857

Since, the constant of proportionality is same for A and C, it will be same for B also.

In this case, for B, we have 28 part and B whole, the constant will be -

COP = Whole / Part

1.42857 = B / 28

B = 1.42857 × 28

B = 40

Therefore, the value for B is obtained as 40.

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A three-column table is given. Part A C D Part 14 28 63 Whole 20 B 90 What is the value of B in the table? 64 50 40 12

rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} \sqrt{3} \sqrt{7}}$, and write your answer in the form\[ \frac{a\sqrt{2} b\sqrt{3} c\sqrt{7} d\sqrt{e}}{f}, \]where everything is in simplest radical form and the fraction is in lowest terms, and $f$ is positive. what is $a b c d e f$?

Answers

The sum of a+b+c+d+e+f=57.

Apparently, you want to simplify: [tex]\frac{1}{\sqrt{2} +\sqrt{3} +\sqrt{7} }[/tex]

so the denominator is rational. It looks like the form you want is:

[tex]\frac{A\sqrt{2}+B\sqrt{3} +C\sqrt{7} +D\sqrt{E} }{F}[/tex]

And you want to know the sum A+B+C+D+E+F.

We can start by multiplying the numerator and denominator by a conjugate of the denominator. Then we can multiply the numerator and denominator by a conjugate of the resulting denominator.

[tex]\frac{1}{\sqrt{2} +\sqrt{3} +\sqrt{7}} .\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{\sqrt{2} +\sqrt{3} -\sqrt{7}} =\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{2\sqrt{6-2} } \\\\\\=\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{2\sqrt{6} -2} .\frac{\sqrt{6}+1 }{\sqrt{6} +1} =\frac{(1+\sqrt{6} )(\sqrt{2} +\sqrt{3} -\sqrt{7})}{10} \\\\\\=\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}+2\sqrt{3}+3\sqrt{2} -\sqrt{42} }{10} =\frac{4\sqrt{2} +3\sqrt{3} -\sqrt{7} -\sqrt{42} }{10}[/tex]

Comparing this to the desired form we have:

A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is : A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57

The sum of interest is 57.

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If the domain of f(x) is -3 ≤ x ≤ 9 and the range of f(x) is 2 ≤ y ≤ 15, then which of the following
statements is correct about the domain and range of 9 (x) = f(x-2) - 8?

Answers

"The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.

What is the Domain and Range of the function?

The domain of a function is the set of all input values (x-values) for which the function is defined. It is the set of all values of x for which the function is defined.

The range of a function is the set of all output values (y-values) that the function can produce. It is the set of all possible values that the function can take on.

The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.

When we shift a function horizontally, the domain remains unchanged, but the range will change. In the case of a shift of -2, the domain of f(x) is still -3≤x≤9

For 9(x) = f(x-2) - 8, it means that we are taking the output of f(x-2) and subtracting 8 from it. So, the range of 9(x) will be (2-8) ≤ y ≤ (15-8) = -6 ≤ y ≤ 7.

In summary,

The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9

The range of 9(x) = f(x-2) - 8 is -6 ≤ y ≤ 7

Hence, statement "The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.

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The line inside this circle is its

A)

radius

B)

center

C)

diameter

D)

circumference

Answers

The line inside the circle depicted in the figure is radius.

A circle is defined as the round shape lacking corners and line. However, it does comprise of all the points in a plane. The center of the circle is the middle point which is equidistant from the outer surface of the circle. The outer surface or boundary of circle is called circumference.

A line joining the centre of the circle with circumference is called radius and the same is exhibited in the adjoining figure. A line that passes through the centre of the circle and touches the circumference at two ends is called diameter. Diameter is double in size to the radius.

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The complete question is attached in the figure.

Using the vertex (5, 17) and a point (11, -109), write your equation in Vertex Form.

Answers

Answer:

y=-3.5(x−5)^2+17

Step-by-step explanation:

Let's assume that since this equation has a vertex that it is a parabola with the form y = ax^2 + bx + c.

Let's rewrite it in vertex form as:

y=a(x−h)^2+k

where h and k are the horizontal (h) and vertical (k) coordinates of the vertex.

The vertex of (5,17) gives us both h (5) and k (17),  Substituting these values gives us:

  y=a(x−5)^2+17

To find a, use the one given point the parabola intersects (11,-109) and solve for a:

y=a(x−5)^2+17

-109=a((11)−5)^2+17

-109=a(6)^2+17

-109-17=a(36)

36a = -126

a = -3.5

This leads us to:

y=-3.5(x−5)^2+17

See the attached graph.

All the information is in the picture help please

Answers

That X, w, and Z w are related we demonstrate that these are identical.

What is congruence of angle?This makes a right triangle with segment y V as the opposite side, and we once more know that X Y and segment y Z are perpendicular. The reason why these Arkan wrote them this time is because, in my mind, they are nooses of similar triangles on the triangles, X, y v um, and our other triangle will be a Z y V. Finally, we wish to demonstrate the congruence of angle visi w with angle v X w, which will be right here. So, it's a little difficult to establish this one in this instance. However, in essence, because we have previously established that X, w, and Z w are related we demonstrate that these are identical. Additionally, we demonstrated that the Zeevi Arkin Group and XVI, which border on the last side, will both inform us that our angles are same. Therefore, given that we have previously established certain elements,

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Suppose Nigel has a bag of colored wristbands,

and he chooses one without looking. The bag

contains a total of

25 wristbands and 6 of

the wristbands are blue.

What is the probability that he will choose a blue wristband

Answers

The probability that he will choose a blue wristband is 6/25.

Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.

Total number of wristbands = 25

Number of blue colour wristbands = 6

As we know, the formula of experimental probability is

Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.

Number of blue colour wristbands = 6

Total number of wristbands = 25

∴ Probability of an Event P(Blue) = 6/25

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I need help with elimination, the first part is 4x+5y=48 and the second part is 7x–3y=−10

Answers

The solution to the system of equations in this problem is given as follows:

(2,8).

How to solve the system of equations?

The system of equations for this problem is defined as follows:

4x + 5y = 48.7x - 3y = -10.

To eliminate the variable y, we multiply the first equation by 3 and the second by 5, hence:

12x + 15y = 144.35x - 15y = -50.

Adding the two equations, the solution for x is obtained as follows:

47x = 94

x = 94/47

x = 2.

Hence the solution for y is obtained as follows:

4(2) + 5y = 48

5y = 40

y = 40/5

y = 8.

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Helpppp
could somebody help me with the following question?

Answers

Answer: y = -4x -2

Step-by-step explanation:

For a linear equation, we can use this formula:

y - y_1 = m(x - x_1)

We have the slope and the coordinates, so we can just plug everything in:

y - 14 = -4( x + 4)

y - 14 = -4x -16

y = -4x -2

Answer: y=-4x-2

Explanation:

Consider the two equations below. Explain completely the similarities and differences in how you would solve each equation. Be clear and complete.

Answers

The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:

x = log3(12)

The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:

x = ∛12

How does the equation compare?

The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.

The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.

As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.

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Pls help me find the answer for this

Answers

2mi = 8min
1mi= 4min
1/4mi= 1min

Simplify
The following expression.

6 1/1 ÷ 6 91/10

A. 18

B. 1/126

C. 216

D. 1/18

Answers

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Explain about the Expression?

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these. A single term or a collection of phrases can be used to create an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.

Expressions that use numbers to perform operations. An example of a numerical expression is 2(3 + 8). At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic expression is 2(x + 8y).

The following elements can be used to determine the algebraic expressions: a single variable or a group of related variables.

              = 6/6 /546/60

               =1 / 9.1

              =0.109

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What is the value of the expression below when y=3 y=3?
3 y^2 - 4 y + 8 3 y 2 − 4 y + 8

Answers

Answer:

When y = 3, we can substitute 3 for y in the expression 3 y^2 - 4 y + 8

3(3^2) - 4(3) + 8

= 3(9) - 12 + 8

= 27 - 12 + 8

= 15

Therefore, the value of the expression 3 y^2 - 4 y + 8 when y = 3 is 15.

Answer:

Basically since y = 3 we just have to remove the 'y' from the equation and replace it with the number 3. (Also pretty sure you wrote the equation twice)

Original Equation:

3 y^2 - 4 y + 8

Modified Equation:

→ 3 (3²) - 4(3) + 8

→ 3 (9) - 12 + 8

→ 27 - 12 + 8

→ 15 (answer)

Equation with 'y' included:

→ y (y²) - 4 (y) + 8

→ y (9) - 12 + 8

→ 27 - 12 + 8

→ 15 (answer)

Which of the following is the product of the rational expressions shown below?

Answers

[tex]\frac{3x^{2} }{x^{2} +x-6}[/tex] is the product of the rational expressions.

What are rational expressions?

Two polynomials' ratio is shown through rational expressions. It denotes a polynomial in the denominator as well as the numerator. It is an algebraic expression that contains an unknown variable and is similar to a fraction in that it is a ratio.

We are given [tex]\frac{3x^{2} }{x^{2} +x-6}[/tex]

This means that the expression has to be multiplied by the number 1 for obtaining the product of the rational expression.

We know that when anything is multiplied by the number 1, we get the number itself.

Hence, [tex]\frac{3x^{2} }{x^{2} +x-6}[/tex] is the product of the rational expressions.

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HURRY PLEASE!!!!!
Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.
Group of answer choices

a) The GCF of the expression is 1

b) The factors common to 20a and 24b are 1, 2, and 4.

c) The GCF of the expression is ab.

d) The factors common to 20a and 15ab are 1, 5, a, and b.

e) The factors common to 20a and 15ab are 1, 5, and a.

Answers

Answer: A, B, E

Step-by-step explanation:

For A:

None of the factors have one same factor they can be divided by besides 1.

For B:

Both 20a and 24b can be divisible by 1,2,4.

For E:

Both 20a and 15ab are divisible by 1,5 and a.

This stuff is hard somebody help me pls

Answers

The roots of quadratic equations:

b = ± 4 a = ± 1 / 2 x = 11 / 4 ± 17 / 4 n = ± 4 x = 3 / 4 ± √(1517 / 80) x = 7 / 8 ± √(5937 / 256) k = - 7 / 10 ± √(2809 / 100) m = 3 / 2 ± √(361 / 4) n = 3 / 2 ± 4 n = 1 / 6 ± 841 / 36 p = ± 4 v = 5 / 6 ± 14 r = - 5 / 3 ± √(718 / 27) x = 11 / 10 ± √(1 / 10) n = 11 / 4 ± 13 / 4 x = ± 5

How to solve quadratic numbers

In this question we need to determine sixteen cases of quadratic equations, whose roots should be determined. This can be done by following procedure:

Write the quadratic equation.Complete the square.Simplify the resulting polynomial into a perfect square trinomial.Clear the independent variable.

Now we proceed to show the solution to each case:

Case 1

b² - 4 = 0

b² = 4

b = ± 4

Case 2

4 · a² - 1 = 0

4 · a² = 1

a² = 1 / 4

a = ± 1 / 2

Case 3

2 · x² = 21 + 11 · x

2 · x² - 11 · x - 21 = 0

2 · [x² - (11 / 2) · x - 21 / 2] = 0

2 · [x² - (11 / 2) · x + 121 / 16] = 2 · (121 / 16) + 2 · (21 / 2)

2 · (x - 11 / 4)² = 289 / 8

(x - 11 / 4)² = 289 / 16

x - 11 / 4 = ± 17 / 4

x = 11 / 4 ± 17 / 4

Case 4

2 · n² = 32

n² = 16

n = ± 4

Case 5

5 · x² = 3 · x + 92

5 · x² - 3 · x - 92 = 0

5 · [x² - (3 / 2) · x - 92 / 5] = 0

5 · [x² - (3 / 2) · x] = 5 · (92 / 5)

5 · [x² - (3 / 2) · x + 9 / 16] = 5 · (92 / 5 + 9 / 16)

5 · (x - 3 / 4)² = 1517 / 16

(x - 3 / 4)² = 1517 / 80

x - 3 / 4 = ± √(1517 / 80)

x = 3 / 4 ± √(1517 / 80)

Case 6

4 · x² = 7 · x + 92

4 · x² - 7 · x - 92 = 0

4 · [x² - (7 / 4) · x - 23] = 0

4 · [x² - (7 / 4) · x + 49 / 64] = 92 + 49 / 64

4 · (x - 7 / 8)² = 5937 / 64

x - 7 / 8 = ± √(5937 / 256)

x = 7 / 8 ± √(5937 / 256)

Case 7

5 · k² = - 7 · k + 138

5 · k² + 7 · k - 138 = 0

5 · [k² + (7 / 5) · k - 138 / 5] = 0

5 · [k² + (7 / 5) · k] = 5 · (138 / 5)

5 · [k² + (7 / 5) · k + 49 / 100] = 5 · (138 / 5 + 49 / 100)

5 · (k + 7 / 10)² = 2809 / 20

k + 7 / 10 = ± √(2809 / 100)

k = - 7 / 10 ± √(2809 / 100)

Case 8

m² - 88 = 3 · m

m² - 3 · m - 88 = 0

m² - 3 · m - 352 / 4 = 0

m² - 3 · m = 352 / 4

m² - 3 · m + 9 / 4 = 361 / 4

(m - 3 / 2)² = 361 / 4

m - 3 / 2 = ± √(361 / 4)

m = 3 / 2 ± √(361 / 4)

Case 9

4 · n² - 7 = 12 · n

4 · n² - 12 · n = 7

4 · (n² - 3 · n + 9 / 4) = 7 + 9

4 · (n - 3 / 2)² = 16

n - 3 / 2 = ± 4

n = 3 / 2 ± 4

Case 10

6 · n² - 2 · n = 140

6 · [n² - (1 / 3) · n] = 140

6 · [n² - (1 / 3) · n + 1 / 36] = 140 + 1 / 6

6 · (n - 1 / 6)² = 841 / 6

n - 1 / 6 = ± 841 / 36

n = 1 / 6 ± 841 / 36

Case 11

4 · p² = 64

p² = 16

p = ± 4

Case 12

6 · v² - 10 · v = 84

6 · [v² - (5 / 3) · v] = 84

6 · [v² - (5 / 3) · v + 25 / 36] = 84

6 · (v - 5 / 6)² = 84

(v - 5 / 6)² = 14

v - 5 / 6 = ± 14

v = 5 / 6 ± 14

Case 13

3 · r² - 77 = - 10 · r

3 · r² + 10 · r = 77

3 · [r² + (10 / 3) · r] = 77

3 · [r² + (10 / 3) · r + 25 / 9] = 77 + 25 / 9

3 · (r + 5 / 3)² = 718 / 9

(r + 5 / 3)² = 718 / 27

r + 5 / 3 = ± √(718 / 27)

r = - 5 / 3 ± √(718 / 27)

Case 14

5 · x² - 11 · x = - 6

5 · [x² - (11 / 5) · x + 121 / 100] = - 6 + 5 · (121 / 100)

5 · (x - 11 / 10)² = 1 / 20

(x - 11 / 10)² = 1 / 100

x - 11 / 10 = ± √(1 / 10)

x = 11 / 10 ± √(1 / 10)

Case 15

2 · n² = 11 · n + 6

2 · n² - 11 · n = 6

2 · [n² - (11 / 2) · n] = 6

2 · [n² - (11 / 2) · n + 121 / 16] = 6 + 2 · (121 / 16)

2 · (n - 11 / 4)² = 169 / 8

(n - 11 / 4)² = 169 / 16

n - 11 / 4 = ± 13 / 4

n = 11 / 4 ± 13 / 4

Case 16

4 · x² = 100

x² = 25

x = ± 5

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find an appropriate scale to use to graph the algebraic tule y= 3x — 11. Consider input values from -5 to 5.

Answers

To graph the algebraic rule y = 3x - 11, we need to consider input values ​​from -5 to 5 and also choose appropriate scaling for the x and y axes.

How to use scale?

A common way to choose a scale is to use 1 or 2 increments on the x and y axes. This makes it easy to draw points and read charts easily.

The x-axis goes from -5 to 5, so you can scale from -5 -4 -3 -2 -1 0 1 2 3 4 5.

For the y-axis, I need to find the minimum and maximum values ​​of y given the input x values.

Substituting the x value into the formula y = 3x - 11 gives the y value.

y = 3(-5) - 11 = -16

y = 3(5) - 11 = 14

So for the y axis you can take -20 -15 -10 -5 0 5 10 15 20

So a good scale for the x-axis is -5 to 5 in increments of 1, and -20 to 20 in increments of 5 for the y-axis. Graphing the equation y = 3x - 11 using these scales makes the graph easier to read and understand.

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Multiply.
(x² - 5x) (2x²+x-3)
O A. 2x+9x3 - 8x² + 15x
OB. 2x4-9x3-8x² + 15x
OC. 4x+9x3-8x² + 15x
OD. 2-9x3-9x² - 15x

Answers

The resultant of the given expression (x² - 5x) (2x²+x-3) is 2x^4 - 7x^3 -8 x^2 + 15x .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

(x² - 5x) (2x²+x-3)

= x^2 ( 2x^2+x-3) - 5x(2x^2 + x - 3)

= 2x^4 + x^3 - 3x^2 - 5x * 2x^2 + x*-5x - 3 * -5x

= 2x^4 + x^3 -3x^2  - 10 x^3 - 5x^2 + 15x

= 2x^4 + x^3 - 10x^3 -3x^2 - 5x^2 + 15x

= 2x^4 - 7x^3 -8 x^2 + 15x .

Hence, The resultant of the given expression (x² - 5x) (2x²+x-3) is 2x^4 - 7x^3 -8 x^2 + 15x .

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what is the answer to this

Answers

The matching of the inequality with the statement will be 1-B, 2-D, 3-A, and 4-C.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The matching of inequality with the statement is given as,

The inequality t < 28 represents that Tia ran the race in under 28 seconds.The inequality t > 28 represents that the temperature is warmer than 28°F.The inequality t < 29 represents that Tony is younger than 29 years old.The inequality t > 29 represents that the table is heavier than 29 kilograms.

The matching of the inequality with the statement will be 1-B, 2-D, 3-A, and 4-C.

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30 5.109 ÷ 100 in decimal

Answers

The result of the division of the number by 100 gives 3.05109 in decimal.

Define the term decimal number?

A decimal is really a number that is divided into two parts: another whole and a fraction.

Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.Then, there are two parts to a decimal number: a whole number portion and a fractional portion. The whole component of something like a decimal number has the same decimal point value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.

For the given number.

= 305.109 ÷ 100

Then point will shift to 2 decimals towards left.

= 3.05109

Thus, the result of the division of the number by 100 gives 3.05109 in decimal.

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Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters. Use estimation to complete the statements below about Adya's soup.

Answers

the remaining soup at Adya's place is 24/114 liters As per the given ratio.

What is the ratio?

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters.

Since the total soup was 9/38 liters

Thus,

Remaining soup at Adya = 9/38 -3/57

LCM of 38 and 57 are 114

Remaining soup at Adya = 27/114 - 6/114

Remaining soup at Adya = 27/114 liters

Therefore, the remaining soup at Adya's place is 24/114 liters.

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1. A TV has a width of 45 inches and a height of 30
inches. What is the length of the diagonal of the TV?

Answers

A TV has a width of 45 inches and a height of 30inches the length of the diagonal of the TV is 54.08inches.

What is Rectangle?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Make a diagonal and a rectangle. Two parallel triangles appear. Pay attention to one of the triangles.

We have a right triangle with a = 45 and b = 30

we have to find the c = ?
Let's find b using the Pythagorean Theorem;

a^2 + b^2 = c^2

45^2 + 30^2 = c^2

2025 + 900 = c^2

2925 = c^2

c = 54.08 inches

Therefore,the diagonal of the TV is 54.08inches.

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Two circle of radii 8cm with centre p and q are given the chord AB of circle with centre P and the chord CD of the circle with centre Q are equal if angle PAB=40 then find angle CQD

Answers

The angle PAB is given as 40 degrees so we can use the sine rule to calculate the lengths of the chords is CQD = 17.7 degrees.

The sine rule states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal to the ratio of any other side to the sine of its opposite angle.

Let us denote the length of chord AB by x and the length of chord CD by y.

Therefore x/sin 40 = y/sin (180-40)

=> x/0.766 = y/0.939

=> x = 0.766*0.939 = 0.723

y = 0.939*0.766 = 0.723

Since AB=CD, x=y=0.723.

We can now use the cosine rule to calculate the angle CQD.

The cosine rule states that the square of the length of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides times the cosine of the included angle.

Therefore CQ^2 = 8^2 + 8^2 - 2(8^2)cosCQD

=> CQ^2 = 64 - 64cosCQD

=> 64 - 64cosCQD = 0.723^2

=> 64 - 64cosCQD = 0.521

=> 64cosCQD = 63.479

=> cosCQD = 63.479/64

=> cosCQD = 0.988

Therefore CQD = cos^-1(0.988)

=> CQD = 17.7 degrees.

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Annette is standing with a tree directly between her and a building. She stands so that, in her eyes, the
top of the tree appears to "touch" the top of the building. If the distance between her and the tree is
30 ft, the distance between the tree and the building is 15 ft, and the tree is 20 ft tall, how tall is the
building? (You may ignore her height.)

Answers

The height of the building is 30 feet.

How to find the height of the building?

Annette is standing with a tree directly between her and a building. She stands so that, in her eyes, the top of the tree appears to "touch" the top of the building.  

The distance between her and the tree is 30 ft, the distance between the tree and the building is 15 ft, and the tree is 20 ft tall.

Therefore, the height of the building can be calculated as follows:

The situation forms two right angle triangle.

Therefore, using similar triangle ratio,

20 / 30 = x / 45

where

x = height of the building

Hence,

45 × 20 = 30x

900 = 30x

x = 900 / 30

x = 30

Therefore,

height of the building  = 30 ft

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where do i put the line pls help i’ll give brainly

Answers

Answer:

5,7

Step-by-step explanation:

GIVING 50 POINTS!

The right triangle below has legs of length a=7 and b=10. The hypotenuse has length c.
(look at the image)

Part 1: compute the total combined area of the four triangles.

Part 2: Compute the area of the large (outer) square.

Part 3: Using your answers from parts 1 and 2, find the area of the small inner square.

Part 4: We are given the side lengths a=7 and b=10. Compute a²+b².

Part 5: use <, >, or = to complete the statement below.​

Answers

Part 1

The area of one triangle is [tex](1/2)(7)(10)=35[/tex]. Multiplying this by 4 yields [tex]\boxed{140}[/tex].

Part 2

[tex](10+7)^2=\boxed{289}[/tex]

Part 3

[tex]289-140=\boxed{149}[/tex]

Part 4

[tex]10^2+7^2=\boxed{149}[/tex]

Part 5

The statement is missing.

1) The total combined area of the four triangles is: 140; 2) The area of the outer square is c² = c * c; 3) The area of the small inner square is: c² - 70; 4) The sum of the squares of the two legs of a right triangle is: 149.

How to solve the area problem?

Part 1:

The area of each triangle is (a * b) / 2, so the total combined area of the four triangles is 4 * (a * b) / 2 = 2 * 7 * 10 / 2 = 70.

Part 2:

The side length of the outer square is c, the hypotenuse, so the area of the outer square is c² = c * c.

Part 3:

The area of the small inner square is the area of the outer square minus the total combined area of the four triangles, so it is c² - 2 * 7 * 10 / 2 = c² - 70.

Part 4:

The formula for the sum of the squares of the two legs of a right triangle is a² + b² = c², so a² + b² = 7² + 10² = 49 + 100 = 149.

Part 5:

c > a and c > b, so c > 7 and c > 10. Therefore, c must be the largest of the three values: a, b, and c.

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