Determine the solution and the reasoning that justifies the solution to the systems of equations.
O (2,7), because this point is true for both equations
O (4, -6), because this point lies only on one of the two lines
(4, -6), because this point makes both equations true
O (2,7), because the lines intersect the x-axis at these points

Answer:

3/8

Step-by-step explanation:

Well, let's start out by figuring out how many apartments have not been scheduled to receive new carpet. We know that 75 have been scheduled and that there are 120 total apartments, so the number of apartments that have not been scheduled is 120 - 75 or 45.

Now, we need to find the fraction of apartments that have not been scheduled to receive new carpet. To do this, we divide the number of apartments that have not been scheduled to receive new carpet by the total number of apartments:

[tex]\frac{45}{120}[/tex]

We can divide both sides by a common factor of 15 to find the simplified fraction and determine our answer.

[tex]\frac{45}{120} /\frac{15}{15} =\frac{3}{8}[/tex]

So, 3/8 of the apartments have not been scheduled to receive new carpet.

Answer:

16 tables

Step-by-step explanation:

So there are 138 students, and 9 sit at each table. This means you do 138/9, which leaves you with 15.3333. However you cant have .3 of a table so there must be 16 tables!

Answer:

Well, the answer is: it depends on what was printed in the problem. The principal square root symbol never has a negative output, so if the test maker printed that symbol, it’s restrictions have to be respected: all square roots then are positive.

Step-by-step explanation:

a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √(x), where the symbol √( ) is called the radical sign or radix.

Answer/Step-by-step explanation:

The square root could be positive or negative because multiplying two negative numbers gives a positive number. The principal square root is the nonnegative number that when multiplied by itself equals a. The square root obtained using a calculator is the principal square root.

Step-by-step explanation:

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.

for the slope a :

x changes by +10 (from -5 to 5)

y changes by +1 (from -4 to -3)

the slope is +1/+10 = 1/10

the equation looks now like

y = (1/10)x + b

let's use the first point.

-4 = (1/10)×-5 + b = -1/2 + b

-3 1/2 = -7/2 = b

the equation is

y = (1/10)x - 7/2

so, the second answer option is correct.

In order of smallest to largest.

1) -7.1

2) -4 1/3

3) -4/5

4) .889753

5) 11/12

6) 0

7) π

8) 3.28

Answer:

4.75 feet

Step-by-step explanation:

Let the height of the flagpole be x

Sin 53 = x/12

x = 12 × Sin 53

x = 12 × 0.3959

x = 4.75 feet

Answer:

15.9

Step-by-step explanation:

The 12 ft is the adjacent side and you are trying to find the opposite side or the height of the flagpole. You use Tan. Lowercase x means multiply.

Tan 53 = X

             --------

               12

To get rid of the 12 multiply both sides of the equation by 12. so

Tan 53 x 12 = X/12 x 12

Tan 53 x 12= X

X= 15.9

Step-by-step explanation:

Pythagoras formula for the relation of the side lengths in a right-angled triangle :

c² = a² + b²

c is the Hypotenuse, the side opposite of the 90 degree angle.

a and b are the "legs".

3.

c² = 10² + 21² = 100 + 441 = 541

c = sqrt(541) = 23.2594066...in

so, none of the provided answers. are you sure you put the right numbers ? maybe the second leg is sqrt(21) instead of 21 ? because then it would be

c² = 10² + sqrt(21)² = 100 + 21 = 121

c = 11in

4.

10² = a² + 6²

100 = a² + 36

64 = a²

a = 8 m

5.

again, there must be something wrong. the height of the triangle cannot be longer than the legs of the triangle.

given the answer options of 5 - 9 cm it cannot be 32cm. maybe you mean 3.2 cm ?

also interesting that it says "attitudes" - plural. what do you mean by that ?

because there is something else missing. like how long are the segments of the Hypotenuse where the height (or altitude) is touching the Hypotenuse ?

with just the Hypotenuse length and the height length we cannot calculate the other parts of the triangle, because we can move the height freely along the Hypotenuse and draw fitting right-angled triangles on that "skeleton".

6.

similar triangles. that means the lengths of corresponding lines (like sides or heights) are all in relation with the same scaling factor.

so, the small triangle has its "height" side of 1 ft, and multiplying with the scaling factor would then give us the height of the flag pole.

what is the scaling factor ? we get that from the pair of corresponding sides we already know : the shadows.

going from the small to the large triangle we have to transform 4ft into 60ft.

what do I have to multiply 4 with to get 60 ?

4 × x = 60

x = 60/4 = 15

so, the flag pole is

15×1 = 15ft tall.

Answer:

75

Step-by-step explanation:

joshua - x

kale - 1/3x

1/3x = 25

x = 25(3)

x = 75

Answer:

y intercept is (0, -4)

equation is y = x - 4

Step-by-step explanation:

The slope is rise/run which you can find by choosing "any" two points on the line. For instance (0,-4) and (4,0)

The rise is the difference in y direction: 0 - - 4 = 4, the graph "rises" by 4.

The run is the difference in x direction: 4 - 0 = 4, the graph "runs" by 4.

So the slope is 4/4 = 1.

The y intercept is the point on the y axis where the line passes through. This is (0,-4). The intercept value is y= - 4.

The equation is slope times x plus y intercept value.

So putting this all together gives you an equation of

y = 1·x + -4

a.k.a.

y = x-4

Answer:

  19. m = -3; f(x) = -3x +5

  21. m = 0; f(x) = 9

  24. m = -3/2; f(x) = -3/2x +18 1/2

Step-by-step explanation:

The slope of the function is given by the slope formula ...

   m = (y2 -y1)/(x2 -x1)

The y-intercept (b) can be found from the table when it includes a point (x, y) = (0, b). If the table doesn't have the y-intercept, it can be found from ...

  b = y -mx

When m and b are known, the slope-intercept equation is ...

  f(x) = mx +b

__

  m = (11 -14)/(-2 -(-3)) = -3/1 = -3

The slope is -3. The function is f(x) = -3x +5.

__

  m = (9 -9)/(2 -3) = 0/-1 = 0

The slope is 0. The function is f(x) = 9.

__

  m = (14 -17)/(3 -1) = -3/2

  b = 17 -(-3/2)(1) = 18 1/2

The slope is -3/2. The function is f(x) = -3/2x + 18 1/2.

Answer:

<1= 60

<2=120

<3=60

<4=60

<5=120

<6=120

<7=60

Step-by-step explanation:

y equals 50° since there is a 90° and a 30°

Answer:

cos^-1 (9/15)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The number of decimal places in the product is the sum of the numbers of decimal places in the factors.

1. the factors have 1 and 2 decimal places, so the product will have 1+2 = 3 decimal places.

2. 1 + 1 = 2 decimal places in the product

3. 2 + 2 = 4 decimal places in the product

4. 1 + 1 = 2 decimal places in the product

_____

Additional comment

If the factor has m decimal places, the place value of its least-significant digit is 10^-m. Similarly, if the factor has n decimal places, the place value of its least-significant digit is 10^-n. When these numbers are multiplied, the place value of the least-significant digit of the product is (10^-m)(10^-n) = 10^-(m+n). That is, there will be m+n decimal places in the product.

Note that the product in problem 3 is 370.4140. That is, the least-significant digit of the product is zero. Many calculators will not show that zero, giving the (false) impression that the product has only 3 decimal places.

Answer:

4.725

2.473.6

3.370.414

5.312.08

Step-by-step explanation:

Answer:

  7 inches tall

Step-by-step explanation:

A graphing calculator quickly finds the solution to the cubic equation. It is convenient to define ...

  f(x) = 4x^3 -28x^2 +144x -1008

so f(x) = 0 gives the value of x that is of interest. That value is x=7.

The box is 7 inches tall.

_____

The equation f(x) = 0 can be divided by 4 to give ...

  x^3 -7x^2 +36x -252 = 0

This can be factored by grouping:

  (x^3 -7x^2) +(36x -252) = 0

  x^2(x -7) +36(x -7) = 0

  (x -7)(x^2 +36) = 0

The only real root is x = 7, which makes a factor zero.

_____

Additional comment

For finding solutions to cubic and higher-degree polynomials, I find a graphing calculator to be an extremely helpful tool. Desmos provides an online calculator and apps for various platforms. It may take a little while to learn how to use it effectively, but it can save immense amounts of time and frustration. Of course, your handheld graphing calculator can be just as useful.

Answer:

Option A

Step-by-step explanation:

[tex]4(6-2x)\\\rule{150}{0.5}\\\rightarrow ((6 * 4) ( -2x*4)) \leftarrow \text{Distribute the '4' into the content in the parenthesis.}\\\\\\\\\rightarrow 6 * 4 = 24\\\\\rightarrow -2x * 4 = -8x\\\\\\\\\rightarrow 4(6-2x) = \boxed{24 - 8x}[/tex]

Hope this helps.

Hey there!

11x + 3 = 6

SUBTRACT 3 to BOTH SIDES

11x + 3 - 3 = 6 - 3

CANCEL out: 3 - 3 because it gives you 0

KEEP: 6 - 3 because it helps you solve for your x-value

11x = 6 - 3

11x = 3

DIVIDE 11 to BOTH SIDES

11x/11 = 3/11

CANCEL out: 11/11 because that gives you 1

KEEP: 3/11 because it simplifies for the x-value

SOLVE

x = 3/11

Therefore, your answer should bed x = 3/11

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

The equation of a straight line is always [tex]y=mx+b[/tex], where m is a constant which is the slope and b is a constant which is the y-intercept.

Substitute these values in:

[tex]y=3x-7[/tex]

The graph would look like the image attached.

Answer:

4 duhh... Ur kidding me??

Answer:

22 because 2+2

Step-by-step explanation:

if we put 2 near 2 it will be 22 so the answer is 22

Answer:

f = 2 6/7

Step-by-step explanation:

[tex]\dfrac 35 \cdot f = 1 \dfrac 57 \\\\\\\implies \dfrac{3f}5 = 1 + \dfrac 57 = \dfrac{12}7\\\\\\\implies 21f = 60\\\\\implies f = \dfrac{60}{21} = \dfrac{20}7 = 2 \dfrac 67[/tex]

The solution is

The total amount for the lunch is given by the equation A = $ 45.648

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount for the lunch be represented as A

Now , the equation will be

The amount for the first lunch = $ 12.35

The amount for the second lunch = $ 14.22

The amount for the third lunch = $ 11.47

The percentage of tip = 20 %

So , the total amount for the lunch without tip = $ 12.35 + $ 11.47 + $ 11.47

On simplifying the equation , we get

The total amount for the lunch without tip = $ 38.04

The amount of tip = total amount for the lunch without tip x percentage of tip

Substituting the values in the equation , we get

The amount of tip = 38.04 x ( 20/100 )

The amount of tip = 38.04 x 0.20

The amount of tip = $ 7.608

So ,

The total amount for the lunch A = total amount for the lunch without tip +  amount of tip

Substituting the values in the equation , we get

The total amount for the lunch A = $ 38.04 + $ 7.608

The total amount for the lunch A = $ 45.648

Therefore , the value of A is $ 45.648

Hence , the total amount is $ 45.648

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ5

[tex]\\ \sf\longmapsto 12x-15[/tex]

Distributive property

Take 3 common

[tex]\\ \sf\longmapsto 3(4x-5)[/tex]

Done

Answer:

Answer will be 1/53 as a fraction, and 0.02 as a decimal.

Step-by-step explanation:

In order to solve this equation, we will first plug in -8 into every x term.

So now we will have:

[tex]f( - 8) = \frac{1}{ - 8 {}^{2} - 11 } [/tex]

{Don't mind the f (-8), just think of it as a sort of place holder.}

Anyways, now we will do -8 × -8, since that's what -8^2 implies:

-8 × -8 = 64

Next do 64 - 11, to get 53.

Now we have 1/53

(You can also divide the numerator by the denominator, to get the answer in decimal form.)

Hope this helps you :)

Sorry if it doesn't.

Answer:

-25 can be expressed as a ratio of -50/2, -75/3, etc

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer: 4 hours 30 minutes

Step-by-step explanation: 36/8 = 4.5 hours

hours = 4, minutes = 0.5*60 = 30

Answer:  (12xy^2)

Step-by-step explanation:

12x^2y^3

(12xy^2)*(xy)

24xy^2

(12xy^2)*(2)

The greatest common factor of the expressions 12x²y³ and 24xy² will be 12xy².

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expressions are given below.

12x²y³ and 24xy²

The factor of the expression 12x²y³ is given as,

12x²y³ = 12 × x × x × y² × y

The factor of the expression 24xy² is given as,

24xy² = 2 × 12 × x × y²

The common factors in both expressions are 12, x, and y². Then the greatest common factor will be given as,

⇒ 12 × x × y²

⇒ 12xy²

The best normal component of the articulations 12x²y³ and 24xy² will be 12xy².

More about the greatest common factor link is given below.

https://brainly.com/question/11221202

#SPJ2

Answer:

2. the car drove at 60 miles per hour

Step-by-step explanation:

:)

The leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial

The standard form of a polynomial expression is written as:

[tex]a_nx^n+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+...[/tex]

A polynomial function has a leading degree that is greater than 2;

Given the polynomial function

[tex]P(x)=4x^3-31x^3-10058x+158040[/tex]

From the given polynomial, the leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial

Learn more here:https://brainly.com/question/19809286

Answer:  what the math question is

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

7 plus 5 (painters plus photographers) equals 12. The remaining (4) adds to 16. 12/16 can be simplified to 3/4

Hope it helps

Would appreciate a brainliest

Answer:

[tex]106 yd^2[/tex]

Step-by-step explanation:

Answer is attached. Let me know if you would like another explanation that would yield the same solution.

Answer:

  ∠A = 44°

Step-by-step explanation:

Let b represent the measure of the exterior angle at B. Let c represent the measure of the exterior angle at C. The sum of angles in the lower triangle is ...

  b/2 +c/2 +68° = 180°

  b +c = 360° -136° . . . . . multiply by 2, subtract 136°

  b +c = 224°

__

The exterior angle b is the supplement of the interior angle there, so the interior angle B is ...

  B = 180° -b

The exterior angle c is the sum of the remote interior angles, so we have ...

  c = B +A

  c = (180° -b) +A

  A = (b +c) -180° . . . . . . . . add b-180° to both sides

  A = 224° -180° = 44° . . . . substitute for (b+c)

The measure of angle A is 44°.

_____

Additional comment

The angle naming is perhaps a little unconventional, but we wanted to use names that made the answer less cumbersome to write. We consider the angle A, B, C to be the interior angles of ΔABC, and we have named the exterior angles at B and C as 'b' and 'c'.

Conventionally, 'b' and 'c' would name the sides opposite angles B and C, respectively. We're not concerned with side lengths here, so we used those letters for an unconventional purpose.