Answer:
9.22 units (3 s.f.)
Step-by-step explanation:
The distance between a pair of points can be found using the distance formula shown below, where [tex](x_1, y_1)[/tex] is the 1st coordinate and [tex](x_2,y_2)[/tex] is the 2nd coordinate.
[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
Substituting the coordinates into the formula:
Distance between (21, 5) and (28, -1)
= [tex]\sqrt{(-1-5)^{2} + (28-21)^{2} } }}[/tex]
= [tex]\sqrt{(-6)^2+7^2}[/tex]
= [tex]\sqrt{85}[/tex]
= 9.22 units (3 s.f.)
Additional:
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1) Simplify the expression. Show your work.
[tex]\sqrt\frac{9x^{3} }{4y^2}[/tex]
2) Simplify the expression (2-5i)(3+7i)-(4+3i). Show your work.
3) Simplify the expression [tex]\sqrt[3]{81}x^{7}y^{9}z^{5}[/tex] . Show your work.
The expressions are simplified to 3x^3/2/ y , 2 - 4i - 35i² and 4x^7y^9z^5
How to simply the expressions1.
Given the expression;
[tex]\sqrt{\frac{9x^3}{4y^2} }[/tex]
Take the square root of the variables;
= [tex]\frac{3x^3^/^2}{y}[/tex]
2. (2-5i)(3+7i)-(4+3i)
expand the bracket
6 + 14i - 15i - 35i² - 4 - 3i
collect like terms
2 - 4i - 35i²
3. Given the expression;
[tex]\sqrt[3]{81} x^7 y^9z^5[/tex]
Take the cube root of the value, we have;
4x^7y^9z^5
Thus, the expressions are simplified to 3x^3/2/ y , 2 - 4i - 35i² and 4x^7y^9z^5
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Write the definition of an absolute number.
Please write a good thought out answer !!
NO LINKSSSSSS.
Answer:
An absolute number is a number that is represents a distance from 0. An absolute number is always positive since the distance between two number is always positive.
Step-by-step explanation:
what is 6(2-7v)+2(v+4)=20
Answer:
v= 0
6(2-0)+2(4)=20 is the simplified version of the equation.
pls do this pls pls pls pls pls pls
Answer:
See below
Step-by-step explanation:
The most important info is the rate ft^2 / min and how many minutes it took to mow.
From this, we need to know how much total area there is. We do this by multiplying the rate by the time.
[tex] \frac{ 4{ft}^{2} }{minute} \times 29minutes = 116 {ft}^{2} [/tex]
Then we need to write out the sum of the whole area in terms of length times width
[tex]6ft \times 14 ft + x \times 4ft = 116 {ft}^{2} [/tex]
Notice how we put x for the unknown variable, this turns it into an easy peasy algebra problem. I leave that to you, solve for x
5. A group of friends are running a
relay race that covers 31 miles. If
each person runs+mile, how
many runners are there?
Answer: 8 runners
Step-by-step explanation:
If you mean that " if each person runs one more mile than the previous runner" then:
First person = 1
Second person = 1+1
.....
(1)+(1+1)+(1+1+1)+(1+1+1+1)+(1+1+1+1+1)+(1+1+1+1+1+1)+(1+1+1+1+1+1+1)+(1+1+1)
1 + 2 + 3 + 4 + 5 + 6 + 7 + 3 =31
(the last runner runs less miles then needed)
8 runnersConvert 3.9 yards to inches.
Answer:
140.4 inches
Step-by-step explanation:
there are 36 inches in a yard
3.9 times 36 is 140.4
Hope It Helps
Sorry If I'm Wrong
3.9 yards is equal to 140.4 inches.
We have,
The concept used to convert 3.9 yards to inches is the conversion factor between yards and inches. The conversion factor states that 1 yard is equal to 36 inches.
By multiplying the given value in yards (3.9 yards) by the conversion factor (36 inches/yard), we can convert the measurement from yards to inches.
This concept of using a conversion factor allows us to convert between different units of measurement.
To convert 3.9 yards to inches, we can use the fact that 1 yard is equal to 36 inches.
So, to convert 3.9 yards to inches, we multiply 3.9 by 36:
3.9 yards * 36 inches/yard = 140.4 inches
Therefore,
3.9 yards is equal to 140.4 inches.
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Help!!!
12. Sam's salary was $42,000 in 1998 and $53,600 in 2002. If Sam's salary follows a linear growth pattern,what
will it be in 2007? Let G represent the growth and express G as a function.
The area of the playing surface at the Olympics stadium in Beijing is 3/5 of a hectare. What area will it occupy on a plan drawn to a scale of 1:500
The area that occupies on a plan drawn to the given scale is 0.024 m²
Given,
The area of the playing surface at the Olympics stadium in Beijing = 3/5 hectare
The scale factor on a plan drawn = 1:500
We have to find the area that occupies on a plan drawn to the given scale:
Applied to the area we consider k² as the area is the product of two dimensions.
So, k = 1/500
Now the area on plan:
a : k² = actual area
a : (1/500)² = (3/5) × 10000
a : (1/250000) = 3 × 2000
a × 250000 = 6000
a = 6000 / 250000
a = 0.024 m²
That is, the area that occupies on a plan drawn to the given scale is 0.024 m²
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Find the value of k such that a is singular. (enter your answers as a comma-separated list.) 0 k 1 k 5 k 1 k 0
The value of k such that a is singular is ±√(5/2).
What do you mean by the term singular?If a singular matrix's determinant is 0, it is a square matrix. Specifically, if and only if det A = 0, a square matrix A is unique. We are aware that the formula A-1 = (adj A) / can be used to get the inverse of a matrix A. Here, the denominator contains det A, which is the determinant of A. We are aware that a fraction with a denominator of 0 is not defined. Since det A = 0, A-1 is not defined. In other words, a single matrix's inverse is not defined. That is to say, there isn't a matrix B such that AB = BA = I.
A singular matrix means that the detA should be 0.
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when $555 {10}$ is expressed in this base, it has 4 digits, in the form abab, where a and b are two different digits. what base is it?
In some base [tex]B[/tex], we have
[tex]abab_B \equiv 555_{10}[/tex]
so that
[tex]aB^3 + bB^2 + aB + b = 555[/tex]
Factorize the left side.
[tex]aB (B^2 + 1) + b (B^2 + 1) = 555[/tex]
[tex](aB + b) (B^2 + 1) = 555[/tex]
Now, [tex]B[/tex] is a positive integer greater than 1, and [tex]a,b[/tex] are positive integers taken from [tex]\{0,1,2,\ldots,B-1\}[/tex]. So consider the prime factorization of 555 on the right side.
[tex](aB + b) (B^2 + 1) = 3\times5\times37[/tex]
which we can write as
[tex](aB + b) (B^2 + 1) = 15\times(6^2 + 1) = (2\times6 + 3) \times (6^2+1)[/tex]
and so the base is 6, and the number in question is 2323₆.
Seleccione todas las que correspondan
¿Qué enunciados describen el movimiento en la imagen?
A. El hombre no está en movimiento con respecto a la boya.
B. El barco está en movimiento con respecto a la boya.
C. El hombre está en movimiento en relación con el barco.
D.El hombre no está en movimiento con respecto al bote.
C. El hombre no se mueve en relación con la caña de pescar.
Lo ciento, pero yo no se mucho Espanol por que yo soy negro y boricua pero mas negro asi que yo nunca aprendió.
Yo esperar una persona quien es muy mejor a Espanol pueda ayudarte! Adios.
(Yo solo escribio ese para la premio!)
A group of friends wants to go to the amusement park. they have $69.75 to spend on parking and admission. parking is $17.25, and tickets cost $17.50 per person, including tax. write an equation which can be used to determine p, the number of people who can go to the amusement park.
Equation and solution of equation :
17.25 + p(17.50) = 69.75
17.25 + 17.50p = 69.75
17.50x = 69.75 - 17.25
17.50p = 52.50
p = 52.50/17.50
p = 3
So three people can go to the amusement park (assuming that they are all travelling together in the same car).
The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
A group of friends wants to go to the amusement park. they have $69.75 to spend on parking and admission. Parking is $17.25, and tickets cost $17.50 per person, including tax.
Let p be the number of people. Then the equation is given as,
17.50p + 17.25 = 69.75
The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.
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Pearce needs to choose a variable to represent the number of wallabies in an exhibit. Which variable would be the best choice? Explain.
The variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit will be D. let w= the number of wallabies on the exhibit.
What is a variable?It should be noted that a variable simply means a symbol that's used to represent a situation in mathematics.
In this case, the variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit so be let w= the number of wallabies on the exhibit.
This is because of the first alphabet used which is w.
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A, B, and C are the centers of the 3 circles. How many
equilateral triangles are there in this diagram?
Find the value of x
file attatched*
x=9
x=15
x=41
x=77
Answer:
find the value of x file attached x9
I need help with 18 and 22 thx
The proportional relationships for these problems are given as follows:
18. y = 0.5x, with constant k = 0.5.
22. y = -0.4x, with constant k = -0.4.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In item 18, we have that when x = 2, y = 1, hence the constant is:
k = y/x = 1/2 = 0.5.
Hence the equation is:
y = 0.5x.
In item 22, we have that when x = -5, y = 2, hence the constant is:
k = y/x = -2/5 = -0.4.
Hence the equation is:
y = -0.4x.
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if h(x)=x2-x find h(3)
Answer:
h(3) = 1
Step-by-step explanation:
[tex]h\left(3\right)=\left(3\right)\cdot \:2-3\\h\left(3\right)=3\cdot \:2-3\\h\left(3\right)=6-3\\h\left(3\right)=3[/tex]
Divide
[tex]\frac{h\cdot \:3}{3}=\frac{3}{3}\\h=1[/tex]
Boca Grande Causeway in Florida is about 1 4/9 times as long as the Golden Gate Bridge in San Francisco the Golden Gate Bridge is about 9000 ft about how long is the Boca Grande Causeway
Answer:
Step-by-step explanation:
Evaluate.
(-8)¹ =
What is it
Answer:
-8
Step-by-step explanation:
Any number raised to the power 1 is that number itself
So (-8)⁻¹ = -8
Can someone please help I will be giving Brainliest to whoever can answer :)
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1}
The inequalities are matched with their correct graph respectively as follows:
D ⇒ {(x, y): y > x²}.G ⇒ {(x, y): y ≥ x²+ 3C ⇒ {(x, y): y ≤ 3x² + 2}A ⇒ {(x, y): y ≥ 2x² - 5x + 1}J ⇒ x²- 3x ≥ 0H ⇒ x² - 3x + 2 ≤ 0B ⇒ {(x, y): y ≤ 1 - x²} B ⇒ {(x, y): y ≥ -1}What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In Geometry, if the leading coefficient of a quadratic equation is greater than (>) zero, the parabolic curve would open upward while the parabolic curve would open downward when the leading coefficient of a quadratic equation is less than (<) zero.
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Complete Question:
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2}
9. {(x, y): y ≥ -1}
In the 1960 Olympics, Wilma Rudolph of the United States won the women's 100 meter run in 11.0 seconds. In 1988, Florence Griffith-Joyner, also of th
United States, won with a time of 10.49 seconds, which is still the fastest women's time to this date. Find the percent of decrease in the winning time.
Round to the nearest tenth.
Step-by-step explanation:
no lo se,no hablo ingles..........
One pygmy shrew weighs 3 3/18 ounces, and another weighs 4 4/7 ounces. Estimate the total weight.
O about 8 1/2
O about 7 1/2
O about 9 ounces
O about 7 ounces
==============================================
Reason:
It might help to draw a number line for this.
3/18 is closer to 0 than it is to 1/2 = 9/18, so the mixed number 3 & 3/18 rounds to 3 when rounding to the nearest half.
4/7 is closer to 1/2 = 4/8 than it is to either 0 or 1, so 4 & 4/7 rounds to 4 & 1/2 when rounding to the nearest half.
Adding 3 to 4 & 1/2 gets 7 & 1/2 since we add the whole parts 3+4 = 7, and the fractional part stays as it is.
-----------
Check:
(3 + 3/18) + (4 + 4/7) = 7.738 approximately
7 + 1/2 = 7.5 exactly
The two results aren't too far off. The estimate of 7 & 1/2 is an underestimate.
Answer:
About 7 1/2 ounces
Step-by-step explanation:
Add your whole numbers first, 3 + 4 = 7
Now the fractions:
3/18 = 1/6
Estimate 4/7 + 1/6, the answer is somewhere between 1/2 and 1 whole. Therefore the answer is about 7 1/2
Check:
3/18 × 7/7 = 21/126
4/7 × 18/18 = 72/126
21/126 + 72/126 = 93/126
The actual answer is 7 31/42, so the closest answer is 7 1/2
HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPP
What does 60 - r represent? What are the units associated with 6(60-r)?
Answer:
360 - 6r
Step-by-step explanation:
just simplify the expression
Find the area of a triangle with a base
of 10m and a height of 12m.
Area: 12(bxh)
Answer:
60
Step-by-step explanation:
1/2(b×h)
1/2(10×12)
1×5×12
60
7. Allan ate 28 jelly beans. Alexis ate 75% of the amount that Allan ate. How many Jelly beans did Alexis eat?
Answer:
21
Step-by-step explanation:
.75 x 28 = 21
Point B (3,1) is translated 2 units to the right and 1 unit up. What is the coordinates of B'?
If Point B [tex](3,1)[/tex] has translated 2 units to the right and 1 unit up, new coordinates of point B' are [tex](5,2)[/tex]
As per the question statement, Point B [tex](3,1)[/tex] is there on a cartesian plane. Point B is translated 2 units to the right and 1 unit up.
Before solving this question, we need to know about cartesian plane system in which, there are four quadrants which are made using positive and negative axes known as positive X and negative X (same for Y axis).
Now point B[tex](3,1)[/tex] lies in the first quadrant and value "3" describes the location of point on X axis and value "1" describes the location of point on Y axis.
If point B [tex](3,1)[/tex] is translated 2 units to the right and 1 unit up, the locations of X and Y axes will change to value "5" on X axis and value "2" on Y axis.
Hence the coordinates of point B' are [tex](5,2)[/tex]
Cartesian Plane: The x-axis and y-axis intersect to form the two-dimensional coordinate plane known as the cartesian plane in mathematics. The origin is the point at which the x- and y-axes cross perpendicularly.To learn more about cartesian plane and coordinate geometry, click on the link given below:
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Solve for x. (5x + 6)(3x - 6) = 0
The value of the given quadratic equation are = x = -(6/5) , x = 2
What is quadratic simple?Quadratics are polynomial equations of the second degree, which means they have at least one squared term. It is also known as quadratic equations. The quadratic equation has the general form: ax2 + bx + c = 0.
So, how are quadratic functions significant?Quadratic functions occupy a distinctive place in the school curriculum. They are functions whose values are easily estimated from input values, therefore they are a modest improvement over linear functions and provide a major shift away from attachment to straight lines.
According to the given information:Given (5x + 6)(3x - 6) = 0
Using the zero factor principle: if ab = 0 then a = 0 and b = 0
So,
(5x + 6) = 0 or (3x - 6) = 0
for the (5x + 6):
(5x + 6) = 0 (subtracting both side by 6)
5x + 6 - 6 = 0- 6
so, x = -(6/5)
Same calculation for (3x - 6) = 0 we get x = 2
The value of the given quadratic equation are = x = -(6/5) , x = 2
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You have a balance of 213.15 in a savings account you make withdrawals of 69.94 and 129.36 find ur new balance SOMEONE PLEASE HELP
to test a hypothesis about a given variable, experimental and control groups are tested in parallel. which of the following best explains the dual experiments?
The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."
What is experimental design?The process of deciding which variables to use in an experiment to test a particular hypothesis is called experimental design. To properly collect data and evaluate the hypothesis, the experimental design method is used.Now,
A specified variable is changed in the experimental group in a well-known fashion. That selected variable is left unaltered in the control group so that comparisons can be conducted. Control variables are variables that are utilized in an experiment to serve as a baseline against which the data from the experimental variables are gathered and evaluated (which is why the other answers are incorrect). In the experimental group, it is advisable to modify just one variable at a time so that any differences from the control group may be quickly linked to the one variable that was altered.Hence, amongst all the given options, The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."
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