a diagonal of rectangle forms a 30 degree angle with each of the longer sides of the rectangle. if the length of the shorter side is 3, what is the length of the diagonal

Answer:

24 and 36

Step-by-step explanation:

2x + 3x = 60

5x = 60

x = 12

Dawn has 2(12) = 24

Jackson has 3(12) = 36

Step-by-step explanation:

To find the number of baseball cards each person received we must first find the total parts

That's

2 + 3 = 5

For Dawn

Dawn's part is 2

We have

2/5 × 60

For Jackson

Jackson's part is 3

That's

3/5 × 60

Hope this helps you

Answer:

4

Step-by-step explanation:

The degree is equal to the largest exponent on a variable. In this instance, it is 4.

Answer:

c is the answer

Step-by-step explanation:

Answer:

Answers                                                     Work

a.60 miles in one hour                               420/7                

b.12 customers in one day                        360/30

c.2.5 meters in I second                            40/16

d.$1.59 for 1 pound                                   7.96/5

Step-by-step explanation:

Answer:

(x+11)(x-11)

Step-by-step explanation:

Hello!

We are given the expression x²-121, and we want to factor it

The expression is a difference of squares expression.

The formula for the difference of squares is written as a²-b² can be factored as (a-b)(a+b)

121 is 11 squared, and x² is x squared

So that means that a=x, and b=11 in this case

Now substitute those values into the formula

a²-b²=x²-121=(x+11)(x-11)

Hope this helps!

Answer:

(x-11)(x+11)

Step-by-step explanation:

x^2 -121

x^2 -11^2

This is the difference of squares  a^2 - b^2 = (a-b)(a+b)

(x-11)(x+11)

Answer:

Step-by-step explanation:

p(x) = ax³ + x² - 2x + b

p(1) = a(1)³ + 1² - 2•1 + b = a + 1 - 2 + b = a + b - 1

a + b - 1 = 0  ⇒   b = 1 - a

p(-1) = a(-1)³ + (-1)² - 2(-1) + b = -a + 1 + 2 + b = - a + b + 3

- a + b + 3 = 0    ∧   b = 1 - a

- a + (1 - a) + 3 = 0

- a + 1 - a + 3 = 0

-2a + 4 = 0

-2a = -4

 a = 2

b = 1 - 2 = -1

Answer: d. savings

Step-by-step explanation:

First, what is an emergency?

Well, it depends on the situation, but suppose that you have a store where you sell edibles.

Some of these edibles may need to be stored in fridges, now suppose that one of the fridges breaks. That is an emergency, now you need to replace it the faster you can. In this point, you need to use savings specially prepared for situations like this.

So the correct option is d: savings.

Answer:

B. False

Step-by-step explanation:

We are given a graph of a function. Shown graph represents a function because there is only unique value of y for each unique value of x.

So, it would pass the vertical line test.

All the vertical lines on the graph would cross the graph at only single point (unique) point.

But if we draw the inverse function graph, each of (x,y) coordinate would switch to (y,x) and the graph would flip to right side.

And if we draw any vertical line on the graph, it could cut the graph at two or more points.

Therefore, it would not pass the vertical line test and it would not be a graph of a function.

The inverse of the function graphed below is not a function as it fails to pass the horizontal test. Hence, B. False is the right option.

A function is a relation between a dependent and an independent variable, say y and x respectively, written as y = f(x). Any such relationship will be called a function if and only if, there is only one value of y corresponding to every x.

We check for a graphed relation to be a function using the vertical test.

The inverse of a function, say y = f(x), is given as x = f⁻¹(y), is also a function when f⁻¹(y) passes the vertical test, or simply y = f(x) passes the horizontal test.

In the question, we are asked to tell whether the inverse of the given function graphed is also a function or not.

To check if the inverse is a function, we perform the horizontal test.

The given graph fails to pass the horizontal test, as for almost every line, the graph intersects two times to the line.

For example, the horizontal line y = 5, the graph intersects at two points.

Thus, the inverse of the function graphed below is not a function as it fails to pass the horizontal test. Hence, B. False is the right option.

Learn more about functions and inverse of functions at

https://brainly.com/question/3831584

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Answer:

Hey there!

x=95

This is because x and the angle of 95 degrees are vertical angles, and vertical angles are congruent to each other.

Let me know if this helps :)

Answer:

7³

Step-by-step explanation:

Using PEMDAS, we see that E (which stands for exponents) comes before M (which stands for multiplication) and A (which stands for addition) so the first operation you should do is 7³.

Twice means muliply by 2

The difference of a number and 7 means subtract a number/variable and 7

Is equal to 9 means =9

2(X - 7) = 9

Answer:

If the order doesn't matter then we have a combination, if the order do matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n!

Step-by-step explanation:

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

Answer:

combination : If the order of numbers  or  operations does not matter

Permutation : when the order of numbers matter ( common example most teachers use : a code of 4 numbers has to be in a certain order and the numbers are from 0 to 9 , how many permutation can you make if you use the number one time)

P=n!/(n-r)!

n! ( are number from 0-9 we have 10 numbers)

r is the number of digits in the code = 4

n!=10*9*8*7*6*5*4*2*1

(n-r)!=(10-4)!=6!=6*5*4*3*2*1

P=5040 ways ( if the order matter)

If the order does not matter

Combination C(n,r)=n!/(n-r)!r!

C(10,4)=(10*9*8*7*6*5*4*2*1)/[(6*5*4*3*2*1)(4*3*2*1)]

Answer:

4.5

Step-by-step explanation:

Hello, please consider the following.

First of all, let's assume that A is different from 0.

[tex]x^2+8x+4\\\\\text{It means that the sum of the zeroes is -8 and the product is 4}\\\\Ax^2+Bx+1=A(x^2+\dfrac{B}{A}x+\dfrac{1}{A})\\\\\text{So the sum of the zeroes is } -\dfrac{B}{A} \text{ and the product is }\dfrac{1}{A}\\\\\text{It comes.}\\\\-\dfrac{B}{A}=-8 <=> \dfrac{B}{A}=8\\\\\dfrac{1}{A}=4[/tex]

So,

[tex]A=\dfrac{1}{4}\\\\B=\dfrac{8}{4}=2\\\\A+B=\dfrac{1+8}{2}=\dfrac{9}{2}=4.5[/tex]

Thank you.

Answer:

Tess wins the prize.

Step-by-step explanation:

[tex]\boxed{\text{Indi}: 2-3}[/tex]

[tex]\boxed{\text{Mark}: -7-(-4)}[/tex]

[tex]\boxed{\text{Tess}: -1-(-7)}[/tex]

The expression of Indi's card is 2 - 3 = -1

The expression of Mark's card is -7 - (-4) = -7+4= -3

The expression of Tess's card is -1 - (-7) = -1+7= 6

inverse of a matrix A is defined as [tex] AA^{-1}=I[/tex]

where I is the identity matrix of the respective order.

Answer:

Hello,

Step-by-step explanation:

Part A:

Yes

Since

y=f(x)

f(0)=4

f(1)=7 : f(1)=f(0)+1*3

f(2)=10= 7+3 : f(2)=f(1)+3 =f(0)+2*3

f(3)=13=10+3: f(3)=f(2)+3=f(0)+3*3

...

f(9)=31=28+3=f(8)+3=f(0)+9*3

f(n)=f(0)+n*3=4+n*3

Part B: y=3x+4

Part C: slope=3 , y-intercept=4

The slope indicate the grow of the plant (how many cm does it grow in function of the height it receives)

y-intercept indicate the original height of the plant.

Answer:

Step-by-step explanation:

It is convenient to let a graphing calculator draw the graph for you. It can also display the solution: (x, y) = (6, 18).

__

The equations of interest are ...

  x + 2y = 42 . . . . . . revenue from sale of x cookies and y chips

  y = 3x . . . . . . . . . . 3 times as many chips as cookies

Answer:

\underline{\text{Variable Definitions:}}

Variable Definitions:

​

x=

x=

\,\,\text{the number of packs of cookies sold}

the number of packs of cookies sold

y=

y=

\,\,\text{the number of bags of chips sold}

the number of bags of chips sold

Each pack of cookies sells for $1, so xx packs of cookies will bring in 1x1x dollars. Each bag of chips sells for $2, so yy bags of chips will bring in 2y2y dollars. Therefore, the total amount 1x+2y1x+2y equals \$42:$42:

1x+2y=42

1x+2y=42

Since Kylie sold 3 times as many bags of chips as packs of cookies, she sold more bags of chips, so if we multiply 3 by the number of packs of cookies sold, we will get the number of bags of chips sold, meaning yy equals 3x.3x.

y=3x

y=3x

\underline{\text{Write System of Equations:}}

Write System of Equations:

​

1x+2y=

1x+2y=

\,\,42

42

y=

y=

\,\,3x

3x

\underline{\text{Solve for }y\text{ in each equation:}}

Solve for y in each equation:

​

\begin{aligned}\color{indianred}{1x}+2y = 42\hspace{10px} & \hspace{10px}\color{green}{y}\color{green}{=}\color{green}{3x} \\[10px] 2y = \color{indianred}{-1x}+42\hspace{10px} & \hspace{10px} & \\[10px] \frac{2y}{2} = \frac{-1x+42}{2}\hspace{10px} & \hspace{10px} & \\[10px] \color{blue}{y} \color{blue}{= -\frac{1}{2}x+21}\hspace{10px}\hspace{10px} & \hspace{10px} & \end{aligned}

1x+2y=42

2y=−1x+42

2

2y

​

=

2

−1x+42

​

y=−

2

1

​

x+21

​

y=3x

​

​

Step-by-step explanation:

Answer:

(a) 283 days

(b) 248 days

Step-by-step explanation:

The complete question is:

The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. ​(a) What is the minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths? ​(b) What is the maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths?

Solution:

The random variable X can be defined as the pregnancy length in days.

Then, from the provided information [tex]X\sim N(\mu=268, \sigma^{2}=12^{2})[/tex].

(a)

The minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths implies that:

P (X > x) = 0.11

⇒ P (Z > z) = 0.11

⇒ z = 1.23

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\1.23=\frac{x-268}{12}\\\\x=268+(12\times 1.23)\\\\x=282.76\\\\x\approx 283[/tex]

Thus, the minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths is 283 days.

(b)

The maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths implies that:

P (X < x) = 0.05

⇒ P (Z < z) = 0.05

⇒ z = -1.645

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.645=\frac{x-268}{12}\\\\x=268-(12\times 1.645)\\\\x=248.26\\\\x\approx 248[/tex]

Thus, the maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths is 248 days.

Answer: B) 87

Step-by-step explanation:

First, order the values from least to greatest:

75, 80, 87, 88, 95

Next, find the value that lies in the middle

75, 80, 87, 88, 95

Therefore, 87 is the median.

Answer:

B: 87

Step-by-step explanation:

Sorry for this very late response. But if anyone wasn't sure if the answer 87 is correct, it is. I can confirm this because I just took the test. I hope I could help! (:

Answer:

It's actually: None of these.

Think about it: In this case we have an inequality, of x ≤ 0.

This basically means, that x can be less than OR equal to 0.

But 0 is neither negative or positive, so we can eliminate the following answer choices:

- all positive integers

- all negative real numbers

- all positive real numbers

- all negative integers

And we are left with "None of these"

Let me know if this helps!

Option B is correct. None of these options is the right answer since zero is neither an integer nor a real number

Before we can decide which option is correct, first we must integers and real numbers are.

Given the set of numbers {x | x ≤ 0}. The set of numbers in the set will be all integers less than zero including zero (zero is not an integer)

Hence the set of numbers are not all negative integers since 0 is not a negative integer.

They are not all positive integers rather they are mostly negative integers

They are not all positive and negative real values because zero is not a real integer.

Hence we can conclude that None of the options is correct.

Learn more here: https://brainly.com/question/2691012

Answer:

(C) [tex]y = 2x+5[/tex]

Step-by-step explanation:

Looking at this graph, we can see that the slope of it is 2. We know this because for every time x increases by 1, y increases by 2.

We also know that the y-intercept of this graph is 5, since it intercepts the y-axis at the value 5.

We can easily create an equation with this info.

[tex]y = 2x + 5[/tex].

Hope this helped!

Answer:

C. y= 2x+5

Step-by-step explanation:

y=mx+b

(+b) is y- intercept

(mx) is the slope.

plot the y- intercept first which the line starts at (0,5)

since the slope isn't a fraction you turn it into one which would be

[tex] \frac{2}{1} [/tex]

It takes 0.57 seconds per copy and he made 6 copies.

6 + 0.57 = 6.57

He added 6 and 0.57 instead of multiplying.

The easiest way to figure this out would be to do the problem by ourselves:

0.57 · 6 = 3.42, so it will take about 3.5 seconds.

We can say that Jasper got a way different answer, so it must be something wrong with the way he multiplied. When we look through the answers and we see that rather than multiplying, Jasper added, so our answer is:

He added 6 and 0.57  instead of multiplying.

Answer:0.60$

Step-by-step explanation:

15=9$

 1=0.60$

Answer:

60 cents

Step-by-step explanation:

Answer:

145.8

Step-by-step explanation:

l.s.f for the two is 3:5

volume scale factor will be 3³:5³ which us 27:125

so 27×675 / 125

= 145.8

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[tex]x+\frac{2}{x} -2-x+\frac{3}{x} -1[/tex]

[tex]= \frac{-3x + 5}{x}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

486cm^2

Step-by-step explanation:

Surface area of cube = (6a^2)

6×9×9=486.

Answer:

-6xy - 16x -24y -64

Step-by-step explanation:

(2x+8)(-3y-8) =

To find the answer,

First multiply, the first number on both sides,

2x * -3y = -6xy

Then the first number on the left side and the second number on the right side,

2x * -8 = -16x

Then the second number on the left side and the first number on the right side,

8 * -3y = -24y

Then the second number on the left side and the second number on the right side,

8 * -8 = -64

Now add all the answers,

-6xy -16x -24y -64

Answer:

-6xy-16x-24y-64

Step-by-step explanation:

(2x+8)(-3y-8)​

Foil

First 2x*-3y = -6xy

outer -8*2x = -16x

inner -3y *8 = -24y

last -8*8 = -64

Add them together

-6xy-16x-24y-64

Answer:

Slope is -.25 =

Minus 25%

Step-by-step explanation:

x1 y1  x2 y2

6 3.5  8 3

(Y2-Y1) (3)-(3.5)=   -0.5  ΔY -0.5

(X2-X1) (8)-(6)=    2  ΔX 2

slope= -  1/4    

B= 5          

Y =-0.25X +5    

The percentage change is -25% the price of fuel is decreased by 25%.

The equation of line is given as,

y = mx + c

Where m is the slope and c is the y-intercept.

Let the data is

x₁= 6 ,   y₁ = 3.5  

x₂ = 8 , y₂ =  3

Calculate the change,

(Y₂ -Y₁ ) = (3)-(3.5)

ΔY = -0.5

(X₂-X₁) = (8)-(6)

ΔX = 2

Calculate the slope,

Slope = ΔY/ ΔX

Slope = -0.5 / 2

Slope = - 1/4 = -0.25

The equation formed by using the above data is,

Y =-0.25X +5    

Therefore, the percentage change is -25% the price of fuel is decreased by 25%.

More about the equation of line link is given below.

https://brainly.com/question/21511618

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Answer:

2

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

m = ( 8-2)/(3-0)

   = 6/3

   = 2

Answer:

2

Brainliest, please!

Step-by-step explanation:

(0, 2)(3, 8)

y = +6

x = +3

y/x = 6/3 = 2