Find the mean of the data in the dot plot below.

Answer:

[tex]2h^{2} + 7hk - 15k^{2}[/tex]

Step-by-step explanation:

Distribute (2h − 3k)(h + 5k).

2h^2 + 10hk - 3hk - 15k^2

2h^2 + 7hk 15k^2

Answer for problem 1: slope = 2, y intercept = 3

Answer for problem 2: slope = 3/4, y intercept = -2

Explanation:

Both equations are in the form y = mx+b. This is known as slope intercept form. This is because we can read off the values of the slope and y intercept very quickly. We have y = 2x+3 match up with y = mx+b. The m is the slope and b is the y intercept. So m = 2 and b = 3 for this equation. A similar situation happens with the other equation as well. It might help to rewrite the second equation into y = (3/4)x + (-2).

Answer:

slope: 1.) 2 ,,, 2.) 3/4

y-int: 1.) (0,3) ,,, 2.) (0,-2)

graph: attached in pictures/ blue line represents y=2x+3 ,,, red line represents y=3/4-2

Step-by-step explanation:

When you have two congruent figures, the vertices are listed in the same order. This means that

Side LM ≅ Side QR, Side MN ≅ Side RS, etc. The same applies for the angles.

Therefore, Side LM ≅ Side QR and Angle MNO ≅ Angle RST.

The complete statements are Side LM is congruent to the side QR and angle ∠MNO is congruent to angle ∠RST.

The two quadrilaterals whose angles and sides of one quadrilateral are the same as the corresponding angles and sides of another quadrilateral then two quadrilaterals are congruent to each other.

The order of the lettering for congruent parts should place the lettering for corresponding parts in the same order.

Given in the question that the quadrilateral LMNO and QRST are congruent.

LMNO ≅ QRST

As we know Congruent Parts of the congruent Figures are also congruent, we have;

side LM is congruent to side QR.

side MN is congruent to side RS.

side NO is congruent to side ST.

side OL is congruent to side TQ.

Similarly, for the corresponding angles of the quadrilaterals, we have;

angle ∠MNO is congruent to angle ∠RST.

angle ∠NOL is congruent to angle ∠STQ.

angle ∠OLM is congruent to angle ∠TQR.

angle ∠LMN is congruent to angle ∠QRS.

Therefore, Side LM is congruent to the side QR and angle ∠MNO is congruent to angle ∠RST.

Learn  more about Congruent quadrilateral

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Answer:

[tex]\frac{35(1 + 35)}{2}[/tex]

Step-by-step explanation:

Given:

The attached

Required

Find the equivalent expression

The interpretation of is to add the sequence:

n = 1,2,3,......35

This can be done using the following formula (Sum of n terms of an AP)

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where n is the number of terms from 1 to 35; [tex]n = 35[/tex]

T1 is the first term; [tex]T_1 = 1[/tex]

Tn is the last term; [tex]T_n = 35[/tex]

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex] becomes

[tex]S_n = \frac{35}{2}(1 + 35)[/tex]

[tex]S_n = \frac{35(1 + 35)}{2}[/tex]

From the list of given options;

Option A is correct

[tex]\frac{35(1 + 35)}{2}[/tex]

The mass of water will be - 3785.41 grams.

We have density of water is 1.00 g/ml.

We have to determine the mass in grams of 1.00 gal of water.

The relation between Mass (m) and Density (ρ) is -

m = ρV

where -  V is the volume of object.

According to the question -

Density of water -  1.00 g/ml

Volume of water -  1 gallon = 3785.41 ml

m = ρV

m = 1 x 3785.41 = 3785.41 grams.

Hence, the mass of water will be - 3785.41 grams.

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Answer:

45

Step-by-step explanation:

20 boys= 5 times the ratio

So, 5x5=25

25 girls and 20 boys= 45 students

Answer:

45 students

Step-by-step explanation:

to make sure there are 20 boys you need to multiply 4 by 5

so multiply the 5 by 5 as well

then add what you get!!

Answer:

When x = 7, y = 4

Step-by-step explanation:

We are simply looking for the y-value for when the graph input x equals 7. When we look at the graph when x = 7, we see that our y-value y equals 4.

Answer:

x=7 y=4

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ 35.805 \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all we need to find the intersection points of y = 12 and

[tex]y=f(x)=e^x+e^{-x}[/tex]

We need to solve the following equation.

[tex]e^x+e^{-x}=12\\\\\text{*** We multiply by }e^x\text{ both side ***}\\\\\left(e^x\right)^2+1=12e^x\\\\\text{*** Let's note } X =e^x\text{, it comes *** }\\\\X^2-12X+1=0[/tex]

[tex]\Delta=b^2-4ac=12^2-4=140=2^2\cdot 35\\\\X_1=\dfrac{12-2\sqrt{35}}{2}=6-\sqrt{35}\\\\X_2=\dfrac{12+2\sqrt{35}}{2}=6+\sqrt{35}\\[/tex]

And, we take the greater solution to solve:

[tex]X=e^x=6+\sqrt{35}<=>\boxed{x=ln(6+\sqrt{5})}[/tex]

Let's note it a.

Let's compute the integral.

We need to compute the following (because 12-f(x) is pair the integral that we are looking for is)

[tex]\displaystyle 2\int\limits^a_{0} {\left(12-(e^x+e^{-x})\right)} \, dx =12*(2a)-2\int\limits^a_{0} {(e^x+e^{-x})} \, dx \\\\=24a-2[e^x-e^{-x}]_{0}^a=24a-2(e^a-e^{-a})[/tex]

We can replace a by the value we already found.

[tex]24\cdot ln(6+\sqrt{35})-2\left( 6+\sqrt{35}-\dfrac{1}{6+\sqrt{35}}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(6+\sqrt{35}-\dfrac{\sqrt{35}-6}{(\sqrt{35}-6)(\sqrt{35}+6)}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{29*6+29*\sqrt{35}-\sqrt{35}+6}{29}\right)\\\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{180+28\sqrt{35}}{29}\right)\\\\[/tex]

= 59.46933...-26.66432...=35.8050...

So the answer is [tex]\boxed{\sf \ \ 35.805 \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: A. 9

Step-by-step explanation:

In the given tree diagram , there are 3 branches , to each branch there are 3 leaf nodes.

By using Fundamental counting principal ,

Number of possible outcomes for the tree diagram = (Number of branches) x (Number of leaf nodes)

[tex]=3 \times 3\\\\=9[/tex]

Hence, the number of possible outcomes for the tree diagram = 9

So, the correct option is A. 9.

Answer:

vertex (-4,-1)

2nd point ( 0,31)

Step-by-step explanation:

f(x) = 2x^2 + 16x + 31

First find the vertex

The x coordinate of the vertex is -b/2a  where ax^2 +bx +c

-16/ 2(2) = -16/4 = -4

Substitute into the function

f(-4) = 2 ( -4)^2 +16(-4) +31

       = 2 *16-64 + 31

       = 31 -64 +31

       = -1

The vertex is at ( -4,-1)

Another point can be x=0

f(0) = 0+16(0)+31

     = 31

( 0,31)

Answer:

12 cm

Step-by-step explanation:

You would only have to focus on the green line and then you just have to divide it by 12 and you get 4 and than you multiply 3 cm by 4 and the answer for the actual length of the green line will be 12 cm.

Answer:

12 cm

Step-by-step explanation:

The ratio of feet to cm is 12:3. Set up a ratio to find the length of the green line in cm.

12 feet ÷ 3 cm = 48  ft ÷ x

Cross multiply and divide.

3 x 48 = 12 × x

144 = 12x

x = 12

The actual length of the green line is 12 cm.

Hope that helps.

Answer:

10+6=16

16*25=400

400+4=404

Step-by-step explanation:

EZ...

Answer:

Hello There. ☆~\《`°---_●£●__---`°》\~☆

An exponential growth function is represented by

f(x)=a(b)^{x},a>0,b>1.

The given functions can be written as,

A)f(x)=.001(1.77)^x,0.001>0,1.77>1

B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1

C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1

D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.

So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), (C).

Hope It Helps!~ ♡

ItsNobody~ ☆

The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.

Exponential growth is the process of gradual increase of quantity over time.

An exponential growth function is represented by

[tex]\rm f(x)=a(b)^{x}[/tex],  a>0,b>1

The given functions can be written as,

A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1

B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex]   2>0,  [tex]\sqrt{1.5}[/tex] >1

C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex],    5>0, 2>1

D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex],        5>0,  1/e.

So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), and (C).

Learn more about exponential growth;

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Answer: y = -1/2x -1

Step-by-step explanation: since the new line is parallel to the given line the slope of both the lines world be same. Therefore putting the new values in the equation

y-y1=m(x-x1)

y-1=-1/2(x+4)

y-1=-1/2x -2

y=-1/2x-1

Answer:

Rotation

Step-by-step explanation:

when you rotate a point it swaps the numarical values x⇄y as well as in some cases it changes its the symbol from negative to positive depending on the quadrant, in this case, it started in quadrant one and ended in quadrant three.

Answer:

v = 7

Step-by-step explanation:

a. v = 5x + 2y

= 5 × 3 + 2 × -4

= 15 + -8

= 7

Sorry I know only the A one anyways , hope this helps :)

Answer:

Step-by-step explanation:

a  v = 5x+ 2y = 5*3 + 2*-4 = 7

b 3p(p+5) = 3p^2 =15p

c 4k = 44

k=44/4 =11

i hope the person who had deleted my answer this much explanation is only required if not please say so that I can correct myself by ellaborating ...

Answer:

[tex]\large \boxed{\sf \ \ A=5, \ \ B=-13 \ \ }[/tex]

Step-by-step explanation:

Hello,

What you did is correct...

[tex](Ax-3)(x-2)=5x^2+Bx+6\\\\\text{*** we develop the left side ***}\\\\Ax^2+(-2A-3)x+6=5x^2+Bx+6[/tex]

... and you found A by identifying the term in [tex]x^2[/tex] to get A = 5, right?

What about the other terms?

We can then identify the like terms:

>>> term in [tex]x^2\\[/tex]

   A = 5

>>> term in x

   -2A+3=B

>>> constant term

   6 = 6

As we know that A=5 it means that B = -2*5-3=-13

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

B = -13

Step-by-step explanation:

Nothing is wrong you just have to complete it..

soo continuing from where you stopped.

Ax² - 2Ax - 3x + 6 = 5x² + Bx + 6

(its supposed to be the equivalence sign [with three dashes] but I am restricted by my keypad, so I made use of the equal to sign [two dashes])

comparing both sides, we can therefore say:

Ax² = 5x²..............i

- 2Ax - 3x = Bx......ii

+6 = +6..............iii

sub the value of A = 5 into ......ii

-2Ax - 3x = Bx

-2(5)x - 3x = Bx

-10x - 3x = Bx

-13x = Bx

B = - 13

Answer:

1. Multiply the first equation by 3

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

3x + 3y - 6

2. Add 3x + 3y = - 6 ( obtained in step 1) to

2x - 3y = - 9 (given) and solve for x

3. x = - 3

4. Substitute the value of x in the first equation

( x + y = - 2) to get y = - 1

5. The solution for the linear system of equations is ( - 3 , 1)

Hope this helps you

Answer:

20

Step-by-step explanation:

Answer:

[tex]\boxed{70\°}[/tex]

Step-by-step explanation:

Angle ABP and angle MAB are corresponding angles.

Corresponding angles are equal.

Angle ABP = 50 degrees

Angle CBP and angle BCQ are corresponding angles.

Corresponding angles are equal.

Angle CBP = 20 degrees

Angle ABC is the sum of angles CBP and ABP.

[tex]50+20=70[/tex]

Answer:

y=x+-2

Step-by-step explanation:

Slope intercept form is y=mx+b

I plugged in the slope for m and y-intercept for b

sorry i did this real fast because it sounded urgent :)

Answer:

21

Step-by-step explanation:

So we know the ratio is 3/4:1

So if she has 28 ounces of white pain, we can do 28*3/4=21. You could also do 28/4 (find out how much 1/4 of the value is) which is 7 and then multiply that by 3. What your basically doing is your putting it into 4 equal parts and then just multiplying by 3 since that's the amount of parts you need/have.

Answer:

(-6,6), (0,12), (4,8)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 2 --> 2(x, y)

Before-> After dilation

2(-3,3) = (-6,6)

2(0,6) = (0,12)

2(2,4) = (4,8)

Please leave a 'thanks' if this helps!

Answer:

The linear factors are:

[tex]x - 2[/tex]

[tex]x + 3[/tex]

[tex]x + 1[/tex]

Step-by-step explanation:

Given

[tex]x^3 + 2x^2 - 5x - 6[/tex]

Required

Select all linear factors of the polynomial

Solving for x - 2;

Equate x - 2 to 0 and solve for x

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

Substitute 2 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex]2^3 + 2(2^2) - 5(2) - 6[/tex]

[tex]= 8 + 8 - 10 - 6[/tex]

[tex]= 0[/tex]

Because, we arrived at 0, then x - 2 is a factor

Solving for x + 3;

Equate x + 3 to 0 and solve for x

[tex]x + 3 = 0[/tex]

[tex]x = -3[/tex]

Substitute -3 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex](-3)^3 + 2(-3^2) - 5(-3) - 6[/tex]

[tex]= -27 + 2(9) + 15 - 6[/tex]

[tex]= -27 + 18 + 15 - 6[/tex]

[tex]= 0[/tex]

Because, we arrived at 0, then x + 3 is a factor

Solving for x - 1;

Equate x - 1 to 0 and solve for x

[tex]x - 1 = 0[/tex]

[tex]x = 1[/tex]

Substitute 1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex](1)^3 + 2(1^2) - 5(1) - 6[/tex]

[tex]= 1 + 2(1) - 5 - 6[/tex]

[tex]= 1 + 2 - 5 - 6[/tex]

[tex]= -8[/tex]

Because, we did not arrived at 0, then x - 1 is not a factor

Solving for x + 1;

Equate x + 1 to 0 and solve for x

[tex]x + 1 = 0[/tex]

[tex]x = -1[/tex]

Substitute -1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex](-1)^3 + 2(-1^2) - 5(-1) - 6[/tex]

[tex]= -1 + 2(1) + 5 - 6[/tex]

[tex]= -1 + 2 + 5 - 6[/tex]

[tex]= 0[/tex]

Because, we arrived at 0, then x + 1 is a factor

Answer:

2

Step-by-step explanation:

The constant of variation is 2 because the variable is x, and its coefficient, 2, is the constant of variation.

Answer: she needs to work 8 hours

Step-by-step explanation:

Answer:

one cocoa pod makes 5/6 bar

to make 35 bars, he needs

35 / (5/6) = 35 * 6/5 = 42 pods

Monday - Friday is 5 days

42/5 = 8.4

Answer:

Wet Suit Willy found the most treasures per dive.

Step-by-step explanation:

Given:

Diver name         Number of dive    Number of boxes

Sam                                  11                        33

Wet Suit Willy                  18                        81

Deep Diving Dan            26                       104

Find:

Who found the most treasures per dive

Computation:

Sam's per dive collection = 33 / 11 = 3 boxes

Wet Suit Willy's per dive collection = 81 / 18 = 4.5 boxes

Deep Diving Dan's per dive collection = 104 / 26 = 4 boxes

Wet Suit Willy found the most treasures per dive.

Answer:

0.53 is the right answer

Answer:

2 and -2

Step-by-step explanation:

● 7q^2 -28 = 0

Add 28 to both sides

● 7q^2-28+28 = 28

● 7q^2 = 28

Divide both sides by 7

●7q^2/7 = 28/7

● q^2 = 4

You can write directly q= 2 or q= -2

To understand it use the absolute value.

● |q| = 2

● q = 2 or q = -2

The solutions are {2, -2}