Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smaller number. Let x represent the smaller number and y represent the larger number. Which equations represent this situation? y = negative four-thirds x + 31. y = 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = 2 x + 7. y = negative four-thirds x + 31. y = negative 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = negative 2 x + 7.

Answer:

x is all real numbers

Step-by-step explanation:

5(x-7) + 42 = 5x+7

Distribute

5x - 35 +42 = 5x+7

Combine like terms

5x +7 = 5x+7

Subtract 5x from each side

7=7

This is always true, so x can be any number

Answer:

Hey there!

5(x-7)+42=5x+7

5x-35+42=5x+7

7=7

Infinite solutions.

Hope this helps :)

Answer:

4 plants

Step-by-step explanation:

If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4

(8 * 4 is 32)

She will have one dollar left but she can't buy another plant since that's not enough.

Answer:

4 plants

Step-by-step explanation:

Take the amount of money she has and divide by the cost per plant

33/8

The amount is 4 with 1 dollar left over

4 plants

Answer:

its 23

Step-by-step explanation:

Answer:

108 m

Step-by-step explanation:

Answer:

$18.3236

Step-by-step explanation:

If the employer reimburses $0.17 per mile driven, we just need to multiply $0.17 by the number of miles that Joe drives.

So, the mileage reimbursement for Joe is:

$0.17 * 107.78 = $18.3236

Answer:

a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.

Step-by-step explanation:

a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:

[tex]V = w \cdot h \cdot l[/tex]

Where:

[tex]w[/tex] - Width, measured in meters.

[tex]h[/tex] - Height, measured in meters.

[tex]l[/tex] - Length, measured in meters.

The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:

[tex]\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l[/tex]

Where [tex]\dot w[/tex], [tex]\dot h[/tex] and [tex]\dot l[/tex] are the rates of change related to the width, height and length, measured in meters per second.

Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the volume of the box is:

[tex]\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)[/tex]

[tex]\dot V = 54\,\frac{m^{3}}{s}[/tex]

The rate of change associated with the volume of the box is 54 cubic meters per second.

b) The surface area of the parallelepiped, measured in square meters, is represented by this model:

[tex]A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)[/tex]

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:

[tex]\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h[/tex]

Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the surface area of the box is:

[tex]\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)[/tex]

[tex]\dot A_{s} = 18\,\frac{m^{2}}{s}[/tex]

The rate of change associated with the surface area of the box is 18 square meters per second.

c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:

[tex]r^{2} = w^{2}+h^{2}+l^{2}[/tex]

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:

[tex]2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l[/tex]

[tex]r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l[/tex]

[tex]\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}[/tex]

Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the length of the diagonal of the box is:

[tex]\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}[/tex]

[tex]\dot r = -1\,\frac{m}{s}[/tex]

The rate of change of the length of the diagonal is -1 meters per second.

Answer:

We know that for a standard dice the probability of obtain a 6 is:

[tex] P=\frac{1}{6}[/tex]

And for this case our value of x=3 and replacing we got:

[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]

[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]

Step-by-step explanation:

For this case we have the following function:

[tex] f(x) = (1-P)^{x-1} P[/tex]

We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try

We know that for a standard dice the probability of obtain a 6 is:

[tex] P=\frac{1}{6}[/tex]

And for this case our value of x=3 and replacing we got:

[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]

[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]

Answer:

13/40

Step-by-step explanation:

The period they have played can be divided into 3 parts:

● The time Amy wins

● The time Lily wins

● The time they tie

So the sum of them is the total time of playing.

Let A be the time Amy wins, L the tile Lily wins and T the time they tie .

●●●●●●●●●●●●●●●●●●●●●●●

Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.

So:

A + P + T = 1

3/8 + 3/10 + T = 1

Multiply 8 by 10 and 10 by 8 so that you get a common denominator.

Cross multiply the numerators and the denominators.

(3*10+3*8)/80 + T = 1

(30 + 24)/80 + T =1

54/80 + T = 1

(27*2)/(40*2) + T = 1

Simplify by 2

27/40 + T = 1

T = 1 - 27/40

Multiply one by 40 to get a common denominator

T = (40-27)/40

T = 13/40

So they have tied 13/40 of the time

Answer:

It is 96 square units

Step-by-step explanation:

Step-by-step explanation:

just substitute the value of g(X) and f(X)

Answer:

[tex]\boxed{Option \ A}[/tex]

Step-by-step explanation:

[tex]f(x) = 2*3^x[/tex]

y intercept is when x = 0

So, Putting x = 0 in the above function

=> f(0) = [tex]2*3^0[/tex]

=> f(0) = 2*1

=> f(0) = 2

So, y-intercept is (0,2)

Answer:

A

Step-by-step explanation:

f(x) = 2 × 3^x

Plug x as 0 to find y-intercept.

2 × 3⁰

2 × 1

= 2

Answer:

x= 78

Step-by-step explanation:

Focus on the blue traingle:

∠BHI= 180° -47° -31° (∠sum of triangle)

∠BHI= 102°

x°= 180° -102° (adj. ∠s on a str. line)

x°= 78°

x= 78

Alternatively,

x°= 47° +31° (ext. ∠ of triangle)

x°= 78°

x= 78

Answer:8

Step-by-step explanation:

You find the average which is adding them all together then dividing by how many numbers you added.

Answer:

Total cost = $4,873

Therefore, the booking cost of hotel 5 would be $4,873

Step-by-step explanation:

Please refer to the attached table.  

The total cost includes the cost of the room and the cost of buffet dinner.

From the given table hotel 5,

The cost of the room for 120 people is found to be $166 per hour.

The conference will last for 5 hours so the total cost of the room is

Cost of room = 5*$166 = $830

From the given table hotel 5,

The cost of the buffet dinner per head is found to be $30.

Since there are total 120 people so the total cost of dinner is

Cost of dinner = 120*$30 = $3600

Total cost = $830 + $3600 = $4430

We are given that hotel 5 has recently increased the total chargers by 10%

Total cost = $4430*1.10

Total cost = $4,873

Therefore, the booking cost of hotel 5 would be $4,873.

Answer: 6 hours

Step-by-step explanation:

Given, Tim and Jim are working on a school project together.

Tim takes 10 hours to complete the school project.

If Jim worked alone, it would take him 15 hours

Let t be the time they both take if they work together.

Then, [tex]\dfrac{1}{t}=\dfrac{1}{\text{Time taken by Tim}}+\dfrac{1}{\text{Time taken by jim}}[/tex]

[tex]\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3+2}{30}=\dfrac{5}{30}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow t=6[/tex]

So, it will take 6 hours to complete the school project together .

Answer:

x ≥ 4

Step-by-step explanation:

Well to find the inequality we need to single out x,

4x - 1 ≥ 15

+1 to both sides

4x ≥ 16

Divide 4 by both sides

x ≥ 4

Thus,

x is greater than or equal to 4.

Hope this helps :)

Answer:

The last graph (to the far right).

Step-by-step explanation:

As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.

Hope this helps!

Answer:

19/70 of NASA shuttle missions were carried out by Discovery.

9/140 of NASA shuttle missions were carried out by Challenger.

17/70 of NASA shuttle missions were carried out by Endeavour.

Step-by-step explanation:

Adding the number of missions carried out by NASA gives us 140 in total.

Discovery's total amount of missions simplified is 19/70.

Challenger's total amount of missions is already in the simplest form.

Endeavour's total amount of missions simplified is 17/70.

Answer:

81/140

Step-by-step explanation:

Well to find the fraction we first need to total amount of NASA missions.

38 + 32 = 70

70 + 34 = 104

104 + 27 = 131

131 + 9 = 140

Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.

38 + 9 + 34 = 81

Now we can make the following fraction,

81/140

This is already in simplest form.

Thus,

the answer is 81/140.

Hope this helps :)

Option A is the correct answer.

Answer:

SAS

Step-by-step explanation:

According to the given information both the triangles are congruent by SAS postulate.

The given triangles are congruent by SAS rule.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Given are two triangles, ABC and DEF,

They have congruent parts, given;

AB ≅ DE

BC ≅ EF

∠ B ≅ ∠ E

The triangles have two congruent sides and one congruent angle between them.

The Side-Angle-Side theorem of congruency states that, if two sides and the angle formed by these two sides are equal to two sides and the included angle of another triangle, then these triangles are said to be congruent.

Hence, The given triangles are congruent by SAS rule.

For more reference on congruent triangles, click;

https://brainly.com/question/12413243

#SPJ2

Answer:

[tex]x = \frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{x}{2} +\frac{3}{4} =\frac{7}{8}[/tex]

→ Find the LCM of the denominators (2,4 and 8)

LCM = 8

→ Multiply the whole equation by 8 to get rid of the fractions

4x + 6 = 7

→ Minus 6 from both sides to isolate 4x

4x = 1

→ Divide both sides by 4 to isolate x

[tex]x = \frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{x}{2} + \frac{3}{4} = \frac{7}{8} [/tex]

Multiply both sides of the equation by 8

[tex] \frac{x}{2} \times 8 + \frac{3}{4} \times 8 = \frac{7}{8} [/tex]

[tex]4x + 6 = 7[/tex]

Move constant to R.H.S and change its sign

[tex]4x = 7 - 6[/tex]

Subtract the numbers

[tex]4x = 1[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{1}{4} [/tex]

Calculate

[tex]x = \frac{1}{4} [/tex]

hope this helps..

Best regards!!

Answer:

B

Step-by-step explanation:

To solve this you do 80/100=.8

You than do .8×60= 48

Answer:

The answer is 2.15%  

Step-by-step explanatio

Answer:

x = 0

Step-by-step explanation:

-7(5-3x)=-35

Divide by -7

-7/-7(5-3x)=-35/-7

5 -3x = 5

Subtract 5 from each side

5-3x-5 = 5-5

-3x=0

Divide by -3

x=0

Answer: x = 0

Step-by-step explanation: Start by distributing the -7 through the parenthses on the left side of the equation.

-7(5) is -35 and -7(-3x) is 21x.

So we have -35 + 21x = -35.

Next, isolate the x term by adding 35 to both sides.

When we do this, we get 21x = 0.

Now divide both sides by 21 and x = 0.

Answer:

(70-55)/4.5=y rounded down to the nearest whole number

Step-by-step explanation:

The first step is to take away the $55 from $70

70-55=15

Simba has $15 to spend on the yoga classes, to find the number of yoga classes she can attend, you divide 15 by the amount a yoga class costs, $4.50

15/4.50=3 1/3

Because she can not have 1/3 of a yoga class, she can attend 3 yoga classes in her budget.

Hope this helps, if you have any questions feel free to ask

Have a good day! :)

Answer:

9 in.

Step-by-step explanation:

Given that the 4 in and 10 in. lines are parallel, the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

-3

Step-by-step explanation:

-3 is the answer

Answer:

-3

Step-by-step explanation:

Answer:

74w+10

Step-by-step explanation:

That's the answer

Answer:

1. true - dilating figures does not change their angle measure

2. true - dilating figures does not change the orientation, so AD would still be on a horizontal line parallel to its current position

Complete Question

The options for the above question is  

a There is not sufficient evidence to warrant rejection of the claim.    

b  There is sufficient evidence to warrant rejection of the claim.

c There is sufficient evidence to support the claim.    

d There is not sufficient evidence to support the claim.

Answer:

Option A is correct

Step-by-step explanation:

From the question we are told that

     The  population mean is  [tex]\mu =[/tex]$47,500

     The sample size is [tex]n = 86[/tex]

      The sample  mean is  [tex]\= x =[/tex]$48,061

      The standard deviation is [tex]\sigma =[/tex]$2,351

       The  level of significance is  [tex]\alpha = 0.02[/tex]

The null hypothesis  is  

     [tex]H_o : \mu =[/tex]$47,500

 The  alternative hypothesis is

      [tex]H_a : \mu \ne[/tex] $47,500

The critical value of  [tex]\alpha[/tex] from the t-Distribution table is  [tex]Z_{\frac{\alpha }{2} } = 2.326[/tex]

Now the test statistics is mathematically evaluated as

       [tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{48061 - 47500 }{\frac{2351}{\sqrt{86} } }[/tex]

      [tex]t = 2.21[/tex]

Now from the values  obtained we can see that

        [tex]Z_{\frac{\alpha }{2} } > t[/tex]

hence we fail to reject the null hypothesis

Hence there is not sufficient evidence to warrant rejection of the claim

Answer:

Sydney's age is 28

Step-by-step explanation:

Let Devaughn be D

And Sydney be S

D=S+8..... equation 1

D+S=64...... equation 2

Substitute equation 1 to equation 2

S+8+S=64

2S+8=64

2S=64-8

2S=56

S=56/2

S=28

Hope it helps

Good luck