solve for k.

6(3k + 15) − 16k = 7k

k =

Answer:

the bottom one

Step-by-step explanation:

Solution,

5n^3+4n^2-9+(-2n^3+7n-5)

= 5n^3+4n^2-9-2n^3+7n-5.

Combine the like terms,

=5n^3-2n^3+4n^2+7n-9-5

=3n^3+4n^2+7n-14

hope it helps

Good luck on your assignment

Answer:

[tex] = 3 {n}^{3} + 4 {n}^{2} + 7n - 14 \\ [/tex]

Step-by-step explanation:

[tex]5 {n}^{3} + 4{n}^{2} - 9 + ( - 2 {n}^{3} + 7n - 5) \\ 5 {n}^{3} + 4 {n}^{2} - 9 - 2 {n}^{3} + 7n - 5 \\ = 3 {n}^{3} + 4 {n}^{2} + 7n - 14[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Tank B

Step-by-step explanation:

To be proportional it must go through the origin, (0,0), And have a constant slope. Tank B follows this

Answer:

117 pounds

Step-by-step explanation:

the ratio is given:

4 : 5

Colin : Dan

Simplest way to solve:

4x = 52

x = 52/4 = 13

now, x is one part of the share.

There are 9 total parts:

9 x 13 = 117.

Hope this helps

Answer:

y = x +2

Step-by-step explanation:

4y=4x+8​

Slope intercept form is

y = mx+b so we need to solve for y

Divide each side by 4

4y/4 = 4x/4 +8/4

y = x +2

The slope is 1 and the y intercept is 2

Answer:

a. Distribute –4 to get –8x + 4 > 5 – 3x

Step-by-step explanation:

Correct first step is:

a. Distribute –4 to get –8x + 4 > 5 – 3x

The first step to solve the given expression is to distribute -4 over 2x and -1 to get –8x + 4 > 5 – 3x

Inequality are expressions not separated by an equal sign. Given the inequality;

–4(2x – 1) > 5 – 3x

The first step to solve the given expression is to distribute -4 over 2x and -1 to get –8x + 4 > 5 – 3x

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Answer:

[tex]2x-16/5[/tex]

Step-by-step explanation:

[tex]2x+14-18+0.8[/tex]

[tex]2x-3.2[/tex]

Answer:

2x + 16/5

Step-by-step explanation:

= 2x + 14 - `18 + 4/5

= 2x + 4 + 4/5

= 2x + 16/5

Hope this helps!

Answer:

Step-by-step explanation:

This is a binomial probability distribution and the probability of success and value is the same for each trial.

Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success is

89.4/100 = 0.894

If exactly 7 of the 10 have the right shape, should the company stop the production line, it means that the probability of getting right shaped tires in this case is 7/10 = 0.7

This is actually below the known probability of success. Therefore, the correct option is

Yes, as the probability of seven having the correct shape is unusual

Answer:

[tex]x=\sqrt{26}-4,\:x=-\sqrt{26}-4[/tex]

Step-by-step explanation:

[tex]x^2+8x=10[/tex]

Write this equation in the form of: [tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]

Solve for a:

[tex]2ax=8x[/tex]

[tex]\frac{2ax}{2x}=\frac{8x}{2x}[/tex]

[tex]a=4[/tex]

Add [tex]a^2=4^2[/tex] to both sides:

[tex]x^2+8x+4^2=10+4^2[/tex]

[tex]\left(x+4\right)^2=26[/tex]

[tex]x+4=\sqrt{26}[/tex]

[tex]x+4-4=\sqrt{26}-4[/tex]

[tex]x=\sqrt{26}-4[/tex]

[tex]x+4=-\sqrt{26}[/tex]

[tex]x+4-4=-\sqrt{26}-4[/tex]

[tex]x=-\sqrt{26}-4[/tex]

Answer:

6

Step-by-step explanation:

Okay so the shape has an area of 60 square inches. The formula for the area of a triangle is A = b*h where A = area, b = base, and h = height

So we are given the value for A (60)

We are given the value for height (10)

So we just need to find the value of the base

So let's set this up as an equation. Input the given values into the area for triangle formula

A = B*h

60 = B * 10

So we need to solve for B. To do that we need to get B alone on one side of the = sign. B is being multiplied by 10 so do the opposite and divide both sides by 10

60 divided by 10 = 6

10 divided by 10 = 1 (don't actually put a 1 down, just drop it)

So we are left with

6 = B

So the base is 6 square inches. To test, put it in the equation:

A = B*h

60 = 6*10

60 = 60

Answer:

Length of shed is 7 yards

Step-by-step explanation:

Mathematically the volume of the shed is the area of the base * height

Area of the base = length * width

let the length be x

Thus, the area of the base = x * 7 = 7x

Now, 7x * 3 = 147

21x = 147

x = 147/21

x = 7 yards

Answer:

[tex]\frac{5\sqrt{6} +35}{43}[/tex]

Step-by-step explanation:

Step 1: Multiply by conjugate

5/(7 - √6) x (7 + √6)/(7 + √6)

5(7 + √6)/43

Step 2: Distribute

(35 + 5√6)/43

Answer:

the answer is have to be equal.

Step-by-step explanation:

you can always equal two similar triangles so that they become congruent.

In the ratio of the length of their sides is equal to one, they are congruent. So, all congruent triangles have to be similar but all similar triangles need not be congruent......the ratio of corresponding sides,AB/A'B'=BC/B'C'=CA/C'A'. If the two triangles are congruent AB/A'B'=BC/B'C'=CA/C'A'=1

I am glad to help you!!!!

Answer:

3ft

Step-by-step explanation:

The value of length of SA is,

⇒ SA = 3 feet

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

Triangle ABC is shown in figure.

Now, Observe the given figure,

Since, Line ST is parallel to the line AC.

Therefore, By Basic Proportionality Theorem which states

" If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion".

Hence, We get;

SB/SA = BT / TC

10 / SA = 9 / 2.7

SA = 2.7 × 10 / 9

SA = 3 feet

Thus, The value of length of SA is,

⇒ SA = 3 feet

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Answer:

Sum of the first 3 terms is 9245

See explanation below

Step-by-step explanation:

The question is not clear. From the question we can tell we are to determine the sum of the first 3 terms of a geometric series. I would show you how to calculate sum of n terms given first term and common ratio.

Let's consider the question below.

Given that the first term is 15 and the common ratio is 6, find the first 3 terms

Solution:

Sum of geometric series has two formulas: one is for common ratio(r) > 1 and the other is for common ratio (r) < 1

Since the r in the question is > 1. We would apply the formular that applies to it.

Sum of the first 3 terms is 9245

See attachment for detail

Answer:

x^2+13x+40

Step-by-step explanation:

To solve this, use the FOIL method. Multiply the first terms, then the outside, then the inside and finally the last terms.

We have the binomials:

(x+5) and (x+8)

The first terms are x and x. The outside terms are x and 8. The inside terms are 5 and x. The last terms are 5 and 8.

Multiply these values.

F (first): x and x

x*x= x^2

O (outside): x and 8

x*8=8x

I (Inside): x and 5

x*5=5x

L ( Last): 5 and 8

5*8=40

Now, add all the products together.

x^2+8x+5x+40

Combine like terms. In this case, the like terms are 8x and 5x.

x^2+13x+40

The final trinomial (three terms) is: x^2+13x+40

Answer:

No other given point lie on the same graph

Step-by-step explanation:

Equation : [tex]y =(x +8)^2+k[/tex]

We are given that The point (-4,7) lies on the graph of [tex]y =(x +8)^2+k.[/tex]

So, Point(-4,7) satisfies the given equation

So,[tex]7=(-4+8)^2+k[/tex]

7=16+k

-9=k

So, The equation is [tex]y =(x +8)^2-9[/tex]

Now substitute the given points

(12,4)

[tex]4=(12+8)^2-9[/tex]

4=400-9

[tex]4\neq 391[/tex]

So,(12,4) not lies on the graph

(-5,72)

[tex]72=(-5+8)^2-9[/tex]

72=9-9

[tex]72\neq 0[/tex]

So,(12,4) not lies on the graph

(5,72)

[tex]72=(5+8)^2-9[/tex]

72=169-9

[tex]72\neq 160[/tex]

So,(12,4) not lies on the graph

(4,12)

[tex]12=(4+8)^2-9[/tex]

12=144-9

[tex]12\neq 135[/tex]

So,(12,4) not lies on the graph

So, No other given point lie on the same graph

Answer:

10.7 feet

Step-by-step explanation:

The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.

The hypotenuse of the triangle is 14 feet (length of ladder)

The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)

We need to find the height of the triangle. We can apply Pythagoras rule:

[tex]hyp^2 = a^2 + b^2[/tex]

where hyp = hypotenuse

a = base of the triangle

b = height of the triangle

Therefore:

[tex]14^2 = 9^2 + b^2\\\\196 = 81 + b^2\\\\b^2 = 196 - 81 = 115\\\\b = \sqrt{115} \\\\b = 10.7 feet[/tex]

The wall reaches 10.7 feet high.

Answer:

Step-by-step explanation:

nonlinear ig?

Answer:

Step-by-step explanation:

The area for a rectangle is A = LW. We know the area and we also know the length. We are solving for the width.

[tex]112=7\sqrt{x}[/tex] and

[tex]16=\sqrt{x}[/tex]

Siince the width is given as the square root of x, and the square root of x is equal to 16, then the width is 16. Now to find the value of x from the last statement in our equation. If

[tex]16=\sqrt{x}[/tex] and we want to solve for x, we will square both sides, since squaring undoes a square root. Since this is an equation, we have to square both sides.

256 = x

The area of the rectangle is 112 units and the width is 16 units

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

A = 112 units

Let the length of the rectangle be L = 7 units

Let the width of the rectangle be W = √x units

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of the rectangle = 7 √x

7√x = 112

Divide by 7 on both sides of the equation , we get

√x = 16

Taking the square on both sides of the equation , we get

x = 16²

x = 256

Therefore , the value of x is 256

Hence , the width of the rectangle is √x = 16 units

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Answer:

36.4miles per gallon

Step-by-step explanation:

Divide 45 1/2 by 1 1/4. This gives 36 2/5

Hope this helps.

Answer:

18,72

Step-by-step explanation:

Complementary angles add to 90 degrees

Multiply the ratio by x

1x+4x = 90

Combine like terms

5x = 90

divide by 5

5x/5 = 90/5

x =18

The first angle is 18 degrees

4*18 =72

The second angle is 72 degrees

Answer:

4 * pi

Step-by-step explanation:

Given r = 10

Formula for the circumference of this full circle is:

2 * r * pi

2 * 10 * pi = 20 * pi

Given one (biggest) part = 16 * pi of this circle.

The other (smaller) part must therefore be:

20 * pi - 16 * pi

4 * pi

Answer:

B) 16%

Step-by-step explanation:

First, we need to standardize 58 and 66 inches using the following equation:

[tex]z=\frac{x-m}{s}[/tex]

Where m is the mean and s is the standard deviation, so 58 and 66 are equivalent to:

[tex]z=\frac{58-70}{4}=-3\\z=\frac{66-70}{4}=-1\\[/tex]

Then, the percent of men whose heights falls between 58 inches and 66 inches is calculated as:

P(58<z<66) = P(-3<z<-1)

So, using the normal table, we get:

P(-3<z<-1) = P(z<-1) - P(z<-3)

P(-3<z<-1) = 0.1587 - 0.0013

P(-3<z<-1) = 0.1574

Finally, 0.1574 rounded to the nearest whole percent is equal to 16%

Answer:

On the circle

Step-by-step explanation:

Graph it

Answer:

On the circle.

Step-by-step explanation:

I recommend using a visual.

Answer:

x = 87

Step-by-step explanation:

the ratio SR / RV is equal the ratio ST / TU (both ratios are equal to 1), and the angle in the vertex S is the same for both triangles SUV and STR, so we can affirm that these triangles are similar (case S-A-S).

Then, we have that the ratio SR / SV is the same as RT / UV:

SR / SV = RT / UV = 1 / 2

RT * 2 = UV

2*(x - 37) = x + 13

2x - 74 = x + 13

x = 87

Answer:Case I

When we know two sides of the right triangle, in which case, we will use the Pythagorean theorem

Case II

When we know 1 side and 1 angle of the right triangle, in which case, we will use good old sohcahtoa

Step-by-step explanation:

Answer:

-12C

Step-by-step explanation:

Simply take 22 and subtract it by 34.

Answer: Think it is -3/5

Step-by-step explanation:

6-5(x)=9

6-5(-3/5)=9

6+3=9

9=9

Answer:

Equation:

5x - 6 = 9

Answer:

x = 3

Step-by-step explanation:

Let's break this down:

When six is subtracted from five times a number, the result is 9

"five times a number" simply means a variable, such as x, is being multiplied by 5

five times a number: 5x

Next step:

When six is subtracted from five times a number, the result is 9

"six is subtracted from" means 6 is being taken away from whatever comes next, in this case, '5x'

six is subtracted from: - 6

Final section:

When six is subtracted from five times a number, the result is 9

"the result is 9" means the entire equation equals nine

the result is nine: = 9

Put it all together:

5x - 6 = 9

Solve:

5x - 6 = 9

     +6  +6

5x = 15

/5     /5

x = 3

Therefore, the value of x is three.

Answer:

m∠R = 112°, m∠S = 112°, m∠T = 68°

Step-by-step explanation:

In a cyclic quadrilateral QRST,

m∠R + m∠T = 180° [Since opposite angles of a cyclic quadrilateral measure 180°]

(3x + 40)° + (5x - 52)° = 180°

8x - 12 = 180

8x = 180 + 12

8x = 192

x = 24

m∠R = (3x + 40) = 3×24 + 40

                          = 72 + 40

                          = 112°

m∠T = 180° - m∠R

        = 180° - 112°

        = 68°

Since m∠Q = 68°

m∠S = 180° - m∠Q

        = 180° - 68°

        = 112°

Therefore, m∠R = 112°, m∠S = 112°, m∠T = 68°

Answer:

112, 112, 68

Step-by-step explanation:

It took me over 15 min to figure out what the answer was. When answering it, you have to be very specific.