Evaluate a + 7b if a = 14 and b =12

Answer:

The correct answer is [tex]9x^{2}-6x[/tex].

Step-by-step explanation:

Consider the provided division:

We need to perform the subtraction in the division:

[tex]6x^{3}+x^{2}-10x[/tex]  ......(1)

[tex]6x^{3}-8x^{2}-4x[/tex]  ......(2)

In order to perform the subtraction simply change the sign of the second expression.

  [tex]6x^{3}+x^{2}-10x[/tex]

[tex]-6x^{3}+8x^{2}+4x[/tex]

----------------------------------------

           [tex]9x^{2}-6x[/tex]

Therefore, the correct answer is [tex]9x^{2}-6x[/tex].

Answer:

Step-by-step explanation:

Answer:

Distance = 3r

Step-by-step explanation:

We are to write an algebraic expression and then simplify it for the given situation:

The distance traveled by a train in three hours with a constant speed of r miles per hour.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

Answer:

Step-by-step explanation:

1.) mean is 4   1,2,3,5,6,7

2.) Four students won 12, 13, 14, 15, 16, or 17 prizes.

A total of 10 prizes were won by all the students.

3.)don't know number 3

the answer for 2 is B because 4 students won 12-17 prizes. They just word it 12,13,14,15,16 or 17.

Answer:

B.

Step-by-step explanation:

Answer:

II

Step-by-step explanation:

Answer:

128/15 min or 8.5 min

Step-by-step explanation:

By using unitary method,

Time required to paint 5/8 of wall = 16 min.

Time required to paint 1/1 of wall = 16×8/5

Hence, Time required to paint 1/3 of wall = 16×8/5×1/3

Answer:

8 8/15

Step-by-step explanation:

simplify the two fractions you have to make them have the same denominater

enthen you can determine the answer.

Answer:

A

Step-by-step explanation:

Answer:

staight angle and supplementary angle

Step-by-step explanation:

Answer: 0.4521 - 0.4879

Step-by-step explanation:

1) Find the standard deviation with the given information:

n=3000

p=47% ⇒ 0.47

1-p= 1 - 0.47 = 0.53

[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.47(0.53)}{3000}}\\\\\\.\ =\sqrt{\dfrac{0.2491}{3000}}\\\\\\.\ =\sqrt{0.00008303}\\\\\\.\ =0.009112[/tex]

2) Find the margin of error (ME) with the given information:

C=95% ⇒ Z = 1.960

σ=0.009112

ME = Z × σ

= 1.96 (0.009112)

= 0.01786

3) Find the confidence interval with the given information:

p = 0.47

ME = 0.01786

CI = p ± ME

= 0.47 ± 0.01786

= (0.4521, 0.4879)

Answer:

Step-by-step explanation:

[tex]-37+n=-56\qquad\text{add 37 to both sides}\\\\-37+37+n=-56+37\\\\n=-19[/tex]

Answer:

n=-93

A. -93 *(first option)*

Step-by-step explanation:

First, you subtract by 37 from both sides of equation.

-37+n-37=-56-37

Then, simplify to find the answer.

-56-37=-93

n=-93 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

6%

Step-by-step explanation:

To solve this you need to subtract 607000 by 572000 to see how many people in the population decreased.

607,000- 572,000= 35,000

Then you put 35,000 over 607,000

also you need x over 100

35000/607,000 x/100

Then do cross product property

35,000*100=3,500,000

607,000* x= 607,000x

3,500,000= 607,000x

Then do 3,500,000 divided by 607,000

You get 5.76%

Round to the nearest percent and get 6%

Final answer:

The rate of decrease of the population from the 2000 census to the 2010 census is 6% when rounded to the nearest percent.

Explanation:

To calculate the rate of decrease of the city's population, we use the population values from the 2000 and 2010 censuses. The population in 2000 was 607,000, and in 2010 it was 572,000. To find the population decrease, subtract the 2010 population from the 2000 population:

Population decrease = Population in 2000 - Population in 2010

Population decrease = 607,000 - 572,000

Population decrease = 35,000

Next, to find the rate of decrease as a percent, we divide the population decrease by the original population (in 2000) and then multiply by 100:

Rate of decrease (%) = (Population decrease / Population in 2000) × 100

Rate of decrease (%) = (35,000 / 607,000) × 100

Rate of decrease (%) = 0.0577 × 100

Rate of decrease (%) = 5.77%

Round this to the nearest percent, and you get a 6% decrease.

===============================================

Here are some reasons why

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{2-(-1)}\implies \cfrac{3}{2+1}\implies \cfrac{3}{3}\implies 1[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1[x-(-1)]\implies y-7=x+1 \\\\\\ y=x+8\implies \boxed{-x+y=8}\implies \stackrel{\textit{standard form}}{x-y=-8}[/tex]

just to point something out, is none of the options, however -x + y = 8, is one, though improper.

Answer:

20 inch

Step-by-step explanation:

Diameter, D = 6.5in

Circumference

= π x D

= 3.142 x 6.5

= 20.42

= 20 in (rounded to nearest in)

Answer:

[ - 5, 3 ]

Step-by-step explanation:

Solve (x - 3)(x + 5) = 0

The zeros are x = - 5 and x = 3

These divide the domain into 3 intervals

(- ∞, - 5 ], [- 5, 3 ], [ 3, + ∞ )

Choose a test point in each interval and consider the sign of the result.

x = - 10 : (- 10 - 3)(- 10 + 5) = (- 13)(- 5) = 65 > 0

x = 0 : (0 - 3)(0 + 5) = (- 3)(5) = - 15 < 0 ← required result

x = 5 : (5 - 3)(5 + 5) = (2)(10) = 20 > 0

The solution is [ - 5, 3 ] or - 5 ≤ x ≤ 3

Answer:

B

Step-by-step explanation:

Right on edge 2021

Answer:

13 students

Step-by-step explanation:

We have a list of four numbers: 1, 2, 3, 4. If 50 persons were to pick a number randomly, it means that the probability of picking any of the numbers is 0.25.

Therefore, from 50 students, 0.25*50 = 12.5 ≈ 13 students aproximately would choose the same number as I did.

Answer:

Each quart is 1.31 to the customer.

Step-by-step explanation:

Cost of 1 quart to  Wong = 0.75

Cost to you or I = 0.75 * 175/100 = 1.31

He sells each quart for 1.31 dollars.

The probability that she will sit at either end by a window is 2/5 or 0.4.

To solve this problem, we first need to determine the total number of places Sharon could sit and then identify which of those places meet the condition of being at either end by a window.

Since the back seat is the full width of the bus and seats five students, there are a total of 5 different places Sharon could choose to sit.

Now we need to identify the places that are at either end by a window. Since it's the back seat of the bus, there would typically be a window at the far left and the far right of the seat.

So, there are two seats that meet our condition:
- One on the far left
- One on the far right

This means out of the 5 available places, there are 2 places that fulfill the condition of Sharon sitting by a window at either end of the back seat.

The probability P that Sharon will sit by a window at either end is therefore the number of favorable outcomes (sitting by a window at either end) divided by the total number of possible outcomes (any of the 5 seats).

P = (Number of favorable outcomes) / (Total number of possible outcomes)
P = 2 / 5

Therefore, the probability that Sharon will sit at either end by a window is 2/5 or 0.4 (if expressed as a decimal).

Answer:

   √6 + √2

= --------------

        4

Step-by-step explanation:

15° = 45° - 30°

So

cos(15)  = cos(45 - 30)

=cos(45)  × cos(30) + sin(45) × sin(30)

= 1/√2  × (√3)/2  + 1/√2 × 1/2

    (√3) + 1

= --------------

     2√2

    (√3) + 1              √2

= -------------- x       ---------

     2√2                  √2

   √6 + √2

= --------------

        4

Answer:

see explanation

Step-by-step explanation:

Using the addition formula for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

and exact values

sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex]

c0s30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex]

Express cos15° = cos(45 - 30 )°, then

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] + ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )

= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]

= [tex]\frac{\sqrt{6}+\sqrt{2}  }{4}[/tex] ← exact value

Answer:

145

step by step explanation:

perimeter definition:

perimeter definition:the continuous line forming the boundary of a closed geometrical figure.

add up the length of the sides:

80+20+45=145

Answer:

Step-by-step explanation:

Rewrite 2x-5y< 15 as follows:  Add 5y to both sides.  Then 2x < 15 + 5y.

Next, subtract 15 from both sides:  2x - 15 < 5y.

Finally, divide all terms by 5:           (2/5)x - 3 < y

Now find the y-intercept of this line.  Let x = 0.  Then y = -3.  Plot (0, -3) on graph paper.  Now, starting at (0, -3), move your pencil point 5 spaces to the right and 2 spaces up.  Plot this new point, (5, -1).  Now draw a dashed line through both (0, -3) and (5, -1).  Shade the area ABOVE this dashed line.

Answer:

is op 4 (-3,7)

Step-by-step explanation:

Use the law of sines:

Sin(angle) = Opposite Leg / Hypotenuse

Sin(30) = 14 / x

x = 14/sin(30)

x = 28

Answer:

One

Step-by-step explanation:

It is one because each spoke has one space in the middle. However some people think it's 64 because they read the question wrong.

Aloha~! My name is Zalgo and I am here to provide a bit more knowledge to you today. The following Improper Fractions have been changed into Mixed Numbers (and also into decimals because I like Math :3):

I hope that this info helps! :D

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Mahalo~! XP)

Answer:

In order; 2 1/4, 2 2/3, 3 5/6, 5 1/2, 3 2/5, 1 7/8, 3 3/10, 2 5/12

Step-by-step explanation:

The way mixed numbers work is how many times (improper fraction) the denominator can go into the numerator.

For example, in the improper fraction 9/4, 4 can go into 9 twice making the whole number a 2, then you get whatever is left and leave it as the fraction; there is 1/4 left making making the mixed number 2 1/4. Use this rule to apply to all the improper fractions.

Check the picture below.

Also check your Unit Circle for the cosine of 30°, if you don't have a Unit Circle yet, this is a good time to get one, you'll need it, you can find many online.

Answer:

x = 5 or 25

Step-by-step explanation:

I think the method I am about to explain is slightly quicker and easier than the method in your question. This works for any 'complete the square' question.

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We want these brackets to multiply out to give x² - 30x, so that they equal the left-hand side of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There is an unwanted term (the + 225, from 15²)! We only want x² - 30x, so we have to remove this term by subtracting it from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we don't have to subtract it from both sides is because the original equation is x² - 30x = - 125, and so we must make sure the left hand side is still equal to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

is the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides of the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root both sides. Be careful here, and remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are two possible values for the right-hand side of the equation, we need to separate our equation into two equations:

1.     x - 15 = 10

and

2.    x - 15 = -10

Now we solve these two simple linear equations for x:

1.     x = 10 + 15   <- add 15 to both sides

        x = 25 This is our first solution.

2.    x = -10 + 15  <- add 15 to both sides again

        x = 5 This is our other solution.

So our two solutions are x = 5 and x = 25!

I have attached the quick version of the working out for this question - that is what you would be expected to write down in a test.

x = 5 or 25

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side (LHS) of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We need these brackets to multiply out the give x² - 30x, so that they = the left-hand side (LHS) of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There are an unwanted term (the + 225, from 15²)! We only need x² - 30x, so we have to remove this term by subtracting this from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we do not have to subtract this from both sides is because original equation is x² - 30x = - 125, and so we must make sure the left hand side is = to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

as the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides by the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root by both sides. Be careful here, or remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are 2possible values for the right-hand side of the equation, we need to separate this equation into 2 equations:

1.     x - 15 = 10

and

2.    x - 15 = -10

Now we have solve these two simple linear equations for x:

1.     x = 10 + 15   <- add 15 to both sides

       x = 25 This is our first solution.

2.    x = -10 + 15  <- add 15 to both sides again

       x = 5 This is our other answer.

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Answer:

[tex]\large\boxed{D.\ 168\ units^2}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a prism:}\\\\V=BH\\\\B-base\ area\\H-height\\\\\text{In the base we have the right triangle.}\\\text{The formula of an area of a right triangle:}\ A=\dfrac{ab}{2}\\\\a,b-legs\\\\\text{We have}\ a=6\ \text{and}\ b=8.\ \text{Substitute:}\\\\B=\dfrac{(6)(8)}{2}=\dfrac{48}{2}=24\\\\\text{Calculate the volume:}\\H=7\\\\V=(24)(7)=168\ units^2[/tex]

To find the volume of a triangular prism, we have to multiply the area of the base by the heigh of the prism.

Let's first identify our values:

7 = height of the prism

6 = base of triangle

8 = height of triangle

First, we have to multiply the base of the triangle by the height of the triangle. The base of the triangle is 6 and the height of the triangle is 8. Then, we have to divide it by 2.

6 × 8 = 48

48 ÷ 2 = 24

Finally, we have to multiply 24 by the height of the prism. 24 × 7 = 168

Therefore, the volume of the prism is 168 [tex]units^{2}[/tex]

Answer:

The volume of the triangular prism is [tex]595\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base

H is the height of the prism

Find the area of the triangular base B

[tex]B=(1/2)bh[/tex]

substitute the given values

[tex]B=(1/2)(14)(17)=119\ units^{2}[/tex]

Find the volume

[tex]V=(119)(5)=595\ units^{3}[/tex]

Answer:

Options B and D

Step-by-step explanation:

we have

[tex]y=\frac{1}{x-3}[/tex] -----> equation A

[tex]y=3-x^{3}[/tex] -----> equation B

Solve the system of equations by graphing

The solution of the system of equations is the intersection point both graphs

The solutions are the points (1.545,-0.687) and (2.956,-22.835)

see the attached figure

The approximate solutions are

(1.5,-0.7) and (2.9,-22.8)

Answer:

Options B and D

Step-by-step explanation:

Answer:

Part 1) The volume of the prism is 3 times greater than the volume of the pyramid

Part 2) The prism would fill only one-third

Part 3) The cylinder and the cone

Step-by-step explanation:

Part 1) How do their volumes compare?

we know that

The volume of a rectangular prism is equal to

[tex]Vprism=BH[/tex]

where

B is the area of the base of rectangular prism

H is the height of the prism

The volume of a rectangular pyramid is equal to

[tex]Vpyramid=\frac{1}{3}BH[/tex]

where

B is the area of the base of rectangular pyramid

H is the height of the pyramid

Compare the volumes

[tex]Vprism=BH[/tex] -----> equation A

[tex]Vpyramid=\frac{1}{3}BH[/tex] -----> equation B

substitute equation A in equation B

[tex]Vpyramid=\frac{1}{3}Vprism[/tex]

[tex]Vprism=(3)Vpyramid[/tex]

The volume of the prism is 3 times greater than the volume of the pyramid

Part 2) If the pyramid was full of water, how much of the prism would it fill up?

Remember that

[tex]Vpyramid=\frac{1}{3}Vprism[/tex]

therefore

The prism would fill only one-third

Part 3) Name another pair of three-dimensional objects that have a relationship similar to this

we have the cylinder and the cone

The volume of the cylinder is equal to

[tex]Vcylinder=\pi r^{2}h[/tex]

The volume of the cone is equal to

[tex]Vcone=\frac{1}{3}\pi r^{2}h[/tex]

Compare the volumes

[tex]Vcylinder=(3)Vcone[/tex]

The volume of the cylinder is 3 times greater than the volume of the cone

The volume of the pyramid is one-third of the volume of the rectangular prism with the same base and height. Therefore, if the pyramid was full of water, it would fill one-third of the prism. Cones and cylinders with the same base and height have a similar volume relationship.

When comparing the volumes of a rectangular pyramid and a rectangular prism that have the same base and the same height, the volume of the pyramid is exactly one-third the volume of the prism. This is because the volume of the prism is calculated by length × width × height, while the volume of the pyramid is ⅓ x (base area) x height, which is ⅓ x (length × width) x height.

If the pyramid was full of water, it would fill up exactly one-third of the prism. This corresponds to the geometric rule that says the volume of a pyramid is one-third the volume of a prism with the same base and height.

Another pair of three-dimensional objects with a similar relationship is a cone and a cylinder. Like the pyramid and prism, if the cone and cylinder have the same base and height, the cone's volume is one-third of the cylinder's volume.

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[tex]\bf \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 2\ln(3)=\ln(x-4)\implies \ln(3^2)=\ln(x-4)\implies \ln(9)=\ln(x-4) \\\\\\ \log_e(9)=\log_e(x-4)\implies e^{\log_e(9)}=e^{\log_e(x-4)}\implies 9=x-4\implies \boxed{13=x}[/tex]