solve n^2+16n=17 by completing the square ​

Answer:

150

Step-by-step explanation:

500 is 125% of 400 (500/400) so you need to get what 125% of 120 is

120                              x   1.25                            =150

^number of children        ^125% as a decimal

To find the number of children after the same percent increase in population as the adults, calculate a 25% increase based on the adult growth from 400 to 500. Applying this to the original child population (120), there were 150 children in 2010.

The question pertains to the percent increase in population and requires finding the number of children in a town given the increase in adult population. Specifically, the child population in 2000 was 120, and the adult population increased from 400 to 500 from 2000 to 2010. Assuming that the child population increased by the same percent as the adult population, we need to calculate this percentage increase and then apply it to the number of children to find the updated child population in 2010.

To find the percentage increase in the adult population:

Since the child population increased by the same percentage, we then:

Therefore, there were 150 children in the town in 2010.

Answer:

An equivalent expression is 18(2 + x)

Step-by-step explanation:

To find this, look for the greatest common factor. Since both terms are divisible by 18 equally, we take 18 out of each term. Then we divide both terms by 18 and express in a parenthesis.

18(2 + x)

The answer is there

YES IT IS RIGHT.YOU ARE RIGHT

Answer:

Should be A pretty sure

Step-by-step explanation:

Answer:

The area of the picnic table is [tex]18.75\ ft^{2}[/tex] or [tex]18\frac{3}{4}\ ft^{2}[/tex]

Step-by-step explanation:

we know that

[tex]1\ yd= 3\ ft[/tex]

Let

L-----> the length of the table

W----> the width of the table

the area of the table is

[tex]A=LW[/tex]

Convert yards to feet

[tex]L=\frac{5}{6}\ yd=\frac{5}{6}*3=\frac{5}{2}\ ft[/tex]

[tex]W=3L[/tex]

[tex]W=3(\frac{5}{2})=\frac{15}{2}\ ft[/tex]

substitute in the formula

[tex]A=\frac{5}{2}(\frac{15}{2})=\frac{75}{4}=18.75\ ft^{2}[/tex]

To calculate the area of the picnic table, convert the length to feet and multiply by the width, also in feet, to find the area in square feet.

The student is asking about the area of a picnic table in square feet when the width is 3 times the length and the length is given as 5/6 yard. To find the area, first, calculate the width by multiplying the length of 5/6 yard by 3, which gives 5/2 yards (or 2.5 yards).

Since there are 3 feet in a yard, we convert the measurements to feet: 5/6 yard is equal to 5/6 * 3 feet, and the width is 2.5 * 3 feet. Next, multiply the length and width in feet to find the area.

It is important to note that converting measurements should retain unit consistency throughout the calculation.

Answer:

Lets say you have 40 apples and 17 "peats". You decide to give your friend, Timmy, 2/3's of the apple, because you know that he loves apples! You also give him 2/7 of your "peats". How many apples and peats, combined, does that leave you with?

Step-by-step explanation:

There really is none.

Another name for temporary worker is contingent employment.

So the correct answer is A.

Hope this helps,

Davinia.

10 students choose cheese that crackers

Answer:

Step-by-step explanation:

It's either 160 or 5 don't ask

Answer:

Part a) The total volume is [tex]98\ ft^{3}[/tex]

Part b) [tex]84\ ft^{3}[/tex]

Step-by-step explanation:

Part a)

Find the total volume

we know that

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

we have

[tex]L=3\frac{1}{2}\ ft=\frac{3*2+1}{2}=\frac{7}{2}\ ft[/tex]

[tex]W=3\frac{1}{2}\ ft=\frac{3*2+1}{2}=\frac{7}{2}\ ft[/tex]

[tex]H=8\ ft[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{7}{2})(8)=98\ ft^{3}[/tex]

Part b) If they are only going to fill the dunking booth 6/7 full, how many cubic feet of water will they need?

Multiply the total volume by 6/7

so

[tex]98(6/7)=84\ ft^{3}[/tex]

Answer:

If we consider real numbers, there is no solution.

If we take into account imaginary numbers, there are 2 solutions. [tex]x=8i, -8i[/tex]

Step-by-step explanation:

We can take 64 to the other side and then take the square root.

Thus, we have:

[tex]x^2+64=0\\x^2=-64\\x=\sqrt{-64}[/tex]

We CANNOT take the square root of a negative number, so there is no solution.

BUT, if we take into account Imaginary Numbers, we can solve:

[tex]x=\sqrt{-64} \\x=\sqrt{(-1)(64)} \\x=\sqrt{-1} \sqrt{64} \\x=8i[/tex]

Where [tex]\sqrt{-1} =i[/tex]

AND, we can take the positive and negative versions of 8i, since squaring would take it back to original.

So the answer would be 8i and -8i

Answer:

So the answer would be 8i and -8i

Check the picture below.

Answer:

Step-by-step explanation:

Better write, "Solve '4 is to 3 as x is to 20' for x."

x = 80/3

Writing out this equation of ratios, we get:

 4        x

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

  3       20

Cross multiplication here yields:

3x = 80, and then x = 80/3.

To solve this proportion problem, set up the equation 4/3 = x/20. Cross multiply and solve for x to get x = 80/3.

This is a proportion problem. We can set up the equation:

4/3 = x/20

To solve for x, we can cross multiply:

4 * 20 = 3 * x

80 = 3x

Divide both sides by 3 to solve for x:

x = 80/3

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Answer:

5q^3+25q^2

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

The cost is arrived to by adding the initial cost of the drone to the total cost of all the extra propellers. The cost of per propeller due to tax being 25 we get the following expression.

That is: 300+ 4(25)

=400

the answer is 1 / 12 I got this because I know that 1/2 equals a half so half of 12 is 6 so 6/12 is simply 1/2

Answer:

[tex]x=\frac{1}{12}[/tex]

Step-by-step explanation:

Let the unknown number be [tex]x[/tex].

The given equation then becomes;

[tex]\frac{5}{12} +x=\frac{1}{2}[/tex]

Group similar terms

[tex]x=\frac{1}{2}-\frac{5}{12}[/tex]

Collect the LCM on the Right Hand Side.

[tex]x=\frac{6-5}{12}[/tex]

This implies that;

[tex]x=\frac{1}{12}[/tex]

Answer:

The vertices of the pre-image are (-2, -2), (1, 1), (3, -1), and (2, -4).

Since the pre-image is reflected across the x-axis, leave each x-coordinate the same, and change the sign of each y-coordinate.

The vertices of the new image are (-2, 2), (1, -1), (3, 1), and (2, 4).

Answer:

[tex] c = - \frac { 5 } { 7 } [/tex]

Step-by-step explanation:

We are given the following equation and we are to solve it for [tex]c[/tex]:

[tex] - 5 = c7 [/tex]

Switching the sides of the equation we get:

[tex] c \times 7 = -5 [/tex]

Then dividing both sides of the equation by 7 to get:

[tex] \frac { c \times 7 } { 7 } = \frac { - 5 } { 7 } [/tex]

[tex] c = - \frac { 5 } { 7 } [/tex]

Answer:

It is the Rectangular Prism.

Step-by-step explanation:

Sry, I don't have enough time to write out an explanation. Hope the answer helped!

Answer:

the cylinder container has the greatest surface area.

Step-by-step explanation:

The volume of cone is calculated by [tex]v=\frac{1}{3}\times\pi\times r^{2}\times h[/tex]

The volume of cylinder is calculated by [tex]v=\pi\times r^{2}\times h[/tex]

The volume of square pyramid is calculated by [tex]v=\pi\times r^{2}\times h[/tex]

The volume of rectangular prism is calculated by [tex]v=\frac{1}{3}\times B\times h[/tex]

The radius of cone is [tex]\frac{6}{3}[/tex]=[tex]2in[/tex], and slant height is 10 in.

height is calculated as h² = l²- r²

h² = l²- r²

h² = 10²- 3²

h² = 100- 9

h² =91

h= 9.54

The volume of cone is  [tex]=\frac{1}{3}\times 3.14\times 3^{2}\times 9.54[/tex]

[tex]=\frac{1}{3}\times 3.14\times 9\times 9.54[/tex]

v=89.8668

The volume of cylinder is [tex]=3.14\times 3^{2}\times 10[/tex]

[tex]=3.14\times9\times 10[/tex]

v=282.6

The volume of square pyramid

The height of pyramid is calculated as h² = l²- r²

h² = 10²- 3²

h² = 100- 9

h² =91

h= 9.54

[tex]v=3.14\times 3^{2}\times 9.54[/tex]

[tex]v=3.14\times 9\times 9.54[/tex]

[tex]v=269.60[/tex]

The volume of rectangular prism[tex]v=\frac{1}{3}\times 6\times 10[/tex]

[tex]v=20[/tex]

Hence, the cylinder container has the greatest surface area.

Answer:

sqrt(50)

Step-by-step explanation:

Since it is a right triangle, we can apply the Pythagorem Theorem.

a^2 + b^2 = c^2

25 + 25 = c^2

50 = c^2

c = sqrt(50)

The length of the diagonal of the square is 5 [tex]\sqrt{2[/tex]

The length of the diagonal of a square is equal to the square root of 2 times the length of a side. In this case, the side length is 5, so the diagonal of the square is 5√2

Let's break down the steps to find the square root of 50:

1. **Given**: We have a right triangle with side lengths:

 [tex]- \(a = 25\)\\ - \(b = 25\)2. Apply the Pythagorean Theorem: \[a^2 + b^2 = c^2\] \[25^2 + 25^2 = c^2\] \[50 = c^2\]3. Solve for \(c\): \[c = \sqrt{50}\]4. Calculate the square root of 50: \[c \approx 7.07\][/tex]

Therefore, the length of the hypotenuse (\(c\)) in this right triangle is approximately 7.07 units

​

.

Answer:

Option F. [tex]200.96\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

in this problem

[tex]D=64\ ft[/tex]

substitute

[tex]C=\pi (64)=64\pi\ ft[/tex] -----> exact value of the circumference

Find the approximate value of the circumference

assume

[tex]\pi=3.14[/tex]

[tex]64\pi\ ft=64(3.14)=200.96\ ft[/tex]

The correct answer is option F. The measurement is closest to the circumference of the base of the observatory is 200.96 ft.

To find the circumference of the base of the observatory, we use the formula for the circumference of a circle, which is [tex]\( C = \pi \times d \)[/tex], where [tex]\( C \)[/tex] is the circumference and [tex]\( d \)[/tex] is the diameter of the circle.

Given that the diameter of the floor of the observatory is 64 feet, we can plug this value into the formula:

[tex]\( C = \pi \times 64 \) feet[/tex]

Using the approximation [tex]\( \pi \approx 3.14159 \)[/tex], we calculate the circumference as follows:

[tex]\( C \approx 3.14159 \times 64 \)[/tex] feet,

[tex]\( C \approx 200.96 \)[/tex] feet.

The complete question is:

An observatory is shaped like a cylinder standing on one of its bases with a dome on top. The diameter of the floor of the observatory is 64 feet, as shown in the diagram.

Which measurement is closest to the circumference of the base of the observatory in feet?

F 200.96 ft

G 3,215.36 ft

H 100.48 ft

J 401.92 ft

[tex]\bold{Hey\ there!} \\ \bold{\ Assoviative \ property\ looks\ looks\ like\ this:(2+3)+4;2+(3+4)}\\ \bold{\ Commutative\ property\ looks\ like\ this:b+c;c+b} \\ \bold{\ Distributive\ property\ looks\ like\ this:a(b+c);a(b)+a(c)}\\ \bold{5(3x+4)=15x+20}\\ \\ \bold{5(3x))=15x} \\ \bold{5(4)=20} \\ \\ \bold{Answer:distributive\ property}\checkmark[/tex]

[tex]\bold{Reason:\ because\ it\ almost\ similar\ to\ the\ example\ shown\ above\ as\ to\ how\ solve\ it!} \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\\frak{LoveYourselfFirst:)}[/tex]

Answer:

Yellow: 50

Red: 25

Step-by-step explanation:

5:10

5 times 5 = 25

10 times 5 = 50

Answer:

Step-by-step explanation:

its B! Hope this helps

The answer is B.

Hope this helps.

Answer:

∠1 - 40°

Step-by-step explanation:

∠1 - 40°

b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.

∠2 - 140°

b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.

∠3 - 40°

b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.

∠4 -

b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.

∠5 - 35°

b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.

~~

I hope that helps you out!!

The measure of angle 5 is 72°.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Lines m and n are parallel,

Also, value of ∠2 = 40°, ∠3 = 68°

First determine the value of angle 5 First determine the value of angle 1,

Since, angle of a line = 180°

∠1 + ∠2 + ∠3 = 180°

∠1 + 40 + 68 = 180

∠1 + 108 = 180

∠1 = 72

Since, lines m and n are parallel,

∠1 = ∠5

∠5 = 72°

So, the value of angle 5 is 72°.

To learn more about Angle on:

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Answer:

B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.

Step-by-step explanation:

Given choices are :

A. a ray is formed by lines that do not cross each other.

B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.

C. a ray is formed by two lines that cross at one point.

D. a ray is formed when two points on a line are labeled

Now we need to determine about which sentence is true about a ray.

We know that a ray has one fixed end point and other point moves infinitely then correct choice is :

B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.

Answer: i think its 1.6 but i could be wrong if im not im glad to help

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i did the test

Answer:

192 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = bh ( b is the base and h the perpendicular height )

here b = 24 and h = 8, hence

A = 24 × 8 = 192 cm²

Answer: 2.35 square miles.

Step-by-step explanation:

To solve this exercise you must apply the formula for calculte the area of a sector in a circle, which is shown below:

[tex]A=r^2\pi(\frac{C}{360})[/tex]

Where C is the central angle in degrees and r is the radius.

Therefore, knowing that:

[tex]C=30\°\\r=\frac{6mi}{2}=3mi[/tex]

When you substitute values, you obtain the following result:

[tex]A=(3mi)^2\pi(\frac{30\°}{360})[/tex]

[tex]A=2.35mi^2[/tex]

Answer:

Area of sector = 2.355 miles²

Step-by-step explanation:

Formula:

Area of circle = πr²

Where r is the radius

Area of sector = πr²(C/360)

Where C is the angle of sector

It is given that radius of circle is 6 miles

To find the are of circle

Here diameter = 6 miles,

radius r = diameter/2 = 3 miles

Area = πr² = 3.14 * 3² = 28.26 miles²

To find area of sector

Here r = 3 and C = 30°

Area of sector = πr²(C/360) = 28.26*(30/360)

= 2.355 miles²

Answer: A WEAK NEGATIVE CORRELATION

Step-by-step explanation:

TOOK THE TEST

Answer:

Factoring  x=1 x=-5

Step-by-step explanation:

I would factor the equation

-1 *6 = -6

-1+6 =5

(x-1) (x+5) =0

Using the zero product property

x-1 =0    x+5 =0

x=1   x=-5