Solve the following system of equations and show all work.
y = −x2 + 4
y = 2x + 1

Answer:

3500[tex]\pi[/tex] = 10995.57 in³ (nearest hundredth)

Step-by-step explanation:

area of a circle = [tex]\pi r^2[/tex]

⇒ area of a semicircle = [tex]\frac{1}{2}\pi r^2[/tex]

⇒ area of a quarter circle = [tex]\frac{1}{4}\pi r^2[/tex]

total area = 5 circles + 10 semicircles + 100 quarter circles

⇒ total area = [tex]5\pi r^2 +(10\times \frac{1}{2}\pi r^2)+(100 \times \frac{1}{4}\pi r^2)[/tex]

⇒ total area = [tex]35\pi r^2[/tex]

If r = 10 inches

⇒ total area = [tex]35\pi \times 10^2=3500\pi =10995.57 \ \textsf{in}^2 \ \textsf{(nearest tenth)}[/tex]

Answer:

see below

Step-by-step explanation:

1. At least 2 points create a line
2. At least 3 points determine a plane
3. The intersection of two distinct planes is a line

3. The intersection of 2 coplanar lines is a point
5. A Plane can contain a line and a point not on the line

Answer:

30feet= 91.5 centimeters

The total of cm in the 1 yard based upon  30.5 centimeters in a foot will be 91.5 centimeters.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.

In another word, multiplication is nothing but changing one value by-product of another value

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

Given that

1 feet = 30.5 centimeters

Given that

1 yard = 3 feet

Hence 1 yard = 3 × 30.5 centimeter.

1 yard = 91.5 centimeters hence in 1 yard there will be 91.5 centimeters

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Answer:

$76

Step-by-step explanation:

Regular price: $95

Discount %= 80%

What is 80% of 95

=) [tex]\frac{80}{100}[/tex]×[tex]\frac{95}{1}[/tex]=  76

So, $76 are discounted

Hope this helps!

Answer:

1.85 grams

Step-by-step explanation:

1 milligram is equal to 0.01 gram

so 1850 should be equal to 1.85 grams

Answer: 1.85 grams of potassium.

Step-by-step explanation: Since 1,000 milligrams is equal to 1 gram, you have to divide 1850 by 1000. The results will be 1.85.

Answer:

6 in

Step-by-step explanation:

The angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

let the third side of the triangle be x , then

[tex]\frac{9}{x}[/tex] = [tex]\frac{6}{4}[/tex] ( cross- multiply )

6x = 36 ( divide both sides by 6 )

x = 6

The third side of the triangle is 6 in

Step-by-step explanation:

angles are bisected by diagonals in parallelogram

11x-2 = 28

11x = 30

x=30/11

Answer:

Not the solution tp the system because the ordered pair should be true for both equations. However the last equation is not true.

Step-by-step explanation:

(-1,-2) is the solution of the system. x + y =-3 and 2x - y = -4*

x + y =-3 :

(-1)+ (-2) = -3

-1-2 =-2   -3=-3

2x - y = -4:

2(-1)-(-2)=-4

(-2) -(-2)= -4

0=-4

(fog)(3) = 22

Step-by-step explanation:

f(x + 3x - 5; g(x)=x²9(3)=3²=9

(fog)(3) = f(g(3)) = f(9)=3-9-5=27

-5-22 [Ans]

Coterminal angles are measured from the positive x-axis. The coterminal angle for angle 45° is (270°+45°).

Coterminal angles are angles that are made by the positive x-axis of the coordinate plane.

Given to us

θ = 45°

We know that coterminal angles are those angles that are measured from the positive x-axis of the coordinate plane.

In order to find the angle coterminal with a 45° angle, we will deduct θ from 360°, therefore we will measure the from positive x-axis but in the clockwise direction.

[tex]\theta _1 = 360^o - \theta\\\\\theta _1 = 360^o - 45^o\\\\\theta _1 = 315^o\\\\\theta _1= 270^o + 45^o[/tex]

Hence, the coterminal angle for angle 45° is (270°+45°).

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Answer:

c.45° + 270°

Step-by-step explanation:

Answer:

8.69 m

Step-by-step explanation:

We have to use the Pythagorean theorem here

Statue is 3.4 tall, that's one leg of the right traingle

Braden is 8 meters away, that's the longer leg of the right triangle

the hypotenuse would be the distance between Braden's head and the top of the statue (let's assume it is X )

x^2 = 3.4^2 + 8^2 = 11.56 + 64 = 75.56

x = 8.69

3(7x + 1)

3 . 7x = 21x

3.1 = 3

3(7x + 1 ) = 21x + 3

The equivalent expression with the fewest symbols possible is 21x+ 3.

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

we have,

3 x (7x+ 1)

By Distributive property we know

a x( b+ c) = a x b + a xc

ax (b-c) = a x b - a x c

So, 3 (7x + 1 )

= 3 (7x)+ 3(1)

= 21x + 3

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Exponent properties help us to simplify the powers of expressions.  The quotient of the given expression [tex]\dfrac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex] is (2∛3 - ∛18).

[tex]{a^m} \cdot {a^n} = a^{(m+n)}\\\\\dfrac{a^m}{a^n} = a^{(m-n)}\\\\\sqrt[m]{a^n} = a^{\frac{n}{m}}\\\\(a^m)^n = a^{m\times n}\\\\(m\times n)^a = m^a\times n^a\\\\[/tex]

Given to us

[tex]\dfrac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex]

We will solve the problem using the basic exponential properties,

[tex]\dfrac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}}\\\\ = \dfrac{6}{\sqrt[3]{9}} - \dfrac{3(\sqrt[3]{6})}{\sqrt[3]{9}}\\\\ = (6\cdot 3^{-\frac{2}{3}}) - [3 \cdot (2 \cdot 3)^{-\frac{2}{3}}3^{-\frac{2}{3}}]\\\\= (2 \cdot 3 \cdot 3^{-\frac{2}{3}}) - [3 \cdot 2^{-\frac{2}{3}} \cdot 3^{-\frac{2}{3}}3^{-\frac{2}{3}}]\\\\[/tex]

[tex]= [2 \cdot 3^{(1-\frac{2}{3})}] - [2^{\frac{1}{3}}\cdot 3^{(1+\frac{1}{3} - \frac{2}{3})}]\\\\= [2 \cdot 3^{(\frac{1}{3})}] - [2^{\frac{1}{3}}\cdot 3^{(\frac{2}{3})}]\\\\= 2\sqrt[3]{3} - \sqrt[3]{2}\sqrt[3]{9}\\\\=2\sqrt[3]{3} - \sqrt[3]{18}[/tex]

Hence, the quotient of the given expression [tex]\dfrac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex] is (2∛3 - ∛18).

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Answer:

A

Step-by-step explanation:

ansawer k lol

A linear function is a straight line formed on a coordinate plane.

To classify an equation as a linear function:

If any of these two occurs in an equation, the line can form a curve in a line, which is a non-linear function. A non-linear function is a curved line formed on a coordinate plane.

Option A - y = x³ + 1:

Option B - 5x/6 = y - 4:

Option C - y = 8x²

Option D - y = 1/5x

Hence, Option B is correct.

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Answer:

11. 130°, obtuse angle

12. 40°, acute angle

13. 90°, right angle

14. 110°, obtuse angle

15. same as 14, I guess?

Step-by-step explanation:

questions 11, 14, 15 - an obtuse angle is an angle greater than 90° but less than 180°

question 12 - an acute angle is an angle that is less than 90°

question 13 - a right angle is exactly 90°

in question 14 the angle starts at 30° and ends at 140° so you subtract 30 from 140

hope this helps :)

Answer:

C

Step-by-step explanation:

1 + 0.02 means the 2% growth every month, power 12 means for 12 month, and power of 2 mean 2 years.

Logarithmic function is the inverse of the exponential function. The logarithmic function that is equivalent to 2⁵ = 32 is log₂32=5.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

Given to us

2⁵ = 32

As we know that we can convert a number powered to another number therefore exponential function into a log function, thus,

[tex]2^5 = 32\\\\\rm log_2 32 = 5[/tex]

Hence, the logarithmic function that is equivalent to 2⁵ = 32 is log₂32=5.

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Answer:

9600

Step-by-step explanation:

30% can also be written as 0.3 so 0.3×32000 is 9600. 9600 kilobytes have been downloaded so far

Answer:

190 pages

Step-by-step explanation:

To solve the # of pages he would read in 5 hours, let's first find the number of pages he reads in one hour.

Next, we multiply 38 by 5.

Therefore, the answer is 190 pages.

Answer:

190 pages

Step-by-step explanation:

Given the following question:

Erin read 76 pages in 2 hours...
How many pages would he have read in 5 hours?

In order to find the answer, we divide the number of pages he read in two hours by two. To find the number of pages he reads in 1 hour, then just multiply that answer by five.

[tex]2h=76p[/tex]
[tex]4h=76+76=152p[/tex]
[tex]76\div2=38[/tex]
[tex]152+38=190[/tex]
[tex]5h=190p[/tex]

In five hours, Erin would have read "190 pages" of his book.

Hope this helps.

Hi there!

The solution to this system of equations is the point where the graphs of the equations intersect.

That point only will make both equations true.

So, where do these graphs meet?

First, look at the x-coordinate. It's -6.

Now, look at the y-coordinate. It's -2.

Thus, the answer is

(-6, -2)

Hope it helps!

Ask me if you have any doubts.

Enjoy your day!

~Misty~

Answer:

There is no way that 4/5 can equal a thing with 3 as a denominator

Step-by-step explanation:

4/5 is already simplified, but it does equal 8/10 or 12/15

Number 1

________________

Supplementary - either of two angles whose sum is 180°.

Complementary - either of two angles whose sum is 90°.

________________

Since we know that supplementary angles are angles that add up to 180° we can make an equation

________________

[tex]65+x=180\\x=115[/tex]

________________

Number 2

Since we know that complementary angles are angles that add up to 90° we can make an equation

________________

[tex]65+x=90\\x=25[/tex]

________________

[tex]{\huge{\boxed{\mathfrak{Answer}}[/tex]

Answer:

yes

Step-by-step explanation:

no

Answer:

1) Slope = -1, y-intercept = 3

2) Slope = 1, y-intercept = -3

3) Slope = -3, y-intercept = 1

4) Slope = 3, y-intercept = -1

Step-by-step explanation:

In order to identify slope and y-intercept, you must find where each variable hits each axis when the other is 0.

For example, to find the y intercept of y=2x-4, you would substitute 0 in for x and solve for y.

y = 2(0)-4  --> y = -4

Thus, the point is (0, -4) with slope of 2. (The slope can be found by identifying the number, m, in front of 'x' from the equation y = mx + b.

Answer:

A. y = 3x-1; slope is 3 and y-intercept is -1

B. -x+3 = y; slope is -1 and y-intercept is 3

C. x-3 = y; slope is 1 and y-intercept is -3

D. y = 1-3x; slope is -3 and y-intercept is 1

Step-by-step explanation: woof

Answer:

6.4% of the lights are faulty

Step-by-step explanation:

Well you can make a proportion out of this question.
so lets do faulty/total

16/250 = x/ 100

Since x/100 is basically finding the percent since percent means out of a hundred.

Cross multiply to solve.

250x= 1600

SOlve for x

X=6.4

6.4 percent of the lights are faulty.

Step-by-step explanation:

with the introduction of fractions it is clear we are multiplying things to get the sequence.

that makes this a geometric sequence, meaning that every new term is created by multiplying the previous term by a certain constant number, the ratio r.

what do we have to multiply with the first term (6) to get -4 ?

6×r = -4

r = -4/6 = -2/3

to check we use the same factor with the second term and see, if we get the predefined third term :

-4 × -2/3 = 8/3

correct, perfect.

so,

a0 = 6

an = an-1 × -2/3 = a0 × (-2/3)^(n-1) = 6 × (-2/3)^(n-1)

for the sum of a finite number of terms of a geometric sequence the formula is :

Sn = a0×(r^n - 1) / (r - 1) if |r| > 1

Sn = a0×(1 - r^n) / (1 - r) if |r| < 1

Sn = a0×n if r = 1

in our case : |-2/3| = 2/3 < 1

S8 = 6×(1 - (-2/3)⁸) / (1 - (-2/3)) =

= 6×(1 - 256/6561) / (3/3 - -2/3) =

= 6×(6561/6561 - 256/6561) / (5/3) =

= 6×(6305/6561) × (3/5) = 2×(6305/2187) × (3/5) =

= 2×(1261/2187) × 3 = 2×(1261/729) =

= 2522/729 = 3.459533608...

≈ 3.46

Answer:

114 books.

Step-by-step explanation:

I'm pretty sure what you have to do is just subtract 16 from 130. (130-16).  

When you do that you get 114 books.  (sorry for basically no explanation.)