how much of the circle is shaded? Write your answer as a fraction in simplest form.
1/4 & 2/7

Answer:

Option A is correct

Values of P = -2 and Q = -31

Step-by-step explanation:

Given the equation: [tex]2x+Q= Px-31[/tex]

Now, we put the given values

A.

Q = -31 and P = -2

2x + (-31) = -2x - 31

2x - 31 = -2x -31  

4x = -31 + 31

4x = 0

x = 0    [one solution]

B.

Q = 31 and P = 2

2x + Q = Px -31

2x + 31 = 2x -31

Subtract 2x from both sides we get

31 = -31        False.

C.

Q = -31 and P = 2

2x + (-31) = 2x - 31

2x - 31 = 2x - 31     [More than one solutions, for any x]

D.

Q = -2 and P = 2

2x + Q = Px -31

2x + (-2) = 2x -31

2x -2 = 2x -31

2x - 2x = -31 + 2      

Combine like term;

0 = -29       False.

Therefore, the values of P and Q results in an equation with exactly one solution is; P = -2 and Q = -31

Answer:

y = 2x^2 + 8x + 8

Step-by-step explanation:

The graph touches the x axis at only one point.

so there is only one real solution.

If there is only one real solution then determinant =0

Now we find out the equation that has determinant 0

Determinant is [tex]b^2 - 4ac[/tex]

Let find b^2 - 4ac for each equation

(a) [tex]y = 9x^2 + 6x + 4[/tex]

a= 9 , b = 6 and c=4

[tex]b^2-4ac= 6^2 - 4(9)(4) = -108[/tex]

determinant not equal to 0

(b) [tex]y = 6x^2 – 12x – 6[/tex]

a= 6 , b = -12 and c=-6

[tex]b^2-4ac= (-12)^2 - 4(6)(-6) = 288[/tex]

determinant not equal to 0

(c) [tex]y = 3x^2 + 7x + 5[/tex]

a= 3 , b = 7 and c=5

[tex]b^2-4ac= (7)^2 - 4(3)(5) = -11[/tex]

determinant not equal to 0

(d) [tex]y = 2x^2 + 8x + 8[/tex]

a= 2 , b = 8 and c=8

[tex]b^2-4ac= (8)^2 - 4(2)(8) = 0[/tex]

determinant equal to 0. So there is only one real solution.

Answer:

It's D. on EtDtGtE

Step-by-step explanation:

Answer:

Current value of house is $106000

Step-by-step explanation:

We are given

A house valued at $100000

gains 6%in value

so,

current value = past house value + gain(%) * (past house value)

past house value =100000

gain(%)=6%

so, we can plug value

Current value is

[tex]=100000+\frac{6}{100}\times 100000[/tex]

[tex]=106000[/tex]

Answer:

It deducts 1.6 each time so the next one would be 22.5  

Equation: 300+35x=1700; where x represents the amount of teams participating in the tournament

Answer: 40 teams competed in the lacrosse tournament

How to solve-

300+35x=1700

300-300+35x=1700-300

35x=1400

35/35x=1400/35

x=40

Answer:

5(b - 3)(b + 1)

Step-by-step explanation:

take out a common factor of 5

= 5(b² - 2b - 3)

to factor the quadratic consider the factors of - 3 which sum to - 2

These are - 3 and + 1, thus

= 5(b - 3)(b + 1)

Answer:

400 yd  

Step-by-step explanation:

There are 2 ft of ribbon for 1 doll.

For 600 dolls,

Ribbon = 600 × 2/1

Ribbon = 1200 ft

=====

Convert feet to yards

1 yd = 3 ft

Ribbon = 1200 × 1/3

Ribbon = 400 yd

Step-by-step explanation:

First, set the x value to be 0:

2(0) + 4y = 28

4y = 28

y = 28/4 = 7

So when x = 0, y = 28/4

Now set the y value as 0:

2x + 4(0) = 28

2x = 28

x = 14

So when x = 14, y = 0

Simply plot these two values:

(0, 7) and (14 , 0)

And join them up, an attatched image shows this graph.

Answer:

y = -1/2 + 7

Step-by-step explanation:

You have to isolate y so...

2x + 4y = 28 is the original problem. Then subtract 2x on both sides. After you subtract 2x, you have to divide 4 to both sides. Then after you divide 4 to both sides, it'll be y = -2/4 + 7. After that, simplify -2/4, and you'll get y = -1/2 + 7 as your answer.

Answer:

No

Yes

Yes

No

Step-by-step explanation:

X's repeat

X's don't repeat

X's don't repeat

X Values repeat

Answer:

60,000 i believe :)

Answer:

10 bracelets

Step-by-step explanation:

we need to convert 5 ft to inches

1 ft = 12 inches

multiply by 5

5 ft = 60 inches

60 inches of yarn, 6 inches per bracelet

60/6 = 10

10 bracelets

Answer:

The correct answer is D.

Step-by-step explanation:

p + 7 = ≤ 50

because I did it for the ECA 3 Exam. :>

The inequality which helps to find the possible values for x will be x + 7 ≤ 50.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Total budget = $50

Ticket cost = $7

Total spent ≤ total budget

x + 7 ≤ 50

x ≤ 43

Hence "The inequality which helps to find the possible values for x will be x + 7 ≤ 50".

For more about inequality,

brainly.com/question/20383699

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Answer:

Given : scale factor(k) = [tex]\frac{3}{4}[/tex]

Labelled the given diagram as A, B , C and D

Also, From the given quadrilateral  figure:

The coordinates are;

A=(-8, 4).

B=(-4, -4),

C=(0, -8) and

D=(4, -4)

The rule of dilation with scale factor k and centered at origin is given by;

[tex](x, y) \rightarrow (kx, ky)[/tex]

or

[tex](x, y) \rightarrow (\frac{3}{4}x, \frac{3}{4}y)[/tex]

Then, the coordinates of the dilated given figures are;

[tex]A(-8, 4) \rightarrow (\frac{3}{4}(-8), \frac{3}{4}(4)) = A'(-6, 3)[/tex]

[tex]B(-4, -4) \rightarrow (\frac{3}{4}(-4), \frac{3}{4}(-4)) = B'(-3, -3)[/tex]

[tex]C(0, -8) \rightarrow (\frac{3}{4}(0), \frac{3}{4}(-8))=C' (0 , -6)[/tex]

[tex]D(4, -4) \rightarrow (\frac{3}{4}(4), \frac{3}{4}(-4)) = D'(3, -3)[/tex]

You can see the graph given below in the attachment

Answer:

See below. The solutions are x=-1/3 and y=-4/3

Step-by-step explanation:

[tex]\frac{1}{2}\log_2 y-\log_4 x = 1\\\frac{1}{2}\log_2 y = \log_4 x+1=\log_4x+\log_4 4=\log_4 4x\\\frac{1}{2}\log_2y = log_44x\\\frac{1}{2}\frac{\log_4y}{\log_4 2}=\log_4 4x\\\log_4y=\log_44x\\4^{\log_4y}=4^{\log_44x}\\y = 4x\\\\x-y = 1\\4x -y = 0\\\rightarrow\\3x=-1\implies x = -\frac{1}{3}, y=-\frac{4}{3}[/tex]

The values of x and y for the Isosceles triangle are 90° and 43° respect.

By observation, the triangle ∆ABC is an Isosceles triangle with the markings on both legs of the triangle so the base angles are equal,

angle C = angle B = 47°.

Since the line AD bisects the angle A, then line AD is perpendicular to the base BC and so angle x is a right angle

x = 90°

Considering the right triangle ∆ADB can evaluate for y as follows;

x + y + angle B = 180° {sum of interior angles of a triangle}

y + 90 + 47 = 180

y + 137 = 180

y = 180 - 137

y = 43°.

Therefore, the values of the x is equal to 90° and that of y is 43° for the Isosceles triangle ∆ABC.

Answer:

(0, 10)

Step-by-step explanation:

x=1 y=9

Up 1 means add 1 to the y coordinate

Left 1 means subtract 1 from the x coordinate

(1-1, 9+1)

(0, 10)

Answer: 17.14 ft

Step-by-step explanation:

The area of the flower bed is 60 ft x 80 ft = 4800 ft²

The perimeter of the sidewalk that surrounds the flower bed is:

The area of the sidewalk is:

area of sidewalk = area of flower bed

280w = 4800

[tex]\text{w}=\dfrac{4800}{280}[/tex]

  [tex]=\dfrac{120}{7}[/tex]

  ≈ 17.14

Answer: 83485

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

Explanation:

The formula we will use is

A = P*(1+r)^t

with

A = final amount = unknown (what we want to find)

P = starting amount = 24000

r = growth rate in decimal form = 0.12

t = number of years elapsed = 11 (since we go from 2014 to 2025)

Plug those values mentioned into the formula. Then use a calculator to simplify

A = P*(1+r)^t

A = 24000*(1+0.12)^11

A = 24000*(1.12)^11

A = 24000*3.47854999334551

A = 83485.199840292

A = 83485

The investment will be worth about 83485 dollars

Answer:

none of the solutions

Step-by-step explanation:

if k(x) = 2x-3x

We can substitute x=9 to find k(9)

k(9) = 2(9) -3(9)

      = 18 -27

      = -9

[tex]p\%=\dfrac{p}{100}\\\\4\%=\dfrac{4}{100}\\\\\dfrac{9}{x}=\dfrac{4}{100}\to\boxed{B.}[/tex]

Answer:

Correct choice is B

Step-by-step explanation:

The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.

Jason  must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex]  He has 30 video games he can sell, then [tex]x\le 30.[/tex]. Thus, the domain of the function is [tex]5\le x\le 30.[/tex]

The range of the function f(x) is

[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]

Answer: Hello mate!

our set of numbers is 6, 2, 3, 2, 4, and 1.

the two extremes of the set are the lower and bigger numbers, so in this case are 1 and 6, so the range of the values in the set is {1,6} and the distance between these points is 6 - 1 = 5.

this means that all the numbers in our set are in the range between 1 and 6.

Answer:

Slope of function A is 6 and slope of function B is 3. Slope of A is twice of slope of function B. The relationship between slopes is

[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]

Step-by-step explanation:

The function A is,

[tex]f(x)=6x-1[/tex]

It can be written as,

[tex]y=6x-1[/tex]

It is the slope intercept form like [tex]y=mx+c[/tex], where m is the slope. On comparing the function A with the slope intercept form, we get the value of slope of function A is 6.

[tex]m_{A}=6[/tex]

The graph of function B passing through the point (1,4), (-1,-2) and (-2,-5).

If a line passing through the points  and , then the slope of line is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Choose any two points of function B. Let the function B is passing through the points (1,4) and (-1,-2).

[tex]m_{B}=\frac{-2-4}{-1-1}[/tex]

[tex]m_{B}=\frac{-6}{-2}[/tex]

[tex]m_{B}=3[/tex]

The slope of function B is 3.

Since slope of function A is 6 and the slope of function B is 3, so we can say that the slope of function A is twice of slope of function B.

[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]

The slope of Function A is 6 and the slope of Function B is 3. Therefore, the slopes of the two functions are not equal.

The equation representing Function A is f(x) = 6x - 1.

The graph representing Function B is a line passing through the ordered pairs (1, 4), (-1, -2), and (-2, -5).

To compare the slopes of the two functions, we can calculate the slope of each function and see if they are equal.

The slope of Function A is 6, and the slope of Function B can be found using the formula (y2 - y1)/(x2 - x1) by choosing any two pairs of ordered points.

For example, using (1, 4) and (-1, -2).

The slope of Function B is (4 - (-2))/(1 - (-1)) = 6/2 = 3.

Since the slope of Function A is 6 and the slope of Function B is 3, we can conclude that the slopes of the two functions are not equal.

Learn more about Slope of functions here:

https://brainly.com/question/12904030

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Answer:

C

Step-by-step explanation:

I am assuming the top and bottom are closed.

Surface are = area of the curved side + 2 * area of the top

=  9* 14 * π + 2 * π * 7^2

= 126π + 98π

= 224π ft^2

Answer:

224

Step-by-step explanation:

plug in the number of years for where x is

34,000(.84)ˣ

and then do

.84ˣ

and then when you get that answer, multiply by 34,000

Answer:

{1}

Step-by-step explanation:

We find determinant for the given matrix and set it equal to -1

To find determinant we apply formula

[tex]|A| = a_{11}(a_{22}a_{33} − a_{32}a_{23}) - a_{12}(a_{21}a_{33} − a_{31}a_{23})+a_{13}(a_{21}a_{32} - a_{31}a_{22})[/tex]

[tex]|A| = x(1x - 2) - 0(7-7) + 0(14-7x) [/tex]

|A| = x^2 - 2x

Now we set the determinant = -1

[tex]x^2 - 2x=-1[/tex]

Add 1 on both sides

[tex]x^2 - 2x + 1=0[/tex]

Now factor it

(x-1)(x-1) = 0

Set each factor =0  and solve for x

x- 1=0 so x=1

To estimate the length of each rope, the division sentence 30 ÷ 3 = 10 can be used, suggesting that each jump rope would be approximately 10 feet long using compatible numbers.

The student's question involves dividing a rope into equal lengths to create jump ropes.

To estimate the length of each jump rope using compatible numbers for the division sentence, we can round 29.8 feet to a number that is easier to divide by 3, such as 30 feet.

Therefore, the division sentence would be 30 ÷ 3 = 10. So, each jump rope would be approximately 10 feet long.

This is an estimate that allows us to perform calculations quickly in our head or on paper, and it is very close to the exact answer.

Final answer:

To estimate the length of each rope from a total length of 29.8 feet when the rope is divided into 3 parts, compatible numbers are used, rounding 29.8 to 30, and the division sentence is 30 ÷ 3, resulting in each estimated rope being about 10 feet long.

Explanation:

To estimate the length of each rope when a 29.8-foot long rope is cut into 3 equal parts, we could use compatible numbers for easier division in our head. Compatible numbers are numbers that are close to the actual numbers and make it easy to do mental arithmetic. We could round 29.8 feet to 30 feet because 30 is divisible by 3. Here's the division sentence using compatible numbers:

30 feet ÷ 3 = 10 feet

Thus, each rope would be approximately 10 feet long. This process is similar to converting units where the scale factor may be omitted at the end when it is 1, as in converting 3.55 m to 355 cm.

Answer:

Two complex roots.

Step-by-step explanation:

F(x)=2x^4 +5x^3 - x^2 +6x-1

is a polynomial in x of degree 4.

Hence F(x) has 4 roots.  There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.

Use remainder theorem to find the roots of the polynomial.

F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0

There is a change of sign in F from 0 to 1

Thus there is a real root between 0 and 1.

Similarly by trial and error let us find other real root.

F(-3) = -1 and F(-4) = 94

SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.

Other two roots are complex roots since no other place F changes its sign

Final answer:

The polynomial function has 4 complex zeros.

Explanation:

A polynomial function is a function of the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_1, a_0 are constants and n is a non-negative integer. The number of complex zeros of a polynomial function is equal to its degree.

The given polynomial function is f(x) = 2x^4 + 5x^3 - x^2 + 6x - 1. The highest power of x in the function is 4, so the degree of the function is 4. Therefore, the function has 4 complex zeros.

Answer: [tex]398.5750[/tex]

Step-by-step explanation:

It is important to remember that the fourth digit after the decimal point is in the ten-thousandth place.

Then, given the  following number:

[tex]398.574986215[/tex]

You can follow these steps in order ti round it to the nearest ten-thousandth:

1. You can identify that the digit in the ten-thousandth place is:

[tex]9[/tex]

2. Identify the digit to the right of [tex]9[/tex]. This is:

[tex]8[/tex]

3. Since:

 [tex]8>5[/tex]

 You must round up. Increase the digit [tex]9[/tex] by 1. (Notice that [tex]9+1=10[/tex], then the digit to the left of  [tex]9[/tex] increases by 1 too). Then:

[tex]398.5750[/tex]

Answer:

y = 3x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 5)

m = [tex]\frac{5+1}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

the line crosses the y-axis at (0, - 1) ⇒ c = - 1

y = 3x - 1 ← equation of the line