Calculate:
a) QR
b) PS
c) The area of quadrilateral PQRS

Answer:

Step-by-step explanation:

The distance between two points can be found by

[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]

where

(x1 , y1) and (x2 , y2) are the points

The distance between (8, 3), (0, -3) is

[tex] \sqrt{ ({8 - 0})^{2} + ({3 + 3})^{2} } [/tex]

[tex] = \sqrt{ {8}^{2} + {6}^{2} } [/tex]

[tex] = \sqrt{64 + 36} [/tex]

[tex] = \sqrt{100} [/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

82 hope this helps

Answer:

64

Step-by-step explanation:

(x-8)^2

derived from the middle term divided by 2

Answer:

64

Step-by-step explanation:

x^2 − 16x + ___

Complete the square

Take the coefficient of the x term

-16

Divide by 2

-16/2 = -8

Then square it

(-8)^2 = 64

Answer:

7 8 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for this is

∠G = 1/2(arcEH - arcHF)

We have angle G (5x - 10) and we have arcEH (195) so we have to solve for x to find the measure of arcEHF so we can add arcEH + arcHF = arcEHF

Filling in the formula with what we have:

[tex]5x-10=\frac{1}{2}(195-(8x+17))[/tex]

which simplifies down a bit to

[tex]5x-10=\frac{1}{2}(195-8x-17)[/tex] which simplifies down a bit more to

[tex]5x-10=\frac{1}{2}(178-8x)[/tex] Multiply both sides by 2 to get rid of the fraction and get:

2(5x - 10) = 178 - 8x which of course simplifies to

10x - 20 = 178 - 8x. Now add 8x to both sides and at the same time add 20 to both sides to get:

18x = 198 so

x = 11. Now we can find the measure of arcHF:

arcHF is 8x + 17, so arcHF is 8(11) + 17 which is 105°.

arcEH + arcHF = arcEHF so

195 + 105 = arcEHF so

arcEHF = 300°

[tex]g(f(x))=(x-7)^3=x^3 - 21 x^2 + 147 x - 343[/tex]

Answer:

Step-by-step explanation:

Number of candies with Forest = 12

Candies containing coconut and chocolate both = Number common in coconut and the chocolate = 3

Candies which do not contain coconut but contain the chocolate = 6

Candies which contain the coconut but do not contain the chocolate = 1

Candies which neither contain the chocolate nor coconut = 2

From the given Venn diagram,

                                                Contain coconut         Do not contain coconut

Contain chocolate                              3                                       6

Do not contain chocolate                 1                                        2

Answer:

10a -7b

Step-by-step explanation:

9a-6b+a-b​

Combine like terms

9a+a   -6b-b

10a -7b

Answer:

10a-7b

Step-by-step explanation:

[tex]9a - 6b + a - b \\ 9a + a - 6b - b \\ 10a - 7b[/tex]

Answer:

111

Step-by-step explanation:

Reducing the given expression:

74(6)       37(6)           111

--------- =  ----------  =  ---------- = 111

   4              2                1

Answer:

Step-by-step explanation:

[tex] \mathsf{(74) \times ( \frac{6}{4} )}[/tex]

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

⇒[tex] \mathsf{ \frac{74 \times 6}{4 \times 1} }[/tex]

⇒[tex] \mathsf{ \frac{444}{4} }[/tex]

⇒[tex] \mathsf{111}[/tex]

[tex] \mathrm{Hope \: I \: helped !} [/tex]

[tex] \mathrm{Best \: regards !}[/tex]

Answer:

part a)

Step-by-step explanation:

Answer:

Surface Area = 85.75 ft²

Step-by-step explanation:

Surface area of pyramid = ½(Perimeter of triangular base * slant height of pyramid) + Area of triangular base

Perimeter of triangular base = sum of all sides of the triangular base = 5+5+5 = 15 ft

Slant height of pyramid = 10 ft

Area of triangular base = ½*base of triangle*height of triangle = ½*5*4.3 = 10.75 ft²

Plug in the above values:

Surface Area = ½(15*10) + 10.75

= (15*5) + 10.75

= 75 + 10.75

Surface Area = 85.75 ft²

Answer:

3000 students

Step-by-step explanation:

If 48% of the students are female, and there are 1440 female students, we can set up a percentage proportion, assuming x is the total amount of students.

[tex]\frac{1440}{x} = \frac{48}{100}[/tex]

We can use the cross products property to find the value of x.

[tex]1440\cdot100=144000\\\\144000\div48=3000[/tex]

Hope this helped!

Answer:

See below.

Step-by-step explanation:

A)

The end behavior is basically how the function behaves as it approaches negative or positive infinity.

As the function approaches negative infinity, we can see that the graph is going up. In other words:

[tex]f(x)\rightarrow\infty\text{ as }x\rightarrow-\infty[/tex]

As the function approaches positive infinity, we can see that the graph is going down. In other words:

[tex]f(x)\rightarrow-\infty\text{ as }x\rightarrow\infty[/tex]

B)

In even-degree polynomials, both ends of the graph will be going the same way. In this graph, the two ends are going opposite ways so this is an odd-degree function.

C)

The number of real zeros is simply the amount of times the graph crosses the x-axis. In the graph, the function does this three times. Thus, the number of real zeros is 3.

Answer:

1) increases on all interval of x = only g(x)

2) approaches an integer as x approaches -∞ = only f(x)

3) y-intercept at (0, 4) = only g(x)

4) x-intercept at (1, 0) = f(x) and h(x)

Step-by-step explanation:

1) The functions that increases on all interval of x are;

f(x) = -2(3)ˣ + 6 decreases on all interval of x

The function g(x) which is 4 × 4ˣ  increases on all interval of x

The function h(x) is observed to be decreasing as x increases, therefore, the only function that increases on all interval of x = g(x)

2) The function that approaches an integer as x approaches -∞ = -2(3)ˣ + 6

-2(3)ˣ + 6 approaches 6 as x approaches -∞ which is only f(x)

3) The functions that have a y-intercept at (0, 4) is only g(x)

4) The function that have a x-intercept at (1, 0) are f(x) and h(x).

Answer:

A) f(x) and g(x)

B) only g(x)

C) All three functions

D) f(x) and h(x)

Step-by-step explanation:

In my uploaded image on the test I have gotten C) wrong but if you graph all three functions, you can see that all three functions have the same style of -∞

end behavior so I think that would be the most logical answer.

Answer:

A. x + 100x/y

Step-by-step explanation:

Machine A= x hours longer to produce 660 widget than machine B

Machine B produces y% more widget per hour than machine A

let

b = Number of hours it takes Machine B to make 660 widgets.

Time taken for Machine A to make the 660 widgets = x + b.

Rate of Machine B = 660/b

Rate of Machine A = 660 / (x + b).

Machine B produces y% more widgets per hour than Machine A:

660 / (x + b)(1 + y/100) = 660/b

1 / (x + b)(1 + y/100) = 1 / b

Multiply both sides by (x+b)

1 + y/100 = (x + b)/b

1 + y/100 = x/b + 1

Subtract 1 from both sides

y/100 = x/b

Take the inverse of both sides

100/y = b/x

Make b the subject

100x/y = b

b=100x/y

The time taken for Machine A to make the 660 widgets is x + b = x + 100x/y.

Answer is A. x + 100x/y

Answer:

v = 63

Step-by-step explanation:

v = 1/2(7)(6)(3)

v = 63

Answer:

(2, 0)

Step-by-step explanation:

2x - y = 4

5x + 2y = 10

Solve by elimination by multiplying the top equation by 2, so the y values will cancel out (-2y + 2y = 0)

4x - 2y = 8

5x + 2y = 10

Add them together and solve for x:

9x = 18

x = 2

Plug in 2 as x in one of the equations to find y:

2x - y = 4

2(2) - y = 4

4 - y = 4

-y = 0

y = 0

The solution is (2, 0)

[tex]35pq^2=5\cdot7\cdot p\cdot q^2\\-14pq^2=-1 \cdot 2\cdot 7\cdot p \cdot q^2\\-21p^2q^3=-1\cdot 3\cdot 7\cdot p^2 \cdot q^3\\\\\text{hcf}(35pq^2,-14pq^2,-21p^2q^3)=7\cdot p \cdot q^2=7pq^2[/tex]

Answer:

Step-by-step explanation:

Original Median (28+46)/2 = 37

Original Mean (222/6) = 37

New Median (46)

New Mean (52)

Mean increases the most.

The mean will increase more.

We have weights of six packages  28, 22, 52, 25, 49, and 46.

We have to find if we include a package that weighs 142 ounces, which will increase more, the median or the mean.

If a set consist of odd number of elements, then the median of that set of numbers is the is the element at the position [tex]\frac{(N+1) }{2}[/tex].

If we don't include the package of 142 ounce, then -

Mean = [tex]\frac{28 + 22 + 52 + 25 + 49 + 46}{6} = 37[/tex]

Median = [tex]\frac{52 + 25}{2} = 38.5[/tex]

After including the package of 142 ounce,

Mean = [tex]\frac{28 + 22 + 52 + 25 + 49 + 46+142}{6} = 52\\[/tex]

Median = Element at [tex]\frac{(N+1) }{2}[/tex] position = 25

Hence, mean increase more.

To solve more questions on mean and median, visit the link below -

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Answer:

x=25

Step-by-step explanation:

you know that both angles equal the same degrees, so the bottom one is 150° so the other is also 150°. You already have 50° so all you need left is 100°. divide 100 by 4 and you get x=25

Answer:

602.88 in³

12

Step-by-step explanation:

Formula for volume of a cylinder = πr² · h

radius (r) = 1/2(diameter)

1. Set up the equation

radius = 4

(3.14)(4²)(3·4)

2. Solve

3.14(16)(12) = 602.88 in³

Formula for volume of a cone = 1/3πr² · h

The formula of a cone is 1/3 the volume of a cylinder. Therefore, a cone that fits perfectly within the dimensions of a cylinder would have a volume equal to 1/3 of the volume of the cylinder.

1. Set up the equation and solve

36 ÷ 3 = 12

Answer:

reflection across y = x

Step-by-step explanation:

Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.

If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)

If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)

If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)

If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)

The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form​​ ​△A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged

Answer:

reflection across y = x

Step-by-step explanation:

Answer is C

Step-by-step explanation:

I assure you that if you check a,b,c, and d by putting them into desmos graphing calculator you can find which graph it is. I plugged the third equation in and found that they were exact. If you want to do it the "smart" way that I teacher would show you, as you look at the answers and determine by certain points on the graph which one lines up. You start with 1/x.

Good Luck

Answer:

Step-by-step explanation:

Yes, due to the presence of that operator " i "

Answer:

Step-by-step explanation:

[tex] \mathsf{ 12 {p}^{2} q - 9 {q}^{2} }[/tex]

In such an expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor.

Factor out 3q from the expression

[tex] \mathsf{ = 3q(4 {p}^{2} - 3q)}[/tex]

Hope I helped!

Best regards!

Factorization of 12p²q-9q² is  3q(4p²-3q).

Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number.

Here, given expression is,   12p²q-9q²

Now, by factorizing this we get,

3q(4p²-3q)

Hence, required factorization is 3q(4p²-3q)

To learn more on factorization click:

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Answer:

The answer is below

Step-by-step explanation:

Given that:

The radius of the circle (r) = 5 units

The central angle (θ) = 25π

A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:

[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2[/tex]

Substituting the radius of the circle and the central angle:

[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}[/tex]

Answer:

v=168

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

3⋅6−2+2​

Use PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction

First we multiply, then add or subtract so,

18 - 2 + 2

Now we subtract,

16 + 2

Now we add,

18

Answer:

4x(x+2) - x(3x+5)

Step-by-step explanation:

the area of the whole box is 4x(x+2)

to find the area of the shaded portion you have to subtract the area of the tiny box from the big box

the area of the tiny box is x(3x+5)

so, 4x(x+2) - x(3x+5) is the expression you can use to find the area of the shaded portion