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Answer:

9) 128
10) 78
11) 31
12) 148

Step-by-step explanation:

9) we know that the segment across from the angle 48° is double the angle.

48 · 2 = 96

The segments around the circle should all add up to 360 so we add the two segments we know to find the unknown segment.

136 + 96 = 232

360 - 232 = 128

The answer for 9 is 128.

10)

61 + 80 = 141

180 - 141 = 39

39 * 2 = 78

The answer for question 10 is 78.

11)

236 + 62 = 298

360 - 298 = 62

62 ÷ 2 = 31

The answer for question 11 is 31.

12)

50 · 2 = 100

100 + 112 = 212

360 - 212 = 148

The answer for question 12 is 148.

An equivalent system of equations using the sum of the system and the first equation is:

[tex]x+4y=8\\5x+5y=10[/tex]

Given:

[tex]x+4y=8\\4x+y=2[/tex]

Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]

Therefore, an equivalent system of equations using the sum of the system and the first equation is:

[tex]x+4y=8\\5x+5y=10[/tex]

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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.

x + 4y = 8

4x + y = 2

x + 4y = 8

5x + y = 2

x + 4y = 8

5x + 5y = 2

x + 4y = 8

4x + 5y = 10

x + 4y = 8

5x + 5y = 10

Considering the angle of the arc, it is found that the value of x is of x = 12º.

It is twice the inside angle.

In this problem, the angle of the arc is of 102º, hence the inside angle is of 51º, which means that we can solve for x as follows:

4x + 3 = 51

4x = 48

x = 12º.

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Answer:

C = 10π ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

to find r use the area formula, that is

A = πr² = 25π ( divide both sides by π )

r² = 25 ( take square root of both sides )

r = [tex]\sqrt{25}[/tex] = 5

then

C = 2π × 5 = 10π ft

Answer:X=12/7

Step-by-step explanation:

Y [tex]\alpha[/tex] X

⇒Y=KX

Where K is the constant

From the question,k=7

⇒ When Y=12,

y=KX

12=7X

X=12/7

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a linear equation is given as:

y = mx + b

Where m is the rate of change and b is the y intercept (initial value of y)

Let y represent the amount of water Jaquan uses to wash x cars, Using the point (2, 24) and (5, 60):

y - 24 = [(60 - 24)/(5- 2)](x - 2)

y = 12x

For 6 cars:

y = 12(6) = 72

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

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Answer: Jaquan uses 72 L to wash 6 cars

Step-by-step explanation:

Answer:

Step-by-step explanation:

Because there is sound and a tune that plays again anytime people are shown having fun at the carnival, the Kit Kat commercial is effective. When the sound is silenced, the commercial's lyrics will come to the viewer's thoughts without any further thought.

The end behavior of the function is as:

as →∞, f(x)→+∞ and as x→-∞, f(x)→+∞

The x-axis "endpoints" of a function's graph are referred to as its "end behavior" in this context.

choosing the polynomial function's greatest degree. The highest degree term will dominate the graph since it will expand more quickly than the other terms as x gets very big or very small.

Function f(x)=2∛x has the following graph:

The behavior of the function at its conclusion is because it leads to infinity.

as  x→∞, f(x)→+∞ and as x→-∞, f(x)→+∞

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Given same lengths and slopes of the opposite sides and nature of the angle between adjacent sides, we have;

The given points are;

L(-5, 4), M(2, 2), N(0, -3), S(-7, -1)

Lengths of the sides are;

Length of LM = √((2-(-5))²+(2-4)²) ≈ √(53)

Length of MN = √((2-0)²+(2-(-3))²) ≈ √(29)

Length of NS = √((0-(-7))²+((-3)-(-1))²) ≈ √(53)

Length of LS = √(((-7)-(-5))²+((-1)-4)²) ≈ √(29)

Therefore;

Slope of LM = (2-4)/(2-(-5)) = -2/7

Slope of MN = (2-(-3))/(0-2) = 5/2

Slope of NS = ((-3)-(-1))/(0-(-7)) = -2/7

Slope of LS = ((-1)-4)/(-7-(-5)) = 5/2

Therefore;

The quadrilateral created by the points L(-5, 4), M(2, 2), N(0, -3), S(-7, -1) is therefore;

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There are 1.40 groups of 5/7 in 1.

8 divided by 5/7 is  11 1/5.

Here is the completed table:

Length (cm)       Percentage

  12                          60% of Ehecatl's old hair

   4                         20% of Ehecatl's old hair

  20                           100% of Ehecatl's old hair

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

In order to determine how many groups of 5/7 are in 1, divide 1 by 5/7

1 ÷ 5/7

1 x 7/5 = 7/5  = 1.40

8 ÷  5/7

8 x 7/5

= 56 / 5

= 11 1/5

The first step is to determine the length of her hair before she cut it

Length of the hair before it was cut = new length / 60%

12 / 0.6 = 20

60% x 20 = 12cm

20% x 20 = 4cm

100% x 20 = 20cm

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The considerations of expressions for each expressions are shown below.

To consider the expressions:

Part 1:

The answer to Part 1 is the letter B,

(7x²+16x+25)

Part 2:

The answer to Part 2 is the letter D,

(7x²-3x+8)

Part 3:

The answer to part 3 is the letter A,

(11x²+6x-6)

Part 4:

The answer to part 4 is the letter C,

(11x²-5x+13)

Therefore, the considerations of expressions for each expression are shown.

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The complete question is given below:
For each expression below, select the letter that corresponds to the equivalent expression given above.

The analogous equation for the square will be; (x-10)²=87.

Algebraic equations with equivalent solutions or roots are called equivalent equations.

Based on information provided, an equivalent equation is created by adding or deleting the same quantity or expression from both sides of a given equation;

Using the original equation as a starting point as;

-20x+ x² + 13 = 0

Now x² - 20x = -13.

We need to take the "x" term's coefficient, or b, to complete the square.

Then Divide by 2 and write the equation in the quadratic formula (ax² + bx + c = 0).Then,

B = -20

b/2 = -10

(b/2)² = 100

x² - 20x +100 = -13 + 100

On the left side,

LHS: (x + b/2)² = (x-10)2

RHS: -13 + 100 = 87

(x-10)² = 87

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Step-by-step explanation:

I just answered this. how often did you post that question ?

she added 54-48 = 6g.

how many % of 48g are these 6g ?

100% = 48

1% = 100%/100 = 48/100 = 0.48g

how many % are 6g ?

as many as how often 1% (0.48g) fits into 6g :

6 / 0.48 = 12.5%

Answer: 1223.07

Step-by-step explanation: you don't round up

Solution of integral  [tex]\int \frac{ds}{s^{2}(s-1)^{2} }[/tex] is  [tex]2ln|\frac{s}{s-1}|-\frac{1}{s}-\frac{1}{s-1}+c[/tex].

We have to evaluate [tex]\int \frac{ds}{s^{2}(s-1)^{2} }[/tex]

By using partial fractions, evaluate the integral

Let [tex]\frac{1}{s^{2}(s-1)^{2} } =\frac{A}{s} +\frac{B}{s^{2}} +\frac{c}{s-1} +\frac{D}{(s-1)^{2} }[/tex]

[tex]1=As(s-1)^{2} +B(s-1)^{2} +Cs^{2}(s-1)+Ds^{2}[/tex]

Put s = 0, 1 = B.1 ⇒ B = 1

Put s= 1, 1 = D ⇒ D = 1

Put s = -1, [tex]1=A(-1)(-2)^{2} +B(-2)^{2} +C(-1)^{2} (-2)+D(-1)^{2}[/tex]

1 = -4A + 4B -2C + D

1 = -4A + 4 -2C + 1

-4 = -4A -2C

2 = 2A + C----------------(1)

Put s = 2, 1 = A(2) + B +C(4) +D(4)

1 = 2A + 1 + 4C +4

-4 = 2A + 4C

-2 = A + 2C---------------(2)

From(1),

C = 2 -2A ---------------(3)

From (2),

⇒ -2 = A + 4 -4A

⇒ -6 = -3A ⇒ A = 2

From (3)

C = 2 - 2(2)

⇒ C = -2

Thus [tex]\int \frac{ds}{s^{2}(s-1)^{2} }= \int (\frac{2}{s} +\frac{1}{s^{2} }- \frac{2}{s-1} +\frac{1}{(s-1)^{2} } )ds[/tex]

= [tex]2 ln|s|-\frac{1}{s} -2ln|s-1|-\frac{1}{s-1}+c[/tex]

= [tex]2ln|\frac{s}{s-1}|-\frac{1}{s}-\frac{1}{s-1}+c[/tex]

Thus,

Solution of integral  [tex]\int \frac{ds}{s^{2}(s-1)^{2} }[/tex] is  [tex]2ln|\frac{s}{s-1}|-\frac{1}{s}-\frac{1}{s-1}+c[/tex].

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The factors of the trinomial based on the information given include:

C. x – 7

E. x + 2

It should be noted that a trinomial is an algebraic expression that has three non-zero terms. Here, the examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. Also, 2a² + 5a + 7 is a trinomial in one variables.

In this case, the algebra tile configuration has 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x. Here, the trinomial is x² - 5x - 14.

The factors will be:

x² - 5x - 14.

x² + 2x - 7x - 14

x(x + 2) - 7(x + 2)

= (x + 2)(x - 7)

A polynomial with three terms is called a trinomial.

In conclusion, the correct options are C and E.

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Using proportions, it is found that 68 more people prefer vanilla than do strawberry.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that, out of 400 people:

Hence the amounts are:

The difference is:

140 - 72 = 68.

68 more people prefer vanilla than do strawberry.

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Answer:

Step-by-step explanation:

The minimum and maximum values are (16/9)√3  and -(16/9)√3.

According to the statement

we have given that the function

First of all, since the constraint's graph is a circle, which is a closed loop, and f is continuous in [tex]R^2[/tex], there must exist a constrained global maximum and minimum value.

Lagrange Multipliers:

f(x,y) = xy^2

g(x,y) = x^2 + y^2

We want ∇f = λ∇g so we get the following system of equations

1. y^2 = 2λx

2. 2xy = 2λy

3. x^2 + y^2 = 4 ← The constraint.

Equation 2 implies that y = 0 or λ = x

We can ignore y = 0, since that will make f(x,y) = 0 and clearly f(x,y) takes on both positive and negative values subject to the constraint.

Plugging in the alternative, λ = x to equation 1 gives y^2 = 2x^2.

Plugging this into the constraint gives 3x^2 = 4 so that x^2 = 4/3 and y^2 = 8/3

Taking square roots gives

x = ±√(4/3) = ±(2/3)√3

y = ±√(8/3) = ±(2/3)√6

At the points < (2/3)√3 , ±(2/3)√6 >, f(x,y) = (16/9)√3 ← Maximum

At the points < -(2/3)√3 , ±(2/3)√6 >, f(x,y) = -(16/9)√3 ← Minimum

So, The minimum and maximum values are (16/9)√3  and -(16/9)√3.

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The expected values of the binomial distribution are given as follows:

1. 214.

2. 21.

3. 31.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For item 1, the parameters are:

p = 3/7, n = 500.

Hence the expected value is:

E(X) = np = 500 x 3/7 = 1500/7 = 214.

For item 2, the parameters are:

p = 0.083, n = 250.

Hence the expected value is:

E(X) = np = 250 x 0.083 = 21.

For item 3, the parameters are:

p = 1/13, n = 400.

Hence the expected value is:

E(X) = np = 400 x 1/13 = 31.

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Answer:

46 and 22

Step-by-step explanation:

let the father b (f) and d son is (s)

so

f=3s.....(1)

(f+10) +(s+10)=68 .... (2)

substitute f=3s in equation (2)

we have

(3s+10)+(s+10)=68

4s+20=68

4s=68-20

4s=48

s=12 .......(3)

substitute (3) in (1)

f=3*12

which f=36

in 10 year time

f+10 =46

s+10=22

Part A: Sasha's solution of the equation incorrect. The solution x = 7.

Part B: The equation have They are unique solutions.

According to the question,

Sasha solved an equation, as shown below:

Step 1: 8x = 56

Step 2: x = 56 – 8

Step 3: x = 48

Step 2 is incorrect, the correct steps to find x, we would divide both sides by 8 so,

8 / 8x = 8 / 56

x = 7.

An equation can have infinitely many solutions only if  the system of an equation has infinitely many solutions when the two lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. Then the have infinitely many solutions.

But, the given equation have unique solutions. Thus, x=7.

Hence, Part A: Sasha's solution incorrect. The solution x = 7.

Part B: They are unique solutions solutions.

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the number of gallons that must be applied is 94 gallons.

Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.

It is denoted with rho, 'ρ'

The formula for density is given as;

Density = mass/ volume

From the information given, we have that

To determine the volume, we need to make it the subject from the formula

Volume = density × mass

Volume = [tex]\frac{9. 4}{100}[/tex]

Volume = 0. 094

The number of gallons is given as;

= Volume × 1000

= 0. 094 × 1000

= 94 gallons

Thus, the number of gallons that must be applied is 94 gallons.

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The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.

Formula used for finding arc length:

⇒ L = 2 π r (θ/360°)

where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.

⇒ L = r × θ

where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.

Here in the question it is given that,

r = 27 units

θ = 20°

Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,

⇒ L = 2 π r (θ/360°)

L = 2 π (27) (20°/360°)

L = π (27) (20°/180°)

⇒ L = 3 π

Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.

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The correct statements about the solids are:

To find which statements are correct:

Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.

The volume of the first triangle is: [tex]2x^{2} h[/tex]

The volume of the second triangle is: [tex]x^{2} h[/tex]

Therefore, the correct statements about the solids are:

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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.

A) The bases are congruent.

B) The solids are similar.

C) The ratio of the volumes of the first solid to the second solid is 8:1.

D)The volume of the first solid is twice as much as the volume of the second solid.

E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more

surface area than the second solid.

Answer:

x > -4

Step-by-step explanation:

[tex]2x+3 \geq 7 \\ \\

2x \geq 4 \\ \\

x \geq 2[/tex]

[tex]2x+9>1 \\ \\ 2x>-8 \\ \\ x>-4[/tex]

So, the union of these solutions is x > -4.

Answer:

look above

Step-by-step explanation:

hope it helps

Answer:

2J - 1

Step-by-step explanation:

Let J = John's age. Sherry is 4 years less than twice as old as John, so Sherry is 2J - 4 years old. Ron is 3 years older than Sherry, so Ron is 2J - 4 + 3 = 2J - 1 years old.

Answer:

$0.71/cup

Step-by-step explanation:

1 gallon = 16 cups

2 gallons = 2 × 1 gallon = 2 × 16 cups = 32 cups

$22.72/(2 gal) = $22.72/(32 cups) = $0.71/cup