S

2. Paul's mother pays "no atten-

tion" to his statement that God

has told him he is lucky. What

do you think Paul might do to

force his mother to notice him?

(Predict)

Given

To find the value of x.

Now,

From the figure,

That implies,

Hence, the value of x is 64.1 degrees.

Answer:

a=10

Step-by-step explanation:

use a^2+b^2=c^2

(a+2)^2+(a-5)^2=(a+3)^2

a^2+4a+4+a^2-10a+25=a^2+6a+9

2a^2-6a+29=a^2+6a+9

a^2-12a=-20

a^2-12a+20=0

quadratic formula→(12+/-8)/2

a=10 or 2

2 is not an option because 2-5=-3 which isn't possible in this case.

so a=10

Apply Pythagorean theorem

There is a side a-5 so 2 is not a answer

The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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a = 7 and b = -4

Evaluate those values into the expression:

Answer:

the answer is D. 6

Step-by-step explanation:

Step-by-step explanation:

Note:

tanA=sinA/CosA i.e tan^2A=sin^2A/cos^2A

tanB=sinB/cosB

cos^2A+sin^2A=1

cos^2B+sin^2B=1

I hope this helps.

I hope it will help you . But I have confused whether you have asked the second question or not . If you have asked , please send that question .

Answer:

it opens up due to the positive x2

Equation for the monthly wage will be → W = 0.07S + 5000

   Given in the question,

Let the total sales of a month = $S

Therefore, commission on this sale = 7% of $S

                                                            = $0.07S

Salary of the month = $5000

Total earnings (W) of the sales person = $(0.07S + 5000)

     Therefore, equation for the monthly wage will be,

W = 0.07S + 5000

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

12 pounds of tea-1 and 8 pounds of tea-2 should be used.

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Substitute the values so (3-2(-1/2))3

Then distribute so (3-(-1))3

Add since it's a double negative to get (4)3

And 4 cubed is 64

We know, factorisation is the process of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Now we should take x common from both the terms.

Answer:

x (x + 10)

Hope you could understand.

If you have any query, feel free to ask.

Answer:

\(\bold{x(x+10)}\)

Step-by-step explanation:

Hi there!

Factoring is the opposite of distributing.

We know what distributing is:

a(b+c)=ab+ac

Well, this is factoring:

ab+ac=a(b+c)

So, let's factorise the given expression:

\(\bold{x^{2} +10x}\)

What's the common term? That's right, x.

So, we factor x out:

\(\bold{x(x+10)}\)

Hope it helps! Enjoy your day!

~Just a teen willing to help others

\(\bold{Besties4Ever:-):-):-)}\)

Answer:

you forgot they/them pronouns are important!

Step-by-step explanation:

The answer will be \(a^{-20-12a}\) that can be find out using exponential function.

What are exponential function ?

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Like, f(x) = \(x^{a}\)

x is base and a is power.

Basic rules to solve this function :

1. If we take the product of two exponentials with the same base, we simply add the exponents:

x^ a * x^ b = x^ a + b.

2. If we take the quotient of two exponentials with the same base, we simply subtract the exponents:

x^ a / x^ b =  x^ a-b

3. We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents:

x^ (a)^ b = x^ (ab).

In given equation, \({a^{2^{-2^5}}/{a^{4a^3}}\)

So the answer is a^(-20-12a).

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If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = √x .

The value of the absolute function is always positive.

The absolute function is given as

f(x) = a√x

The function g is related to one of the parent functions g(x) = 2 √x

Then the parent function f(x);

f(x) = √x

If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x).

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After answering the provided question, we can conclude that So the total  equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "\(2x + 3 = 9\)" asserts that the statement "\(2x + 3\)" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "\(x^2 + 2x - 3 = 0\)," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's call Sarah's reading time "r" in minutes.

We can deduce from the problem:

Sarah painted for 5 minutes.

Because she spent twice as much time reading as she did painting,\(r = 2*5 = 10.\)

She hiked for 35 minutes longer than she read, so \(h = r + 35.\)

To calculate Sarah's total time spent on these three activities, simply add the times:

Time spent painting + time spent reading + time spent hiking = total time

Time total =\(5 + 10 + (r + 35)\)

Time total = \(50 + r\)

So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.

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The LCD of 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) is (x+2)^2(x-2)^2(x+2)(x-2) = (x+2)^3(x-2)^3.

To find the lowest common denominator (LCD) of three fractions, we need to identify the factors of each denominator and select those factors that are common to all denominators.The given fractions are: 1/ (x+2)^2, 3/ (x-2)^2, and 4/ (x^2-4).

The first denominator (x+2)^2 can be factored using the formula for the difference of two squares. The denominator of 3/(x-2)^2 can also be factored using the formula for the difference of two squares.

Finally, the denominator of 4/(x^2-4) can be factored using the formula for the difference of two squares and the formula for the sum of two squares.

So, 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) can be rewritten as follows:1/ (x+2)^2 = A/(x+2) + B/(x+2)^2. Multiplying both sides by (x+2)^2 gives:1 = A(x+2) + B ... (1)3/ (x-2)^2 = C/(x-2) + D/(x-2)^2.

Multiplying both sides by (x-2)^2 gives:3 = C(x-2) + D ... (2)4/ (x^2-4) = E/(x-2) + F/(x+2). Multiplying both sides by (x^2-4) gives:4 = E(x-2)(x+2) + F(x+2)(x-2) ... (3)

Now, we need to solve these equations for A, B, C, D, E, and F. First, we will solve equation (1) for A and B by substituting x = -2, which gives A = -1/4. Then we will substitute x = -2 again and solve for B, which gives B = 1/4. Next, we will solve equation (2) for C and D by substituting x = 2, which gives C = 3/4.

Then we will substitute x = 2 again and solve for D, which gives D = -3/4. Finally, we will solve equation (3) for E and F by substituting x = 2 and x = -2, which gives E = 1/2 and F = 1/2.

Now, we have A = -1/4, B = 1/4, C = 3/4, D = -3/4, E = 1/2, and F = 1/2. The LCD is the product of all the factors that appear in the denominators of the fractions, each raised to the highest power that appears.

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Answer:

96 $

Step-by-step explanation:

2

\( \frac{2}{5} \)

2

\(2 \times 240\)

\(480 \div 5\)

the answer is 96$

Answer:

96$

Step-by-step explanation:

Answer:

C) 1/2

Step-by-step explanation:

6 out of 12, so 1/2

The equivalent equations to 1/2(6x + 8) = x − 8 include:

A. 4 = -2x - 8

E. 2x + 4 = -8

It should be noted that an equation shows the relationship between the variables. This usually illustrated by having and equal to sign.

In this case, 1/2(6x + 8) = x − 8 will be:

3x + 4 = x - 8

Collect like terms

3x - x = -8 - 4.

2x = -12

Divide

x = -12/2

x = -6

Therefore, 4 = -2x - 8

2x = -8 - 4

2x = -12

x = -12/2 = -6

Therefore, A is correct.

E. 2x + 4 = -8

2x = -8 - 4

2x = -12

x = -12/2

x = -6

E is also correct.

The correct options are A and E.

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The domain of the function f(x) = (-x + 3)^2 is x ≤ 3, indicating that the function is defined for all real numbers less than or equal to 3. No Option is correct.

To determine the domain of the given function f(x) = (-x + 3)^2, we need to identify the values of x for which the function is defined.

In this case, the function is defined for all real numbers, except for any values of x that would result in an undefined operation or create a complex number.

The function involves squaring the expression (-x + 3), which means the expression inside the square root must be non-negative to avoid complex numbers. Thus, (-x + 3) must be greater than or equal to 0.

Solving the inequality (-x + 3) ≥ 0, we can find the range of x values that satisfy this condition.

Adding x to both sides of the inequality, we have 3 ≥ x.

This inequality implies that x must be less than or equal to 3. No Option is correct.

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The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

From the question, we have the following parameters that can be used in our computation:

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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Answer:

c. y=2x−48

Explanation:

It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept

It also says he earns $2 per hot dog, so that will be our slope (rate of change)

Hope it helps! :]

y = 2x - 48 equation represents the profit earned by the x hot dog sold.

A linear equation is an algebraic expression in which highest power of the given variable is equals to one.

Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.

It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.

We need to establish an equation that represents the total profit,

According to the question,

x represents the number of hot dogs sold

y represents the total profit earned

Cost required for supply = $48

Profit on each hot dog sold = $2

As per the condition given, the required linear equation is =

y = 2x - 48

Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.

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Answer:

The answer is 140 cubic in

Step-by-step explanation:

The formula for the volume of a prism is V=Bh, where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw. Hope this helped! :) (ps. I am sorry if it does not help.)

Answer:

140 cubic inches

Step-by-step explanation:

8x5x3.5

8x5 = 40

40x 3.5= 140

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Answer:

frist answer is

6080

second answer is 72 square yard

Answer:

Step-by-step explanation:

Fraction :x/y

numerator x = y - 2

Now the fraction can be written as: (y-2)/y

3 is added to both denominator and numerator.

After adding 3, the new fraction = \(\frac{y-2 +3 }{y + 3 } = \frac{y+ 1 }{y +3}\)

The sum of the new fraction and the original fraction is 53/35

\(\frac{y+1}{y+3} + \frac{y-2}{y} = \frac{53}{35}\\\\\frac{(y+1)*y}{(y+3)*y}+\frac{(y-2)*(y+3)}{y(y+3)}=\frac{53}{35}\\\\\frac{y^{2}+y}{y^{2}+3y}+\frac{y^{2}+y-6}{y^{2}+3y}=\frac{53}{35}\\\\\frac{y^{2}+y+y^{2}+y-6}{y^{2}+3y}=\frac{53}{35}\\\\\frac{2y^{2} + 2y - 6}{y^{2}+3y}=\frac{53}{35}\\\\\)

35*(2y² + 2y - 6) = 53 *(y² + 3y)

35*2y² + 2y * 35 - 6*35 = 53 *y² + 53*3y

70y² + 70y -  210 = 53y² + 159y

70y² + 70y -  210 - 53y² - 159y = 0

70y² - 53y² + 70y - 159y - 210 = 0

          17y²  - 89y - 210 = 0

Answer:

17y^2 - 89y - 210 = 0

Step-by-step explanation:

Original fraction: x/y

The numerator is 2 les than the denominator, x = y - 2

Original fraction: (y - 2)/y

New fraction:

Add 3 to the numerator and denominator of the original fraction:

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

Add the new fraction and old fraction and get 53/35.

(y - 2)/y + (y + 1)/(y + 3) = 53/35

35y(y + 3)[(y - 2)/y] + 35y(y + 3)[(y + 1)/(y + 3)] = 35y(y + 3)(53/35)

35(y + 3)(y - 2) + 35y(y + 1) = 53(y^2 + 3y)

35(y^2 + y - 6) + 35(y^2 + y) = 53y^2 + 159y

17y^2 - 89y - 210 = 0

Answer:

C) The figures are congruent.

Step-by-step explanation:

Given

Translation and rotation on a figure

Required

Select the true option

Rotation and translation are rigid transformation and as such they do not change the size of the figure being transformed.

The implies that, the figure being transformed and the resulting figure will have the same dimension and the same angle measure.

(c) is correct

Answer:

c

Step-by-step explanation:

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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