Match each equation with a value of x that satisfies it. ​

The value of the variable(s) in the figure is  60°, explaination is given below.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that function at those values of the considered variables.

We are given that;

The variables; (5y)⁰,(2x)°,120⁰,1080

Now,

The first two expressions are both equal to 1, because any number raised to the power of 0 is always 1.

The third expression, 120°, is an angle measurement in degrees. In a triangle, the sum of the interior angles is always 180°. So, if we let x and y be the other two angles in the triangle, we have:

x + y + 120° = 180°

Simplifying this equation, we get:

x + y = 60°

Therefore, the answer of the given function will be  60°.

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Answer:

it has a constant rate of change

Step-by-step explanation:

i took the test and got it right

The composite function (f + g)(x) is (f + g)(x) = 9x² - x - 8

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

f(x)=3x²+42-6

g(x)=62-5²-2

Express properly

So, we have the following representation

f(x) = 3x² + 4x -6

g(x) = 6x² - 5x - 2

The composite function is then calculated as

(f + g)(x) = f(x) + g(x)

So, we have

(f + g)(x) = 3x² + 4x -6 + 6x² - 5x - 2

Evaluate

(f + g)(x) = 9x² - x - 8

Hence, the function is (f + g)(x) = 9x² - x - 8

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Answer:

pls explain it so that I can solve it there is no explanation for the answer

Account Compounding Interest after 6 years

1 quarterly

A1 = -$1798.42

2 monthly $

A2 = -$1798.01

3 daily $

A3 =  -$1797.96

1) An account with quarterly compounding: After 6 years, the formula to calculate the interest is:

Interest = Principal \(\times\)(1 + (rate / \(n))^{(n * t)}\) - Principal

Substituting the given values:

Principal = $2200

Rate = 3% = 0.03

n = 4 (quarterly compounding)

t = 6 years

Interest = $2200 \(\times\) (1 + (0.03 / \(4))^{(4 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0075)^{(24)}\) - $2200

Interest ≈ $401.58 - $2200

Interest ≈ -$1798.42 (rounded to two decimal places).

2) An account with monthly compounding: After 6 years, the formula remains the same, but the compounding frequency changes:

   Principal = $2200

   Rate = 3% = 0.03

   n = 12 (monthly compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(12))^{(12 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0025)^{(72)}\) - $2200

Interest ≈ $401.99 - $2200

Interest ≈ -$1798.01 (rounded to two decimal places)

3) An account with daily compounding: Using the same formula with the compounding frequency:

   Principal = $2200

   Rate = 3% = 0.03

   n = 365 (daily compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(365))^{(365 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.000082)^{(2190)}\) - $2200

Interest ≈ $402.04 - $2200

Interest ≈ -$1797.96 (rounded to two decimal places)

In all three cases, the interest earned is negative, indicating that the accounts would have lost money rather than gained interest.

This suggests that there might be an error in the calculations or the provided interest rates. It's important to verify the given information to ensure accurate calculations and resolve any discrepancies.

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It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer: b + p ≤ 7

Step-by-step explanation:

Let's use b to represent the number of bags of popcorn purchased and p to represent the number of bags of pretzels purchased.

Since Cai can buy a maximum of 7 bags of popcorn and pretzels altogether, we know that:

b + p ≤ 7

This is the inequality that represents the possible values for the number of bags of popcorn purchased (b) and the number of bags of pretzels purchased (p).

Answer:

1.12

Step-by-step explanation:

the intersection points are (1, 7) and (4, 13), So the correct option is A.

To see that, we need to see when the two equations:

y = -x²+7x+1

y = 2x + 5

Can be solved simultaneously for a point (x, y). So we need to solve a system of equations.

y = -x²+7x+1

y = 2x + 5

We can rewrite:

-x²+7x+1 = y =  2x + 5

Then we can solve this for x:

-x²+7x+1 =  2x + 5

x² - 5x + 4 = 0

This is just a quadratic equation, the solutions are:

\(x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*(1)*(4)} }{2} \\\\x = \frac{5 \pm 3 }{2}\)

So we have two values of x:

The correspondent values of y are:

y = 2*(4) + 5 = 13

y = 2*(1) + 5 = 7

Then the intersection points are (1, 7) and (4, 13)

Then the correct option is A. The dog will catch the frisbee.

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The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

b < 3

Step-by-step explanation:

3 ( b - 5 ) < - 2b

3 ( b ) - 3 ( 5 ) < - 2b

3b - 15 < - 2b

3b + 2b < 15

5b < 15

b < 15/5

b < 3

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

Answer: 1/3

Step-by-step explanation:

In a multiple-choice examination with 3 choices for each question, the probability of guessing the correct answer is 1/3. Since you are trying to guess exactly 6 of 10 answers correctly, this means that you will be guessing incorrectly on 4 of the 10 questions. The probability of guessing incorrectly on a single question is 2/3.

To find the probability of guessing exactly 6 of 10 answers correctly, we can use the binomial probability formula, which is given by the following expression:

P(x) = (n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

In this formula, n is the total number of trials, x is the number of successes, p is the probability of success on a single trial, and 1-p is the probability of failure on a single trial.

Plugging in the values for this problem, we get:

P(6) = (10!/(6!(10-6)!) * (1/3)^6 * (2/3)^4

= 210 * (1/3)^6 * (2/3)^4

= 210 * (1/3^6) * (2/3^4)

= 210 * (1/3^6) * (1/3^2)

= 210 * (1/3^8)

= 210 * (1/6561)

= 0.0322

So the probability of guessing exactly 6 of 10 answers correctly in a multiple-choice examination with 3 choices for each question is approximately 0.0322, or about 3.22%.

Answer:

take 1/4 to the other side since 1/2 and 1/4 are like terms then solve for X getting 16/5 as the answer

Have a wonderful time

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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Angles at the center of a circle add up to 360 degrees.

The measure of angle GEH in the circle is (d) 116 degrees

The given parameters are:

\(\mathbf{\angle FEG = 64^o}\)

Since line FH is the diameter of the circle;

It means that:

\(\mathbf{\angle FEG + \angle GEH = 180^o}\) --- By angle on a straight line theorem

Substitute 64 for FEG

\(\mathbf{64 + \angle GEH = 180^o}\)

Subtract 64 from both sides

\(\mathbf{\angle GEH = 180^o - 64}\)

Evaluate like terms

\(\mathbf{\angle GEH = 116^o}\)

Hence, the measure of angle GEH in the circle is (d) 116 degrees

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Answer:

x < -8

Step-by-step explanation:

−3x>24

Divide each side by negative 3, remembering to flip the inequality

-3x/-3 < 24/-3

x < -8

Answer:

x<-8

Step-by-step explanation:

−3x>24

Multiply both sides by (-1) (reverse the inequality)

(-3x)(-1)<24(-1)

Simplify;

3x<-24

Divide both sides by 3

3x/3<-24/3

Simplify

3x/3<-24/3

Simplify; 3x/3

=x

Simplify; -24/3

Divide the numbers;24/3=8

=-8

x<-8

Hope this helped!!!

Answer:

Hi!

\(x=5\)

Step-by-step explanation:

\(9x-13+13=32+13\\9x=45\\\frac{9x}{9}=\frac{45}{9}\\=5\)

Answer:

the answer is 5

Step-by-step explanation:

9 x 5 -13= 32

Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Answer:

22

Step-by-step explanation:

4

Answer:

It is a rational number

Step-by-step explanation:

Answer:

13/20 = 65%

Step-by-step explanation:

1/4 = 25%

7/10 = 70%

13/20 = 65%

Only the last one had the correct percentage.

Answer:

x=2

Step-by-step explanation:

Let x be the number

30 - 6x = x+16

Add 6x to each side

30 -6x+6x = x+16+6x

30 = 7x+16

Subtract 16 from each side

30-16 = 7x+16-16

14 = 7x

Divide each side by 7

14/7 = 7x/7

2 =x

Answer:

2

Step-by-step explanation:

let the number be x

given, 30 decreased by 6 times the number=30-6x

that is same as 16 more than the number= x+16

equating these 2 equations since they are equal

30-6x=x+16

6x+x=30-16

7x=14

x=2

The req. number is 2