The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = -4, y = 6

Answer:

I think 1,600

Step-by-step explanation:

Andre's account after t years is \(V_h=538.45(1.025)^t\) since is option C.

The Amount accumulated at the end of a interest year is the sum of the principla amount and the interest gained on the principal amount.

As Andres start the savings account after 3 years so, the equation representing the value of Andre's account after t years is-\(v_h=500(1.025)^{t-3}\).

Also, the amount accumulated in the mean 3 years will be-

\(A=500(1.025)^3\)

=$538.45

Hence, another way of writing the equation representing the value of Andre's account after t years is-\(V_h=538.45(1.025)^t\)

As a result, option C is the correct answer.

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Answer:

\(\frac{11}{6}\) units

Step-by-step explanation:

To find the x- intercepts let y = 0 , that is

6x² - 7x - 3 = 0 ← in standard form

(3x + 1)(2x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - \(\frac{1}{3}\)

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \(\frac{3}{2}\)

Find the difference of the 2 x- intercepts using absolute value

distance = | \(\frac{3}{2}\) - (- \(\frac{1}{3}\) ) | = | \(\frac{3}{2}\) + \(\frac{1}{3}\) | = | \(\frac{11}{6}\) | = \(\frac{11}{6}\)

The length of an edge of the cubical tank is approximately 9.41 cm.

To find the length of an edge of the cubical tank, we can use the given information.

We know that the water in the cubical tank was poured into an empty rectangular container until it was completely filled. Therefore, the volume of water in the rectangular container is equal to the volume of the cubical tank.

Let's assume that the length of an edge of the cubical tank is x cm. Since it is a cube, the volume of the cubical tank is x^3 cubic cm.

Now, let's calculate the volume of the rectangular container. We know that there were 788 cm of water left in the cubical tank. So, the volume of the rectangular container is 788 cubic cm.

Since the volume of the cubical tank is equal to the volume of the rectangular container, we have the equation: x^3 = 788.

To solve for x, we take the cube root of both sides of the equation: x = ∛788.

Calculating this, we find that x ≈ 9.41 cm.

Therefore, the length of an edge of the cubical tank is approximately 9.41 cm.

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Answer:

We can not see the image, so i will answer this in a general way.

We know that a linear equation can be written as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

In this case, we know that this line has a slope equal to -2, then the line is:

y = -2*x + b

Now, suppose that in the image we can see that this line passes through the point (j, k)

Then we can replace x by j, and y by k in the line equation, to get:

k = -2*j + b

Now we can solve this for b:

b = k + 2*j

Then we can conclude that a line with a slope equal to -2, that passes through the point (j, k) is:

y = -2*x + (k + 2*j)

Answer:

Hopes it helps

Step-by-step explanation:

Len

Simplifying

5(3 + -8x) = 0

(3 * 5 + -8x * 5) = 0

(15 + -40x) = 0

Solving

15 + -40x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + -40x = 0 + -15

Combine like terms: 15 + -15 = 0

0 + -40x = 0 + -15

-40x = 0 + -15

Combine like terms: 0 + -15 = -15

-40x = -15

Divide each side by '-40'.

x = 0.375

Simplifying

x = 0.375

Monty

Simplifying

7 + -2(-5x) = 0

Remove parenthesis around (-5x)

7 + -2 * -5x = 0

Multiply -2 * -5

7 + 10x = 0

Solving

7 + 10x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.

7 + -7 + 10x = 0 + -7

Combine like terms: 7 + -7 = 0

0 + 10x = 0 + -7

10x = 0 + -7

Combine like terms: 0 + -7 = -7

10x = -7

Divide each side by '10'.

x = -0.7

Simplifying

x = -0.7

Nailany

Simplifying

7 + -6 + -16x = 0

Combine like terms: 7 + -6 = 1

1 + -16x = 0

Solving

1 + -16x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -16x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -16x = 0 + -1

-16x = 0 + -1

Combine like terms: 0 + -1 = -1

-16x = -1

Divide each side by '-16'.

x = 0.0625

Simplifying

x = 0.0625

The correct option is (D). Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

Given a local manufacturing plant, employees must complete new machine set ups within 30 minutes.

The new machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. The typical worker needs five minutes to adjust to their surroundings before beginning their duties.

To find the percentage of new machine set ups completed in less than 25 minutes, we need to calculate the z-score. For this, we will use the formula:

z = (X - μ) / σ

where X = 25 minutes, μ = 22 minutes, and σ = 4 minutes

z = (25 - 22) / 4z = 0.75

We can now look up the percentage of the area under the normal distribution curve that corresponds to z = 0.75. Using a standard normal distribution table, we find that the area to the left of z = 0.75 is approximately 0.7734.

So, the percentage of new machine set ups completed in less than 25 minutes is approximately 77.34%.

Therefore, the correct option is (D).Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

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The common ratio of the sequence is 0.5.

The common ratio of a geometric sequence can be found by dividing any term by its previous term. Let's call the first term "a" and the common ratio "r". Then we have:

third term = a * r^2 = 100

eighth term = a * r^7 = 3.125

We can divide the equation for the eighth term by the equation for the third term to eliminate "a":

\((a * r^7) / (a * r^2) = 3.125 / 100\)

\(r^5 = 0.03125\)

r = 0.5

Therefore, the common ratio of the sequence is 0.5.

We are given two terms of a geometric sequence and are asked to find the common ratio. We can use the formula for the nth term of a geometric sequence to write two equations involving the first term "a" and the common ratio "r". By dividing the two equations, we can eliminate "a" and solve for "r". In this case, we get a fifth degree equation for "r", which we can solve using a calculator or by recognizing that 0.03125 is equal to 1/32, and therefore r is equal to the fifth root of 1/32, which simplifies to 0.5.

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The simplification of csc²x-cscx+2/CSCX-1 = 1/sin²(x) - sin(x) / (sin²(x)-1)

First, let's recall the definition of cosecant (csc): it's the reciprocal of sine, so csc(x) = 1/sin(x).

Next, we can simplify the equation by substituting the definition of cosecant into the equation:

csc²x-cscx / CSCX-1 = (1/sin(x))² - (1/sin(x)) / (1/(sin(x))-1)

Next, we can simplify the numerator and denominator using algebraic identities:

(1/sin(x))² = 1/sin²(x)

(1/sin(x)) / (1/(sin(x))-1) = sin(x) / (sin²(x)-1)

So, the equation becomes:

1/sin²(x) - sin(x) / (sin²(x)-1)

And this is the simplified form of the equation.

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Answer:

4/7 = 0.57142857……

Step-by-step explanation:

integer NO cause it has a decimal

irrational NO cause it can be written as a fraction

Natural NO cause it has decimals

Rational YES because it’s a fraction

whole NO cause decimals

Real YES cause it’s a number

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

-9z²

Step-by-step explanation:

-(3z)²

-(3z * 3z)

-(9z)

-9z²

Best of Luck!

\(area \: \: of \: \: the \: \: given \: \: figure \: \: = \: \: 108 \: unit {}^{2} \)

The critical values for the 95% confidence interval for the population standard deviation with n=15 and α=0.05 are 6.262 and 26.119

We must utilise the chi-square distribution with (n-1) degrees of freedom to establish the crucial values for the confidence interval for the population standard deviation.

With n=15 and α=0.05, we can find the critical values using a chi-square table or a calculator. For a 95% confidence interval (α=0.05), the critical values are:

Lower critical value = chi-square value at (n-1) degrees of freedom and

α/2 = chi-square value at 14 degrees of freedom and 0.025

= 6.262

Upper critical value = chi-square value at (n-1) degrees of freedom and

1-α/2 = chi-square value at 14 degrees of freedom and 0.975

= 26.119

Therefore, the critical values for the 95% confidence interval for the population standard deviation with n=15 and α=0.05 are 6.262 and 26.119 (rounded to three decimal places).

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Complete question is below

determine the critical values for the confidence interval for the population standard deviation from the given values. round your answers to three decimal places. n=15 and α=0.05.

The answer is 1 / 9.

Larry had 1/3 of a Submarine sandwich left over from the excursion. If sharing with 3 friends, they must divide equally.

To do this, 1/3 of the sandwich should be divided into three equal parts. This can be written as:

1/3÷3

To simplify this expression, division can be converted to multiplication by multiplying the reciprocal of the divisor (3) by the dividend (1/3). That is:

1/3 ÷ 3 = 1/3 × 1/3

Multiplying the numerator and denominator gives:

1/3 × 1/3 = 1/9  

Therefore, each person will get 1/9 of the original sandwich.

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The domain of the function f(x) is all real numbers except -14 and -4, since these values would make the denominator zero. In interval notation, the domain can be expressed as (-∞, -14) U (-14, -4) U (-4, +∞).

To find the domain of the function f(x) = 24/(x^2 + 18x + 56), we need to determine the values of x for which the function is defined.

The function f(x) involves division by the expression x^2 + 18x + 56. For the function to be defined, the denominator cannot be equal to zero, as division by zero is undefined.

To find the values of x for which the denominator is zero, we can solve the quadratic equation x^2 + 18x + 56 = 0.

Using factoring or the quadratic formula, we can find that the solutions to this equation are x = -14 and x = -4.

Therefore, the domain of the function f(x) is all real numbers except -14 and -4, since these values would make the denominator zero.

In interval notation, the domain can be expressed as (-∞, -14) U (-14, -4) U (-4, +∞).

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not sure how the format is for the question but i think its

for the second column: y=2+2, y=6+2, y=7+2

for third column: 4, 8, 9

for the fourth column: (2,4), (6,8), (7,9)

for the according to the table:

(6,8), when his brother is 6 he is 8

for the graph: graph out the points (2,4), (6,8), (7,9)

another solution can be when he is 5 his brother is 3

(these should be right)

Answer:

8) Table

2...

6...

7...

According to table 6, the point (6,8) means when his brother is 8 Trisjohn is 6

For the graph plot points at (2,4) (6,8) and (7,9) and connect with a straight line

When Kimarius is 5 his brother is 3

Have a lovely day :)

An equation to represent the other lengths, X, of the triangle is 2X+7=23.

An isosceles triangle is one that has two equal-length sides in geometry. The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception. The faces of bipyramids and a few Catalan solids are examples of isosceles triangles, as are the isosceles right triangle, the golden triangle, and others.

Isosceles triangles have been the subject of mathematical research since the time of the Babylonians and the Egyptians.

Given,

Perimeter of an isosceles triangle=23 meters

The base of a triangle=7 meters

P=2X+b

2X+7=23

Therefore, an equation to represent the other lengths, X, of the triangle is 2X+7=23.

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Answer:

(a)18

(b)1089

(c)Sunday

Step-by-step explanation:

The problem presented is an arithmetic sequence where:

We want to determine the number of Sundays in the 120 days before Christmas.

(a)In an arithmetic sequence:

\(\text{The nth term}, T_n=a+(n-1)d\\T_n \leq 120\\$Therefore:$\\1+7(n-1) \leq 120\\1+7n-7\leq 120\\7n-6\leq 120\\7n\leq 120+6\\7n\leq 126\\$Divide both sides by 7$\\n\leq 18\)

Since the result is a whole number, there are 18 Sundays in which Aldsworth advertises.

Therefore, Aldsworth advertised 18 times.

(b)Next, we want to determine the sum of the first 18 terms of the sequence

1,8,15,...

\(\text{Sum of a sequence}, S_n=\frac{n}{2}( 2a+(n-1)d)\\S_{18}=\frac{18}{2}( 2*1+(18-1)*7)\\=9(2+17*7)\\=9(2+119)\\=9*121\\S_{18}=1089\)

The sum of the numbers of days published in all the advertisements is 1089.

(c)SInce the 120th day is the 18th Sunday, Christmas is on Sunday.

Answer:

27.74 is the difference

Step-by-step explanation:

23.3° C - (-4.44° C)

23.3 + 4.44

27.74

first you combine like terms

25m + 43,200 = 45,675 - 200m

then you add 200m to both sides

225m + 43,200 = 45,675

then you subtract 43,200 from both sides

225m = 2,475

then you divide both sides by 225

m = 11

Answer:

t = 74 / 9

Step-by-step explanation:

-9(t - 2) = 4(1 - 15)

-9t + 18 = 4 - 60

-9t + 18 = -56

 -18      -18

-9t = -74

/-9     /-9

t = 74 / 9

t = 8.22

Answer:

t = 74 / 9 ~= 8.222

Step-by-step explanation:

-9 ( t - 2 ) = 4 ( 1 - 15 )

-9 * t + -9 * -2 = 4 * 1 + 4 * -15

-9t + 18 = 4 + -60

-9t + 18 = -56

-9t = -56 + -18

-9t = -74

t = 74 / 9

Alternatively:

-9 ( t - 2 ) = 4 ( 1 - 15 )

-9 * t + -9 * -2 = 4 ( - 14 )

-9t + 18 = -56

-9t = -56 + -18

-9t = -74

t = 74 /9

Cheers.

Answer:

the answer is d

Step-by-step explanation:

brainliest pls

Answer:

It's B or D, but I think D.

Step-by-step explanation: