What is the x-intercept of the line containing the points (-6,10) and (12,-2)?

Answer:

5

Step-by-step explanation:

Final answer:

Using the GCF of 10 and 15, which is 5, we cross-cancel the fractions 5/15 and 5/10 to reduce them to 1/3 and 1/2 respectively. Multiplying these reduced fractions, we obtain the final answer of 1/6.

Explanation:

To solve the fraction 5/15 × 5/10, we first identify the Greatest Common Factor (GCF) of the numerators and denominators. The GCF of 10 and 15 is 5. Using this GCF, we cross-cancel to reduce the fractions before multiplying.

Firstly, we divide both 10 and 15 by the GCF, which gives us:

10 ÷ 5 = 2

15 ÷ 5 = 3

Applying cross-cancellation to the original expression, we get:

(5 ÷ 5) / (15 ÷ 5) × (5 ÷ 5) / (10 ÷ 5)

1/3 × 1/2

Multiplying these reduced fractions gives us:

1/3 × 1/2 = 1/6

Thus, the result of multiplying 5/15 by 5/10, after cross-cancelling the common factors, is 1/6.

Answer:

Step-by-step explanation:

y-intercept is for x = 0. Substitute x = 0 to the equation of a function

[tex]y=3\left(\dfrac{8}{9}\right)^x[/tex]

[tex]y=3\left(\dfrac{8}{9}\right)^0=3(1)=3[/tex]

Hey there!

Answer:

A. -4

Explanation:

All you do is evaluate:

[tex]-(-(-4))\\= -4[/tex]

= A. -4

Therefore, that is how you got your answer.

Hope this Helps!

Answer:

A. -4

Explanation:

All you do is evaluate:

= A. -4

Therefore, that is how you got your answer.

Hope this Helps

y=mx+b where m is the slope and b is the y intercept.

Final answer:

Linear equations are written as y = mx + b or y = a + bx, where 'm' or 'b' in the first form and 'b' in the second represents the slope and 'b' in the first form and 'a' in the second represents the y-intercept. The equation can model relationships where 'y' changes at a constant rate with 'x', forming a straight line graph.

Explanation:

Understanding Linear Equations

Linear equations represent relationships between variables that result in a straight line when graphed on a Cartesian plane. These equations are typically written in the form y = mx + b or in a statistical context as y = a + bx. Here, 'y' is the dependent variable and 'x' is the independent variable. The constant 'm' or 'b' in the first equation and 'b' in the second represents the slope of the line, which indicates the rate of change of 'y' with respect to 'x'. The constant 'b' in the first equation and 'a' in the second equation represents the y-intercept, which is the point where the line crosses the y-axis, at which point 'x' equals zero.

Graphically, the slope denotes the steepness and the direction of the line, while the y-intercept gives us the starting point of the line on the graph. For example, in the equation y = 6x + 8, the slope is 6 and the y-intercept is 8. This means that for every one unit increase in 'x', 'y' will increase by 6 units, and when 'x' is 0, the value of 'y' is 8.

Different scenarios can be modeled using linear equations, such as calculating the total number of hours required based on the square footage (y = x + 4), determining the total payment based on the number of students (y = 100(x) + 2,000), or finding the total cost of attendance over a number of years (y = 3,000(x) + 500).

The linear equation is also applicable in understanding real-world issues, such as tracking the number of flu cases over the years, where the number of cases depends on the year.

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex], then

[tex]a^{x^2-5x}[/tex] = [tex]a^{6}[/tex], hence

x² - 5x = 6 ( subtract 6 from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 1

Answer:

Step-by-step explanation:

Using the rule of exponents:

a^{m} ÷ a^{n} = a^{(m-n)} , then

aˣ² ÷ a^{5x}  = a⁶

⇒ a^{x^2 - 5x} = a⁶

⇒ x² - 5x = 6

x² - 5x - 6 = 0

(x - 6)(x + 1) = 0 [middle term splitting]

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6     ║     x + 1 = 0 ⇒ x = -1

Hello. The answer to your problem is (3, 1). I've included a screenshot of the graph.

The simple interest earned on $600 put in the bank with 7% rate for 2 years is $84.

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

[tex]I=\dfrac{Prt}{100}[/tex]

Here, I is the interest amount on the principal amount of P with the rate of r in the time period of t.

Given information-

The principal amount put in the bank is $600.

The rate of simple interest is 7 percent.

The number of years is 2.

Put the value in the above formula as,

[tex]I=\dfrac{600\times7\times2}{100}\\[/tex]

Solve it further as,

[tex]I=84[/tex]

Thus, the simple interest earned on $600 put in the bank with 7% rate for 2 years is $84.

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4/18=.2222x100=22.22%

Answer:

CD = two square root of 10 end square root

Step-by-step explanation:

To find the length of a segment, use the distance formula. Substitute the order pairs for the endpoints of the segment. CD has the end points (-7, -4) and (-1, -2).

[tex]d = \sqrt{(y_2-y_1)^2 + (x_2-x_1)^2} \\\\d = \sqrt{(-4--2)^2 + (-7--1)^2} \\\\d = \sqrt{-2^2 + -6^2}\\\\d = \sqrt{4 + 36}\\\\d=\sqrt {40} = 2\sqrt{10}[/tex]

The constant variation is k=-13/2

Answer:

k = - 6.5

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 4 when y = - 26, hence

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-26}{4}[/tex] = - [tex]\frac{13}{2}[/tex] = - 6.5

-2v -4 = -2x

just move the +2 to the other side then multiply by a common multiple.

Solutions to systems of equations are typically found at the point where the lines intersect on a graph. For linear equations, this is represented by the equation y = mx + b. Quadratic equations also have solutions known as roots, and ones based on physical data typically have real, positive roots.

Due to the incomplete equation and graph not provided, we can first discuss general methods for finding solutions to systems of equations. One common method is the intersection of two lines on a graph, which illustrates the system of equations. Here, the zeros on the two-dimensional (x-y) graph represent the solution to the equations:

In this scenario, the y-axis represents the variable V, and the x-axis represents the variable X. The primary task is to find the point where these two lines intersect on the graph - this is the solution to the system of equations. The equation of a line is typically a linear equation, represented as y = mx + b, where m is the slope and b is the intercept.

If the equations are quadratic, these also have solutions, known as roots. Quadratic equations constructed on physical data always have real roots, but often only those having positive values are of any significance.

Without the specifics of your graph, an exact solution cannot be provided.

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Answer:

Step-by-step explanation:

Put x = 5 and y = 7 to the equation ax - 2y = 1 and solve for a:

(a)(5) - (2)(7) = 1

5a - 14 = 1       add 14 to both sides

5a - 14 + 14 = 1 + 14

5a = 15        divide both sides by 5

5a : 5 = 15 : 5

a = 3

Valerie's monthly income tax payment is $235.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Now, Based on Valerie's annual salary of $24,000, her monthly salary would be,

$24,000 / 12

$2,000

Hence, To calculate her income tax, we first need to determine how much of her earnings are over $944.

⇒ $2,000 - $944

⇒ $1,056

Thus, Valerie's earnings over $944 are $1,056.

Next, we'll calculate the income tax on that amount.

$1,056 x 0.15 = $158.40

So Valerie pays $158.40 in income tax each month.

Additionally, she pays a fixed amount of $76.60 each month, which brings her monthly total to:

⇒ $158.40 + $76.60 = $235.

Therefore, Valerie's monthly income tax payment is $235.

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Answer:   [tex]\bold{x^{\frac{1}{3}}y^{\frac{1}{2}}}[/tex]

Step-by-step explanation:

[tex]\sqrt[6]{x^2y^3} =x^{\frac{2}{6}}y^{\frac{3}{6}}=x^{\frac{1}{3}}y^{\frac{1}{2}}[/tex]

Answer:  F) 7 mph

Step-by-step explanation:

The line you drew is correct but you read the graph wrong.  

The line drawn from 15 hours of training (bottom axis) meets the "line of best fit" at the average running speed (left axis) between 6 and 8, which is 7.

Hey there!

Let's start by solving for x.

Take the first equation, y = -3x - 7, and substitute in the second equation, y = x + 9, for y.

We now have:

x + 9 = -3x - 7

Add 3x to both sides.

4x + 9 = -7

Subtract 9 from both sides.

4x = -16

Divide each side by 4.

x = -4

Let's use the second equation, y = x + 9, to solve for x.

Put in the value we just solved for.

We now have:

y = -4 + 9

Simplify.

y = 5

Let's check our answer, starting with the first equation, y = -3x - 7.

Put in the values for x and y.

5 = -3(-4) - 7

5 = 12 - 7

5 = 5

Do the same with the second equation, y = x + 9.

5 = -4 + 9

5 = 5

The solution to the system of equations is (5, -4).

Hope this helps!

Answer:

(-4, 5)

Step-by-step explanation:

Since y = -3x - 7 in the first equation, substitute y of the second equation with -3x - 7:

-3x - 7 = x + 9

Subtract x from both sides. Add 7 to both sides.

-4x = 16

Divide both sides by -4.

x = -4

Now, substitute -4 for x in the second equation.

y = -4 + 9

y = 5

The solution is:

x = -4; y = 5

As an ordered pair, the solution is:

(-4, 5)

Answer:

Mrs. Jones gave 5/8 of the pizza to Gary.

Step-by-step explanation:

We are given that Mrs. Jones had [tex]1\frac{4}{8}[/tex] pizzas left from which she gave some to Gary.

Now that she is left with [tex]\frac{7}{8}[/tex] pizza left, we are to find the fraction of the pizza she gave to Gary.

Assuming [tex]x[/tex] to be the fraction she gave to Gary, we can write it as:

[tex]1\frac{4}{8} - x = \frac{7}{8}[/tex] = 5/8

Answer:

The correct answer is 5/8

Step-by-step explanation:

It is given that,Mrs. Jones had 1 4/8 pizzas left after a party. After giving some to Gary, she had 7/8 pizza left

Let 'x' be the fraction of pizza given to Gary

To find the value of x

We can write,

1 4/8 - 7/8 = x

12/8 - 7/8 =x

x = (12 - 7)/8 = 5/8

Therefore the fraction of a pizza given to Gary = 5/8

Answer:

[tex]\frac{5(x-3)}{6}[/tex]

No excluded values.

Step-by-step explanation:

To simplify the fraction expression, multiply by the reciprocal.

[tex]\frac{5}{x+2} * \frac{x^2-x-6}{6}  =\frac{5(x^2-x-6)}{6(x+2)}=\frac{5(x-3)(x+2)}{6(x+2} = \frac{5(x-3)}{6}[/tex]

Excluded values are values which make the denominator 0 but since there is no variable in the denominator then there are none.

Answer:

Step-by-step explanation:

Seems to be a

The only correct statement that identifies the right angle is:

Option A: ∠DEF is a right angle

To identify the true statements of the diagram, we will need to look at each of the options to get:

Option A: ∠DEF is a right angle:

We see that the line FA is a straight line and we also see that the line DE is perpendicular to FA and as such we can say that:

∠DEF = ∠DEA = 90°

Option B: m∠DEA = m∠FEC:

This is not true because we can clearly see that m∠DEA is a right angle while  m∠FEC is an acute angle.

Option C: m∠BEA = m∠BEC:

We can't really say if they are equal because we are not told it ED is a bisector of ∠AEC

Option D: EB bisects  ∠AEF

This is wrong as it is not a bisector

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Answer:

The answer is (D) ⇒ a = 11.71 , b = 15.56

Step-by-step explanation:

* In ΔABC

∵ m∠A = 45°

∵ m∠B = 110°

∴ m∠C = 180 - 45 - 110 = 25°

By using the sin Rule

∵ a/sin(A) = b/sin(B) = c/sin(C)

∵ c = 7

∴ a/sin(45) = b/sin(110) = 7/sin(25)

∴ a = (7 × sin(45)) ÷ sin(25) = 11.71

∴ b = (7 × sin(110)) ÷ sin(25) = 15.56

∴ The answer is (D)

Answer: a= 11.71 and b= 15.56

Step-by-step explanation:

A pex

4²+4⁸=(2²)²+(2²)8

=2⁴+2⁸

=16+256

=272

it's from the properties of indices

Answer:f(x)=x

Step-by-step explanation:

Answer:

y = -3x² has the narrowest graph

Step-by-step explanation:

D)  y = -3x² has the narrowest graph.  That coefficient "3" stretches the graph of x² vertically.

On the other hand, B) has the widest graph.

Answer:                                  -7=0 --> Impossible

Step-by-step explanation:  

2x-7+x-11= 3x-11

2x+x-7-11=3x-11

3x-18=3x-11

3x-18+11=3x

3x-7-3x=0

-7=0

Impossible

We combined like terms on both sides to solve 2x - 7 + x - 11 = 3x - 11. However, this led to the false equation -18 = -11, indicating a potential error in the given problem.

The equation to solve is 2x - 7 + x - 11 = 3x - 11. The goal is to find the value of x.

The first step is to combine like terms on the left side of the equation. We combine 2x and x to get 3x and -7 and -11 to get -18. So, the problem becomes 3x - 18 = 3x - 11.

From here, we subtract 3x from both sides to isolate x on one side. This gives us -18 = -11. This equation is, however, incorrect.

This discrepancy could arise from a mistake in the original problem, notably, the content loaded 2x - 7 + x - 11 = 3x - 11.

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Answer:

Replace x^2 with m

Step-by-step explanation:

x^8-3x^4+2=0

We want to write this as a quadratic, which means as am^2+bm +c

x^8  needs to become m^2

Let m = x^4

Then m^2 = x^4^2 = x^8

Our equation becomes

m^2 -3m +2 =0

Replace x^2 with m

Answer:

Replace x with  [tex]y^{1/4}[/tex]

Step-by-step explanation:

The general  form of a quadratic equation is  [tex]ax^{2}[/tex] + bx + c.

To  find a substitution  we have to think of a way of substituting ‘x’ to make it have a power of 2,

Here, we will use [tex]y^{1/4}[/tex]  

[tex]x^{8}[/tex] - [tex]3x^{4}[/tex] +2 = 0

let x = [tex]y^{1/4}[/tex]

so it gives

([tex]y^{1/4}[/tex])^8 – 3( [tex]y^{1/4}[/tex] )^4 +2 = 0

[tex]y^{2}[/tex] – 3y + 2 = 0

Solving the equation

[tex]y^{2}[/tex]  - 2y – y + 2 =0

([tex]y^{2}[/tex] – 2y) -1(y – 2) = 0

y(y - 2) -1(y - 2) = 0

(y-1) (y-2)

:- y = 1 or y = 2

Since x = [tex]y^{1/4}[/tex]  

When y = 1

X = [tex]1^{1/4}[/tex]

X = [tex]4\sqrt{1}[/tex]

X = 1

and when  y = 2

X = [tex]2^{1/4}[/tex]

X = [tex]4\sqrt{2}[/tex]

X = 1.1892...

the answer is going to be C

circumference = pi times the diameter , so i used 3.14 as pi and used the values in the answer choices to determine the diameter

12 is the closest because 12 times 3.14 is 37.68 which is very close to 37.5

pls mark brainliest

Answer:

The only possible numbers are 6 and 0.

Step-by-step explanation:

We are given the following information in the question:

Let x and y be the two numbers whose difference is 6 and whose sum is also 6.

We can write it in the form of the equation:

[tex]x - y = 6\\x+y =6\\\\\text{Adding the two equations}\\(x-y) + (x+y) = 12\\2x =12\\x = 6\\\\\text{Putting this value of x in one of the equations}\\6 + y = 6\\y = 0[/tex]

Hence, the only possible numbers are 6 and 0.

It is possible as the numbers are 0 and 6.

Let the numbers be a and b.

Based on the question, the equation to solve the question will be:

a - b = 6 ........ i

a + b = 6 ........ ii

From equation i, a = 6 + b

Put the above into equation ii

a + b = 6

(6 + b) + b = 6

6 + 2b = 6

2b = 6 - 6.

2b = 0

b = 0/2

b = 0

Therefore, the value of a will be:

a = 6-0 = 6.

The numbers are 0 and 6.

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Answer:

1

Step-by-step explanation:

Change of Y is 0 and change of x is any number.

0/any number = 0

To fill a rectangular prism with dimensions 9in. by 4in. by 1.5in. using half-inch cubes, you need to divide the volume of the prism (54in.^3) by the volume of a cube (0.125in.^3), resulting in 432 cubes needed.

To determine how many half-inch cubes are needed to fill the rectangular prism, we must first calculate the volume of the prism and then the volume of a single cube. Next, we divide the volume of the prism by the volume of a cube to find the number of cubes needed.

Calculating the Volume of the Rectangular Prism

The volume of a rectangular prism is found by multiplying its length by its width by its height. Volume of the prism = length × width × height = 9in. × 4in. × 1.5in. = 54in.3.

Calculating the Volume of a Cube

The volume of a cube is found by raising the length of an edge to the third power. Volume of a cube = edge length3 = (0.5in.)3 = 0.125in.3.

Number of Cubes Needed

To find the number of cubes needed to fill the prism, divide the volume of the prism by the volume of a cube. Number of cubes needed = Volume of the prism / Volume of a cube = 54in.3 / 0.125in.3 = 432.

Therefore, 432 half-inch cubes are needed to fill the rectangular prism.

Answer:

[tex]y = \frac{2}{3}x + \frac{23}{3}[/tex]

Step-by-step explanation:

To write the equation of a line with a point and a slope, use the point-slope form of a linear equation. Substitute m = 2/3 and the point (-4,5) into the equation.

[tex]y - y_1 = m(x-x_1)\\y - 5 = \frac{2}{3}(x --4)\\y - 5 = \frac{2}{3}(x+4)[/tex]

Convert to slope intercept form by using the distributive property.

[tex]y - 5 = \frac{2}{3}(x+4)\\y - 5 = \frac{2}{3}x +\frac{8}{3}\\y = \frac{2}{3}x + \frac{8}{3} + 5\\y = \frac{2}{3}x + \frac{23}{3}[/tex]