what is the value of y in the triangle?

Step-by-step explanation:

Answer:

\(y = \frac{1 - 7}{2} = - 3 \\ x = \frac{ - 2 + 4}{2} = 1\)

Answer:

i got (1, -3) from using the midpoint formula witch is

Step-by-step explanation:

X1 + X2 ,  Y1 + Y2

    2               2

-2 + 4 ,  1 + -7

    2         2

    ( 1, -3)

Answer:

y= -2/3x-3

Step-by-step explanation:

If by the SAS similarity theorem, in ΔABE ≈ΔACD the AD is 24 units.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles. When two objects have the same shape but different sizes, they can be said to be comparable. This indicates that comparable shapes superimpose one another when amplified or demagnified.

If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be similar (corresponding sides). Similar triangles may have varied side lengths when compared individually, but they must all have equal angles and the same ratio of their side lengths.

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Answer:

a.  £2,500

b.  £3,125

Step-by-step explanation:

The computation is shown below:

a. The original monthly expenditure is

Let us assume the original monthly expenditure be x

Monthly expenditure = x -15% of x

£2,125 = x - 0.15x

£2125 = 0.85x

x = £2125 ÷ 0.85

= £2,500

b. Now the monthy income is

Let us assume the monthly income be y

£2,500 = 80% of monthly income

£2,500 = 80% of y

y = £2,500 ÷ 80%

= £3,125

Answer: Jalen has more string then Kelly

Step-by-step explanation:

Converting Kelly's string from yards, to inches to match up with Kelly's length of string we use the formula:

#yd = (# × 36) = total amount of "

Inputting the information in the formula, It'd look like this:

5 yd = (5 × 36) = 108"

therefore, from this information the answer to the question, is Jalen.

Answer:

-3

Step-by-step explanation:

 f(x)=2x^2 - 3x - 2

if x = 1

f(1) = 2(1)^2 - 3(1) - 2

= 4 - 3 - 2

= -3

Hope this helps :)

Pls brainliest...

Answer: 10) √85 units    12) 4 units

Step-by-step explanation:

          \(\boxed {l=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}}\)

10) (8,5)   (-1,3)

\(x_1=8\ \ \ \ x_2=-1\ \ \ \ y_1=5\ \ \ \ \ y_2=3\\\\l=\sqrt{(-1-8)^2+(3-5)^2} \\\\l=\sqrt{(-9)^2+(-2)^2} \\\\l=\sqrt{81+4}\\\\l=\sqrt{85}\ units\)

12) (-6,-10)   (-2,-10)

\(x_1=-6\ \ \ \ \ x_2=-2\ \ \ \ \ y_1=-10\ \ \ \ y_2=-10\\\\l=\sqrt{(-2-(-6)^2+(-10-(-10))^2} \\\\l=\sqrt{(-2+6)^2+(-10+10)^2}\\\\l=\sqrt{4^2+0^2} \\\\l=\sqrt{4^2} \\\\l=4\ units\)

The number of freshmen that are students is 738

Let y represent the number of students that are freshmen

The freshmen class is made up of 480 female students

This number represents 65% of the freshmen class

Therefore the total number of students that are freshmen can be calculated as follows

y × 65/100= 480

65y/100= 480

Cross multiply both sides

65y= 480 × 100

65y= 48000

y= 48000/65

y= 738.4

≅ 738

Hence 738 students are freshmen

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The sales fell short of the goal by $350.

What is a linear equation in two variables?

A linear equation in two variables is an equation that can be written in the form of ax + by = c, where a, b, and c are constants and x and y are variables. The graph of a linear equation in two variables is a straight line in the coordinate plane.

Let's write the equations based on the given information:

The total number of tickets sold should be 500.

d + s = 500

The total revenue generated should be $3,350.

8.5d + 5.5s = 3,350

To solve for d and s, we can use the system of equations method.

Multiplying the first equation by 5.5 and subtracting from the second equation, we get:

8.5d + 5.5s = 3,350

-5.5d - 5.5s = -2,750

3d = 600

d = 200

Substituting the value of d in the first equation, we get:

200 + s = 500

s = 300

Therefore, 200 adult tickets and 300 student tickets were sold to raise exactly $3,350.

Now, let's consider the second part of the problem.

Let x be the number of adult tickets sold. Then the number of student tickets sold is 3x.

So, the total number of tickets sold = x + 3x = 4x

Given that, the total number of tickets sold is 480.

4x = 480

x = 120

So, the number of adult tickets sold = 120

The number of student tickets sold = 3x = 360

The revenue generated from the adult tickets = 120 x $8.5 = $1,020

The revenue generated from the student tickets = 360 x $5.5 = $1,980

Therefore, the total revenue generated = $1,020 + $1,980 = $3,000

The sales fell short of the goal by $3,350 - $3,000 = $350.

Hence, the sales fell short of the goal by $350.

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Answer:

Step-by-step explanation:

Hello,

let s regroup the terms

2ax - 15 = 3(x + 5) + 5(x - 1) *** add 15 to both sides ***

<=> 2ax = 15 + 3x + 15 + 5x - 5 *** develop to remove the parentheses***

<=> 2ax = 8x + 25 *** simplify ***

<=> (2a-8)x = 25 *** subtract 8x from both sides ***

<=> (a-4)x=25/2 *** divide by 2 both sides ***

There is no solution is a-4 = 0 ,

because it would mean 0 = 25/2 and this is not possible

So it gives a = 4

Thanks

In the case when no value of x satisfies the equation so there the value of a should be 4.

Since

the equation is  

2ax - 15 = 3(x + 5) + 5(x - 1)

2ax = 15 + 3x + 15 + 5x - 5

2ax = 8x + 25

(2a-8)x = 25

So a = 4

hence, In the case when no value of x satisfies the equation so there the value of a should be 4.

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Answer:

10

Step-by-step explanation:

There are 10 groups of 2/5 in 4 which represent the given fraction.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Equivalent fractions have the same value regardless of their numerators and denominators. When simplified, 6/12 and 4/8 are both equal to 1/2, indicating that they are equivalent in nature.

To find out how many groups of 2/5 are in 4, you will need to divide 4 by 2/5.

To do this, you can follow these steps:

Rewrite the fraction 2/5 as a decimal by dividing the numerator by the denominator. This gives you 0.4.

Divide 4 by 0.4 to find the number of groups of 2/5 that are in 4.

For example, if you divide 4 by 0.4, you get:

4 / 0.4 = 10

Therefore, there are 10 groups of 2/5 in 4.

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Answer:

24

Step-by-step explanation:

2 cups = 1 pint

2 cups = 12 serving

1 pint = 12 serving

2 pint = 12 x 2

2 pint = 24 serving

The derivative of the function h(x) = f(x)g(x), where f(x) = -3x^2 + 4x - 1 and g(x) = -x^2 + 4x + 3, can be found by applying the product rule. Evaluating h'(4) will give us the slope of the tangent line to the function h(x) at x = 4.

1. To calculate h'(4), we substitute x = 4 into the derivative expression. The derivative of h(x) is determined by the sum of the product of the derivative of f(x) with respect to x and g(x), and the product of f(x) with the derivative of g(x) with respect to x.

2. To compute h'(x), we apply the product rule, which states that for functions u(x) and v(x), the derivative of their product is given by u'(x)v(x) + u(x)v'(x). Applying this rule to h(x) = f(x)g(x), we have:

h'(x) = f'(x)g(x) + f(x)g'(x).

First, let's find f'(x) and g'(x):

f'(x) = d/dx(-3x^2 + 4x - 1) = -6x + 4,

g'(x) = d/dx(-x^2 + 4x + 3) = -2x + 4.

3. Now, substituting these derivatives and the given functions into the derivative expression for h'(x):

h'(x) = (-6x + 4)(-x^2 + 4x + 3) + (-3x^2 + 4x - 1)(-2x + 4).

4. To find h'(4), we substitute x = 4 into the derivative expression:

h'(4) = (-6(4) + 4)(-(4)^2 + 4(4) + 3) + (-3(4)^2 + 4(4) - 1)(-2(4) + 4).

Simplifying this expression will yield the numerical value of h'(4), which represents the slope of the tangent line to the function h(x) at x = 4.

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Complete question is;

If Pablo invests $4200 for 3 years and earns $630

A) what is the simple interest rate?

B) Pablo’s goal is to have $5000 after 4 years. Is it possible with a rate of 6%? Explain.

Answer:

A) Rate = 5%

B) Yes, it is possible for him to earn $5000 after 4 years with an interest rate of 6%

Step-by-step explanation:

A) Formula for interest is;

i = PRT

We are given;

i = 630

P = 4200

T = 3

Making R the subject;

R = i/PT

R = 630/(4200 × 3)

R = 0.05

This is 5%

B) Formula for value of principal after interest period is;

A = P(1 + RT)

P = 4200

R = 6% = 0.06

T = 4 years

Thus;

A = 4200(1 + (0.06 × 4))

A = $5208

Thus, it is possible for him to earn $5000 after 4 years with an interest rate of 6%

We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,(\(H_{0}\)):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,(\(H_{A}\)) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ \(\sqrt{p'(1-p')/n}\) ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ \(\sqrt{0.231( 1- 0.231)/ 273}\)

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

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To determine if the yearbook photo is a dilation of the original photo, we need to compare the dimensions and check if there is a consistent scaling factor between the two.

Original photo dimensions: 4 inches by 6 inches.

Yearbook photo dimensions: 6 2/3 inches by 10 inches.

To check if it's a dilation, we can compare the ratios of corresponding sides:

Ratio of width:

Yearbook photo width / Original photo width = (6 2/3) / 4 = (20/3) / (12/3) = 20/12 = 5/3

Ratio of height:

Yearbook photo height / Original photo height = 10 / 6 = 5/3

The ratios of the corresponding sides are equal, with both being 5/3. This indicates that there is a consistent scaling factor of 5/3 between the original photo and the yearbook photo.

Therefore, the yearbook photo is indeed a dilation of the original photo, and the scale factor is 5/3. This means that each dimension of the yearbook photo is 5/3 times the corresponding dimension of the original photo.

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Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Since it involves decimal values, this is a continuous random variable.

In this problem, the time assumes decimal values, hence it is a continuous random variable.

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Answer:

Suppose you travel a distance of 100 miles, and it takes 1 1/2 hours to do it. Your average speed is then 100 miles divided by 1.5 hours which equals 66.67 miles per hour.

Step-by-step explanation:

Answer:

for a half an hour the car travels 13.75 miles

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Inequalities are used to show the relationship between unequal expressions.

The inequalities that represent the maximum weights are:

Let the maximum weight be represented with x

In inequality, maximum means less than or equal to i.e. \(\le\)

(a) 2 axles

The maximum weight, here is 40000.

So, the inequality is:

\(x \le 40000\)

(b) 3 axles

The maximum weight, here is 60000.

So, the inequality is:

\(x \le 60000\)

(c) 4 axles

The maximum weight, here is 80000.

So, the inequality is:

\(x \le 80000\)

See attachment for the graphs of each inequality

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Answer:

95 people ate pizza

Step-by-step explanation:

Add the ones highlighted

To solve the improper integral, we can use integration by substitution. First, we will substitute

Given the improper integral `∫(1 - dx)/(1 + x^2)`

`x = tanθ` and then solve the integral.

When `x = tanθ`, we have `dx = sec^2θ dθ`.

Substituting the values, we get:

`∫(1 - dx)/(1 + x^2)` becomes `∫(1 - sec^2θ dθ)/(1 + tan^2θ)`

Let us simplify the equation.

We know that `1 + tan^2θ = sec^2θ`.

Thus, the integral `∫(1 - dx)/(1 + x^2)` becomes

`∫(1 - sec^2θ dθ)/sec^2θ`

We can write this as: `∫(cos^2θ - 1)dθ`

Now, we have to solve this integral.

We know that `∫cos^2θdθ = (1/2)θ + (1/4)sin2θ + C`.

Thus,

`∫(cos^2θ - 1)dθ = ∫cos^2θdθ - ∫dθ

= (1/2)θ + (1/4)sin2θ - θ

= (1/2)θ - (1/4)sin2θ + C`

Now, we need to substitute the values of `x`.

We have `x = tanθ`.

Thus, `tanθ = x`.

Using Pythagoras theorem, we can say that

`1 + tan^2θ = 1 + x^2 = sec^2θ`.

Thus, we can write `θ = tan^(-1)x`.

Now, we can substitute the values of `θ` in the equation we found earlier.

`∫(cos^2θ - 1)dθ = (1/2)θ - (1/4)sin2θ + C`

= `(1/2)tan^(-1)x - (1/4)sin2(tan^(-1)x) + C`

Hence, the solution to the given improper integral `∫(1 - dx)/(1 + x^2)` is `(1/2)tan^(-1)x - (1/4)sin2(tan^(-1)x) + C`.

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The improper integral ∫(1 - dx) / (1 + x²) evaluates to C, where C is the constant of integration.

An improper integral is a type of integral where one or both of the limits of integration are infinite or where the integrand becomes unbounded or undefined within the interval of integration. Improper integrals are used to evaluate the area under a curve or to calculate the value of certain mathematical functions that cannot be expressed as a standard definite integral.

To evaluate the improper integral ∫(1 - dx) / (1 + x²), we can follow these steps:

Step 1: Identify the type of improper integral:

The given integral has an unbounded interval of integration (-∞ to +∞), so it is a type of improper integral known as an improper integral of the second kind.

Step 2: Split the integral into two parts:

Since the interval of integration is unbounded, we can split the integral into two separate integrals as follows:

∫(1 - dx) / (1 + x²) = ∫(1 / (1 + x²)) dx - ∫(1 / (1 + x²)) dx

Step 3: Evaluate each integral:

We will evaluate each integral separately.

For the first integral:

∫(1 / (1 + x²)) dx

This is a familiar integral that can be evaluated using the arctan function:

∫(1 / (1 + x²)) dx = arctan(x) + C₁

For the second integral:

-∫(1 / (1 + x²)) dx

Since this integral has the same integrand as the first integral but with a negative sign, we can simply negate the result:

-∫(1 / (1 + x²)) dx = -arctan(x) + C₂

Step 4: Combine the results:

Putting the results of the individual integrals together, we have:

∫(1 - dx) / (1 + x²) = (arctan(x) - arctan(x)) + C

= 0 + C

= C

Therefore, the value of the improper integral is C, where C is the constant of integration.

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Answer:

15

Step-by-step explanation:

This was quite easy.

Distribute the 7

f(1)=(14-7)+8

Simplify

f(1)=7+8

f(1)=15

\(\to \bold{f(1) = 7(2-1) +8}\\\\\)

            \(\bold{= 7(1) +8}\\\\\bold{= 7 +8}\\\\\bold{= 15}\\\\\)

The final answer is "15"

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The probability that the mean run time for the 40 runners is between 141 and 143 minutes is approximately 0.4394

Probability is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

Mean is a measure of central tendency that represents the average value of a set of numbers.

According to the given information :

Using the Central Limit Theorem, we know that the sample mean follows a normal distribution with a mean of 142 and standard deviation of 8/√40 = 1.2649. To find the probability that X is between 141 and 143, we standardize the values:

z1 = (141 - 142) / 1.2649 = -0.7925

z2 = (143 - 142) / 1.2649 = 0.7925

Using a standard normal table or calculator, we can find the area between -0.7925 and 0.7925 to be 0.4394. Therefore, the probability that the mean run time for the 40 runners is between 141 and 143 minutes is approximately 0.4394.

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The scenario described expressed as an inequality could be written thus :

The problem could be written thus :

The inequality expression :

Divide both sides by 63 to isolate m

This means that, David will need to save $63 for 5 months in other to be able to afford his birthday cost.

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The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

We have,

\(u = sin^{-1)}(2x)\)

dv = 4 dx

Taking the derivative of u, we get:

du/dx = 1 / √(1 - (2x)²)

Integrating dv, we get:

v = ∫4 dx = 4x

Now, applying the integration by parts formula:

∫4 \(sin^{-1}(2x) dx\) = uv - ∫vdu

Plugging in the values, we have:

∫4 \(sin^{-})(2x) dx = sin^{-1}(2x) \times\) 4x - ∫(4x / √(1 - (2x)²)) dx

At this point, we need to evaluate the integral on the right side.

Let's perform a substitution to simplify it:

Let u = 1 - (2x)²

Differentiating u with respect to x, we get:

du/dx = -4(2x) = -8x

Solving for dx, we have:

dx = -du / (8x)

Substituting these values, the integral becomes:

∫(4x / √(1 - (2x)²)) dx = ∫(-4x / (8x x √u)) (-du / (8x))

Simplifying, we get:

∫(4x / √(1 - (2x)²)) dx = ∫(-1 / (2√u)) du

= -∫(1 / (2√u)) du

= -√u + C

Substituting back the value of u, we have:

∫(4x / √(1 - (2x)²)) dx = -√(1 - (2x)²) + C

Therefore,

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

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The complete question:

a) Evaluate the integral ∫4 sin^(-1)(2x) dx using integration by parts.