What 2 numbers have a difference of 8

Answer:

what population census

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Shawn should use the point-slope formula ⇒ y - y₁ = m(x - x₁) and the y-intercept is -12.

We already know that the point-slope formula goes as such -

⇒ y - y₁ = m(x - x₁)

We have also been told that the slope of the line is 4 and the line passes through the point (1,-8). So, point (1,-8) = (x₁ , y₁) and the slope, m = 4.

Using the given values and the formula of point-slope, we get -

⇒ y - (-8) = 4(x - 1)

⇒ y + 8 = 4x - 4

⇒ 4x - y = -12

⇒ y = 4x - 12

This is the equation of the line.

From this, we get the y-intercept = -12

The complete question that you might be looking for is given below -

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept, and what is the y-intercept of the line?

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The distance between the given points (2, -2) and (-4, -7) is √61 units

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:

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

The distance between the given points (2, -2) and (-4, -7) is:

\(Distance=\sqrt{(-7-(-2))^2+(-4-2)^2}=\sqrt{25+36}=\sqrt{61}\)

The distance between the given points (2, -2) and (-4, -7) is √61 units

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Answer:

y = -2x+7

Step-by-step explanation:

equation of line formula:

\(y = mx + c\)

m = slope, c = y-intercept

1) find the slope using the given coordinates

slope formula:

\( \frac{y2 - y1}{x2 - x1} \)

i) (3,1)

x1=3

y1=1

ii) (7,-7)

x2=7

y2=-7

substitute the values into the formula

\(m = \frac{ - 7 - 1}{7 - 3} \)

\(m = \frac{ - 8}{4} \)

\(m = - 2\)

so now half of the equation is complete as we have the the value of m. substitute the value of m into the slope formula.

\(y = - 2x + c\)

2) find the value of c

to find the value of c, we must substitute either coordinate into the half equation. so, i choose the coordinate (3,1). if you substitute the coordinate (7,-7) , you will get the same value of c.

(3,1)

x = 3

y = 1

\(y = - 2x + c\)

\(1 = - 2(3) + c\)

\(1 = - 6 + c\)

\(1 + 6 = c\)

\(c = 7\)

substitute the value of c into the half equation and that is your straight line equation

\(y = - 2x + 7\)

Answer:

Step-by-step explanation:

Answer:

\(m_{perpendicular}\) = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

Answer:

the answer is A

Step-by-step explanation:

be my friend please

Step-by-step explanation:

Frequency of a mass-spring system is:

f = √(k/m) / (2π)

Given f = 2/π Hz and m = 20 kg:

2/π Hz = √(k / 20 kg) / (2π)

4 Hz = √(k / 20 kg)

16 s⁻² = k / 20 kg

k = 320 kg/s²

k = 320 N/m

If the 20 kg mass is replaced with an 80 kg mass, the frequency is:

f = √(320 kg/s² / 80 kg) / (2π)

f = √(4 s⁻²) / (2π)

f = 2 Hz / (2π)

f = 1/π Hz

The sprint constant is 320 N/m

And, the frequency is \(1\div \pi Hz\)

Since A 20-kilogram mass is attached to a spring. And, the frequency of simple harmonic motion is 2/p cycles/s.

Now we know that

\(f = \sqrt (k\div m) \div (2\pi)\)

Here

\(f = 2\div \pi Hz\)

and m = 20 kg:

So,

\(2\div \pi Hz = \sqrt (k \div 20 kg) / (2\pi)\\\\4 Hz = \sqrt(k \div 20 kg)\\\\16 s^{-2} = k \div 20 kg\)

k = 320 kg/s²

k = 320 N/m

Now the frequency is:

\(f = \sqrt(320 kg/s^2 \div 80 kg) \div (2\pi)\\\\f = √(4 s^{-2}) \div (2\pi )\\\\f = 2 Hz \div (2\pi)\)

\(f = 1\div \pi Hz\)

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Answer:

x = 3

Step-by-step explanation:

x^5 = 243

Take the fifth root of each side which is the same as raising each side to th 1/5 power. Also, 243 = 3^5.

x^5 = 3^5

(x^5)^(1/5) = (3^5)^(1/5)

x = 3

Answer:

3

Step-by-step explanation:

x^5= 243

I guess we're looking for x

so what we do is just find the fifth root of 243

and that's 3

The equation in vertex for the parabola for y in terms of x is y = -0.009(x - 75)² + 55

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

Vertex = (75, 55)

Point = (100, 49.375)

The equation in vertex form for a parabola is represented as

y = a(x - h)² + k

Where

Vertex (h, k) = (75, 55)

Point (x, y) = (100, 49.375)

So, we have

y = a(x - 75)² + 55

Substitute (x, y) = (100, 49.375) in y = a(x - 75)² + 55

49.375 = a(100 - 75)² + 55

So, we have

625a = -5.625

Divide by 625

a = -0.009

Substitute a = -0.009 in y = a(x - 75)² + 55

y = -0.009(x - 75)² + 55

Hence, the equation is y = -0.009(x - 75)² + 55

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Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.

The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.

Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.

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Thus after 12 minutes concentration of drug is 0.045.

The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula \(c(t) = 0.05(1-e^{-0.2t} )\)

Drug concentration is amongst the most important determinants of clinical response to a drug.

Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.

Thus after 12 minutes concentration of the drug is = C(5).

Now

C(5) = \(0.05(1-e^{-0.2t} )\)

= \(0.05(1-e^{-2.4} )\)

= 0.05(1-0.0907)

= 0.05×0.9093

= 0.045

The drug concentration is 0.045.

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A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is

f(x) = x(x - 1)(x + 4)(x - 6).

Given:

x₁ = 1

x₂ = -4

x₃ = 0

x₄ = 6

Utilize the fact that x - b is a factor of the polynomial if b is a root.

Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.

The polynomial is,

f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)

f(x) =  (x - 1)(x - (-4))(x - 0)(x - 6)

     = (x - 1)(x + 4(x)(x - 6)

Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).

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Answer: k=11

Step-by-step explanation:

Answer:

Step-by-step explanation:

A=1/2 a p                 a is apothem;  p is perimeter of base

p=22*5 =110

a you need to find by making a triangle with the radius and finding the angle of the right triangle

All external angles of any polygon =360

divide by 5 and then 2 to find triangle

=54

Use tan 54 = a/11

a=15.14

A= 1/2 *15.14 *54

408.8

Answer:

The answer is 24

Step-by-step explanation:

(5x4) the first part 5x4 is 20 so then (1x4) the second part 1x4 is 4 so when you add 20 + 4 it will be 24.

Answer:

20 + 4

Step-by-step explanation:

Evaluate in the parenthesis first.

5 x 4 = 20

1 x 4 = 4

bring them down

20 + 4

Keep the plus sign.

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

#3 maybe be wrong, sorry if it is

Answer:

  (c)  (6, -3)

Step-by-step explanation:

Reflection over both axes is the same as reflection across the origin, or rotation 180° about the origin. It has the effect of negating both coordinates:

  (x, y) ⇒ (-x, -y) . . . . . reflection over both axes

The coordinates of A are (-6, 3), so the coordinates of A' will be ...

  A(-6, 3) ⇒ A'(6, -3)

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

or was it 11??

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

Step-by-step explanation:

A) = (35,?)

B) = POSITIVE

C) = 601

Answer:

Step-by-step explanation:

We need to know what converse of a statement means to solve the problem. The converse of the given statement is, if a=bc then a/b=c.

The converse of a conditional statement is created by exchanging the condition and the result. If a statement is p--->q then the converse of the statement is q--->p. In the given question we have been given the condition as a/b=c and the result if the condition satisfies is a=bc. To find the converse of this statement we need to make the result, the condition and the condition will be the new result. So the condition for converse will be a=bc and the result if the condition satisfies will be a/b=c.

Therefore the converse of the given statement is, if a=bc then a/b=c.

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