plsssssszz answerrrrrr

Approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.

The perpendicular line to a point is the path that travels the shortest distance between them.

The equation for the indicated line is -x + 2y = 14, which can be expressed as the following in slope and intercept form:

The y-intercept is 7, and the slope, m1, is 1/2.

Consequently, the line's equation is:

Therefore, the coordinates of the point on line A(-1/4, 5) that coincides with the perpendicular from the line -x + 2y = 14 (y = x/2 + 7) are as follows:

The location on the line -x + 2y = 14 (y = x/2 + 7) that is perpendicular to the point A(-1/4, 5) has the coordinates: (-1, 6.5)

The following formula is used to calculate the distance between points A and B:

Where: (x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)

Using the values as plug-ins, we have;

[tex]\begin{aligned}&I_{A B}=\sqrt{(6.5-5)^2+((-1)-(-1 / 4))^2}=\sqrt{(-0.75)^2+(1.5)^2}=\sqrt{\frac{45}{16}}=\frac{3}{4} \cdot \sqrt{5} \\&l_{A B}=\frac{3}{4} \cdot \sqrt{5} \approx 1.677\end{aligned}[/tex]

Therefore, approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.

Know more about lines here:

https://brainly.com/question/18831322

#SPJ9

Thunder from a bolt of lightning can travel 1/5 miles in one second.

Given, distance = 1/10 mile and

time = 1/2 second .

we need to find distance travelled in one second.

The distance travelled by thunder bolt from lightning in one second can be calculated using unitary method. So, to calculate we will relate the known distance with given time. Further, we will compare it at with desired time.

So, distance travelled in 1/2 second = 1/10 mile

Hence, distance travelled in 1 second = 1/10 ₊ 1/10

Shifting 2 to the numerator and 10 to the denominator. The new fraction will be -

Distance travelled in 1 second = 2/10 = 1/5

Distance travelled in 1 second = 1/5 mile

Hence, thunder from a bolt of lightning can travel 1/5 miles in one second.

Learn more about Distance here:

brainly.com/question/4931057

#SPJ9

Using inverse variation, the function model will be y = 48. 1/x and the value of y at x = -5 will be -48/5

Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.

Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.

Inverse variation is y = k. 1/x

given y = 4

x = 12

So, 4 = k. 1/12

So, the value of k = 48

We can conclude that the value of constant variation is 48

when x = -5, the value of y will be -

y = k.1/x

y = 48 . 1/-5

y = -48/5

To learn more about constant and inverse variation from given link

https://brainly.com/question/9404351

#SPJ4

The expression has to be written in it's prime factor form. 27 = 3x3x3 = 3^3 in index form. 3=3^1 . By power rule (a^m)^n = a^mn.

(3^1)^1/4+(3^3)^1/4

3^1/4 + (3^2x3^1)^1/4

3^1/4+3^2/4x3^1/4

3^1/4(1+3^1/2)

Find out more on indices at: brainly.com/question/28595106

#SPJ4

On simplifying the expression √5 x³ . √40 x y⁷ we get 10√2 x⁴y⁷

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

Given,

√5 x³ . √40 x y⁷

⇒ √5 × √40 × x⁴ × y⁷

⇒ √200 × x⁴y⁷

⇒ 10√2 x⁴y⁷

To learn more about multiplication from given link

https://brainly.com/question/4721701

#SPJ4

log (2x) = -1 => x = 0.05, by properties of logarithm.

Given: log (2x) = -1

Raising both sides to 10, in order to remove the logarithm:

=> [tex]10^{log_{10}(2x)} = 10^{-1}[/tex]

=> 2x = [tex]\frac{1}{10}[/tex] ( as [tex]a^{log_a(x)} = x[/tex])

=> x = [tex]\frac{1}{20} =[/tex] 0.05

Hence, log (2x) = -1 => x = 0.05, by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

ln e⁸³ = 83, by definition and properties of logarithm.

Now,

In the question, ln (e)⁸³, a = e

By property of logarithms, [tex]log_b(a)^{m}=m(log_b(a))[/tex],

=> 83 (ln (e)) = 83 [tex]log_e(e)[/tex]

Since, [tex]log_e(e)[/tex] = 1, ln (e)⁸³ = 83 (1) = 83.

Hence, ln e⁸³ = 83, by definition and properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

APR, or effective annual rate, can also be called an effective annual rate or EAR when "r" is the annual interest rate and "n" is the number of compounding periods to be completed each year. :D

Answer: the length is 23 feet     the width is 14 feet

Step-by-step explanation:

Let  the length is x feet

Hence, the width is (x-9) feet

The perimeter of a rectangular pool is:

P=(2)(x+(x-9))

74=(2)*(2x-9)

74=(2)(2x)-(2)(9)

74=4x-18

74+18=4x-18+18

92=4x

(4)(23)=(4)(x)

Divide both parts of the equation by 4:

23 feet=x

23-9=x-9

14 feet=x-9

Answer:

24

Step-by-step explanation:

8 * 12 = 96

96 / 4 = 24

Have a great night! :D

Hope this helps.

The equation of the line that is perpendicular to the given line and that passes through the given points is x + 3y = 6

From the question, we are to determine the equation of the described line.

First,

We will determine the slope of the line that the equation was given.

The equation of the line is

y = 3x - 9

Comparing the equation to the general form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

Thus,

By comparison,

m = 3

That is, the slope of the given line is 3

NOTE: Two lines are perpendicular if the product of their slope is -1.

That is,

m₁ × m₂ = -1

3 × m₂ = -1

m₂ = -1/3

The slope of the line that is perpendicular to the given line is -1/3.

We have that the line passes through the point (3, 1).

Then,

Using the point-slope form of the equation of a line

y - y₁ = m(x - x₁)

m = -1/3

x₁ = 3

y₁ = 1

Then,

y - 1 = -1/3(x - 3)

Multiply through by 3

3(y -1) = -1(x - 3)

3y - 3 = -x + 3

3y + x = 3 + 3

x + 3y = 6

Hence, the equation of the line that is perpendicular to the given line and that passes through the given point is x + 3y = 6

Learn more on Equation of a line here: https://brainly.com/question/11752607

#SPJ1

Answer:

for (a) i got 15

Step-by-step explanation:

AE=17, AB=16 which makes AM=8

so from there u do pythagorean theorem

17^2 - 8^2 = 225

√255= 15

Answer:

26.565⁰

Step-by-step explanation:

Triangles AEM and BEM are congruent since
AE = BE
m∠AME = m∠BME=90°
and EM is the common side

So AM = BM = AB/2 = 16/2 = 8

Triangle EAM is a right triangle with hypotenuse AE = 17 and AM = 8

So EM² = (17² - 8²) by the Pythagorean theorem
EM² = 289 - 64 = 225
EM = √225 = 15 cm

To find m∠ECM, note that triangle ECM is a right triangle with m∠EMC = 90° and the side opposite ∠EMC = EC, the side opposite ∠ECM is EM

By the law of sines

EC/sin90 = EM/sin(∠ECM)

So,

sin(∠ECM) = EM/EC since sin 90 = 1

So we have to compute EC

Again note that the triangle MCB with sides BM, MC and BC is a right triangle with m∠CBM = 90°

The hypotenuse is MC

So MC ² = MB² + BC² = 15² + 30² = 1125

MC = √1125 = 33.54 cm

Therefore
sin(∠ECM) = EM/MC = 15/33.54 = 0.4472

m∠ECM = sin⁻¹ (0.4472)

= 26.565⁰

To be honest I am not 100% sure of this answer, please check and see if this works. Thanks

Possible coordinates for points B  (-3, 13)

Given that

point A (5 , -7)

and there are 8 points between A and B.

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

The equation of a circle centerd in the point (x0, y0) is:

(x - x0)² + (y - y0)² = r²

where r = radius of the circle

So we can draw a circle of 8 units around A, and get:

(X - 5)² + (Y - (-7))² = 8²

So from this equation we can find all the possible values of B.

Y = √(8² - (X- 5)²) - 7

So for a given value of X, you can find the value of Y. where (8² - (X-5)²) can not be a negative number, so

8² ≥ (X - 5)²

So X = -3 (because (-3 - 5)² = 8²)

to X = 13 (because (13 - 5)² = 8²)

So X is in the range (-3, 13)

To learn more about Circle

visit - https://brainly.com/question/17152241

#SPJ9

Cost of 25 pound flour is $30.75.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Price of 3 pound flour = $3.69

She needs 25 pounds of flour to make enough cookies for a bake sale.

Now, Price of 3 pound flour = $3.69

Hence, Cost of 1 pound flour = $3.69 ÷ 3 = $1.23

So, Cost of 25 pound flour = 25 x $1.23

                                          = $30.75

Therefore, Cost of 25 pound flour is $30.75.

Learn more about the multiplication visit:

https://brainly.com/question/24613775

#SPJ1

The period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

A periodic function goes through 5 complete cycles in 4 min

From the question:

f = 5/4 cycles per minutes

f = 5/240 cycles per seconds  [1 minutes = 60 seconds]

f = 1/48

Period = 1/f

Period = 48 minutes

Thus, the period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

The period of the given periodic function is 48 sec.

A periodic function is a function which returns same values at regular intervals. Let f be a periodic function then  

f( x +P ) = f(x) , for every x in the domain of f and P is some non zero constant

P is the regular interval or period after which a periodic function returns same values.

P=[tex]\frac{1}{f}[/tex]

where [tex]f[/tex] is the frequency of the periodic function

or [tex]f[/tex] = no of cycles per unit time

Given that a periodic function goes through 5 cycles in 4 min

therefore frequency for this periodic function , f  is given by

[tex]f=\frac{5}{4}[/tex] cycles per min

or

[tex]f=\frac{5}{4*60} \\f=\frac{5}{240} \\[/tex]

[tex]f=\frac{1}{48}[/tex]   cycles per sec

Thus,

Period of the given periodic function , P =[tex]\frac{1}{f}=1/\frac{1}{48}=48[/tex] sec

Learn more about periodic functions at https://brainly.com/question/9060937

#SPJ1

Let’s solve this step-by-step

First factor the equation,

(9x - 5) (4x - 5) = 0

Then set each factor equal to zero,

9x - 5 = 0 and 4x - 5 = 0

Both x = 5 / 9 or x = 5 / 4 are correct

Answer:

1/4, alternate forms are .25 and 2^-2

Step-by-step explanation:

Square Root of 25 is 5

6-5 =1

1/4

The standard form for the equation of this line is equal to 3A - 4B = 12.

A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

In Mathematics, the standard form of a linear equation is given by the following:

Ax + By = C.

When C = 24, the line passes through point (4, 0) and we have;

Ax + By = C.

4A + B(0) = 24.

4A = 24

A = 24/4

A = 6

When C = 24, the line passes through point (0, -3) and we have;

A(0) + B(-3) = 24

-3B = 24

B = -24/3

B = -8

Therefore, the standard form for the equation of this line is given by:

6A - 8B = 24

Dividing all through by 2, we have:

3A - 4B = 12

Read more on equation of a line here: https://brainly.com/question/18894822

#SPJ1

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage at which the dress was sold from its original price is 28%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The selling price of the dress = $56

The original price of the dress = $200

The percentage at which the dress was sold from its original price.

= 56/200 x 100

= 56/2

= 28 %

Thus,

The percentage at which the dress was sold from its original price is 28%.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office

Given data

Zarah's office is 2 cm wide and 4 cm long

Another office is 8 cm long and 4 cm wide

Area of an office = length * width = long * wide

Area of Zarah's office = 4 cm * 2 cm = 8 cm2

Area of another office = 8 cm * 4 cm = 32 cm2

comparing the two areas

say by how much is 32 cm2 greater than 8 cm2

32 cm2 / 8 cm2 = 4

The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office.

Read more about area calculation here: https://brainly.com/question/25292087

#SPJ1

Answer:

No solution

Step-by-step explanation:

Given equation:

[tex]w+5w+4=3(2w-1)[/tex]

Distribute the parentheses:

[tex]\implies w+5w+4=3 \cdot 2w- 3 \cdot 1[/tex]

[tex]\implies w+5w+4=6w- 3[/tex]

Combine like terms:

[tex]\implies 6w+4=6w-3[/tex]

Add 3 to both sides:

[tex]\implies 6w+4+3=6w-3+3[/tex]

[tex]\implies 6w+7=6w[/tex]

Subtract 6w from both sides:

[tex]\implies 6w+7-6w=6w-6w[/tex]

[tex]\implies 7=0[/tex]

As 7 ≠ 0 there is no solution.

Answer:

8.4

Step-by-step explanation:

7 x .2 is the increase 1.4

Add 1.4 to 7 to get 8.4

Answer:

30

Step-by-step explanation:

Quadratic Formula

Answer:

A. 69 strides per minute

Step-by-step explanation:

In order to find the strides per minute divide 759 by 11

➟ 759/11

➟ 69

∴ Her rate was 69 strides per minute

[tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.

Given: [tex]6^{2x} = 10[/tex]

Taking logarithm on both sides:

=> log ([tex]6^{2x}[/tex]) = log 10

=> 2x (log 6) = log 10 ( as [tex]log_b(a)^m = m (log_b(a))[/tex])

=> 2x = [tex]\frac{log10}{log6}[/tex]

=> 2x = [tex]\frac{1}{0.778}[/tex]

=> 2x = 1.285

=> x = 0.642

Hence, [tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

Answer:

a.

D=[-6,4)

R=(-3,4]

b.

D=[-6,7)

R=[-1,6)

Step-by-step explanation:

[,] <-- used for when the point is included in the answer (closed circle or greater than/less than or equal to sign)

(,) <-- used for when the answer does not include point (open circle or greater than/less than sign   not equal to)

Plug in the points where shown on each line.

Hey again! Just answered your last domain and range question so I hope I helped again!

Answer:

y = 5x + 7

Step-by-step explanation:

I am guessing, but you are leaving something out.

y = the total cost.

x = the number of shirts.

Answer:

The total cost for the 7 shirts including tax is 7n + 6

Step-by-step explanation:

We want to find the Cost of 7 t-shirts and $6 tax.

Now, the let the cost of the 7 shirts be n. Thus, we can now say that cost of 7 shirts is 7n.

Now, since there is an additional cost of $6 for tax, we can now say that the total cost for the 7 shirts including tax is expressed as;

7n + 6

Thus, we conclude that the total cost for the 7 shirts including tax is 7n + 6

Answer:

Step-by-step explanation:

1 1/2 cups = 1.05