Find the distance between a point (–7, –19) and a horizontal line at y = 3. Question 18 options: A) 13 B) 22 C) –16 D) 16

Answer:

Below

Step-by-step explanation:

Using the proprtionality relation:

● 8/10 =5/x

● (4*2)/(5*2) = 5/x

Simplify using 2

● 4/5 = 5/x

Multiply both sides by 5

● (4/5)*5 = (5/x)*5

● 4 = 25/x

Switch x and 4

● x= 25/4

■■■■■■■■■■■■■■■■■■■■■■■■■

Again use the proportionality relation but this time with y.

● 8/10 =7/y

8/10 = 4/5

● 4/5 = 7/y

Multiply both sides by 5

● (4/5)*5 =(7/y)*5

● 4 = 35/y

Switch 4 and y

● y = 35/4

Answer:  A.   A=(1000-2w)*w      B. 250 feet

C.  125 000 square feet

Step-by-step explanation:

The area of rectangular is A=l*w    (1)

From another hand the length of the fence is 2*w+l=1000        (2)

L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.

Express l from (2):

l=1000-2w

Substitude l in (1) by 1000-2w

A=(1000-2w)*w        (3)   ( Part A. is done !)

Part B.

To find the width w  (Wmax) that corresponds to max of area A   we have to dind the roots of equation (1000-2w)w=0  ( we get it from (3))

w1=0  1000-2*w2=0

w2=500

Wmax= (w1+w2)/2=(0+500)/2=250 feet

The width that maximize area A is Wmax=250 feet

Part C.   Using (3) and the value of Wmax=250 we can write the following:

A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets

The unit cost of Brand B is less than Brand A, Evelyn for shop for Brand B.

Unit price is the price of one(unit) quantity of any substance.

The Brand A detergent costs $54 for 6 loads of laundry

Brand B detergent costs $63 for 9 loads of laundry

The unit price of both the detergent has to be compared to find the best among both

Unit cost for Brand A = 54/6 = $9

1 load of Brand A costs $9

Unit cost of Brand B = $63/9 = $7

1 load of Brand B costs $7

As, the unit cost of Brand B is less than Brand A, Evelyn for shop for Brand B.

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Answer:

[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

Step-by-step explanation:

Hello,

"Find the sum of the following infinite geometric series"

infinite

   We will have to find the limit of something when n tends to [tex]+\infty[/tex]

geometric series

   This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.

The sum is something like

           [tex]\displaystyle \sum_{k=0}^{+\infty} a_k[/tex]

First of all, we need to find an expression for [tex]a_k[/tex]

First term is

   [tex]a_0=7[/tex]

Second term is

    [tex]a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}[/tex]

Then

   [tex]a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}[/tex]

and...

   [tex]a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}[/tex]

Ok we are good, we can express any term for k integer

   [tex]a_k=a_0\cdot (\dfrac{4}{9})^k[/tex]

So, for n positive integer

[tex]\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}][/tex]

And the limit of that expression when n tends to [tex]+\infty[/tex] is

   [tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

as

   [tex]\dfrac{4}{9}<1[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

43\ 12 , 35/ 6

Step-by-step explanation:

43\ 12 , 35/ 6

Answer:  B: (3, -7)

Step-by-step explanation:

4x + 4y = -9

         y = 2x - 13

Use Substitution:

4x + 4(2x - 13) = -9

4x + 8x - 52 = -9

       12x - 52 = -9

               12x = 43

                   [tex]x=\dfrac{43}{12}[/tex]

None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.

Plan B: Input the choices into the equation to see which one makes a true statement.

               4x + 4y = -9

A) (x, y) = (-3, -7)

               4(-3) + 4(-7) = -9

                -12   +   -28 = -9

                             -40 ≠ -9

B) (x, y) = (3, -7)

               4(3) + 4(-7) = -9

                12   +   -28 = -9

                             -16 ≠ -9

C) (x, y) = (3, 7)

               4(3) + 4(7) = -9

                12   +   28 = -9

                            40 ≠ -9

D) (x, y) = (-3, 7)

               4(-3) + 4(7) = -9

                -12   +   28 = -9

                              16 ≠ -9

Obviously there is something wrong with the first equation because none of the options provide a true statement.

               y = 2x - 13

A) (x, y) = (-3, -7)

               -7 = 2(-3) - 13

               -7  = -6    -13

                -7 ≠ -19

B) (x, y) = (3, -7)

               -7 = 2(3) - 13

               -7  = 6    -13

                -7 = -7                   this works!!!

C) (x, y) = (3, 7)

               7 = 2(3) - 13

               7  = 6    -13

                7 ≠ -7

D) (x, y) = (-3, 7)

               7 = 2(-3) - 13

               7  = -6    -13

                7 ≠ -19

Option B is the only one that provides a true statement so this must be the answer.

Answer:

[tex]y = kx[/tex]

Step-by-step explanation:

y is directly proportional to x.

[tex]y \propto x[/tex]

[tex]y = kx[/tex]

Where k is as the constant of proportionality.

Answer:

y = kx

Step-by-step explanation:

Y is directly proportional to x which means that

=> y ∝ x

=> y = kx

Where k is the constant of proportionality.

Answer:

4x^2 + 5x^2 + 4xy

Explanation

You need 2 like terms this could be of the form:

ax^2 + bx^2 + c

1 term with a coefficient of 5, sub in b = 5

ax^2 + 5x^2 + c

1 term with 3 factors, c = 4xy

This would mean it has a factor of 4,x and y.

So final equation is (a could be any value I give it a value of 4 for convenience)

4x^2 + 5x^2 + 4xy

Step-by-step explanation:

Answer:

upper box is 0

middle box is 3 and

the downer box is 6

Step-by-step explanation:

Have a nice day

Answer:

x = 4

Step-by-step explanation:

x - 6 = -2

Add 6 to each side

x-6+6 = -2+6

x = 4

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

[tex]x - 6 = -2[/tex]

Add 6 on both sides of the equation. The [tex]x[/tex] variable should be isolated on one side.

[tex]x - 6 +6= -2+6[/tex]

[tex]x=4[/tex]

The value of [tex]x[/tex] is 4.

Answer:

50 mph

Step-by-step explanation:

The total distance is 350 miles.

The total time is 3 hr + (240 mi / 60 mph) = 7 hr.

The average speed is 350 mi / 7 hr = 50 mph.

Answer:

[tex]\large \boxed{\sf \ \ (-5,0) \ and \ (4,0) \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to find the zeroes of

[tex]-0.25x^2-0.25x+5=0\\\\\text{*** multiply by -4 ***} \\ \\x^2+x-20=0\\\\\text{*** the sum of the zeroes is -1 and the product -20=-5x4 ***}\\\\x^2+5x-4x-20=x(x+5)-4(x+5)=(x+5)(x-4)=0\\\\x=4 \ or \ x=-5[/tex]

and then g(4)=0 and g(-5)=0

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:(-5,0) (4,0)

I took the test hope it helps you (:

Answer:

a)d = 180,91 m

b)t = 11,76 seg

Step-by-step explanation:

Para el lanzamiento de proyectil, la ecuación que nos da la velocidad en V(y) es:

V(y)  = Voy - g*t

en donde Voy = Vo * senα    ( donde Vo es la velocidad inicial, α el angulo del disparo.

Si en esta ecuación hacemos V(y) = 0 estamos en el punto donde el componente en el eje y de la velocidad del proyectil es cero, ese punto es el punto medio del recorrido.

0 =  Vo*sen 60⁰     - g*t

g*t  =  Vo* √3/2

t  = { 32 [m/s] * √3 }2*9,8 [m/s²]

t = 16*√3  / 9,8

t = 2,8278 seg

El tiempo total del primer recorrido es entonces por simetría

t₁ = 2 * 2,8278           t₁  = 5,6556 seg

La distancia del primer impacto al suelo es:

x = Vox * t₁                        ( Vox es constante   Vx = Vo*cos 60⁰ )

x  =  32 * (1/2) * 5,6556

x₁  =  90,49 m

Aplicando los mismos criterios ahora para el segundo bote

Ahora Vo = 32 -  32*(1/4)

V = 24 m/s

g*t  =  24 * sen 50⁰

t =  24* 0,7660/ 9,8  

t =  1,8759

2*t  = 2*1,8759

t₂  = 3,7518 seg

x₂  =  Vox * t₂

x₂  =  24* 0,6428*3,7518

x₂  =  57,88 m

Y para el tercer bote Vo =  24 - 24(1/4)        Vo = 18 m/s     α = 40⁰

t = 18 *0,6428/9,8

t  = 1,18

2t  = t₃  = 2*1,18

t₃ = 2,36 seg

x₃  = Vox * 2,36                Vox = Vo*cos 40      Vox = 18*0,7660  

Vox = 13,79

x₃  = 13,79*2,36

x₃  = 32,54 m

La distancia total será

d = x₁  + x₂ + x₃

d  =  90,49  + 57,88 + 32,54

d = 180,91 m

y el tiempo total será la suma de los tiempos

t =  t₁  +  t₂  +  t₃

t  = 5,65 + 3,75 + 2,36

t = 11,76 seg

Answer:

0.3110

Step-by-step explanation:

This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.

The general formula for a binomial distribution is:

[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]

Where n is the sample size and k is the desired number of successes.

The probability of k=2 in a sample of n =6 is:

[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]

The probability is 0.3110

Answer:

a) How long will it take to repay the loan?

20 years

b) What amount of interest does the purchase pay?

$134,896

Step-by-step explanation:

a) How long will it take to repay the loan?

In the above question, they are asking you for the Loan duration

The Formula for Loan duration(T) =

ln (- m/(r÷n) × C - m)/In (1 + r/n)

Where:

m = monthly payments = $1395.40

C = Amount of mortgage =$200,000

r = Interest rate = 5.7% = 0.57

n = compounded quarterly = 4

T = ln (- 1395.40/(0.57÷4) × 200,000 - 1395.40)/In (1 + 0.57/4)

T = 20 years.

Therefore, it will take 20 years to repay the Loan.

b) What amount of interest does the purchase pay?

The total number of payments =

Loan duration × Number of months

Number of months = 12 months( because it is monthly payment)

Loan duration = 20 years

Total number of payments = 240 payments.

In the question, we are given the amount paid monthly payment as

$1,395.40

Total amount paid = Monthly payments × Total number of payments

= $1,395.40 × 240

= $334,896

The amount of Interest the purchase pay = $334,896 - $200,000

= $134,896

Answer: C

Step-by-step explanation:

For system of equations, the solution is the point or points where the equations intersect. The point they meet signifies that they are the same at the x and y point.

Looking at the graph, we see 2 intersection points. They are (0,-8) and (4,8). Therefore, C is the correct answer.

Answer:

The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.

Step-by-step explanation:

68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years

So, the ages lies between x₀ + σ and x₀ - σ

So, the ages lie between 58 - 8.25 = 49.75 years

and 58 + 8.25 = 66.25 years

So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.

Answer:

[tex]\huge\boxed{(6;\ -31)}[/tex]

Step-by-step explanation:

Let: [tex]f(x)=ax^2+bx+c[/tex].

The coordinates of the vertex:

[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]

We have

[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]

Substitute:

[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]

The vertex form of an equation of a quadratic function:

[tex]f(x)=a(x-h)^2+k[/tex]

We have:

[tex]f(x)=x^2-12x+5\to a=1[/tex]

Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]

Answer:

( P -2w) /2 = l

Step-by-step explanation:

P= 2W + 2l

Subtract 2W from each side

P= 2W -2W + 2l

P -2W = 2l

Divide by 2

( P -2w) /2 = l

Answer:

A. [tex]\frac{P - 2w}{2} = l[/tex]

Step-by-step explanation:

Well in,

P = 2w + 2l

to solve for l we need to single it out.

P = 2w + 2l

-2w

P - 2w = 2l

divide everything by 2

[tex]\frac{P - 2w}{2} = l[/tex]

Thus,

the answer is A.

Hope this helps :)

Answer:

70.59 feet

Step-by-step explanation:

There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.

1. Divide 76 by 14

76 ÷ 14 = 5.43

2. Multiply the longer length of 13 parts

5.43 · 13 = 70.59

The longer length of the wire 70.59 feet

There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.

1. Divide 76 by 14

76 ÷ 14 = 5.43

2. Multiply the longer length of 13 parts

5.43 · 13 = 70.59

In algebra, a decimal number can be defined as a range whose entire number part and the fractional element are separated by means of a decimal point. The dot in a decimal range is referred to as a decimal point. The digits following the decimal factor show a price smaller than one.

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Answer:

Step-by-step explanation:

To identify the null hypothesis, the null hypothesis is the default statement while the alternative hypothesis is the opposite of the null and always tested against the null hypothesis.

The alternative hypothesis depending on the case study can give rise to a one-tailed or a two-tailed test. The one tailed test includes either less than or greater than option and not both while the two tailed test involves both.

In this case study,

the null hypothesis is u1 (representing the city in particular) = u2 (representing other cities)

The alternative hypothesis is u1 (representing the city in particular) =/ u2 (representing other cities).

This, this test due to its not equal to sign is a two tailed test, the two results might differ maybe with one higher than the other, or lower than the other.

Answer:  800 feet²

Step-by-step explanation:

Lets remove the brackets from the function's expression

A(x) = -2x²+80x

So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max

As we know Xmax= (X1+X2)/2 , where X1 and X2 are the roots of the function A(x)

Lets find X1 and X2

x(80-2x)=0

x1=0   80-2*X2=0

x2=40

So Xmax= (0+40)/2=20

So Amax= A(20)= 20*(80-2*20)=20*40=800 feet²

Answer:

[tex]d \approx 5.8[/tex]

Step-by-step explanation:

Just use the distance formula.

[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]

[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]

[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]

[tex]d=\sqrt{9+25}[/tex]

[tex]d=\sqrt{34[/tex]

[tex]d \approx 5.8[/tex]

Answer:

18.9 units of fencing

Step-by-step explanation:

First find the perimeter

P = 2(l+w)

P = 2( 2.5+1.28)

P = 2( 3.78)

P =7.56m

We need 2.5 units of fencing for each meter

Multiply by 2.5

7.56*2.5

18.9 units of fencing

Answer:

Julio needs to purchase 18.9 units of fencing.

Step-by-step explanation:

I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.

As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.

2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.

Hey there! I'm happy to help!

First, let's find the area of the two circles that make up the top and bottom of the cylinder. To find the area of a circle, you square the radius multiply it by pi (we will use 3.14)

15.8²=249.64

249.64×3.14=783.8696

Since there are two of these circles we multiply this by 2.

783.8696×2=1567.7392

Now, for the rectangle. To make a cylinder, you take a rectangle and wrap it around the top and bottom circles. One side of this rectangle is the height of the cylinder, and the other is the circumference of the circle (one side wraps all the way around the circle, which is the circumference).

The circumference is the diameter multiplied by 3.14 (pi). The diameter is twice the radius.

15.8×2=31.6

31.6×3.14=99.224

We multiply this by the height.

99.224×4.4=436.5856

Now, we add the areas of the circles and the rectangle.

1567.7392+436.5856=2004.3 (rounded to nearest tenth)

This is closest to D. 2005.3 ft². It is probably a bit off because I used 3.14 instead of actual pi.

Have a wonderful day! :D

Answer: $68.4

Step-by-step explanation:

Given: Annual Premium = $110

Average insurance payout = $1600

Likelihood of having an accident= 2.6% = 0.026 [we divide perecnt by 100 to convert it into decimal]

Then, Expected value = (Annual Premium) - (Likelihood of having an accident) x (Average insurance payout )

= $110  - (0.026) x ($1600)

= $(110-41.6)

= $68.4

Hence, the company's expected value of this insurance policy : $68.4

A total of 32/3 strips can be derived from the ribbon.

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Here, we have,

to determine the number of strips:

From the question, we have the following parameters

Length of a roll of ribbon = 4 meters

Also, from the question;

We have

Length of a piece of ribbon = 5/12 meter

The number of strips of ribbon is the quotient of the Length of a roll of ribbon and the Length of a piece of ribbon

This is represented as

Number of strips = Length of a roll of ribbon/Length of a piece of ribbon

So, we have

Number of strips = (4 )/(5/12)

Evaluate the quotient

Number of strips = 32/3

Hence, the number of strips is 32/3

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complete question:

How many strips of a ribbon can be cut from a roll of ribbon that is 4 4/9 meters long if each piece is 5/12 meters long

Answer:

Linear

The 500 hundred gallons is adding up by the hours. Linear- first difference.

Answer:

Yes, because the four points in the upper right corner from the same pattern as the four points in the lower left corner.

Step-by-step explanation:

The correlation coefficient for the points in the lower left corner equals zero.

The four points in the upper right corner have the same correlation coefficient because the four points in the upper right corner from the same pattern as the four points in the lower left corner.

Answer:

The overall shape of the data

Step-by-step explanation:

For us to know what shape a data is, it must fulfil 4 conditions

From the question, Ralph observed that the classmates time are symmetrical along the x-axis.

Therefore he is observing the shape of the data since one of the conditions have been fulfilled.

Thank you!