What is 71.2×0.58 = ?

Set up a ratio of height over shadow length:

3.2/1.29 = X/39.25

Cross multiply:

1.29x = 3.2 * 39.25

Simplify:

1.29x = 125.6

Divide both sides by 1.29:

x = 97.364 meters

Round to the nearest meter = 97 meters

Answer:

6y + 42

Step-by-step explanation:

Answer: 6y+42

Step-by-step explanation:

When you distribute, you multiply the coefficient by each term in the parenthesis.

6y+42

In an arithmetic sequence, consecutive terms differ by a fixed number d :

[tex]a_8=a_7+d[/tex]

[tex]a_9=a_8+d=a_7+2d[/tex]

[tex]a_{10}=a_9+d=a_7+3d[/tex]

and so on up to

[tex]a_{19}=a_7+12d[/tex]

Solve for d :

[tex]140=32+12d\implies12d=108\implies d=9[/tex]

Work backwards to find the first term in the sequence, and hence the n-th term:

[tex]a_6=a_7-d[/tex]

[tex]a_5=a_6-d=a_7-2d[/tex]

and so on down to

[tex]a_1=a_7-6d[/tex]

So the first term is

[tex]a_1=32-6\cdot9=-22[/tex]

which means the n-th term is

[tex]a_n=a_1+(n-1)d=-22+9(n-1)=9n-31[/tex]

[tex]S_n[/tex] denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:

[tex]\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511[/tex]

Distribute the summation and recall the formulas,

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]

[tex]\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1[/tex]

[tex]\implies511=9\cdot\dfrac{n(n+1)}2-31n[/tex]

[tex]\implies1022=9n^2-53n[/tex]

[tex]\implies9n^2-53n-1022=0[/tex]

[tex]\implies(n-14)(9n+73)=0[/tex]

[tex]\implies n=14\text{ or }n=-\dfrac{73}9[/tex]

n must be a positive integer, so we the sum is obtained from the first n = 14 terms.

Answer:

4 times

Step-by-step explanation:

1 quart is equivalent to 32 fluid ounces.

If each eruption consumes 8 fluid ounces of vinegar. Assuming that the amount of vinegar required per eruption is constant, the number of times Tanvi can make her volcano erupt is:

[tex]n=\frac{32}{8}\\n=4\ times[/tex]

Tanvi can make her volcano erupt 4 times  with 1 quart of vinegar.

Answer:

Step-by-step explanation:

Answer:

(x + 2)

Step-by-step explanation:

When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).

Alternatively, we can use synthetic division or long division to get our answer.

Answer:

x + 2

Step-by-step explanation:

got it right edg '22

Answer:

I think it is either 85 or 51 because the question was not specific

Step-by-step explanation:

I am not entirely sure if you mean Jose changed jobs or added a new job on top but i will do both.

34/2=17

17+34=51

OR

51+34=85

Answer:

51 miles.

Step-by-step explanation:

That would be 34 * 1 1/2

= 34 * 3/2

= 17 * 3

= 51 miles.

Answer:

The length of arc EF is 11.3

Step-by-step explanation:

Since both angles are congruent, we can say that they are equal in value

Mathematically, the length of an arc can be calculated using the formula;

L = theta/360 * 2 * pi * r

where theta is the angle subtended and r is the radius of the circle

So for circle A, we have;

18.08 = theta/360 * 2 * π * 8

theta = (360 * 18.08)/16π

Theta = 406.8/π

Now we shall substitute this angle in the second circle to get its length

L = 406.8/π * 1/360 * 2 * π * 5

L = 406.8/36 = 11.3

Answer:

3/4 teaspoons of pepper

Step-by-step explanation:

1/4 teaspoons : 3 potatoes = x teaspoons : 9 potatoes

(1/4)/3 = x/9

3x = 9 * 1/4

x = 3 * 1/4

x = 3/4

Answer: 3/4 teaspoons of pepper

Answer:

B

step-by-step explanation:

1/4 over 3 p/9

Answer:a

Step-by-step explanation:

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

Answer:

A) 52.5 inches²

Step-by-step explanation:

The equation for the area of a trapezoid is a=1/2h(b1+b2). This basically means that you take the height of the trapezoid, multiply it by the top base plus the bottom base and divide that by 2. When you do this, you take 8.5 plus 6.5, which equals 15, and multiply that by 7 to get 105. After you get this, you divide it by 2 to get 52.5 inches².

Answer:

C = pi * d

Step-by-step explanation:

C = 2 * pi *r

We can replace 2 * r with d since the diameter is twice the radius

C = pi * 2*r

C = pi * d

Answer:

what is your question?

Answer:

28

Step-by-step explanation:

The angle mBFD inscribes the arc mBD, so we have that:

mBFD = mBD/2

76 = mBD/2

mBD = 152°

The angle mBOD is a central angle related to the arc mBD, so we have that:

mBOD = mBD = 152°

In the quadrilateral BODC, the sum of internal angles needs to be equal to 360° (property of all convex quadrilaterals). The angles mCBO and mCDO are right angles, because EDC and ABC are tangents to the circle.

So, we have that:

mBOD + mCDO + mBCD + mCBO = 360

152 + 90 + mBCD + 90 = 360

mBCD = 360 - 90 - 90 - 152

mBCD = 28°

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L has been drawned

3- 45000L / 50 = 900L

.. ..

Answer:

Step-by-step explanation:

Volume of a rectangular solid = l × w × h

where

l is the length

w is the width

h is the height

From the question

l = 12 feet

w = 3 feet

h = 4 feet

Volume = 12 × 3 × 4

= 144 feet

Hope this helps you.

Answer:

V = 3534 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

the radius is 7.5 and the height is 20

V = pi ( 7.5)^2 * 20

V =1125 pi cm^3

Using the pi button for pi

V =3534.291735 cm^3

Rounding to the nearest whole number

V = 3534 cm^3

Answer:

b)3534 cm^3

Step-by-step explanation:

To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.

Answer:

x = -3

Step-by-step explanation:

When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....

x/3 - 1 = -2

x/3 = -1             ( add 1 on both side)

x = -3               (x3 on both side)

A=4[tex]\pi -8[/tex]

that is your answer :-)

Answer:

[tex]A = 4\pi - 8[/tex]

Step-by-step explanation:

ody

Answer:

That is true, but there is no question being asked.

Answer:

The amount to be invested now or the present value is $119,484.51

Step-by-step explanation:

FV=PV(1+r/n)^nt

Make PV the subject of the formula

PV=FV/(1+r/n)^nt

Where,

PV=present value=?

FV=future value=$140,000

r=interest rate=8%

n=number of periods=4

t=time=2 years

PV=FV / (1+r/n)^nt

=140,000 / (1+0.08/4)^4*2

=140,000 / (1+0.02)^8

=140,000 / (1.02)^8

=140,000 / 1.1717

=119,484.5096

Approximately 119,484.51

PV=$119,484.51

The amount to be invested now or the present value is $119,484.51

Answer:

X=1

Step-by-step explanation:

12x-14=-2

    +14 +14

12x=12

x=1

Answer:

x = 1

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 14 to both sides:

12x - 14 = -2

12x - 14 (+14) = -2 (+14)

12x = -2 + 14

12x = 12

Next, divide 12 from both sides:

(12x)/12 = (12)/12

x = 12/12

x = 1

x = 1 is your answer.

~

Answer:

Solve

(15x+y)and 20x+10y

2

Answer:  (0, 0) & (3, √3)

Step-by-step explanation:

Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.

The coordinates of intersection can be determined by solving a system of equations.

Equation 1: y = √x

Equation 2: (x - 2)² + y² = 2²

I will use the Substitution method with Equation 2 to solve for x:

(x - 2)² + (√x)² = 2²        substituted y with √x

x² - 4x + 4 + x = 4           expanded binomial

x² - 3x + 4 = 4                 added like terms

x² - 3x = 0                       subtracted 4 from both sides

x(x - 3) = 0                       factored

x = 0     x - 3 = 0             applied Zero Product Property

            x = 3

Next, solve for y using Equation 1:

x = 0:    y = √0 = 0

x = 3:    y = √3

Coordinates of intersection are: (0, 0) & (3, √3)

Answer:

(0, 0) & (3, √3)

Step-by-step explanation:

Answer:

y=2x+3

Step-by-step explanation:

the gradient is 2 and the y intercept is 3

Answer:

y = 2x + 3

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 )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 5) ← 2 points on the line

m = [tex]\frac{5-3}{1-0}[/tex] = 2

The line crosses the y- axis at (0, 3) ⇒ c = 3

y = 2x + 3 ← equation of line

Answer:

(2)They are perpendicular.

Step-by-step explanation:

Answer:

126 people

Step-by-step explanation:

9/5 is the ratio tea/coffee

let x be the one who preferred coffee and x+36 preferred tea

9/5=x+36/x

9x=5x+5(36)

9x-5x=180

4x=180

x=180/4=45

x=45 coffee

x+36=45+36=81

45+81=126

check : 81/45= 9/5

Answer:

The correct answer to this question would be: "Survey every customer whose name is picked randomly from a list of all customers."

Step-by-step explanation:

"Survey every customer whose name is picked randomly from a list of all customers."

Answer:

The larger the degree, the steeper the graph's branches towards the right and left edges.

Step-by-step explanation:

Yes, there is a relationship between the degree of a polynomial and how steep its branches are at their end behavior (for large positive values of x, and to the other end: towards very negative values of x).

This is called the "end behavior" of the polynomial function, and is dominated by the leading term of the polynomial, since at very large positive or very negative values of the variable "x" it is the term with the largest degree in the polynomial (the leading term) the one that dominates in magnitude over the others.

Therefore, larger degrees (value of the exponent of x) correspond to steeper branches associated with the geometrical behavior of "power functions" (functions of the form:

[tex]f(x)=a_n\,x^n[/tex]

which have characteristic end behavior according to even or odd values of the positive integer "n").

Recalling the behavior of such power functions, the larger the power (the degree), the steeper the graph.

Answer:

The car's average speed for the entire journey = 84.315 km/h

Step-by-step explanation:

Correct Question

A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.

Solution

Average speed is given as total distance travelled divided by total time taken.

So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.

- The car travels the 50 km first part of the journey at a speed of 25 m/s.

25 m/s = 90 km/h

We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.

Speed = (Distance/Time)

Time = (Distance/Speed)

Distance = 50 km, Speed = 90 km/h

Time = (50/90) = 0.5556 hr

- The next part, the car covers 120 km at a speed of 80 km/h

Time = (Distance/Speed) = (120/80) = 1.5 hr

- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.

35 minutes = (35/60) hr = 0.5833 hr

Here, we need to calculate the distance covered for the last part.

Speed = (Distance/Time)

Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km

Total distance covered = 50 + 120 + 52.5 = 222.5 km

Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr

Average Speed = (222.5/2.6389) = 84.315 km/h

Hope this Helps!!!