Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.

9792381 ÷ 13ven: ΔABC with vertices A(-3,0), B(0,6), and C(4,6),

find equation of the three altitudes in

The number of gorillas at the safari park is 4.

Let the number of gorillas at the safari park be x.

It is given that there are 24 more buffalo than there are gorillas.

Number of buffalo at the safari park = 24 + x

There are 7 times as many wallabies as there are gorillas.

Number of wallabies at the safari park = 7x

Now, the number of buffalo is the same as the number of wallabies.

So, we equate their numbers to find the value of x i.e. number of gorillas.

24 + x = 7x

7x - x = 24

6x = 24

x = 4

Therefore, the number of gorillas at the safari park is 4.

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The expression of the length in terms of w is l = 20 - w cm

The expression of the area in terms of w is  20w - w² cm²

The greatest area that the rectangle could have is 400cm²

It is crucial to note that the calculating the perimeter of a rectangles is expressed as;

Perimeter = 2( l +w )

Where;

From the information given, the perimeter of the rectangle is 40cm

Now, substitute the value for perimeter

40 = 2( l +w )

Divide both sides by the coefficient, we have;

40/2 = 2(l + w)/2

Find the quotient

l + w = 20

Make 'l' the subject of formula

l = 20 - w cm

The formula for determining the area of a rectangle is expressed as;

Area = lw

Now, substitute the value of l as 20 -w in the formula, we have;

Area = 20- w(w)

expand the bracket

Area = 20w - w² cm²

For the greatest area;

Length = perimeter/4 = 40/ 4 = 20 cm

Width =perimeter/4 = 40/ 4 = 20cm

Area = 20(20)

Area = 400cm²

Thus, the expression of the length is l = 20 - w cm

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Answer:

you know it's a very good question

Step-by-step explanation:

I have no idea

Answer:

Step-by-step explanation:

first from the lower triangle, the unknown length is [tex]\sqrt{10^2-4^2} =\sqrt{100-16}=\sqrt{84}[/tex] so then x is equal to [tex]\sqrt{84-4^2}=\sqrt{68}[/tex] or about 8.2

The point slope form of the given equation is [tex](y-3)=\frac{-1}{7} (x-3)[/tex] .

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

If a line passes through the point  with slope m, then the point slope form of the line is

[tex](y-y_{1} )=m(x-x_{1} )[/tex]

Given that,

The slope of the line m = [tex]\frac{-1}{7}[/tex].

From the graph it is clear that the line passes through the point (3,3).

Substitute x₁= 3, y₁= 3 and  in the above equation.

[tex](y-3) = \frac{-1}{7}(x-3)[/tex]

Hence, The point slope form of the given equation is [tex](y-3)=\frac{-1}{7} (x-3)[/tex] .

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The above question is not complete.

Answer:

y = (5/2)x - 4

Step-by-step explanation:

(0, -4) and (2, 1)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁         1 - (-4)         1 + 4        5

m = ------------- = ------------ = --------- = --------

         x₂ - x₁         2 - 0            2            2

y - y₁ = m(x - x₁)

y - (-4) = (5/2)(x - 0)

y + 4 = (5/2)x - 0

   -4                 -4

----------------------------

y = (5/2)x - 4

I hope this helps!

Step-by-step explanation:

0.75x+2

2 is taken and 0.75 is not optional therfore

0.75=x(per square foot) =0.75x

and

$2 fee is required

so they must pay 2 dollars plus 0.75 everysquare foot

answer:

0.75x+2

The most appropriate choice for division will be given by

Quotient of [tex]\frac{3382}{6}[/tex] is between 563 and 564

What is division?

The process of dividing a certain number into equal parts is called division

The answer obtained after division is called quotient and the other part is the remainder. The number which is divided is called the dividend and the number by which the dividend is divided is called divisor.

General rule of division

Divisor x Quotient + Remainder = Dividend

Here,

Quotient of [tex]\frac{3382}{6}[/tex] = 563

563 is between 562 and 564

So, quotient of [tex]\frac{3382}{6}[/tex] is between 563 and 564

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Answer:

(a) There are 22 workers are available in the factory.

Step-by-step explanation:

(a) Let the number of workers in the factory be x.

Basic rate = $15

Working hours in a week  = 48 hours

Total wages in a week = $ 15840

If no overtime is to be paid then according to question,

Amount paid to 1 worker = 48 X 15 = $ 720

Amount paid to x worker = 720x

15840 = 720

x = 15840/720

x = 22

The graph of the linear equation y = 20 + 10x for the given scenario is attached below.

The Cartesian coordinates of a specific point on the Euclidean plane can be thought of as each solution inside the scenario involving two variables.

Here the equation is given as  y = 20 + 10x

Therefore at x = 0 ,  y = 20 and at y = 0, x = -2

This represents that the fixed monthly fee is 20 and the daily fee is 10.

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Answer:

i think its c because every time the it goe it goes were its suposefd to

Step-by-step explanation:

hope this helps dont minf my typing

Answer:

z = 6

Step-by-step explanation:

The angle in the middle is a right angle with a measure of 90°

Together, all three angles, makes a stright angle which is measured 180°.

So we can write the following equation to find the value of z:

5z + 1 + 59 = 90 (we don'thave to include the middle angle since we already its measure)

add like terms

5z + 60 = 90 subtract 60 from both sides

5z = 30 divide both sides by 5

z = 6

Alex has 56 books.

Let the number of books Santiago has be x. So, after the donation, the number of books with Santiago is (x - 84). Let the number of books with Alex be y.

Before the donation -

x = 2y : equation 1

After the donation -

y = 2(x - 84) : equation 2

Keep the value of x from equation 1 in equation 2

y = 2(2y - 84)

Performing multiplication on Right Hand Side of the equation

y = 4y - 168

Rearranging the equation

4y - y = 168

Performing subtraction on Left Hand Side of the equation

3y = 168

y = 168 ÷ 3

Performing division on Right Hand Side of the equation

y = 56

Therefore, Alex has 56 books.

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The distance travelled by Jack to Mexico on Tuesday is 876 miles.

The distance travelled by Jack to Mexico on Wednesday is 986 miles.

To determine the total miles he drove ,

The sum of the distance travelled by Jack to Mexico on Tuesday and Wednesday.

Let the total miles drove is denoted as T.

Thus the total miles drove is 1862 miles.

Answer:

9/20

Step-by-step explanation:

3/10 + 1/4

find a common denominator, which is 20 here

6/20 + 5/20 = 11/20 he used

left over is 9/20

A number line which represents the given number (2.379) is plotted and shown in the image attached below.

A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In conclusion, the number (2.379) should be placed close to 4 as plotted on the number line shown in the image attached below.

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Answer:

(5y-3)+(4y+1)+(5y-3)+(4y+1) = 176

18y - 4 = 176

18y = 180

y = 10

BC = 4y + 1 = 4(10) + 1 = 41 units

EXPLANATION

We can get the circunference of the circle by applying the Pythagorean Theorem as shown as follows:

Repalcing terms:

Aplying the square root to both sides:

The circunference is 13 inches.

Answer:

No

Step-by-step explanation:

Two different inputs can not have the same output. Although they can have two different outputs and the same input the reverse is not a thing. Each input has only one output, and the fact that it is the same output does not matter. It is supposed to be a function and by definition, functions are a special kind of relations allowing precisely one output for each input.

Answer:

Equation

Step-by-step explanation:

Equations require equal signs.

Answer:

156

Step-by-step explanation:

This is a question in proportion and ratio

Since the ratio in which the sweets are shared is 3: 4 : 5 we can say that the proportion of total sweets that June gets is 3/(3 + 4 + 5) = 3/12 = 1/4

Let the total number of sweets be S

Then 1/4th of this will be June's share and we are given that the actual number June gets is 30

So we have 1/4 x S = 39

Multiplying both sides by 4:
4 x 1/4 x S = 39 x 4

S = 156

So there were 156 sweets altogether

Let x be the number of miles and y the total cost; therefore, the equations that model the two plans are

Then, set y_A=y_B as shown below

Therefore, once the mileage is greater than 100 miles, the total cost of plan B will be less than that of plan A.

30

Angle = 67°

To solve the question, we will use an illustration:

To get the horizontal distance from the base of the skycrapper to the ship, we will apply tangent ratio:

opposite = 903 ft

adjacent = horizontal distance from the base of the skycrapper to the ship = x

To the nerest hundredth, the horizontal distance from the base of the skycrapper to the ship is 383.30ft

GIven a graph.

to find the solution of the system of equaion.

The intersection point is the soution of the system of equation in the graph.

thus, (2,7) is the solution of the given system of equation.

The answer is, option A The solution is (2, 7) because the solution to the system must satisfy both equations simultaneously.

ANSWER

t = 10.27

EXPLANATION

Step 1: Given

Step 2: Divide both sides by 500

Step 3: Take the natural logarithm of both sides

Step 4: Divide both sides by 0.0675

Hence, t = 10.27 (rounded to the nearest hundredth).

The Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

You have the first line:

You can identify that the y-intercept is:

You can find the x-intercept substituting the following value of "y" into the equation of the line:

And, after the substitution, you can solve for "x":

Now you know that the first line passes through these points:

Then, you can graph it.

Given the second line:

You can identify that:

And you can find the x-intercept by following the same procedure applied for the first line:

Then, this line passes through these points:

Now you can graph it.

See the graph below:

By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.

The answer is: First option.

Answer:

12:14

Step-by-step explanation:

RED=12

YELLOW=14

what is the ratio red to yellow u put the amount of red first then the amount of yellow