How long is the shorter leg of the triangle?

Answer:

2.

Step-by-step explanation:

(4x-5)(x+3)

=4x^2+12x-5x-15

=4x^2+7x-15

Answer:

54ft squared

Step-by-step explanation:

All faces:

Front: 2*3/2=4.5f squared * 2 (other side)= 9ft squared

Sides: 10*3/2= 15ft squared * 2 (other side)= 30ft squared

Bottom: 3*10/2= 30/2= 15ft squared

=54 ft squared

Surface area of the triangular prism is 96 feet.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

A triangular prism has 2 triangular bases and 3 rectangular lateral faces.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

There are 2 triangles at the top and bottom.

Here base = 3 feet and height = 2 feet

Total surface area on the top and bottom = 2 × [tex]\frac{1}{2}[/tex] × base × height

                                                                     = base × height

                                                                     = 3 × 2

                                                                     = 6 feet

There are 3 rectangular faces.

Area of the rectangle = Length × width

Here, length = 10 feet and width = 3 feet

Area of the rectangular face = 10 × 3 = 30 feet

Since there are 3 rectangular faces,

Total lateral surface area = 3 × 30 = 90 feet

Total surface area of the triangular prism = 90 + 6 = 96 feet

Hence the total surface area of the given triangular prism is 96 feet.

Learn more about Surface Area here :

https://brainly.com/question/29101132

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Answer:

B. 10.9

Step-by-step explanation:

Area of triangle= 1/2*24*h

∠N=90° ⇒ Area of triangle= 1/2*MN*ON

MN²= h²+(24-7)²

ON²= h²+7²

Answer:

A

Step-by-step explanation:

We can see that the two triangles are similar, and are in a 17:1 ration since 51/3 = 17

Now we can set up the equation

144-x = 17x

adding x to both sides we get

144 = 18x

dividing by 18 we get

x = 8

Now we plug x = 8 back in and get

144-8 = 136

Answer:

The answer is 72.

Step-by-step explanation:

You have to put in the values of a and b into the expressions :

[tex] {a}^{2} {b}^{3} - {(ab)}^{2} [/tex]

[tex]let \: a \: = - 2 \\ let \: b = 3[/tex]

[tex] {( - 2)}^{2} \times {(3)}^{3} - {( - 2 \times 3)}^{2} [/tex]

[tex] = 4 \times 27 - { (- 6)}^{2} [/tex]

[tex] = 108 - 36[/tex]

[tex] = 72[/tex]

Answer:

C

Step-by-step explanation:

The formula for the volume of a cylinder is [tex]\pi r^2 h[/tex], since you are multiplying the area of the base (a circle) by the height of the cylinder to find the volume. Therefore, the volume of this cylinder is:

[tex]\pi r^2 h= \\\\3.14 \cdot 8^2 \cdot 15=\\\\3.14 \cdot 960=\\\\3014.4[/tex]

Hope this helps!

Answer:

[tex]3014.4ft^3[/tex]

even though this is not the most precise answer, ths is the answer you will be looking for

Step-by-step explanation:

To find the volume of a cylinder you use the formula [tex]V=\pi r^2h\\=\pi *8^2*15\\=3015.93ft^3[/tex]

Answer:

[tex]\frac{x^2+4x-1}{x(x+2)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x+5}{x+2}[/tex] - [tex]\frac{x+1}{x^2+2x}[/tex] ← factor denominator

= [tex]\frac{x+5}{x+2}[/tex] - [tex]\frac{x+1}{x(x+2)}[/tex]

We require the fractions to have a common denominator.

Multiply numerator/denominator of first fraction by x

= [tex]\frac{x(x+5)}{x(x+2)}[/tex] - [tex]\frac{x+1}{x(x+2)}[/tex]

Subtract terms on numerator leaving the common denominator

= [tex]\frac{x^2+5x-x-1}{x(x+2)}[/tex]

= [tex]\frac{x^2+4x-1}{x(x+2)}[/tex]

Answer:

a on edge

Step-by-step explanation:

Answer:

B)

D)

Step-by-step explanation:

B) 1 and 13 are x intercepts so true

D) greatest profit is when price is 7; after that profit is getting smaller because function is decreasing

Answer:

5:00 pm -> 1700 hours

6:45 pm -> 1845 hours

8:05 am ->  0805 hours

12:59 am -> 0059 hours

0400 hours -> 4:00 am

1500 hours -> 3:00 pm

0010 hours -> 12:10 am

0240 hours -> 2:40 am

Step-by-step explanation:

12:xx am -> 00xx

all times from 1:00 am to 9:59 am stay nearly the same 0100 to 0959

all times 10:00 am to 12:59 pm stay nearly the same 1000 to 1259

all times 01:00pm to 12:00pm + 12 -> 1300 to 2400

Answer:

Step-by-step explanation:

10,12,13,20, 21,

Answer:

x^3   +  3x^2    +   9x    +  27   +   88 / [x - 3]

Step-by-step explanation:

x ^4 + 7 by x - 3 x^3   +  3x^2    +   9x        +  27 x - 3  [  x^4  +   0x^3    +   0x^2    +   0x    +   7   ]. x^3  -    

3x^3 ________________________________ 3x^3   +     0x^2 3x^2  

-     9x^2 ______________ 9x^2      +   0x 9x^2

   -    27x ____________ 27x    +   7 27x  

 -  81 _________ 88 S

Answer:  So the result is :      x^3   +  3x^2    +   9x    +  27   +   88 / [x - 3]

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Hope this helps.

Answer:

Question 1:

The sum of interior angles of a polygon can be found by the following formula:

(n-2) × 180

Where n is the no. of sides

A pentagon has 5 sides

So,

= (5-2) × 180

= (3) × 180

= 540 degrees

Question 2:

Since The sum of interior angles of a regular octagon is 1080 and the total interior angle are 8

So, Measure of interior angle = [tex]\frac{1080}{8}[/tex]

Measure of interior angle = 135 degrees

Question 3:

Since, one interior angle in a hexagon measures 120 degrees.

So,

The interior angle should be subtracted by 180 to get the exterior angle.

Exterior angle = 180-120

Exterior Angle = 60 degrees

Answer:

-1/2

Step-by-step explanation:

Slope is change in x over change in y

so..

2-(-4)

over

-1-11

so...

-6/12 or -1/2

Answer:

[tex]m=A-\frac{2n}{Z}[/tex]

Step-by-step explanation:

Multiply by 2:

2n = Z(A - m)

Divide by Z:

[tex]\frac{2n}{Z} =A-m[/tex]

Subtract A:

[tex]-m=\frac{2n}{Z}-A[/tex]

Multiply by -1:

[tex]m=A-\frac{2n}{Z}[/tex]

Answer:

The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

P( E∪F)  [tex]= \frac{24}{36}[/tex]

Step-by-step explanation:

Given Each number cube has sides numbered 1 through 6

Two distinct number cubes are rolled together

Total number of exhaustive cases n(S) = 36

Let 'E' be the event of getting sum is even

n(E) = {(1,3),(1,5), (2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4), (4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)} = 17

[tex]P(E) = \frac{n(E)}{n(S)} = \frac{17}{36}[/tex]

Let 'F' be the event of getting sum that is a multiple of '3'

n(F) = {(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3),(6,6) = 12

[tex]P(F) = \frac{n(E)}{n(S)} = \frac{12}{36}[/tex]

n((E∩F) = {(2,4),(3,3),((4,2),(5,1),(6,6)} =5

[tex]P(En F) = \frac{n(En F)}{n(S)} = \frac{5}{36}[/tex]

The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

P( E∪F) = P(E) + P(F) - P( E∩F)

            [tex]\frac{17}{36} +\frac{12}{36} - \frac{5}{36} = \frac{24}{36}[/tex]

Answer:

The maximum height the ball will reach is 29,141 feet.

The time when it reached its maximum height is 1.094 seconds.

2,443 seconds after throwing the ball, it will touch the ground.

Step-by-step explanation:

The function h (t) = - 16t² + 35t + 10 is a quadratic function of the form f (x) = ax² + bx + c, where a = -16, b = 35 and c = 10. To calculate the maximum height, you must then find the maximum of the function. In other words, Quadratic functions have a maximum (if a <0) or a minimum (if a> 0). This point is the vertex of the parabola.

The vertex coordinate on the x axis can be calculated by:

[tex]x=\frac{-b}{2*a}[/tex]

The value of the vertex on the y axis is obtained by substituting the value of "x vertex" in the function f (x), that is, by calculating f ([tex]\frac{-b}{2*a}[/tex]).

In this case, where h ([tex]\frac{-b}{2*a}[/tex]) is the maximum height:

[tex]t=\frac{-b}{2*a}=\frac{-35}{2*(-16)} =1.09375[/tex]≅ 1.094 seconds

So: h(1.094)= -16*1.094² + 35*1.094 + 10

h(1.094)=29.151

The maximum height the ball will reach is 29,141 feet.

The time when it reached its maximum height is 1.094 seconds.

To calculate the number of seconds after the ball is thrown it will hit the ground, you must calculate the roots of the quadratic function. For this you must apply:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]  

where x1, x2 are the two roots of the function f(x)=a*x² +b*x + c

In this case:

[tex]t1,t2=\frac{-35+-\sqrt{35^{2}-4*(-16)*10 } }{2*(-16)}[/tex]

Solving, you get t1=-0.256 and t2=2.443

Since the time cannot be negative, 2,443 seconds after throwing the ball, it will touch the ground.

Answer:

1:    Y=0.8x+72         =         x=1.25y−90

2: 20x+32y=43          =          x= -8/5y + 43/20

First question steps:

Solved for x

Step 1: Flip the equation.

Step 2: Add -72 to both sides.

Step 3: Divide both sides by 0.8.

Second question steps:

Step 1: Add -32y to both sides.

Step 2: Divide both sides by 20.

Answer:

1:    Y=0.8x+72         =         x=1.25y−90

2: 20x+32y=43          =          x= -8/5y + 43/20

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Hope this helps.

Answer:3x^2-5x+2=0

Step-by-step explanation:

Format of a quadratic equation= ax^2 +bx+c

Let x=1 and 2/3

When x=1

x-1=0.......(1)

When x=2/3

x-2/3=0.........(2)

Compare the equations

(x-1)(x-2/3)=0

x^2-2/3x-x+2/3=0

x^2-5/3x+2/3=0

Multiply all terms by 3

3x^2-5x+2=0

Answer:

-39,063

Step-by-step explanation:

In this geometric, sequence, you are multiplying by -5. So, we can continue the sequence by mulitplying 375(your last value) by -5 and so on, until we have 7 total terms.

Now we add the terms together:

-3+15+-75+375+-1875+9375+-46875

=-3+15-75+375-1875+9375-46875

=-39063

Hope this helps :)

Answer:

p(x)= 6(x+2)^2 -3

Step-by-step explanation:

Start with equation reworded

6x^2+24x+21

Factor

6(x^2+4x+7/2)

Complete the square

6(X^2 + 4x + 2^2 - 2^2 + 7/2)

Use binomial formula

6((x+2)^2 - 2^2 + 7/2)

Simplify

6((x+2)^2 - 1/2)

Expand

6(X+2)^2 - 3

Answer:

p(x)= 6(x+2)^2 -3

Step-by-step explanation:

Answer:

less than 3

9/4

Step-by-step explanation:

Answer:

less than 3

9/4

Step-by-step explanation:

boom!!!

Answer:

Milliliters is 1 Deciliter

Step-by-step explanation:

Answer:

Austin's football

Step-by-step explanation:

If you graph the equation for James's ball, you will find that the maximum height is at 5.125 feet. For Austin, it is over 8 feet. Therefore, Austin's ball goes higher. Hope this helps!

Answer:

austin's

Step-by-step explanation:

Answer:

If you're going to the left, 1, if you're going to the right 3.

If you meant to write -2, then to the left -3 and to the right =-1

<-------------------------------------------------------------->

    -3        -2        -1        0      1          2        3

Answer:

Nesesito ayuda sobre estas dos preguntas la1 y la ocho pero tiene que tener sentido con las demas

Step-by-step explanation:

Answer:

1. 6 should be added to both sides

2. f=19

Step-by-step explanation:

When solving equations like this, we have to isolate the variable. To do this, perform the inverse operation to both sides of the equation.

-6+f=13

This can be rewritten as:

f-6=13

6 is being subtracted from f. In order to get f by itself, we have to get rid of the 6 being subtracted from f. The inverse of subtraction is addition. Add 6 to both sides.

f-6+6=13+6

f= 13+6

f=19

Answer:

explained below

Step-by-step explanation:

Because the electro has a smaller mass than the mass of the proton, scientific notation is usually used so that the numbers are on the same "scale" but if we see the scientific notation we may be able to identify which is greater and which is less, due to that the exponent is less the number is smaller and on the contrary if the number is greater, it is a larger number.

In the image I leave an example of the use of scientific notation in this area

Answer: D 2

Step-by-step explanation: Because slope is the diffrence between the two points y/x which is 6/3 which is equal to 2

Answer:

Slope= 2

Step-by-step explanation:

There are three steps in calculating the slope of a straight line when you are not given its equation.

Step One: Identify two points on the line.

Step Two: Select one to be (x1, y1) and the other to be (x2, y2).

Step Three: Use the slope equation to calculate the slope.

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Answer:

(2,17)

Step-by-step explanation:

This is because x is the input and y is the output. All you have to do is create a value for x the substitute it in the equation. Next solve for y 0.5 times 2 is 1, plus 16 is 17. Then just put your values in an order pair.

Answer:

8,20

Step-by-step explanation:

Answer: U = 600 m/s

Step-by-step explanation:

Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.

After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.

From the first statement

Speed = distance/ time

Distance = speed × time

1500 = Ut

Make t the subject of the formula

t = 1500/U ..... (1)

From the second statement

Distance = speed × time

1500 = (U + 100) × ( t - 0.5 )

Open the bracket

1500 = Ut - 0.5U + 100t - 50

Collect the like terms

1550 = Ut - 0.5U + 100t .... (2)

Substitutes equation 1 into 2

1550 = 1500U/U - 0.5U + 100(1500/U)

1550 = 1500 - 0.5U + 150000/U

1550 - 1500 = (150000 - 0.5U^2)/U

Cross multiply

50U = 150000 - 0.5U^2

0.5U^2 + 50U - 150000 = 0

Divide all by 0.5

U^2 + 100U - 300000 = 0

Using completing the square method

U^2 + 100U = 300000

U^2 + 100U + 50^2 = 300000 + 50^2

(U + 50)^2 = 302500

U + 50 = sqrt(302500)

U + 50 = +/-(550)

U = 50 + 550 or 50 - 550

U = 600 or - 500

Since U is of the same direction, it is

positive. Therefore, the previous speed of the aeroplane is 600 m/s

Answer:

500km/hr

Step-by-step explanation:

The formula for Speed (km/hr) = Distance / Time

Where S = Speed

D = Distance

T = Time

S = D/T

From the question, the aeroplane covered a distance of 1500 km

S = 1500/ T

ST = 1500

Time taken( T ) = 1500/S ......... Equation 1

We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time

This is expressed mathematically as:

The new speed =S + 100km/hr

The new Time taken = 1500/ S - 1/2....... Equation 2

Also since Time = Distance / Speed

The new Time taken also = 1500/ S + 100 ......... Equation 3

Step 1

We would simplify Equation 2:

Time = 1500/S - 1/2

Find the Lowest common multiple = 2

Time = (2 × 1500 - S )/ 2S

Time = 3000 - S / 2S ......... Equation 4

Step 2

Equate Equation 4 and 3 together since they are both equal to time taken

1500/ S + 100 = 3000 - S / 2S

We cross multiply

2S × 1500 = (S + 100) ( 3000 - S)

3000S = 3000S - S² + 300000 - 100S

3000S - 3000S + S² - 300000 + 100S = 0

S² + 100S - 300000 = 0

Step 3

We solve for S = Speed by using factorisation method.

S² + 100x - 300000 = 0

S² - 500S + 600S - 300000 = 0

(S² - 500S) + (600S - 300000) = 0

S(S - 500) + 600(S - 500) = 0

(S - 500) (S + 600) = 0

S - 500 = 0, S = 500

S + 600 = 0 , S = -600

Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr