melissa is driving along a highway at a constant soeed of 65 mph. how long does it take her to travel 90 miles?

Answer:

SA: 456

V: 408

Step-by-step explanation:

To find the volume of this prism, you first need to find the area of the triangular base. The base has dimensions 6 by 8, and since it's a triangle, the area of the base is 6*8/2=24. Multiplying this by the length of the prism, you get a volume of 24*17=408. For the surface area, you need to find and add together the areas of all of the surfaces. We have already determined that the area of the two triangular bases are 24. The rectangle formed by the leg with length 6 has area 6*17=102, the one with length 8 has area 136, and the hypotenuse has area 170. Adding all of this together, you get a surface area of 24+24+102+136+170=456 square centimeters. Hope this helps!

Formula of surface area: T.S.A = ph + 2b

p: represents the perimeter of the base, h

h: the height of the prism and B

B: the area of the base.

6 + 8 + 10 = 24

24 x 17 = 408cm^2

Formula of Volume:

V: of a prism is the area of the base

B: times the height h

h: height

V=Bh

8 x 7 = 56cm^3

Answer:  

1

Step-by-step explanation:

8-1,2,4.....

25-1,5...

Answer:

A

Step-by-step explanation:

Answer:

D. The slope is 7, and (2, -4) is on the line.

Step-by-step explanation:

y+4=7(x-2)

y+4=7x-14

Subtract 4 from both sides

y=7x-18

The slope is 7. (y=mx+b, m is the slope, b is the y-intercept)

(0, -18), (1, -11), (2, -4), (3, 3), (4, 10) are points on the line.

The answer that is true out of all of them is D. The slope is 7, and (2, -4) is on the line.

Answer:

[tex]4\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{32}= \\\\\sqrt{2\cdot 16}= \\\\\sqrt{2\cdot 4^2}= \\\\4\sqrt{2}[/tex]

Hope this helps!

Answer:

[tex]4\sqrt{2} \\[/tex]

Step-by-step explanation:

4 times the square root of 2 is equivalent to the square root of 32.

Answer:

a-4/5+1/6 (n-1)

Step-by-step explanation:

Answer:

a-4/5+1/6 (n-1)

Step-by-step explanation:

Answer:

Q1. x = 10

Q2. x = 7

Step-by-step explanation:

The steps are :

Q1.

[tex]5x - 6 = 3x + 14[/tex]

[tex]5x - 3x = 14 + 6[/tex]

[tex]2x = 20[/tex]

[tex]x = 20 \div 2[/tex]

[tex]x = 10[/tex]

Q2.

[tex]6x - 11 = 4x + 3[/tex]

[tex]6x - 4x = 3 + 11[/tex]

[tex]2x = 14[/tex]

[tex]x = 14 \div 2[/tex]

[tex]x = 7[/tex]

Answer:

[tex]x=10, \: x=7[/tex]

Step-by-step explanation:

[tex]5x -6 = 3x + 14[/tex]

[tex]5x -6+6-3x = 3x + 14+6-3x[/tex]

[tex]5x -3x = 14+6[/tex]

[tex]2x=20[/tex]

[tex]x=\frac{20}{2}[/tex]

[tex]x=10[/tex]

[tex]6x - 11 = 4x + 3[/tex]

[tex]6x - 11+11-4x = 4x + 3+11-4x[/tex]

[tex]6x-4x = 3+11[/tex]

[tex]2x=14[/tex]

[tex]x=\frac{14}{2}[/tex]

[tex]x=7[/tex]

Answer:

x² - 10x + 16 = 0

Step-by-step explanation:

Given the solutions x = 8 and x = 2 , then the factors are

(x - 8) and (x - 2) and the equation is

(x - 8)(x - 2) = 0 ← expand left side using FOIL

x² - 10x + 16 = 0

Hello!

The cost of the book is $150.

CP = [tex]\frac{SP(100)}{100 + PP}[/tex]

Basically, what this formula is saying is that to find the cost price (CP), we must multiply the sale price (SP) by 100, and divide the product by the sum of 100 + profit percentage (PP).

CP = [tex]\frac{180(100)}{100 + 20}[/tex]

CP = [tex]\frac{18000}{120}[/tex]

CP = 150

Answer:

$150

Step-by-step explanation:

let cp=x

(20/100*x) +x=180

1/5x+x=180

6x/5=180

6x=180*5

x=(180*5)/6

x=150

Answer:

No it is not a function

Step-by-step explanation:

Answer:

30 and 32

Step-by-step explanation:

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

Using the distance formula:

[tex]x=\sqrt{(5-(-2))^2+(3-(-3))^2}=\sqrt{7^2+6^2}=\sqrt{49+36}=\sqrt{85}[/tex]

Hope this helps!

Answer:

Speed in km/hr = 518.4 km/hr

Step-by-step explanation:

Speed = 144 m/s

To convert m/s to km/her, you just need to multiply it by 3.6

Speed in km/hr = 144 × 3.6

Speed in km/hr = 518.4 km/hr

Answer:

518.40km/h

Step-by-step explanation:

144m/s

it means that in 1 sec it does 144m

we are searching how many km it does in 1 hour

1 hour = 60*60=3600 sec

so in 3600 sec (= 1 hour) it does 144*3600 m

and 1 km = 1 000m

so in 1 hour it does 144*3600/1000 = 144*3.6 = 518.40

the speed of the car is 518.40km/hr

hope this helps

Answer:

27

Step-by-step explanation:

#3 is 1/3^3, and #4 is 1/x. The x is obviously 3^3 simplified, which is 27.

I see that you are in high school. Im in 7th grade and i can do this lol.

For any triangle, the three angles always add to 180

(y+10)+(2y)+(50) = 180

3y+60 = 180 ... combine like terms

3y+60-60 = 180-60 ... subtract 60 from both sides

3y = 120

3y/3 = 120/3 .... divide both sides by 3

y = 40

Answer: RS

Step-by-step explanation:

A greater angle of a triangle is opposite a greater side. If angle Q is greater than angle R, then side RS is greater than side QS.

Because Q is the larger angle in the triangle, Then RS is the longest side.

Answer:

6p^5 q^3

Step-by-step explanation:

download the app cymath for these types of questions

this (^) means exponents

-----

Number 5:

2p^2qx3p^3q^2

Take out the constants (2x3)p^2p^3qq^2

Simplify 2x3 to 6, 6p^2p^3qq^2

6p^2+^3q^1+^2

simplify 2+3 to 5, 6p^5q^1+^2

simplify 1+2 to 3

6p^5 q^3

Answer:

-3

Step-by-step explanation:

Because when y is 4, x is 4/-2 = -2

So when y is 6,

x= 6/-2

= -3

Answer: [tex]\sqrt[3]{5x}[/tex]

Answer:

69.08 cm

Step-by-step explanation:

Volume of each container

= l*b*h

= 20cm*30cm*50cm

= 30000cm ^3

= 0.03 m^3

The volume of 200 of these containers

= 0.03*200

= 6 m^3

The volume of the tank is also equal to 6m^3

Volume of tank = πr^2h

πr^2h= 6

πr^2= 6/4

r^2 = 6/4*7/22

= 42/88

= 0.477

r= √0.477

= 0.6908m

= 69.08cm

Answer:

Base radius  = 69.08 cm.

Step-by-step explanation:

Volume of each container = 20*30*50

= 30,000 cm^3

200 of these has a volume of  

200 * 30000

= 6,000,000 cm^3.

The volume of the cylinder = π r^2 h

= π r^2 * 400 = 6000000

r^2 = 6000000 / (π  * 400)

r^2 = 4774.65

r = 69.08 cm.

Answer:

Thinking Process

(i) Firstly, determine the factors of quadratic polynomial by splitting middle term.

(ii) The two different values of zeroes put in bioquadratic polynomial.

(iii) In both the case if remainder is zero, then bioquadratic polynomial is divisible by

quadratic polynomial.

Answer:

2x⁴ - 5x³ + 2x² - x + 2=

2x²(x²-3x+2) +x³-2x² -x +2=

2x²(x²-3x+2) + x(x²-3x+2) +x² -3x +2=

(x²-3x+2)(2x²+x+1)

since x²-3x+2 is the factor of the given polynomial, we can state the polynomial is divisible by x²-3x+2

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

note: x²+3x+2 is not the factor of the given polynomial

Answer:

314cm²

Step-by-step explanation:

Surface area(sphere) =4πr²

4 * 3.14 * (5²)

4 * 3.14 * 25

Hence, Surface area is 314sq.cm

Answer:

It takes 0.619 hours (approximately 37 minutes) for the van to catch up with the storm.

They have driven 33.43 miles

They will catch up when their distances are equal.

Step-by-step explanation:

The speed of the van is 54 mph, and the speed of the storm is 33 mph. They are going in the same direction, so the relative speed is the difference of their speeds:

relative speed = 54 - 33 = 21 mph

Now, to find the time when the van reaches the storm, we just need to use the equation:

distance = speed * time

13 = 21 * t

t = 13 / 21 = 0.619 hours

The distance traveled by the van is:

distance = 54 * 0.619 = 33.43 miles

The van will catch up when the distances are equal (the distance of the storm is 13 + 33*0.619 = 33.43 miles)

Answer:

The most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 vacations in the next year is 241.

Step-by-step explanation:

The best estimate for the proportion of clients who expect to go on 3 vacations is the same proportion of the sample.

Sample:

45 clients.

Of those, 21 expected to go on 3 vacations in the next year.

21/45 = 0.4667

Out of the 516 clients:

0.4667*516 = 240.8

Rounding up

The most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 vacations in the next year is 241.

Answer:

The distance between their house on the map is 10 inches.

Step-by-step explanation:

In order to calculate the distance from Jeremy's friend house to his we can apply a rule of three in a way that 60 miles is related to "x" inches in the same proportion as "1 1/2" inches is related to 9 miles. Before applying that it'll be for the best if we convert the mixed fraction to a pure fraction as shown below:

[tex]d = 1\frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}[/tex]

Creating the rule of three:

[tex]\frac{60}{9} \frac{\text{miles}}{\text{miles}} = \frac{x}{\frac{3}{2}} \frac{\text{inches}}{\text{inches}}\\\\9*x = \frac{60*3}{2}\\\\x = \frac{180}{18}\\\\x = 10 \text{ inches}[/tex]

The distance between their house on the map is 10 inches.

Answer:

7.02

Step-by-step explanation:

[tex]\frac{18}{100}[/tex] x 39 = 7.02

First write 18% as a decimal by moving the

decimal point two places to the left to get .18.

Next, the word "of" tells us we need to multiply.

So we multiply (.18)(39) to get 7.02.

So 7.02 is 18% of 39.

Answer:

The similarities are

1) Two triangles are similar when they meet either the (Angle Angle) AA, (Side Side Side) SSS or (Side Angle Side) SAS criteria

2) When two triangles meet either of the above similarity criteria they automatically meet the other similarity criteria

3) The ratio of their equivalent sides are equal such that when ΔABC is similar to ΔDCE we have;

AB/DC = AC/DE = BC/CE

The observed differences are

1) Triangles that meet the SAS and SSS Similarity Theorem criteria can be said to be congruent, that is they have both the same side sizes and angle sizes while triangles that meet only the AA Similarity Postulate criteria may or may not be congruent

2) The number of possible triangles formed by the SAS or SSS Similarity Theorem criteria is only one while the number of possible triangles formed by the AA Similarity Postulate criteria is infinite

3) A triangle that meets either the SAS or SSS Similarity Theorem criteria also meets the AA Similarity Postulate criteria

4) A triangle that meets either the AA Similarity Postulate criteria does not necessarily meet the AA Similarity Postulate criteria.

Step-by-step explanation:

The similarity postulates are;

The Angle Angle Similarity Postulate also known as AA

The Side Side Side Similarity Theorem also known as SSS

The Side Angle Side Similarity Theorem also known as SAS

Answer:

1-√10

1+√10

Step-by-step explanation:

Answer:

a3 + b3 = a3 + b3

Step-by-step explanation:

I'm not sure what you are asking for but this equation is true if that's the problem.

Multiply all the variables and then combine like terms.

On the left side we end out as a3 + b3 which is equal to the right side. Hope this helps!

Answer:

A is the answer i believe

Step-by-step explanation:

Answer:

x= 50

Step-by-step explanation:

The unknown angle is also x since we have an isosceles triangle and the bases angle are the same

The sum of the angles of a triangle are 180 degrees

x+x+80 =180

2x+80 = 180

Subtract 80 from each side

2x= 180-80

2x= 100

Divide by 2

2x/2 =100/2

x= 50

Answer:

[tex]x=50[/tex]°

Step-by-step explanation:

This is an isosceles triangle since 2 of it's sides are the same length. That means the missing angles are the same. Since a triangles' interior angles add up to 180°, we get:

(180°-80°)÷2=x°

100°÷2=x°

50°=x°

x°=50°