Which choice is equivalent to the product below?

Answer:

4.375 sq. in.

Step-by-step explanation:

multiply 1.25 by 3.5 and you get 4.375

9514 1404 393

Answer:

  3. $6000 at 8%; $5000 at 5%

  4. 66 2/3 gallons of 9%; 133 1/3 gallons of 6%

Step-by-step explanation:

For many mixture problems, it works well to let a variable represent the amount of the largest contributor used in the mix.

3. Let x represent the amount invested at 8%. Then the total interest is ...

  8%x +5%(11000-x) = 730

  3%x = 730 -550

  x = 180/0.03 = 6000

$6000 was invested at 8%; $5000 was invested at 5%.

__

4. Let x represent the number of gallons of 9% content. Then the alcohol content of the mix is ...

  9%x +6%(200 -x) = 7%(200)

  3%x = 1%(200) . . . . . subtract 6%(200)

  x = 200/3 = 66 2/3 . . . . . divide by 3%

  200 -x = 133 1/3

66 2/3 gallons of 9% wine and 133 1/3 gallons of 6% wine should be used.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

y - x = -5

y =  x-5

y = 2x² - 3x - 5

x-5 = 2x² - 3x - 5

2x² - 4x = 0

x² - 2x  = 0

x(x - 2) = 0

x = 2, 0

(x,y) = (2,-3), (0,-5)

Answer:

13 ingredients

Step-by-step explanation:

The number of different recipes that can be made from 2 ingredients = 78

Since there are no two recipes that share the exact same two ingredients ;

The number of recipes in Mark's kitchen is:

nCk = 78

k = Number of ingredients per recipe = 2

n = total number of ingredients in kitchen

Total recipes made = 78

n! / (n-r)!r! = 78

n! / (n - 2)!2! = 78

n(n-1)(n-2)! / (n-2)! * 2 * 1 = 78

n(n - 1) / 2 = 78

n(n-1) = 156

n² - n = 156

n² - n - 156 = 0

Factorize :

n² - 13n + 12n - 156 = 0

n(n - 13) +12(n-13) = 0

(n-13) = 0 ; (n+12) = 0

n = 13 or n = - 12

n cannot be negative

Hence, n = 13

Number of ingredients is 13

Answer:

no idea

Step-by-step explanation:

Answer:

The answer is 7

Step-by-step explanation:

5x+2x=49-2x+2x

7x=49+0

7x/7=49/7

x=7

The number is 7 if five times a number is 49 greater than the product of 2 and the opposite of the number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Five times a number is 49 greater than the product of 2 and the opposite of the number.

Let the number is x:

From the statement "Five times a number is 49 greater than the product of 2 and the opposite of the number" we can frame a linear equation in one variable:

5x + 2x = 49 - 2x + 2x

After solving the above equation:

7x = 49

x = 49/7

x = 7

Thus, the number is 7 if five times a number is 49 greater than the product of 2 and the opposite of the number.

Learn more about the linear equation here:

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Answer:

214

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=4x-1

y-1=4(x-7)

y-1=4x-28

y=4x-27

Answer:

45mm

Step-by-step explanation:

First, find the whole area of the square, which is 225 mm squared.

Then, we have to find the area of the shaded trapezoid. Remember, the area of the trapezoid is [tex]\frac{h(b^{1}+b^{2} }{2}[/tex]

We get the area of the trapezoid to be 180 mm.

We subtract 180 from 225 mm to get 45 mm as our answer.

Answer:

ΔFGH≅ΔYZX

Step-by-step explanation:

Answer:

Step-by-step explanation: potential energy Ep = mgh

And g = 9.81 m/s². Ep = 0.0008 kg·9.81 m/s²· 22 m , unit is J

Answer:

3.56 cm.

Step-by-step explanation:

1/3 π r^2 h = V

1/3 π (5.13)^2 h  = 98

h = 98 / (1/3 π (5.13)^2)

=  98 / 27.55899

= 3.556.

Cone is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

If the volume and radius of a cone are 98 cm and 5.13 cm.

The height of the cone is 3.56 cm.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

Example:

The cone has a radius of 2 cm and a height of 3cm.

The volume of a cone:

= 1/3 x 3.14 x 4 x 3

= 12.56 cm³

We have,

Cone:

Volume = 98 cm

Radius = 5.13 cm

Height of the cone = h

The volume of a cone:

V = 1/3πr²h

98 = 1/3 x π x (5.13)² x h

[ Take π = 3.14 ]

98 = 1/3 x 3.14 x 26.31 x h

Multiply 3 on both sides.

98 x 3 = 3.14 x 26.31 x h

Divide both sides by (3.14 x 26.31).

h = (98 x 3) / (3.14 x 26.31)

h = 294 / 82.61

h = 3.56 cm

Thus,

If the volume and radius of a cone are 98 cm and 5.13 cm.

The height of the cone is 3.56 cm.

Learn more about cones here:

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Answer:

Step-by-step explanation:

1. cotx = 0

2. cosx = 1

So the solution set is:

Answer:

14. x=30, y=15, z=165

15. x=10, y=25

Step-by-step explanation:

Answer:

1)

x= 30

y=15

z=150

2)

x= 10

y=25

Step-by-step explanation:

1)

2x+90+x=180

3x+90=180

x= 90/3=30

2y= x

2y=30

y= 30/2=15

2y+z= 180

30+z= 180

z= 150  

2)

3x= 5x-20

5x-3x=20

x=20/2=10

2y+4y+ (5x-20) = 180

6y+30= 180

y= 150/6= 25

I hope im right!!

Answer:

Step-by-step explanation:

a = 12 mm

Surface area of cube = 6a²

                                   = 6 * 12 * 12

                                   = 864 cubic mm

This is because alternate exterior angles are congruent when we have parallel lines like this.

Angle 2 and angle 8 are both outside the parallel lines, so that's what makes them exterior angles. Also, they are on alternating sides of the transversal line (angle 2 on the left, angle 8 on the right). So that's where the "alternating" comes from. The other pair of alternate exterior angles is angle 1 and angle 7.

Answer:

(At least) 10 centimeters.

Step-by-step explanation:

The radius of the ice cream scoop is 2.5 cm and the radius of the cone is also 2.5 cm.

We want to determine the height of the cone such that it will fit all of the ice cream when it melts without any spilling.

First, we will find the volume of the ice cream scoop. The volume for a sphere is given by:

[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]

Since the radius is 2.5 cm, the volume of the full ice cream scoop is:

[tex]\displaystyle V=\frac{4}{3}\pi (2.5)^3[/tex]

Use a calculator:

[tex]V\approx 65.4498\text{ cm}^3[/tex]

The volume of a cone is given by:

[tex]\displaystyle V=\frac{1}{3}\pi r^2h[/tex]

The radius of the cone is 2.5 cm. Therefore:

[tex]\displaystyle V=\frac{1}{3}\pi(2.5)^2h=\frac{1}{3}\pi(6.25 h)=\frac{6.25\pi}{3}h[/tex]

The volume of the cone should be equal to the volume of the scoop. So:

[tex]\displaystyle 65.4498=\frac{6.25\pi}{3}h[/tex]

Solve for h:

[tex]\displaystyle h\approx 65.4498\Big(\frac{3}{6.25\pi}\Big)=10\text{ cm}[/tex]

The height of the cone should be (at least) 10 cm.

Answer:

You are supposed to correct the equation here not solve it.

Answer:

the answer is b

Step-by-step explanation:

you have to divide 6.50 by 5 to see how much 1 bar will cot

6.50 divided by 5 is 1.3

Answer:

B=5.44 i think hopefully

Answer:

2

Step-by-step explanation:

First you find what is in the parentheses

2+7 =9

9-1 = 8

Then find the exponent because on PEMDAS

2 * 2 = 4

Then divide

8 divided by 4 = 2

2 is your answer