A U.S. penny has a mass of 2.5 grams. A U.S. quarter has a mass of 5.67 grams. What is the total mass of the two coins?

Given:

The graphs of two parabolas.

To find:

The equation of the quadratic function with given graphs.

Solution:

(a)

The factor form of a parabola is

[tex]y=a(x-b)(x-c)[/tex]

Where, a is a constant, b and c are x-intercepts.

From the graph (a) it is clear that the graph intersect the x-axis at -1 and 3. So, b=-1 and c=3.

[tex]y=a(x-(-1))(x-3)[/tex]

[tex]y=a(x+1)(x-3)[/tex]            ...(i)

Put x=0 and y=3 because the y-intercept is (0,3).

[tex]3=a(0+1)(0-3)[/tex]

[tex]3=-3a[/tex]

[tex]\dfrac{3}{-3}=a[/tex]

[tex]-1=a[/tex]

Putting a=-1 in (i), we get

[tex]y=-1(x+1)(x-3)[/tex]

[tex]y=-(x+1)(x-3)[/tex]

Therefore, the equation of the parabola is [tex]y=-(x+1)(x-3)[/tex].

(b)

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]

Where, a is a constant and (h,k) is vertex.

From the the graph (b), it is clear that the vertex of the of the parabola is at point (2,0) and y-axis is (0,8). So, h=2, k=0.

[tex]y=a(x-2)^2+0[/tex]

[tex]y=a(x-2)^2[/tex]            ...(ii)

Put x=0 and y=8 because the y-intercept is (0,8).

[tex]8=a(0-2)^2[/tex]

[tex]8=4a[/tex]

[tex]\dfrac{8}{4}=a[/tex]

[tex]2=a[/tex]

Putting a=2 in (ii), we get

[tex]y=2(x-2)^2[/tex]

Therefore, the equation of the parabola is [tex]y=2(x-2)^2[/tex].

Answer:

900

Step-by-step explanation:

because if you do 400×5m then that's 900

and that's how much work you did by just pushing 5 meters with 400 N

Answer: 0.06

because 100 has two zeros, the move the number of zeros to the left so the answer is 0.06

Complete question :

Mr. Hopkins has a 1 meter wire he is using to make clocks. Each fourth meter is marked off with 5 smaller equal lengths. If Mr. Hopkins bends the wire at ¾ meter, what fraction of the marks is that?

Answer:

15 th ; 15/20

Step-by-step explanation:

Length of wire = 1 m

Number of fourth length possible = 1 ÷ 1/4 = 1 * 4/1 = 4

Each fourth length divided into 5 equal sizes :

Hence. Total number of equal spaced division :

5 * 4 = 20

If wire is bent at 3/4 meter :

Fraction of the mark

3/ 4 of 20

3/4 * 20

(3 * 20) / 4

60 / 4

= 15th

= 15/ 20

Step-by-step explanation:

Given n = 4

2n = 2* 4= 8

n + 2 = 4 + 2 = 6

3(n + 4) = 3( 4 + 4) = 3 * 8 = 24

Hope it will help :)

Answer:  1. у %3 2х

Step-by-step explanation: Find the distance between (0, 0) and (-3, 4) pair of points

Answer:

Step-by-step explanation:

Perpendicular lines have negative-reciprocal slopes

The line will have a slope of:

The equation is:

Use the pair (6, 2) to find the value of b:

The line is:

Answer:

ummmmmmmmm

Step-by-step explanation:

Answer: x=4.373

Step-by-step explanation: Have a brilliant day mate -Lily ^_^

Answer:

x=4.373 (put a repetend at the top of three last digit)

Step-by-step explanation:

Combine rational expressions and isolate variable x

Answer:

Step-by-step explanation:

The greatest common factor they share is 4.

[tex]4(x^3+8)[/tex]

Answer:

Equation: 3x + 7 = 16

Unknown Number: 3

Step-by-step explanation:

You must first develop an equation representing this problem:

3x + 7 = 16

Then, you can solve for the unknown number.

3x + 7 = 16

3x = 9

x = 3

Answer:

55%

Step-by-step explanation:

11/20 = x/100

cross multiply

Answer:

55%

Now we can see that our fraction is 55/100, which means that 11/20 as a percentage is 55%.

Step-by-step explanation:

Answer:

find the cordinates of each letter or number then find witch is greater or less than when your answering it

Step-by-step explanation:

Answer:

The equation required to find the volume of concrete is:

L X W X H.

Step-by-step explanation:

L = Lenght

W = Width

H = Height

To calculate the required volume for concrete, you'd need to multiply the measures of all the dimensions together such as the lenght and the breath (which gives you the Area) and the thickness or height of the staircase.

If the calculation is being expressed in Feet, the answer will also be expressed as Volume of concrete in Cubic feet.

Cheers

Answer: 175

Step-by-step explanation:

To determine the actual distance using the map scale of 1 inch = 50 miles, you would multiply the number of inches shown on the map by 50.

For this problem:  3   1/2 •  50 =   7/2 • 50 =  175 miles

The two cities are 175 miles apart.

Answer:

c. g is the variable

Step-by-step explanation:

Answer:

The only true answer is that g is the variable

C

Answer and explanation:

The ratio 1:2 is different from the ratio 2:1. The ratio 1:2(one to two) means a comparison of two sizes; the ratio of one part of that thing to the ratio of two parts of that thing. Likewise, the ratio 2:1 is the comparison of two parts of a thing to the ratio of one part of the thing. For the ratio 2:1, we could say for example that for every two crushed tomatoes there is one tomato paste.

Answer:

$600,000

Step-by-step explanation:

interest = 3/100 × 40,000 = $1200

4 months = 1/3 years

[tex]p = \frac{100 \times i}{rt} = \frac{100 \times 1200}{3 \times \frac{1}{3} } = 120000[/tex]

$120,000 in 1 year

5years, 120,000×5 = $600,000

Answer:

here u go

Step-by-step explanation:

$600,000

Step-by-step explanation:

interest = 3/100 × 40,000 = $1200

Answer:

x(6x^2+1)

Step-by-step explanation:

To factor an equation, we have to take out the greatest common factor of both terms. In this case, that term would be x. Then we can out x outside of the parantheses and your distributive property to rewrite this equation.

Answer:

4√5

Step-by-step explanation:

if this isnt the answer u needed lmk!!

Answer:

8 58/61.

Step-by-step explanation:

546/61 = 8 remainder 58

so it's 8 58/61.

Answer:

a) 26; b) 5a+10;

Step-by-step explanation:

f(8)=3(8)+2

    =24+2

    =26

g(a+2)=5(a+2)

         =5a+10

Answer:

The reason why the area is 2a+3a+4a is because ax2=2a ax3=3a and ax4=4a know we know each segment so after that you add the segments to get the are equation which is 2a+3a+4a.

The reason why the area is also (2+3+4)a is because you just factored the orginial equation and if you use the distributive property they equal the same.

Step-by-step explanation:

If this answer helped you then please consider liking this and marking it as brainliest :)

Answer:

try 6 because when u put them in order than u are by a 8 and a 7

Step-by-step explanation:

please tell me if i right

Given:

12cm to 2.5mm

To find:

The simplified for of given statement.

Solution:

We know that,

1 cm = 10 mm

12 cm =120mm

We have,

12cm to 2.5mm

It can be written as

[tex]\dfrac{12\ cm}{2.5\ mm}=\dfrac{120\ mm}{2.5 mm}[/tex]

[tex]\dfrac{12\ cm}{2.5\ mm}=\dfrac{120}{2.5}[/tex]

[tex]\dfrac{12\ cm}{2.5\ mm}=48[/tex]

Therefore, the value of 12 cm to 2.5 mm is 48 or 48:1.

Answer:

length of third side is 10 units.

Step-by-step explanation:

let x be the missing side

by pythagorus :