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Advocard [28]
3 years ago
9

A container holds 8 quarts of lemonade. How much is this in gallons?

Mathematics
1 answer:
Arturiano [62]3 years ago
8 0

2 Gallons is 8 quarts.

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The height of a triangle is 8ft greater than the base. The area of the triangle is 136.5 square ft. Find the length of the base
mixer [17]

Answer:

the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.

Step-by-step explanation:

Note that the formula for the area of a triangle is A = (1/2)(base)(height).  Let's abbreviate that to A = (1/2)(b)(h).   We are told that h = b + 8.

Then A = 136.5 = (1/2)(b)(b + 8), or

               (after multiplying both sides by 2)

          A = 273 = b^2 + 8b

                which, when put into standard quadratic form, becomes:

b^2 + 8b - 273 = 0

The coefficients of this quadratic are a = 1, b = 8 and c = -273.

Thus, the discriminant is b^2 - 4ac, or 64 - 4(1)(-273) = 1156 = 17^2.

The roots are then

      -8 ± √1156            -8 ± 17

x = --------------------  =  ------------ = 9/2 and -25/2

              2                          2

Only the root 9/2 makes sense here, because measurements of length are positive.

Thus, the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.

3 0
3 years ago
Drag the tiles to the correct boxes to complete the pairs.
Inga [223]
-2 a b are a match. hope this helps 2-2=4
8 0
3 years ago
Match each transformation of function fwith a feature of the transformed function.
Grace [21]

The functions and their properties are

  • The function f(x) has its vertical asymptote at x = 0
  • The x-intercept of the function h(x) is (0.5,0)

<h3>How to match the functions and their properties?</h3>

The equations of the functions are given as:

f(x) = ln(x)

g(x) = -1/2f(x - 2)

h(x) = f(x - 1/2)

From the given graph, we can see that the function f(x) has its vertical asymptote at x = 0

h(x) = f(x - 1/2) implies that the function f(x) is shifted 1/2 units right to form h(x)

This means that the x-intercept of the function h(x) is 1/2 units to the right of the x-intercept of the function f(x)

Hence, the x-intercept of the function h(x) is (0.5,0)

Read more about functions at:

brainly.com/question/4025726

#SPJ1

6 0
2 years ago
A homogeneous 1300 kg bar AB is supported at either end by a cable. calculate the stress acting in bronze bar in N/mm² if stress
tino4ka555 [31]

Answer:

4553332 is the answer

Step-by-step explanation:

5 0
3 years ago
Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home.
CaHeK987 [17]

Answer:

Carlos has practiced piano for \frac{29}{20}=1\frac{9}{20} hours.

Carlos needs to practice \frac{11}{20} hours.

Step-by-step explanation:

We have been given that Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home.

First of all, we will find piano practiced before school and after school by adding both amounts as:

\frac{3}{4}+\frac{7}{10}

Make a common denominator:

\frac{3*5}{4*5}+\frac{7*2}{10*2}

\frac{15}{20}+\frac{14}{20}

Add numerators:

\frac{15+14}{20}

\frac{29}{20}  

Therefore, Carlos has practiced piano for \frac{29}{20} hours.

Now, we will subtract \frac{29}{20} from 2 find number of hours Carlos needs to practice to reach his goal.

2-\frac{29}{20}

\frac{2*20}{20}-\frac{29}{20}

\frac{40}{20}-\frac{29}{20}

\frac{40-29}{20}

\frac{11}{20}

Therefore, Carlos needs to practice \frac{11}{20} hours before going to bed in order to meet his goal.

7 0
3 years ago
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