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

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