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2 years ago

6

A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box co

me with now?

1 answer:

siniylev [52]2 years ago

4 0

The cereal box now contains 22.2 ounces

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The equation y=750x represents the number of dollars y Olivia earns in x weeks. Determine if there is a constant of variation. I

Klio2033 [76]

Answer:

<h3>There is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.</h3>

Step-by-step explanation:

Given the equation y = 750x which represents the number of dollars y Olivia earns in x weeks, from the equation, it can be inferred that the number of dollars olivia earns is DIRECTLY PROPORTIONAL to the number of weeks. This relationship is therefore a direct variation.

In direct variation, increase in a variable will lead to corresponding increase in the other variable and vice versa by a factor known as the constant of variation.

For example if y is directly proportional to x, it is written mathematically as shown;

$y\alpha x$

$y=kx\\$

$k = y/x$

where k is the constant of proportionality.

comparing the general expression above with the equation in question,

y = 750x

k = 750

Therefore we can conclude that there is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.

5 0

3 years ago

How many pounds of a 23% zinc alloy must be mixed with a 42% zinc alloy to make 516 pounds of a 37.25% zinc alloy?

nydimaria [60]

Answer:

(A)129 Pounds

Step-by-step explanation:

Let x be the number of 23% zink alloy

Therefore:

Since the total result is 516 pounds

The number of pounds of 42% zink alloy =516-x pounds

We then have the resulting equation:

0.23x+0.42(516-x)=0.3725*516

0.23x+216.72-0.42x=192.21

Colect like terms

0.23x-0.42x=192.21-216.72

-0.19x=-24.51

Divide both sides by 129

x=129 pounds

Therefore, the number of pounds of 23% zink alloy that must be mixed is 129 pounds.

6 0

3 years ago

Susan is 5.5 ft tall and casts a shadow that it is 4 ft long on the ground. She is walking through a park and finds the shadow o

Vika [28.1K]

Answer:

22 ft

Step-by-step explanation:

Height of Susan/Length of shadow = Height of sculpture/Length of Shadow of sculpture

5.5 ft/4 ft = x/16ft

Cross Multiply

4 × x = 5.5 × 16

x = 5.5 × 16/4

x = 22 ft

The height of the sculpture is 22 ft

4 0

2 years ago

Translate this verbal expression to an algebraic expression.

puteri [66]

C. 2(x+10) is the correct answer

3 0

2 years ago

Read 2 more answers

Calculate the length of sides triangle pqr and determine weather or not triangle is a right angled. P(-4,6) q(6,1) r(2,9)

Tom [10]

$\bold{\huge{\underline{ Solution }}}$

<h3><u>Given </u><u>:</u><u>-</u></h3>

We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

<h3><u>To</u><u> </u><u>Find </u><u>:</u><u>-</u></h3>

<u>We </u><u>have </u><u>to </u><u>calculate </u><u>the </u><u>length </u><u>of </u><u>the </u><u>sides </u><u>of </u><u>given </u><u>triangle </u><u>and </u><u>also </u><u>we </u><u>have </u><u>to </u><u>determine </u><u>whether </u><u>it </u><u>is </u><u>right </u><u>angled </u><u>triangle </u><u>or </u><u>not </u>

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>Here</u><u>, </u><u> </u><u>we </u><u>have </u>

Coordinates of P =( x1 = -4 , y1 = 6)
Coordinates of Q = ( x2 = 6 , y2 = 1 )
Coordinates of R = ( x3 = 2 , y3 = 9 )

<u>By </u><u>using </u><u>distance </u><u>formula </u>

$\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}$

<u>Subsitute </u><u>the </u><u>required </u><u>values </u><u>in </u><u>the </u><u>above </u><u>formula </u><u>:</u><u>-</u>

Length of side PQ

$\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}$

$\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ 100 + 25 }}$

$\sf{ = }{\sf\sqrt{ 125 }}$

$\sf{ = 5 }{\sf\sqrt{ 5 }}$

Length of QR

$\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}$

$\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}$

$\sf{ = }{\sf\sqrt{16 + 64 }}$

$\sf{ = }{\sf\sqrt{80 }}$

$\sf{ = 4 }{\sf\sqrt{5 }}$

Length of RP

$\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}$

$\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}$

$\sf{ = }{\sf\sqrt{ 36 + 9 }}$

$\sf{ = }{\sf\sqrt{ 45 }}$

$\sf{ = 3}{\sf\sqrt{ 5 }}$

<h3><u>Now</u><u>, </u></h3>

We have to determine whether the triangle PQR is right angled triangle

<h3>Therefore, </h3>

<u>By </u><u>using </u><u>Pythagoras </u><u>theorem </u><u>:</u><u>-</u>

Pythagoras theorem states that the sum of squares of two sides that is sum of squares of 2 smaller sides of triangle is equal to the square of hypotenuse that is square of longest side of triangle

<u>That </u><u>is</u><u>, </u>

$\bold{ PQ^{2} + QR^{2} = PR^{2}}$

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>,</u>

$\bold{ 125 + 80 = 45 }$

$\bold{ 205 = 45 }$

<u>From </u><u>above </u><u>we </u><u>can </u><u>conclude </u><u>that</u><u>, </u>

The triangle PQR is not a right angled triangle because 205 ≠ 45 .

6 0

2 years ago