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3 years ago

7

Cathrine was concerned about her report card grade. She had 5 tests the whole semester. If her scores on each test were 93, 82,

74, 92 and 67 what is the mean/average of her grade?

1 answer:

enyata [817]3 years ago

4 0

Answer:

81.6

Step-by-step explanation:

mean/average of her grade = sum of all scores/the number of scores

= (93+82+74+92+67)/5

= 81.6

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Using a graphing utility, find the exact solutions of the system. Round to the nearest hundredth and choose a solution to the sy

Margaret [11]

Answer:

Part 1) The exact solutions are

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ and $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

$y=x^{2} +3x$ ----> equation A

$y=2x+5$ ----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

<em>Find the exact solutions of the system</em>

equate equation A and equation B

$x^{2} +3x=2x+5\\x^{2} +3x-2x-5=0\\x^{2} +x-5=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} +x-5=0$

so

$a=1\\b=1\\c=-5$

substitute in the formula

$x=\frac{-1\pm\sqrt{1^{2}-4(1)(-5)}} {2(1)}$

$x=\frac{-1\pm\sqrt{21}} {2}$

so

The solutions are

$x_1=\frac{-1+\sqrt{21}} {2}$

$x_2=\frac{-1-\sqrt{21}} {2}$

<em>Find the values of y</em>

<em>First solution</em>

For $x_1=\frac{-1+\sqrt{21}} {2}$

$y=2(\frac{-1+\sqrt{21}} {2})+5$

$y=-1+\sqrt{21}+5\\\\y=4+\sqrt{21}$

The first solution is the point $(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$

<em>Second solution</em>

For $x_2=\frac{-1-\sqrt{21}} {2}$

$y=2(\frac{-1-\sqrt{21}} {2})+5$

$y=-1-\sqrt{21}+5\\\\y=4-\sqrt{21}$

The second solution is the point $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Round to the nearest hundredth

<em>First solution </em>

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ -----> $(1.79,8.58)$

$(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$ -----> $(-2.79,-0.58)$

see the attached figure to better understand the problem

6 0

3 years ago

You plan to go skiing this weekend in Tennessee. The ski resort charges $18.50 per hour in addition to a $100 deposit to rent sk

Rina8888 [55]

Answer:

Part a) $y=18.50x+100$

Part b) The total cost is $\$220.25$

Part c) see the explanation

Step-by-step explanation:

Part a) Write a linear equation to represent this situation

Define the variables

Let

x ----> the number of hours

y ----> the total cost in dollars

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or the unit rate

b is the y-intercept or initial value (value of y when the value of x is equal to zero)

In this problem we have that

The unit rate or slope is equal to

$m=\$18.50\ per\ hour$

The y-intercept or initial value is equal to

$b=\$100$

substitute

$y=18.50x+100$

Part b) Use the equation to find the total cost to rent skis from 8:30 am to 3:00 pm

Remember that

3:00 pm=15:00

so

from 8:30 am to 3:00 pm, the total hours is equal to

15:00 -8:30=6:30=6.5 h

For x=6.5 h

substitute in the linear equation and solve for y

$y=18.50(6.5)+100\\y=\$220.25$

Part c) What does your answer mean in context of the problem?

we have that

y=220.25

That means -----> The total cost to rent skis for 6.5 hours is equal to $220.25

8 0

3 years ago

In one basketball season, Susan threw the ball and it went in the basket 56 times. If 7/8 of the baskets Susan threw were worth

Ket [755]

Answer:

119

Step-by-step explanation:

Divide the number of baskets (56) by the denominator:

56 ÷ 8 = 7

Multiply by 7 to get the amount of 2 point baskets and multiply by 1 to get the amount of 3 point baskets. (they both add up to 56 baskets)

7 × 7 = 49

7 × 1 = 7

multiply the 49, 2 point baskets by 2 and the 7, 3 point baskets by 3 and add them together to get the total points.

49 × 2 = 98

7 × 3 = 21

98 + 21 = 119

6 0

3 years ago

Which equation is true?

enot [183]

Lets solve all of these:-

#1

√361 = 361 · 2

?
√361 = 361 · 2
√361 = 19
361 · 2 = 722

19 ≠ 722
So this equation is not true

#2:-

√361 = 19²

?
√361 = 19²
√361= 19
19² = 19 · 19 = 361

19 ≠ 361
So this equation is not true

√361 = 361 ÷ 2

?
√361 = 361 ÷ 2
√361 = 19
361 ÷ 2 = 180.5

√361 ≠ 361 ÷ 2
So this equation is not true

√361 = √19²
√361 = 19
√19² = 19

19 = 19

SO the last one is right. Hope I helped ya!! xD

4 0

3 years ago

A rectangular picture frame has side lengths of 12 in by 9.5 in what is the length of the diagonal of the picture

OleMash [197]

Answer:

Length of diagonal of picture = 15.30 inches

Step-by-step explanation:

Given that:

Side lengths of picture frame = 12 inches by 9.5 inches

As the picture is rectangular, the diagonal will form hypotenuse of right angled triangle.

Using Pythagorean theorem;

a²+b²=c²

Putting the values in the theorem

$(12)^2 + (9.5)^2 = c^2 \\144+90.25=c^2\\c^2 = 234.25$

Taking square root on both sides

$\sqrt{c^2}=\sqrt{234.25}\\c=15.30$

Hence,

Length of diagonal of picture = 15.30 inches

3 0

3 years ago