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4 years ago

7) The area of rectangle A is twice the area of square B. Find x. 12

Mathematics

1 answer:

Veronika [31]4 years ago

6 0

Answer:

Step-by-step explanation:

A=2B

AreaA= Area of a rectangle=Base* height = base (12-x)*height(4) = 48-4x

AreaB = Area of rectangle=base(x) *Height(x) =x^2

Since A=2B

48-4x =2x^2

Divide both sides of the equation by 2

24-2x=x^2

Put everything all on one side

X^2-2x-24=0

(x+4)(x-6)=0

X=-4 and x=6

Only x makes sense since it’s not negative or else your base or one of your sides would be negative

So x=6

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There are 27 girls and 36 boys who want to participate in a math competition. If each team must have the same ratio of girls and

Reptile [31]

Since the ratio of girls and boys must be the same in each team, and all the competitors must be involved, it means that each team's ratio of boys : girls must be equal to the total ratio of Boys : Girls = 36 :27= 4 / 3.

Now 4 / 3, the most simplified version of 36 / 27, happens by dividing the numerator & demoninator by 9 (the greatest number it can divide by). So the greatest number will be 9 teams, each of 4 Boys & 3 Girls

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3 years ago

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5

Anuta_ua [19.1K]

Answer:

$y = \frac{3}{2} x-11$

Step-by-step explanation:

We are to find the equation a line that passes through the point (8, 1) and which is perpendicular to a line whose equation is $y = - \frac{2}{3} x+5$ .

We know that the slope of line which is perpendicular to another line is the negative reciprocal of the slope of the other line so it will be $\frac{3}{2}$ .

Then, we will find the y-intercept of the line using the standard equation of a line:

$y=mx+c$

$1=\frac{3}{2} (8)+c$

$c=-11$

Therefore, the equation of the line will be $y = \frac{3}{2} x-11$ .

7 0

3 years ago

Read 2 more answers

Mr. Sullivan places tiles numbered 1 through 18 in a bag and assigns a number to represent each of the 18 students in his class.

Marat540 [252]

Answer:

Mr. Sullivan <u>is</u> being fair because one tile has <u>an equal</u> probability of being selected over another tile.

Step-by-step explanation:

The process is fair because every tile has the same probability of being selected, and as the selection goes on, the selected students are removed.

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3 years ago

A squirrel found 48 acorns in a 3-day period. Each day the squirrel found 5 more acorns than the day before. How many acorns did

murzikaleks [220]

Answer:

Step-by-step explanation:

3 days= 15 acorns so take 15 away from 48

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3 years ago

A random sample of 11 university students produced the following data, where x is the minutes spent studying per day, and y is t

SIZIF [17.4K]

Answer:

16.373,16.4

Step-by-step explanation:

Given that a random sample of 11 university students produced the following data, where x is the minutes spent studying per day, and y is the first exam score (out of a maximum of 100 points).

x y

11 39

13 55

14 43

17 46

19 69

22 75

24 77

25 78

28 77

31 93

34 92 Observations 11

ANOVA

df SS MS F Significance F

Regression 1 3214.095153 3214.095153 69.46052448 1.59367E-05

Residual 9 416.4503017 46.27225574

Total 10 3630.545455

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 16.37281677 6.48384963 2.525169105 0.0324919 1.705329914 31.04030362 1.705329914 31.04030362

x 2.369323595 0.28428592 8.33429808 1.59367E-05 1.726224167 3.012423023 1.726224167 3.012423023

We get regression line as y =2.369x+16.373

a) value of intercept = 16.373

b) 16.4

8 0

3 years ago