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3 years ago

Pls i need answer with explanation asap.

Mathematics

1 answer:

Mandarinka [93]3 years ago

5 0

Answer:

4 can be rewrite as 2•2, and that's the same as 2².

8 can be rewrite as 2•2•2, and that's the same as 2³

So we can rewrite the whole expression as:

2^x = (2²)⁸•(2³)⁴

2^x = 2¹⁶•2¹²

2^x = 2²⁸

So x = 28

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The area of a trapezoid with height z is 20 sq .cm. The length s of the parallel sides are (2z+3) and (6z-1) cm. Find the height

const2013 [10]

Answer:

Area of a trapezoid = ½(a + b)h, where a and b are the lengths of the parallel sides and h is its height.

From your information 20 = ½(2z + 3 + 6z – 1)z = ½(8z + 2)z = z(4z + 1)

Solve 20 = 4z² + z which is 0 = 4z² + z – 20 using the quadratic formula

Step-by-step explanation:

6 0

3 years ago

. A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $24,700

lozanna [386]

Answer:

1) P(x) =14400x+10300 2)y=-4x+19 3) $y=\frac{-2x}{3} -14$ 4) x=-11

(Please check the pictures for better understanding)

Step-by-step explanation:

1) Firstly, let's organize the data. Let the dependent variable x be the years, and the Range P(x) the Profit. So arranging these linear functions y=ax+b and plugging the coordinates for each point (1, 24700) and (4, 67900). Goes:

24,700=x+b

67,900=4x +b

1.1)Solving for b, this Linear System of Equation by the Addition Method goes:

$24,700=x+b*(-4)\\67,900=4x+b\\----------\\-98,800=-4x-4b\\67,900=4x+b\\ -----------\\-30900=-3b\\\frac{3b}{3} =\frac{30900}{3}\\ b=10300$

1.2) Now, let's find the slope based on those two points (1, 24700) and (4, 67900) and using the formula to find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{67900-24700}{4-1}\\ m=\frac{43200}{3}\\ m=14400$

So now we can write this Linear Equation for the Profit:

P(x) =14400x+10300

2) An equation of the line perpendicular to 4y=x-8 has a slope equal to $m_{2}$ =- $\frac{-1}{m_{1}}$ the line. In this case, an equation perpendicular to 4y=x-8 .

Rearranging the given equation of the line 4y=x-8 goes:

$y=\frac{x}{4} -\frac{8}{4} \\ y=\frac{x}{4}-2$

2.1) The slope of this new line is equivalent to m=-4 since -4 is opposite inverse value for the slope of its perpendicular line (1/4).

If the line passes through the point (6,-5), then this point already belongs to this line.

Then, we can write.

-5=-4(6)+b

-5=-24+b

-5+24=-24+24+b

b=19

Now we can write the function:

y=-4x+19

3) Firstly, let's rearrange the equation. Into a General Equation of the Line y=ax+b

2x+3y=5

-2x+2x+3y=5-2x

3y=5-2x

$\frac{3y}{3} =\frac{5}{3} -\frac{2x}{3}$

$y=\frac{-2x}{3}+\frac{5}{3}$

3.2) Let's find out b, the linear coefficient by plugging the coordinates of the point (-3,-8).

Also, Parallel lines have the same value for the slope such as $m_{1}=m_{2}$

-8=-3(-2/3)+b

-8=2+b

-8-2=2-2+b

b=-10

Then the equation of this parallel line is:

$y=\frac{-2x}{3} -10$

4) Now on this last question, we have to find an equation of the line through the point (-11,-4) perpendicular to another line y=15

Suppose the slope of the first line is $m_{1}$ and the value of the slope of its perpendicular is $m_{2}=\frac{-1}{m_{1}}$

y=15 is a horizontal line with slope equals zero, we can rewrite it as y=0x+15.

Then the slope is zero for horizontal lines.

A perpendicular line to a horizontal line is a vertical one.

In addition to this, a vertical line passes through only one point in the x-axis. Then, there is no horizontal variation. This leads the formula of a slope to an undefinition for Real Set.

$m=\frac{y_{2}-y_{1}}{0}$

The only perpendicular line which passes through the point (-11,-4) to y=15 is the line x=-11.

7 0

3 years ago

IN NEED OF ANSWER :( A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the th

vichka [17]

Answer:

a = 33ft

b= 66ft

c = 48 ft

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

a (shortest side)= a
b (second side)=2a (twice the length of the shortest side)
c (third side)= a+15 ( 15 feet more than the length of the shortest side)

Since:

Perimeter = a+b+c

Replacing with the values given:

147 = a+2a+(a+15)

147 = a+2a+a+15

147-15 = a+2a+a

132 = 4a

132/4 = a

33 ft= a

Substituting a =33 in the other expressions:

b=2a = 2(33) = 66 ft

c= a+15 = 33+15 = 48 ft

3 0

4 years ago

PLEASE HELP IM DESPERATE <br><br> If a1=9 and an=- 3an-1 – 5 then find the value of a5.

melomori [17]

Answer:

A5 is approximately 5.8 by 8.3 inches in size, and it's the closest in size to the U.S. paper size called the “half-letter” size, at 5.5 by 8.5 inches. But here's how all the A-series sizes break down: A0 paper is 841 by 1189 millimeters, approximately 33.1 by 46.8 inches.A5 measures 148 × 210 millimeters or 5.83 × 8.27 inches. In PostScript, its dimensions are rounded off to 420 × 595 points.A5148 x 210mm5.8 x 8.3 inch

3 0

3 years ago

Read 2 more answers

In a poker hand, John has a very strong hand and bets 5 dollars. The probability that Mary has a better hand is .04. If Mary had

mr_godi [17]

Answer:

When Mary raises the probability that she has a better hand is 0.273

Step-by-step explanation:

In the poker game it is given that the probability that Mary has a better hand than John is 0.04.

Let the event that Mary has a better hand than John be A.

Let the event that that Mary raises the stakes be B.

It is also given that if Mary has a better hand than John then she would raise with a probability of 0.9

Therefore p(B | A) = 0.9

If Mary has a poorer hand she will raise with a probability of 0.1

Therefore p(B | A') = 0.1

Given that Mary raises the probability that she has a better hand is given by

p(A | B)

$= \frac{p(A\cap B)}{p(B)}$ = $\frac{p(A)p(B | A)}{p(A)p(B | A) + p(A')p(B | A')} = \frac{(0.04 \times 0.9) }{(0.04 \times 0.9) + (0.96 \times 0.1)} = \frac{36}{36 + 96} = \frac{36}{132} = \frac{3}{11}$

= 0.273

So when Mary raises the probability that she has a better hand is 0.273

3 0

4 years ago