MATHEMATICS HIGH SCHOOL

How do you write 245%as a fraction, mixed number, or whole number in simplest form?

Answers

Answer 1

Answer:

245 over 100 as a fraction

2 with 45 over 100 as a mixed number

2 with 9 over 20 as a mixed number simplest form

49 over 20 as a non mixed fraction in simplest form (improper fraction)

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Pamela has 4 pink ribbons, 3 green ribbons, and 1 blue ribbon. what fraction of Pamela's ribbons are green?

Answers

The total number of ribbons is 8 because 4 + 3 + 1 is 8
The number of green ribbons is 3
That means that 3 out of the 8 ribbons are green
Answer: 3/8

4 + 3 + 1 = 8
1 of those 8 is green
1/8

Which line has a slope of 5/8 and goes through the point (8, 2)

Answers

The slope $m$ and a point $(x_(0),\;y_(0))$ that the line goes through, give us a equation for the line:

$y-y_(0)=m\cdot (x-x_(0))\n\n y-2=(5)/(8)\cdot (x-8)\n\n\n y-2=(5)/(8)\,x-(5)/(8)\cdot 8\n\n\n y-2=(5)/(8)\,x-5\n\n\n y=(5)/(8)\,x-5+2\n\n\n \boxed{\begin{array}{c} y=(5)/(8)\,x-3 \end{array}}$

1) The points (-2,5) and (2,3) lie on the same line. Write the equation of the line in slope-intercept form. Type your answer in as y=mx+b. 2) The slope of a line is -12, and the line passes througin the point (0,8). Write the equation for the line in slope intercept form. Type your answer in as y=mx+b.

Answers

Answer:

1) The equation of the line is y = $(-1)/(2)$ x + 4

2) The equation of the line is y = -12x + 8

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

m is the slope of the line, m = Δy/Δx (chang of y/change of x)

b is the y-intercept (value y at x = 0)

Let us solve the two questions

∵ points (-2, 5) and (2, 3) lie on the same line

→ Find the slope m

∵ Δ x = 2 - (-2) = 2 + 2 = 4

∵ Δ y = 3 - 5 = -2

∴ m = $(-2)/(4)=(-1)/(2)$

∴ The slope of the line is $(-1)/(2)$

→ Substitute the value of m in the form of the equation above

∴ y = $(-1)/(2)$ x + b

→ To find b substitute the x and y in the equation by the coordinates

of a point on the line

∵ Point (-2, 5) lies on the line

∴ x = -2 and y = 5

∵ 5 = $(-1)/(2)$ (-2) + b

∴ 5 = 1 + b

- Subtract 1 from both sides

∴ 5 - 1 = 1 - 1 + b

∴ 4 = b

→ Sustitute it in the equation

∴ y = $(-1)/(2)$ x + 4

The equation of the line is y = $(-1)/(2)$ x + 4

∵ The slope of the line is -12

∴ m = -12

∵ The line passes through point (0, 8)

∵ b is the value of y at x = 0

∴ b = 8

→ Substitute the values of m and b in the form of the equation above

∴ y = -12x + 8

The equation of the line is y = -12x + 8

Final answer:

The equations of the lines are y=-0.5x+4 and y=-12x+8 respectively. For the first line, the slope is computed using provided points and the y-intercept is calculated using one of the points and the slope. For the second line, we use provided slope and point to write the equation.

Explanation:

Firstly, let's deal with the first part of the question. To write the equation of the line, we first need to calculate the slope. The slope (m) is calculated as (y2-y1)/(x2-x1). Using the points (-2,5) and (2,3) we find m=(3-5)/(2-(-2))= -2/4 = -0.5. The y-intercept (b) is the y value when x = 0. To find b, let's use the point (-2,5) and the slope in the equation y=mx+b. We get 5=(-0.5)*-2+b, hence b= 5-1= 4. So line equation is y=-0.5x+4.

For the second part of the question, we know that the slope (-12) and it passes through the point (0,8). So the y-intercept is 8 when x=0. Therefore, the equation of this line is y=-12x+8.

Learn more about Line Equations here:

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Which solid figure has one polygon base?A. pyramid
B. cone
C. cylinder
D. prism
Question #6TrueFalse
A rectangular prism with a height of 6 m, a length of 5 m, and a width of 4 m will have a different surface area than a rectangular prism with a height of 5 m, a width of 6 m, and a length of 4 m.
TrueFalse
Question #7MultipleChoice Score:
The volume of a rectangular prism is 288 ft3. If its height is 6 feet and its length is 8 feet, what is its width?
A. 6 feet B. 8 feet C. 9 feet D. 12 feet
Question #8MultipleChoice
A cube is 6 feet on each side. What is its volume?

Answers

Q1: The answer is A. pyramid.
A pyramid has one polygon base. A prism has two polygon bases. A cone has one circular base. A cylinder has two circular bases.

Q6: The answer is false.
Surface area of a rectangular prism is:
A = 2(wl + hl + hw)
A1 = 2(4*5 + 6*5 + 6*4) = 2(20+30+24) = 2*74 = 148
A2 = 2(6*4 + 5*4 + 5*6) = 2(24+20+30) = 2*74 = 148

Q7. The answer is A. 6 feet
The volume of rectangular prism is:
V = w * l * h
w = ?
So, just replace the knowing facts:
288 = w * 8 * 6
288 = w * 48
w = 288/48 = 6

Q8: The answer is 216 ft³
The volume of the cube is:
V = a³
Since a = 6, then:
V = 6³ = 216

Answer: #1 is pyramid

Step-by-step explanation: a pyramid can have any polygon as a base

God bless

Carmen has a sign with dimensions 5 ft × 7.5 ft. She wants to reduce it to make a postcard. Postcard sizes are 3.5 in. × 5 in., 4 in. × 6 in., and 4.25 in. × 6 in. Which size postcard should she use? Explain.

Answers

Answer:

The size of the post card she should use is 4 in. × 6 in.

Step-by-step explanation:

The parameters given are;

Dimensions of sign = 5 ft. × 7.5 ft

Hence, the ratio of the side sizes are;

5:7.5 which is the same as 2:3, therefore, to obtain the most accurate design of the sign on the post card, the size of the post card must be in direct proportion to the size of the sign which gives;

Side length ratio of post card = 2:3 = 4:6 = 4 in. × 6 in.

The size of the post card she should use is therefore = 4 in. × 6 in.

Round off 4252 to one significant figure

Answers

The answer is 4000 because in sig fig, you don't count the zeros after the number unless there is a decimal after 0.

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