MATHEMATICS HIGH SCHOOL

1: An isosceles triangle XYZ has an equal side XY and XZ of length 16 cm. Of the third side YZ is 20 cm, calculate the altitude the triangle Leave Answer in surd form

Answers

Answer 1

Answer:

Answer:

2√39 cm

Step-by-step explanation:

ΔXYZ is an isosceles triangle & XY = XZ, therefore:

YX' = X'Z

= 20 ÷ 2

= 10 cm

ΔXYZ' is a right triangle, therefore:

XY² = YX'² + XX'²

16² = 10² + XX'²

XX'² = 256 - 100

XX' = √156

= 2√39 cm

Related Questions

Posie plotted 3 points from the equation y = 2x on this coordinate grid. She drew a straight line through the points. Which ordered pair would also be on this line? A. (0, +2) B. (+8, +10) C. (+8, +16) D. (+4, +2)
What is the value of this expression 210/7-18+4*6-20 A)112 B)76 C)28 D)16
There are 10 sports balls in the equipment closet. Three are kickballs . Write the portion of the balls that are kickballs as a fraction, as a decimal, and in word form
What are the next four multiples of the fraction 2/6
3) Dori created a 2 letter code to get into her waterproof iPad. She only used the letters ABC and D because she was afraid she might forget the combination. Well, Dori forgot anyway and now wants to make a list of all possible combinations so she can get back in A Make a list of all the possible 2 letter codes.

Based on the data in the video ( 100 pages for $5.25,200 pages for $7.75,300 pages for $10.25,400 pages for $12.75 ), a) How well will a line model the data? b) Find an equation for price in terms of the number of pages, n Price

Answers

Answer: Price (P) = 0.025n + $2.75

Step-by-step explanation:

a) Based on the data provided, a line model will reasonably fit the data. The given data points form a consistent pattern, where the number of pages increases linearly with the price.

b) To find an equation for price in terms of the number of pages, we can use the slope-intercept form of a linear equation: y = mx + b.

Let's use the data points to determine the slope (m) and y-intercept (b) of the equation.

Using the points (100, $5.25) and (400, $12.75):

Slope (m) = (12.75 - 5.25) / (400 - 100) = 7.5 / 300 = 0.025

Now, let's substitute one of the data points into the equation to solve for the y-intercept (b). Let's use the point (100, $5.25):

$5.25 = 0.025(100) + b

$5.25 = 2.5 + b

b = $5.25 - $2.5 = $2.75

Final answer:

The relationship between the number of pages and the price is linear, so a line will model the data well. The equation of the price per page can be found using the point-slope form of a line equation, which in this case leads to the equation: Price = $0.025*Pages + $5.00.

Explanation:

To determine how well a line will model the given data, it is essential first to examine the relationship between the number of pages and the price. Here, we observe a consistent increase of $2.50 for every 100 extra pages. This suggests a linear relationship, meaning a line should model the data well.

To find the equation for the price in terms of the pages, we can use the point-slope form of a line equation, y - y1 = m(x - x1). Here, (x1, y1) is a point on the line, and m is the slope of the line. The slope (m) can be found by determining the difference in price (y values) divided by the difference in pages (x values). The slope will be ($7.75 - $5.25)/(200 - 100) =$2.50/100 pages = $0.025/page.

Choosing the first data point (100, $5.25) as our point on the line, the price equation (Price = m * Pages + b) becomes Price = $0.025 * Pages + $5.00. Thus, based on the data, a line model is well-suited to represent the relation between the number of pages and the price.

Learn more about Linear Relationships and Line Models here:

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Miley music has a sale on music CDs all music CDs are discounted 15% Marianas receipt indicates that she saved $3 on her CD purchase what is the full price of her music CD before the discount

Answers

Answer: The original price of her music CD before discount is $20.

Step-by-step explanation:

Let x be the original price of her music CD.

Discount rate = 15%

At discount she saved = $3

So, According to question, our equation becomes

15%x= 3

0.15x= 3

x=$20

Hence, the original price of her music CD before discount is $20.

If x is the price before a sale
x-0.15x=x-3
0.85x=x-3
3=0.15x
x=20

The original price is $20

Henry took out a 4 year loan for 5,000 and payed 4.2% simple annual interest. Ingrid took out a 6 year loan for 5,000 and payed 3.9% simple annual interest. What is the difference between the mounts of interest Henry and Ingrid payed for their Loans

Answers

Answer:

Ingrid pays 330 more than Henry.

Henry pays 330 less than Ingrid.

Step-by-step explanation:

SI = Simple Interest

P = Principal

R = Rate

T = TIme

Henry

=> SI = P x R x T / 100

=> SI = 5,000 x 4 x 4.2 /100

=> SI = 50 x 4 x 4.2

=> SI = 200 x 4.2

=> SI = 840

Ingrid

=> SI = P x R x T / 100

=> SI = 5,000 x 6 x 3.9 / 100

=> SI = 50 x 6 x 3.9

=> SI = 300 x 3.9

=> SI = 1170

1170 - 840

=> 330

Ingrid pays 330 more than Henry.

840 - 1170

=> -330

Henry pays 330 less than Ingrid.

The sales tax rate is 8%. Estimate the tax on a jacket that costs $69.95.

Answers

Answer:

8% is the same as (.08)x69.95=.556 or .56 ( because of rounding )

so .56 plus 69.95= $70.51

Step-by-step explanation:

Add 8% and 69.95 and then add 69.95 again to that answer and ta da!

The local grocery store usually sells large bottles of water for $2.69 each. This week they have a promotion, 3 large bottles for $6.30. How much less is the cost of a large bottle this week with the promotion?

Answers

Answer:

$0.59

Step-by-step explanation:

We first find the unit rate of the large water bottles after the promotion. To do this we divide 6.3 by 3 to get 2.1. Then we want to subtract 2.69 by 2.1 to get our final answer, $0.59.

The formula for density is given by p=m/v where p is density, M is mass and V is volume. If a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml7.7
7.7278
7.73
0.1