Answers
============================================================
Explanation:
Check out the attached image. I've added in points A through D. The points A,B,C are the vertices of the largest triangle. Point D is directly below point A, and point D is on segment BC.
To find the area of the largest triangle ABC, we need the base length BC, which is broken up into segments x and y
x = length from C to D
y = length from D to B
Let's find x first
Triangle ADC is a right triangle, so we can use the pythagorean theorem
a^2 + b^2 = c^2
x^2 + 15^2 = 17^2
x^2 + 225 = 289
x^2 = 289 - 225
x^2 = 64
x = sqrt(64)
x = 8
Follow similar steps to find y
a^2 + b^2 = c^2
y^2 + 15^2 = 25^2
y^2 + 225 = 625
y^2 = 625 - 225
y^2 = 400
y = sqrt(400)
y = 20
Therefore
BC = x+y
BC = 8+20
BC = 28
The base of the triangle ABC is BC = 28 units
b = base
b = 28
The height is AD = 15
h = height
h = 15
We can now find the area of triangle ABC
Area = b*h/2
Area = 28*15/2
Area = 420/2
Area = 210
The area of the triangle is 210 square inches
Related Questions
what is the slope of the line through (-2,3) and (1,1)?
Answers
This is found by using the equation y2 - y1/x2 - x1. Filling in for each factor, you would have 1-3/1+2 (since subtracting a negative makes it positive). This will give you a final answer of -2/3.
Here is a graph of the full equation of the line.
I hope this helps!
This table shows the size, in acres, of four large water parks. What is the median of the sizes of the four water parks? 60 acres 63 acres 64 acres 65 acres Park Size (in Acres) A 66 B 70 C 60 D 60
Answers
The median size of the four water parks, given as 66, 70, 60, 60 acres, is 63 acres.
Explanation:To find the median of the sizes of the four water parks, we first need to list the sizes in ascending order. Given the sizes are 66, 70, 60, 60, the arranged list becomes 60, 60, 66, 70.
As there are four numbers, the median is the average of the middle two numbers. So by adding 60 and 66 and then dividing by 2, we find that the median size of the water parks is 63 acres.
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Mary and Jerry are exercising on a track
-Mary is walking at a rate of 3 miles per hour
-Jerry starts jogging at a rate of 4 miles per hour after Mary has been walking for 15 minutes
-Jerry jogs 2 miles as Mary continues walking and they both stop at the same time
Enter the total distance, in miles, that Mary walks around the track
Answers
With Mary's rate of walk, 3 miles per hour, we can just convert it to minutes and find the distance she has covered after 30 minutes.
3 miles/ 60 minutes, multiplying both numerator and denominator by 1/2, we will have 1.5 miles/30 minutes. Therefore, Mary has covered a distance of 1.5 miles around the track after the walk.
Answer:
2.25
Step-by-step explanation:
Mary walks for 15 mins which is 0.75 mi. Jerry then starts jogging for 2 miles which is 30 minutes because he is jogging at 4 mph. This means Mary walked for 30 minutes which is 1.5 mi.
0.75+1.5=2.25
If a recipe requires 3/4 cup of water and Lisa wants to make only 1/3 of the recipe.how many cups of water should she use?
I got the answer 1/4 but I just want to make sure it’s right
Answers
1/3 of the recipe = 1/3 x 3/4 = 1/4 cup
Answer: 1/4 cup
if f(x)=x/2 and g(x) = x-3,what is the value of g(f(8))
Answers
g(x) = x - 3
f(8) = 8/2 = 4
g(f(x)) = 4 - 3 = 1
Answer g(f(8)) = 1
The first thing to do is find out what f(x) put into g(x) is and what it means.
Step One
Put f(x) into g(x). This means wherever you see an x in g(x) you put f(x)
g(x) = x - 3
g( f(x) ) = f(x) - 3
g( f(x) ) = x/2 - 3
Step Two
When you know what g(f(x)) you now put an 8 wherever you see an x.
Find g(f(8)) = x/2 - 3
g(f(8)) = 8/2 - 3
g(f(8)) = 4 - 3
g(f(8)) = 1
1 <<<<< answer.
at davidson's bike rentals it cost $42 to rent a bike for 8 hours. how many hours of bike use does a customer get per dollar?
Answers
PLEASE someone do this math EASY picture attached
Answers
5/8 ÷ 3/2 = (5/8 × 2/3) = 10/24 = 5/12
5/12 × 2/3 = 10/36 = 5/18
Your answer is 5/18
Hope this helps :)
Answer:
5/18
Step-by-step explanation:
5/8 ÷ 3/2
switch 3/2 to 2/3
5/12 × 2/3
10/36 divide each 2 5/18
The table below shows the deliveries for Floral World for the week. What is the mean, or average, number of deliveries per day?
Answers
13+15+17+19+16=80
80 divided by 5 is 16. The answer is 16
Can I have Brainliest?
Thanks!!
Answer:
The average number of deliveries per day is 16 deliveries.
Step-by-step explanation:
The mean of a data set is the average value within it. Means are used as a way of describing data and finding the central tendency. To calculate the mean of a data set, add all values of all data points, then divide the resulting number by the amount of data points.
13 + 15 + 17 + 19 + 16 = 80
80 / 5 = 16
So, the average number of deliveries made per day by Floral World is 16 deliveries.
In 2/3 of a hour, workers had installed 2/5 of a foor. At the rate,what fraction of the flooring is finished after 1 hour?
Answers
2/3 hour is 40 minutes, so 1/3 is 20 minutes.
40 minutes have passed and 2/5 of the progress on the floor is complete. In 20 minutes, 1/5 of the work is complete. Add 20 minutes to 40 minutes to get 60 minutes, or an hour.
Because of this, we need to add the progress of 20 minutes and 40 minutes. 1/5+2/5=3/5.
The first military strike of the Civil War was at
Bull Run
Lexington
Fort Sumter
Gettysburg
Answers
social security number contains nine digits 0 0 0 0 0 0 0 0 0 how many different Social Security numbers can be formed using in a in a numerals from 0-9
Answers
Second spot: 9 choices (0-9)
Third spot: 9 choices (0-9)
.
.
.
Ninth spot: 9 choices (0-9)
There are 9 choices for each digit, meaning we need to compute 9^9 to figure out how many possible social security numbers there are.
9^9 = 387420489 possible social security numbers
1,000,000,000 social Security numbers can be formed using the numerals 0-9.
What is combination?A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.
The formula for combination is:[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]
where, n = Total number of items to be selected from.
r = Number of items to be selected.
According to the given problem,
Social security number contains nine digits.
A digit can be any number between 0-9.
For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.
Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.
Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.
Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.
Same for third, fourth .. . . ninth digit.
Using the formula of combination, total number of ways would be,
= [tex]9 ~times~~ ^{10}C_{1}[/tex]
= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]
= 1000,000,000 ways
Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.
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if y=q x 5,and if q=10,then what is y?
a.2
b.5
c.30
d.50
Answers
The value of y is 50
Using the expression given:
y = q × 5 q = 10substitute the value of q into the expression
Now we have :
y = 10 × 5
y = 50
Hence, the value of y is 50
A rectangle field is five times as long as it is wide. If the perimeter of the field is 288 yards, what are the field's dimensions?
Answers
[tex]x + x + 5x + 5x = 288 \\ 12x = 288 \\ x = 24[/tex]
Width = 24 yards
Length = 24 x 5 = 120 yards
Area =
[tex]24 \times 120 = 2880 \: sq. \: yrds[/tex]
Hope this helps. - M
log base 6 (2x+1) = log base 6 (x-3) + log base 6 (x+5)
Answers
Use the rules of logarithms to rewrite as a single log. Then take the antilog and solve the resulting quadratic.
[tex]\log_{6}(2x+1)=\log_{6}(x-3)+\log_{6}(x+5)=\log_{6}((x-3)(x+5))\\\\2x+1=(x-3)(x+5)=x^{2}+2x-15\\\\0=x^{2}-16=(x-4)(x+4)[/tex]
The term [tex]\log_{6}(x-3)[/tex] is only defined for x > 3, so the only solution to this equation is x = 4.
Jason is covering an ottoman with fabric. The ottoman is in the shape of a rectangular prism that is 37 cm long, 21 wide, and 30 cm high. How much fabric is needed to cover the sides and top of the ottoman? Explain your strategy.
Answers
Final answer:
Jason needs 4,257 square centimeters of fabric to cover the sides and top of his rectangular prism shaped ottoman, calculated by finding the area of each side and adding them together.
Explanation:
To calculate the amount of fabric needed to cover the sides and top of a rectangular prism shaped ottoman with dimensions 37 cm in length, 21 cm in width, and 30 cm in height, we start by determining the surface area of the ottoman that needs covering. We ignore the bottom surface, assuming the ottoman sits directly on the floor.
First, calculate the area of each side:
Top/bottom surface (only top applies here) = length × width = 37 cm × 21 cm = 777 cm²
Front/back surface = length × height = 37 cm × 30 cm = 1,110 cm² (two sides, so × 2)
Left/right side = width × height = 21 cm × 30 cm = 630 cm² (two sides, so × 2)
Next, add all the calculated areas together:
777 cm² (top) + 2,220 cm² (front/back) + 1,260 cm² (left/right) = 4,257 cm²
Therefore, Jason needs 4,257 square centimeters of fabric to cover the sides and top of the ottoman.
a $1,400 loan has a simple annual interest rate 4%. how much simple interest is paid on the loan for 1 year?
Answers
The simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year is $56.
Explanation:The subject of your question is simple interest calculation. The formula for calculating simple interest is: principal amount x interest rate x time. You are asked to calculate the simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year. Let's proceed step-by-step:
Convert the interest rate of 4% to a decimal by dividing by 100. So, 4/100 = 0.04.The time is 1 year, so you don't need to convert it.Substitute the values into the simple interest formula. Therefore, the simple interest is: $1,400 x 0.04 x 1 = $56.So, the simple interest paid on the loan for 1 year is $56.
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Help I don’t understand this
Answers
- 4x - 8 = 24
Add 8 to each side
- 4x = 32
Divide each side by - 4
x = - 8
So your ordered pair is (- 8, 8).
((cosx)/(1+sinx))+((1+sinx)/(cosx)=2secx
Answers
A group of people were asked if they enjoy going to concerts or movies.
The table shows the probabilities of the results.
Answers
They are not independent because P(movies|concerts)=0.25 ≠ P(movies)=0.6, and P(concerts|movies)=0.25 ≠ P(concerts)=0.55
Answer:
Option: B is the correct answer.
Enjoying movies and concerts are not independent since,
[tex]P(movies|concerts)\neq P(movies)[/tex]
and [tex]P(concerts|movies)\neq P(concerts)[/tex]
Step-by-step explanation:
We know that if two events A and B are independent then:
[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]
where P denote the probability of an event.
Now, we know that:
[tex]P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}[/tex]
Similarly:
[tex]P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}[/tex]
If movies and concerts are independent then:
[tex]P(movies|concerts)=P(movies)[/tex]
Similarly:
[tex]P(concerts|movies)=P(concerts)[/tex]
We have:
[tex]P(movies)=0.6[/tex]
[tex]P(concerts)=0.55[/tex]
[tex]P(concerts|movies)=\dfrac{0.25}{0.6}[/tex]
[tex]P(movies|concerts)=\dfrac{0.25}{0.55}[/tex]
Hence,
Enjoying movies and concerts are not independent
Since,
[tex]P(movies|concerts)\neq P(movies)[/tex]
and [tex]P(concerts|movies)\neq P(concerts)[/tex]
a certain number is the same as the square root of the product of 8 and the number find the number
Answers
The number is given by the equation n = 8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as n
And , a number is the same as the square root of the product of 8 and the number
Substituting the values in the equation , we get
n = √ ( 8 x n ) be equation (1)
On simplifying the equation , we get
n = √8n
Taking squares on both sides of the equation , we get
n² = 8n
Divide by n on both sides of the equation , we get
n = 8
Therefore , the number is 8
Hence , the equation is n = 8
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Use a 10-square model to solve. What percent of 80 is 40?
Answers
Hope this is right!
:)
Solve the linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.
j = –0.45
j = –0.25
j = 0.25
j = 0.45
Answers
[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1 \\ - 9.5j - 5.5 = 0.5j - 1 \\ - 10j = 4.5 \\ j = \frac{4.5}{ - 10} = - 0.45 [/tex]
Based on calculations the correct answer is A
Answer:
Based on calculations the correct answer is A
Step-by-step explanation:
Find the greatest common factor for the list of terms 110x3, 30x4,60x8
Answers
30×4 = 3×5×2×2×2
60×8 = 3×2×2×5×2×2×2
Greatest common factor = 2×3×5
= 30
Hope this helps!
30x⁴ = 10x³(3x)
60x⁸ = 10x³(6x⁵)
Answer: GCF = 10x³
Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.
Answers
The coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).
Explanation:To find the coordinates of the point that divides the line segment AB in the ratio of 1:4, we can use the formula:
x = (x1 + 1/n * (4 * x2)) / (1 + 1/n)
y = (y1 + 1/n * (4 * y2)) / (1 + 1/n)
Substituting the given coordinates into the formula, we have:
x = (10 + 1/4 * (4 * 2)) / (1 + 1/4) = 8
y = (4 + 1/4 * (4 * 8)) / (1 + 1/4) = 6
Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).
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Plzz help me asap i need help
I willgive brainliest
Answers
Day 1: 8km=4.97miles
Day 2: 10miles=16.09km
Day 3: 9miles=14.4km
9.6km=5.9miles
I really hope this helps! Not really sure what exactly the answer you are looking for is but this should help you figure it out
whats the slope of the line y+6=1/3(x-4)
Answers
y + 6 = 1/3 x - 4/3
y = 1/3 x 22/3
⇒ Slope = 1/3
Answer: 1/3
A number m minus 3 is more than -4
Answers
> = more than/greater than
Expression:
m - 3 > -4
If you have to also solve:
m - 3 > -4
add 3 to both sides
m > -1
ANSWER: expression is m - 3 > -4;
expression solved for m is m > -1
Hope this helps! :)
When 54 is added to a number the result is the same as when the number is multiplied by 3. What is the number? Show working out.
Answers
54 + x = 3x
2x = 54
x = 27
54 divides by 3 is 18.
18 plus 54 is 72
18 Times 3 is 72
Owen’s math book weighs 2 pounds 13 ounces. His science book weighs 1 pound 15 ounces. His backpack weighs 1 pound 1 ounce. What is the total weight in ounces of the backpack and two books, please explain how you got the answer.
Answers
STEP 1:
convert each weight given to ounces only; multiply each pound by 16 ounces per pound, then add the additional ounces each item weighs
Math Book:
= (2 pounds * 16 ounces/lb) + 13 ounces
= 32 + 13
= 45 ounces
Science Book:
= (1 pound * 16 ounces/lb) + 15 ounces
= 16 + 15
= 31 ounces
Backpack:
= (1 pound * 16 ounces/lb) + 1 ounce
= 16 + 1
= 17 ounces
STEP 2:
total the number of ounces of each item in step 1
= 45 oz math book + 31 oz science book + 17 oz backpack
= 93 ounces total
ANSWER: The total weight of the backpack and two books is 93 ounces.
Hope this helps! :)
Paul wrote a check to the dentist for $345.69. He’ll use the check register to record his transaction. What will be his new balance?
Answers
Answer:
The answer is $704.73
Step-by-step explanation:
Answer:
The answer is A. $704.73
Step-by-step explanation: