The height of a triangle is 5 cm more than its base. The area of the triangle is 52 square centimeters. What is the base of the triangle?
Answers
Answer:
the base is 8 cm
Step-by-step explanation:
basically, we need to set up a system of equations.
if we know the area of a triangle is 1/2bh, and that h = b + 5, (because we want them to equal one another in the equation), we can then make two different equations and substitute the h for b.
1/2bh = 52 and h = b+5
subsitute in the (b+5) for the h in the first equation to get
(1/2)(b)(b+5) = 52
multiply both sides by two to get rid of the 1/2
b)(b+5) = 104
now multiply the bs together!
b^2 + 5b = 104
If you know how to factor, we can make this
b^2 +5b -104 and then
(b+13)(b-8) = 0
solve for b to get b = -13, 8, and -13 isn't a real distance, so the only option for b is 8 square centimeters.
Plugging this back into the original equations to get the height (and checking that it is actually right,) we get a height of 13.
When you plug in the 13 and 8 into the area equation, you get
(8)(13)(1/2) = 52
52 = 52
so it works!
lmk if anything is confusing- i know I kind of breezed by the factoring part, but if you have a calculator you can keep dividing 104 by random numbers until you get the right difference if you get kind of lost. The formula
[-b+-sqrt(b^2-4ac)]/2a is another way you could always get the right answer, (from the form Ax^2 + Bx + C), but it's pretty time consuming and I'm not sure whether you've actually learned that yet..
hope that helps! :)
Related Questions
22. which month did the business make the most profit
23. which month did the business make the least profit
Answers
Answer:
JulyMarchis your answer. I HOPE YOUR DAY GOES GREAT.
Question 3
1 pts
Use the number line below to find the midpoint of segment AB
midpoint of segment AB (answer1]
Answers
Answer:
The midpoint is -4
Jenny completed four-fifths of her summer reading assignment. Her classmate Antonio completed seven-eighths of his assignment, and classmate Jerry completed three-fourths of his assignment. Which student read the least? Which student read the most? Which student fell in the middle? (Show all work.)
Answers
Answer:
Jerry, Antonio, Jenny
Step-by-step explanation:
To solve this, we can represent the numbers as fractions, make them have one common denominator, and go from there
First, we can represent these as fractions:
Jenny:
four-fifths = 4/5
Antonio:
seven-eighths = 7/8
Jerry:
three-fourths = 3/4
Next, we can find the lowest common multiple. We can do this by listing the multiples of each number until something is in common for all 3
4:
4, 8, 12, 16, 20, 24, 28 ,32, 36, 40, 44, 48
8:
8, 16, 24, 32, 40, 48, 56, 64
5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
One number that is in common is 40.
Our next step is to find out what we need to multiply each number by to equal 40. We can do this via division.
4:
40/4 = 10
8:
40/8 = 5
5:
40/5 = 8
Next, we can multiply the numerator and denominator by the same number, essentially multiplying it by 1. For example, 4/5 * 5/5 = 20/25, which is still equal to 4/5 because 5/5 = 1 and multiplying any number by 1 keeps it the same.
3/4 * 10/10 = 30/40
7/8 * 5/5 = 35/40
4/5 * 8/8 = 32/40
We can see that 3/4 (Jerry) is the lowest, 7/8 (Antonio) is the highest, and 4/5 (Jenny) is in the middle
solve for x of the given angle
Answers
Answer:
m<ABC = 92
Step-by-step explanation:
(3x + 23) and 4x are equal angle wise. So we have the equation:
(3x + 23) = 4x
3x = 4x - 23
-x = -23
x = 23
Multiply x by 4 which is 92
Which of the following is equal to square root of 3 and square root of 6.
Answers
Answer:
the answer is the second option which is 6⅓
Answer:
6^1/6
Step-by-step explanation:
Rewriting with the exponents as fractions
(6^1/3) ^1/2
We know a^b^c = a^(b*c)
6^(1/3*1/2)
6^1/6
Help ASP!
Sarah has 80 pennies. Lou
has 10 times as many
pennies as Sarah.
Joe has 1/10 as many
pennies as Sarah. How many
pennies do Lou
and Joe have together?
Answers
Joe has 8 pennies
Therefore they have 808 pennies
if two adjacent sides of rectangle having perimeter 21 cm are in the ratio 3:4 what is the area of the rectangle is ...cm ?
Answers
Given,
l/b=3/4
=> l = 3b/4
We have,
P = 2(l+b)
=> 21 = 2(3b/4 + b)
=> 21*2= 7b
=> b = 6cm
Similarly,
l = 4.5cm
Thus, Area = l*b
=> Area = 4.5*6
=> Area = 27cm^2
I’ll give you 50 points if it’s answer correctly
Answers
Answer:
. The line passes through the quadrants I, II and III. ii. The line intersects the Y-axis at (0, 1).
Find the midpoint, M, of AB.
А
M
B
[?]
22
Answers
Answer:
M=11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
To find the midpoint ( or middle) we take the average of the endpoints
(A+B)/2 = (0+22)/2 = 22/2 = 11
Find the fraction that is exactly halfway between 3/7 and6/7 pls help
Answers
Answer:
[tex]\frac{9}{14}[/tex]
Step-by-step explanation:
1. Add two fractions together.
[tex]\frac{3}{7}[/tex] + [tex]\frac{6}{7}[/tex] = [tex]\frac{9}{7}[/tex]
2. Divide by 2.
[tex]\frac{9}{7}[/tex] ÷ 2 = [tex]\frac{9}{14}[/tex]
A farmer notes that in a field full of horses and geese there are 30 heads and 84 feet. How many of each animal are there?
Answers
Answer:
There are 12 horses and 18 geese.
Step-by-step explanation:
We are given that in a field full of horses and geese, a farmer notes that there are 30 heads and 84 feet.
We can write a system of equations using the given information.
Let the amount of horses there are be represented by h and geese by g.
Assuming each horse and geese has only one head, we can write that:
[tex]\displaystyle h + g= 30[/tex]
And assuming that each horse has four feet and each geese has two feet, we can write that:
[tex]4h + 2g = 84[/tex]
This yields a system of equations:
[tex]\displaystyle \left\{\begin{array}{l} h + g = 30 \\ 4h + 2g = 84 \end{array}[/tex]
We can solve it using substitution. From the first equation, isolate either variable:
[tex]g = 30 - h[/tex]
From the second, we can first divide by two:
[tex]2h + g = 42[/tex]
And substitute:
[tex]2h + (30 - h) = 42[/tex]
Combine like terms:
[tex]h + 30 = 42[/tex]
Subtract:
[tex]h = 12[/tex]
Therefore, there are 12 horses.
And since the total number of animals is 30, there must be 30 - 12 or 18 geese.
In conclusion, there are 12 horses and 18 geese.
The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).
a) Write down the expression for the sum of the first (n − 1) terms.
b) Find the first term and common difference of the above sequence.
Answers
Answer:
(a).
[tex]S_{n} = \frac{n}{2} (4n + 20) \\ \\S _{n - 1} = \frac{(n - 1)}{2} (4n - 4 + 20) \\ \\ S _{n - 1} = \frac{(n - 1)}{2} (4n + 16) \\ \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2} \\ \\ { \boxed{S _{n - 1} = {2 {n}^{2} + 6n - 8}}} \\ [/tex]
(b).
from general equation:
[tex]S _{n - 1} = \frac{(n - 1)}{2} (4n + 16)[/tex]
first term is 4n
common difference:
[tex]16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = \frac{16}{n - 2} [/tex]
plz plz help fast no trolls plz thx
Answers
Find the missing lengths of the sides.
A) a = 6^3 ft, b = 6^3 ft
B) a = 12 ft, b = 12 ft
C) a = 6 ft, b = 6 ft
D) a = 6 ft, b = 6^2 ft
Answers
Answer:
The choose B) a=12, b=12
Step-by-step explanation:
sin45= a/12√2 —> a=12
cos 45= b/12√2 —> b=12
I hope I helped you^_^
What two rational expressions sum to 2x+3x2−2x−15?
Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answers
The rational expressions that sum to [tex]\frac{2x+3}{(x+3)(x-5)} = \frac{2x}{(x+3)(x-5)} + \frac{3}{(x+3)(x-5)}[/tex]
The given expression is:
[tex]\frac{2x+3}{x^2-2x-15}[/tex]
Factorize the denominator
[tex]x^2-2x-15\\x^2-5x+3x-15\\x(x-5)+3(x-5)\\(x+3)(x-5)[/tex]
The given expression therefore becomes:
[tex]\frac{2x+3}{(x+3)(x-5)}[/tex]
This can be split into the sum:
[tex]\frac{2x+3}{(x+3)(x-5)} = \frac{2x}{(x+3)(x-5)} + \frac{3}{(x+3)(x-5)}[/tex]
Learn more here: https://brainly.com/question/17103002
Answer: 2x+3/x^2-2x-15 = 13/8(x-5) + 3/8(x+3)
Step-by-step explanation: I took the test and used the answer above and got the answer wrong, then the test gave me this answer:
Use the order of operations to simplify the expression below. 990 ÷ (12-9)
Answers
Hi ;-)
[tex]990:(12-9)^2=990:3^2=\\\\=990:(3\cdot3)=990:9=\boxed{110}[/tex]
Is 0.14 equivalent to a. 8/12, b. 5/8, c. 2/3, d. 7/50, e. 4/5, f. 5/3, g. 19/25, h. 1/3, i. 2/9, j. 1/33, k. 4/9
Answers
Answer:
7/50
Step-by-step explanation:
7 divided by 50 equals 0.14 in decimal format.
Kelsey deposited $3,600 in a bank account with annual interest rate 4.25%. How much interest was earned in 5 years?
Answers
Answer:
765
Step-by-step explanation:
1)4.25/100=0.0425
2)0.0425*3600=153
3)153*5=765
brainiest to whoever is right there
Answers
Answer:
If we divide 360 degree into four parts the all four parts hold 90 degree and the degree of angle DMB= 60.
60 degree.
Cindy had $100 in her savings account. The bank accidentally charged her a $30 service fee. How much money does that leave her with as a balance? *
Answers
Answer:
$70
Step-by-step explanation:
Find how much money she has left by subtracting 30 from 100:
100 - 30
= 70
So, she has $70 left in her balance.
Please help!! Will give brainlist is answer right
Answers
Answer:
AStep-by-step explanation:
The formula d=rt is used to calculate the distance traveled by an object moving at a constant average speed during an elapsed time . How long would it take a pilot to fly 1240 miles at an average speed of 220 mph?
Answers
Answer:
Approx 5.64 hours
Step-by-step explanation:
d=rt
t=d/r
To find the time, divide distance by velocity
1240 / 220 = approx 5.64 hours
Simplify: (5x² – 3x + 7x) + (9x² + 2x² + 7x)
O 14x2 – x2 + 14x
O 14x2 + 13x
O 16x4 + x3
O 16x2 + 11x
O 16x2 – 11x
Answers
Answer:
16x^2+11x
Step-by-step explanation:
(5x² – 3x + 7x) + (9x² + 2x² + 7x)
Combine like terms
5x^2+9x^2+2x^2-3x+7x+7x
16x^2+11x
the score analysis of a school show the following.
180student register for Economics, 90 student Economics and political science,10 student Economics only, 150 student Economics and Geography, 120 student political science and Geography, 210 Geography, total number of students that register for the subjects= 250. find the number of students who register for.
1. political science
2. political science and Geography but not econs
3. Economics and political science but not Geography
Answers
Answer:
Economics and political science but not Geography
is right answer i think
Which equation is represented by the graph?
Answers
Answer:
The choose D. y=|x|–1
Your choice is right
I hope I helped you^_^
Triangle JKL is similar to triangle PQR. What is the measure of angle R?
Please answer as soon as possible.
Answers
Answer:
x = 43°
Step-by-step explanation:
59 + 78 + x = 180
137 + x = 180
(137 - 137) + x = 180 - 137
x = 43°
find a formula for the arithmetic sequence consisting of the positive multiples of 4
Answers
9514 1404 393
Answer:
4n
Step-by-step explanation:
For positive multiple number 'n', the value is 4n.
a[n] = 4n . . . . . where a[n] is the n-th term of the sequence
Answer:
an = 4n
Step-by-step explanation:
got it right on test
a fair six sided die is rolled find the probability of getting a 2
Answers
Answer:
1/6
Step-by-step explanation:
A number is multiplied by 16, and that product is added to 4. The sum is equal to the product of 4 and 9. Find the number.
Answers
Answer:
The number is 2
Step-by-step explanation:
x * 16 + 4 = 9*4
x * 16 + 4 = 36
x * 16 + 4 - 4 = 36 - 4
x * 16 = 32
x * 16 / 16 = 32 / 16
x = 2
Answer:
The number is 2
Step-by-step explanation:
let the number be "a"
16a+4=4×9
16a+4=36
16a=36-4
16a=32
a=2
Help please! Describe how figure 20 will look like
Answers
9514 1404 393
Answer:
Each colored block in Figure 20 will be a 20×20 square of smaller squares of the same color. The red-green pattern will be identical.
Step-by-step explanation:
Each colored block in Figure N is an N×N array of small blocks the same color. The pattern of red and green N×N blocks is the same from one figure to the next. We expect Figure 20 to fit this description.