Answer:
the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in
Step-by-step explanation:
The general area-of-a-triangle formula is A = (1/2)(base)(height), or = (1/2)bh.
Here b = h + 7.
Applying the area formula given above: A = 39 in^2 = (1/2)(h + 7)(h), or
78 in^2 = h^2 + 7h,
Rewriting this, in standard quadratic form, we get h^2 + 7h - 78 = 0
-7 ± (49 - 4[1][-78])
Applying the quadratic formula to find h: h = ----------------------------
2
-7 ± (49 + 312) -7 ± 19
or h = ----------------------- = ------------- = {-13, 6}
2 2
Discard the negative 13 root; the height must be a positive quantity.
Thus, the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in
2. Find the simple interest paid to borrow $4800 for 6 years at 7%.
Answer:
$2016
Step-by-step explanation:
Simple Interest equation: I = Prt
So,
P = $4800
r = [tex]\frac{7}{100}[/tex] = 0.07
t = 6
I = (4800) · (0.07) · (6)
Thus,
The simple interest is $2016.
AAAAAAAAA help please
Find the slope and y-Intercept of the line in the graph. Drag and drop each number into the correct box
to complete the statement.
7
(0,5)
4 3
2
1
0
(3,-1)
-1
-2
3
TO
de
8 7
0 1 2
55
The slope is m
and they-intercept is b =
Answer:
slope = - 2, y- intercept = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-5}{3-0}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
The y- intercept is the point on the y- axis where the line crosses
The y- intercept = 5
determine x+3 is a factor of P(x)=-2x^3-4x^2-7
Answer:
p(0)= -7
Step-by-step explanation:
find the gcf of 27 and 3
Answer:
Step-by-step explanation:
27x3=81
Answer:
It's 3 hope it's help....
Simplify the following and write your answer in simplest radical form:
√-14*√-22
Steps are in the attachment.
Note :-
=》2 is taken as negative & also taken out of the square root as it's the common factor.
______
⚜ Hope it helps :))
a grower wishes to mix a one peso per gram chemical with 80 centavo per gram chemical to produce mixture of 200 grams chemical which he can sell for 84 centavo a gram. how many grams of each price of chemical should he use
40 grams of $ 1 per gram and 160 grams of $ 0.80 per gram should be used.
Since a grower wishes to mix a one peso per gram chemical with 80 cent per gram chemical to produce mixture of 200 grams chemical which he can sell for 84 cent a gram, to determine how many grams of each price of chemical should he use you must perform the following calculation:
(150 x 1 + 50 x 0.8) / 2 = 95 (140 x 1 + 60 x 0.8) / 2 = 94 (100 x 1 + 100 x 0.8) / 2 = 90 (50 x 1 + 150 x 0.8) / 2 = 85 (40 x 1 + 160 x 0.8) / 2 = 84
Therefore, 40 grams of $ 1 per gram and 160 grams of $ 0.80 per gram should be used.
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how many prime numbers are multiples of 5 please
Answer:
the only number would be 5
Step-by-step explanation:
5 is the first and only prime multiple of 5
There are only ''one'' prime number are multiples of 5.
What is Prime number?
Prime numbers are number that have only two factors, 1 and themselves.
Given that;
The prime numbers multiples of 5.
Now,
The multiples of 5 = 5, 10, 15, 20, 25, ...
But there are only one prime number (that is; 5) which are multiple of 5.
Thus, There are only ''one'' prime number are multiples of 5.
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#SPJ2
22 divided by 2,737 include the remainder
Answer:
124.409
Step-by-step explanation:
sana makatulong sa inyong lahat
A man is 32 years older than his son ten year ago he was three times as old as his son was then find the present age of each?
Answer:
son 26 age
Father 58 age .........
Is (x + 6) a factor of f(x) = x3 − 3x2 + 2x − 8? Show how to use either the remainder theorem or the factor theorem to explain your reasoning.
Answer:
x + 6 is not a factor of f ( x ) = x³ - 3x² + 2x - 8 because when -6 is substituted into the function, the answer is not 0.
Step-by-step explanation:
→ Substitute x = -6 into f ( x )
( 6 )³ - 3 × ( 6 )² + ( 2 × 6) - 8
→ Simplify
216 - 108 + 12 - 8
→ Simplify further
112
help ??? on edu math review
Answer:
It must be C.
Step-by-step explanation:
x² - 9 = 16
=> 16 + 9 = x²
=> 25 = x²
=> x = 5
Referring to the options, C is the only one that is accurate to me. Hoped this helped.
IN THE MIDDKE IF EXAM PLS HELPQuestion 3(Multiple Choice Worth 4 points)
Find the length of the unknown side. Round your answer to the nearest whole number.
5 in
5 in
7 inches
10 inches
25 inches
50 inches
Answer:
7 inches
Step-by-step explanation:
5 square + 5 square=50
the square root of 50 is 7.07
7.07 to the nearest whole number is 7
Answer:
7 Inches
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
5² + 5² = c²
50 = c²
[tex]\sqrt{50}[/tex] = c
c = 7.07
ROUND
c = 7 inches
What is the slope of a line perpendicular to the line whose equation is
3x + 3y = –27. Fully simplify your answer.
Answer:
1
Step-by-step explanation:
Perpendicular lines always have the opposite slope (meaning that you have to switch the numerator and denominator) and sign when comparing to the given equation.
To start off, convert the equation to be formatted into y=. You do this by first subtracting the 3x from both sides of the equation so that it now reads 3y=-3x-273y=−3x−27 . Now, divide the whole equation by three in order to get rid of the value attached to the y. The equation should now read to be: y=-x-9y=−x−9 . Now, just switch the the slope into its opposite (which is the reciprocal) and switch the negative sign into a positive.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 15 yards ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 yard per second, and the adults hobbled after them at a rate of 4 yards per second. Soon they were side-by-side. How long did that take? How far did the adults go?
It took seconds for the adults to go yards and catch up to the kids?
A system of equations is simply a system that contains related equations of multiply variables
It took 5 seconds for the adults to go 20 yards and catch up to the kids
Let x represents the time of the race
The kids started 15 yards ahead, and they raced at 1 yard per second.
So, the kids' equation is represented as: [tex]\mathbf{k =15 + x}[/tex]
The adults' raced at 4 yards per second.
So, the adults' equation is represented as: [tex]\mathbf{a =4x }[/tex]
When they are side by side, we have the following equivalent equation
[tex]\mathbf{4x = 15 + x}[/tex]
Subtract x from both sides
[tex]\mathbf{3x = 15}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 5}[/tex]
It means that, it took the adults 5 seconds to catch up with the kids
Substitute 5 for x in any of the equations to calculate the distance travelled.
[tex]\mathbf{a =4 \times 5}[/tex]
[tex]\mathbf{a =20}[/tex]
It means that, the adults catch up with the kids at 20 yards
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Answer:
The adults went 123 yards and caught up to the kids in 41 seconds
Step-by-step explanation:
ixl :)
How many solutions for
55l=50l+5
Answer:
Zero
Step-by-step explanation:
The question is impossible to answer. 501+5 does not equal 551, 501+5 equals 506.
My mom gave me $20 for grocery’s. She needed cat food which was $8.50 for a 35 pound bag. And the rest of the money she needed to buy socks for my dad which are a $1.50 for two pairs how many pairs of socks can I buy.
Answer:
15 pairs
Step-by-step explanation:
total:$20
cat food: $8:50
two pair of socks: $1.50
$20 - $8.50= $11.50(the rest of the money)
the rest is divided by the price of the socks to obtain how may socks you can pay with $11.50.
$11.50÷$1.50≈ 7.6
Now you multiply 7.6 by two to get the exact amount of socks with the offer.
7.6×2≈15.2
15.2≈15
So with $11.50 you will buy 14 socks for 1.50 every two pairs and a pair for 0.75
Walmart was having a sale on stereo systems. Danny wants the stereo that is originally $140
but it is on sale for 25% off. How much will Danny have to spend?
Answer:
$105
Step-by-step explanation:
Turn 25% to decimal
25% = 0.25
Now multiply it to 140
140 x .25
= $35
The discount price is 35$
Now subtract it to 140
140 - 35
= $105
Answer:
See below:
Step-by-step explanation:
Hello! I hope you are having a nice day!
We can solve this problem in two steps; Comprehending and Solving.
I'll start off with Comprehending.
Comprehending
We can start solving the problem by setting up an equation to help us solve the problem.
We know the original price is $140 and we get a 25% off.
We also know that 25% is equal to [tex]\frac{1}{4}[/tex].
Hence we can solve for this by multiplying [tex]140*\frac{1}{4}[/tex].
Solving
We can solve the problem by using the equation that we found out above.
We can use algebra to find out and simplify it!
[tex]140*\frac{1}{4}= x\\70*\frac{1}{2}=x\\x= 35[/tex]
But wait! We have only found out what 25% of $140 is, we still need to subtract it from the original equation.
$140-$35=$105
We've gotten our answer of $105.
Cheers!!
Please Help! I don't understand how the Alabama paradox works. I will give you a lot of points!
--PLEASE show all work
The table shows the populations, in thousands, of the three states in a country with a population of 3760 thousand. Use Hamilton's method to show that the Alabama paradox occurs if the number of seats in congress is increased from 24 to 25
Answer:
State A loses a seat to State B when the total is increased
Step-by-step explanation:
The "work" is most easily done by a spreadsheet, as the calculations are easily defined and very repetitive.
The "fair share" of seats is the fraction the population is of the total, multiplied by the total number of seats. It will generally be a mixed number (integer plus fraction).
If the whole number is 1 or greater, the number of seats allocated at least that whole number.
If not all seats are allocated, the fractions are sorted in decreasing order, and 1 additional seat is added to the allocation for each state, working down the list, until all of the seats are allocated.
__
The attachment shows State A has the highest fraction when the number of seats is 24. Only one additional seat needs to be allocated in that case. State A gets that extra seat.
When the number of seats is 25, States B and C have the highest fractions. Each of them gets one additional seat, and State A gets no additional seats. This results in the appearance of State A giving up a seat to State B.
_____
Additional comment
Hamilton's apportionment method was used for a number of years in the US. The method now in use is substantially different. The current method would divide the 24 seats so that A=3, B=6, C=15. The 25th seat would be given to State A.
Kayla drives her new car to work every day. It uses 1 3/5 gallons of gas for each round trip. How many round trips to work can Kayla drive on a 16-gallon full tank of gas?
Answer:
16 road trips
Step-by-step explanation:
If an amount of $25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $28,500? The function describing your balance is M(n) =25,000(1+0.04/2)^2n, where n is time in years. Round up your answer to the next period.
It will take 3 years and 4 months to accumulate $ 28,500.
To determine, if an amount of $ 25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $ 28,500, the following calculation must be performed:
25,000 x (1 + 0.04 / 2) ^ (2X) = 28500 25000 x 1.02 ^ 2X = 28500 1.02 ^ 2X = 28500/25000 1.02 ^ 2X = 1.14 1.02 ^ 6.62 = 1.14 6.62 / 2 = X 3.33 = X
Therefore, it will take 3 years and 4 months to accumulate $ 28,500.
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Please can someone show me their working on these, as I'd really like to know where I went wrong.
Answer:
C
Step-by-step explanation:
You were on the right track, but 3-2 = 1, so the exponent of (x-4) is 1.
Answer:
C and B
Step-by-step explanation:
(6)
[tex]\frac{(x-4)^3(3x+6)}{(x-4)^2}[/tex]
Cancel (x - 4)³ on numerator with (x - 4)² on denominator
leaving (x - 4) on numerator and 1 on denominator
= (x - 4)(3x + 6) → C
--------------------------------------------------
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
4a² × 7[tex]a^{\frac{1}{2} }[/tex]
= 4 × 7 × a² × [tex]a^{\frac{1}{2} }[/tex]
= 28 × [tex]a^{\frac{4}{2} }[/tex] × [tex]a^{\frac{1}{2} }[/tex]
= 28 × [tex]a^{(\frac{4}{2}+\frac{1}{2}) }[/tex]
= 28[tex]a^{\frac{5}{2} }[/tex] → B
9,962÷41. What dose it =
Answer:
242.975609756
Step-by-step explanation:
Answer:
242.975
Step-by-step explanation:
TIP: u can use a calculator if your teacher allows you, it would be faster :)
The total cost of going to the theatre for 18 people is £803.16.
How much will each person need to pay to cover the total cost?
The swimming club need to raise £135 for transport to the swimming gala.
They buy 20 tracksuits for £15.98 each and will sell them to raise money.
What percentage profit should they add to the cost of the tracksuits to raise the £135 they need?
Answer:
Step-by-step explanation:
The investment was
20(£15.98) = £319.60
After the sale, they want to have
£319.60 + £135.00 = £454.60
Which means each suit sells for
£454.60/20 = £22.73
The markup was
£22.73 - £20.00 = £2.73
which as a fraction of the purchase price is
£2.73/£20.00 = 0.1365
0.1365(100) = 13.65%
2y = 8x- 70
What’s the slope and y intercept?
Answer:
slope = 4, y- intercept = - 35
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2y = 8x - 70 ( divide through by 2 )
y = 4x - 35 ← in slope- intercept form
with slope m = 4 and y- intercept c = - 35
What is the equation of this line?
Answer:
y = x
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line
m = [tex]\frac{1-0}{1-0}[/tex] = [tex]\frac{1}{1}[/tex] = 1 , then
y = x ← equation of line
If an amount of $25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $28,500? The function describing your balance is M(n) =25,000(1+0.04/2)^2n, where n is time in years. 20 points and WILL GIVE BRAINLIEST!
It will take 3.3 years to accumulate $28,500 on this account
According to the compound amount formula expressed as:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P is the principal = $25,000
A is the amount = $28,500
r is the rate in decimal = 4% = 0.04
n = 2 (semi annualy)
Substitute the given parameters into the formula as shown:
[tex]28,500=25,000(1+\frac{0.04}{2} )^{2t}\\1.14=(1+0.02)^{2t}\\1.14 = (1.02)^{2t}\\ln1.14 = 2tln1.02\\2t=\frac{ln1.14}{ln1.02}\\2t= \frac{0.13103}{0.01980}\\2t= 6.6177\\t = 3.30yrs[/tex]
Hence it will take 3.3 years to accumulate $28,500 on this account
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what you've learned from it. Was it a success or a challenge?
how much water should be added to 5 gallons of 50% acid solution to get a 20% solution?
ASAP!!! PLS
Answer:
22.5
Step-by-step explanation:
50%of5+20%=22.5
50/100×5=2.5
2.5+20=22.5%
Answer:
3 gallons
Step-by-step explanation:
10=100 percent
10/5 =2
5-2=3
3 gallons