Question :-
A Triangle has an Area of 48 cm² . The Height of the Triangle is 6 cm . What is the Base of the Triangle ?Answer :-
Base of Triangle is 16 cm .Explanation :-
As per the provided information in the given question, we have been given that the Area of Triangle is 48 cm² . It's Height is given as 6 cm . And, we have been asked to calculate the Base of Triangle .
For calculating the Base of Triangle , we will use the Formula :-
[tex] \bigstar \: \: \: \boxed{ \sf{ \: Area \: _{Triangle} \: = \: \frac{1}{2} \: \times \: B \: \times \: H \: }} [/tex]
Where ,
B denotes to the Base .H denotes to the Height .Therefore , by Substituting the given values in the above Formula :-
[tex] \dag \: \: \: \sf { Area \: _{Triangle} \: = \: \dfrac{1}{2} \: \times \: Base \: \times \: Height } [/tex]
[tex] \longmapsto \: \: \: \sf {48 \: = \: \dfrac {1}{2} \: \times \: Base \: \times \: 6 } [/tex]
[tex] \longmapsto \: \: \: \sf {48 \: \times \: 2 \: = \: 1 \: \times \: Base \: \times \: 6} [/tex]
[tex] \longmapsto \: \: \: \sf {96 \: = \: 1 \: \times \: Base \: \times \: 6} [/tex]
[tex] \longmapsto \: \: \: \sf {96 \: = \: 6 \: \times \: Base } [/tex]
[tex] \longmapsto \: \: \: \sf {Base \: = \: \dfrac {96}{6} } [/tex]
[tex] \longmapsto \: \: \: \textbf {\textsf {Base \: = \: 16 \: cm}} [/tex]
Hence :-
Base of Triangle = 16 cm .[tex] \underline {\rule {180pt} {4pt}} [/tex]
A triangle has an area of 48 square centimetres. The height of the triangle is 6 centimetres. What is the base of the triangle ?
Given : - Area of triangle = 48 cm²Height of triangle = 6 cmTo Find : -Base of triangle Formula Used : -[tex] \blue{\boxed{Area \: of \: triangle = \frac{1}{2} \times b \times h}}[/tex]
Where ,
b = Base of triangleh = Height of triangle Concept : -In this question the concept belongs to the areas of two dimensional shapes i.e. how we can find length , breadth or height with the help of given area .
So let's get started : -[tex] \longmapsto \: 48 = \frac{1}{2} \times b \times 6[/tex]
Now , transposing 2 to left hand side :
[tex] \longmapsto \: 48 \times 2 = 1 \times b \times 6[/tex]
Now , multiplying 48 with 2 and multiplying b with 1 and 6 :
[tex] \longmapsto \: 96 = 6b[/tex]
Now , transposing 6 to left hand side :
[tex] \longmapsto \: \cancel\frac{96}{6} = b[/tex]
Now , by cancelling them we get :
[tex] \longmapsto \: \red{ \boxed{ \sf{b = 16 \: cm}}}[/tex]
Therefore , base of triangle is of 16 cmVerifying : -We know that area of triangle is equal to 48 cm². So :
[tex] \rightarrow \: \frac{1}{ \cancel2} \times \cancel{16} \times 6 = 48[/tex]
Now , by cancelling 16 with 2 we get :
[tex] \rightarrow \: 8 \times 6 = 48[/tex]
So , by multiplying we get :
[tex] \rightarrow \: 48 = 48[/tex]
That means :
[tex] \rightarrow \: L.H.S = R.H.S[/tex]
Hence , Verified .Therefore, our answer is valid .#Keep LearningWhich is the best definition for adjacent angles?
Answer:
Adjacent Angles are 2 angles with common sides and a common vertex that don't overlap in any way.
Step-by-step explanation:
Leave a comment if you need any more help. Give Brainiest, please.
Write the recursive formula for the following sequence 2, 8, 32, 128
Answer:
an+1 = 4an
Step-by-step explanation:
an+1 = 4an commonratio: r=4
2
2x4=8
8x4=32
32x4=128
I need lateral surface
Answer:
un rhgdb tennis felicidades ID remix estoy do do ID do ID Rockband do ID do TX
Solve for n:
n
---- = 1
20
A. n = 23
B. n = 15
C. n = 20
D. n = 32
Answer:
The answer is C
Step-by-step explanation:
[tex]\frac{n}{20}*20 = 1 * 20[/tex]
1 x 20 = 20
Answer:
C) n = 20
Step-by-step explanation:
hope it helps!
Find the value of x. 1222° 0 111 O 55 O 42 O 138
Based on the outside angles theorem, the value of x is: 42°
What is the Outrside Angles Theorem?The outside angles theorem states that the measure of the angle that is formed outside a circle when two tangents or secants intersect is half the measure of the diffrence of the intercepted arcs.
Given the following:
One arc measure = 222°The second arc measure = 360 - 222 = 138°Therefore, based on the outside angles theorem, we would have the following:
x = 1/2(222 - 138)
x = 42°
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The table below shows a proportional relationship. True or False?
True
False
Answer:
False
Step-by-step explanation:
2/10 is not equal to 4/16.
9
These lists show the ages of attendees in a yoga class and a dance dass
Yoga: 18, 31, 17, 14, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Select from the drop-down menus to correctly complete each statement about the attendees in the two cases
The median age of the attendees in the yoga class is
the median age of the attendees in the dance
The range of ages of the attendees in the yoga class is
the range of ages of the attendees in the conce
Answer:
median is 20
Step-by-step explanation:
due to both of them having it in there 1 time
Answer:
The Median Age: Yoga Class (31) Dance Class (30)
The Range: Yoga Class (17-44) Dance Class (20-47)
Step-by-step explanation:
Find the slope of the line passing through the points(-9,-6) and (-4,5)
Hey there!
We're given 2 points that the line intersects, so we can easily determine the line's slope.
This is the formula:
[tex]\bold{\displaystyle\frac{y2-y1}{x2-x1} }[/tex]
[tex]\bold{\displaystyle\frac{5-(-6)}{-4-(-9)}}[/tex]
[tex]\bold{\displaystyle\frac{5+6}{-4+9}}[/tex]
[tex]\bold{\displaystyle\frac{11}{5}}[/tex]
Hence, the answer is
[tex]\boxed{\boxed{\bold{\frac{11}{5} }}}[/tex]
Hope everything is clear.
Let me know if you have any other questions!
#LearningDoesn'tEnd
:-)
[tex]\rule{200}{2}[/tex]
Lori puts up a sign for her business 500 meters from the main entrance. She once read that it takes the average adult 6 minutes to walk 500 meters. She decides to test this by having 200 adults walk the 500 meters from her sign to her store. Which of the following is the sample in Lori's experiment?
Step-by-step explanation:
She decided to test this by 200 adults, so. Divide 6 by 500 = 0.012 (200)=2.4mins.
Answer: The 200 adults
Step-by-step explanation:
WILL MARK BRAINLIEST
Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y-6= -5(x-3)
y - 6 = - 5 * x - 5 * (-3)
y - 6 = -5x + 15
y + 5x = 15 + 6
5x + y = 21
Answer:
5x + y = 21.
Step-by-step explanation:
y - 6 = -5(x - 3)
y - 6 = -5x + 15
5x + y - 6 = 15
5x + y = 15 + 6
5x + y = 21.
The giraffes at the Liberia zoo eat 75 pounds of food per day, and 52.5 pounds per day comes from acacia leaves. How much of their diet comes from other types of leaves?
Julia, the zookeeper, used the equation 52.5 + x = 75 to find the answer. Which equation is an equivalent equation that can be used to solve the problem?
Answer:
Step-by-step explanation:
75-52.5=x
Betsy, a recent retiree, requires $5,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $5,000 in interest per year?
A. The amount of money invested at 13% = ___
B. The amount of money invested at 5% = ___
A. The amount of money that Betsy should invest n B-rated bonds at 13% is $20,000.
B. The amount of money that Betsy should invest in a certificate of deposit (CD) at 5% is $50,000.
How are CDs different from Bonds?Certificates of deposit (CDs) are short-term investments in financial institutions (money market) while Bonds are long-term investments in the stock exchange (capital market).
CDs pay reduced interest rates when compared to bonds'.
Data and Calculations:The amount required per year in interest = $5,000
Total investible funds = $70,000
Interest rate of B-rated bonds = 13%
Interest rate in CD = 5%
Since Betsy is not interested in realizing more than $5,000 in interest per year, she should invest $50,000 in the CD and $20,000 in the B-rated bonds.
The interest in CD = $2,500 ($50,000 x 5%)
The interest in bonds = $2,600 ($20,000 x 13%)
Total interest in CD and bonds = $5,100 ($2,500 + $2,600)
Thus, Betsy should invest $50,000 in the CD and $20,000 in the B-rated bonds.
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Pam kicked a soccer ball down the field. Part of the ball's path, including its highest
point, is described by the function below, where f(x) is the height of the ball in feet.
According to the function, what is the ball's maximum height, in feet? (Use only the
digits 0-9 to enter the height.)
f(x) =
12x2+2x
Answer:
maximum height is 45/4 in feet
The maximum height of the ball is 45/4 in feet
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given tha Pam kicked a soccer ball down the field. Part of the ball's path, including its highest point, is described by the function below, where f(x) is the height of the ball in feet.
F(x)= 12x^2+2x
Thus for this quadratic , the max value will occur at x= -b/2a
= - 2 / (2 x 1/12) = -12
Plug in -12 to find the max height
= (-12)^2 + 2 x-12
= 45/4 in feet
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CAN SOMEBODY HELP ME SOLVE THIS EQUATION
What expression is equivalent to 12x^4/4x^16 helpppp
Answer: 48x/64
Work (assuming ^ is multiplication):
12x^4/4x^16
12x ^ 4x = 48x
4 ^ 16 = 64
the length of a rectagle is 6 ft longer than its width. if the perimeter of the rectangle is 64 ft, find its length and width
Answer:
19 and 13
Step-by-step explanation:
width = x
length = x + 6
2x + 2(x + 6) = 64
2x + 2x + 12 = 64
4x = 64 - 12
4x = 52
x = 13
x + 6 = 19
Answer:
19 and 13
Step-by-step explanation:
At the beginning of the summer,
Shay had $27 in her savings
account. Shay worked as a
lifeguard and by the end of the
summer had a total of $575 in
her savings account. How much
did Shay save over the summer?
Maya sells candles to her 5 neighbors. Each neighbor buys 2 boxes of candles. There are 6 candles in each box. What is the total number of candles that all of her neighbors will get?
A.
16 candles
B.
30 candles
C.
40 candles
D.
60 candles
Answer:
D. 60 Mark brainliest<3
Step-by-step explanation:
Each neighbor buys 2 boxes which contains 6 candles meaning they in total contain 12.
5x12 = 60
What is the value of x?
13 m
15 m
Answer:
which one?
Step-by-step explanation:
find the value of x in the diagram
Answer: there is something off screen i cant see so i cant help you 183- what?
Step-by-step explanation:
need help with geometry question
zeros.
Find a polynomial of the specified degree that has the given
Degree 5; zeros -4, -3, 0, 4,3
Answer:
f(x)=x(x+4)(x+3)(x-4)(x-3)
Step-by-step explanation:
hello :
an polynomial is : f(x)=(x+4)(x+3)(x-0)(x-4)(x-3)
means : f(x)=x(x+4)(x+3)(x-4)(x-3)
What is 1 * 2 = + * 1 = + + 2 2 + 1 8 5 / 9
Whoever answers it gets grevious
Answer:
Can you use a specific question please
Step-by-step explanation:
Answer: = 17 7/
Step-by-step explanation:
8 1/5 + 9 1/2 = 177/
10
= 17 7/
Evan owns a small business selling ice-cream. He knows that in the last week 83
customers paid cash, 8 customers used a debit card, and 2 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
debit card or a credit card as a percent to the nearest whole number.
The probability that the next customer will pay with a debit card or a credit card is 12%.
What is the probability that the next customer would pay with a debit card or a credit card?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the next customer would pay with a debit card or a credit card = (number of customers that paid with a debit card + number of customers that paid with a credit card) / total number of customers
(8 + 2)/ 83 = 0.12 = 12%
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[tex] \\ { \rm{If \: }{\tt{A = \left [ \: \begin{array}{ c c c} \: \: \: \: 2 & -3 & - 5 \\ - 1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1& - 3 & - 4\end{array} \: \: \: \right] \: and \: B = \left[\begin{array}{c c c} \: \: \: \: 2 & - 2 & - 4 \\ - 1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & - 2 & - 3\end{array} \right]}}}, { \rm{shown \: that \: AB = A \: and \: BA = B}}[/tex]
[tex] \: [/tex]
Don't Spam
Explain well
Answer:
Given:
[tex] \\ {\tt{A = \left [ \: \begin{array}{ c c c} \: \: \: \: 2 & -3 & - 5 \\ - 1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1& - 3 & - 4\end{array} \: \: \: \right] \: and \: B = \left[\begin{array}{c c c} \: \: \: \: 2 & - 2 & - 4 \\ - 1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & - 2 & - 3\end{array} \right]}}[/tex]
Matrix A is of order 3 × 3 and Matrix B is of order 3 × 3
To Show:
Matrix AB = A , BA = BFormula Used:
[tex]\\ { \rm{ \left[ \begin{array}{c c c} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array} \right] \times \left[ \begin{array}{c c c} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{array} \right] = \: \left[ \begin{array}{c c c} \: \: a_{11}b_{11} + a_{12}b_{21} + a_{13}b_{31} & a_{11}b_{12} + a_{12}b_{22} + a_{13}b_{32} & a_{11}b_{13} + a_{12}b_{23} + a_{13}b_{33} \\ \: \: a_{21}b_{11} + a_{22}b_{21} + a_{23}b_{31} & a_{21}b_{12} + a_{22}b_{22} + a_{23}b_{32}&a_{21}b_{13} + a_{22}b_{23} + a_{23}b_{33} \\ \: \: a_{31}b_{11} + a_{32}b_{21} + a_{33}b_{31}&a_{31}b_{12} + a_{32}b_{22} + a_{33}b_{32} & a_{31}b_{13} + a_{32}b_{23} + a_{33}b_{33}\end{array} \right]}}[/tex]
If A is a matrix of order a×b and B is a matrix of order c×d , then matrix AB exits and is of order a×d , if and only if b = c.
[tex] \: \: [/tex]
If A is a matrix of order a×b and B is a matrix of order c×d , then matrix BA exits and is of order c×b , if and only if d = a.
[tex] \: \: [/tex]
____________________________________________________________________For Matrix AB, a = 3, b = c = 3, d = 3 , thus Matrix AB is of order 3×3
[tex]\\ { \rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right] \times \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] = \left[\begin{array}{c c c} \: \: \: \: 2(2)-3(-1)-5(1) & \: \: \: \: 2(-2)-3(3)-5(-2) & \: \: \: \: 2(-4)-3(4)-5(-3) \\ -1(2)+4(-1)+5(1) & -1(-2)+4(3)+5(-2) & -1(-4)+4(4)+5(-3)\\ \: \: \: \: 1(2)-3(-1)-4(1) & \: \: \: \: 1(-2)-3(3)-4(-2) & \: \: \: \: 1(-4)-3(4)-4(-3) \end{array} \right]}}[/tex]
[tex]\\ {\rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 4 + 3 - 5 & \: \: \: -4 -9 + 10 & \: \: -8 - 12 + 15 \\ -2 - 4 + 5 & \: \: \: \: \: \: + 2 + 12 - 10 & \: \: \: \: \: 4 + 16 - 15 \\ \: \: \: \: \: 2 + 3 - 4 & \: \: -2 - 9 + 8 & -4 - 12 + 12 \end{array} \right] = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right]}}[/tex]
[tex]\\ {\rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right] = Matrix \: A}}[/tex]
Matrix AB = Matrix A____________________________________________________________________For Matrix BA, a = 3, b = c = 3, d = 3 , thus Matrix BA is of order 3 × 3
[tex]\\ {\rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] \times \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: \: 1 & -3 & -4 \end{array} \right]}}= \left[ \begin{array}{c c c} \: \: \: \: \: 2(2) -2(-1) -4(1) & \: \: \: \: 2(-3) -2(4) -4(-3) & \: \: \: \: 2(-5) -2(5) -4(-4) \\ \: -1(2) + 3(-1) + 4(1) & -1(-3) + 3(4) +4(-3) & -1(-5) + 3(5) + 4(-4) \\ \: \: \: \: \: 1(2) -2(-1) -3(1) & \: \: \: \: 1(-3) -2(4) -3(-3) & \: \: \: \: 1(-5) -2(5) -3(-4) \end{array} \right][/tex]
[tex]\\{ \rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 4 + 2 - 4 & \: \: \: -6 -8 + 12 & \: \: -10 - 10 + 16 \\ -2 - 3 + 4 & \: \: \: \: \: \: +3 + 12 - 12 & \: \: \: \: \: + 5 + 15 - 16 \\ \: \: \: \: \: 2 + 2 - 3 & \: -3 -8 +9 & \: \: \: \: \: -5 -10 + 12 \end{array} \right] = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right]}}[/tex]
[tex]\\{ \rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] = Matrix \: B}}[/tex]
Matrix BA = Matrix B____________________________________________________________________ans this sum plsss .
Answer:
See below ↓
Step-by-step explanation:
3.
2/512/253/73/83/104.
Draw a number of spacing 0.25 eachStart from -1 to 1-2/8 = -0.25 [mark on line]3/6 = 0.5 [mark on line]5.
Midpoint of -2/5 and 1/2M = [-2/5 + 1/2] / 2M = [1/10] / 2M = 1/20At the store grapes are on sale. You can buy 3 pounds for
$2 dollars. At that rate, how many pounds can you buy
for $8? Show how you know.
Answer:
If you buy 3 pounds for $2, and have 8 dollars to spend, then multiply 2x4 to get $8. Since we multiplied by 4 for the money, we do the same thing for the pounds of grapes. So, we multiply 3x4 to get 12 pounds. So, you can buy 12 pounds of grapes for $8.
Step-by-step explanation:
Hope this helps! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP.
what is the angle measure of an arc bounding sector with an area of 5pie square miles?
if the diameter is 20, the its radius must be half that or 10.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}[/tex]
Find the mean of the data.
55,64,58,43,49,67
Answer:
56
Step-by-step explanation:
Step 1: Order the data
43,49,55,58,64,67
Step 2: Count all numbers and add them up
43+49+55+58+64+67=336 and we have 6 numbers in total so... 336 ÷ 6
Step 3: Divide!
336 ÷ 6 = 56
Hope this helps you!
The regular price of a color TV is $539.22. During a sale, Hill TV is selling the TV for $456.56. Determine the percent decrease in the price of the TV
Hey there!
Answer: = 15.3296% decrease
How to Calculate Percentage Decrease
Subtract starting value minus final value=> 539.22 - 456.56
=> 79.66
Divide that amount by the absolute value of the starting value=> 79.66 ÷ 539.22
=> 0.153296
Multiply by 100 to get percent decrease=> 0.153296 × 100
=> 15.3296%
If the percentage is negative, it means there was an increase and not an decrease.
Therefore, percentage decrease is 15.3%