The area of a triangle is found by multiplying half of the measure of its base by its height. The area of the following right triangle is 18 square centimeters.
A. Write and solve an equation to find the value of h. Include all of your work in your answer.
B. In two or more complete sentences, verify your answer using mental math.
50 points
Answers
Answer:
[tex]\sf Area\:of\:a\:triangle=\dfrac12 \times base \times height[/tex]
Given:
area = 18 cm²base = 6 cmheight = (h + 1) cmSubstitute the given values into the equation and solve for h:
[tex]\sf \implies 18 = \sf \dfrac12 \times 6 \times (h+1)[/tex]
[tex]\sf \implies 18 = \sf \dfrac62 (h+1)[/tex]
[tex]\sf \implies 18 =3(h+1)[/tex]
expand using distributive property of addition [tex]a(b+c)=ab+ac[/tex]:
[tex]\sf \implies 18=3h+3[/tex]
subtract 3 from both sides:
[tex]\sf \implies 3h=15[/tex]
divide both sides by 3:
[tex]\sf \implies h=5[/tex]
To verify:
Half of the base is 3 cm.
If h=5, then the height of the triangle is 6 cm.
Multiplying 3 by 6 is 18.
This matches the given area, so we can verify that h = 5.
Answer:
Below!
Step-by-step explanation (a):Given:
Area of Triangle = 18 cm²Base of Triangle = 6 cmHeight of (Triangle = (h + 1) cmFormula:
[tex]\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}[/tex]
Substitute the measures into the formula:
[tex]:\implies 18 \ \text{cm}^{2} = \dfrac{1}{2} \times 6 \times \text{(h} + 1\text{)}[/tex]
SImplify the R.H.S:
[tex]:\implies18 \ \text{cm}^{2} = 3 \times \text{(h} + 1\text{)}[/tex]
Divide both sides by 3:
[tex]:\implies \dfrac{18}{3} = \dfrac{3 \times \text{(h} + 1\text{)}}{3}[/tex]
Simplify both sides:
[tex]:\implies 6 = \text{(h} + 1\text{)}[/tex]
Subtract 1 both sides:
[tex]:\implies 6 - 1 = \text{h} + 1- 1[/tex]
Simplify both sides:
[tex]:\implies 5= \text{h}[/tex]
Step-by-step explanation (b):Reviewing on how to verify our answer:
We can verify our answer by substituting the value of "h" in (h + 1) to determine the height of the triangle. Then we can substitute the height and the base in the "area of triangle" formula (1/2 x Base x Height).
Note: Keep in mind that the evaluated area should be 18 cm², as said in the question. If the area evaluated is different from 18 cm², then the value of "h" is incorrect.Verifying our answer through mental math:
Clearly, the height of the triangle is 6 cm, as when "h" is substituted in the expression (h + 1), we get 5 + 1.As said above, the formula for determining the area of a triangle is 1/2 x Base x Height. Clearly, half of 6 is 3. Lastly, when 6 (Base) and 3 (Half of the height) are multiplied, we get 18 cm², which is the area stated in the question.Thus, the value of "h" is verified through mental math.
Related Questions
If f(x) = x3 – 2x2, which expression is equivalent to f(i)? –2 i –2 – i 2 i 2 – i
Answers
Answer:
Answer
d) 2 – i
Explanation
f(x) = x³ – 2x²
When x = i, we proceed as follows.
Note: i =
i² =(√-1)(√-1) = -1
i³ = (√-1)(√-1)(√-1) = -1(√-1) = -1i = -i
f(x) = x³ – 2x²
f(i) = i³ – 2i²
= -i – 2(-1)
= -i + 2
= 2 – i
Step-by-step explanation:
Jill has a coupon for 15% off at her favorite restaurant, Downtown Noodles. You can use a function to estimate how much Jill will pay if the bill is x dollars
Answers
Answer:
Step-by-step explanation:
Let function p(x) be the price that is reduced by 15% if the bill is x dollars.
Since the price is not payed in full 100% is reduced by 15% we only pay
100 - 15 = 85 % of the original price.
p(x) = x· (100% - 15 %) = x· 85% = 0.85 x
The function used to calculate any bill that is reduced by 15% is:
p(x) = 0.85x
x - is the bill before being reduced by the coupon
If you could put wings on any species of animal, what animal would you choose?
Answers
Answer:
Humans
Explanation:
So I can have wings :)
Answer:
If I could put wings on any species of animal, I would choose a Unicorn because then the Unicorn can fly and look at all the enviroment.
Step-by-step explanation:
63.1 X 2.2 step by step
Answers
Answer:
138.82
Step-by-step explanation:
Line up the numbers on the right - do not line the decimal points.
Start on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
then you add the products.
Answer:
138.82
Step-by-step explanation:
Multiply the numbers using the normal multiplication process. Now, count the number of digits after the decimal point in both the numbers. Add these 2 values & put the decimal point in the product by counting the digits from the left side of the place value. The answer is 138.82.
=》 Check the attachment for the steps.
_____________
Hope it helps ⚜
…. I need help again oof
Answers
Answer:
m∠WVZ=90°
m∠XVW=90°
Step-by-step explanation:
m∠WVY=m∠WVZ+m∠ZVY
180°=9x-15°+90°
180°=9x+75°
180-75=9x
105°=9x
⇒x = [tex]\frac{35}{3}[/tex]
So. m∠WVZ is
[tex]=9(\frac{35}{3})-15=3\times35-15\\=105-15=90[/tex]
m∠WVZ=90°
and same will be the m∠XVW
m∠XVZ=m∠XVW+m∠WVZ
180°=m∠XVW+90°
m∠XVW=180°-90°
m∠XVW=90°
1. Given that the third and sixth terms of an A.P. are 13 and 22 respectively, find the sum
of the first n terms in terms of n.
Answers
Answer:
1
+t
3
+t
5
=39
t
2
+t
4
+t
6
=51
To find:
t
10
=?
Solution:
Let a be the first term and d be the common difference.
t
1
+t
3
+t
5
=39
or, a+a+2d+a+4d=39
or, 3a+6d=39
or, a+2d=13 .............(i)
t
2
+t
4
+t
6
=51
or, a+d+a+3d+a+5d=51
or, 3a+9d=51
or, a+3d=17
Subtracting eqn. from eqn. we get,
d=4
Putting value d=4 in eqn.(i) we get,
a+2×4=13
or, a=13−8
or, a=5
Now, t
10
=a+9d
t
10
=5+9×4
t
10
=5+36
t
10
=41
divide the sum of 65 12 and 8 3 by their difference
Answers
Step by step explanation:
oliver bought 7 bags of candy each bags cost 1.50 i need help step buy step
Answers
oliver bought 7 bags of candy each bags cost 1.50
Answer-$10.50
Answer:
10.5
Step-by-step explanation:
you take 1.50 and times it by how many bags there are so 7
1.50×7=10.5
help me out pls
What does obliviousness mean?
• 1.
being interested in something
• 2. being unaware of something
( 3. being impressed by something
hm
• 4. being confused by something
Answers
Answer:
Obliviousness: Being unaware of something.
What is the average rate of change for this quadratic function for the interval from x = 2 to x = 4? O A. -12 B. 12 C. -6 O D. 6
Answers
D. 6.
We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].
We will use formula [tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(-2)-f(-4)}{-2--4}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6--6}{-2+4}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6+6}{2}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{12}{2}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=6[/tex]
Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.
Answer:
6
Step-by-step explanation:
because i am in credit recovery and i had a test on it
What is the true solution to the equation below? 2 l n e superscript l n 2 x baseline minus l n e superscript l n 10 x baseline = l n 30
Answers
The true solution x for the logarithmic equation which is shown below will be 75.
[tex]2 \ln e^{\ln 2x} - \ln e ^{\ln 10} = \ln 30[/tex]
What is a logarithm?Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The logarithmic equation is given below.
[tex]2 \ln e^{\ln 2x} - \ln e ^{\ln 10} = \ln 30[/tex]
We know that the properties of the logarithm
[tex]e ^{\ln x} = x\\\\a \ln b = \ln b^a\\\\\ln a - \ln b = \ln (\dfrac{a}{b})[/tex]
Then we have
[tex]\begin{aligned} 2 \ln 2x - \ln 10x &= \ln 30\\\\\ln (2x)^2 - \ln 10x &= \ln 30\\\\\ln 4x^2 - \ln 10x &= \ln 30\\\\\ln \dfrac{4x^2 }{10x} &= \ln 30\\\\\ln \dfrac{2x}{5} &= \ln 30 \end{aligned}[/tex]
Taking anti-log, then we have
[tex]\rm \dfrac{2x}{5} = 30\\\\2x \ = 150\\\\x \ \ = 75[/tex]
More about the logarithm link is given below.
https://brainly.com/question/7302008
Answer:
x = 75 or b
Step-by-step explanation:
Trust me
help pls
y = -x + 4
y = x - 2
Answers
X-2 = -x + 4
Put unknowns on one side and knowns on other side
2x = 6
X= 3
No need to find y because only 1 answer has 3 as x.
Answer is (3,1)
Answer:
Option c
(3,1)
Step-by-step explanation:
Solving system of equations:
y = -x + 4 ----------(I)
y = x - 2 -----------(II)
Add equation (I) & (II). So, x will be eliminated and we can find the value of y.
(I) y = -x + 4
(II) y = x - 2 {Now add}
2y = 2
Divide both sides by 2
y = 2/2
y =1
Substitute y = 1 in any of the equations. Here, we are substituting in equation (II)
1 = x - 2
1 + 2 = x
x = 3
the volume of the right triangular prism shown below is 178.75 cubic feet. write and solve equation to find the value of x
Answers
Answer:
i think
Step-by-step explanation:
sorry i dont know the answer im just a children's
Factor x3 – 7x2 – 5x 35 by grouping. what is the resulting expression? (x2 – 7)(x – 5) (x2 – 7)(x 5) (x2 – 5)(x – 7) (x2 5)(x – 7)
Answers
The factored expression ofx^3 - 7x^2 -5x +35 is (x^2 - 5)(x - 7)
What is an expression?An expression is an algebraic term used for a mathematical statement that includes addition subtraction multiplication and division
x^3 – 7x^2 – 5x + 35
factor the given equation
x^2(x – 7) – 5(x - 7)
Factor out x - 7
(x^2 - 5)(x - 7)
Therefore, the factored expression is (x^2 - 5)(x - 7)
To learn more about the factored expression visit:
https://brainly.com/question/723406
Answer:
c. (x^2 - 5)(x - 7)
Step-by-step explanation:
c. (x^2 - 5)(x - 7)
The consecutive angles of a parallelogram are________?
Answers
Answer:
supplementary
Consecutive angles are supplementary (A + D = 180°). If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram separates it into two congruent triangles.
Answer:
Supplementary
Step-by-step explanation:
The consecutive angles of a parallelogram are supplementary.
Two angles that add up to 180° are called supplementary angles.
This can be proven by creating a parallelogram and extending all segments to create two parallel lines transversing another set of two parallel lines.
I drew a diagram of this shape and considering that all the opposite lines are parallel, the central shape is a parallelogram.
Looking at the diagram attached, we know that the angle of a straight line is 180° (represented by the yellow of Angle 1 and the pink angle next to it) All angles of the same color are congruent by angle theorems consisting of corresponding and vertical angles.
If pink is x, and yellow is y, then we can say that x + y = 180°
So, therefore we can say that the consecutive angles of the parallelogram (Angle 1 and Angle 2) sum up to 180°, because they are made up of one pink angle and one yellow angle ( x and y )
What's the answer? I need it asap.
"You have recently purchased a new backpack as show in the picture. The main section of the backpack is made of a rectangular prism and half a cylinder. The front pocket is also a rectangular prims. Use the diagram to find the volume of your new backpack. Write a paragraph with 4-5 sentences, following the RACE format, to explain how you calculate the answer."
Answers
h-hey baddie! UwU! The answer is 24. Hope this helps onichan!-
help me pls desperate please plspls
Answers
Area of semi circle = π r²/2
= π 20 × 20 / 2
= 200 π
= 628 cm² (approx)
Answer:
To the nearest whole number : 628
Step-by-step explanation:
The formula for the area of a circle is :
To work out the area you would first need to work out the radius. You can do this by dividing the diameter of 40 cm by 2, this gives you 20 cm. This is because the radius is half of the diameter.
Now that we have worked out the radius, the next step would be to work out the area. You can do this by multiplying pi by the radius of 20 squared, this gives you 1256.64.
The final step is to work out the area of this semi-circle. You can do this by dividing the area of 1256.64 by 2, this gives you 628.32 . This is because a semi-circle is half of a circle.
1) Divide 40 by 2.
2) Multiply pi by 20 squared.
3) Divide 1256.64 by 2.
Hello, I was just doing some practicing for adding integers. I did some problems on my own and I was wondering if I am on the right track.
Answers
Answer:
Yes, It looks great! I would suggest moving on to a littler harder problems like dividing integers! You can also look up integers practice and they will give you problems to solvle! If you dont know how to do it yet then you can simply skip but, You are doing wonderful!!! Good job and Good luck!
Step-by-step explanation:
Janis was offered two different jobs when she graduated from college. she made the graph and table to show how much she would earn over time at each job. earnings over time for job 1 earnings over time for job 2 a graph entitled earnings over time for job 1 has year on the x-axis and earnings in dollars on the y-axis. a line with positive slope goes through (0, 40,000) and (10, 60,000). y = 2,000 x 40,000. a 2-column table entitled earnings over time for job 2 has 7 rows. the first column is labeled year with entries 10, 12, 14, 16, 18, 20, 22. the second column is labeled earnings in dollars with entries 55,000, 60,000, 65,000, 70,000, 75,000, 80,000, 85,000. when will janis’s salary be the same for job 1 and job 2, and how much will she be earning at that point? the salaries will be the same in year 20, and she will be earning $80,000. the salaries will be the same in year 16, and she will be earning $70,000. the salaries will be the same in year 12, and she will be earning $60,000. the salaries will be the same in year 10, and she will be earning $55,000.
Answers
The salaries will be the same in year 20 and she will be earning $80,000. So, the first option is correct.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We will first create an equation to represent the data.
To find the slope we use the formula
m = (y₂-y₁)/(x₂-x₁)
= (60,000-55,000) / (12-10)
= 5,000/2 = 2500
Writing this in point-slope form, we have
y-y₁ = m(x-x₁)
y-55,000 = 2500(x-10)
Converting to slope-intercept form,
y-55,000 = 2500 × x - 2500 × 10
y - 55,000 = 2500x - 25,000
y = 2500x + 30,000
Now we set this equal to the equation from the graph:
2500x + 30,000 = 2000x + 40,000
Subtract 2000x from both sides:
2500x + 30,000 - 2000x = 2000x + 40,000 - 2000x
500x + 30,000 = 40,000
500x = 40,000 - 30,000
500x = 10,000
x = 10,000/500
x = 20
The salaries will be the same in year 20.
y= 2000(20) + 40,000
y= 40,000 + 40,000
= 80,000
The salary in year 20 will be $80,000.
Learn more about a point-slope form;
https://brainly.com/question/12743204
Use the formula a2 – b2 = (a b)(a – b) to factor completely. what are the factors of 36x8 – 49? (9x4 – 1)(4x2 49) (36x4 – 7)(x2 7) (6x4 – 7)(6x4 7) (6x8 – 7)(6x 7)
Answers
The factors of 36x^8 – 49 are (6x^4-7)(6x^4+7).
We are given to factor the following polynomial completely:
36x^8 – 49.
We have to find the complete factor of the given polynomial.
Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor
What is the formula for (a^2-b^2)?
The formula for (a^2-b^2)= (a+b) (a-b).
Therefore applying the given formula we have,
[tex]F=(6x^4)^2-7^2[/tex]
[tex]F=(6x^4)^2-7^2\\F=((6x^4)-7)(6x^4)+7)[/tex]
Thus, the required factors are
[tex]F=((6x^4)-7)(6x^4)+7)[/tex]
Therefore,option (C) is correct.
To learn more about factors visit:
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The factors of 36x^8 – 49 are (6x^4-7)(6x^4+7).
We are given to factor the following polynomial completely:
36x^8 – 49.
We have to find the complete factor of the given polynomial.
Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor
What is the formula for (a^2-b^2)?
The formula for (a^2-b^2)= (a+b) (a-b).
Therefore applying the given formula we have,
b
Thus, the required factors are
b
A company orders 27 boxed lunches from a deli for $194.40. Assume each boxed lunch is the same price. If C represents the total cost in dollars and cents of the lunch order for any number,b, of boxed lunches ordered, write a proportional equation for c in terms of b that matches the context
Answers
[tex]C = 7.2b[/tex]
Step-by-step explanation:From the question we have that,
27 boxes --------------- $194.40
b boxes --------------- C
Using the Rule of Three we have that,
[tex]27C = 194.40b[/tex]
Since we want a function that represents C in terms of b ( C = f(b) ) we can isolate C on the equation,
[tex]C = \frac{194.40}{27}b = 7.2b[/tex]
first to answer correctly will be marked brainliest
Answers
Answer:
D & B
Step-by-step explanation:
[tex]f(x)=(x-2)^{2} -3[/tex]
The vertex: (2, -3)
[tex]f(2)=(2-2)^{2} -3=0-3=-3[/tex]
Hope this helps
Answer:
1) D. f(x) = (x - 2)² - 3
2) B. (2, -3)
Step-by-step explanation:
hope this helps!
Find the volume of the following cube:
1.) 6 cm
2.) 3 in
3.) 7 m
Find the volume of the following rectangle:
1.)
L = 10 in
W= 4 in
H = 2 in
2.)
L = 20 cm
W= 10 cm
H = 5 cm
Answers
32004cm^3
volume of rectangle
1. 203.2 cm^3
2. 1000 cm^3
Marcus has three random samples of the same size from a population of 700 people. In one sample, 53% of people have a library card. In another, 51% of people have a library card. In the third, 43% have a library card. Based on the three samples, how many people with a library card should he expect are in the population?
a.301
b.357
c343
d.371
pls answer quick
Answers
Answer:
343
Step-by-step explanation:
Finding? How many people with a library card should he expect in the population?
Important? Population = 700. Sample 1= 53%. Sample 2 = 51%. Sample 3 = 43%.
How? Average the 3 samples percentages together. The percent sign tells us what the sample size is (% = out of 100). Set up the proportions for library card to sample size and then library card to population. Cross multiply.
His balls were 6 feet tall he wanted them to be 20. 4 tall how much does he need to grow {i-Ready} pls help
Answers
Answer:
14.4
Step-by-step explanation:
20.4-6 = 14.4
So his balls should grow 14.4 inches/feet/centimeters (whatever measuring tool you're asked to use)
Are you sure it's balls though
Answer:
20.4-6=14.4
since he wants his balls to grow you need to subtract how much he wants them tp grow by how tall the already are
Step-by-step explanation:
There are 6 girls and 4 boys in the debate club at Columbus High School. The principal randomly selects one student from the debate club to represent the school in a competition. What is the probability that the selected student is a girl?
Answers
Answer:
60% chance a girl is picked
Step-by-step explanation:
There is 10 students in total. 6 out of 10 are girls. We can represent this in a fraction 6/10. Now we convert the fraction into a percentage 60%.
What is the quotient? startfraction 2 m 4 over 8 endfraction divided by startfraction m 2 over 6 endfraction startfraction 24 over (m 2) squared endfraction startfraction (m 2) squared over 24 endfraction two-thirds three-halves
Answers
The quotient of the equation is 1.5.
What is the quotient?The quotient is the number that is generated when we perform division operations on two numbers. Basically, it is the result of the division method.
The given equation is;
[tex]\rm \dfrac{2m+4}{8}\div \dfrac{m+2}{6}[/tex]
By fraction, a quotient is a number obtained by dividing the dividend by the divisor which is a simple division of numerator and denominator.
The solution of the equation is determined in the following steps given below.
[tex]=\rm \dfrac{2m+4}{8}\div \dfrac{m+2}{6}\\\\=\rm \dfrac{2m+4}{8}\times \dfrac{6}{m+2}\\\\=\rm \dfrac{2(m+2)}{8}\times \dfrac{6}{m+2}\\\\=\dfrac{2\times 6}{8}\\\\=\dfrac{12}{8}\\\\=1.5[/tex]
Hence, the quotient of the equation is 1.5.
Learn more about quotient here;
brainly.com/question/17431959
Answer:
2/3
Step-by-step explanation:
What is the quotient?
StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction
StartFraction 24 Over (m + 2) squared EndFraction
StartFraction (m + 2) squared Over 24 EndFraction
Two-thirds
Three-halves
PLS HELP I USED ALL MY POINTS ON THIS I NEED HELP ASAP!!!!!!!!!! ʕ •ᴥ•ʔ
Answers
Answer:
(12, 6 )
Step-by-step explanation:
locate 12 cups of flour on the x- axis, then go vertically up to meet the line at (12, 6 )
that is 6 cups of sugar would be used with 12 cups of flour.
Each of the teams in a mixed volleyball league consists of 5 men and 5 women. there are 9 men and 10 women, including julia, who are trying out for a team. how many possible teams would include julia?
Answers
There are 9 men and 10 women, including Julia, who are trying out for a team. so there are 31,752 possible teams that would include Julia.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
Each of the teams in a mixed volleyball league consists of 5 men and 5 women.
There are 9 men and 10 women, including Julia, who are trying out for a team.
The number of combinations for men
= (9 × 8 × 7 × 6 × 5)/(1 × 2 × 3 × 4 × 5)
=126.
The number of combinations for women
= (10 × 9 × 8 × 7 × 6)/(1 × 2 × 3 × 4 × 5)
=252.
The number of the possible team would include Julia
(126 × 252) = 31,752.
Learn more about combinations;
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If the side of a square is 3/4 feet, what is the area of the square?
Answers
Answer:
The area is 3 feet
Step-by-step explanation:
The answer is 3 ft because if you do ¾×4 because of the four sides you will get 12/4 and that equals 3