A square has side length x and a triangle has a base (3x - 2) and height (2x + 4). At what value of x will the two figures have the same area?
Show work and explain all steps.
Answers
Answer:
0.73
Step-by-step explanation:
Data obtained from the question include the following:
Length (L) of square = x
Base (b) of triangle = (3x – 2)
Height (h) of triangle = (2x + 4)
Area of square = L²
Area of square = x²
Area of triangle = ½bh
Area of triangle = ½(3x – 2) (2x + 4)
Expand
½ [3x(2x + 4) –2(2x + 4)]
½[6x² + 12x – 4x – 8]
½[6x² + 8x – 8]
3x² + 4x – 4
Area of triangle = 3x² + 4x – 4
Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:
Area of triangle = area of square
Area of triangle = 3x² + 4x – 4
Area of square = x²
Area of triangle = area of square
3x² + 4x – 4 = x²
Rearrange
3x² – x² + 4x – 4 = 0
2x² + 4x – 4 = 0
Solving by formula method
a = 2, b = 4, c = –4
x = – b ± √(b² – 4ac) / 2a
x = – 4 ± √(4² – 4×2×–4) / 2×2
x = – 4 ± √(16 + 32) / 4
x = – 4 ± √(48) / 4
x = (– 4 ± 6.93)4
x = (– 4 + 6.93)4 or (– 4 – 6.93)4
x = 0.73 or –2.73
Since the measurement can not be negative, the value of x is 0.73.
Related Questions
Which way would you choose to solve 3/x=6/14 ?
Explain your reasoning.
Answers
Answer:
I'd cross multiply to solve this equation.
Step-by-step explanation:
Since we have a fraction where we're finding a ratio:
[tex]\frac{3}{x} = \frac{6}{14}[/tex],
I'd find it easiest to cross multiply. This is because we are finding an equivalent to a ratio, so cross multiplication works best here.
Let's solve it.
[tex]14\cdot 3 = 42\\42\div6=7[/tex]
x = 7
Hope this helped!
In a school, half of the 300 students saw Zootopia, 180 students saw Finding Dory, and 45 students did not see either movie. How many students saw both movies?
Answers
Answer:
150
Step-by-step explanation:
Answer:
150 = half of 300
± 180
230
soooo 230 students
Step-by-step explanation:
PLEASE PLEASE HELP IM BEING TIMED The two-way table represents data from a survey asking students whether they plan to attend college, travel, or both after high school. A 4-column table with 3 rows. The first column has no label with entries travel, not travel, total. The second column is labeled college with entries 43, 24, 67. The third column is labeled not college with entries 10, 5, 15. The fourth column is labeled total with entries 53, 29, 82. Which is the marginal relative frequency for students who plan to attend college? Round the answer to the nearest percent. 18% 22% 35% 82%
Answers
Answer: 82%
Step-by-step explanation:
- - - - - - - - college - - not college - - - - total
Travel - - - - 43 - - - - - - - 10 - - - - - - - - 53
Not travel - 24 - - - - - - - 5 - - - - - - - - - 29
Total - - - - 67 - - - - - - - 15 - - - - - - - - - 82
Marginal relative frequency of students who plan to attend college:
(Number of students who plan to attend the college / Total number of the students)
Number of students who plan to attend college = 67
total number of students = 82
Marginal relative frequency = 67/82
= 0.8170731
= (0.8170731) * 100%
= 81.7% = 82%
Answer:
a: 14/50
b: 15/50
c: 21/50
Step-by-step explanation:
on edge
The side length of each square is 6 units. Find the areas of the inscribed shapes.
Answers
Answer:
a) A₁ = 18 unit²
b) A₂ = 20 unit²
c) A₃ = 12 unit²
d) A₄ = 12 unit²
Step-by-step explanation:
a) Given that the side length of square is 6 units, we have;
The height of the square = The height of the triangle = 6 units
The base of the triangle = The side length of the square = 6 units
The area of a triangle A₁ = 1/2×base×height = 1/2×6×6 = 18 unit²
b) The side of the square A₂ forms an hypotenuse side to the side length 2 and 4 on sides of the circumscribing square
The length of the side = √(4^2 + 2^2) = 2·√5
A₂ = The area of a square =Side² = (2·√5)² = 20 unit²
c) The base length of the triangle, A₃ + 2 = The side length of the circumscribing square = 6 units
∴ The base length of the triangle, ₃₂ = 6 - 2 = 4 units
The height of the triangle, A₃ = The side length of the circumscribing square = 6 units
The area of a triangle A₃ = 1/2×base×height = 1/2×4×6 = 12 unit²
d) Figure, A₄, is a parallelogram;
The area of a parallelogram = Base × Height
The base of the parallelogram, A₄ + 4 = 6 units
Therefore, the base of the parallelogram, A₄ = 6 - 4 = 2 units
The height of the parallelogram = The side length of the circumscribing square = 6 units
The area of a parallelogram A₄ = 2× 6 = 12 unit².
The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter. The cost of every mirror is proportional to the cube of the mirror's radius. What is the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors? Express your answer as a common fraction.
Answers
Answer:
The answer is 1/5
Step-by-step explanation:
The equations 9 x minus 10 y = 6, 8 x minus 10 y = negative 23, 9 x + 10 y = negative 16, and 8 x + 10 y = 13 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (negative 2, 0.75) and (negative 2, 1.5). Blue line goes through (negative 1.75, 0) and (1, negative 2). Pink line goes through (negative 1.5, negative 2), and (1.5, 0.75). Purple line goes through (0, 1.25) and (1, 0.5). PLEASE ANSWER IS 2 MINUTES WILL GIVE BRAINLIEST Which is the approximate solution for the system of equations 8 x minus 10 y = negative 23 and 9 x + 10 y = negative 16? (–2.3, 0.5) (–2.5, 1) (–2.3, –0.5) (–2.5, –1)
Answers
Answer:
Step-by-step explanation:
The two equations are 8x-10y=-23 and 9x+10y=-16.
If you plug them both into a graphing calculator, you will see that the point where they cross (the solution) is (-2.3, 0.5).
The answer is A.
Answer:
i think it is A
Step-by-step explanation:
if right pls give brainliest
Nvm it is right pls give brainliest i need 5 to get to next rank
Todd bought a jet ski through a interwar free payment plan. The ski was $2000 and his payments were $250 each. What percent of the total cost are the payments?
Answers
Answer:
12.5%
Step-by-step explanation:
The price for the ski = $2000
The payments made each = $250
percentage of the total cost that the payment is = ?
The percentage will be calculated as
the ratio of the payments made to the price of ski times 100%
250/2000 x 100%
==> 0.125 x 100% = 12.5%
If a equals 15, then what number does 2a - 5 equal?
Answers
Answer:
25
Step-by-step explanation:
a=15
2(15)-5=25
30-5=25
Answer:
25
Step-by-step explanation:
The problem substituting a for 15 would be 2(15)-5
2*15 is 30, then -5 is 25.
The surface area of a sphere is 3000 m square units. What is the volume of the sphere to the nearest hunderedth?
Answers
Answer:
The answer is
15448m³Step-by-step explanation:
To find the volume of the sphere we must first find the radius
Surface area of a sphere = 4πr²
where r is the radius
From the question surface area = 3000m²
3000 = 4πr²
Divide both sides by 4π
750/π = r²
Find the square root of both sides
r = 15.45 cm
Volume of a sphere is 4/3πr³
So we have
4/3π(15.45)³
= 15448.06
= 15448m³ to the nearest hundredth
Hope this helps you
how many ways can you order a hot dog with the choices below?
Answers
Answer:
8
Step-by-step explanation:
2 x 2 x 2 = 8
you have 2 choices each time, with or without
A solid square pyramid has a mass of 750 g. It is made of a material with a
density of 8.05 g/cm'. Given that the height of the pyramid is 13.5 cm, find the
length of its square base.
Answers
Answer:
4.55cmStep-by-step explanation:
The unit of a volume: [tex]cm^3[/tex]
The unit of a density: [tex]\dfrac{g}{cm^3}[/tex]
The density is [tex]\dfrac{mass}{volume}[/tex]
Substitute:
[tex]\dfrac{8.05g}{cm^3}=\dfrac{750g}{V}[/tex]
cross multiply
[tex]8.05gV=750gcm^3[/tex]
divide both sides by 8.05g
[tex]V\approx93.17cm^3[/tex]
The formula of a volume of a square pyramid:
[tex]V=\dfrac{1}{3}a^2H[/tex]
a - length of square base
H - height of a pyramid
We have:
[tex]V=93.17cm^3;\ H=13.5cm[/tex]
Substitute:
[tex]93.17=\dfrac{1}{3}a^2(13.5)[/tex]
multiply both sides by 3
[tex]279.51=13.5H[/tex]
[tex]297.51=13.5a^2[/tex]
divide both sides by 13.5
[tex]a^2\approx20.7\to a=\sqrt{20.7}\approx4.55(cm)[/tex]
Answer:
Step-by-step explanation:
volume of pyramid=1/3×base area×height
let the length of base=x
base area=x²
volume V=1/3×x²×13.5=4.5 x²
mass=volume×density
750=4.5 x²×8.05=36.225 x²
x²=750/36.225
x=√(750/36.225)≈4.55 cm
what is a continent To eliminate the terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 9x + 3y = -18 Second equation: 8x + 7y = 10
Answers
Answer:
To eliminate solve for y, we need to eliminate x and we will do that by multiplying the first equation by 8 and multiply the second equation by 9.
y=6
Step-by-step explanation:
In the equations:
9x + 3y = -18 -----------------------------------------------------------------(1)
8x + 7y = 10 --------------------------------------------------------------------(2)
To solve for y, we will have to eliminate x
To eliminate x, we will follow the steps below;
multiply equation (1) through by 8 and multiply equation (2) through by 9
The resulting equations are
72x + 24y = -144 ----------------------------------------------------------(3)
72x + 63y = 90 -----------------------------------------------------------(4)
Then we will go ahead and subtract equation (4) from equation (3)
39y =234
divide both-side of the equation by 39
39y /39=234/39
y=6
Need help ASAP please
Answers
Explanation:
The probability that Ben hit on Tuesday:
18/30 = 3/5
The probability that Ben hits for total:
(84 + 30 + 36 + 18)/(120 + 50 + 40 + 30)
= 168/240 = 7/10
c). B
Because 3/5 = 0.6 and 7/10 = 0.7 which mean the total one is more reliable
Which of the following options could represent a possible set of interior angles of a triangle? 100°, 130°, and 130° 30°, 70°, and 80° 25°, 3°, and 35° 45°, 105°, and 120°
Answers
Answer:
2) 30, 70, 80
Step-by-step explanation:
Well there has to be 3 angles that all add up to 180°.
1)
100+130+130
=360
2)
30+70+80
= 180
3)
25+3+35
=63
4)
45 + 105 + 120
=150
150+120
270
A walking path across a park is represented by the equation y=-3x - 3.A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3,6). Identify the equation that represents the new path.
Answers
Answer:
[tex]y=\frac{1}{3} x+7[/tex]
Step-by-step explanation:
We need to find the equation of a line perpendicular to [tex]y=-3x-3[/tex], which passes through the point (-3, 6).
Recall that a line perpendicular to a line of the form: [tex]y=mx+b[/tex], must have a slope which is the opposite of the reciprocal of the slope of the original line. that is, a slope of the form;
[tex]slope=-\frac{1}{m}[/tex]
Then, in our case, since the original line has slope "-3", a perpendicular line to it should have a slope given by:
[tex]slope=-\frac{1}{-3} =\frac{1}{3}[/tex]
We now know the slope, and also a point for this new line, so we use the point-slope form of a line:
[tex]y-y_0=m_\perp\,(x-x_0)\\y-6=\frac{1}{3} (x-(-3))\\y-6=\frac{1}{3} x+\frac{3}{3} \\y-6=\frac{1}{3} x+1\\y=\frac{1}{3} x+7[/tex]
Write a polynomial f(x) that satisfies the given conditions.
8
Degree 3 polynomial with integer coefficients with zeros -5i and
5
Answers
Answer:
f(x) = x^3 -5x^2 +25x -125
Step-by-step explanation:
For zero x=a, one of the factors is (x -a). If the polynomial has integer coefficients, its complex roots come in conjugate pairs. So, the roots are ...
roots: -5i, 5i, 5
factors: (x -(-5i))(x -5i)(x -5)
Multiplying these out gives your polynomial as ...
f(x) = (x^2 +25)(x -5)
f(x) = x^3 -5x^2 +25x -125
Large samples of women and men are obtained, and the hemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:
negative 1.76 g divided by dL less than mu 1 minus mu 2 less than minus 1.62 g divided by dL
−1.76 g/dL<μ1−μ2<−1.62 g/dL. Complete parts (a) through (c) below.
a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
Answers
Answer:
a) Because the confidence interval does not include 0 it appears that there
is a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.
b)There is 95% confidence that the interval from −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2
c) 1.62 < μ1−μ2< 1.76
Step-by-step explanation:
a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
Given:
95% confidence interval for the difference between the two population means:
−1.76g/dL< μ1−μ2 < −1.62g/dL
population 1 = measures from women
population 2 = measures from men
Solution:
a)
The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in men is not equal and that the women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in men.
b)
There is 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.
c)
If we interchange men and women then
confidence interval range sign will become positive.μ1 becomes the population mean of the hemoglobin level in menμ2 becomes the population mean of the hemoglobin level in women So confidence interval becomes:1.62 g/dL<μ1−μ2<1.76 g/dL.
There is a significant difference between the mean level of hemoglobin in women and in men.
How to interpret the confidence intervalThe confidence interval of the mean is given as:
[tex]-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL[/tex]
The above confidence interval shows that the confidence interval is exclusive of 0.
This means that 0 is not part of the confidence interval
Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.
Read more about confidence intervals at:
https://brainly.com/question/17097944
The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below.
On a coordinate plane, a graph of a function is in quadrants 1 and 4. The function goes through the x-axis at (2, 0), (3, ), and (4.5, 0).
How many roots of f(x) are rational numbers?
0
1
2
3
Mark this and return
Answers
Answer:
it'd be 3! :)
Step-by-step explanation:
took quiz
to be sure, the graph goes like
/ , then a hill like shape, then goes U, and then goes up
The number of rational roots of the equation are 3.
What is the root of an equation?The root of an equation are the solutions to an equation. The equation as shown is a cubic equation hence will have three roots shows as (2, 0), (3, 0), and (4.5, 0).
It thus implies from the foregoing that the number of rational roots of the equation are 3.
Learn more about root of an equation:https://brainly.com/question/12029673
#SPJ5
What is the sine value of pi over 6? negative 1 over 2 1 over 2 negative square root 3 over 2 square root 3 over 2
Answers
Answer:
1/2
Step-by-step explanation:
[tex]sin(\frac{\pi }{6} )=\frac{1}{2}[/tex]
sin(pi) = 0
sin(7pi/6) = -1/2
sin(pi/6) = 1/2
sin 3pi/2 = -1
sin pi/2 = 1
sin pi/3 = √3/2
sin 4pi/3 = -√3/2
Answer:
1/2
Step-by-step explanation:
I got it right on the exam.
Answer choice
C) All nonnegative real numbers
D) All positive integers
Answers
The number of boxes can't be negative or in fractions.
so the domain would be "All whole numbers from 0 to 10"
Answer:
A) All whole numbers from 0 to 10.
Step-by-step explanation:
The domain of a function is given by the available values of the independent variable.
In this case you have that the independent variable is the number of boxes, and the available values of this variable are integers in between 0 and 10, by including 0 and 10.
Then, the domain of the functions composed by all positive integers number from 0 to 10 including 0 and 10.
A) All whole numbers from 0 to 10.
In one design being considered for the containers shaped like a rectangular prism, each
container will have a height of 114 inches and length of 74 inches. What will be the within
inches, of the container?
A.3
B.4
C.14
D.15
Answers
Answer:
your answer is A 3 inches
is the folllowing shape a square? how do you know
Answers
Answer:If it has 4 equal sides
If the angles are 90°
Hope this may helps you
Answer:
A square is characterized by
4 equal sides.Each angle measures 90°Diagonals meet and bisect each other at 90°Opposite sides are parallel and equal.Diagonals are equal.Hope this helps ;) ❤❤❤
evaluate 1/2^-2x^-3y^5 for x=2 and y=-4
Answers
Answer:
[tex] - \frac{1}{32} [/tex]Step-by-step explanation:
Given,
x = 2
y = - 4
Now, let's solve:
[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]
plug the values
[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]
A negative base raised to an odd power equals a negative
[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]
Determine the sign of the fraction
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]
Write the expression in exponential form with a base of 2
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]
Calculate the product
[tex] - \frac{1}{ {2}^{5} } [/tex]
Evaluate the power
[tex] - \frac{1}{32} [/tex]
Hope this helps...
Best regards!!
What is the best first step to solve this equation 8x =25 ?
Answers
Hey there!
"8x = 25"
In order for you to solve for "x-value" (or the equation) we have to DIVIDE both of your sides by 8
8x/8 = 25/8
Cancel out: 8x/8 because that gives you the value of 1 and you don't need it at the moment (in that equation that is)
Keep: 25/8 Because it solves for your equation
Your x equals: 25/8 aka 1 1/8 aka 3.125 (you could choose any one of these as your answer because they are all correct)
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
y=-*x+9
y=-*x+5
y=-3x – 1ly
y=-3x + 25
Answers
Answer:
y = -3x - 11
Step-by-step explanation:
(y - y1)/(x - x1) = (x2 - x1)/(y2 - y1)
(y - 7)/(x + 6) = (-3 + 6)/(6 - 7)
(y - 7)/(x + 6) = 3/-1 = -3
y - 7 = -3(x + 6)
y - 7 = -3x - 18
y = -3x -18 - 7
y = -3x - 11
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
Answers
Real solutions please WILL GIVE BRAINLIEST
Answers
Answer:
the answer is A=2
Step-by-step explanation:
a real solution is a solution that uses real numbers. This equation has 2 real solutions.
Answer:
A. 2 real solutions
Step-by-step explanation:
One graph is a parabola and 1 graph is a straight line and they intersect twice.
If some of the omitted variables, which you hope to capture in the changes analysis, in fact change over time within entity, then the FE estimator a. will be unbiased only when allowing for heteroskedastic-robust standard errors. b. may still be biased. c. will only be unbiased in large samples. d. will always be unbiased.
Answers
Answer:
d. will always be unbiased.
Step-by-step explanation:
When some of variables are omitted the estimator on indulge charge regressor may still be unbiased. If there is a special case where T = 2 then the FE estimator will be unbiased. Fixed effect regression model has different intercepts.
A woman bought a cup
of beans for 12 and sold it
for ₦15. What was her
percentage profit
Answers
Answer:
25 %Step-by-step explanation:
Given,
Cost price ( CP ) = 12
Selling price ( SP ) = 15
Since, CP < SP , she made a profit
Actual profit = SP - CP
plug the values
[tex] = 15 - 12[/tex]
Subtract the numbers
[tex] = 3[/tex]
Profit = 3
Now,
Profit percent = [tex] \frac{actual \: profit}{cost \: price} \times 100[/tex] %
Plug the values
[tex] = \frac{3}{12} \times 100[/tex] %
Calculate
[tex] = 25[/tex] %
Hope this helps...
Best regards!!
Answer:
25%
Step-by-step explanation:
Cost Price: ₦12
Selling Price: ₦15
Profit: ₦15 - ₦12 = ₦3
Profit Percentage = [tex]\frac{profit}{cost price}[/tex] × [tex]\frac{100}{1}[/tex]
Profit Percentage = [tex]\frac{3}{12}[/tex] × [tex]\frac{100}{1}[/tex]
Profit Percentage = [tex]\frac{1}{4}[/tex] × [tex]\frac{100}{1}[/tex] = 25%
Final Answer = 25%
Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?
Answers
Answer:
in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.
Step-by-step explanation:
If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.
In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.
Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]
Now, to simplify this expression:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]
Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.