Answers
Area of a triangle = 1/2 x length x height.
80 = 1/2 x (x+1) (2x-2)
Multiply both sides by 2:
160 = (x+1)(2x-2)
Expand the right side:
160 = 2x^2 -2
Add 2 to both sides:
162 = 2x^2
Divide both sides by 2:
81 = x^2
Take the square root of both sides:
x = 9
Now find the length of the s1des:
(x+1) = 9+1 = 10
2x-2 = 2(9) -2 = 18-2 =16
The shorter side is 10
Related Questions
Which of the following is the solution of the system of equations shown?
(2,-2)
(2,2)
(-2,2)
(-2,-2)
Answers
Answer:
(-2,-2)
Step-by-step explanation:
The graph doesn't have unit marks, but you can see that the x- and y-coordinates of the intersection are equal, and they are both negative.
(-2,-2)
What is the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰?
Answers
Given:
a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.
To find:
The GCF of given terms.
Solution:
Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.
The given terms are
[tex]a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}[/tex]
Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is
[tex]GCF=a^{24}\times b^{20}[/tex]
[tex]GCF=a^{24}b^{20}[/tex]
Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.
Find the midpoint of the line segiment with the given endpoints. (-9,-7) and (-8,-5)
Answers
Answer:
what's your question I am not understanding
3.
On a coordinate plane, a line segment has P(6,2) and Q(3,8).
Point M lies on PQ and divides the segment so that the ratio
of PM:MQ is 3:2. What are the coordinates of point M?
A. (4.5, 5.0)
B. (5.6, 4.2)
C. (4.8, 4.4)
D. (4.2, 5.6)
Answers
Answer:
[tex]M(x,y) = (4.8,4.4)[/tex]
Step-by-step explanation:
Given
[tex]P(x_1,y_1) = (6,2)[/tex]
[tex]Q(x_2,y_2) = (3,8)[/tex]
[tex]m:n = PM:MQ = 3 : 2[/tex]
Required
Determine the coordinates of M
To solve this, we make use of the following partition formula:
[tex]M(x,y) = (\frac{nx_2+mx_1}{n+m},\frac{ny_2+my_1}{n+m})[/tex]
Substitute values for m, n, x's and y's
[tex]M(x,y) = (\frac{2*3+3*6}{2+3},\frac{2*8+3*2}{2+3})[/tex]
[tex]M(x,y) = (\frac{24}{5},\frac{22}{5})[/tex]
[tex]M(x,y) = (4.8,4.4)[/tex]
Option D is correct
The coordinates of the vertices of triangle ABC are A(9.-10), B(-15, 0), and C(15, 10). A dilation centered at (0, 0) is perfomed on triangle ABC to produce triangle ABC. The coordinates of the vertices of triangle A'B'C' are A' (13.5, -15), B(-22.5, OJ, and C(22.5, 15). Find the scale factor. will mark brainlyst
Answers
Explanation: I plotted the points on a graph and calculated the length of AC (20) and A’C’ (30)
The answer should be 30/20 = 1.5
I hope this helps!
Why are there so many songs about rainbows
And what's on the other side?
Rainbows are visions, but only illusions
And rainbows have nothing to hide
So we've been told, and some choose to believe it
I know they're wrong, wait and see
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
Who said that every wish would be heard and answered
When wished on the morning star?
Somebody thought of that, and someone believed it
Look what it's done so far
What's so amazing that keeps us stargazing
And what do we think we might see?
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
All of us under its spell
We know that it's probably magic
Have you been half asleep, and have you heard voices?
I've heard them calling my name
Is this the sweet sound that calls the young sailors?
The voice might be one and the same
I've heard it too many times to ignore it
It's something that I'm supposed to be
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
La-da-da, de-da-da-do
La-da-da-da-da-de-da-do
Answers
Answer:
You can’t see a rainbow from the other side. There is no other side. A rainbow happens when light is reflected from water droplets. If you get to the other side of the rain and look back, you can’t see the reflection. It would be like going behind a movie projection screen. You can’t see anything from the back side.
Step-by-step explanation:
Please help!
Consider matrices A, B, and C.
Which matrix represents (A-B)-C?
Answers
Answer:
B.) I cant insert a 2x2 matric but the [5 7
7 4] matrix is correct
Step-by-step explanation:
I got a 5/5 on the test so I know that B is the correct answer
The matrix which represents (A-B)-C will be the matrix in option (B).
What is the matrix?matrix, a collection of numbers lined up in rows and columns to produce a rectangular array. The elements of the matrix, also known as the entry, are the numerals.
In another word, a matrix is a set of variables that are arranged in such a good way that we can create algebraic equation from that.
In computer graphics, where they have been used to describe picture transformations and other alterations, matrices have vital applications as well in many sectors.
Given that the matrix
A - B = [first raw 3 ,1 in second raw 2 ,0]
Now (A - B) - C = [ first raw 5 ,7 in second raw 7 , 4]
Hence, the correct option is (B).
For more about matrices
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A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices- a, b, c, d, e- and only one correct answer. What is the probability that he answered both of the problems correctly? Write your answer as a fraction in simplest form.
Answers
1 correct answer out of 5 = 1/5
1/5 x 1/5 = 1/25
PLEASE HELP ASAP 20 POINTS
The newly proposed city park is rectangle shaped. Blake drew a scale drawing of the park and used a scale of 1 cm: 20 ft
1) If the width on the scale drawing of the city park is 25 centimeters, what is the actual width of the park?
A) 250 feet
B) 400 feet
C)500 feet
D)750 feet
2) If the width on the scale drawing of the city park is 25 centimeters and the length is 30 centimeters, what is the actual area of the park?
A) 75,000 ft^2
B) 110,000 ft^2
C) 300,000 ft^2
D) 750,000 ft^2
Answers
Answer:
a ,c ,b
esa son creo pero nose
The actual dimensions of the rectangular park are 500 cm by 600 cm and actual area of the park is 300,000 ft²
What is scale?A scale is a set of levels or numbers which are used in a particular system of measuring things or are used when comparing things.
Given that, Blake drew a scale drawing of a rectangle shaped park and used a scale of 1 cm: 20 ft
We need to find the actual width if the width on the scale drawing of the city park is 25 cm, and actual area if the width on the scale drawing of the city park is 25 cm and the length is 30 cm,
a) The given measurement of width in the drawing is 25 cm,
We have,
1 cm = 20 ft
∴ 25 cm = 20 × 25
= 500 ft
b) The given measurement of the width on the scale drawing of the city park is 25 cm and the length is 30 cm,
Actual width = 500 ft
Actual length = 20 × 30 = 600 ft
Area of rectangle = length × width
Actual area = 500 × 600
= 300,000
Hence, the actual dimensions of the rectangular park are 500 cm by 600 cm and actual area of the park is 300,000 ft²
Learn more about scales, click;
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Can someone help plzzz!!!
Answers
Answer:
4
Step-by-step explanation:
4•4•4 = 64
Answer:
4
Step-by-step explanation:
cubic root of 64 is 4, since 4^3 = 64
f(x)=x-7 and g(x)=2x-3
find f(g(4))
Answers
Answer:
f(g(4)) = -2
Step-by-step explanation:
First, find g(4) by plugging in 4 as x into the function:
g(x) = 2x - 3
g(4) = 2(4) - 3
g(4) = 8 - 3
g(4) = 5
f(g(4)) can be found by finding f(5), since g(4) = 5
Find f(5) by plugging in 5 into the function:
f(x)= x - 7
f(5) = 5 - 7
f(5) = -2
So, f(g(4)) = -2
A book has 244 pages. Theo has read 81 pages so far. About what percent
of the book has Theo read?
A. 82%
B. 66%
C. 50%
D. 33%
Answers
Answer:
33%
Step-by-step explanation:
81 pages ÷244 pages ×100=33%
Answer:
D. 33% (rounded)
How do I find the volume of this pyramid
Answers
Answer:
10*10*12 = 120 ÷ 3 = 40
Step-by-step explanation:
The formula to find a pyramid's volume is
V = [tex]\frac{l*w*h}{3}[/tex] (length 'times' width 'times' height, divided by 3)
Given this circle puzzle what would angle 1-12 be? (Geometry)
Answers
But I think it would be 20
1/1-cos x
+
1/1+cos x
Answers
Answer:
2 csc^2 x
Step-by-step explanation:
using a common denominator, that is
((1+cosx)+(1-cosx))/(1-cos^2c) = 2/sin^2x
Answer:
sin^2x
Step-by-step explanation:
(1+cosx)(1-cosx)
Difference of squares
1-cos^x
Pythagorean identity
sin^2x
A tree casts a 16-foot-long shadow on level ground. A forestry student uses a clinometer to determine that the sun is at a 70° angle of elevation.
What is the height of the tree to the nearest whole foot?
Use the on-screen keyboard to enter the number in the box below.
Answers
Answer:
Tree is [tex]43.84[/tex] feet tall
Step-by-step explanation:
Shadow casted by tree [tex]= 15[/tex] feet
Angle of elevation of sun [tex]= 70[/tex] degrees
Tangent of angle of elevation is equal to the ration of height of tree and its shadow
tan [tex]70 = \frac{t}{16}[/tex]
Height of the tree is equal to [tex]16 *[/tex] tan [tex]70[/tex]
Height of the tree [tex]= 16 * 2.74 = 43.84[/tex] feet
HELP ITS URGENT!!! May someone PLEASEE help me?
Answers
Answer:
79
Step-by-step explanation:
angle c and angle a are congruent
angle d and angle b are congruent
Answer:
Angle a is 79 degrees
Step-by-step explanation:
I'm currently in alg 2 so i'm out of practice but there's some theorem that states that the opposite angles are equal to each other.
calcular la altura que podemos alcanzar una escalera de 3 metros apoyada sobre ma pared si la parte inferior la situamos a .07 metros de esta.
Answers
the size of a rectangular photo frame is 12 11/16cm by 8 3/4cm. Which of the following gives the product of these dimensions rounded to the nearest whole number of centimeters
answers
A) 12 cm x 8 cm
B) 12 cm x 9 cm
C) 13 cm x 8 cm
D) 13 cm x 9 cm
Answers
Answer:
D
Step-by-step explanation:
the answer can't be A or C because we know that 8 3/4 rounds to 9
so we have to figure out if 12 11/16 is closer to 12 or 13
anything above 8/16 should round up; therefore, 11/16 should round the 12 to be 13
A = [1, 3, 5, 7, 9)
B = (2, 4, 6, 8, 10)
C = {1, 5, 6, 7, 9)
AU (Bn C) =
Answers
Answer:
the second one
Step-by-step explanation:
I think
The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately $85,000 (The Wall Street Journal, August 6, 2013). Suppose that an independent study of middle-level managers employed at companies located in Atlanta, Georgia, was conducted to compare the salaries of managers working at firms in Atlanta to the national average. The following data show the salary, in thousands of dollars, for a 8. sample of 15 middle-level managers.
108 83 106 73 53 85 80 63 67 75 124 55 93 118 77
a. Compute the median salary for the sample of 15 middle-level managers. How does the median for this group compare to the median reported by The Wall Street Journal?
b. Compute the mean annual salary and discuss how and why it differs from the median a. b. computed in part (a).
c. Compute the first and third quartiles.
Answers
Answer:
Median = $80,000 ; Mean = $84,000 ; Q1 = 67,000 ; Q3 = 106,000
Step-by-step explanation:
Given the data :
108 83 106 73 53 85 80 63 67 75 124 55 93 118 77
Reorderd data :
53, 55, 63, 67, 73, 75, 77, 80, 83, 85, 93, 106, 108, 118, 124
The median salary:
1/2(n+1)th term
Sample size, n = 15
1/2 (15 + 1)th term
1/2(16)th term
8th term = 80
Median is $80,000
Median reported by Wall Street Journal approximately $85000
The obtained and reported values are close
The mean annual salary :
ΣX / n = 1260 / 15 = 84
Mean annual salary = $84,000
Mean is the average of all earnings combined, median is the mid value of he data.
First and third quartile :
Q1 = 1/4(n+1)th term
Q1 = 1/4(16)th term
Q1 = 4th term = 67
Third quartile:.
Q3 = 3/4(n+1)th term
Q3 = 3/4(16)th term
Q3 = 12th term = 106
What is the answer please
Answers
I need to know the answer ASAP
Answers
Q2) Four O’clock
solve each equation for given variable
- 12 = 6i- 6
Answers
Explanation:
First get the variable by itself. To do that, add six to both sides of the equation. You will have -6 = 6i. Than divide both sides by 6. It will give you i = -1.
-12 + 6 = 6i - 6 + 6
-12 + 6 = 6i
(-12 + 6)/6 = (6i)/6
(-12 + 6)/6 = i
i = (-12 + 6)/6
Is 3.5 and 3.55 a equivalent decimal?
Answers
Casper write the algebraic expression 5b + 3.79. I represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese. Identify any variables, coefficients, and termsin the expression.
Answers
Answer:
yes
Step-by-step explanation:
Solve the equation. Select all equivalent forms of the answer.
X-8= 5x + 3
[mark all correct answers]
a. -2.75
b. -0.36
c. -11
4
d. 1
e.
Answers
Two chemical plants, one at Macon and one at Jonestown, produce two types of fertilizer, low phosphorus (LP) and high phosphorus (HP). At each plant, the fertilizer is produced in a single production run, so the two types are produced in fixed proportions. The Macon plant produces 1 ton of LP and 3 tons of HP in a single operation, and it charges $600 for what is produced in one operation, whereas one operation of the Jonestown plant produces 1 ton of LP and 1 ton of HP, and it charges $1,000 for what it produces in one operation. If a customer needs at least 100 tons of LP and 180 tons of HP, how many production runs from each plant should be ordered to minimize the cost.
Answers
9514 1404 393
Answer:
100 runs from Macon
Step-by-step explanation:
A graph of the requirements shows the feasible region is bounded by a polygon with vertices (Macon, Jonestown) = (0, 180), (40, 60), and (100, 0).
Checking costs of these solutions, we find the lowest cost to be obtained when ...
100 production runs should be ordered from Macon
Mori just replaced the showerhead in her bathroom. the old one used 5.75 gallons per minute of water. Her new showerhead uses 2.5 gallons per minute. how many times has much water did Mori's old showerhead use?
Answers
Answer:
3.25
Step-by-step explanation:
Plzzz helpppppp!!!!!!
Answers
Answer:
(c) [tex]h(3) = 1[/tex]
Step-by-step explanation:
Given
The attached graph
Required
Find h(3)
The formula to use in solving this is:
[tex]y = h(x)[/tex]
Substitute 3 for x
[tex]y = h(3)[/tex]
From the attached graph, the value od x = 3 points to the value of y = 1.
So, we have:
[tex]y = 1[/tex]