Answers
Answer:
25
Step-by-step explanation:
If ΔDGH ~ ΔDEF , then [tex]\frac{DG}{DE}[/tex] = [tex]\frac{GH}{EF}[/tex]
[tex]\frac{x+3}{2x-1}[/tex] = [tex]\frac{52}{91}[/tex]
After cross-multiplication: 52(2x - 1) = 91(x + 3)
104x - 52 = 91x + 273
13x = 325
x = 25
Answer:
x = 25Step-by-step explanation:
DGH~DEF ⇒ their corresponding sides are proportional
then
[tex]\frac{DG}{DE} =\frac{GH}{EF}[/tex]
then
[tex]\frac{52}{91} =\frac{x+3}{2x-1}[/tex]
then
[tex]\frac{4}{7} =\frac{x+3}{2x-1}[/tex]
then
4(2x-1) = 7(x+3) [cross multiply]
then
8x - 4 = 7x + 21
then
8x - 7x = 21 + 4
then
x = 25
Related Questions
An open box is to be made from a square piece of cardboard, 18 inches by 18 inches, by removing a small square from each corner and folding up the flaps to form the sides. What are the dimensions of the box of greatest volume that can be constructed in this way
Answers
The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.
How to solve the dimension?
Let x be the side of the square to remove. Then the volume of the box is:
V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³
To find the maximum volume, differentiate and set it to 0:
V'(x) = 324 - 144x + 12x²
0 = x² - 12x + 27
0 = (x - 9)(x - 3)
x = 3 or 9
When x = 3,
V"(x) =-144+24x
V"(3) =-144+72=-72<0
so volume is maximum at x=3
Therefore the box is 12x12x3 and the volume is 432.
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tree is casting a 35 ft shadow when the sun is at a 56° angle of elevation. How tall is the tree?
Answers
Sandra wrote p(x) = 30x + 5x2 in vertex form. Her work is below.
1. p(x) = 5x2 + 30x
2. p(x) = 5(x2 + 6x)
3. (six-halves) squared = 9;
4. p(x) = 5(x2 + 6x + 9) – 5(9)
5. p(x) = 5(x + 3)2 – 45
What is the vertex of this function? Is it a maximum or a minimum?
What is the axis of symmetry of this function?
Answers
Answer:
Step-by-step explanation:
hello :
p(x) = 5(x + 3)2 – 45
the vertex is the point : A(-3 ; -45)
minimum -45
the axis of symmetry is the line when an equation is : x = -3
When using the order of operations to simplify (7 + 3) * 4 - 1 + (6 + 8), which operation should be performed first?
Answers
Answer:
addition because it's in parentheses and following PEMDAS parentheses comes first so you do addition first.
I hope you find this helpful :D
Answer:
(7+3)
After that you do (6+8)
Explanation:
Use PEMDAS
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Use the equation below to find c, if a=43 and b= 53.
C= = 180-a-5
Answers
Answer:
180-a-5
180-43-5
180-48
180-48=132
c=132
The growth of plants in one week are recorded for 6 plants with a sample standard deviation of 4inches and sample mean of 11 inches.
t* at the 0.05 significance level=__
Margin of error = ___
Confidence interval = _____
Answers
Answer:
from my side it's blurry
Margin of error = 0.8226401
Confidence interval = (9.17736,10.82264)
We have given data for one week recorded for 6 plants.
With a sample standard deviation of 1 inch and a sample mean of 10 inches.
For this sample, it is given that,
Sample size = n = 6
Sample SD = s = 1
Sample mean = x = 10
At a 0.10 significance level, the critical point is with t-distribution (n-1)df=5 df,
t* =2.015048
Margin of error = E=2.015048*s/ √n = 0.8226401
Confidence interval
= (9.17736,10.82264)
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Nick is painting his bedroom. Each of the four walls measures 10 feet by 14 feet. He will not paint the ceiling. What is the total area that Nick will paint?
Answers
Answer:
560 ft^2
Step-by-step explanation:
You need to find the surface area of the walls
wall 1 10*4 = 140
wall 2 10*4 = 140
wall 3 10*4 = 140
wall 4 10*4 = 140
140 +140 +140 +140= 560
Pamela made a profit of $3250 after selling stocks for $10500 after 4 years. What was her average annual percentage gain?
Answers
Pamela's average annual percentage gain was = 7.7%
Calculation of annual percentage gainThe start up capital (P) = $10500
The simple interest (SI) = $3250
Time (T) = 4 years
Rate = ?
But SI = P × T × R /100
Make R the subject of formula,
R = SI × 100/P × T
R = 3250 × 100/ 10500 × 4
R = 325000/ 42000
R = 7.7%
Therefore, Pamela's average annual percentage gain was = 7.7%
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Easy math 2 pictures
Answers
Answer:
See below
Step-by-step explanation:
x = hours
Payless charges = 50 + 60x
Squad charges = 80 + 50x when are they equal ?
50 + 60x = 80 + 50x
x = 3 hours
Surface area = 2 * ( 10 *5 + 5*3 + 3*10) = 190 ft^2
x ^ 3 + 3x ^ 2 = 36x + 108
pls help
Answers
Answer:
x can equal several things that would fit
-3
-6
or
6
Step-by-step explanation:
Find the quotient: 5/8 divided by 3.
Answers
Answer:
5/24
Step-by-step explanation:
Instead of dividing 5/8 by 3/1, you could multiply by the reciprocal to get the same answer.
5/8 · 1/3
Hope that helps!
1.) If the function f(x) = (x – 3)^2+ 2, the minimum value occurs when x is
1)-2
2)2
3)-3-
4) 3
Answers
Answer:
2
Step-by-step explanation:
A rectangular picture with perimeter 27 cm is glued in the center of a rectangular piece of cardboard. There is a 1 cm margin ( of empty cardboard) all around the picture. What is the perimeter of the piece of cardboard.
Answers
Answer:
35 cm
Step-by-step explanation:
Each dimension of the picture is increased by twice the width of the margin. If the original picture has dimensions L×W, then the cardboard has dimensions (L+2)×(W+2).
The perimeter formula tells you the perimeter is ...
P = 2(L +W)
__
The cardboard perimeter will be ...
P' = 2((L +2) +(W +2)) = 2(L +W +4)
P' = 2(L +W) +8
P' = P +8
If the original perimeter is 27 cm, the cardboard perimeter is ...
P' = 27 +8 = 35 . . . . cm
The perimeter of the cardboard is 35 cm.
If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour:
Answers
The proportion of the workers earning more than $13 per hour is greater than the proportion earning less than $13 per hour.
What is a normal distribution?A normal distribution is a probability distribution that is symmetric around the mean of the distribution. This means that the there are more data around the mean than data far from the mean. A normal distribution is also known as the Gaussian distribution. When depicted on a graph, a normal distribution is bell-shaped.
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Which shows how to determine the volume of the pyramid?
10 cm
8 cm
12 cm
V-3(1268)(10)
OV-2(12)(10)
8
V-=(12(B)(10)
Answers
Answer:
V = 1/3(12×8×10)
Step-by-step explanation:
V= 1/3×base area×height
V = 960/3
V = 320cm^3
The volume of the pyramid is,
⇒ V = 320 cm³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Height of pyramid = 10 cm
Length of pyramid = 12 cm
Width of pyramid = 8 cm
Hence, We get;
The volume of the pyramid is,
V= 1/3 × base area × height
V = 1/3 (12×8×10)
V = 960/3
V = 320 cm³
Thus, The volume of the pyramid is,
⇒ V = 320 cm³
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3 Evaluate( 2+i) squarerooted power 8
Answers
Answer:
[tex](i+2)^4[/tex]
Step-by-step explanation:
assuming the equation is [tex](\sqrt{2+i})^8[/tex] this simplifies to [tex](i+2)^4[/tex] where i =[tex]\sqrt{-1}[/tex]
Step-by-step explanation:
[tex]( \sqrt{2 + i} ) {}^{8} = (2 + i) {}^{ \frac{1}{2} \times8 } [/tex]
[tex](2 + i) {}^{4} [/tex]
Split this up
[tex](2 + i) {}^{2} \times (2 + i) {}^{2} [/tex]
Use the Perfect Square Trinomial
[tex](a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
[tex](2 { }^{2} + 2(2)i + {i}^{2} )(2 {}^{2} + 2(2)i + {i}^{2} [/tex]
[tex] {i}^{2} = - 1[/tex]
so
[tex](3 + 4i)(3 + 4i)[/tex]
[tex]9 + 24i - 16[/tex]
[tex] - 7 + 24i[/tex]
Carter Is organized text book on his bookshelf. He had an English textbook, a math textbook, a physics textbook, and a writing textbook. How many different ways can he line the textbook up on his bookshelf
Answers
Carter can line the books up on his bookshelf in 24 different ways.
Help picture below problem 13
Answers
Answer:
B. Obtuse
Step-by-step explanation:
An obtuse angle is defined as one that extends beyond 90 degrees. An acute angle is defined as one that is less than 90 degrees. A right angle is one that is 90 degrees.
Help asap for brainliest
Answers
Answer:
282 ft
Step-by-step explanation:
Area of 2 triangles = 6+6
= 12 ft
Area of 3 rectangles = 90+90+90
= 270 ft
therefore
the surface area = 12 + 270
= 282 ft
I think that I am right
Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y=(4/3)x
Answers
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = 4/3 x
So : product for two slopes = -1 means : m×4/3=-1
m = -3/4
now : y = -3/4 x+b
but this line :
through the point (4,2) : 2 =(-3/4)(4)+b....... b=5
conclusion :
the equation is : y = -3/4x +5
A triangle is graphed on the coordinate grid below.
What are the coordinates of the image of this triangle after a dilation, with a center of dilation at the origin and a scale factor of 2.
Explanation please!! Thank you
Answers
Answer:
The answer is D
Still stuck? Get 1-on-1 help from an expert tutor now.
Step-by-step explanation:
3125 - [72 - 4(11 - 4)]} =
Answers
Answer:
25
Because its right
also I just took a test that has this problem.
Common factor of 20,88,40
Answers
common factors: 1, 2, 4
GCF: 4
The circumference of a circle is 17π in. What is the area, in square inches? Express your answer in terms of π?
Answers
Answer:
22.97
Step-by-step explanation:
17 divided by pi is 5.41
5.41 divided by 2 is 2.075
r^2(pi)
is 2.075 x 2.075 x 3.41 is 22.97
A central angle has its vertex on the ___________ and is _________ its intercepted arc.
Answers
Answer:
first blank:center
second blank: equal to
Step-by-step explanation:
A central angle has its vertex (the point or corner of the angle) at the center of a circle. The arc (curved piece of the circle) that is cut off by the angle (intercepted arc) has the same measure as the angle. see image
After begging his parents for 3 years, Ed is finally going to clown college! On the first day, his juggling instructor divides a box of bean bags equally among the 17 clowns in Ed's class. Each clown gets 4 bean bags. Which equation can you use to find the number of bean bags b in the instructor's box? Solve this equation for b to find the number of bean bags in the instructor's box. bean bags Questions
Answers
The equation that can be used to determine the number of bean bags in the instuctor's box is b = 17 x 4.
The number of bean bags in the instructor's box is 68.
What is multiplication?
Multplication is a mathematcial operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.
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please I need to know this answer identify and calculate the perimeter for the quadrilateral
Answers
Step-by-step explanation:
but that is really, really simple.
is the problem that you don't know what a perimeter is ?
a perimeter is the whole distance you have to "walk", if you would "go" around the whole object.
that means you would have to go along every side until you reach the starting point again.
therefore, the perimeter is simply the sum of all side lengths.
P = 8.6 + 3.1 + 6.67 + 5.37 = 23.74 yds
the height does not play any role in this (but it would be important to calculate the area).
I don't understand these huge numbers you have there in the " P =" line.
where are they coming from ? in any case they have nothing to do with this quadrilateral.
Which expression does this power represent?
10^8
10 × 8
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8
8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8
Answers
Answer:
10^8 represents 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Step-by-step explanation:
Because it is to the 8th power, this means it's multiplied by itself 8 times.
Answer: It represents b 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Step-by-step explanation:
Which of the following is the estimated amount of salt that will dissolve at 47 degrees?
30.74
142.06
24.72
35.08
Answers
Ths solubility curve can be used to obtain the amount of salt dissolved (solubility).
What is the solubility curve?The solubility curve is a plot of the solubility of a substance against the temperature. It serves the purpose of being used to show the solubility of a susbtance at different temperatures. This question is incomplete hence we can not be able to deduce the solubility of the salt at this temperature.
If the solubility curve has been ploted, then we can be able to estimate the solubility of the salt from the graph.
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MAX POINTS Help please and thanks
What is the period and frequency of the function graphed and how would the equation be written?
Answers
Answer:
Frequency is total number of complete cycle, made in a unit time.
Period is the time taken to complete a cycle.
Step-by-step explanation:
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The required equation is :
[tex]\qquad \bf \dashrightarrow \:y =a \cos(bx) + k[/tex]
Now, let's find the required values :
period (p) = 6[distance between any successive Crest or trough]
a = - 4 (flipped)b = 2π/p = 2π/6 = π/3k = -2Distance of starting position from origin = k
Now, plug in the values ~
[tex]\qquad \bf \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]
