use similar triangles to calculate the height h cm of triangale abe
The height of ∆EBA is 24cm in the given question where two triangles are similar.
What are similar triangles?Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion. The " symbol here denotes the similarity of triangles.
We know that in two similar triangles, the ratio of corresponding sides are equal to ratio of their heights.
We have given that ∆DBC ≅ ∆EBA
So,
⇒ (36-h)/h = DC/AE
⇒ (36-h)/h = 10/20
Using cross multiplication
⇒ 20(36-h) = 10h
⇒ 720 - 20h = 10h
⇒ - 20h -10h = -720
⇒ -30h = -720
⇒ 30h = 720
⇒ h = 720/30
⇒ h = 24
Thus, the height of ∆EBA is 24cm in the given question where two triangles are similar.
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Full question
Use similar triangles to calculate the height, h cm, of triangle ABE.
10 cm
С
В.
36 cm
E
20 cm
for a math assignment, jane has to roll a set of six standard dice and record the results of each trial. she wonders how many different outcomes are possible after rolling all six dice. what is the total number of possible outcomes for each trial?
Different possible outcomes after rolling all six dice is equal to 36. Total number of possible outcomes for each trial is equal to 6.
As given in the question,
For Math Assignment
The total set of standard dice = 6
After rolling each dice,
Possible outcomes after each trial = { 1,2,3,4,5,6 }
The total number of possible outcomes for each trial = 6
Different possible outcomes after rolling all six dice = 6 × 6
= 36
Therefore, different possible outcomes after rolling all six dice is equal to 36. Total number of possible outcomes for each trial is 6.
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Determine whether the polygons are similar. If so, identify the correct similarity ratio and the similarity statement.
The two polygons are calculated to be similar and the correct statement to show the similarity is in option A
How to show that the polygons are similar
To show that the polygons are similar we show that
The angles of the corresponding sides are equal The ratio of the sides chosen are equalComparing the angles
< P ≅ < C< G ≅ < H< A ≅ < J< R ≅ < KComparing the ratio of corresponding sides
10.5 / 7 = 12 / 8 = 6 / 4 = 9 / 6 = 3 / 2
This shows that option A is the correct choice
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Sarah, Leah, Haley, Lindsay, and Kim bought 4 bottles of water to share among themselves. They divided each bottle of water into 5 equal portions. Sarah took 1 portion from each bottle of water. Which equation represents how much of a bottle of water Sarah took?
Sarah has taken 4/5 portion of the available water bottles.
How is a ratio determined?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. A ratio is a comparison or condensed version of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio can be defined as the number that can be used to represent one quantity as a percentage of another.
Given, Total number of water bottles bought = 4
Total number of people sharing the bottles = 5
Since each bottle is divided in equal portion, each portion of bottle = 1/5
Also, Sarah took one portion from each of the four bottles, thus
Sarah has portion of water = 4*(1/5) = 4/5
Sarah has taken 4/5 portion of the available water bottles.
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What is the answer to this need a fast answer plssssssssssssssssssss
Answer:
-2
Step-by-step explanation:
hope this helps
Answer:
Slope = -2
Step-by-step explanation:
slope = (y2-y1) / (x2-x1)
choose 2 points
i choose (2, -1), and (5, -7)
slope = (-7 - (-1))/(5-2)
slope = (-6)/3
slope = -2
List the first five multiples of 20. List the first five multiples of 30..
Answer:
First five multiples of 20 are: 20,40,60,80 and 100.
First five multiples of 30 are: 30,60,90,120, and 150.
Answer: for 20 it is 20,40,60,80,100
For 30 it is 30,60,90,120,150
Step-by-step explanation:
here’s another way you can multiply 20 and 30 by 1 and above hope this will help
DE has a length of 5 cm. What is the length of the image of DE after applying the comp
A. 2.5 cm
B. 5 cm
C. 10 cm
D. 20 cm
Please select the best answer from the choices provided
OA
OB
The correct option: B. 5 cm, the image of DE will have the same length as DE, i.e. 5 cm.
What is defined by the term transformation?A transformation is a method of modifying a polygon or even other two-dimensional element on a plane as well as coordinate system. Two-dimensional figures keep moving around a plane as well as coordinate system using mathematical transformations.A preimage, also known as an inverse image, is the this double shape that exists before any transformation. The estimate after transformation is depicted in the image.For the given question;
DE segment length is 5 cm.
The transformation implemented to DE now is; Rx degrees R₀.-270 degrees.
That is, DE is the segment.
270° counter-clockwise rotation about the origin, then reflected across the x-axis
It is necessary to determine the length of a segment that is the image of DE.
Because, as we all know,
The only transformation that affects the figure's measurements is 'dilation.'
As a result, rotation and reflection have no effect on the shape and size of a segment DE.
Therefore, the image of DE will have the same length as DE, i.e. 5 cm.
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The complete question is-
DE has a length of 5 cm. What is the length of the image of DE after applying the composition Rx degrees R₀.-270 degrees?
A. 2.5 cm
B. 5 cm
C. 10 cm
D. 20 cm
Choose the brand of chips with the lowest price per ounce.Brand A 20 ounces for $2.50Brand B 32 ounces for $3.25 O Brand AO Brand BO Both brands have the same price per ounce.O Not enough information is given
Answer:
Brand B
Explanation:
The cost for each brand is given below:
• Brand A: 20 ounces for $2.50
,• Brand B: 32 ounces for $3.25
To determine the price per ounce for each brand, divide the cost by the number of ounces.
[tex]\begin{gathered} \text{Price Per Ounce for Brand A: }\frac{\$2.50}{20\text{ ounces}}=\$0.13\text{ per ounce} \\ \text{Price Per Ounce for Brand B: }\frac{\$3.25}{32\text{ ounces}}=\$0.10\text{ per ounce} \end{gathered}[/tex]This, we see that Brand B has the lowest price per ounce.
b. Fred got a score of 84 on the test. Write a division sentence using negative numbers
where the quotient represents the number of questions Fred answered incorrectly.
Answer:
Step-by-step explanation:
What is the Product Rule of Exponents?When multiplying two numbers with the same base, their powers/exponents would be added.For example, .Given:(a²c)³Therefore:(a²c)³ = (a²c)(a²c)(a²c) (a²c)³ = (a²c)³ = Therefore, applying the product rule of exponents, (a²c)³ = .
Please help me! Thank you :)
The required measure of x and y for the concurrent triangle is 4 and 2 respectively.
In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
here,
Since the triangle is are concurrent triangle,
x + 4 = 4y - - - - (1)
x = y + 2 - - - - (2)
Solving the above system of the equation,
y + 2 + 4 = 4y
6 = 3y
y = 6 / 3
y = 2
Now put this y in equation 2
x = 2 + 2
x = 4
Thus, the required measure of x and y for the concurrent triangle is 4 and 2 respectively.
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Write each fraction as a decimal 3\5
Answer:
0.6
Step-by-step explanation:
3/5 as a decimal is 0.6; divide the numerator by the denominator. :)
The perimeter of the rectangle below is 88 units. Find the length of side QR.
Write your answer without variables.
Answer: QR = 21 Units
P = 2(l) + 2(w)
[tex]88= 2(4z-1) + 2(3z+3)[/tex]
[tex]88 = 8z-2+6z+6[/tex]
[tex]88 +2-6= 8z+6z[/tex]
[tex]84=14z[/tex]
[tex]\frac{84}{14} =\frac{14z}{14}[/tex]
[tex]6 = z[/tex]
[tex]QR = 3z+3[/tex]
[tex]QR = 3(6) +3[/tex]
QR = 21 Units
Calculate the rise and run to find the slope of each line! Please help me!!!
The slope of a line indicates how steep it is. Slope is defined mathematically as "rise over run" (change in y divided by change in x).
slope of the line = -5/4.
How do you find a slope of a line?Choose two points on the line and calculate their coordinates. Determine the difference in y-coordinates between these two points (rise). Determine the difference in x-coordinates between these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).The slope of a line indicates how steep it is. Slope is defined mathematically as "rise over run" (change in y divided by change in x).The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It is usually simple to graph a line using y=mx+b.The line pass through the points (-3, 2) and (1, -3)
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here, m = slope of the line
m = -3-2/1 +3 = -5/ 4
slope of the line = -5/4.
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For each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning.
a. The distance around a circular track.
b. The total number of equally-sized tiles on a circular floor.
c. The amount of oil it takes to cover the bottom of a frying pan.
d. The distance your car will go with one turn of the wheels
It is listed below whether area or circumference needs to be calculated.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge. A sphere's circumference is equal to the length of any one of its great circles. The distance around a circle is its circumference, however this cannot be used as a definition if, as in many introductory presentations, distance is defined in terms of straight lines.
(a) Circumference needs to be calculated.
(b) Area needs to be calculated.
(c) Area needs to be calculated.
(d) Circumference needs to be calculated.
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What is the image point of (-1,9) after the transformation R 270∘ ∘r y-axis?
The image point of the point (-1, 9) after the transformation R270° or y-axis as required in the task content is; (1, 9).
What is the image point of (-1,9) after the transformation R 270∘?It follows from the task content that the image of the point under the rotation transformation; R270° be determined.
Since the pre-image point (-1, 9) exists in the 2nd quadrant, it follows that the transformation; R270° indicates a reflection over the y-axis.
Hence, only the x-coordinate of the pre-image changes sign and therefore, the image is; (1,9).
Ultimately, the image point is; (1, 9).
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How much would you pay for 2.5 kg of potatoes at $1.69/kg?
Answer:
2.5kg potatoes would approx. cost 4.23$
Step-by-step explanation:
cost of 1kg potato = 1.69$
Therefore, cost of 2kg of potato = 1.69X2
=3.38
cost of 0.5kg of potato = 1.69\2
= 0.85
Total cost of 2.5kg potato = 2kg + 0.5kg
= 3.38 + 0.85
= 4.23$
Answer:
$4.225
Step-by-step explanation:
2.5kg times per 1.60kg
2.5x1.6=4.225
25x^2-4
factor completely
The factorization of the quadratic expression 25x² - 4 gives us (5x + 2)(5x - 2) where; x = -2/5 or 2/5
How to factorize a quadratic equation?We are given the quadratic equation as;
25x² - 4
Now, this quadratic equation can be written as;
25x² + 10x - 10x - 4
We can group this using algebra properties to get;
(25x² + 10x) - (10x + 4)
Collecting like terms gives us;
5x(5x + 2) - 2(5x + 2)
Thus, the factorization is;
(5x + 2)(5x - 2)
The values of x will be;
5x + 2 = 0
x = -2/5
Or 5x - 2 = 0
x = 2/5
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-6.235 as a mixed number
Answer:
-6 47/20
Step-by-step explanation:
Simplify and write an exponential form (2^3) (2^5•2^0x^5/ 3^2x^3y^4)
Answer:
8 · (32 · x^5 / 9 x^3 y^4)
if the degree of he monimial is -xy^3m (where m is a constant) is 10, then the value of m is ______
The value of m that makes the expression a monomial is 10/3
How to determine the value of m?From the question, the given parameters are
Monomial: -xy^3m
Degree = 10
The degree of a polynomial is the highest power of the polynomial
This means that
Degree = 10
Degree = 3m
Substitute the known values in the above equation
So, we have
3m = 10
Divide both sides of the equation by 3
m = 10/3
Hence, the value of m is 10/3
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The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 10 members, how many ways could the officers be chosen?
Answer:
210 ways
Step-by-step explanation:
This is a combinatorics problem of the general nature of choosing r elements from a sample of n elements
It is indicated by the term
[tex]C(n,r) = $\displaystyle \binom{n}{r} = \dfrac{n!}{( r! (n - r)! )$}\\\\[/tex]
where n! represents the factorial of n = n x (n-1) x (n-2) x .... 3 x 2 x 1
With n = 10, r = 3 there are C(10, 3) ways of choosing the officers
[tex]C(n,r) = C(10,4)\\\\= \dfrac{10!}{4! (10 - 4)! }\\\\\\[/tex]
[tex]= \dfrac{10!}{4! \times 6! }[/tex]
[tex]$\displaystyle = 210[/tex]
.038 ÷.02 I need help to show the work for this problem.
Answer:
The answer would be 1.9
There really is no way to show the work on this problem since it is decimals
Which polynomial function could be represented by the graph below?
-8-8-4
8
6
+
2
-6
do
2 4
Of(x) = x² + x - 2
Of(x) = 2x2 + 2x - 4
O f(x)=x²-x-2
Of(x) = 2x² -2x - 4
6
8 X
The equation of the polynomial function is y = x² + x - 2
How to determine the equation of the polynomial function?The polynomial function is represented on the given graph
From the graph, we can see that:
The curve of the graph crosses the x-axis at the following points
x = -2 and x = 1
This means that the equation of the polynomial function can be calculated as
y = (x - x₁) * (x - x₂)
Where
x₁ = -2 and x₂ = 1
Substitute x₁ = -2 and x₂ = 1 in the equation y = (x - x₁) * (x - x₂)
So, we have
y = (x + 2) * (x - 1)
Open the brackets
y = x² + 2x - x - 2
Evaluate
y = x² + x - 2
Hence, the equation is y = x² + x - 2
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Determine the x- and y-intercepts of the graph of x + 3y = 9.
Then plot the intercepts to graph the equation.
Line
Isabela has already taken 16 quizzes during past quarters, and she expects to have 1 quiz during each week of this quarter. How many weeks of school will Isabella have to attend this quarter before she will have taken a total of 26 quizzes?
Data:
Quiz taken: 16
Quiz each week: 1
You can express this as a equation:
Q= Total of quizes taken
W= weeks
As each week the number of quizes Q increase in 1 the change is k=1, and Isabela has already taken 16 quizzes. The number of quizzes can be represented as:
[tex]Q=Q_0+kW[/tex]Q0 is the number of quizzes Isabela has already taken.
[tex]Q=16+W[/tex]Then, to have a total of 26 quizzes Isabela have to attend:
Q=26
W=?
[tex]26=16+W[/tex]You can find the number of weeks by clearing of the equation above the W:
Substract in both sides of the equation 16:
[tex]26-16=16-16+W[/tex][tex]10=W[/tex]Then, Isabela have to attend 10weeks this quarter to have a total of 26 quizzeswhat is the division law of exponents?
When subtracting 538 - 446, why is there no digit in the hundreds place?
Answer:82
Step-by-step explanation:
Because you need to regroup the numbers, therefore leaving 4-4, which is just a 0, (don't include the 0 in a number).
The width of a rectangle is 7t-7.5 feet and the length is 7.5t+10 feet. Find the perimeter of the rectangle.
The perimeter of the rectangle is 29t + 5
Define Perimeter.
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
Given,
width = 7t - 7.5
length = 7.5t + 10
we know, the perimeter of the rectangle (p) = 2 ( l + w)
put the value in given formula,
p = 2 * (7.5t + 10 + 7t - 7.5)
p = 2 * ( 14.5t + 2.5)
p = 2 * 14.5t + 2.5 * 2
p = 29t + 5
Hence, the perimeter of the rectangle is 29t + 5
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Find the slope intercept form of 5x+20y=600
PLEASE SHOW ALL STEPS!!!!!!!
Answer:
[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{1}{4}x+30[/tex]
[tex]\textsf{Slope}: \quad -\dfrac{1}{4}[/tex]
[tex]\textsf{$y$-intercept}: \quad 30[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]5x + 20y = 600[/tex]
To convert the given equation to slope-intercept form:
Subtract 5x from both sides.Divide both sides by 20.[tex]\boxed{\begin{array}{rccccccc}5x &+ & 20y & = & 600&&&\\-5x & & & && -5x &&\\\\\cline{1-8}\\& & \dfrac{20y}{20} & = & \dfrac{-5x}{20} & + & \dfrac{600}{20}\\\\&& y&=&-\dfrac{1}{4}x & + & 30\end{array}}[/tex]
[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{1}{4}x+30[/tex]
[tex]\textsf{Slope}: \quad -\dfrac{1}{4}[/tex]
[tex]\textsf{$y$-intercept}: \quad 30[/tex]
please help me with this.
The equation for g(x) = -(x + 1)² - 4.
Where f(x) = x².
Solution:
The given parent function is ,
f(x)= x²
Begin by solving the equation f(x) = x². Write the equation for the g(x) graph that has been flipped or reflected over the x-axis.f1(x) = -f(x)
So,
f1(x) = -x²
Apply the equation and create an equation for the graph of g(x).It has also been moved down 4 units.
f2(x) = f1(x) -4
f2(x) = -x² - 4
Apply the equation from above step. Create an equation for the graph of g(x).1 unit has also been shifted to the left.
g(x) = f2( x + 1)
g(x) = -(x + 1)² - 4
As a result, the required equation is.
g(x) = -(x + 1)² - 4.
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