Please help!! I need to find the Length of Side EF and The scale factor from both triangles
Answers
The required answers for given similar triangles are DF= 3, EF= 2.25, and scale factor 4/3 respectively.
What is Similarity?In geometry, two geometrical triangle are similar if they have the same shape, and corresponding sides are equate by some factor. More accurately, one can be obtained from the other by uniformly scaling.
According to given data:For length of side DF, ratio of corresponding sides is equal.
⇒ [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]
⇒ [tex]\frac{2}{1.5}=\frac{4}{DF}[/tex]
⇒ DF = 3
Similarly for EF,
[tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]
⇒[tex]\frac{2}{1.5}=\frac{3}{EF}[/tex]
⇒ EF = 2.25
At last, by using same concept of similarity scale factor is
[tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]
⇒ [tex]\frac{AB}{DE} =\frac{4}{3}[/tex]
This is our scale factor for both triangle.
To know more about similarity visit:
brainly.com/question/26451866
#SPJ13
Related Questions
1. Harper is going to create a graph of the equation y = -0.5x + 12. Which of the following will be true about the graph?
The graph will contain the origin.
The graph will increase from left to right.
The graph will cross the x-axis at (12, 0).
The graph will have a slope of -0.5.
Answers
The statement that would be true concerning the graph would be that the graph will have a slope of -0.5.
What is a slope?A slope is defined as the difference between a chosen point on the vertical and horizontal axis.
The slope of a straight line graph has a constant equation that is used to determine its slope. Thus;
y = mx + b
Where m = the measure of the steepness of the straight line graph.
From the equation of the graph that was given;
y = -0.5x + 12. The slope of the graph which is represented by 'm' would be -0.5.
Learn more about graph slope her:
https://brainly.com/question/28337360
#SPJ1
which is a reasonable estimate for the amount of kernels serena needs to make 6 cups of popcorn
Answers
Answer:
four tablespoons to make 6 cups of popcorn.
Step-by-step explanation:
1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.
Help me in this proportion maths problems
Answers
y is inversely proportional to the square of x, here y in terms of x is 2/5.
From the given problem y is inversely proportional to the square of x.
A table of values for x and y is shown.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the table:
(a) As we know that, y is inversely proportional to the square of x,
Here k is proportionality constant.
y∝1/x²
y= k/x²
4=k/1²
k=4
So, y in terms of x is y=4/x²
(b) Putting the value of y=25, we get:
25=4/x²
x²=4/25
x=2/5
Therefore, y is inversely proportional to the square of x, here y in terms of x is 2/5.
To learn more about the proportional relationship visit:
brainly.com/question/12917806.
#SPJ1
Help! Consider the following three systems of linear equations.
Answers
Answer:
b & d
Step-by-step explanation:
PLEASE HELP
*IMAGE BELOW*
Answers
Or
H= x^2-8x-8/x
How long will it take for $3, 900 to double if it is invested at 8% annual interest compounded 2 times a year?
Enter in exact calculations or round to 3 decimal places.
It will take___years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take___ years.
Answers
The number of years to double the investment is 8.824 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $3,900
R = 8%
n = 2
A = 2P = 2 x 3,900 = $7,800
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]
78/39 = [tex](1.04)^{2t}[/tex]
2 = [tex](1.04)^{2t}[/tex]
Taking logs on both sides.
log 2 = 2t log(1.04)
0.30 = 2t x 0.017
0.30/0.017 = 2t
17.65 = 2t
Divide both sides by 2.
t = 17.65 / 2
t = 8.824 years.
Thus,
The number of years to double the investment is 8.824 years.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ1
4/9 - 1/2 Subtract.
- Simplest form.
-1/9 - (-2/5) Evaluate.
- Simplest form.
Answers
Answer:
Step-by-step explanation:
Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18
The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.
I need help with math
Answers
The leading coefficients and parabolic equations, considering the vertices, are given as follows:
1. a = 7/4, y = 7/4(x - 4)² - 1.
2. a = -2, y = -2(x + 1)² + 2.
Equation of parabola with vertex (h,k)
The equation of a parabola with vertex given by (h,k) is presented as follows:
y = a(x - h)² + k.
In which a is the leading coeffiicent.
For item 1, the coordinates of the vertex is given as follows:
(4,-1).
Hence:
h = 4, k = -1, and the equation is:
y = a(x - 4)² - 1.
When x = 6, y = 6, hence the leading coefficient is calculated as follows:
6 = a(6 - 4)² - 1
4a = 7
a = 7/4.
Thus the equation is:
y = 7/4(x - 4)² - 1.
For item 2, the vertex is:
(-1,2).
Hence:
y = a(x + 1)² + 2.
When x = 0, y = 0, hence the leading coefficient is calculated as follows:
0 = a(0 + 1)² + 2
a = -2.
Hence the equation is:
y = -2(x + 1)² + 2.
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
#SPJ1
Problem 6 Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.
A: EFGH is a rectangle.
B: EFGH is a rhombus.
C: Diagonal FH bisects angles EFG and EHG.
D: Diagonal FH is perpendicular to side FE.
E: Angle EHF is congruent to angle FGH.
F: Angle FEH is congruent to angle FGH.
Answers
The statements which are as a result of corresponding parts of congruent triangles being congruent are:
Diagonal FH bisects angles EFG and EHG. Angle EHF is congruent to angle FGH. Proof of congruent triangles being congruent1) EFGH is a rectangle.
The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.
2). EFGH has 4 congruent sides.
The above statement is also false. EFGH has two opposite sides are congruent.
3). Diagonal FH bisect angles EFG and EHG.
The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.
4). Diagonal FH is perpendicular to side Fe.
The above case is not true in general.
5). Angle FEH is congruent to angle FGH.
Read more on congruent triangles:
https://brainly.com/question/18392828
#SPJ1
a circular curve is to be constructed with a 225 ft radius and an interior angle of 55 degrees. the separation between the stakes along the arc is 50 ft. assuming the curve is laid out from point to point, what is the last deflection angle?
Answers
The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°
In the given question we have,
Radius of circular curve (R) = 225 ft
intersection or central angle in circular curve (I or delta) = 55°
separtion between stakes alaong arc = 50 ft
Angle of deflection is measured from tangent at PC or PT to any point .
deflection angle formula
deflection angle = (Lc /L)(I/2)
where, Lc is long chord and L is lenth of arc , I is central angle
first we find out the value of Lc and L
using formula , R = Lc / 2sin(I/2)
Lc = 225× 2 sin(55°/2) = 208 ft
L = R × I ×π/180°
L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft
put all the vales in deflection angle formula we get ,
deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°
To learn more about circular curve, refer :
https://brainly.com/question/1293183
#SPJ4
Mr karki divided a sum of Rs 1,80,000 between his son and daughter in the ratio of 4:5 find the sum obtained by eachof them.
Answers
Answer:
Rs 80,0000 and Rs 100,000
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide the amount by 9 to find the value of one part.
Rs 1,80,000 ÷ 9 = Rs 20,000 , then
4 parts = 4 × Rs 20,000 = Rs 80,000 ← amount son receives
5 parts = 5 × Rs 20,000 = Rs 100,000 ← amount daughter receives
The sum obtained by the son is Rs. 80,000 and the daughter is Rs. 1,00,000.
Mr. Karki divided Rs. 1,80,000 in a ratio of 4:5 between his son and daughter.
Let the common multiple be x
∴ The son obtained Rs. 4x --------1
And daughter obtained Rs. 5x --------2
As the total sum is Rs. 1,80,000
∴ 4x + 5x = 180000
9x = 180000
x = 180000/9
∴ x = Rs. 20000
Putting the value of x in 1 and 2 we get,
The sum obtained by son = 4x = 4*20000 = Rs. 80000
And the sum obtained by daughter = 5x = 5*20000 = Rs. 100000
Thus, the son obtained Rs. 80,000 while the daughter obtained Rs. 1,00,000 which is in the ratio of 4:5.
To learn more about ratios,
brainly.com/question/1504221
Rafe buys a cake for $12. The sales tax is 10%. How much is the sales tax?
A. $1.20
B.$10
C.$12
D.$13.20
Answers
Answer:
A $1.20
Step-by-step explanation:
Answer: A) $1.20
Step-by-step explanation: To get 10% of a number, you just need to divide by 10, so 12 ÷ 10 = 1.2.
let x be the exam grade of a random student taking calculus 1 at uiuc. suppose professor smith takes a random sample of 140 students from the calculus 1 class to see how they did on the exam. in his sample, he got a mean of 86 and a standard deviation of 11. approximate the probability that (the sample mean) would be higher than 88.4 or smaller than 84.4?
Answers
The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = 86
sample size, n = 140
standard deviation, σ = 11
The probability
P(z > 88.4) + P(z < 84.4)
z score for z < 88.4
z = (88.4 - 86) / 11
= 0.21818 p value = 0.41364
z score for z < 84.4
z = (84.4 - 86) / 11
= -0.14545
p value for z < -0.14545 = 0.44218
The probability required = 0.41364 + 0.44218 = 0.85582
Learn more about p - values at:
https://brainly.com/question/28940355
#SPJ1
Solve the system of equations.
Answers
Answer:
(7,5)
Step-by-step explanation:
[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]
3 math questions for 50 points.
Answers
2 = J
3 = B
Hope This Helps :)
Can anyone write the equation of this graph?
Answers
The translated absolute value function graphed is defined as follows:
y = |x - 3| + 5.
What is the absolute value function?The absolute value function, of vertex (h,k), is defined by the following piecewise rule, depending on the input of the function:
f(x) = |x - h| + k = x - h + k, x - h ≥ 0.f(x) = |x - h| + k = -x + h - k, x - h < 0.In this problem, the coordinates of the vertex are given as follows:
h = 3, as the x-coordinate of the vertex is of 3.k = 5, as the y-coordinate of the vertex is of 5.Hence the vertex is given by the following point:
(3,5).
Then the equation graphed is defined by the rule presented as follows:
y = |x - 3| + 5.
Which is a translation of 3 units right and 5 units up of the standard absolute value function.
More can be learned about the absolute value function at https://brainly.com/question/3381225
#SPJ1
11. Write an equation in vertex form for the parabola below.
Answers
Answer:
Step-by-step explanation:
1. The vertex is where the parabola is changing from increasing to decreasing
2. From the picture, we can see that the vertex is at (1,2)
3. The formula for vertex form is f(x)=a(x-h)^2+k
4. Vertex is (1,2) or (h,k)
5. You can see that the parabola opens upside down like a "n" so it has been reflected in the x axis
6. So, your equaltion is f(x)=-(x-1)^2+2
7. In this cause you can see that a=-1, but if not given you would choose a random point on the parabola and plug it in :). Example:(0,1): 1 = a(0-1)^2+2
a=-1.
8. Your answer: f(x)=-(x-1)^2+2
giving Brainly show work
Answers
Answer:
Step-by-step explanation:
5 1/2 +2x = 25
25- 5 1/2 = 2x
19 1/2 = 2x
x = 9.75
It took him about 9.75 weeks to lose at least 25 pounds.
Answer:
10 or more weeks------------------
Weight lossFirst week - lost 5 and 1/2 pounds,Following weeks - lost 2 pounds per week,Total - at least 25 pounds.Set inequality and find the least whole number2w + 5.5 ≥ 252w ≥ 25 - 2.52w ≥ 19.5w ≥ 19.5/2w ≥ 9.75 ≈ 10It took Mr. Henry at least 10 weeks to lose 25 pounds.
Ibram got a job selling bags of peanuts at the local fairground. He is paid a fixed amount of $340 per week plus $0.84 per item sold. This is represented by the equation P = 0.84 + 340 where P is the amount he is paid for the week and n is the number of bags of peanuts he sold. How much will Ibram be paid if he sells 380 bags of peanuts? If Ibram sells 380 bags of peanuts, he will earn S How many bags of peanuts did Ibram sell if he earned $1,087.60? for the week. If Ibram has earned $1,087.60, he sold bags of peanuts.
Answers
Answer:
Assuming the bags sold were for 1 week period.
1. $659.20 for 1 week and 380 bags of peanuts
2. 890 bags
Step-by-step explanation:
The equation is missing the variable, n (the number of bags sold). I'll take the liberty to add it after the $0.84/bag term, where it belongs:
P = 0.84n + 340
The 340 is $340/week. n must be in units of "bags/week."
1. How much will Ibram be paid if he sells 380 bags of peanuts?
P = $0.84n + $340
n = 380 bags (we will assume in 1 week).
P = $0.84n + $340
P = $0.84(380) + $340
P = $659.20
2. How many bags of peanuts did Ibram sell if he earned $1,087.60?
P = $0.84n + $340
P = $1087.60
$1087.60 = $0.84n + $340
$1087.60 - $340 = $0.84n
$0.84n = $1087.60 - $340
$0.84n = $747.60
n = 890 bags ( ! - I'm impressed)
Determine whether the function is one-to-one. If it is, find a formula for its inverse.
f(x) = 4/9x+8
Answers
Answer:
87c
Step-by-step explanation:
What was the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64
Answers
the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64 was $ 68.73
We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:
Xw= Cw/Cm * 100%
Where:
Cw: cost of coverage for a woman of 50 years.
Cm: coverage cost for a 30-year-old man.
Xw= 819.73/1192.64 *100%
= 68.73
learn more about of percentage here
https://brainly.com/question/11941499
#SPJ4
Please can someone answer this question it would be much appreciated
Thanks so much :)
Answers
I need help too on this one
Answer:
you lowest tempeture in the mesosphere is -96
Step-by-step explanation:
what is the function rule in slope intercept form
Answers
Answer:
The picture is not Clear. Please provide a better view of the question.
Step-by-step explanation:
The points (4, -3) and (x, 3) lie on the same straight line.
If the slope of the line is 2, what is the value of x ?
Answers
answer:
(1,3)
step-by-step explanation:
desmos.
The value of x will be equal to 7 for the given slope of 2 for the line.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
2 = ( 3 + 3 ) / ( x - 4)
2(x-4) = 6
2x - 8 = 6
2x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.
To know more about slopes follow
https://brainly.com/question/3493733
#SPJ2
if a seed is planted, it has a 65% chance of growing into a healthy plant. if 12 seeds are planted, what is the probability that exactly 3 don't grow?
Answers
There is a 136.13 probability that 3 won't increase.
Only 0.65% of seeds will grow into robust plants.
There is a 0.35 probability that a seed won't grow into a robust plant.
In this case, n = 12 and r = 3.
11 seeds will sprout if 1 seed doesn't germinate. Raising 0.65 to the power of 11 and 0.35 to the power of 3 will result in the following: 11 seeds develop, and we use the 11th power; 3 seeds do not grow, so we use the power of 3:
So, the response is:
[tex]{}^{12}C_3[/tex] × [tex]{(chance of successful growth) }^{11}[/tex]x [tex](chance of Unsuccessful growth)^3[/tex]
= [tex]{}^{12}C_3[/tex] × [tex]0.65^{11}[/tex] × [tex]{0.35}^3[/tex]
= 362880 × 0.008750 × 0.042875
= 136.13
Learn more about the probability at
https://brainly.com/question/29214023?referrer=searchResults
#SPJ4
196 prime factorization pls help
Answers
The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
Which bird is closer to the ground after 8 minutes?
The
eagle
is closer to the ground.
How much closer?
feet
hurry
Answers
The hawk is closer to the ground after 8 minutes
It is 130 feet closer
How to determine the valuesWe have the equation as;
y = −20x+350. This represents the altitude y in feet of a hawky=−10x+400. This represents the altitude y in feet of the eagleAlso, x represents the descending time in minutes
Now, let's substitute the value of x as 8 minutes in the equations
If x = 8
For equation (1)
y = - 20(8) + 350
expand the bracket
y = - 160 + 350
y = 190 feet
For equation (2)
y = -10(8) + 400
expand the bracket
y = -80 + 400
y = 320 feet
The hawk is closer after 8 minutes
The distance from the ground(eagle) - The distance from the ground(hawk)
320 - 190
130 feet
Hence, the hawk is closer to the ground
Learn more about functions here:
https://brainly.com/question/25638609
#SPJ1
two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
Answers
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
To learn more about function, visit:
https://brainly.com/question/21145944
#SPJ4
a shelf in the metro department store contains 80 colored ink cartridges for a popular ink-jet printer. seven of the cartridges are defective. (a) if a customer selects 2 cartridges at random from the shelf, what is the probability that both are defective? (round your answer to five decimal places.)
Answers
The probability that both are defective when a customer selects 2 cartridges at random from the shelf will be 0.00766.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The probability of choosing defective cartridge=7/80
So, the probability of choosing 2 defective cartridge=(7/80)²
=0.00765625
=0.00766
When a customer randomly chooses two cartridges from the shelf, the likelihood that both are flawed is 0.00766.
To know more about probability,
https://brainly.com/question/11234923
#SPJ4
please can someone solve this and tell me how at the end, it's gives -2 alpha beta instead of +2 alpha beta
I need answers ASAP pleeeeaase!!!!!
Answers
The value for the given expression [tex]\alpha ^{2} + \beta ^{2}[/tex] will be [tex](\alpha +\beta )^{2}-2\alpha \beta[/tex].
What are Algebraic Identities?
Algebraic identities are algebraic equations that hold true for any value of each of their variables. In factoring polynomials, they are also used.
As we know, [tex](a+b)^{2} = a^{2} +2ab + b^{2}[/tex] then,
For the given question, [tex](\alpha +\beta )^{2} = \alpha ^{2} +2\alpha \beta + \beta ^{2}[/tex]
Now, subtracting [tex]2\alpha \beta[/tex] on both sides then, we get
or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} +2\alpha \beta + \beta ^{2}-2\alpha \beta[/tex]
or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} + \beta ^{2}\\[/tex]
or, [tex]\alpha ^{2} + \beta ^{2}=(\alpha +\beta )^{2}-2\alpha \beta[/tex]
That's how the value [tex]-2\alpha \beta[/tex] comes.
To learn more about Algebraic Identities
https://brainly.com/question/28853516
#SPJ13
