Answers
In the given triangles,
∠B = ∠A
∠T = ∠M
Since, two angles of a triangle are equal, the third angle will also be equal.
Also, ΔLBT is similar to ΔHAM ........(by Angle - Angle similarity)
Now,
⇒ LB/HA = BT/AM = LT/HM ..........(Sides of similar triangles are proportional)
⇒ LB/HA = BT/AM
⇒ 4/HA = 6/10
⇒ 10 x 4 = HA x 6
⇒ HA = 40/6
⇒ HA = 20/3
⇒ HA = 6 2/3
What are Similar Triangles?Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size. Triangle resemblance is shown by the symbol ~ in this case.It is possible to prove that the corresponding sides of two triangles with congruent angles (also known as equiangular triangles) are proportionate. The AAA Similarity Theorem refers to this.Numerous synthetic (coordinate-free) Euclidean geometry proofs are based on similar triangles.The angle bisector theorem, geometric mean theorem, Menelaus' theorem, and Pythagorean theorem are only a few examples of basic conclusions that can be proven in this fashion. The fundamentals of right triangle trigonometry are also provided by similar triangles.
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Related Questions
Use the diagram below to find x x = 34x = 32x = 30x = 28
Answers
Given the following question:
Alpha Industries is considering a project with an initial cost of $7.9 million. The project will produce cash inflows of $1.63 million per year for 7 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.58 percent and a cost of equity of 11.25 percent. The debt-equity ratio is .59 and the tax rate is 21 percent. What is the net present value of the project?
Answers
The net present value of the project of the company Alpha Industries is $494,918.
Given,
The initial cost of the project = $7.9 million
Cost of debt = 5.58 percent
Cost of equity = 11.25 percent
The debt-equity ratio= .59
Tax rate = 40 percent.
Let us assume
Equity be $x, then
Total = $1.59x
Respective weights = Pretax cost of debt × (1 - tax rate)
=5.58% × (1 - 0.4)
Respective weights = 3.348%
WACC = Respective costs × Respective weights
WACC = (x ÷ 1.59x × 11.25%) + (0.59x ÷ 1.59x × 3.348)
WACC = 8.318%
The present value of annuity = Annuity × (1 - (1 + interest rate)^ - time period] ÷ Rate
=1.63 × [1 - (1.08317811321)^-7]÷ 0.08317811321
= $1.63 × 5.150256501
The present value of annuity = $8,394,918.10
The net present value = The present value of cash inflows - The present value of cash outflows
= $8,394,918.10 - $7,900,000
The net present value of the the project = $494,918
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Please helpp..Use the simple interest formula to determine the missing value.
p=$951.63, r= 6.5%, t= ?, i = $123.71
t=years
Answers
Using the simple interest formula, the value of time (t) is 103 years.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest. Ordinary simple interest and exact simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest. The simple interest calculation formula is the same for both approaches.So, the simple interest rate formula:
A = P (1 + rt)We need to find the value of time (t), then the formula will become:
t = (1/r)(A/P - 1)Insert the values as follows:
t = (1/6.5)(951.63/123.71) - 1)t = 102.96Rounding off: t = 103 years
Therefore, using the simple interest formula, the value of time (t) is 103 years.
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The probability that an individual is left-handed is 12%, In a randomly selected class of 30students, what is the probability of finding exactly 4 left-handed students?
Answers
Given that:
- The probability that an individual is left-handed is 12%.
- There are 30 students in the class.
You need to use this Binomial Distribution Formula, in order to find the probability of finding exactly 4 left-handed students :
[tex]P(x)=\frac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]Where "n" is the number being sampled, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case:
[tex]\begin{gathered} n=30 \\ x=4 \\ p=\frac{12}{100}=0.12 \end{gathered}[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]P(x=4)=\frac{30!}{(30-4)!4!}(0.12)^4(1-0.12)^{30-4}[/tex][tex]P(x=4)\approx0.2047[/tex]Hence, the answer is:
[tex]P(x=4)\approx0.2047[/tex]The graph of y=√x is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph off(x)?$ 10-10-88 10 x
Answers
We must apply some transformations to the function:
[tex]y=g(x)=\sqrt[3]{x}.[/tex](1) A reflection across the y-axis is given by the transformation:
[tex]g(x)\rightarrow h(x)=g(-x)=\sqrt[3]{-x}=-\sqrt[3]{x}.[/tex](2) A translation down 2 units is given by the transformation:
[tex]h(x)\rightarrow f(x)=h(x)-2=-\sqrt[3]{x}-2.[/tex]Plotting the function f(x), we get the following graph:
AnswerRound to the nearest tenths 62.32
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Answer:62.3
Step-by-step explanation:
can you check to see if my work is correct?
Answers
The Solution.
[tex]P=-\frac{1}{250}T^2+2.8T-394[/tex]To obtain the maximum value of T, we differentiate with respect to x and equate to zero.
[tex]\begin{gathered} \frac{dP}{dT}=2(-\frac{1}{250}T)+2.8\text{ =0} \\ \\ -\frac{1}{125}T+2.8=0 \\ \\ -\frac{T}{125}=-2.8 \\ \text{Cross multiplying, we get} \\ T=125\times2.8=350^oF \end{gathered}[/tex]To get the maximum value of P, we shall substitute 350 for T in the given function.
[tex]\begin{gathered} P=-\frac{1}{250}(350^2)+2.8(350)-394 \\ \\ P=-490+980-394 \\ P=96\text{ percent} \end{gathered}[/tex]The correct answer is T = 350 degrees Fahrenheit , and P = 96 percent.
What is the first point you would graph the function 3x+1/2y=2
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First, let's clear y to get the slope-intercept form:
[tex]\begin{gathered} 3x+\frac{1}{2}y=2 \\ \\ \rightarrow6x+y=4 \\ \Rightarrow y=-6x+4 \end{gathered}[/tex]This way, we can conclude that the y-intercept is 4. This is the first point we have to graph:
[tex](0,4)[/tex]The numbers of students in the 9 schools in a district are given below. (NOTE THAT THESE ARE ALL ALREADY IN ORDER FROM LEST TO GREATEST)
Answers
Given:
The data is:
240,256, 307, 310, 325, 333, 359, 363, 378
Required:
If the number 378 changes to 261 then
(a) What happens to the median
(b) What happens to the mean
Explanation:
(a)The number of terms = 9
Median = 5th term
Median = 325
if the term 378 changed to 261 then the data will be:
240,256, 261 307, 310, 325, 333, 359, 363
Median = 310
Thus the median is decreasing.
Decreased value = 325 - 310 = 15
(b) Mean is given by the formula:
[tex]mean=\frac{sum\text{ of observation}}{Total\text{ number of observation}}[/tex][tex]\begin{gathered} mean\text{ = }\frac{240+256+307+310+325+333+359+363+378}{9} \\ mean\text{ =}\frac{2871}{9} \\ mean\text{ =319} \end{gathered}[/tex]if the term 378 changed to 261 then
[tex]\begin{gathered} mean=\text{ }\frac{240+256+307+310+325+333+359+363+261}{9} \\ mean=\text{ }\frac{2754}{9} \\ mean=\text{ 306} \end{gathered}[/tex]Thus the mean is decreasing.
Decreased value = 319 - 306 = 13
Final answer:
(a) median is decreased by 15
(b) mean is decreased by 13
ahmed want to make a triangle, he has rods that measure 9 inch and 15 inches. the rods cannot be cut. which is the length of a rod he could use to complete the triangle?
Answers
The length of the rod that he could use to complete the triangle is 12 inches. This is solved based on the principle of Pythagorean Triples.
What are the Principles of Pythagorean Triples?Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as a² + b² = c², where a, b, and c are positive integers. In this case, 'c' is the 'hypotenuse,' or the triangle's longest side, while 'a' and 'b' are the other two legs of the right-angled triangle.
Pythagorean triples are denoted as (a,b, c). The most well-known Pythagorean triple example is (3, 4, 5). We can see that the numbers 3, 4, and 5 meet the equation a² + b² = c².
To prove that the length of the rod that should be used to complete the triangle is 12. Let's subject the values to the Principles of Pythagorean Triples.
Given:
9,
let's assume that 15 is the longest side.
Thus,
If we are correct,
9² + 12² should equal 15²
9² = 81
12² = 144
15² = 225
81 + 144 =225
Hence the length of the rod that must be used to complete the triangle is 12 inches.
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A money market account offers 1.25% interest compounded monthly. If you want to save $500 in two years, how much money would you need to save per month?
Answers
If you want to save $500 in two years, you need to save $20.58 per month with a 1.25% interest compounded monthly.
How is the periodic saving determined?The monthly savings can be determined using an online finance calculator as follows:
N (# of periods) = 24 months (2 x 12)
I/Y (Interest per year) = 1.25%
PV (Present Value) = $0
FV (Future Value) = $500
Results:
Monthly Savings = $20.58
Sum of all periodic savings = $494.04
Total Interest = $5.96
Thus, the investor needs to save $500 in two years to save $20.58 monthly.
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Murray has tossed a coin 120 times. The coin landed on heads 54 times. What is the experimental probability that the coin will land on heads on the next toss?
Answers
Answer:
Explanation:
Experimental probability = number of favorable outcomes/number of total outcomes
From the information given,
number of favorable outcomes = 54
number of total outcomes = 120
The experimental probability that the coin will land on heads on the next toss = 54/120
Dividing the numerator and denominator by 6,
The experimental probability that the coin will land on heads on the next toss = 9/20
3. Use the slope and y-intercept to complete thetable of values with solutions that includeonly integers. (1 point total)y=2x-3=xу
Answers
given the equation:
y = 5/4x - 3
to complete the table for the values of x and y using intergers
fristly,
when x = -4
y = 5/4(-4) - 3
y = -5 - 3
y = -8
when x = 0
y = 5/4(0) - 3
y = 0 - 3
y = -3
when = 4
y = 5/4(4) - 3
y = 5 - 3
y = 2
when x = 8
y = 5/4(8) - 3
y = 5(2) - 3
y = 10 - 3
y = 7
so completing the table:
y = 5/4x - 3
x y
-4 -8
0 -3
4 2
8 7
find the surface area of the triangular prism 7 6 7 9
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The surface area of the triangular prism will be 217.95 cm²
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
It is given that,
Base side, a = 7 sm
Base side, b = 6 cm
Base side, c = 7 cm
Height, h = 9 cm
The surface area of a triangle prism: The formula for a triangular prism's surface area is,
A=bh+(b₁+b₂+b₃) units²
where b is the base of a triangular face, h is the height of a triangular face, b₁ is the side of the triangular base, b₂ is the side of the triangular base, and l is the prism's length.
The surface area of the triangular prism will be,
[tex]\rm A = ah + bh + ch + \dfrca{1}{2} \sqrt{-a^4 +2(ab)^2 +2(ac)^2 -b^4+2(bc)^2 -c^4}[/tex]
Substitute the given values,
[tex]\rm A = 7 \times 9 + 6 \times 9 + 7 \times 9 + \dfrac{1}{2} \times \sqrt{-7^4 + 2(7 \times 6)^2 +2 (7\times 7)^2 -6^4 + 2(6 \times 7)^2 - 7^4} \\\\ A = 217.94 \ cm^2[/tex]
Thus, the surface area of the triangular prism will be 217.95 cm².
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Can you someone solve for x
-2x + -3 = 1x
Answers
Answer: x = -3/2
Step-by-step explanation:
Equation:
x -2x + -3 = 1x
Combine Like Terms:
x - 2x + -3 = 1x
-x - 3 = 1x
+x +x
[tex]-3 = 2x[/tex]
[tex]\frac{-3}{2} = \frac{2x}{2}[/tex]
-3/2 = x
find the volume of a conebase diameter of 10 ydheight 6 ydsuse the value 3.14 for pie
Answers
Given
The formula
[tex]\begin{gathered} \text{The volume of a cone =}\frac{1}{3}\pi r^2h \\ \\ \pi=3.14 \\ r=5 \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} \text{The volume of a cone =}\frac{1}{3}\pi r^2h \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times5^2\times6 \\ \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times25^{}\times6 \\ \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times150 \\ \\ \text{The volume of a cone =}3.14\times50 \\ \\ \text{The volume of a cone =}157yd^3 \end{gathered}[/tex]The final answer
[tex]\text{The volume of a cone =}157yd^3[/tex]The weight of 8 eggs is 496 grams. Identify the constant of proportionality of total weight to number of eggs.
Group of answer choices
60
56
62
58
Answers
-5 ( -10-2(-3)) to the 2nd power . numerical exponents
Answers
The value of -5 ( -10-2(-3)) to the 2nd power is -6480.
What is an exponent?It should be noted that an exponent simply means the number through which another number can be multiplied by itself.
Based on the information given, it should be noted that PEDMAS will be used. This implies:
P = parentheses
E = Exponents
D = division
M = multiplication
A = addition
S = subtraction
-5 ( -10-2(-3)² will be illustrated thus:
It's important to calculate the value in the parentheses first according to PEDMAS.
= -5 [(-12(-3)]²
= -5 (36)²
= -5 × 1296
= -6480
The value is -6480.
In this case, the concept of PEDMAS is used to get the value.
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the ratio of the measures of three angles of a triangle is 3:6:1. Find the measurements of each angle
Answers
Gabe, you are doing great. Now you need to solve for x:
3x + 6x + x = 180
10x = 180
dividing by 10 at both sides:
10x/10 = 180/10
x = 18 That is the answer you have.
Finally, you need to multiply the ratio for the value of x, you just calculated:
Side 1 = 3 * 18
Side 2 = 6 * 18
Side 3 = 1 * 18
which integer could represent the fact that the water level of a pool decreases by 4 feet
Answers
-4
1) In this question, there's not much information so let's think of a rule
2) We can sketch this out:
We could even write a function that describes this, which "W" stands for Water Level and "t":
3) So if the level of water is decreasing by 4 feet each and every water level from now on is negative.
whats an inequality to compare the numbers
11 and -9
Answers
The inequality comparison
What is Inequality?
Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.
Given, numbers are
11 and -9
an inequality to show all numbers: from (11) to (–9) inclusive
-9 ≤ x ≤ 11
Hence, inequality to compare the numbers
11 and -9 is -9 ≤ x ≤ 11
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Finding the vertex focus directrix and axis of symmetry of a parabola
Answers
Equation:
[tex](y+1)^2=6(x-5)[/tex]The vertex is given by the following formula:
[tex](y-k)^2=4p(x-h)[/tex]where the vertex is (h, k). Thus, in our equation k = -1 and h = 5, and the vertex
is (5, -1).
Additionally, the focus is given by (h+p, k). In our case:
[tex]p=\frac{6}{4}=\frac{3}{2}[/tex]Then, the focus is:
[tex](5+\frac{3}{2},-1)[/tex]Simplifying:
[tex](\frac{13}{2},-1)[/tex]The directrix is x = h - p:
[tex]x=5-\frac{3}{2}=\frac{7}{2}[/tex]Finally, the axis of symmetry is y = -1.
Prove that the following four points will form a rectangle when connected in orderby showing the diagonals are congruent. Show all work.AIO. -3). B(-4.0). C(2. 8). D(6. 5)
Answers
SOLUTION
For the four points to form a rectangle, the length of the diagonals will be equal.
This means that we have to find the distance between the point BD and AC. If
BD = AC, then the four points would form a rectangle.
[tex]\begin{gathered} Dis\tan ce\text{ betw}ee\text{n points B and D, that is BD} \\ \text{Distance betw}ee\text{n two points = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ BD=\text{ }\sqrt[]{(6-(-4)^2+(5-0)^2} \\ BD=\sqrt[]{10^2+5^2} \\ BD=\sqrt[]{125} \\ BD=\text{ 5}\sqrt[]{5} \end{gathered}[/tex]Now let's find AC
[tex]\begin{gathered} AC=\text{ }\sqrt[]{(2-0)^2+(8-(-3)^2} \\ AC=\sqrt[]{2^2+11^2} \\ AC=\sqrt[]{4+121} \\ AC=\sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]So, since BD = AC, the four points A, B, C and D would form a rectangle.
solve P=2M+2M for G
G=?
Answers
G=P-2M/2
Step-by-step explanation:
P=2G+2M
p - 2M = 2G
G=P - 2M/2
Find the equation of the line that passes through the two points (2, -1) and (5, 5). Write your answer in standard form.
Answers
Explanation
Given the points two points (2, -1) and (5, 5) we can find the equation of a line using the point-slope formula.
[tex]\begin{gathered} y_-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ Where\text{ x}_1,y_1=2,-1 \\ x_2,y_2=5,5 \end{gathered}[/tex]Therefore, we will have;
[tex]\begin{gathered} y-(-1)=\frac{5-(-1)}{5-2}(x-2) \\ y+1=\frac{6}{3}(x-2) \\ y+1=2(x-2) \\ y+1=2x-4 \\ 2x-y=1+4 \\ 2x-y=5 \\ \end{gathered}[/tex]Answer: 2x-y=5
The sum of a number and 4 times it’s reciprocal is 13/3. Find the number(s).
Answers
Let the unknown number be "x"
We will write an algebraic equation from the word problem given. Then we will solve for "x".
Given,
Sum of number (x) and 4 times the reciprocal is 13/3
We can convert it into an algebraic equation:
[tex]x+(4\times\frac{1}{x})=\frac{13}{3}[/tex]Now, let's solve for the unknow, x,
[tex]\begin{gathered} x+(4\times\frac{1}{x})=\frac{13}{3} \\ x+\frac{4}{x}=\frac{13}{3} \\ \frac{x^2+4}{x}=\frac{13}{3} \\ 3(x^2+4)=13\times x \\ 3x^2+12=13x \\ 3x^2-13x+12=0 \\ (x-3)(x-\frac{4}{3})=0 \\ x=3 \\ x=\frac{4}{3} \end{gathered}[/tex]The numbers are
[tex]\begin{gathered} 3 \\ \text{and} \\ \frac{4}{3} \end{gathered}[/tex]The length of a rectangle is 5yd less than twice the width, and the area of the rectangle is 33yd^. Find the dimensions of the rectangle.
Answers
Let l be the length of the rectangle and w its width.
From this, we have:
I) w - l = 5
II) l*w = 33
From I, we have w = 5 + l
Applying this to equation II, we have: l(5+l) = 33
l^2 + 5l - 33 = 0
The positive root of this equation is l = [sqrt(157) - 5]/2 = 3.8 yd (rounded to the nearest tenth)
Applying this to equation I, we have: w - 3.8 = 5, which implies w = 5 + 3.8 = 8.8 yd
How many solutions does the system have? 2x + 3y = -6 3a - 4y = -12 no solutions O exactly one solution O infinitely many solutions
Answers
Therefore, it has exactly one solution.
Translate PreImage coordinates left 9 units and down 1 unit.
Answers
Given
A(11,9)
B(11,3)
C(5,3)
D(5,9)
In the coordinate system (x,y), x determines the horizontal position, and y determines the vertical position. Having a translation of 9 units left, and 1 unit down, means that each coordinate system will be translated as (x-9 , y-1).
[tex]\begin{gathered} (x,y)\Longrightarrow(x-9,y-1) \\ \\ A(11,9)\Longrightarrow A^{\prime}(11-9,9-1)\Rightarrow A^{\prime}(2,8) \\ B(11,3)\operatorname{\Longrightarrow}B^{\prime}(11-9,3-1)\operatorname{\Rightarrow}B^{\prime}(2,2) \\ C(5,3)\operatorname{\Longrightarrow}C^{\prime}(5-9,3-1)\operatorname{\Rightarrow}C^{\prime}(-4,2) \\ D(5,9)\operatorname{\Longrightarrow}D^{\prime}(5-9,9-1)\operatorname{\Rightarrow}D^{\prime}(-4,8) \end{gathered}[/tex]Therefore, the coordinates of the post image are A'(2,8), B'(2,2), C'(-4,2), D'(-4,8).
Round the decimal number to the nearest thousandth.
11.59978
Answers
Answer:
Step-by-step explanation:
