Given a planar trapezoid ABCD whose height is BE. It is known that AB = 8cm A = 60 *, find the height ofthe trapezoid.
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Solution:
Given the trapezoid:
To solve for the height of the trapezoid, we use the trigonometric ratio.
From the trigonometric ratios,
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]In this case, in the triangle AEB, θ is ∠A.
Thus,
[tex]\sin A=\frac{BE}{AB}[/tex]By cross-multiplying, we have
[tex]\begin{gathered} BE=AB\times\sin A \\ =8\times\sin60 \\ =8\times\frac{\sqrt{3}}{2} \\ \Rightarrow BE=4\sqrt{3}\text{ cm} \end{gathered}[/tex]Hence, the height of the trapezoid is
[tex]4\sqrt{3\text{ }}\text{ cm}[/tex]
Related Questions
Solve the following equation for x by using the quadratic formula. If there is more than one solution, enter your solutions as a comma-separated list, like "1, 3".2x^2+9x+7=0
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Answer:
Explanation:
Given the equation:
[tex]2x^2+9x+7=0[/tex]• The coefficient of x², a=2
,• The coefficient of x, b=9
,• The constant, c=7
Substitute these values into the quadratic formula:
[tex]\begin{gathered} x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ \implies x=\dfrac{-9\pm\sqrt[]{9^2-4(2)(7)}}{2\times2}=\dfrac{-9\pm\sqrt[]{81-56}}{4}=\dfrac{-9\pm\sqrt[]{25}}{4} \\ \implies x=\dfrac{-9\pm5}{4} \end{gathered}[/tex]Thus, the values of x are:
[tex]undefined[/tex]
Could you help me with how to multiply polynomials(5x - 1)(2x^2 -3x + 4)
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ANSWER:
[tex](5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-17x^2+23x-4[/tex]STEP-BY-STEP EXPLANATION:
We have the following multiplication of polynomials:
[tex]\mleft(5x-1\mright)\mleft(2x^2-3x+4\mright)[/tex]When multiplying two polynomials we must bear in mind that all the terms of the first polynomial must be multiplied by all the terms of the second polynomial, like this:
[tex]\begin{gathered} \mleft(5x-1\mright)\mleft(2x^2-3x+4\mright)=5x\cdot2x^2+5x\cdot-3x+5x\cdot4+(-1)\cdot2x^2+(-1)\cdot-3x+(-1)\cdot4 \\ (5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-15x^2+20x-2x^2+3x-4 \\ (5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-17x^2+23x-4 \end{gathered}[/tex]Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote atx = 2 and x = 1.
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Solution
Step 1
Horizontal Asymptotes of Rational Functions
The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
If N is the degree of the numerator and D is the degree of the denominator, and…
N < D, then the horizontal asymptote is y = 0.
N = D, then the horizontal asymptote is y = ratio of leading coefficients.
N > D, then there is no horizontal asymptote.
Step 2
Identify Vertical Asymptotes of a Rational Function
Factor the numerator and denominator.
Simplify by canceling common factors in the numerator and the denominator.
Set the simplified denominator equal to zero and solve for x.
Step 3
x = 2 and x = 1
x - 2 and x - 1
The denominator expression will be (x-2)(x-1)
Step 4
[tex]\begin{gathered} The\text{ rational fraction is} \\ \\ y=\frac{1}{(x-2)(x-1)} \end{gathered}[/tex]Final answer
[tex]y\text{ = }\frac{1}{(x-2)(x-1)}[/tex]What is the range 12 ,20,18,25,6
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The maximum of data is 25
The minimum of data is 6
Then, the range is:
range = maximum - minimum
range = 25 - 6
range = 19
The gas/oil ratio for a certain chainsaw is 50 to 1.a. How much oil (in gallons) should be mixed with 13 gallons of gasoline? b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
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1) We can write the following ratio for this, considering the ratios and the quantities:
a)
[tex]\begin{gathered} \frac{50}{1}=\frac{13}{x} \\ 50x=13 \\ x=\frac{13}{50}\text{ (or 0.26g)} \end{gathered}[/tex]Notice that on the left side, the ratio gas/oil, and on the right side is the quantity of gas and the unknown quantity of oil.
So, so far we have 13/50 gallons of oil that must be mixed with gasoline.
b) For now, we need to convert that from gallons to fluid ounces so we can write out the following product:
[tex]\begin{gathered} x=\frac{13}{50}\times128 \\ x=33.28fl\text{ oz} \end{gathered}[/tex]So 13/50 or 0.26 gallons of oil. b) 33.28 fl oz.
A certain college has been raising tuition every year since the year it opened. The function T = 12,000 (1+.03)* represents the tuition, T, after x years. If the college opened in the year 1990, what was the tuition in 2020?
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if ace of 21 = 856 find ace 20 and ace of 22 given a common ratio of 1/4.
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Answer:
[tex]a_{20}=214,a_{22}=3424[/tex]Explanation:
We are told that the common ratio between the numbers is 1/4, meaning each consquetive number is
Solve for x. 4x-39>-43 and 8x+31<23with an example of a graphic line
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Given:
[tex]4x-39>-43and8x+31<23[/tex]Solve the inequality separately,
[tex]\begin{gathered} 4x-39>-43 \\ 4x>-43+39 \\ 4x>-4 \\ x>-1 \end{gathered}[/tex]Also,
[tex]\begin{gathered} 8x+31<23 \\ 8x<23-31 \\ 8x<-8 \\ x<-1 \end{gathered}[/tex]As the given inequality give x > -1 and x < -1 it shows that there is no solution for the given inequality.
The graph is given as,
The red region shows the inequality 4x -39 > -43 and blue region shows 8x +31 < 23.
Answer: Option D.
given the function f defined by the formula f(x)=2x+1 find the following: Evaluate f(0)
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At a given function:
[tex]\text{ f(x) = 2x + 1}[/tex]At f(0), it means that we substitute x by 0.
We get,
[tex]\text{ f(x) = 2x + 1}[/tex][tex]\text{ f(0) = 2(0) + 1}[/tex][tex]\text{ f(0) = 1}[/tex]Therefore, f(0) = 1.
which value must be added to the expression x^2 + x to make it a perfect-square trinomial
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A perfect square trinomial is written in the form
[tex]undefined[/tex]To get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of _____.A.the denominatorB.xC.1D.the numerator
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Given:
To get rid of radicals in the denominator of a fraction
Required:
you should rationalize the denominator by multiplying the fraction by what
Explanation:
In fraction, a number is said to be a quotient, in which the numerator is divided by the denominator.
there are three types of fraction
1. Proper fraction
2. Improper fraction
3. Mixed
Final answer:
But to get rid of radival in the denominator of a fraction, you should rationalize the denimonator by multiplying the fraction with 1
can someone please help?just in case if the picture seems blurry, the question says the take off ramp is parallel to the waiting ramp, and the interest ramps are parallel. Given that the measure of angle a is 88 find the measure of each remaining angles
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Solve for x. 3 0 - 7 21 Answer: Submit Answer
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Cross multiply:
[tex]3\cdot21=x\cdot7[/tex]Isolate x:
[tex]63=7x[/tex][tex]\frac{63}{7}=x[/tex][tex]x=9[/tex]The value y of a computer after its purchase is given by y(t)=3200-200t
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Problem Statement
The question gives us an equation that gives us the value of a computer after its initial value at purchase. The equation given is:
[tex]\begin{gathered} y(t)=3200-200t, \\ \text{where,} \\ t=years\text{ afer year of purchase} \\ y=\text{value of the computer} \end{gathered}[/tex]We are asked to find:
a. The y-intercept and its meaning.
b. The slope and its meaning
Solution
To solve this question, we simply need to compare the equation given to the general slope-intercept equation. The general slope-intercept equation is given by:
[tex]\begin{gathered} y(t)=mt+c \\ \text{where,} \\ c=y-\text{intercept} \\ m=\text{slope of the equation} \end{gathered}[/tex]With this equation, we can compare with the equation given in the question:
[tex]\begin{gathered} y=mt+c \\ y=3200-200t \\ \text{This implies that:} \\ \\ \text{slope(m)}=-200 \\ y-\text{intercept}=3200 \end{gathered}[/tex]Thus, let us answer the questions:
a. The y-intercept and its meaning:
The y-intercept is 3200.
When we vary the time variable in the equation given, we can get a sense of what this y-intercept means. This is done below:
[tex]undefined[/tex]Using y= sin x OR y= cos x [Sinusoidal function] as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.
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Using
[tex]y=\sin (x)[/tex]5 units right: Let's use the following rule:
[tex]\begin{gathered} y=f(x-5) \\ so\colon \\ y=\sin (x-5) \end{gathered}[/tex]Reflect on x-axis: Let's use the following rule:
[tex]\begin{gathered} y=-f(x) \\ so\colon \\ y=-\sin (x-5) \end{gathered}[/tex]2 units down: Let's use the following rule:
[tex]\begin{gathered} y=f(x)-2 \\ so\colon \\ y=-\sin (x-5)-2 \end{gathered}[/tex]Horizontal compression with factor 2: Let's use the following rule:
[tex]\begin{gathered} y=f(2x) \\ so\colon \\ y=-\sin (2x-5)-2 \end{gathered}[/tex]Let's graph the parent function, and the new function:
The blue graph is the parent function and the red graph is the new function after the transformations applied.
The domain and the range of the new function are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\mright\rbrace_{\text{ }}or_{\text{ }}D\colon(-\infty,\infty) \\ R\colon\mleft\lbrace y\in\R\colon-3\le y\le-1\mright\rbrace_{\text{ }}or_{\text{ }}R\colon\lbrack-3,-1\rbrack \end{gathered}[/tex]Find the equation of the line using the given information and the point slope form. Express the equation in slope intercept form points (5,6) Points(-1,4)
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step 1
Find out the slope
m=(4-6)/(-1-5)
m=-2/-6
m=1/3
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=1/3
point(5,6)
substitute
6=(1/3)(5)+b
solve for b
6=(5/3)+b
b=6-5/3
b=13/3
therefore
y=(1/3)x+13/3Use synthetic division to find the result when 4x3 + 13x2 + 6x + 9 is divided byx + 3.
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To solve this question, observe the figure and observe the steps below:
1) Organize the coefficient of the dividend according to the figure.
2) Write the zero of the divisor according to the figure.
3) Write down the first coefficient (4).
4) Multiply the coefficient by -3 and write it below 13 (second coefficient). Then, sum the result (-12) with 13. Write the answer (1).
5) Do the same with the other values, according to the figure.
6) The coefficients of the quotient are the values in green and the remainder is the value in red.
Answer: The quotient is:
[tex]4x^2+1x+3[/tex]You have $5,000 to invest and want it to grow to $20,000 in two years. What interest rate would you need to find to make this possible?I wan answer and explanation.
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ANSWER
The interest rate is 150%
EXPLANATION:
Given that;
The initial amount is $5000
The total amount $20, 000 after 2 years
Total period of the investment is 2 years
To find the interest rate, follow the steps below
1. Find the interest on the investment after two years
In the given data,
The initial amount (principal) is $5000
The total amount after 2 years is $20, 000
Recall that,
Total amount = Interest + principal
20, 000 = interest + 5000
subtract 5000 from both sides of the equation
20, 000 - 5,000 = interest + 5000 - 5000
15,000 = interest
Therefore, the interest on the investment after 2 years is $15, 000
Step 2; Find the interest rate using the simple interest formula
[tex]\text{ I }=\text{ }\frac{P\times R\times T}{100}[/tex]Where
I is the interest
P is the principal
R is the interest rate
T is the time of the investment
[tex]\begin{gathered} \text{ 15, 000 }=\text{ }\frac{5000\times\text{ r}\times\text{ 2}}{100} \\ \text{ } \\ \text{ 15000 }=\text{ }\frac{10,000r}{100} \\ \text{ 15, 000 }=\text{ 100r} \\ \text{ Divide both sides by 100} \\ \frac{15,000}{100}\text{ }=\text{ }\frac{100r}{100} \\ \text{ r }=\text{ 150\%} \end{gathered}[/tex]Therefore, the interest rate is 150%
Write a quadratic equation with 7 and 2/5 as its roots. Write the equation in the form ax2 + bx+c= 0, where a, b, and c are integers.
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As given by the question
There are given that the roots: 7 and 2/5.
Now,
Since the roots are integers, we can write the equation in the given form using a = 1.
Then,
b is the opposite of the sum of the roots
So,
[tex]\begin{gathered} b=-((7)+(\frac{2}{5})) \\ b=-(\frac{35+2}{5}) \\ b=-\frac{37}{5} \end{gathered}[/tex]And
c is the products of the roots
So,
[tex]\begin{gathered} c=7\times\frac{2}{5} \\ c=\frac{14}{5} \end{gathered}[/tex]Now,
The desired quadratic equation is:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2-\frac{37}{5}x+\frac{14}{5}=0 \\ 5x^2-37x+14=0 \end{gathered}[/tex]Hence, the correct option is A.
*i will give you brainliest and 100 pts* Find the value of y. 3 cm 5 cm х 6 cm 2 cm 3cm. y = [?] cm Enter a decimal rounded to the nearest tenth. Enter
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We have to use the secant theorem, which states
[tex](y+3)\cdot3=(9+2)\cdot2[/tex]Then, we solve for y
[tex]\begin{gathered} 3y+9=11\cdot2 \\ 3y=22-9 \\ y=\frac{13}{3}=4.3 \end{gathered}[/tex]Hence, y is equal to 4.3 cm.Solve the given equation over the interval [0,2%): 3 tanº x+tan x = 0.7%x= 0 and x= - and x=6.6x= 0 and x=76and x=11%657 119x= 0 and x= and x=66es andSTx= 0 and x= - and x =6od x = F and =
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OPTION C
5.Line AB is 14 inches long. What is the approximate area of this circle?АBa. 42 square inchesb. 615 square inchesc. 160 square inchesd. 154 square inches
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The area of a circle is given as
A =
Scott borrowed $8000 at a rate of 19%, compounded annually. Assuming he makes no payments, how much will he owe after 8 years? Round your answer to the nearest cent
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To answer this question we will use the following formula for compounded interest:
[tex]A=A_0(1+r)^t,[/tex]where A is the final amount, A₀ is the initial amount, r is the interest rate as a decimal number, and t is the number of times that the interest rate is applied.
Substituting A₀=8000, r=0.19, and t=8 we get:
[tex]A=8000(1+0.19)^8\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=8000(1.19)^8, \\ A\approx32171.08 \end{gathered}[/tex]Answer: $32171.08.
Multiply 1.42 x 0.3
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the given problem is 1.4*0.3
here the answer is 0.42
[tex]undefined[/tex]Translate to an algebraic expression, but do not simplify.the difference of 10 and -16Simplify the translated phrase if possible.
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When you have a phrase as the difference of a and b, the algebraic expression is b being subtractd from a.
The difference of 10 and -16:
[tex]10-(-16)[/tex]Simplify:
[tex]\begin{gathered} =10+16 \\ =26 \end{gathered}[/tex]Then, the algebraic expression is; 10-(-16) and simplified is 26What value is a discontinuity of x^2+5x+2/x^2+2x-35
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Solution:
Given the expression:
[tex]\frac{x^2+5x+2}{2x^2+2x-35}[/tex]A function f(x) has disconituity at x=a if
[tex]\lim_{x\to a}f(x)[/tex]exists and is finite.
The function is thus undefined at x=a or when
[tex]\lim_{x\to a}(f(x))\ne f(a)[/tex]From the given function, we have
[tex]\begin{gathered} \frac{x^2+5x+2}{x^2+2x-35} \\ factorize\text{ the denominator,} \\ \frac{x^2+5x+2}{x^2-5x+7x-35}=\frac{x^2+5x+2}{x(x-5)+7(x-5)} \\ \Rightarrow\frac{x^2+5x+2}{(x-5)(x+7)} \end{gathered}[/tex]The function is undefined at
[tex]\begin{gathered} x-5=0 \\ \Rightarrow x=5 \\ x+7=0 \\ \Rightarrow x=-7 \end{gathered}[/tex]Hence, there is discontinuity at
[tex]x=5,\text{ x=-7}[/tex]Solve for h.A=3h Can anyone help me?
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You have the following expression:
[tex]A=3h[/tex]In order to solve for h, use the division property of equality. In this case divide by 3 both sides:
[tex]\begin{gathered} \frac{A}{3}=\frac{3h}{3} \\ \frac{A}{3}=h \end{gathered}[/tex]Hence, the solution for h = A/3
6<-3kWhy is the answer -2Shouldn’t it be positive 2
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we are given the following inequality:
[tex]6<-3k[/tex]To solve for "k" we will divide both sides by -3, since we are dividing by a negative number we will change the direction of the inequality sign, we get:
[tex]\frac{6}{-3}>-\frac{3k}{-3}[/tex]Solving the operations we get:
[tex]-2>k[/tex]Therefore, the solution is the numbers that are smaller than negative 2.
Americans said money mistakes cost them $1,230, on average, last year alone, According to U.S. Census Bureau data from 2018, the latest release, the median household income was $61,372. What percent of their income did they lose on mistakes?
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EXPLANATION.
The first thing to do is analyze the data that the exercise gives us, it tells us that a year the cost of error for money was 1230, but the income was 61,372, for this exercise we must find the percentage with a rule of three .
The exercise is as follows.
The total income 61,372 represents 100 percent, how much does 1230 represent?
[tex]undefined[/tex]Question is in the picture.The options underneath are $100 per person $15 per person $10 per person and eight dollar per person I chose $100 but I need it to be explained
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The graph provided plots the cost of a hall against the number of guests. The blue graph represents "Cosmic Hall".
The cost per person is the slope of the line that represents the hall in consideration.
The slope is calculated using the formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, two points can be picked as shown below:
[tex]\begin{gathered} (x_1,y_1)=(0,6000) \\ (x_2,y_2)=(500,10000) \end{gathered}[/tex]Hence, the slope is calculated to be:
[tex]\begin{gathered} slope=\frac{10000-6000}{500-0}=\frac{4000}{500} \\ slope=8 \end{gathered}[/tex]