Answers
ANSWER
[tex]11.04\text{ or }\frac{-2+\sqrt{580}}{2}[/tex]EXPLANATION
Given that:
In the figure provided, the triangle EFG is similar to the triangle is ECD
FE = 12
CD = 12
FG = CF + 2
To find the length CF, apply the similarity triangle theorem
[tex]\frac{\text{ FE}}{\text{ CF}}\text{ }=\frac{\text{ FG}}{CD}[/tex]Substitute the given data into the above equation
[tex]\begin{gathered} \text{ }\frac{12}{CF}=\frac{CF+2}{12} \\ \text{ cross multiply} \\ \text{ 12}\times12\text{ }=\text{ CF\lparen CF + 2\rparen} \\ \text{ 144 }=\text{ CF}^2\text{ }+\text{ 2CF} \\ CF^2\text{ }+\text{ 2CF -144 =0} \\ \text{ Find CF using the general formula} \\ x\text{ }=\text{ }\frac{-b\pm\sqrt{b^2-\text{ 4ac}}}{\placeholder{⬚}} \\ \text{ a }=1,\text{ b}=2,\text{ c}=-144 \\ \text{ x }=\frac{-2\text{ }\pm\sqrt{2^2-4\times1\times(-144)}}{2} \\ \text{ x}=\text{ }\frac{-2\pm\sqrt{4+576}}{2} \\ \text{ x }=\text{ }\frac{-2\pm\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+24.083}{2} \\ \text{ x }=\frac{22.083}{2} \\ \text{ x }=11.04 \\ \text{ Therefore, CF is 11.04 or }\frac{-2+\sqrt{580}}{2} \end{gathered}[/tex]Related Questions
what does the "The probability of a correct inference:" means in this question and how can i solve it
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The probability that the test-taker doesn't use drugs is the ratio of the number of people who take drugs to the total number of people. Hence the probability that the test-taker doesn't take drug is
= 194/450
= 0.4311
2.
1/2=_/12Find the answer for the blank space
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We have to fill the blank to have an equivalent fraction:
[tex]\begin{gathered} \frac{1}{2}=\frac{x}{12} \\ \frac{1}{2}\cdot12=x \\ x=6 \end{gathered}[/tex]Answer: 6
Hello! I need some help with this homework question, please? The question is posted in the image below. Q21
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To find the zeros of the polynomial given, we will first have to find some simpler zeros first then factor the polynomial so we can use the quadratic equation.
Since we can assume this question is to be solved without external tools, it is likely that two of the roots are simple ones.
So, we can try to use the rational root theorem to find these simpler ones.
Since the leading coefficient is 1 and the constant term is -18, if there are rational roots, they can be written as a fraction of a factor of -18 divided by a factor of 1.
The only factor of 1 is 1, so we now that if there are rational roots, they have to have denominator equal to 1.
The factors of 18 are 1, 2, 3, 6, 9 and 18.
Also, we have to consider the possibilities of positive and negative.
It is easier to test the lower ones, so let's start by testing 1/1 and -1/1. For either to be a zero, the polynomial has to result in 0:
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=1 \\ 1^4+1^3+7\cdot1^2+9\cdot1-18=1+1+7+9-18=18-18=0 \end{gathered}[/tex]So, x = 1 is a zero of the polynomial.
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=-1 \\ (-1)^4+(-1)^3+7(-1)^2+9(-1)-18=1-1+7-9-18=-2-18=-20 \end{gathered}[/tex]So, x = -1 is not a zero.
Now, let's try the next factor, 2/1 and -2/1:
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=2 \\ 2^4+2^3+7\cdot2^2+9\cdot2-18=16+8+28+18-18=52 \end{gathered}[/tex]So, x = 2 is not a zero.
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=-2 \\ (-2)^4+(-2)^3+7(-2)^2+9(-2)-18=16-8+28-18-18=8+10-18=0 \end{gathered}[/tex]So, x = -2 is also a zero of the polynomial.
We could continue, by we only need 2 zeros, so this is enough.
Now we know x = 1 and x = -2 are zeros of the polynomial, we can use synthetic division to factor the polynomial:
1 | 1 1 7 9 -18
| 1 2 9 18
| 1 2 9 18 0
Using the last line, we have that the remainder is 0 and the quotient is:
[tex]x^3+2x^2+9x+18[/tex]So, we have that:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x^3+2x^2+9x+18)[/tex]Now, we can use synthetic division again on the quotient, but now use the other zero, x = -2:
-2 | 1 2 9 18
| -2 0 -18
| 1 0 9 0
Since x = -2 is a zero, we also got a remainder of 0, and the quotient is:
[tex]\begin{gathered} x^2+0x+9 \\ x^2+9 \end{gathered}[/tex]So, we can rewrite the polynomial as:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x+2)(x^2+9)[/tex]Now, we can just find the zeros of the remainer factor, x² + 9, so:
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt[]{-9} \\ x=\pm\sqrt[]{9}\sqrt[]{-1} \\ x=\pm3i \end{gathered}[/tex]This means that the complex zeros of the given polynomial are:
[tex]\begin{gathered} x=1 \\ x=-2 \\ x=3i \\ x=-3i \end{gathered}[/tex]And the factored usinf complex factors is:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x+2)(x-3i)(x+3i)[/tex]
hi, need help how the graph looks like for this [tex]y \ \textless \ \frac{1}{2} x - 2[/tex][tex]y \leqslant - 2x + 4[/tex]
Answers
Solution:
Given:
[tex]\begin{gathered} y<\frac{1}{2}x-2 \\ y\leq-2x+4 \end{gathered}[/tex]Using a graph plotter, the graph of the two inequalities is shown;
i am not sure what I am doing wrong here
Answers
We know that segment RS is a diameter of the circle, this means that arcs RS an RST measure 180°. Now that we know that an using the ratio for arcs RT and TS given we have:
[tex]\begin{gathered} RT+5RT=180 \\ 6RT=180 \\ RT=\frac{180}{6} \\ RT=30 \end{gathered}[/tex]Now, we know that an angle inscribed in a circle is half its intercepted arc, then we have:
[tex]m\angle RST=\frac{30}{5}=15[/tex]Therefore, we have that arc RT is 30° and angle RST is 15°
Tell whether x and y show direct variation, inversevariation, or neither. Explain your reasoning.X 24.68y -5 -11 -17 -23The products xy areThe ratios Y areХSo, X and y show
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Neither
1) Firstly, we can start filling in the blanks.
2) The products xy are:
[tex]xy=-10,-44,-102,-184[/tex]We're simply multiplying each x-entry by its output y.
The ratios y/x are:
[tex]\frac{y}{x}=-\frac{5}{2},-\frac{11}{4},-\frac{17}{6},-\frac{23}{8}[/tex]So, x and y show:
Note that xy is not constant, for their product differs. So it is not an
inverse variation.
On the other hand, y/x is not constant as well. So it is not a direct variation.
3) Hence, it's neither direct nor inverse.
Find y if the point (5,y) is on the terminal side of theta and cos theta = 5/13
Answers
For this problem we have a point given (5,y) and we know that this point is on a terminal side of an angle, we also know that:
[tex]\cos \theta=\frac{5}{13}[/tex]If we know the cos then we can find the sin on this way:
[tex]\sin \theta=\frac{y}{13}[/tex]Then we can apply the following identity from trigonometry:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]Using this formula we got:
[tex](\frac{5}{13})^2+(\frac{y}{13})^2=1[/tex]And we can solve for y:
[tex]\frac{y^2}{169}=1-\frac{25}{169}=\frac{144}{169}[/tex]And solving for y we got:
[tex]y=\sqrt{169\cdot\frac{144}{169}}=\sqrt{144}=\pm12[/tex]And the two possible solutions for this case are y=12 and y=-12
Which expressions are equivalent to the one below? Check all that apply. 9x 36* D A Св. х5 B. | * c. c. 36 D D. 9.9X+1 36 DE E. LASSE F. 9.9x-1
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To answer this question we will use the following properties of exponents:
[tex]\begin{gathered} (\frac{a}{b})^x=\frac{a^x}{b^x}, \\ a^x*a^y=a^{x+y}. \end{gathered}[/tex]Now, notice that:
[tex]9=\frac{36}{4}.[/tex]Therefore:
[tex]9^x=(\frac{36}{4})^x.[/tex]Using the first property we get that:
[tex]9^x=\frac{36^x}{4^x}.[/tex]Now, notice that x=1+x-1, then:
[tex]9^x=9^{1+x-1}=9*9^{x-1}.[/tex]Answer: Options A, E, and F.
an architect wants to create a rectangular sun porch in a house. he wants it to have a total area of 92 square feet, and it should be 12 feet longer than it is wide. what dimensions should he use for the sun porch? round to the nearest hundredth of a foot
Answers
we can write 2 equations
[tex]\begin{gathered} x\times y=92 \\ \end{gathered}[/tex][tex]x+12=y[/tex]where x is the wide and y the long
we can replace y=x+12 from the second equation on the first
[tex]x\times(x+12)=92[/tex]and solve x
[tex]\begin{gathered} x^2+12x=92 \\ x^2+12x-92=0 \end{gathered}[/tex]factor ussing
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a is 1, b is 12 and c -92
replacing
[tex]\begin{gathered} x=\frac{-(12)\pm\sqrt[]{12^2-4(1)(-92)}}{2(1)} \\ \\ x=\frac{-12\pm16\sqrt[]{2}}{2} \\ \\ x=-6\pm8\sqrt[]{2} \end{gathered}[/tex]the two solutions are
[tex]\begin{gathered} x_1=5.31 \\ x_2=-17.31 \end{gathered}[/tex]the solution must be positive because it is a measure
so x=5.31feet
now we can replace the value of x on any equation to solve y(I will replace on the second equation)
[tex]\begin{gathered} x+12=y \\ 5.31+12=y \\ y=17.31 \end{gathered}[/tex]so the measurements are x=5.31 and y=17.31
21/8 and 7/8 in a mixed number
Answers
EXPLANATION:
To convert a fraction to a mixed number we must follow the following steps:
1.First we divide the numerator by the denominator.
2.The quotient becomes the integer part.
3.The remainder that the division gives, becomes the new numerator, and the quotient becomes the whole part, the denominator if it remains the same.
The exercise is as follows: 21/8
Now since 7/8 is a proper fraction, that is to say that its numerator is less than the denominator, it cannot be converted into a mixed fraction.
which of the triangles cannot be proved congruent? so a different tutor gave me the answer which is D. But he told me to ask another tutor to tell me how to type out how I got the answer.
Answers
The triangles that cannot be proved congruent are the triangles in option D. We are not told that the other side is congruent to the corresponding side of the other triangle.
To prove they are congruent, we need to know the other side is congruent and prove this using the SSS postulate.
In the other cases, we can be proved they are congruent by:
• Case A ---> SAS postulate.
,• Case B ---> ASA postulate.
,• Case C ---> SSS postulate (the triangles share a common side)
In summary, we only have that the triangles in D cannot be proved congruent since we have two corresponding congruent sides, and one angle (vertical angle) to be congruent corresponding parts. It would be an SSA method. However, this method is not Universal, and it is not enough to demonstrate they are congruent.
Team Arrow shoots an arrow from the top of a 1600-foot building on Earth-51. The arrow reaches a maximum height of 1840 feet after 4 seconds.Write an equation for the height of the arrow, h, in feet as a function of the number of seconds, t, since the arrow was shot.Round to 3 decimal places as needed. After how many seconds will the arrow reach the ground?Round to 3 decimal places as needed.
Answers
We will have the following:
***First:
[tex]h=h_0+v_0\cdot t+\frac{1}{2}g\cdot t^2[/tex]Now, we will determine the value for the speed:
[tex]1840=1600+v_0\cdot(4)+\frac{1}{2}(-32.17)\cdot(4)^2\Rightarrow240=4v_0-\frac{25736}{25}[/tex][tex]\Rightarrow\frac{31736}{25}=4v_0\Rightarrow v_0=\frac{7934}{25}\Rightarrow v_0=137.36[/tex]So, the equation for the height of the arrow (h) in feet as a function of the number of seconds t is:
[tex]h=1600+317.36t+\frac{1}{2}gt^2[/tex]Here "g" is the gravitational pull of earth.
***Second:
We will determine how much time it would take for the arrow to hit the ground as follows:
[tex]0=1600+317.36t+\frac{1}{2}(-32.17)t^2\Rightarrow-\frac{3217}{200}t^2+317.36t+1600=0[/tex][tex]\Rightarrow t=\frac{-(317.36)\pm\sqrt[]{(317.36)^2-4(-\frac{3217}{200})(1600)}}{2(-\frac{3217}{200})}\Rightarrow\begin{cases}t\approx-4.163 \\ t\approx23.893\end{cases}[/tex]So, afeter 23.893 seconds the arrow would hit the ground.
Find the area of the figure. (Sides meet at right angles.)4 m5 m15 m5 m5 m4 m4 m
Answers
The area of the figure will be the area of the rectangle of the top, plus the area of the rectangle of the bottom:
The area of the rectangle of the top is:
[tex]A1=w1\cdot h1=5\cdot4=20m^2[/tex]The area of the rectangle of the bottom is:
[tex]A2=w2\cdot h2=14\cdot4=56m^2[/tex]so, the total area is:
[tex]A=A1+A2=20m^2+56m^2=76m^2[/tex]The number of newly reported crime cases in a county in New York State is shown inthe accompanying table, where x represents the number of years since 2006, and yrepresents number of new cases. Write the linear regression equation that representsthis set of data, rounding all coefficients to the nearest tenth. Using this equation,estimate the calendar year in which the number of new cases would reach 767.Years since 2006 (x) New Cases (y)099619232882389248405813
Answers
Solution
For this case we have the following data:
x y
0 996
1 923
2 882
3 892
4 840
5 813
sum xi = 15
sum yi = 5346
sum xi yi = 12788
sum xi^2 = 55
And we want to find and equation like this one:
y= mx+ b
So then we can estimate the slope using least squares and we have:
[tex]m=\frac{n\sum ^n_{i=1}x_iy_i-\sum ^n_{i=1}x_i\sum ^n_{i=1}y_i}{n(\sum ^n_{i=1}x^2_i)-(\sum ^n_{i=1}x_i)^2}[/tex]Replacing we have:
[tex]m=\frac{6\cdot12788-(15\cdot5346)}{6(55)-(15)^2}=\frac{-3462}{105}=-32.971[/tex]m= -32.971
And the intercept would be:
[tex]b=\frac{\sum^n_{i=1}y_i}{n}-m\cdot\frac{\sum^n_{i=1}x_i}{n}=\frac{5346}{6}-(-32.971)\cdot\frac{15}{6}=973.429[/tex]b= 973.428
Then the equation would be:
y= -32.971x+ 973.428
And we can find the value of x for y = 767 and we got::
767 = -32.971x+ 973.428
Solcing for x we have:
767- 973.428 = -32.971 x
x= 6.26
Regression Equation: y= -32.9x + 973.4
Final Answer: 2012
you hiked 400 feet up a steep hill that has 25° angle of elevation as shown in the diagram.give each side of an angle measure rounded to the nearest whole number.a =b =m
Answers
Notice that the problem is described by a right angle triangle for which we know the length of the hypotenuse (400 ft), and also know one of the triangle's acute angles (25 degrees)
Base on this knowledge, we can start by finding the other acute angle of the triangle (
This means : 25 + 90 +
Then we can solve for angle
115 +
subtract 115 degrees from both sides to isolate
< B = 180 - 115 = 65
then we have the measure of angle < B = 65 degrees.
Now we can find the value of the side adjacent to the angle 25 degrees by using the cosine trigonometric ratio:
[tex]\begin{gathered} \cos (25)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (25)=\frac{adjacent}{400} \\ \text{adjacent}=400\cdot\cos (25) \\ \text{adjacent}=362.52 \end{gathered}[/tex]Then the side named "b" measures 362.52 ft
We can do something similar to find the measure of side a, but using the trigonometric ratio for the sine function:
[tex]\begin{gathered} \sin (25)=\frac{opposite}{\text{hypotenuse}} \\ \sin (25)=\frac{a}{\text{hypotenuse}} \\ \sin (25)=\frac{a}{400} \\ a\text{ = 400}\cdot\sin (25) \\ a=169.05 \end{gathered}[/tex]Then the measure of side a is 168.05 ft
Now, notice that the problem wants you to round the side measures to the nearest whole number, so you need to type the following:
a = 169 ft
b = 363 ft
angle
What is the solution to 2x + 2 (x – 5)= 6 ? Show your work. explainhow you solved the equation.
Answers
Step 1
eliminate the parenthesis, use distributive property
[tex]\begin{gathered} 2x+2(x-5)=6 \\ 2x+2x-10=6 \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 2x+2x-10=6 \\ 4x-10=6 \end{gathered}[/tex]Step 3
add 10 in both sides
[tex]\begin{gathered} 4x-10=6 \\ 4x-10+10=6+10 \\ 4x=16 \end{gathered}[/tex]Step 4
divide each side by 4
[tex]\begin{gathered} 4x=16 \\ \frac{4x}{4}=\frac{16}{4} \\ x=4 \end{gathered}[/tex]so, the answer is x=4
what are the unit prices for 100 sheets for $.99 and 500 sheets for $4.29
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Answer:$.0099/sheet; $.00858/sheet;500 sheets
Step-by-step explanation:
Hello do you no how to do Solving Equations Puzzle
Answers
1 - The right and the left side must weight the same, and the weight of both the right and the left side would be 24, therefore each side must weight 12.
2 - Since the heart = 2, and 2*heart + square = 12 , then square = 8
3 - Now, since square = 8 and square + moon = 12, then moon=4
To summarize
heart = 2, square = 8 , moon = 4.
Steven flew from Boston to Orlando with a stop in Atlanta to switch planes. His first flight leftBoston at 12:00 P.M. and was 3 hours and 45 minutes long. Steven was in Atlanta for 2 hours and 30 minutes, and his flight from Atlanta to Orlando was 1 hour and 30 minutes long. Whattime was it when Steven landed in Orlando?
Answers
Answer:
07:45 pm
Explanation:
Steven landed in Orlando after the sum of the following time
3 hours and 45 minutes
2 hours and 30 minutes
1 hour and 30 minutes
If we add the hours and the minutes, we get:
3 hours + 2 hours + 1 hour = 6 hours
45 minutes + 30 minutes + 30 minutes = 105 minutes
But 1 hour = 60 minutes, so
6 hours and 105 minutes = 7 hours and 45 minutes
because
105 - 60 = 45
Since the flight left Boston at 12:00 pm, it was 07:45 pm when Steven landed in Orlando.
Find d and then find the 20th term the sequence. Type the value of d (just the number) in the first blank and then type the 20th term(just the number) in the second blank.a1=6 and a3=14
Answers
We have that an arithmetic sequence can be defined by the following explicit formula:
[tex]a_n=a_1+(n-1)\cdot d[/tex]where n represents the index of each term in the sequence and d represents the common difference beteen each term. a1 is the first term of the sequence.
In this case we have that the first term is a1 = 6, and also we have that a3=14. We can use the formula to find the common difference:
[tex]\begin{gathered} a_3=a_1+(3-1)d \\ \Rightarrow a_3=a_1+2d \\ \Rightarrow14=6+2d \end{gathered}[/tex]solving for d, we get:
[tex]\begin{gathered} 2d+6=14 \\ \Rightarrow2d=14-6=8 \\ \Rightarrow d=\frac{8}{2}=4 \\ d=4 \end{gathered}[/tex]therefore, the value of d is d = 4.
We have now the explicit formula for the sequence:
[tex]\begin{gathered} a_n=6_{}+4(n-1) \\ \end{gathered}[/tex]then, for the 20th term, we have to make n = 20 on the formula, and we get the following:/
[tex]\begin{gathered} a_{20}=6+4(20-1)=6+4(19)=6+76=82 \\ \Rightarrow a_{20}=82 \end{gathered}[/tex]therefore, the 20th term is 82
For what of 0, in degree, is sin= con 58⁰?
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Answer: We want to find angle 'theta' for which:
[tex]\sin (\theta)=\cos (58)[/tex]In general, the following is always true:
[tex]\cos (\theta)=\sin (90-\theta)\rightarrow(1)[/tex]Therefore we have the following:
[tex]\cos (58^{\circ})=\sin (90-58)=\sin (32^{\circ})[/tex]Therefore the angles that we were interested in is:
[tex]\theta=32^{\circ}[/tex]
write an equation to represent"three consecutive integers is 12 less than 4 times the middle integer'
Answers
Consider that the three consecutive integers are:
least integer = n
middle integer = n + 1
greatest integer = n + 2
THe expression "three consecutive integers is 12 less than 4 times the middle integer" can be written as follow:
n + (n + 1) + (n + 2) = 4(n +1) - 12
In order to find the numbers, proceed as follow:
n + (n + 1) + (n + 2) = 4(n +1) - 12 cancel parenthesis
n + n + 1 + n + 2 = 4n + 4 - 12 simplify like terms
3n + 3 = 4n - 8 subtract 4n and 3 both sides
3n - 4n = - 8 - 3
-n = -11
n = 11
Hence, the three consecutive integers are:
n = 11
n + 1 = 12
n + 2 = 13
rogers flight took off at 9:27 am. the flight is scheduled to land at 1:05 pm. if the flight lands on schedule , how long is the flight?
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We need to calculate the time of thr flight, so we have to calculate the different between the landing time and the take off time:
[tex]\begin{gathered} 1\colon05pm=13\text{hours 5minutes} \\ 9\colon27\text{ am = 9hours 27 minutes} \\ \Delta t=1\colon05pm-9\colon27am=(13-9)\text{hours (5-27)minutes} \\ \Delta t=4hours\text{ (-22)minutes=3hours (60-22)minutes} \\ \Delta t=3\text{ hours 38 minutes} \end{gathered}[/tex]The flight is 3 hours 38 minutes long.
GraphON4andon the number line to show how each fraction relates to 1.Click each dot on the image to select an answer.十+01Compare.our24.36Eng
Answers
2/6 = 1/3 = 0.3333
0.333 is less than 1 so it should be on the left side of the graph.
4/3 = 1.333
1.333 is greater than 1 so it should be on the right side of the graph .
So the bigger dot on the left hand side which is before 1 should be 2/6 while the smaller dot on the right hand side which is after 1 should be 4/3 .
1. Jeremy is going to show off his skateboarding skills. He has a ramp that must beset up torise from the ground at a 30° angle. If the height from the ground to the platform is 8 feet,how far is the end of the ramp to the base of the platform? How long is the ramp up to thetop of the platform?
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this is a question that involves angle of elevation and right angled triangles.
first, a diagram deoicting the scenerio is drawn below;
using the SOHCAHTOA rule for right angled triangles, we would name he distance of the ramp to the platform; x
y is length of the ramp up to the platform (the side opposite the right angle), H
8ft is the height from the ground to the platform ( the distance of the side opposite the angle), O
x is the length of the end of the ramp to the base of the platform( is the adjacent) A
THEREFORE, we will be applying TOA
[tex]\begin{gathered} \tan \theta=\text{ opposite/adjacent} \\ \cos 30=\frac{O}{A} \\ \cos 30=\frac{8}{X} \\ 0.8660=\frac{8}{x} \\ x=\frac{8}{0.8660} \\ x=9.24ft \end{gathered}[/tex]the end of the ramp is 9.24ft from the base of the platform
[tex]\begin{gathered} \sin 30=\frac{posite}{\text{hypotenuse}} \\ \sin 30=\frac{8}{y} \\ 0.5=\frac{8}{y} \\ y=\frac{8}{0.5} \\ y=\text{ 16ft} \end{gathered}[/tex]the ramp is 16ft long up to the top of the platform
Which of the following graphs represents the equation 2x - 8y = 32?
Answers
Answer:
C
Step-by-step explanation:
2x-8y = 32
2/2 x - 8/2 y = 32/2
x - 4y = 16
if x = 0
-4y = 16
-4/-4 y = 16/-4
y = -4
If x = 16
16-4y = 16
-4y = 0
-4/-4 y = 0/-4
y = 0
I would like to know if I answered the question correctly
Answers
INFORMATION:
We have the next system of equations:
[tex]\begin{cases}{x-5y=-16} \\ {9x+9y=72} \\ {4x-6z=-8}\end{cases}[/tex]And we need to determine if (4, 4, 4) is a solution of the system.
STEP BY STEP EXPLANATION:
To know if the ordered triple is a solution of the system, we need to that (4, 4, 4) means x = 4, y = 4 and z = 4.
Then, to know if it is a solution we must replace the values on each equation to verify if the values are solutions
We have three equations:
1. x - 5y = -16
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 4-5\cdot4=-16 \\ 4-20=-16 \\ -16=-16 \\ \text{ TRUE} \end{gathered}[/tex]2. 9x + 9y = 72
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 9\cdot4+9\cdot4=72 \\ 36+36=72 \\ 72=72 \\ \text{ TRUE} \end{gathered}[/tex]3. 4x - 6z = -8
Replacing x = 4 and z = 4, we obtain
[tex]\begin{gathered} 4\cdot4-6\cdot4=-8 \\ 16-24=-8 \\ -8=-8 \\ \text{ TRUE} \end{gathered}[/tex]Finally, since the three equations are true when x = 4, y = 4 and z = 4, the ordered triple is a solution
ANSWER:
Yes
Answer please the picture scanner deal won’t scan over this and i don’t know how to type it out
Answers
Solution
We are given the arithmetic sequence
[tex]\begin{gathered} a_1=5 \\ a_n=a_{n-1}-4 \end{gathered}[/tex]To find an explicit formula
[tex]\begin{gathered} First\text{ }Term=5 \\ a=5 \end{gathered}[/tex]From the second recursive formula
[tex]\begin{gathered} a_n-a_{n-1}=-4 \\ Common\text{ }Difference=-4 \\ d=-4 \end{gathered}[/tex]The nth term of an Arithmetic sequence is given by
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=5+(n-1)(-4) \end{gathered}[/tex]Therefore, the answer is
[tex]a_{n}=5+(n-1)(-4)[/tex]Solve the system by the addition method x + 2y = - 26x + 3y = - 30
Answers
We are asked to solve the following system of equations via the addition method:
x + 2 y = - 2
6 x + 3 y = - 30
so via the addition method we will try to eliminate one of the variables by multiplying for the appropriate factor that would ease tha process. We notice that if wemultiply the whole first eqaution by the factor (-6), we will be able to in the second step eliminate the term in "x" by combining both equations term by term.
So we do that: Multiply the whole first equation by "-6":
(-6) (x + 2 y ) = (-6) (-2)
- 6 x - 12 y = 12
now we combine this with the second equation term by term to eliminate the term in x:
- 6 x - 12 y = 12
+
6 x + 3 y = - 30
_______________
0 - 9 y = - 18
Now divide both sides by "-9" to isolate y:
y = - 18 / (-9)
y = 2
Now we use y = 2 in the very first equation to solve for the variable x:
x + 2 y = - 2
x + 2 (2) = -2
x + 4 = - 2
subtract 4 from both sides:
x = - 2 - 4
x = - 6
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
Answers
From the given model, the length of the wall is 9/8 ft, the width of the walk is 1/2 ft, and the height of the wall is 11/8. The volume of the portion of security wall that Tim has constructed so far is 99/128 cu ft.
What is the Volume of the Block?From the given image of the building model we see that part of a security world castle is shown.
We see that the length has 9 blocks.
Since the length has a total of 9 blocks and each side length is 1/8 ft, then we say that;
Length = 9*(1/8) = 9/8 ft
We also observe that the height has 11 blocks and as such;
height = 11*(1/8) = 11/8 ft
Meanwhile the width will have a length of: 1/2 ft
Formula for volume is;
Volume = length * height * width
Thus;
Volume = (9/8) * (11/8) * (1/2)
Volume = (9 * 11 * 1)/(8 * 8 * 2)
Volume = 99/128 cu ft
Read more about Volume of block at; https://brainly.com/question/23269406
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Complete question is;
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
Based on the model,the length of the wall is ___ft, the width of the walk is 1/2 ft, and the height of the wall is ___. The volume of the portion of security wall that Tum has constructed so far is ___ cu ft.