the triangle in the figure had a hypotenuse equal to 40 units what is the approximate length of x
25.7 units
30.6 units
47.7 units
52.2 units
(Srry I’m spamming I know nothing on this test)
Answers
If the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
The length of the hypotenuse = 40 units
The angle = 50 degrees
Here we have to apply the trigonometric function
we know
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
Here we have to use the equation of sin θ
Substitute the values in the equation
sin 50 = x/40
x = 40×sin 50
x = 30.64 units
Hence, if the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
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Related Questions
May I please get help with numbers (4), (5), and (6). I have tried multiple times to find the correct answers for each of them but still could not get the accurate or at least correct answers for each of them. I would appreciate it so much if I could get help
Answers
EF =21
4) Let's find out the measure of the line segment EF, using the Trapezoid Midsegment Formula:
[tex]M=\frac{B+b}{2}[/tex]4.1) We can plug into that the lengths of AD and BC:
[tex]M=\frac{18+24}{2}=\frac{42}{2}=21[/tex]Note that the Midsegment is the average of the bases of a trapezoid.
4.3) Hence, the answer is 21
The function f(x) = 5x+3 is one to one. Find an equation for f-1(x) the inverse function.
Answers
Given the function:
[tex]f\mleft(x\mright)=5x+3[/tex]To find the inverse function, we make x the subject of the equation.
[tex]\begin{gathered} 5x=f(x)-3 \\ x=\frac{f(x)-3}{5} \end{gathered}[/tex]Next, we replace x with f-1(x) and f(x) with x.
Therefore, the inverse function is:
[tex]f^{-1}(x)=\frac{x-3}{5}[/tex]what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x + 8) ?A) shifted up B) shifted left C) shifted right D) shifted down
Answers
Solution
- In order to solve the question, we need to understand the rules guiding the translation of graphs. This rule is given below:
[tex]\begin{gathered} f(x)\to f(x+h) \\ \text{ If h is positive, then, the graph is shifted to the left} \\ \text{ If h is negative, then, the graph is shifted to the right} \end{gathered}[/tex]- The question given to us has h = 8. This means that h is positive, therefore, the graph of f(x) must be shifted to the left by 8 units
Final Answer
The answer is "Shifted Left" (OPTION B)
a standard Normal distribution, what percentage of observationnd the z-table here.4.95%5.48%6.06%95.05%
Answers
SOLUTION:
Case: Z-scores and probabilities
Given: z-score of standard normal distribution, z= 1.65
Required: To get the percentage of observation
Method: We will be reading it off the z-score table
Step 1: First we see what the table looks like
Step 2: From the table, we trace 1.65 by looking at 1.6 on the column title and 0.05 on the row title
Step 3: We observe the value is 0.4505
This translates to 45.05%.
However, we are interested in the values above the 45.05%. So everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score
To get the z-score above this, we do:
1 - 0.9505
P(> z) = 0.0495 or 4.95%
Final answer:
A) The answer is 4.95%
A biologist wants to determine the effect of a new fertilizer on tomato plants. What would be the control?All PlantsPlants not treated with the Fertilizer.The FertilizerPlants treated with the Fertilizer.
Answers
Remember that the control variable does not change in the experiment or in any study.
So the control here will be all the plants because you can not control the type of the plant.
Answer:b
Step-by-step explanation:
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 2". Let B be the event "the outcome is greater than 4". Find P(A or B). Outcome Probability 1 0.15 2 0.31 3 0.35 4 0.08 5 0.11
Answers
The general rule of P(A or B) is given by the formula
[tex]undefined[/tex]The diamond method for factoring: Fill in the missing value
Answers
Consider a quadratic expression, let "m" and "n" represent the factors.
The diamond method of factoring is the following:
On the left of the diamond, there is one of the factors, for example, "m", of the right of the diamond you will find the other factor "n".
On the top of the diamond, you will find the product of both factors, on the bottom of the diamond you will find the sum of the factors.
Looking at the given diamond, you know the result of the product and the sum of both factors:
[tex]m*n=-15[/tex][tex]m+n=14[/tex]Using these expressions, you can find both factors.
- First, write the second expression for one of the variables, for example, for "n"
[tex]\begin{gathered} m+n=14 \\ m=14-n \end{gathered}[/tex]- Second, replace the expression obtained on the second equation:
[tex]\begin{gathered} m*n=-15 \\ (14-n)n=-15 \end{gathered}[/tex]Distribute the multiplication
[tex]14n-n^2=-15[/tex]Zero the expression and order the terms from greatest to least:
[tex]\begin{gathered} 14n-n^2+15=-15+15 \\ 14n-n^2+15=0 \\ -n^2+14n+15=0 \end{gathered}[/tex]- Third, use the quadratic expression to determine the possible values of n:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant
For the quadratic expression obtained, where "n" represents the x-variable.
[tex]-n^2+14n+15=0[/tex]The coefficients are:
a= -1
b=14
c=15
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ n=\frac{-14\pm\sqrt{14^2-4*(-1)*15}}{2*(-1)} \\ n=\frac{-14\pm\sqrt{196+60}}{-2} \\ n=\frac{-14\pm\sqrt{256}}{-2} \\ n=\frac{-14\pm16}{-2} \end{gathered}[/tex]Solve the sum and difference separately to determine both possible values for "n"
→Sum:
[tex]\begin{gathered} n=\frac{-14+16}{-2} \\ n=\frac{2}{-2} \\ n=-1 \end{gathered}[/tex]→Difference:
[tex]\begin{gathered} n=\frac{-14-16}{-2} \\ n=\frac{-30}{-2} \\ n=15 \end{gathered}[/tex]- Finally, determine the possible value/s of m:
For n=-1
[tex]\begin{gathered} m+n=14 \\ m+(-1)=14 \\ m-1=14 \\ m=14+1 \\ m=15 \end{gathered}[/tex]For n=15
[tex]\begin{gathered} m+n=14 \\ m+15=14 \\ m=14-15 \\ m=-1 \end{gathered}[/tex]So, the factors are -1 and 15 and the diamond is:
Cobalt-60 has a half-life of about 5 years. After 20 years, how many grams of a2,076 gram sample will remain? Round to the hundredths place, if answer doesn'thave a tenths place then use a zero so the answer does.
Answers
Solution:
The formula for half-life is given below as
[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{\frac{t1}{2}}}[/tex]Where the given values are
[tex]\begin{gathered} N_0=2076g \\ t=20years \\ t^{\frac{1}{2}}=5years \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} N(t)=N_{0}(\frac{1}{2})^{\frac{t}{\frac{t\times1}{2}}} \\ N(t)=2076\times(\frac{1}{2})^{\frac{20}{5}} \\ N(t)=2076\times(\frac{1}{2})^4 \\ N(t)=\frac{2076}{16} \\ N(t)=129.75g \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow129.75g[/tex]Select the quadratic equation that has no real solution.9x2–25x-30 = 09x? – 25x +30 = 09x2-30x +25= 0o 9x2-30x – 25 = 0
Answers
SOLUTION:
We are to select the quadratic equation that has no real solution.
Facts about Quadratic equations;
When considering,
[tex]b^2\text{ - 4ac}[/tex]If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
Looking at all the four options, I have examined all and the only one found to be negative is the second option. Let's consider it together
a = 9, b = -25 and c = 30
(b x b ) - 4 x a x c
(-25 x -25) - 4 (9) (30)
625 - 1080
- 455
-455 < 0
Since the discriminant is less than this quadratic equation is expected to have no real solution.
You can as well try the other three options one is zero and the remaining two are greater than zero.
An airplane travels at 550 mph. How far does the airplane travel in 5 1/2 hours
Answers
Answer:
At a speed of 550mph, the airplane covers 3,025 miles in 5 1/2 hours.
Explanation:
Given:
• The speed of the airplane = 550 miles per hour
,• Time taken = 5 1/2 hours
We want to find out how far the airplane travels.
The distance covered is calculated using the formula:
[tex]Distance=Speed\times Time[/tex]Substitute the given values:
[tex]Distance=550\times5\frac{1}{2}[/tex]Simplify:
[tex]\begin{gathered} Distance=550\times\frac{11}{2} \\ =275\times2\times\frac{11}{2} \\ =275\times11 \\ =3025\text{ miles} \end{gathered}[/tex]The airplane covers 3,025 miles in 5 1/2 hours.
I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Answers
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
kindly asking for help to clarify this question and mathematical problem .
Answers
As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C
Evaluate the expression when x= -1/4 and y= 31. 2xyI don't understand his question.
Answers
The expression is 2xy
we will substitute x and y by the given values
x = -1/4 and y = 3
[tex]2xy=2\times(\frac{-1}{4})\times(3)[/tex]We put the values of y in the expression
Now we will calculate the value
[tex]2xy=\frac{2\times-1\times3}{4}[/tex]We will multiply the numbers in the numerator
[tex]2xy=\frac{-6}{4}[/tex]We will simplify the fraction by divide up and down by 2
[tex]\begin{gathered} 2xy=\frac{-\frac{6}{2}}{\frac{4}{2}}=\frac{-3}{2} \\ 2xy=-\frac{3}{2} \end{gathered}[/tex]6-Find the measure of ∠AEB.A. 122°B. 132°C. 142°D. 152°7-Find the measure of ∠BEC.A. 58 °B. 48°C. 38°D. 28°8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°9-Find the measure of ∠FEB.A. 142°B. 180°C. 90°D. 0°10-Find the measure of ∠FED.A. 0°B. 180°C. 45°D. 90°
Answers
The answer for 6 is C. 142°
Explanation
∠AEB = 180 - ∠AEF (Sum of angle on a straight line)
∠AEB = 180 - 38 = 142°
Find the equation of the linear function represented by the table below inslope-intercept form.xy1-3 -723-114-15
Answers
To find the linear equation, we use two points from the table (1, -3) and (3, -11). First, we have to find the slope with the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=-3 \\ y_2=-11 \end{gathered}[/tex]Let's those coordinates to find the slope.
[tex]\begin{gathered} m=\frac{-11-(-3)_{}}{3-1}=\frac{-11+3}{2}=\frac{-8}{2}=-4\to m=-4 \\ \end{gathered}[/tex]The slope is -4.
Now, we use the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-4(x-1) \\ y+3=-4x+4 \end{gathered}[/tex]Now, we solve for y to express it in slope-intercept form.
[tex]\begin{gathered} y+3=-4x+4 \\ y=-4x+4-3 \\ y=-4x+1 \end{gathered}[/tex]Therefore, the equation in slope-intercept form is y = -4x+1.write a quadratic equation in the form of ax²bx+c=0
Answers
The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
In order to write the equation, we would substitute values for a, b and c. If a = 3, b = 8, c = 25, the equation would be
3x^2
what are three requirements for fully defining a reference point?
Answers
1 - reference point should consist of abstract coordinates.
2- it should be stationary
3- it should be related to all the variables in the frame.
A newsletter publisher believes that more than 31% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.01 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer
Answers
The null hypothesis is H0: P = 0.31 and the alternative hypothesis is Ha: P > 0.31.
What is a null hypothesis?The null hypothesis is simply to predict that there is no effect of relationship between the variables.
The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that more than 31% of their readers own a Rolls Royce.
The null hypothesis is P = 0.31. while the alternative hypothesis will be that it's greater than 0.31.
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Downhill RacerA snowboardertravels 105 metersin 7 seconds.A skier travels for4 seconds andcovers 72 metersHow far will a skier travel in 2minutes? Explain how you figured it out.
Answers
To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).
A skier travels for 4 seconds and covers 72 meters.
Constant Rate (Speed):
[tex]\text{ }\frac{\text{ Distance Traveled}}{\text{ Time}}\text{ = }\frac{\text{ 72 meters}}{\text{ 4 seconds}}\text{ = }18\text{ meters/second}[/tex]Determining the distance covered in 2 minutes:
Step 1: Convert the time in minutes into seconds.
[tex]\text{ 2 (minutes) x }\frac{\text{ 60 seconds}}{\text{ 1 (minute)}}\text{ = 2 x 60 seconds = 120 seconds}[/tex]Step 2: Multiply the time by the constant rate (speed) of the skier.
[tex]\text{ Distance Traveled = 120 (seconds) x }18\text{ }\frac{\text{ meters}}{\text{ (second)}}[/tex][tex]\text{ = 120 x 18 meters}[/tex][tex]\text{ Distance Traveled = 2,160 meters}[/tex]Therefore, in 2 minutes, the skier travels 2,160 meters.
Which answer choice gives a correct version of this problem? -35 ÷ -7
A.) - (-35/-7) or B.) -35/7 or C.) 35/7 or D.) 35/-7
(Please note that I'm not looking for the total value rather I'm looking for what (-35 ÷ (-7) is as a fraction.)
Answers
The perimeter of the triangle below is 91 units. Find the length of the side QR. write your answer without variables.
Answers
Given:
The perimeter of the triangle, P=91.
The sides of the triangle are,
PR=4z
QR=z+3
PQ=5z-2.
The perimeter of the triangle can be expressed as,
[tex]\begin{gathered} P=PR+QR+PQ \\ P=4z+z+3+5z-2 \\ P=10z+1 \end{gathered}[/tex]Now, put P=91 in the above equation to find the value of z.
[tex]\begin{gathered} 91=10z+1 \\ 91-1=10z \\ 90=10z \\ \frac{90}{10}=z \\ 9=z \end{gathered}[/tex]Now, the length of the side QR can be calculated as,
[tex]\begin{gathered} QR=z+3 \\ QR=9+3 \\ QR=12 \end{gathered}[/tex]Now, the length of QR is 12 units.
(a) Teresa owns 9 shares of a certain stock. Yesterday the total value of her shares went down by90 dollars. What was the change in value for each share?dollarsHelp ASAP PLEASE
Answers
we have that
Divide $90 by the number of shares
so
90/9=$10
the answer is $10
Cube A has a side length of 8 inches and cube B has a side length of 2 inches. What isthe ratio of the volumes of cube B to cube A?ABMath Bits.com8"2"O 16Submit AnswerOhO 30da
Answers
The ratio of the volume of cube B to the volume of cube A is 1/64
Explanation:The volume of cube A is 8^3 = 512 cubic inches
The volume if cube B is 2^3 = 8 cubic inches
The ratio of the volume of cube B to the volume of cube A is:
8/512 = 1/64
help meeeee pleaseeeee!!!
thank you
Answers
The value of x is -2.
We are given a graph of a function f(x).
We have to find the value of x when the value of f(x) is -3.
We know that x- axis represents x and the y-axis shows f(x).
Hence, the x and y coordinates of a point on the line will be (x, f(x)).
To find the value of x , I will check the coordinates of the point (x, -3) because it is given that f(x) is -3.
Using the graph, we found the coordinates of that point to be (-2,-3).
Hence, we can say that,
x = -2
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Look at triangles A through F shown in the rectangles below.Which triangles are acute triangles?
Answers
The acute triangles are those whose all 3 angles have a measure less than 90 degrees.
We need to follow the next image:
Let us check each triangle.
Triangle A:
It has a right angle, hence, it can not be an acute triangle.
Triangle B:
All three sides are less than 90 degrees. Hence, it is an acute triangle
Triangle C:
It has an angle with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle D
All three sides are less than 90 degrees. Hence, it is an acute triangle.
Triangle E
It has a side with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle F
It has a right angle, hence, it can not be an acute triangle.
Hence, the correct answer is H. B and D
N8) solve the system using substitution method and then graph the equations.2x - 4y = -23x + 2y = 3-
Answers
Solution
Given:
2x - 4y = -2
3x + 2y = 3
Substitution method
[tex]\begin{gathered} From\text{ 3x+2y=3} \\ 3x=3-2y \\ x=\frac{3-2y}{3} \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ }x=\frac{3-2y}{3}\text{ into the first equation} \\ 2x-4y=-2 \\ 2(\frac{3-2y}{3})-4y=-2 \\ \frac{6-4y}{3}-4y=-2 \\ Multiply\text{ }trough\text{ by 3} \\ 6-4y-12y=-6 \\ 6-16y=-6 \\ -16y=-6-6 \\ -16y=-12 \\ y=\frac{-12}{-16} \\ y=\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ y=}\frac{3}{4}\text{ into }x=\frac{3-2y}{3} \\ x=\frac{3-2(\frac{3}{4})}{3}=\frac{3-\frac{3}{2}}{3}=\frac{\frac{6-3}{2}}{3}=\frac{\frac{3}{2}}{3} \\ x=\frac{3}{6} \\ x=\frac{1}{2} \end{gathered}[/tex][tex]Thus,\text{ x=}\frac{1}{2},y=\frac{3}{4}[/tex]Graphical method:
Plot the graph of the two equations on the same graph
The point of intersection of the two graphs gives the solution to the system of equations
The point of intersection is (0.5, 0.75)
Which in fraction gives (1/2, 3/4)
Thus. x = 1/2, y= 3/4
ABC is dilated by a factor of 5 produce A'B'C.What is A'C, the length of AC after the dilation? What is the measure of angle A?
Answers
We have that the scale factor is 5, then, the dilation is an enlargement.
Then, the new lengths are:
[tex]\begin{gathered} A^{\prime}C^{\prime}=5AC=5\cdot5=25 \\ A^{\prime}B^{\prime}=5AB=5\cdot4=20 \\ B^{\prime}C^{\prime}=5BC=5\cdot3=15 \end{gathered}[/tex]therefore, A'C' =25.
Finally, the dilations don't affect the angles, therefore, angle A remains with the measure of 37°
im having a hard time understanding this could you please help me
Answers
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9
An elevator car starts on the second floor of a building 27 feet above the ground. The car rises 4.2 feet every second on its way up to the 15th floor. Assuming the car doesn’t slow down or make any stops , how long will it take the car to reach a height of 102 feet above the ground?
Answers
17.86 seconds
Explanation:The starting point of the elevator car = 27 feet above the ground
The endpoint point of the elevator car = 102 feet above the ground
The total distance traveled by the elevator car = 102 feet - 27 feet
The total distance traveled by the elevator car = 75 feet
Time taken by the elevator car to rise 4.2 feet = 1 second
Time taken by the elevator car to rise 75 feet = 75/4.2 seconds
Time taken by the elevator car to rise 75 feet = 17.86 seconds
Therefore, it takes the car 17.86 seconds to reach a height of 102 feet above the ground
There are 6000 students at Mountain High School, and 1/4 of these students are seniors. If 2/3 of the seniors are in favor of the school forming a debate team and 1/5 of the remaining students (not seniors) are also in favor of forming a debate team how many students do not favor this idea?
Answers
hello
tp solve this question, let's get the data out
we have a total of 6000 students. 1/4 of the students are seniors, let's find the numbers of seniors in the school
the number of senior students are
[tex]\frac{1}{4}\times6000=1500[/tex]we have 1500 seniors in the school.
we can find the seniors in support of a debate team by multiplying 2/3 by 1500
[tex]\frac{2}{3}\times1500=1000[/tex]now we know that 1000 students are in support of the debate team. let's subtract the numbers of students in support of debate team from numbers of seniors in the schoolto giveus the numbers of seniors that are not in support of debate team.
[tex]1500-1000=500[/tex]500 seniors from the school are not in support of a debate team.
Also note that 1/5 of the remaining students are not in support of the debate team.
which would be
[tex]\begin{gathered} 6000-1500=4500 \\ \frac{1}{5}\times4500=900 \end{gathered}[/tex]now, we can add the numbers of seniors that are not in support of a debate team plus number of remaining students not in support of a debate team
[tex]500+900=1400[/tex]from the calculationabove, a total of 1400 students are not in support of the idea
