The hypotenuse of an isosceles right triangle is 6cm longer than either of its legs. Note that an Isosceles right triangle is a right triangle whose legs are the same length, find the exact length of its legs and it’s hypotenuse
Answers
We know by the pythagorean theorem that
We know that the length of the hypotenuse squared will be equal to the sum of the legs squared. The problem says that the legs have the exact same length and the hypotenuse is 6cm longer, so we can write
Where "a" is the leg length, see that we can apply the pythagorean theorem here, and it will be
[tex]a^2+a^2=(a+6)^2[/tex]See that now c = a + 6, and b = a.
We can simplify that expression
[tex]2a^2=(a+6)^2[/tex]We know that
[tex](a+6)^2=a^2+12a+36[/tex]Therefore our equation will be
[tex]2a^2=a^2+12a+36[/tex]Now we pass all the terms for one side and we will have a quadratic equation
[tex]-a^2+12a+36=0[/tex]We can use the formula for the quadratic equation and find out the solutions
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Using it
[tex]\frac{-12\pm\sqrt[]{12^2-4\cdot(-1)\cdot36}}{2\cdot(-1)_{}}[/tex]Now we can just do all the calculus
[tex]\frac{-12\pm\sqrt[]{144^{}+144}}{-2_{}}=\frac{12\pm\sqrt[]{2\cdot12^2}}{2}=\frac{12\pm12\sqrt[]{2}}{2}[/tex]Then the solution are
[tex]\begin{cases}a_1=6+6\sqrt[]{2} \\ a_2=6-6\sqrt[]{6}\end{cases}[/tex]Even though we have two solution, see that the second one is negative, and we can't have negative length! Then the length of its legs will be
[tex]a=6+6\sqrt[]{6}[/tex]And the hypotenuse will be a + 6, then
[tex]h=6+6+6\sqrt[]{6}=12+\sqrt[]{6}[/tex]Therefore, the legs and the hypotenuse length is
[tex]\begin{gathered} l=6+\sqrt[]{6} \\ h=12+6\sqrt[]{6} \end{gathered}[/tex]We can write it approximately as
[tex]\begin{gathered} l=14.485\text{ cm} \\ h=20.485\text{ cm} \end{gathered}[/tex]If we want a more rough approximation we can say it's
[tex]\begin{gathered} l=14.5\text{ cm} \\ h=20.5\text{ cm} \end{gathered}[/tex]
Related Questions
The finishing time for a runner completing the 200-meter dash is affected by the tail-wind speed, s. The change, t, in a runner's performance is modeled by the function shown below:t = 0.0119s^2 - 0.308s - 0.0003Predict the change in a runner's finishing time with a wind speed of 5 meters/second. Note: A negative answer means the runner finishes with a lower time. Round to the nearest hundredth.
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The change, t, in a runner's performance is modeled by:
[tex]t=0.0119s^2-0.308s-0.0003[/tex]Here s is the tall-wind speed.
It's required to find the change in a runner's finishing time with a wind speed of s = 5 m/s.
Substitute in the equation:
[tex]t=0.0119(5)^2-0.308(5)-0.0003[/tex]Operating:
[tex]\begin{gathered} t=0.0119(25)-1.44-0.0003 \\ \\ t=0.2975-1.44-0.0003 \end{gathered}[/tex]Calculating:
t = -1.24
(-2,-7);y=-2 the equation is
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Answer: -2= 5/2x -2
Step-by-step explanation:
Can you please help me out with a question
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In the figure, the value of angle inscribed, m[tex]\text{Inscribed angle=}\frac{1}{2}\times Intercepted\text{ arc}[/tex]In the figure, Hence,
[tex]\begin{gathered} mTherefore, m ZWX= 230º.Estimate 71.91-56.423 by first rounding each number to the nearest whole number.
Answers
Answer:
16
Step-by-step explanation:
71.91 ~ 72
56.423 ~ 56
72-56=16
Given the following figure is a parallelogram, solve for x.
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The given figure is a parallelogram. The opposite angles of a parallelogram are congruent.
From the information given,
angle E and angle G are opposite
Thus,
94 = 11x + 6
11x = 94 - 6 = 88
x = 88/11
x = 8
Stephanie and two friends want to Vancouver for a winter weekend Stephanie May 7 cups of apple cider everyone includes Stephanie wants an equal amount of all the the apple cider how much apple cider should each person get
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Number of persons = 3
Number of cups of apple made is =7
Then the number of equal cider, everyone must have is:
[tex]\frac{7}{3}\text{ = 2}\frac{1}{3}\text{ cups of apple cider.}[/tex]The freezing point of water is 0 °C. Imanis refrigerator is set at 4°C and her freezer is set at -19°C. which change in temperature would bring imanis refrigerator or her freezer to the same temperature as the freezing point of water?A: +23°CB: +15°CC: -19°CD: -4°C
Answers
The freezing point of water is 0 °C
The tempreature of Imanis refrigerator = 4degree C
and the freezer is -19 degreeC
So, the net tenpreature of refrigerator is 4+(-19)
The net tempreature = (-15) degreeC
We want
Ten yards of a particular kind of wire cost $15.30 . What is the cost of the wire per foot?
Answers
Given:
Length of wire = 10 yards
Total cost of wire = $15.30
To be able to determine the cost of wire per foot, let's first convert the unit of measure of the wire's length from yards to feet.
Recall: 1 yard = 3 feet
Step 1: Convert the measure of the wire length from yards to feet.
[tex]\text{ 10 (yards) x }\frac{\text{ 3 feet}}{\text{ 1 (yard)}}\text{ = }\frac{\text{10 x 3}}{\text{ 1}}\text{ feet}[/tex][tex]\text{ = 30 feet}[/tex]Therefore, 10 yards is equivalent to 30 feet.
Step 2: Divide the total cost by the total length of wire in feet.
[tex]\text{ Cost of wire per foot = }\frac{\text{ Total cost of wire}}{\text{ Total length of wire}}[/tex][tex]\text{ = }\frac{\text{ \$15.30}}{\text{ 30 feet}}[/tex][tex]=\text{ \$0.51 per foot}[/tex]Therefore, the cost of the wire per foot is $0.51
Graph the line with the slope -3/4 passing through the point (5,2)
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We need to first determine the expression of the line, for that we will use the point slope form, which is given below:
[tex]y-y_1=m\cdot(x-x_1)[/tex]Where m is the slope and (x1, y1) are the coordinates of a known point on the line.
[tex]\begin{gathered} y-2=-\frac{3}{4}(x-5) \\ y=-\frac{3}{4}(x-5)+2 \\ y=-\frac{3}{4}x+\frac{15}{4}+2 \\ y=-\frac{3}{4}x+\frac{15+8}{4} \\ y=-\frac{3}{4}x+\frac{23}{4} \end{gathered}[/tex]Now we need to graph it, for that we need two points. We already know the coordinates of one of them (5,2), now we need another, we can use the point for which x is equal to 0.
[tex]\begin{gathered} y=-\frac{3}{4}\cdot0+\frac{23}{4} \\ y=\frac{23}{4} \end{gathered}[/tex]Now we have (0, 23/4). We need to draw a line that passes
The parent function of the function g(x) = (x-h)² + k is f(x) = x2. The vertex of the function g(x) is located at (9,-8).
What are the values of h and k?
g(x) = (x-
².
Answers
Answer:
The values of h and k are 9 and -8, respectively
Step-by-step explanation:
This is how to determine the values of h and k
The vertex of the function g(x) is located at (9, –8)
The vertex of a function is represented as:
Vertex = (h,k)
This means that:
(h,k) = (9,-8)
By comparison, we have:
h = 9 and k = -8
So, the values of h and k are 9 and -8, respectively
For each function, determine whether it is a polynomial function.Function(a) g(x) = 5x (x-3)²(b) f(x)=-3√√x(c) v(x)=9x³+4x(d) u(x)=1---XIs the function a polynomial?YesNoOO
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Explanation:
A polynomial function is a function where the exponents are whole numbers, i.e. >0 and natural. The coefficients are real.
Answer:
a) Yes
b) No.
c) No
d) No
In a survey, 315people said they drivetheir car to work. Thisrepresents 90% of thepeople surveyed.How many peoplewere surveyed?
Answers
We know that 90% is equivalent to 315 people and we want to know how many people are equivalent to 100%. So, using the rule of three, we get:
90% ------------------- 315
100% ------------------ X
Where X is the number of people surveyed.
Solving for X, we get:
[tex]X=\frac{100\cdot315}{90}=350[/tex]Therefore, 350 people were surveyed.
Answer: 350 people
Will give brainlist PLEASE HELP ASAP!!!! If it says college math, that's false.
The graph below represents the money collected at the skating rink on Friday. Find the domain when the maximum number of people allowed in the skating rink is 75 people.
A=0 ≤ x ≤ 75
B= 20 ≤ y ≤ 320
C= 0 ≤ y ≤ 75
D= 20 ≤ x ≤ 320
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Answer:
A is correct.
0 < x < 75 represents the correct domain.
A dresser and nightstand costs $900. If the dresser costs $150 more than the nightstand, what does each piece cost separately?
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We will solve this problem using a system of linear equations.
[tex]\text{Let D=dresser's cost and N=nightstand's cost}[/tex]We are given the following relationship between the variables
[tex]\begin{gathered} D+N=900,\text{ (1)} \\ D=N+150,\text{ (2)} \end{gathered}[/tex]Replacing the value of D from equation (2) in equation (1)
[tex]N+150+N=900[/tex]Solving for N
[tex]\begin{gathered} 2N+150=900 \\ 2N=900-150 \\ 2N=750 \\ N=\frac{750}{2}=375 \end{gathered}[/tex]Replacing the value of N in equation (2)
[tex]\begin{gathered} D=375+150 \\ D=525 \end{gathered}[/tex]The answer is the nightstand costs $375 and the Dresser costs $525
The difference between eight times a number and three is equal to negative nineteen. What is the number?-22-33
Answers
Given:
The difference between eight times a number and three is equal to negative nineteen.
Required:
We want to find that number
Explanation:
Take the unknown number x
Now,
The difference between eight times a number and three is equal to negative nineteen means
[tex]\begin{gathered} 8x-3=-19 \\ 8x=-19+3 \\ 8x=-16 \\ x=-2 \end{gathered}[/tex]Final answer:
-2
Two students, 100 meters apart on the same path, arewalking towards one other. Student A has a speed of 2meters each second; Student B has a speed of 3 meterseach second. Let's suppose they start to walk to eachother when t=0. How many seconds will it take for thestudents to bump into one another? Give your answer tothe nearest whole number
Answers
D = RT
Where
D is distance
R is speed
T is time
Distance of student 1:
[tex]D_1=2t[/tex]Distance of student 2:
[tex]D_2=3t[/tex]Now,
When they meet, their distance would total 100, so we can write:
[tex]D_1+D_2=100[/tex]We can also write:
[tex]D_1=100-D_2[/tex]The hypotenuse of a right triangle is 6 meters long, and one leg is 2 meters long. How long is the other leg?
Answers
To find the leg, we have to use the Pythagorean's Theorem
[tex]c^2=a^2+b^2[/tex]Where c = 6, a = 2.
[tex]\begin{gathered} 6^2=2^2+b^2 \\ b^2=6^2-2^2 \\ b=\sqrt[]{36-4} \\ b=\sqrt[]{32} \\ b\approx5.7 \end{gathered}[/tex]Hence, the other leg is 5.7 meters long.What is the scale factor of XYZ to UVW?y836075V83"1556°4156X9018W410A. 5B.14OOC.011aD. 4
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In order to solve this exercise, it is important to remember that when two figures are similar the corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are equal.
In this case, you know that the triangle XYZ and the triangle UVW are similar triangles. Let be "k" the scale factor of XYZ to UVW.
Based on the explained above, you can set up the following:
[tex]k=\frac{UV}{XY}[/tex]You can identify that:
[tex]\begin{gathered} UV=12 \\ XY=60 \end{gathered}[/tex]Then, substituting values into the equation, you get that:
[tex]k=\frac{12}{60}=\frac{1}{5}[/tex]The answer
Question 15.I need help with this question to make sure that I have the right answer.my answer was number 2
Answers
Given the graph that shows the results of the survey, you know that it shows the results of 3 price surveys conducted at 4 area supermarkets in 3 months.
Notice that the white bar represents the results of September, the dashed bar represents the results in November and the black bar represents the results in March.
You can identify that on the x-axis are written the 4 area supermarkets and, on the y-axis are represented the prices in dollars.
Therefore, in order to identify the supermarket that lowered the price of the frozen beef dinners by the greatest dollar amount between September and November, you need to identify the supermarket that has the shortest dashed bars and white bars.
In this case, you can identify that the lowest price in September and November is:
[tex]\text{ \$}1.50[/tex]And it corresponds to Warehouse.
Hence, the answer is: Option (2).
Find the missing side cround to is inches 3 you x inches 1 10 inches
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Given,
The measure of the hypotenuse is 15 inches.
The measure of the base is 10 inches.
The measure of the perpendicular is x inches.
By Pythagoras theorem,
[tex]\text{hypotenuse}^2=\text{perpendicular}^2+\text{base}^2[/tex]Substituting the values then,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{perpendicular}^2+\text{base}^2 \\ 15^2=x^2+10^2 \\ 225=x^2+100 \\ 225-100=x^2 \\ x=\sqrt[]{125} \\ x\approx11.18 \end{gathered}[/tex]Use the approximate half-life formula for the case described below. Discuss whether the formula is valid for the case described.Urban encroachment is causing the area of a forest to decline at the rate of 5% per year. What is the half-life of the forest? What fraction of the forest will remain in 30 years?(Type an integer or decimal rounded to the nearest hundredth as needed.)
Answers
ANSWER:
EXPLANATION:
Give the rate of decline as 5% per year, we'll go ahead and use the below formula to determine the half-life of the forest;
[tex][/tex]Order the numbers form least to greatest 99.98, 100.1, 98.89, 100.01
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Answer: 98.89, 99.98, 100.01, 100.1
98.89 < 99.98 < 100.01 < 100.1
Hopes this helps!
How to convert 9.4 degrees has feet and inches
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Solution
[tex]9.4\text{degree --> inches}[/tex]To convert degrees to inches you must multiply the width of the control surface in inches by the sine of the angle.
How to convert degrees to inches?
First, determine the control surface width.
Measure the control surface width in inches.
Next, determine the angle.
Measure the angle in degrees.
Finally, calculate the deflection.
Calculate the linear deflection in inches using the formula above.
[tex]9.4degree=3.72inches[/tex]Find the area of the isosceles triangle.
Answers
Check the picture below.
well, we know the triangle is an isosceles, so it has twin sides coming from the "vertex" down to the "base", running an angle bisector from the "vertex" will give us a perpendicular to the "base", let's find its height.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{5}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{13^2 - 5^2}=h\implies 12=h[/tex]
so we simply need to get the area of a triangle whose base is 10 and height is 12.
[tex]A=\cfrac{1}{2}(\underset{b}{10})(\underset{h}{12})\implies \boxed{A=60}[/tex]
Suppose y varies directly with x when x is -2 y is 10 write the equation that relates x and y
Answers
The form of the equation of the direct proportional is
[tex]y=kx[/tex]k is the constant of variation
We can find it from the initial values of x and y
Since at x = -2 y = 10, then
Substitute x by -2 and y by 10 to find k
[tex]\begin{gathered} x=-2,y=10 \\ 10=k(-2) \\ 10=-2k \end{gathered}[/tex]Divide both sides by -2 to find k
[tex]\begin{gathered} \frac{10}{(-2)}=\frac{-2k}{(-2)} \\ -5=k \end{gathered}[/tex]The value of k is -5
Then the equation is
[tex]y=-5x[/tex]QuestionGetting selected as class secretary is A and having pizza for lunch is B. If these events are independent events, usingP(A) = 0.70, and P(B) = 0.67, what is P(AB)?
Answers
From the question, we have two events that do not affect each other. They seem independent events. The probability of occurring the two events at the same time is given by the formula:
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]Then, since we have that P(A) = 0.70 and P(B) = 0.67, then, we have:
[tex]P(A\cap B)=0.70\cdot0.67=0.469[/tex]Then, P(AB) = 0.469.
What is the meaning of the slope of the equation in this context?
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ANSWER
It is the cost for printing each DVD
EXPLANATION
We want to find out what the slope of the equation represents.
The equation given is a linear equation. The slope of a linear equation represents the rate at which the dependent variable changes with respect to the independent variable.
The independent variable is the number of DVDs while the dependent variable is the cost to make the DVDs.
Hence, the slope represents the cost of the DVDs per DVD. In other words, it represents the cost for printing each DVD.
need help with this problem
Answers
First option describes line e: Each point is less than 4 units from the y-axis.
The second option describes line f:
Describe and correct the error a student made in finding the average rate ofchange for f(x) = 0.5x2 over the interval - 4sxs - 2.
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ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Find the amount and the percent increase. Fill in the chart
Answers
Answer:
Amount of increase = 60
Percent of increase = 40%
Explanation:
The amount of increase is equal to the difference between the new amount and the original amount. So, it is equal to:
New amount - Original amount = 210 - 150 = 60
Then, the percent of the increase is equal to the amount of increase divided by the original amount, so:
Amount of increase/Original amount = 60/150 = 0.4
Therefore, the answers are:
Amount of increase = 60
Percent of increase = 0.4 = 40%