Find the length of the legs of a night triangle whose hypotenuse is 25cm and whose area is 84cm use phytagorean theorem.
Answers
Answer:
Explanation:
Here, we want to find the length of the legs of the right triangle given the area and the length of the hypotenuse
We have the sketch of the triangle as shown below:
According to Pythagoras' the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides
Thus, mathematically:
[tex]a^2\text{ + b}^2\text{ = 25}^2[/tex]Mathematically, we have the area calculated as:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times b\times h \\ \\ 84\text{ = }\frac{1}{2}\times a\times b \\ \\ a\text{ = }\frac{168}{b} \end{gathered}[/tex]Now, we have two equations to solve simultaneously
Substitute equation ii into i
We have that as:
[tex][/tex]
Related Questions
10Estimate the solution to the following system of equations by graphingOA (1,7)OB. (-1,1)OC.OD. (-1,-1)
Answers
we have the system of equations
-4x + 5y =8
6x - y = 11
Using a graphing tool
Remember that
the solution is the intersection point of both lines
The answer is the option AThe House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
Answers
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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Benjamin & Associates, a real estate developer, recently built 185 condominiums in McCall,Idaho. The condos were either three-bedroom units or four-bedroom units. If the total numberof bedrooms in the entire complex is 657, how many three-bedroom units are there? How manyfour-bedroom units are there?
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we have the following:
x = number of three bedroom
y = number of four bedroom
therefore,
[tex]\begin{gathered} x+y=185 \\ 3x+4y=657 \end{gathered}[/tex]27. If figure A and figure B are similar with a ratio of similarity of 2, and the perimeter of figure A is 28 units,what is the perimeter of figure B?
Answers
SOLUTION
Since the two shapes are similar, that is A and B similar with a ratio of 2, then we have that
[tex]\begin{gathered} \frac{length\text{ A}}{lemgth\text{ B}}=\frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{28}{perimeter\text{ B}} \end{gathered}[/tex]Cross multiplying we have
[tex]\begin{gathered} 2Perimeter\text{ B = 28} \\ Perimeter\text{ B = }\frac{28}{2} \\ =14\text{ units } \end{gathered}[/tex]hence the answer is 14 units
I am having so much trouble with my assignment. can you please help me with number 8 and 10.
Answers
We have to solve this system of equations by substitution.
8) First, we find the value of one of the variables in function of the other using one of the 2 equations (first equation, in this case). Then, we use the other equation and replace the variable we just cleared (x, int his case) and solve for the other variable (y).
Then, after calcualting y, we can use the first equation to calculate x.
[tex]\begin{gathered} x+4y=0 \\ x=-4y \end{gathered}[/tex][tex]\begin{gathered} 3x+2y=20 \\ 3(-4y)+2y=20 \\ -12y+2y=20 \\ -10y=20 \\ y=\frac{20}{-10} \\ y=-2 \end{gathered}[/tex][tex]\begin{gathered} x=-4y=-4(-2) \\ x=8 \end{gathered}[/tex]Answer: x=8, y=-2.
10)
[tex]\begin{gathered} x-3y=-2 \\ x=3y-2 \end{gathered}[/tex][tex]\begin{gathered} 10x+8y=-20 \\ 10(3y-2)+8y=-20 \\ 30y-20+8y=-20 \\ 38y=-20+20 \\ 38y=0 \\ y=0 \end{gathered}[/tex][tex]x=3y-2=3\cdot0-2=0-2=-2[/tex]Answer: x=-2, y=0
The current in a simple electrical circuit is inversely proportional to the resistance. If thecurrent is 30 amperes (an ampere is a unit for measuring current) when the resistance is 5ohms, find the current when the resistance is 7.8 ohms.
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Hello there. To solve this question, we'll have to remember some properties about inversely proportional terms.
Let's start labeling the terms:
Say Current is given by I, Resistance is given by R and voltage is given by V.
By Ohm's Law, we know that:
[tex]V=R\cdot I[/tex]In fact, this is the definition we need to find the answer.
But, to understand why the question mention the fact that they are inversely proportional, note:
We say two numbers x and y are inversely proportional when:
[tex]x\cdot y=k[/tex]Their product is equal to a constant. k is the constant (of proportionality).
Now, using the given values in the question, we can solve this question.
If the current is 30 ampère when the resistance is 5 ohms, we have to find the current when the resistance is 7.8 ohms.
First scenery:
[tex]V=30\cdot5[/tex]Multiply the numbers
[tex]V=150[/tex]Second scenery:
[tex]V=7.8\cdot I[/tex]Plugging V = 150, we get:
[tex]150=7.8\cdot I[/tex]Divide both sides of the equation by a factor of 7.8
[tex]I=\frac{150}{7.8}[/tex]Simplify the fraction by a factor of 2
[tex]I=\frac{75}{3.9}[/tex]Using a calculator, we get the following approximation
[tex]I\approx19.2\text{ A}[/tex]A is for Ampère.
Which of the following could be the product of two consecutive prime numbers? A. 2 B. 10 C. 14 D. 15
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15 because it is the product of 3 and 5 which are consecutive prime numbers.
If an account is compounded annually at 9%, how much interest will a principal of $12,300 earn in 16 months? Round your answer tothe nearest cent. Note: Assume 365 days in a year and 30 days in a month.
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From the question, we have the given information.
[tex]\begin{gathered} \text{Principal =\$12300} \\ \text{rate}=9\text{\%} \\ \text{number of times compounded =1} \\ \text{Time =16 months =}\frac{4}{3}years \end{gathered}[/tex]We will use the formula below to solve the question
[tex]\text{Amount =P(}1+\frac{r}{n})^{nt}[/tex]Therefore;
[tex]\begin{gathered} \text{Amount}=12300(1+\frac{9}{100})^{\frac{4}{3}} \\ =12300(\frac{109}{100})^{\frac{4}{3}} \\ =13797.71 \end{gathered}[/tex]Since the Amount = 13797.71, we can get the interest by using the formula below.
[tex]\begin{gathered} \text{Interest= Amount- Principal} \\ =13797.71-12300 \\ =1497.71 \end{gathered}[/tex]Answer: Interest =$1497.71
Please help ASAP thank you
Answers
Answer:
Shade 6 strips out of the 9.
Step-by-step explanation:
Let us find 2/3 of 9
We can write 2/3 of 9 as 2/3 × 9
To multiply fractions through the following steps:
Now, 2/3 × 9 = (2 × 9) / 3 = 18/3 = 6
A quadrilateral has two angles that measure 110° and 120°. The other two angles are in aratio of 6:7. What are the measures of those two angles?andSubmit
Answers
From the problem, two angles in a quadrilateral are 110 and 120 degrees.
Note that the sum of interior angles in a quadrilateral is 360 degrees.
Then the sum of the other two angles will be :
[tex]360-(110+120)=130[/tex]And the angles are in a ratio of 6 : 7.
Multiply the ratio by a common factor "x"
[tex]6x\colon7x[/tex]Then take the sum and equate it to 130 degrees.
[tex]6x+7x=130[/tex]Solve for x :
[tex]\begin{gathered} 13x=130 \\ x=\frac{130}{13} \\ x=10 \end{gathered}[/tex]Now, substitute x = 10 to the ratio.
[tex]\begin{gathered} 6(10)\colon7(10) \\ 60\colon70 \end{gathered}[/tex]Therefore, the other two angles are 60 and 70 degrees.
ANSWER :
60 and 70 degrees
Which inequalities are shown on the graph?Find your inequalities in the grid below. Check the ONE box that pairs the two correct inequalitiesY-3-1 y>-**-172-**-1 y<-**-1<3+3y>+3y< <+3y2 ++3D D D DOOOO"OOOOPreviousPauseO Search for anything0-
Answers
From the graph we could see that y = x + 3 for the first line . The shaded line is where y is less than or equals to x + 3.
For the second line we can see that y = x - 1 . The shaded line is where y is greater than or equals to x - 1 . Therefore, the inequalities are as follows
[tex]\begin{gathered} y\leq x+3 \\ y\ge x-1 \end{gathered}[/tex]Xavier wants to compare two websites based on customer ratings in order to decide on which website to make a big purchase. He creates a boxplot for each website with the same number of ratings. (look at the graph)What can Xavier NOT include?A. Website A has a higher median rating B. Website A has a larger interquartile range C. Website A has larger rangeD. Website A has a lower median rating E. Website A has a lower first quartile value
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D.
Since the median of the blue box is upper from the orange one we conclude that the median is higher in website A.
Therefore, the wrong statement is D.
I need help with this question please help me asap?
Answers
Answer
Explanation
• Range (R): the amount between the upper and lower limit.
Please help me
I give brainliest
worth 15 points
The amount of money in a bank account is given by the function y = 200(1+0.05), where y is in dollars and t is measured in months since the account was opened.
What is the percent rate of growth of the bank account?
Enter your answer in the box.
Answers
Answer:
60% annual rate
Step-by-step explanation:
Your equation is incorrect
It should be Y = 200 (1+.05)^t
T is the number of compounding periods per year (12 to a year)
.05 is the periodic interest rate ( 1/12 th of the annual)
.05 * 12 = .6 Which is 60% <=====REALLY high annual rate!
Eric is a software salesman. His base salary is 2300, and he makes an additional $90 for every copy of History is Fun sells. Let P represent his total pay (in dollars) and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
Answers
Equation
P = 2300 + 90(N)
Total payment after selling 23 copies of History is Fun.
P= 2300 + 90(23)
P= 2300 + 2070 (Multiplying)
P= 4370 (Adding)
The answer is $4370
what is the length of the dominant line in the time graph below? l leave your answer in simplest radical form.
Answers
Let's first calculate the lenght of the side of the rectangle.
[tex]l=\sqrt[]{8^2+5^2}=\sqrt[]{64+25}=\sqrt[]{89}[/tex]so we get that the dotted line is:
[tex]d=\sqrt[]{2^2+89}=\sqrt[]{93}[/tex]so the answer is square root of 93
Math problem attached
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2. 65 x 10⁶ ft³ of oil will be required to fill the pipe.
What is rounding off ?
Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.
It is given that :
length of pipe l = 800 mi.
we know that :
1mi = 5280 ft.
8 mi = 5280 x 8 = 42240 ft.
also, diameter of pipe d = 48 in.
then, radius r = d/2 = 24in.
and, 1 in. = 0.833 ft.
24 in = 24 x0.833 ≈ 20 ft.
Now, volume of pipe V will be :
V = πr²l
V = 3.14 x (20)² x 42240
V = 2654017.5
V = 2. 65 x 10⁶ ft³
Therefore, 2. 65 x 10⁶ ft³ of oil will be required to fill the pipe.
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Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
Answers
Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
we have 2/3
Multiply by 8/8
(2/3)(8/8)=16/24
therefore
the answer is 16HELP ASPAPP The general form of an equation is x2+y2−25x+3y+1=0.
What is the equation of the circle in standard form?
Answers
Answer:
the first (top) answer option. ... = 129/100
Step-by-step explanation:
the for me qualifying or disqualifying term is the constant term as the product and sum of all the constant parts.
the general form has the constant parts
... + 1 = 0
so, all the constant terms from the squares on the left side minus the constant term on the right side must be 1.
let's start from the bottom : the 4th answer option.
the constant parts are
... + (-1/5)² + ... + (3/2)² = 121/100
... + 1/25 + ... + 9/4 = 121/100
... + 0.04 + ... + 2.25 = 1.21
... + 2.29 - 1.21 = ... + 1.08
and NOT 1. so, this is wrong.
the 3rd answer option.
... + (-1/3)² + ... + (-3/2)² = 221/100
... + 1/9 + ... + 9/4 = 221/100
... + 0.111111... + ... + 2.25 = 2.21
... + 0.111111... + ... + 2.25 - 2.21 = 0
... + 0.111111... + ... + 0.04 = 0
... + 0.111111 + 0.04 = 0.15111111...
and NOT 1. so, this is wrong.
the 2nd answer option.
... + (-1/5)² + ... + (3/2)² = 229/100
... + 1/25 + ... + 9/4 = 229/100
... + 0.04 + ... + 2.25 = 2.29
... + 2.29 - 2.28 = ... + 0
and NOT 1. so, this is wrong.
the first answer option.
... + (-1/5)² + ... + (3/2)² = 129/100
... + 1/25 + ... + 9/4 = 129/100
... + 0.04 + ... + 2.25 = 1.29
... + 2.29 - 1.29 = ... + 1
this IS 1. so, this is correct.
this corresponds now to the original
... + 1 = 0
Answer: Choice A (May vary from test to test)
Step-by-step explanation:
(x-1/5)^2 + (y+3/2)^2 = 129/100
Just an FYI:
I can't stress this enough... Add equation symbols when applicable, for example: √,^,/, etc. You can't expect to have someone give the correct answer when you literally typed the equation out incorrectly.21. A seamstress made 3 different skirts out of the same material. Each skirt required a dif- ferent amount of material. The chart below shows the number of yards y required for each skirt and the total cost C of the ma- terial. What is the equation for finding the cost per skirt made from the same material? Skirt А B C у 2.5 3.5 4 C С $15.60 $21.84 $24.96
Answers
Could you please share the chart the problem refers to?
We are asked to find an equation that gives the cost (C) of the skirt as a function of the number of yards (y) of material used.
The information given is:
y = 2.5 then C = $15.60
y = 3.5 then C = $21.84
y = 4 then C = $24.96
when the cost is $15.60, the amount of material in yards is 2.5 yards
so let's find the cost per yard as the quotient cost in $ divided by yard of material
Cost/yards = $21.84/3.5 = 6.24 $ per yard
The quotient gives the same value for all the three cases:
$15.60 / 2.5 = $6.24 per yard
$24.96 / 4 = $6.24 per yard
then the cost is going to be given by the equation:
C = 6.24 * y
This is the equation they asked you to find (naming "C" the cost, and "y" the number of yards of material used.
The equation contains ""unknowns"
Recall that the question is:
What is the equation for finding the cost per skirt made from the same material?
So they want a mathematical formula/equation that allows everyone to estimate the cost (C) given the number of yards of mwterial used (y)
So if you give the following equation (called equation because it must contain an "equal" sign):
C = 6.24 * y
A second problem gives you the amount paid for number of pounds of blueberries
The data says:
3 pounds cost $5.4
7 pounds cost $12.6
We proceed as before, and get that the amount per pound is obtained via the quatient: Price (C) divided by number of pounds (p)
C / p = $5.4 / 3 = $1.8 per pound
that gives us the equation:
C = $1.8 * p
Given that sin(0)= 10/ 13 and 0 is in Quadrant II, what is cos(20)? Give an exact answer in the form of a fraction. ,
Answers
SOLUTION
Given the image in the question tab, the following are the solution steps to the answer
Step 1: Write out the function
[tex]\begin{gathered} \sin \theta=\frac{10}{13} \\ \text{since }\sin \theta=\frac{opp}{hyp} \\ \therefore opp=10,\text{ hyp=13} \end{gathered}[/tex]Step 2: Solve for the adjacent using the pythagoras theorem
[tex]\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ 13^2=10^2+adj^2 \\ \text{adj}^2=13^2-10^2 \\ \text{adj}=\sqrt[]{169-100} \\ \text{adj}=\sqrt[]{69} \end{gathered}[/tex]Step 3: Calculate the value of cos2Ф
[tex]\begin{gathered} cos2\theta=\cos ^2\theta-\sin ^2\theta \\ \cos 2\theta=(\frac{\text{adj}}{\text{hyp}})^2-(\frac{opp}{hyp})^2 \\ \cos 2\theta=(\frac{\sqrt[]{69}}{13})^2-(\frac{10}{13})^2 \\ \cos 2\theta=\frac{69}{169}-\frac{100}{169} \\ \cos 2\theta=-\frac{31}{169} \end{gathered}[/tex]Hence, the value of cos2Ф is -31/169.
Solve for x using trigonometry. Round to the nearest tenth. (hint: One decimal place) 17 x 19
Answers
By definition,
sin(angle) = opposite/hypotenuse
From the picture,
sin(x) = 17/19
x = arcsin(17/19)
x = 63.5°
A line passes through the point -8, -5 and has a slope of -3/2 Write an equation in slope-intercept form for this line.
Answers
Answer:
[tex]y = - \frac{3}{2} x - 17[/tex]
Step-by-step explanation:
[tex] - 5 = - \frac{3}{2} ( - 8) + b[/tex]
[tex] - 5 = 12 + b[/tex]
[tex]b = - 17[/tex]
[tex]y = - \frac{3}{2} x - 17[/tex]
Which expression is equivalent to (2-3x) (2+3x) ?
Answers
Answer:
[tex]4-9x^{2}[/tex]
Step-by-step explanation:
in the first parenthesis, multiply the FIRST number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex](2-3x)(2+3x)[/tex]
it would look like:
[tex]2(2) = 4\\2(3x) = 6x[/tex]
Next, multiply the SECOND number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex]-3x(2) = -6x\\-3x(3x) = 9x^2[/tex]
Now, add like terms. Your answer should either be:
[tex]4+6x-6x+9^2[/tex] OR [tex]4 -9x^2[/tex]
How would I convert 900,000km to miles?
Answers
EXPLANATION
Since we have 900,000 kilometers, and 1 kilometer is equivalent to 0.621371 kilometers, we can apply the unitary method in order to get the needed conversion as shown as follows:
[tex]\text{?miles}=900,000\operatorname{km}\cdot\frac{0.621371}{1\text{kilometer}}=559233\text{ miles}[/tex]?miles = 900,000 km * (0.621371/ 1 km) = 559,233 miles
The solution is 559,233 miles
Write the slope-intercept form of the equation of each line.4) -3+y=2/5x
Answers
where
[tex]\begin{gathered} \text{slope}=\frac{2}{5} \\ y-\text{intercept}=3 \end{gathered}[/tex]Explanation
the equation of a line in slope-intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Step 1
then, isolate y
[tex]-3+y=\frac{2}{5}x[/tex]i) add 3 in both sides
[tex]\begin{gathered} -3+y=\frac{2}{5}x \\ -3+y+3=\frac{2}{5}x+3 \\ y=\frac{2}{5}x+3 \end{gathered}[/tex]Hence, the answer is
[tex]y=\frac{2}{5}x+3[/tex]where
slope=2/5
y-intercept=3
I hope this helps you
3A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed.Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents ofMississippl would purchase the new product. Identify a problem with the study.The conclusion is based on a small sample.
Answers
The main problem of the research conducted is the number of participants who polled for the new product. If we want to conduct a study that represents a state, the number of participants must be close as possible to the total population of the state. Of course, 24 participants is very small sample size when we compare it to the population of the state, which means we cannot easily conclude that 50% of the residents would like to purchase the new product based on just 24 participants.
Answer: a. The conclusion is based on a small sample
A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walkercharge for a 45 minute walk? Write an equation in function notation for the situation, and then use it tosolve the problem. Determine if the given statement is True or False.
Answers
hello
from the question given, the dog walker charges a flat rate of $6 and an extra $30 per hour.
we can write out an equation in function notation
let the number of hours be represented by x
[tex]f(x)=6+30x[/tex]now we can proceed to solve the cost of the walk for 45 minutes
[tex]\begin{gathered} 1hr=60\min s \\ \text{xhr}=45\min s \\ x=\frac{45}{60} \\ x=\frac{3}{4} \\ \text{therefore 45mins = 3/4 hours} \end{gathered}[/tex]now we can input the value into the equation and know the cost for 45 minutes walk
[tex]\begin{gathered} f(x)=6+30x \\ x=\frac{3}{4} \\ f(x)=6+30(\frac{3}{4}) \\ f(x)=6+22.5 \\ f(x)=28.5 \end{gathered}[/tex]from the calculation above, the cost of 45 minutes walk will cost $28.5
Find the solutions of the given system of equations: x2 + y2 = 68 and y = 4x.
Answers
Given the system of equations:
[tex]\begin{gathered} x^2+y^2=68 \\ y=4x \end{gathered}[/tex]We can solve it by substituting the second equation into the first as follows:
[tex]\begin{gathered} x^2+(4x)^2=68 \\ \\ Operating: \\ \\ x^2+16x^2=68 \\ 17x^2=68 \end{gathered}[/tex]Dividing by 17:
[tex]x^2=\frac{68}{17}=4[/tex]Applying square root on both sides:
[tex]\begin{gathered} x=\pm\sqrt{4} \\ x=\pm2 \end{gathered}[/tex]There are two solutions for x and they produce two solutions for y.
For x = 2
y = 4*2 = 8
For x = -2
y = 4*(-2) = -8
Thus, the solutions are:
(2,8) and (-2, -8)
given ABCD is congruent EFGH. solve for x. Round the answers to the nearest hundredth
Answers
As ABCD is congruent withEFGH, it means that both figures have the same mesarurements, even if their orientation is different.
Then, you have that the angle in A is congruente with the angle in E, the angle B is congruent with the angle F, the angle C is congruent with the angle G, the angle D is congruent with the angle H.
[tex]\begin{gathered} \angle A=\angle E \\ \angle B=\angle F \\ \angle C=\angle G \\ \angle D=\angle H \end{gathered}[/tex]Then:
[tex]3x^2-4x+10=16[/tex]You solve the x from the equation above:
1. Equal the equation to 0
[tex]\begin{gathered} 3x^2-4x+10-16=0 \\ 3x^2-4x-6=0 \end{gathered}[/tex]2. Use the quadratic equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(3)(-6)}}{2(3)} \\ x=\frac{4\pm\sqrt[]{16+72}}{6} \\ x=\frac{4\pm\sqrt[]{88}}{6} \\ x_1=\frac{4-\sqrt[]{88}}{6},x_2=\frac{4+\sqrt[]{88}}{6} \\ x_1=-0.896,x_2=2.230 \end{gathered}[/tex]3. As you get two solutions for x. You need to prove which is the right solution:
with x1:
[tex]\begin{gathered} 3x^2-4x+10=16 \\ 3(-0.896^2)-4(-0.869)+10=16 \\ 11.17\ne16 \end{gathered}[/tex]with x2:
[tex]\begin{gathered} 3x^2-4x+10=16 \\ 3(2.23^2)-4(2.23)+10=16 \\ 15.99\approx16 \end{gathered}[/tex]As you can see the right solution is x2, because if you subtitute the x in the equation of the angle A that must be equal to 16, just the x2 gives an approximate value to 16.
Then, the solution for the x is x=2.23