Answers
Answer:
Step-by-step explanation:
An isosceles triangle is one that has 2 sides that are the same length, like ours here. Because of the Isosceles Triangle Theorem, if 2 side lengths are congruent, then the angles opposite those sides are congruent, as well. That means that both base angles are 53 degrees. However, we are looking for the altitude, or height, of the triangle. That changes everything. Drawing in the height serves to cut the triangle in half, splitting both the vertex angle (the angle at the top of the triangle) and the base exactly in half. Now we have 2 right triangles which are mirror images of each other. We only need concentrate on one of these triangles. What the triangle looks like now:
One base angle is 90 degrees and the other is 53 degrees. By the Triangle Angle-Sum Theorem, the third angle has to be a degree measure which ensures that all the angles add up to 180. Therefore, the third angle measures 180 - 90 - 53 = 37. Even still, besides knowing all the angle measures, we really don't need any besides the 53 degree one.
As far as side lengths go, the base is 12 (because the height cut it in half). To find a missing side in a right triangle you either use Pythagorean's Theorem or right triangle trig, depending upon the info you're given. We only have enough to use right triangle trig.
We have the base angle of 53, which is our reference angle, the side next to, or adjacent to, the reference angle, and we are looking for the side length opposite the reference angle. This is the tan ratio where
[tex]tan\theta=\frac{opp}{adj}[/tex] where tangent of the reference angle is equal to the side opposite the reference angle over the side adjacent to the reference angle. Filling in that ratio:
[tex]tan53=\frac{opp}{12}[/tex] and multiply both sides by 12 to get
12tan53 = opp and do this on your calculator to get that
opp = 15.9 inches
Related Questions
If you were asked to equate the sides of an equation, how would you do that
Answers
Answer:
you would divide an equation from the multiple and then you would simplify the equation for an answer
Solve the equation
1/x + 1/3x = 4
Answers
Answer:
x = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{x} + \frac{1}{3x} = 4[/tex] (Multiply everything by LCM)
[tex]3x*\frac{1}{x} + 3x*\frac{1}{3x}=3x*4[/tex] (Simplify the fractions)
[tex]3+1=12x\\4=12x\\x=4/12\\x=\frac{1}{3}[/tex]
If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
Answers
Answer:
3
Step-by-step explanation:
We are going to be using cofunction identity cos(90-x)=sin(x).
Apply to either side but not both.
cos(22f − 1) = sin(7f + 4)
sin(90-[22f-1])=sin(7f+4)
90-[22f-1]=7f+4
Distribute
90-22f+1=7f+4
Combine like terms
91-22f=7f+4
Add 22f on both sides
91=29f+4
Subtract 4 on both sides
87=29f
Divide 29 on both sides
3=f
f=3 is between 0 and 90
Answer:
The answer is "3."
Step-by-step explanation:
Just submitted the test and got the answer correct!
Chad gets an annual salary of 25,000. He and his family spend 3500 per year on food. What percent of his salary is spent on food
Answers
Answer:
[tex]\frac{x}{100}[/tex] x 25000 = 3500
[tex]x[/tex] x 250 = 3500
x = 3500/250
x = 350/25
x = 14%
What does 1/8 equal to
Answers
Answer:
0.125
Step-by-step explanation:
It could be a lot of things, but if you mean the decimal form then it would be 0.125. Just divide 1 by 8.
Find the product.
(-2 x2 ) 3 ·3 x
Answers
Answer: -24x^7
Step-by-step explanation:
pemdas so you do parentheses first therefore getting (2x^2)^3x3x
remove the parentheses
do -8x^6x3x
after that you end up with -24x^7
Simplify (-2x^2) ^3 by raising each term by 3:
-2^3x^6
Now you have
-2^3 x^6 times 3x
-2^3 = -8
x^6 tomes x = x ^7
-8 x 3 = -24
Answer is -24x^7
If y = 2x3 - 4x and dx, dt equals 4 , find dy, dt when x = 1. Give only the numerical answer. For example, if dy, dt = 3, type only 3
Answers
Work Shown:
y = 2x^3 - 4x
dy/dt = 2*3*x^2*dx/dt - 4*dx/dt
dy/dt = 2*3*1^2*4 - 4*4
dy/dt = 8
notice how I used the chain rule for step 2.
Solve for x. Round to the nearest tenth, if necessary. Calculating Sin or Cos or Tan
Answers
Answer:
1.06
Step-by-step explanation:
cos41⁰ = 0.8 ÷ X
X = 0.8 ÷ cos41⁰
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a right triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
x = Hyp (for this question)
Cos(41) = 0.8 / Hyp
use your algebra skillz
Hyp = 0.8 / Cos(41)
use your calculator to fund Cos(41) into 0.8
Hyp = 1.060010395 (that's all the decimal places my calc would go out to )
x = 1.1 ( rounded to nearest 10th )
-2
Simplify the expression
4ab
Assume a = 0,6=0.
1
16a2b2
a²b²
4
-162²62
16ab2
Answers
Answer:
D
Step-by-step explanation:
(4ab)^2 = 4^2a^2b^2 = 16a^2b^2
Determine the area of the triangle.
223.6 square units
248.7 square units
447.1 square units
458.4 square units
Answers
Answer:
223.6 square units. or 223.569 square units
Answer:A
Step-by-step explanation:I took the test
help plsssssssssssss i really need helpppp
1. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
Answers
Answer:
y= x + 3
Step-by-step explanation:
we know that
The linear equation in slope-intercept form is equal to
y= mx + b
where
m is the slope
b is the y-intercept
step 1:
Find the slope
Take two points from the graph
see the attached figure
about (37,40) and (47,50)
The formula to calculate the slope between two points is equal to: y2-y1
x2-x1
substitute
M= 50-40/47-37
10/10 = 1
step 2:
Find the y-intercept
we have: m=1
point (37,40)
substitute in the linear equation: 40= (1) (37) + b
solve for b: 3
therefore
The linear equation is: y = x + 3
Find each measure
Please help me
Answers
Answer:
11:90
12: 90
13: 90
14:90
15:180
16: 135
17:225
Step-by-step explanation:
I don't know if this is entirely true but I hope it helps
Find cos R.
A. cos R =29/21
B. cos R =21/20
C. cos R =21/29
D. cos R =20/29
Answers
Answer:
The answer is 12 %R
Step-by-step explanation:
Answer:
[tex]\text{C. }\cos R=21/29[/tex]
Step-by-step explanation:
In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse.
From the diagram, we know:
Angle R's adjacent side is 21The hypotenuse (longest side) of the right triangle is 29Therefore, the cosine of angle R must be [tex]\boxed{\frac{21}{29}}[/tex]
Find the area of the parallelogram
Answers
Answer:
32
Step-by-step explanation:
8x4=32
Answer:need more time to solve-
Step-by-step explanation: A= b x h
Express as a trinomial.
(2x-6)(2x-8)
Answers
Answer:
192
Step-by-step explanation:
calculator
What is the measure of angle ABC?
Answers
Answer:
the answer is already in the question
D. 130°
D. 130
Jimmy has a 4-kilometer head start on Higgs. How long will it take Higgs to catch Jimmy if Jimmy travels at 6 kilometers per hour and Higgs travels at 8 kilometers per hour?
Answers
Answer:
6x+4 = 8x
4=2x
x=2 hrs
Step-by-step explanation:
The number of students in a geometry class is four
fifths the number of students in a Spanish class.
The total number of students in both classes does
not exceed 54. What is the greatest possible
number of students in the Spanish class?
Answers
Answer:
Step-by-step explanation:
Givens
Let the number in the Spanish Class = x
Then the number in the Geometry Class = (4/5) x
Equation
x + (4/5)x < 54
Solution
x + (4/5)x < 54
4/5 = 0.8
x + 0.8x < 54
1.8x < 54 Divide both sides by 1.8
1.8x / 1.8 < 54/1.8
x < 30
The sign used in the equation is less than, not less than or equal to.
The number of students taking Spanish cannot equal 30. There must be 29 in the Spanish Class.
HELP QUICKLY PLEASE!!
Answers
Answer:
D
Step-by-step explanation:
Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect
Find the product of the Mixed numbers.
2 2/3 x 1 1/2
what statemets are correct? Check all that apply.
1. write the mixed numbers as improper fractions
2. multiply the numerators to get 24.
3. multiply the denominators to get 6.
4. write the improper fractions as a mixed number
5. The product is 4.
6. The product is 2 2/5
Answers
Answer:
1., 2., 3., 5.
Step-by-step explanation:
2 2/3 x 1 1/2 =
= (2 * 3 + 2)/3 * (1 * 2 + 1)/2
= 8/3 * 3/2
= 24/6
= 4
Answer:
Write the mixed numbers as improper fractions.
Multiply the numerators to get 24.
Multiply the denominators to get 6.
Write the improper fraction as a mixed number.
The product is 4.
Step-by-step explanation:
the other person is wrong
I purposely got this question wrong so I can see the right answers
these are the correct answers
(edge)
Need help, please answer this
Answers
Answer:
In this exercise we need to solve the equation
3(x-2) = 2x + 6 - 2
We operate the parentheses and the right side
3(x-2) = 2x + 4
3x - 6 = 2x + 4
We add 6 to both sides
3x -6 + 6 = 2x + 4 + 6
3x = 2x + 10
We substract 2x
3x - 2x = 2x + 10 - 2x
x = 10
x = 10
Step-by-step explanation:
A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (-4, 0) and (6.0). The y-intercept of
the first parabola is (0,–12). The y-intercept of the second parabola is (0, -24). What is the positive difference between
the a values for the two functions that describe the parabolas ? Write your answer as a decimal rounded to the nearest
tenth.
Answers
Answer:
∆a = 1/2
Step-by-step explanation:
parabolas cross the x-axis at (-4, 0) and (6, 0)
y = a(x + 4)(x - 6)
At the y-intercept x = 0
y = a(0 + 4)(0 - 6)
y = -24a
-----------------------
y-intercept of the first parabola is (0,–12)
-12 = -24a
a = 1/2
-----------------------
y-intercept of the second parabola is (0, -24)
-24 = -24a
a = 1
----------------------
What is the positive difference between the a values
∆a = 1 - 1/2
∆a = 1/2
Annie invests $400 in a bank that offers 5.5% simple annual interest after 6 years her investment will increase by blank dollars
Answers
Answer:
Her investment will increase by 551.54 dollars
Step-by-step explanation:
So we know that the exponential function formula is f(x)=a(1+r)^x
So knowing that we can input values
So now we have f(x)=400(1+0.055)^6
Since it is annual we will only have the interest yearly so that changes are equation to look like this f(x)=400(1+0.055/1)^6
So next we have to add 1 and 0.055 which is 1.055
So we input that into the equation so now we have f(x)=400(1.055/1)^6
Now we have to do (1.055/1) to the power of six, so we get 1.37884280676
Now we have to 1.37884280676 times 400, which would be 551.537122705.
Assuming they want to the nearest 100th it would be 551.54
So the answer is 551.54 dollars
Hopefully, that helped. If I made any mistake or I am incorrect feel free to correct me. :)
AT first, shop A had 156 kg of rice and shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice left in Shop A was 4 times that of Shop B. How many kilograms of rice did Shop B sell
(Please give an easy method)
Answers
Answer:
44 kg, and since both sold the same amount so did A.
Let me know if this method doesn't make sense though and I should be able to explain it.
Step-by-step explanation:
Both shops sold the same amount, let's call it x.
At the end, let's say shop B had y left, this means A would have 4y left, since the question says "After each shop sold the same quantity of rice, the amount of rice left in Shop A was 4 times that of Shop B"
So this means A started with 156, sold x and was left with 4y, or in math 156 - x = 4y
B you could write 72 - x = y
Now you have a system of equations.
156 - x = 4y
72 - x = y
There are a number o ways to look at this. If you graph them you want the (x, y) coordinates where they intersect, or in other words the x and y values that work for both of these equaions.
The methods all wing up making you solve for one variable and plugging it into the other equation to solve for the other. The easiest method is probably canceling out.
156 - x = 4y
72 - x = y
Now, for these two the goal is to make one of the variables go away by adding or subtracting one equation from the other. You could also multiply one by something. In fact here are all possibilities.
If you subtract one from the other here is what would happen.
156 - x = 4y
-(72 - x = y)
_________
156 - x = 4y
-72 + x = -y because you distribute the minus sign
_________
84 = 3y because 156-72 = 84, -x + x = 0 so they canceled out and 4y - y = 3y
28 = y because you divide both sides by 3.
It's all just algebra after the addition/ subtraction. You could also do it the other way subtracting 156 - x = 4y from 72 - x = y. Either way would cancel the xs. But now that you know y = 28 you can plug that into either of the equations again to find x.
156 - x = 4y
156 - x = 4(28)
156 - x = 112
156 = 112 + x
44 = x
72 - x = y
72 - x = 28
72 = 28 + x
44 = x
Now, if you wanted to cancel the ys initially you would have to multiply.
156 - x = 4y
72 - x = y
Normally subtracting just got rid of the xs. You would need to multiply the bottom one by 4 to get rid of ys.
156 - x = 4y
288 - 4x = 4y
Now if you subtracted one from the other the 4ys would cancel. You could also divide the top one by 4 and get
39 - x/4 = y
72 - x = y
here you have a fraction though and that's gonna make things a little more difficult.
Let me know if this method doesn't make sense though and I should be able to explain it.
If AVB has a measure of 88° and VM is its angle bisector, what is the
measure of AVM?
A. 88°
B. 22°
C. 176°
D. 44
Answers
Answer:
B. 22°
Step-by-step explanation:
Angle bisector divides an angle into two equal angles.
Angle AVM = Angle MVM = Angle AVB / 2
Angle AVM = Angle AVB / 2
Angle AVM = 88 / 4
Angle AVM = 22°
Answer:
44
Step-by-step explanation:
4. Convert 23 miles per hour to kilometers per minute. (1 mile = 1.609 kilometers)
Answers
Answer:
Ewan ko lng po when you find someone ma mas better less sa kanya
EXERCISE 81 Solve each of the following word problems: 1) A triangular shaped roof is 4 metres in all sides. What is its perimeter
Answers
Answer:
12 m/metersStep-by-step explanation:
3 sides= triangle
so.. 4m+4m+4m= 12 meters
product of -2/3 and 5 2/4?
Answers
Answer: [tex]-\frac{11}{3}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{3} *5\frac{2}{4} \\\\\\=-\frac{2}{3} *5\frac{1}{2} (5\frac{1}{2} =\frac{5*2}{2} +\frac{1}{2} =\frac{10+1}{2} =\frac{11}{2})\\\\\\=-\frac{2}{3} *\frac{11}{2} =-\frac{11}{3}[/tex]
Find the area.
A hexagon with side length 6m.
Answers
Answer:
93.53m.
Step-by-step explanation:
.
Manny’s bedroom door is 9 feet tall and 3 feet wide. a new door would cost $1.00 per square foot. how much would a new bedroom door cost in total?
Answers
Answer:
It will cost a total of $27.00.
Step-by-step explanation:
Manny's bedroom door is 9 feet tall and 3 feet wide.
The new door costs $1.00 per square foot.
And we want to find the total cost of the new door.
Since the door is a rectangle 9 feet tall and 3 feet wide, its total area is:
[tex]\displaystyle 9\cdot 3 = 27\text{ ft}^2[/tex]
And since it costs $1.00 per square foot, we can simply multiply it to the total area. Hence:
[tex]\displaystyle 27\text{ ft}^2\cdot \frac{\$ 1}{\text{ ft}^2}=\$27.00[/tex]
It will cost a total of $27.00.
Answer:
A new bedroom door costs $27.00
Step-by-step explanation:
The bedroom door mentioned here is in a rectangular shape. That is commonly used in these type of questions:
The area of a rectangle is length x width:
9 feet x 3 feet = 27 square feet
If a new door would cost $1.00 per square feet, the total cost will be the area of the door times $1.00:
27 x 1 = 27
Therefore a new door would cost $27.00
Hope this helps