Part A
Each triangle shown is a 45-45-90 triangle. The numbers refer to the angle measures. These types of triangles are known as isosceles right triangles.
The two legs of these triangles are the same length. So for this specific triangle, the two legs are 28 units each.
The hypotenuse can be found using the pythagorean theorem
\(a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\m = \sqrt{28^2+28^2}\\\\m = \sqrt{2*28^2}\\\\m = \sqrt{2}*\sqrt{28^2}\\\\m = \sqrt{2}*28\\\\m = 28\sqrt{2}\\\\\)
We can avoid using the pythagorean theorem by remembering the rule that the hypotenuse is exactly sqrt(2) times that of either leg length.
\(\text{hypotenuse} = \text{leg}*\sqrt{2}\)
This shortcut only applies to 45-45-90 triangles.
Answer: \(m = 28\sqrt{2}\)
=============================================================
Part B
Again we can use the pythagorean theorem to find the missing variable.
\(a^2+b^2 = c^2\\\\t^2+t^2 = 24^2\\\\2t^2 = 576\\\\t^2 = 576/2\\\\t^2 = 288\\\\t = \sqrt{288}\\\\t = \sqrt{144*2}\\\\t = \sqrt{144}*\sqrt{2}\\\\t = 12\sqrt{2}\\\\\)
Or we could follow the steps like this
\(\text{hypotenuse} = \text{leg}*\sqrt{2}\\\\\text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}}\\\\\text{t} = \frac{24}{\sqrt{2}}\\\\\text{t} = \frac{24\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\text{t} = \frac{24\sqrt{2}}{2}\\\\t = 12\sqrt{2}\\\\\)
The second set of steps only apply for 45-45-90 triangles.
Answer: \(t = 12\sqrt{2}\\\\\)
=============================================================
Part C
Like mentioned earlier, the two leg lengths are the same.
Therefore, \(b = \frac{9\sqrt{2}}{2}\)
=============================================================
Part D
Multiply the leg lengths by the factor sqrt(2) to determine the hypotenuse
\(\text{hypotenuse} = \text{leg}*\sqrt{2}\\\\\text{J} = 30\sqrt{2}*\sqrt{2}\\\\\text{J} = 30*2\\\\\text{J} = 60\\\\\)
Or you could use the pythagorean theorem as an alternative route.
60 POINT QUESTION. Middle school math, ordered pairs.
Answer:
(0,2)
(3,0)
Step-by-step explanation:
Hello!
I am here with a few geometry questions today.
For these 3 problems the answer is true or false.
When you answer this question please be sure to explain your answer and show work.
Good luck! Have a great day!
Answer:
True, True, FalseStep-by-step explanation:
The triangle ACB is isosceles as AC = BC
CQ is the perpendicular bisector of angle C.
The first two choices are true.
Lets verify the third one:
m∠QCB = m∠QCA3x + 7 = 4x - 84x - 3x = 7 + 8x = 15m∠QCB = 4*15 - 8 = 52° ≠ 26°
This is false
Answer:
True, true, and then false.
Step-by-step explanation:
For the first one, line CQ does bisect angle ACB. Bisect means to cut in half or split directly down the middle.
For the second one, CQ is perpendicular. You know when an angle is perpendicular by the 90° right angle (or small square in the corner).
Finally, the last problem you just have to simplify and add up all the angles in one half of the triangle. If you do add them up, angle QCB is not 26°.
I hoped this helped you! :D *I AM ALWAYS WILLING TO HELP YOU WITH OTHER PROBLEMS!
With warm regards,
Philip
How much is 1/4 divided buy 3
Answer:
0.0833
Step-by-step explanation:
1/4 divided by 3 = 0.0833
Hope this helps:)
A national grocery store chain designed a study to determine whether its customers would be interested in home delivery. The
chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who
hopped in the chain's stores were interested in the service. What is the sample in the study?
The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.
The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.
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what is the horizontal cross section of the figure shown helpppp ill give brainliest answer
Answer:
Square
Step-by-step explanation:
Probably square
5x - 2y = -15 and 3x + 8y = 37 elimination please
Answer:
the answer is d i took the quiz
Step-by-step explanation:
Anyone know the answer?
Answer:what answer screenshot glitching
Step-by-step explanation:
What number makes the equation true?
+ 13 = 47
Answer:
x=34
Step-by-step explanation:
Just take 47-13=34
How do I solve for this?
A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 5 cycles every second, and the distance between the highest point and the lowest point of the oscillation is 12 cm. Find an equation of the form y = a sin
To find the equation for the simple harmonic motion of a mass suspended from a spring, you need to determine the amplitude (a) and the sine function. The equation is y = a sin (2π/T) t, where T is the period.
Explanation:To find the equation of the form y = a sin for the simple harmonic motion of a mass suspended from a spring, we need to determine the values of a and sin.
The given information states that the mass completes 5 cycles every second and the distance between the highest point and the lowest point of the oscillation is 12 cm. The period (T) of one cycle can be calculated by dividing 1 second by the number of cycles per second. In this case, T = 1/5 = 0.2 seconds. The amplitude (a) is half of the total distance between the highest and lowest points, which is 12 cm. Therefore, a = 12/2 = 6 cm.Now we can plug these values into the equation
y = a sin (2π/T) t,
where
T is the period t is the time.So, the equation for the simple harmonic motion is y = 6 sin (2π/0.2) t.
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understanding graphs of exponential functions
The value of b in the exponential function is between 0 to 1.
We have,
In the exponential function y = b^x, b is the base of the exponential function. It is a positive constant that is raised to the power of x to obtain the value of y.
The base b can be any positive real number except for 1, and it determines the shape and behavior of the exponential function.
For example,
If b is greater than 1, the function will be an increasing exponential function, while if b is between 0 and 1, the function will be a decreasing exponential function.
The larger the value of b, the steeper the exponential function will be.
We see that
y is decreasing when x is increasing.
This means,
The function is a decreasing exponential function.
So,
The value of b is between 0 to 1.
Thus,
The value of b in the exponential function is between 0 to 1.
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when a relation is drawn on an xy-plane what is another name for the set of all x values from its graph
When a relation is drawn on an xy-plane, another name for the set of all x values from its graph is a function.
What is a function?It should be noted that a function simply means an expression or rule that defines a relationship between variables.
In this case, when a relation is drawn on an xy-plane, another name for the set of all x values from its graph is a function.
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HELPPPP IF YOU CAN pls?
Answer:
i'm not sure but here's some encouragement- YOU CAN DO IT
Step-by-step explanation:
zalman started solving 53 times 26 by breaking the problem into parts. Here is what he has done so far 50 times 20=1000 50 times 6=300 3 times 20= 60 what does he still need to multiply
Answer:
3 * 6 = 18
Step-by-step explanation:
53 * 26 =
= (50 + 3) * (20 + 6)
= 50 * 20 + 50 * 6 + 3 * 20 + 3 * 6
= 1000 + 300 + 60 + 18
Answer: 3 * 6 = 18
T
What is the domain of the equation that is graphed?
(-9,)
(-3, 16)
• (-0,16)
15
(-7,1)
(-0,-7) and (1...)
O (-0,3)
10
0 (-3,00)
(0,7)
(-7,0)
(1.0)
- 10
Answer:
Step-by-step explanation:
(-9,)
(-3, 16)
• (-0,16)
Solve the following differential equations:
The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
How to explain the equationBased on the information, dy/dx + 3y = 2x³ e^(-3x)
The integrating factor is e^(∫3 dx) = e^(3x),
e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)
d/dx (e^(3x) y) = 2x^3
e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C
C is an arbitrary constant of integration.
y = (1/2) x^4 e^(-3x) + C e^(-3x)
The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
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What is a decimal that is equivalent to the fraction
52/100
Answer:
52/100 as a decimal is 0.52.
Step-by-step explanation:
= 52 ÷ 100 = 0.52
The algebra tiles represent the perfect square trinomial x2 + 10x + c.
What is the value of c?
c =
HELP ME PLEASE, YOU WILL GET 100 points
Answer:
I believe that it is the first one. N+89=12.
the answer is 89-n=12
100 Points! Algebra question. Graph the function. Photo attached. Thank you!
The cost of each pound of grass seed is $6.
A graph of the solution for the cost of each pound of grass seed is shown below.
How to determine the cost of each pound of grass seed?In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.
Let the variable x represent the cost of each pound of grass seed.
Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;
3.6x + 1.30 = 22.90
3.6x = 22.90 - 1.30
3.6x = 21.60
x = 21.60/3.6
x = $6.
In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.
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Please look at the photo. Thank you!
The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x
How to calculate the composite functionsFrom the question, we have the following equations that can be used in our computation:
h(x) = x² + 3
f(x) = 3/4x
From the above, we have
(h o h)(x) = h(h(x))
So, we have
(h o h)(x) = (x² + 3)² + 3
Also, we have
(f o f)(x) = 3/[4(3/4x)]
Evaluate
(f o f)(x) = x
Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x
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explain 3 factors that should be considered in the construction of index numbers
1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.
2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.
3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`
construction of index number is also available in two parts:
1. simple
2. weighted
1. simple: the simple method is classified into simple aggregative and simple relative.
2. weighted: the weighted method is classified into a weighted aggregative and weighted average.
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HELP PLEASE THIS IS DUE IN 5 MINUTES
Answer:
Part A:
Since Jasmine has more cousins rhan Brenda, who has 4 cousins, then the amount of cousins that Jasmine has (j) is greater than 4 so j > 4
Part B:
We have a number line and we draw an arrow starting from 4 and going to the right.
Hope this helped!
Answer:
4.8h - 2.3d - 14
Step-by-step explanation:
Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the function.
f(x) = -2(x - 5)(x-7)
The vertex (3, -16) is the maximum point on our quadratic equation.
Maximum and minimum values of the function:When we compare the given Quadratic function with the general form
ax² +bx +c,
If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.
If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.
Here we have
f(x) = -2(x - 5)(x-7)
f(x) = -2 [x²-7x - 5x + 35 ]
f(x) = -2 [x²-12x + 35 ]
f(x) = -2x² + 12x - 35
Compare f(x) with ax²+ bx + c
=> a = -2, b = 12, and c = - 35
Here,
a = -2 is a negative value then the function f(x) will have maximum value
And the graph of the function opens down.
The formula for the x coordinate of the vertex = -b/2a
The coordinate of x = -(12)/2(-2) = 3
Now substitute x = 3 in f(x) to find y-coordinate
=> f(3) = - 2(3)² +12(3) - 35
=> f(3) = -2(9) + 36 - 35
=> f(3) = - 16
Therefore, y-coordinate = -16
Therefore,
The vertex (3, -16) is the maximum point of the quadratic equation.
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How many elements are there in this set: {red, orange, yellow, green, blue, indigo, violet}?
income from operations of $231,000. In addition, it received interest income of $23,100 and received dividend income of $29,700 from another corporation. Finally, it paid $11,000 of interest income to its bondholders and paid $45,000 of dividends to its common stockholders. The firm's federal tax rate is 21%. What is the firm's federal income tax? Do not round intermediate calculations. Round your answer to the nearest dollar.
The firm's federal income tax is $57,168.
To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.
In this case, the firm's total income consists of income from operations, interest income, and dividend income.
Total income:
Income from operations = $231,000
Interest income = $23,100
Dividend income = $29,700
Total income = $231,000 + $23,100 + $29,700 = $283,800
Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:
Total expenses = Interest paid to bondholders = $11,000
Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800
Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:
Federal income tax = Taxable income * Federal tax rate
Federal income tax = $272,800 * 0.21 = $57,168
Therefore, the firm's federal income tax is $57,168.
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Select the correct statement.
a.)
With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.
b.)
With a p-value of 0.03 and a significance level of 6%, you failed to reject the null hypothesis.
c.)
With a p-value of 0.01 and a significance level of 3%, you failed to reject the null hypothesis.
d.)
With a p-value of 0.02 and a significance level of 5%, you failed to reject the null hypothesis.
The correct statement regarding p-values and decision of the hypothesis is given by:
c.) With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.
Given that;
To find the correct statement regarding p-values and decision of the hypothesis
Since, Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.
If it is less, it is rejected.
Hence the correct statement for this problem is given by:
c.) With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.
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Pam and Tina went for a 12 mile hike (round trip) to the top of a mountain. It took 5 hours. They were able to hike 1 mile per hour faster on the way down. How fast did they hike going up the mountain
Answer:
2 mph
Step-by-step explanation:
The relationship between time, speed, and distance is ...
time = distance/speed
If s is the speed going up the mountain, then s+1 is the speed coming down. The total trip time for 6 miles up and 6 miles down is ...
6/s +6/(s+1) = 5
6(s+1) +6s = 5(s)(s+1)
5s^2 -7x -6 = 0 . . . . subtract the left side, simplify to standard form
(s -2)(5s +3) = 0 . . . . factor
s = 2 or -3/5 . . . . values that make the factors 0
Their speed was 2 miles per hour going up the mountain.
__
Check
It took 6/2 = 3 hours to go up the mountain, and 6/(2+1) = 2 hours to come down, for a total of 5 hours.
help mee please i need help
Answer:
this hard
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Which is the graph of f(x) =3 sqrtx/4?
Step-by-step explanation:
f(x) = 3√x /4
x=0 => y = 0
x=1 => y = 0.75
x=4 => y = 1.5 ==> (4, 1.5)
x=16=>y= 3
the right answer is the second graph
HELPPPPPPPPPPPPPPPPPPPPPPp
Answer:
162
Step-by-step explanation:
to find the surface area of the rectangles do base x height
5 x 10 = 50
there are 3 sides on a triangle so do 50 x 3 = 150
now we need to find the area of the triangles
the formula for the surface area would be base x height ÷ 2
3 x 4 = 12
12 ÷ 2 is 6
because there are 2 triangles you would need to multiply it by 2
6 x 2 is 12
add it all together
12 + 150 is 162