Your friend is making a pattern for quilt pieces. Her pattern is a right angle with two acute angles that complementary. The measure of one of the angles is to be 12° more than half the measure of the other angle. Find the measure of each angle of the triangle. Show your work using the format above.
Answers
Answer:
The measure of angle 1 is 52° and the measure of angle 2 is 38°
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x ----> the measure of angle 1
y ----> the measure of angle 2
we know that
[tex]x+y=90\°[/tex] -----> equation A
[tex]y=\frac{x}{2}+12[/tex] ----> equation B
Substitute equation B in equation A and solve for x
[tex]\frac{x}{2}+12+x=90\°[/tex]
[tex]\frac{x}{2}+x=90\°-12\°[/tex]
[tex]\frac{3x}{2}=78\°[/tex]
[tex]x=(2)78/3=52\°[/tex]
Find the measure of y
[tex]y=\frac{52}{2}+12=38\°[/tex]
therefore
The measure of angle 1 is 52° and the measure of angle 2 is 38°
The two acute angles in the triangle are 52° and 38°. This is found by setting up and solving two equations based on the problem's conditions.
Explanation:This question is about solving an equation related to two acute angles in a triangle. Let's denote the smaller angle as 'x' and the larger angle as 'y'. Since the two angles are complementary, we can write an equation like 'x + y = 90'. The problem states that one angle is 12° more than half the other. We can formulate this as 'y = x/2 + 12'. To solve for 'x' and 'y', we need to substitute 'y' from the second equation into the first one to get 'x + x/2 + 12 = 90'. Multiplying through by 2 to eliminate the fraction gives '2x + x + 24 = 180', which simplifies to '3x = 156'. Solving for 'x' gives 'x = 52'. Substitute 'x' into either of the original equations gives 'y = 52/2 + 12 = 38'. Thus, the two acute angles in the triangle are 52° and 38°.
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Related Questions
Show all work to multiply
Answers
Answer:
-42+10i
Step-by-step explanation:
*start with the square roots
\sqrt{-25} \\ =5i
\sqrt{-100} \\ = 10i
*then insert values
(2+5i)(4-10i)
*Use FOIL to multiply
2x4 + 2x-10i + 5ix4 + 5ix10i
*Simplify
8-10i+20i+50i(squared)
*Add like terms
-42+10i
*( i squared = -1 )
What is the equation of the least squares regression line for the data set?
Answers
Answer:
y = 1.862x − 0.138
Step-by-step explanation:
The equation of the least squares regression line is ŷ = -173.51 + 4.83x.
Explanation:The equation of the least squares regression line for a data set is represented as ŷ = a + bx, where a is the y-intercept and b is the slope of the line. To calculate the values of a and b, you minimize the sum of squared errors (SSE). Using calculus, you can determine the values that make SSE a minimum. In this case, the equation of the least squares regression line is ŷ = -173.51 + 4.83x.
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Need help answering this!
Answers
Answer:
Wrong
Step-by-step explanation:
Since 54 / 12 is 4.5
Answer:
Step-by-step explanation:
the answer is b
Find the slope and y-intercept of the line that is y=−2/3x+5 and passes through the point (−6,4)
Answers
Use the point-slope formula.
y - y_1 = m(x - x_1)
y - 4 = (-2/3)(x + 6)
y - 4 = (-2/3)x - 4
y = (-2/3)x - 4 + 4
y = (-2/3)x + 0
y = (-2/3)x
Slope = -2/3
y-intercept = 0, which means the x-axis.
Find the area of the shaded region. All angles are right angles.
Answers
Answer: 147
Step-by-step explanation:
First, 9 x 4 = 36
Again, 9 x 4 = 36
Finally 15 x 5 = 75
So, 36 + 36 + 75 = 147
PLEASEEEE ASAPP
what is g(2) = 3(2)^2 - 5(2) + 5
Answers
Answer:
Step-by-step explanation:
[tex]g(x) = 3x^{2} - 5x + 5[/tex]
[tex]g(2) = 3(2^{2}) - 5(2) + 5[/tex]
[tex]g(2) = 3(4) - 10 + 5[/tex]
[tex]g(2) = 12 - 10 + 5[/tex]
[tex]g(2) = 7[/tex]
G(2)=3(4)-10+5
G(2)=12-10+5
G(2)= 7
Kendra wants to know the average height of the 30,000 ninth grade students in Florida. She randomly selects 1,000 ninth graders in Florida, assuring that the group accurately represents all ninth grade students in Florida. Kendra finds their average height to be 65 inches. What assumption can be made regarding the approximate average height of all ninth grade students in Florida?
Answers
No assumptions can be made regarding the average height of ninth grade students in Florida because there is not enough information.
B.
The approximate average height of ninth grade students in Florida is greater than 65 inches.
D.
No assumptions can be made regarding the average height of ninth grade students in Florida because the sample size is too small.
Based on Kendra's random selection of 1,000 ninth graders in Florida and finding their average height to be 65 inches, we can make the assumption that the approximate average height of all ninth-grade students in Florida is close to 65 inches.
We have,
The assumption is based on the principle of random sampling, where a representative sample from a larger population can provide valuable insights into the characteristics of the entire population.
By randomly selecting 1,000 ninth graders, Kendra aimed to ensure that the group accurately represents all ninth-grade students in Florida.
While there might be some variation or margin of error, the average height of the sampled group can provide a reasonable estimate of the average height of all ninth-grade students in Florida.
Therefore,
Based on the random sample, we can assume that the approximate average height of all ninth-grade students in Florida is around 65 inches.
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A printer cartridge with 2 1 ⁄2 milliliters of ink will print off 2 ⁄3 of a box of paper. How many milliliters of ink will it take to print an entire box?
Answers
Answer:
3 3/4 mls ink.
Step-by-step explanation:
2/3 of a box corresponds to 2 1/2 mls of ink
So one box .............................. 2 1/2 / 2/3 = 5/2 / 2/3
= 5/2 * 3/2
= 15 / 4
= 3 3/4 mls ink.
It would take approximately 3.75 milliliters of ink to print off an entire box of paper. This is based on the given that 2.5 milliliters prints off 2/3 of a box and the conversion to a full box.
Explanation:The question is asking about the amount of ink it will take to print an entire box of paper. We are given that a printer cartridge with 2.5 milliliters of ink will print off 2⁄3 of a box of paper. So, if 2.5 ml prints 2⁄3 of a box, we want to find out how much ink prints 1 full box. This is a simple ratio question.
Set up the ratios like this: 2.5 ml (ink) / (2⁄3 box) = X ml (ink) / (1 box) Simplifying this, you find that X = 2.5 ml / 2⁄3, which, when calculated, equals approximately 3.75 ml. This means it will take approximately 3.75 milliliters of ink to print off an entire box of paper.
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what is the slope of the line that passes through the points (-8,-6) and (-18,6)? write your answer in simplest form.
Answers
Slope = -6/5
Work is provided in the image attached.
The slope of the line passing through the given points is -6/5.
Explanation:The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1).
In this case, the coordinates of the two points are (-8, -6) and (-18, 6). Applying the formula, we have: m = (6 - (-6)) / (-18 - (-8)) = 12 / (-10) = -6/5.
Therefore, the slope of the line that passes through the points (-8, -6) and (-18, 6) is -6/5.
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Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change. How much did each avocado cost if they are each the same amount?
Answers
Answer:
$1.10
Step-by-step explanation:
We have been that Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change.
First of all, we will find amount paid for 5 avocados by subtracting $4.50 from $10.
[tex]\text{Amount paid for 5 avocados}=\$10-\$4.50[/tex]
[tex]\text{Amount paid for 5 avocados}=\$5.50[/tex]
Now, we will divide $5.50 by 5 to find cost of each avocado.
[tex]\text{Cost of each avocado}=\frac{\$5.50}{5}[/tex]
[tex]\text{Cost of each avocado}=\$1.10[/tex]
Therefore, the cost of each avocado is $1.10.
Consider the quadratic function:
f(x) = x2 – 8x – 9
Vertex: (StartFraction negative b Over 2 a EndFraction, f (StartFraction negative b Over 2 a))
What is the vertex of the function?
(
,
)
Answers
Answer:
vertex = (4, - 25 )
Step-by-step explanation:
Given a quadratic function in standard form : f(x) = ax² + bx + c : a ≠ 0
The the x- coordinate of the vertex is
[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 8x - 9 ← is in standard form
with a = 1, b = - 8, thus
[tex]x_{V}[/tex] = - [tex]\frac{-8}{2}[/tex] = 4
Substitute x = 4 into f(x) for corresponding value of y
f(4) = 4² - 8(4) - 9 = 16 - 32 - 9 = - 25
vertex = (4, - 25 )
Answer:
vertex is (4,-25)
Step-by-step explanation:
[tex]f(x) = x^2 - 8x - 9[/tex]
To find out the vertex we use formula
[tex]x=\frac{-b}{2a}[/tex]
From the given f(x), the value of a=1, b=-8 and c=-9
Plug in the values in the formula
[tex]x=\frac{-(-8)}{2(1)}[/tex]
x=4
Now find the value of y
plug in 4 for x in f(x)
[tex]f(4) = 4^2 - 8(4)- 9=-25[/tex]
The value of y is -25
The vertex is (4,-25)
A restaurant has 36 tables. If each can sit five people, how many can be seated at the restaurant?
Answers
Answer:
180 people
Step-by-step explanation:
If there are 5 people for each table and there are 36 tables, so then you would need to multiply 36 by 5, because you wouldn't want to add 5 people 36 times lol, so then when you multiply them together, you would get 180 people in total in the restaurant. :-)
hope this helped! ♡
Ramona and Josh and money by babysitting the amount of food for one evening or shown on the table and graph to charge per hour
Answers
Answer:
Where's the table and graph?
Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.
Which statements describes how the location of segment EG affects the area of EFGH?
A.) the area of EFGH is 1/4 of the area of the rectangle if E and G are not midpoints
B.) The area of EFGH is 1/2 of the area of the rectangle only if E and G are midpoints
C.) The area of EFGH is always 1/2 of the area of the rectangle.
D.) The area of EFGH is always 1/4 of the area of the rectangle.
Answers
Answer:
C
Step-by-step explanation:
EFGH is a kite, so EF ≅ FG and EH ≅ HG.
The area of the kite consists of two area of triangles EFG and EHG.
1. Area of triangle EFG:
[tex]A_{\trangle EFG}=\dfrac{1}{2}\cdot EG\cdot h,[/tex]
where h is the height drawn from point F to the side EG.
1. Area of triangle EHG:
[tex]A_{\trangle EHG}=\dfrac{1}{2}\cdot EG\cdot H,[/tex]
where H is the height drawn from point H to the side EG.
3. Note that
[tex]EG \cong \text{rectangle's length}[/tex]
[tex]h+H\cong \text{rectangle's width}[/tex]
So,
[tex]A_{\text{kite }EFGH}\\ \\=A_{\triangle EFG}+A_{\triangle EHG}\\ \\=\dfrac{1}{2}\cdot EG\cdot (h+H)\\ \\=\dfrac{1}{2}\cdot \text{rectangle's length}\cdot \text{rectangle's width}\\ \\=\dfrac{1}{2}A_{\text{rectangle}}[/tex]
Thus, option C is true (the area of the kite doesn't depend on ratio in which points E and G divide the side)
Answer:
C.) The area of EFGH is always 1/2 of the area of the rectangle.
Step-by-step explanation:
find an equation of the line that passes through the point (3,-1) and is perpendiculor to line with slope -1/2
Answers
Answer:
perp. 2
y + 1 = 2(x - 3)
y + 1 = 2x - 6
y = 2x - 7
What is 15 divided by 1/5?
Answer this ASAP THIS IS URGENT AND REALLY EASY BUT I AM DUMB AND DONT KNOW THE ANSWER SO PLEASE HELP ME ON THIS IMMEDIATELY THIS IS VERY IMPORTANT!!!!!!!!!!!!
Answers
Answer:
75
Step-by-step explanation:
Answer:75
Step-by-step explanation:
1/5=.2
15/.2=75
❗❗❗❗❗❗❗HELP❗❗❗❗❗❗❗
Select the table of values where the quadratic function changes direction at a different value of x than the others.
Imagine that this is a graph.
A.
x -3 -2 -1 0 1 2 3
y 2 3 2 -1 -6 -13 -22
B.
x -3 -2 -1 0 1 2 3
y 2 3 2 -1 -6 -13 -22
C.
x -3 -2 -1 0 1 2 3
y 4 3 4 7 12 19 28
D.
x -3 -2 -1 0 1 2 3
y 1 -1 1 7 17 31 49
Answers
D,the quadratic function turning point is (-2,-1) while the other graphs change direction at (-2,3)
Step-by-step explanation:
The point where the graph of a quadratic function changes direction is called a turning point.This is the point where the curve changes to face up or down according to the function.The functions in A,B and C have a common turning point (-2,3) that also appears in the table.The function in D has a turning point at (-2,-1) that is different from the other three functions.
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3. Students in a sixth-grade class were asked which team was their favorite. The results are shown in the table. Find the ratio of students who preferred the Buccaneers to the total number of responses.
Answers
Answer:
37:103
Step-by-step explanation:
First, you have to identify how many people preferred the Bucaneers. That would be 74.
Secondly, you have to figure out the total number of responses. To do this, you add up ALL of the responses. They key word TOTAL is telling you this.
Thirdly, you write it as a ratio. This can be with the two numbers side by side, a fraction, or in a written response.
Lastly, you simplify your final answer.
Hope this helped!
Please help me I don't know
Answers
factorise 3×15×1/15
Answers
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
[tex]3.15.\frac{1}{15}\\\\3.\frac{15}{15}\\\\3.1\\\\3[/tex]
What is the answer to 5-1/3n=-2
Answers
Answer:
21 = n
Step-by-step explanation:
[tex]5 - \frac{1}{3}n = -2[/tex]
-5 - 5
________________
-⅓n = -7
____ __
-⅓ -⅓
21 = n
* Dividing by a fraction is the exact same as multiplying by its multiplicative inverse:
[tex]\frac{-7}{-\frac{1}{3}} = -7 \times -3 = 21[/tex]
I am joyous to assist you anytime.
What is the value of x?
12 units
15 units
20 units
24 units
Answers
Answer:
Answer: The value of x is 15 units. Step-by-step explanation: In the given triangle RSQ and ΔRST it is given that. ∠RTS ≅ ∠SRQ ≅ 90°.
Step-by-step explanation:
Answer:
20 units
Step-by-step explanation:
I got it wrong with 15 for the cumulative exam on EDGE 2020/2021
Find the first and second derivative of the function defined by the parametric equation.
x = 3e and y= 3^3t - 1
Answers
Answer:
Step-by-step explanation:
Given two parametric equations [tex]x(t)[/tex] and [tex]y(t)[/tex], the first derivative can be found using the following equation:
[tex]\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
In this problem, [tex]x(t) = 3e[/tex] and [tex]y(t) = 3^{3t} - 1[/tex]. Finding the derivative of each of these functions with respect to [tex]t[/tex] gives us the following:
[tex]\frac{dx}{dt} = 0[/tex]
[tex]\frac{dy}{dt} = 3^{3t + 1}\log{3}[/tex]
Because [tex]\frac{dx}{dt} = 0[/tex], that means the function is a vertical line and has an infinite first derivative.
Final answer:
The first derivative of the x-component is zero, and the first derivative of the y-component is 27. The second derivatives of both components are zero.
Explanation:
To find the first and second derivatives of the function defined by the parametric equation, we need to differentiate each component with respect to the parameter (in this case, t). Let's start with x = 3e, which is a constant, so its derivative is zero. Next, let's differentiate y = 3^3t - 1. The derivative of 3^3t with respect to t is (3^3)(1) = 27, and since the derivative of -1 with respect to t is 0, the y-component's derivative is 27.
Now, to find the second derivative, we differentiate the derivatives we found. The second derivative of x is still zero since the first derivative is zero. The second derivative of y (27) is also zero since it is a constant. Therefore, the first and second derivatives of the parametric equation are dx/dt = 0 and dy/dt = 27, respectively.
(20 POINTS PLZ HELP!!) plz answer all questions
(question A) What is the absulote value of |-10 + -4|
(question B) what is the absolute value of |5+2|
(question C) what is the absolute value of |--8.7|
(question D) what is the absolute value of -|-9.2|
Answers
Answer:
answer to question a is -14
answer to question b is 10
answer to question c is -56
answer to question d is -18
Step-by-step explanation:
Answer:
The answer to your question is below
Step-by-step explanation:
Absolute value of a number, is the value without considering its sign. For example, when we measure distance, we do not say -50 meters, we say "50 meters" because for distance, do not exist negative values.
(A) What is the absolute value of |-10 + -4|
| - 10 + -4| = | - 10 - 4| = | - 14 | = 14
(B) what is the absolute value of |5+2|
| 5 + 2 | = |7| = 7
(C) what is the absolute value of |--8.7|
| - - 8.7 | = | 8.7 | = 8.7
(D) what is the absolute value of -|-9.2|
- | - 9.2 | = - 9.2
WENDYS PAY IS $423.00 19% OF THAT IS SUBTRACTED FOR TAXES HOW MUCH IS LEFT AFTER PAYING TAXES
Answers
Answer:
$342.63
Step-by-step explanation:
0.19 * 423 = 80.37
423 - 80.37 = 342.63
Can u help me to simplify this expression 36+6÷3+2
Answers
Answer: 40
Step-by-step explanation: You need to divide first because of the order of operations. This gives you 36+2+2, which is 40
Answer:
The correct answer is 40
Step-by-step explanation:
When solving use PEMDAS
"Please excuse my dear aunt sally"
there are no parentheses or exponents so look for and multiplication or division and you see that there is division so solve:
6÷3 = 2
Then look for addition or subtraction and solve:
36+2+2=40
the answer is 40.
Have a blessed day.
what is the value of the expression -2(3x-2)+x+9 when the x=-3?
Answers
-2(-9-2)+(-3)+9
22-3+9
19+9
28
Brainliest please? Thanks! ❤️
Value of expression at x = -3 is 28.
What is linear equations?All the mathematical equations which have any variable and constant in them are linear equations where variables are not fixed.
Given expression -2(3x-2)+x+9 at x=-3
simplify equation
-6x+4+x+9 = -5x+13
substitute x= -3
-5(-3)+13 = 15+13= 28
Hence the value at x= -3 is 28
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Three brothers earn money by doing yard work. The brothers split the money equally. Write an expression that describes how much money each brother earns.
Answers
Answer:
m/3
Step-by-step explanation:
lets say they earn $600
we will use the variable m
m=money
so....
m/3
is your answer
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
Answers
X+6=0
X=-6
(-6,0)
X-3=0
X=3
(3,0)
can someone help me solve this?
Answers
1.8
to find the circumference of a circle you have to multiple the diameter by pi (3.14). so if you have the circumference already just switch around the equation (since you don’t know the diameter) to 10.99 divided by 3.14 to find the diameter and you get 3.5. but thats the diameter and you have to find the radius so divide 3.5 by two and you get 1.75 and 1.75 rounded to the nearest tenths is 1.8
Answer is provided in the image attached.