Based on the definition of supplementary angles, the measure of both angles are: 80° and 100°.
What are Supplementary Angles?The sum of angles that are supplementary to each other equals 180 degrees.
Let the measure of the supplementary angle be x.
The other angle will be: x + 20.
(x + 20) + x = 180
x + 20 + x = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80°
The other angle will be x + 20 = 80 + 20 = 100°.
The measure of the angles are: 80° and 100°.
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The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2+4x-60. The cost, in dollars, of producing the toy cars can be modeled by 3X2-x+ 200. The number of toy cars sold is represented by X
The equation that represents the profit function is P(x) = 5x - 260
How to determine the profit function?The given parameters are:
C(x) = 3x^2 - x + 200 --- cost function
R(x) = 3x^2 + 4x - 60 --- revenue function
The profit function is calculated as:
P(x) =R(x) - C(x)
This gives
P(x) = 3x^2 + 4x - 60 - 3x^2 + x - 200
Evaluate the like terms
P(x) = 5x - 260
Hence, the equation that represents the profit function is P(x) = 5x - 260
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One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the length of the hypotenuse.
In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearesttenth of a cm, how long is that leg?
Evaluate: sin (Arccos(5/13))
Evaluate: tan(Arctan(π/6))
1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,
[tex]x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}[/tex]
This means that the length of the hypotenuse is:
[tex]\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}[/tex]
2) (Diagram attached) We know that
[tex]\cos 51^{\circ}=\frac{x}{58}\\x=58 \cos 51^{\circ} \approx \boxed{36.5}[/tex] (in cm)
3) From the Pythagorean identity,
[tex]\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}[/tex]
4) [tex]\frac{\pi}{6}[/tex]
A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
d=√(-4-42.78)^2 + (3-44.78)^2
The expression is equal to 3sqrt(517)/5
write an even number between 7 and 16 draw a picture and then write a sentence to explain why it is an odd number
Answer: An even number between 7 and 16 would be 10.
Step-by-step explanation: I am not sure how I am supposed to draw a picture of the number other than drawing the number itself. However, 10 is an even number because it is a composite number and is divisible by 2. 10 is an even number, not an odd number. Hope this helps!
the number of keys on the keyring minus 2
Translating the given phrase into a variable expression is equal to k - 2.
What is a variable expression?A variable expression refers to a mathematical equation which can be used to show the relationship that exist between a numerical quantity and a variable.
Next, we would translate the given phrase into a variable expression as follows:
Let the number of keys on the keyring be k.
Therefore, the variable expression is equal to k - 2.
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Complete Question:
Translate the phrase into a variable expression. Use the letter k to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.
The number of keys on the keyring minus 2?
If you can please give me a step by step explanation
Step-by-step explanation:
4(y+8)=9
for this sum first we need to multiply 4to y and 4 to 8
4y+32=9
then u need to -9 from both sides
4y=23
y=23/4
u will get the answer
what's a quarter of 46.5
Answer:
11.625 or mixed number form 11 [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
divide 46.5 by 4
which expression is equivalent to (3x² + 3x - 3) - (6x² - 4x - 2)?
Answer:
A. [tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]
Step-by-step explanation:
For this problem, we have to combine like terms.
Let's look at the equation:
[tex](12x^{4} -4x^{3} +7x+6)+(3x^{2} -4x+14)[/tex]
[tex]12x^{4[/tex], [tex]-4x^{3}[/tex], [tex]3x^{2}[/tex] do not have any other like terms, so we keep all in the final answer.
[tex]7x[/tex] and [tex]-4x[/tex] are like terms, so we combine them. [tex]7x-4x=3x[/tex]
14 and 6 are like terms, so we combine them. 14+6 = 20
Let's put everything into the final equation:
[tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]
So, the final answer is A. [tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]
Hope this helps! If you have any questions about my work, leave them in the comments below!
Gray can ride his bike 6miles in 20 minutes at this rate how many miles can he ride in 100 minutes
Which newspaper is actually closest to the percentage of voters who support the governor reelection?
No Links Please
The newspaper that is actually the closest to the percentage of voters who support the governor's reelection is the tribune at 71%.
What is the sample size of a population?The sample size (n) is the total number of completed responses gathered from a survey sampling process.
From the given information, using the formula for standard error of a sample proportion:
= √ [p (1-p) / n)]
71% of 1100 of the tribune = 0.0136867% of 900 of the herald = 0.0148381% of 700 of the times = 0.01567Therefore, the sample size of the tribune has the greatest and closest estimate to the actual percentage of voters that supports the governor for reelection,
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Bailey went out to dinner. It cost $ 45.00. He wanted to leave a 20% tip for his waitress. Find the tip.
Answer:
The tip should be $9.00
Step-by-step explanation:
I need help with 7 and 4 and 9 also 10
I will give the most higher points I got
a house and lot cost $120,000. if the house cost 3 times more than the lot, how much did the house cost?
Answer:
$90,000
Step-by-step explanation:
We can can use substitution for this. First, we need to create two separate problems that represent this situation. The house and the lot together cost 120000, so we can make the equation h+l=120000. We also know that the house is worth 3 lots, so we can make the equation h=3l. Because h=3l, we can substitute for h, making the equation 3l+l=120000, or 4l=120000. To isolate l, we have to divide both sides by 4. If we do that, we get l=30000. Now, we have to substitute to find h. Our new equation is h+30000=120000. To isolate h, we have to subtract 30000 from each side. If we do this, we get h=90000. That's our answer.
Hope this helps!
Which polygon is a convex heptagon?
A polygon has 7 sides. No angles go inside of the shape.
A polygon has 8 sides. No angles go inside of the shape.
A polygon has 8 sides. One angle goes inside of the shape.
A polygon has 7 sides. One angle goes inside of the shape.
Option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
As we know, a convex heptagon is a polygon with seven sides, seven internal angles, and seven vertices, which means that a convex heptagon has seven sides.
A convex heptagon is a polygon that has 7 sides. No angles go inside of the shape.
Thus, option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.
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Answer: the first option
Step-by-step explanation:
The length of ribbon A is 56 feet and the length of ribbon B is 59 feet.
The exact length of ribbon C is 34 feet longer than the estimated difference in lengths of ribbon A and B.
What is the length of ribbon C?
Note - Use 0,12 or 1 as benchmarks.
The length of ribbon C is 37 feet.
What is the length of ribbon C?The equation that can be used to determine the length of ribbon C is:
C = 34 + ( length of ribbon B - length of ribbon A)
C = 34 + (59 - 56)
C = 34 + 3
c = 37 feet
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Please help , I litteraly have a F in Math
Answer:
A=3
B=31
Step-by-step explanation:
A)5-2=3
b)
17-10=7
10-5=5
7-5=2
2×7=14
14+17=31
Pls help me with number
Answer:
Total people = 240
Step-by-step explanation:
Let the total number of people by 'x'.
[tex]\sf \text{Number of men =$ \dfrac{1}{4}*x$} \\[/tex]
[tex]\sf \text{Number of women =$\dfrac{1}{3}x$}[/tex]
Number of children = 100
When we subtract the total number of men and women from the total people 'x', we get the number of children.
[tex]\sf x - \left(\dfrac{1}{4}x+\dfrac{1}{3}x\right)= 100\\\\x - \left(\dfrac{1*3}{4*3}x+\dfrac{1*4}{3*4}x\right)=100\\\\[/tex]
[tex]x- \dfrac{4+3}{12}x=100\\\\x - \dfrac{7}{12}x = 100\\\\ \dfrac{12}{12}x-\dfrac{7}{12}x = 100\\\\ \dfrac{5}{12}x=100\\[/tex]
[tex]\sf x = 100*\dfrac{12}{5}\\[/tex]
x = 20 * 12
x = 240
Total number of people = 240Learners have to demonstrate knowledge and skills in calculating quantities
such as mass, length, perimeter, temperature and the volume of objects. When
teaching conversions, emphasis must be placed on multiplication by a
thousand (since "kilo" means thousand) and one thousandth (since "milli"
means one thousandth). Design an instructional activity to explain how you
would teach grade 4 learners the conversion of units when measuring length.
Refer to page 25 of the CAPS document, the second bullet under
‘Calculations and problem-solving involving length’. Your focus should be
on whole number
The instructional activity to explain the conversion will be:
What real-life situations require you to convert measurements from one unit to another?What is the difference between standard and metric measurement? What should the conversion lessons include?The lessons should include:
How to convert within standard units of distance, mass, and timeThe relationship between metric conversions and decimal numbers in the base-ten systemHow to convert metric measurements of distance and mass.Learn more about instructional activity on:
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What is the next number in this sequence?
38 57 76
Answer:
the next sequence is 76+19= 95
Answer:
Next number = 95
Step-by-step explanation:
Hi! Let me help you out.
_________________
To determine the next number in this sequence, we should determine the common difference.
We can do it like this.
[tex]\longmapsto\sf 76-57=19[/tex]
See. I took the third term, and subtracted the second term from it.
Continue.
[tex]\longmapsto\sf 57-38=19[/tex]
↪
The number we obtain after subtracting is the common difference.
So we should take the third term, "76", and add the common difference, "19" to it.
We obtain 95. Which is the final answer.
⇨Hope that this helped you out! have a great day ahead.⇦
Best Wishes!
[tex]\star\bigstar\overline{\textsf{Reach far. Aim high. Dream big.}}[/tex]
◆◈-Greetings!-◈◆
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if a quarter kilogram costs rs 60 then how much will cost for 150 grams
Answer:
R s. 36
Step-by-step explanation:
1kg ⇒ 1000g
So, a quarter kilogram means,
[tex]\frac{1}{4}[/tex] × 1kg = 1000g × [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{4}[/tex] × 1kg = 250g
According to the question,
250g = R s. 60
So, now they're asking for the price of 150g.
Let that price be x.
250g ⇒ R s. 60
150g ⇒ x
Use cross multiplication to find the value of x.
250x = 60 × 150
250x = 9000
Divide both sides by 250.
x = R s. 36
what is the symbol called ? (i just need the symbol dont solve!)
Answer:
The symbol is a variable called x, which is a mathematical term used to substitute values in mostly linear and quadratic equations.
Answer:
a term.
Step-by-step explanation:
(I'm assuming you're asking about the underlined,)
therefore the 9x is a term
(top line)
the 9 is a coefficient
the x is a variable
5 is a constant
- (subtraction sign) is the operator.
9x - 5 is an expression
(bottom line)
the 3x is also a term
x is the variable
3 is a coefficient
4 is the constant
the + (addition sign) is the operator
3x + 4 is the expression.
the answer would be a constant and a term
hope this helps:)
Lawrence needs to be at his job by 5:00 p.m.
It takes him 20 minutes to ride his bike to his job, 30 minutes to eat dinner, and 45 minutes to do his homework.
Which time does he need to start his homework?
A.
3:00 p.m.
B.
3:25 p.m.
C.
3:35 p.m.
D.
4:20 p.m.
Answer:
B. 3.25 p.m.
Step-by-step explanation:
[tex]20 + 30 + 45 = 96 \: minutes \\ 95 \: minutes \: = 60 \: minutes + 35 \: minutes \\ 95 \: minutes \: = 1 \: hour \: 35 \: minutes\\ 5.00 \: p.m. - 1 \: hour \: 35 \: minutes = 3.25 \: p.m.[/tex]
17.
select the correct answer
what is the equation of the problem shown with its focus on this graph?
Options are in photo!
Answer:
B
Step-by-step explanation:
( PLEASE HELP WITH THIS QUESTION)
You are studying a single-celled organism under a microscope. Is it possible for this organism to be classified as fungi?
Answer: Yes it is possible
Example: Yeast is a single-celled fungus.
There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.
A rectangle patio has a perimeter of 38 feet. If the length of the patio is 5 feet less than twice the width, find the dimensions of the patio
Answer:
The length is 11ft.
The width is 8ft.
Step-by-step explanation:
Hello!
Perimeter of a rectangle: [tex]P = 2(l + w)[/tex]
P = perimeterl = lengthw = widthWe know that the length is 5 ft less than twice the width, which can be expressed by the equation: l = 2w - 5. We can plug in 38 for "P".
We can substitute the equation for l, and solve for the width.
Solve for W[tex]P = 2(l + w)[/tex][tex]38 = 2((2w - 5) + w)[/tex][tex]38 = 2(3w - 5)[/tex][tex]38 = 6w - 10[/tex][tex]48 = 6w[/tex][tex]8 = w[/tex]The width is 8. We can solve for the length by plugging it back into the equation l = 2w - 5
Solve for Ll = 2w - 5l = 2(8) - 5l = 16 - 5l = 11The length is 11.
The dimensions are 11 ft and 8 ft.
The regular hexagon has a radius of 4 in.
A regular hexagon has a radius of 4 inches.
What is the approximate area of the hexagon?
24 in.2
42 in.2
48 in.2
84 in.2
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
What is the approximate area of the hexagon?Given that;
Radius of the regular hexagon = 4inArea A = ?Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.
Angle of one triangle in the regular hexagon = 360°/6 = 60°.
To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.
We find the perpendicular height using Pythagoras theorem
h = √( (4)² - (2)² )
h = √( 16 - 4 )
h = √( 12 )
h = √( 2² × 3 )
h = 2√3
Now, we determine the area of a single triangle.
Area = (1/2) × base × height
Area = 0.5 × 4 × 2√3
Area = (4√3)in²
Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6
Area of regular hexagon = 6 × (4√3)in²
Area of regular hexagon = 24(√3)in²
Area of regular hexagon = 41.57in² ≈ 42in²
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
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Answer: b
Step-by-step explanation:
Argelis had þhe following containers of paint leftover, 1/2 gallon, 3/4 quarts and 1/4 gallon. How many quarts of paint does argelis have left
3.75 quarts of paint does Argelis have left with her.
What is Gallons?A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces.
Here, we know that,
1 gallons = 4 quarts
so, 1/2 gallons = 1/2 X 4 = 2 quarts.
and 1/4 gallons = 1/4 X 4 = 1 quarts.
Now, total paint left with Argelis = 1/2 gallons + 3/4 quarts + 1/4 gallons
= 2 quarts + 3/4 quarts + 1 quarts
= 3 quarts + 3/4 quarts
= 15/4 quarts or 3.75 quarts
Thus, 3.75 quarts of paint does Argelis have left with her.
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please help i need the answer ASAP
Answer:
I believe what you would have to do is add each number so the top left box would be two and the bottom right would be 11
Step-by-step explanation:
Solve the following inequality using both the graphical and algebraic approach: 8 minus x greater-than-or-equal-to 5 (8 minus x) Graph A On a coordinate plane, a line goes through (0, 8) and (8, 0). Another line goes through (8, 0) and (7, 10). Graph B On a coordinate plane, a horizontal line is at y = 5 and another line goes through (8, 0) and (0, negative 8). a. x greater-than-or-equal-to 8 Graph A b. x less-than-or-equal-to 8 Graph A c. x greater-than-or-equal-to 8 Graph B d. x less-than-or-equal-to 8 Graph B
The given inequality (8 - X ≥ 5(8 - x)) is solved using graphs method and the result is (Option A); that is x ≥ 8 Graph A.
The inequality is given as: 8-x≥5(8-x)
The next step algebraically is to open the brackets. Hence,
8-x ≥ 40 -5x
Next, we collect like terms
= -x+5x ≥ 40-8
= 4x ≥ 32
Make x the subject of the statement by dividing both sides with 4
= x ≥ 8
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