Answers
We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.
Thus, the sum of x-6 and 5x, must be equal to 90°.
(a) Write an equation:
[tex]x-6+5x=90[/tex](b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.
Combining like terms:
[tex]6x-6=90[/tex]Adding 6 from both sides:
[tex]\begin{gathered} 6x-6+6=90+6 \\ 6x=96 \\ \end{gathered}[/tex]Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{96}{6} \\ x=16 \end{gathered}[/tex]Now that we have x, we find angle 1:
[tex]m\angle1=x-6=16-6=10[/tex]And the measure of angle 2:
[tex]m\angle2=5x=5(16)=80[/tex]Related Questions
it's Hamilton path and Hamilton circuitweighted graph / graph theoryyou have to add each angle up and find the answer for each row 12 grade math
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What you need to do in order to solve this is add the values that are defined by the begining and end points declared in there:
[tex]A\text{ B D E C A}[/tex]that means the distance defined by AB, BD, DE, EC & CA:
[tex]4+8+11+10+8\text{ = 41}[/tex]And in the same manner all of the other series of distances.
Brandon's car used 10 gallons to travel 310 miles. At what rate does the car use gas, in miles per gallon?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
Given:
At 10 gallons, the car is able to cover 310 miles.
Find: At 1 gallon, the car can travel ____ miles.
Solution:
First, let's fill in the number line with the given values.
To solve for the question mark at 1 gallon, simply divide 310 by 10.
[tex]310\div10=31[/tex]Hence, the car uses gas at 31 miles per gallon.
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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Find the reference angle of [tex] \frac{ - 13\pi}{6} [/tex]
Answers
Reference angle
The reference angle of a given angle A is the acute angle that A forms with the x-axis
We need to calculate the reference angle of
[tex]\frac{ - 13\pi}{6}[/tex]This angle is greater than any angle of a single turn on the trigonometric circle.
Let's convert the improper fraction to a mixed fraction:
[tex]-\frac{13\pi}{6}=-2\pi-\frac{\pi}{6}[/tex]-2π corresponds to a complete turn around the circle, so we can discard that part and take only the -π/6
Since it's a negative angle, it runs clockwise and is located at the IV quadrant. The reference angle is π/6 because it's the angle it forms with the x-axis.
We'll include an image of the angle below
What is the sum of -15 + 182A. 33B. 3c. -3 D-33Your answer
Answers
-15 + 18 is the same as 18 - 15, which is equal to 3.
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
Answers
Answer: y=80+2x
Step-by-step explanation:
In y=mx+b format the answer is y=80+2x
A circle is sliced into 16 pieces and rearranged into a shape that looks like aparallelogram. The dashed line indicates the base of the shape. The base isapproximately equal to which part of the circle?
Answers
All of the base of the slice corresponds to the circumference of the circle, but since half of it just accounts for the base of the parllelogram therefore, the base is approximately equal to only half of the circumference.
By noon, the temperature in Nome had risen by 13 degrees. What was the temperature there at noon (Nome is -27 currently)
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If there will be an increase of 13 degrees, the temperature will be -14 degrees.
What was the temperature there at noon?We know that by noon, the temperature had risen by 13 degrees, and currently the temperature is -27 degrees.
A "rise" in temperature means that the temperature increases, so the temperature at noon will be 13 degrees more than now, and now it is -27 degrees, so we will get:
-27° + 13° = -14°
The temperature at noon will be -14°.
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4. -X2 + 10 5x + 3 5x+3 6r 4x2 + 2x - 7 I need the perimeter.
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The perimeter is the sum of all sides, therefore:
[tex]\begin{gathered} P=(5x+3)+(4x^2+2x-7)+(-x^2+10)+(5x+3) \\ add_{\text{ }}like_{\text{ }}terms\colon \\ (5x+5x+2x)+(4x^2-x^2)+(3+3+10-7) \\ 3x^2+12x+9 \end{gathered}[/tex][tex]\begin{gathered} 3x^2+12x+9 \\ \frac{1}{3}(3x^2+12x+9)=x^2+4x+3 \end{gathered}[/tex]The factors of 3 that sum to 4 are 3 and 1. So:
[tex]x^2+4x+3=(x+3)(x+1)[/tex]The distance from the Old North Church in Boston to Charlestown is approximately 1,410 meters . Even on fast horse , that distance would take several minutes to travel . On April 18 , 1775 , lanterns were shown from the steeple of the Old North Church across the Charles River to warn American patriots that British soldiers were travelling Inland via water . The speed of light is approximately 3 x 10 to the power of 8 meters per second . How many seconds did it take for the light to be visible in Charlestown ?
Answers
We were told that the distance from the Old North Church in Boston to Charlestown is approximately 1,410 meters.
Given that the speed of light is approximately 3 x 10 to the power of 8 meters per second and
speed = distance/time
It means that the number of seconds it took for the light to be visible in Charlestown is also the time it took the light to travel through 1410 meters
Therefore,
time = distance/speed
time = 1410/3 * 10 ^8 = 0.0000047 seconds
time = 4.7 * 10^-6 seconds
What is the measure of the base of the rectangle if the area of the triangle is 32 ft2 ?A) 8 ftB) 16 ft C) 32 ftD) 64 ft
Answers
Answer:
B) 16 ft
Explanation:
The area of a triangle is equal to
[tex]Area\text{ =}\frac{Base\times Height}{2}[/tex]We know that the area is 32 ft² and the height is 4 ft, so replacing these values, we get
[tex]32=\frac{\text{Base}\times4}{2}[/tex]Now, we can solve for the base. So multiply both sides by 2
[tex]\begin{gathered} 32\times2=\frac{\text{Base }\times4}{2}\times2 \\ 64=\text{Base }\times4 \end{gathered}[/tex]Then divide both sides by 4
[tex]\begin{gathered} \frac{64}{4}=\frac{Base\times4}{4} \\ 16=\text{Base} \end{gathered}[/tex]Therefore, the measure of the base is 16 ft
find the area of the figure below, composed of a rectangle with two semicircles removed.
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This is a composite shape composed of a rectangle with two semicircles removed. The area will be calculated by subtracting the area of the two semicircles from the area of the rectangle
The area of a rectangle is given by:
[tex]\begin{gathered} Area(rectangle)=length\cdot width \\ length=12 \\ width=6 \\ Area(rectangle)=12\cdot6=72 \\ Area(rectangle)=72 \end{gathered}[/tex]The area of the two semicircles is given by:
[tex]\begin{gathered} Area(2semicircles)=2(\frac{1}{2}\pi r^2) \\ Area(2semicircles)=\pi r^2 \\ r=\frac{diameter}{2}=\frac{6}{2}=3 \\ Area\mleft(2semicircles\mright)=\pi\cdot3^2=3.14\cdot9=28.26 \\ Area\mleft(2semicircles\mright)=28.26 \end{gathered}[/tex]Therefore, the area of the figure is:
[tex]\begin{gathered} Area(figure)=Area(rectangle)-Area(2semicircles) \\ Area(figure)=72-28.26 \\ Area(figure)=43.74\approx43.7 \\ Area(figure)=43.7 \end{gathered}[/tex]what is the value of the expression below when w=2 8w+10
Answers
Given the expression:
8w + 10
To find the value when w = 2, we need to substitute 2 for w in the expression.
Therfore, we have:
[tex]8(2)\text{ + 10}[/tex][tex]16\text{ + 10 = 26}[/tex]Therefore, the value of the expression when w = 2 is 26
ANSWER:
26
The perimeter of the triangle below is 91 units. Find the length of the side QR. write your answer without variables.
Answers
Given:
The perimeter of the triangle, P=91.
The sides of the triangle are,
PR=4z
QR=z+3
PQ=5z-2.
The perimeter of the triangle can be expressed as,
[tex]\begin{gathered} P=PR+QR+PQ \\ P=4z+z+3+5z-2 \\ P=10z+1 \end{gathered}[/tex]Now, put P=91 in the above equation to find the value of z.
[tex]\begin{gathered} 91=10z+1 \\ 91-1=10z \\ 90=10z \\ \frac{90}{10}=z \\ 9=z \end{gathered}[/tex]Now, the length of the side QR can be calculated as,
[tex]\begin{gathered} QR=z+3 \\ QR=9+3 \\ QR=12 \end{gathered}[/tex]Now, the length of QR is 12 units.
Which statement best describes the growth rates of the functions below?
Answers
ANSWER:
D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4
STEP-BY-STEP EXPLANATION:
We can see from the graphs that the growth is the same from 0 to 2 and then the exponential function grows faster, therefore, strictly speaking, the correct answer is D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4
Which question can be answered by finding the quotient of ?
A. Jared makes of a goodie bag per hour. How many can he make in of an hour?
B. Jared makes of a goodie bag per hour. How many can he make in of an hour?
C. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?
D. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?
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Below question can be answered by finding the quotient of :
C. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?
What is quotient ?In arithmetic, a quotient is a number obtained by dividing two numbers. A quotient is widely used throughout mathematics and is often referred to as the whole number or fraction of a division or ratio.
The number we get when we divide a number by another is the quotient. For example, 8 ÷ = 2; here the result of division is 2, so it is a quotient. 8 is the dividend and is the divisor.
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leon wrote an expression that is equivalent to (30+6)÷12 witch expression could be the one leon wrote
Answers
ANSWER
(3 · 3 · 2 · 2) ÷ (3 · 2 · 2)
EXPLANATION
The given expression is also equivalent to 36 ÷ 12 - because 30 + 6 = 36.
In the equivalent expression we have:
[tex]\begin{gathered} 3\cdot3\cdot2\cdot2=36 \\ 3\cdot2\cdot2=12 \end{gathered}[/tex]Therefore it's 36 ÷ 12 too
Rewrite 25% as a fraction in simplest form.
Answers
Answer:
1/4
Step-by-step explanation:
Please help me with this sample question.Find f(0)Find f(1)Find f(2)
Answers
In order to find the values of f(0), f(1) and f(2), we just need to find in the graph for the value of the function (that is, the value of y) for the values of x equal to 0, 1 and 2 respectively.
Looking at the graph, for x = 0 we have y = -7, therefore f(0) = -7
For x = 1 we have y = -2, therefore f(1) = -2
For x = 2 we have y = -5, therefore f(2) = -5
Michael bought groceries and spent $46.85 before including the sales tax of 7%. What is the total purchase price after tax?
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We are told that a 7% tax is applied to the original sales price, in order to determine the tax amount we just have to multiply the original price ($46.85) by the tax percentage (0.07 as 7% in decimal form), then we get:
Tax amount = 0.07×46.85 ≈ 3.28
By adding the tax amount to the original price we should get the final price, like this:
Total purchase price = 46.85 + 3.28 = 50.13
Then, the total purchase price after tax is $50.13
what is 503472 rounded to the nearest thousend
Answers
Answer: 503,000
Step-by-step explanation:
The best way to understand the concept is to look at a round to the nearest thousand example: what is 52437 rounded to the nearest thousand?
As the hundredth digit is 4, which is less than 5, the number should be rounded down to 52000. As for 52678, as the hundredth digit is 6, which is larger than 4, it will be rounded up to 53000.
Make an estimate. Then divide using partial-quotients division. Write your remainder as a fraction and pls make it make sense
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Notice that 812 is close to 810 and 17 is closer to 15 than to 20; thus, a possible estimate is
[tex]\frac{810}{15}=54[/tex]However, 800/20 is a more straightforward approximation. Both can be used since you are not being asked for a specific approximation.
Partial-quotients division
Thus, the answer is quotient equal to 47 and remainder equal to 13/17.
3. Define and find the value of the central angle theinscribed angle, and the arc associated with both.Central angle:namemeasureInscribed angle:namedoYmeasureArc:namemeasure
Answers
Given
Answer
Central angle
Name XOY
Measure 90
Inscribed angle
name XZY
Measure 45
Arc
name XY
Measure = circumference of circle/4
Square meters of ceiling Number of tiles 1 10.75 10 100.75 9.3 100 What is the value of the red X? Write your answer as an algebraic expression using variable "a".
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x = 9a + 1.75
slope = (100.75 - 10.75)/(10 - 9) = 90/9 = 9
offset: 10.75 = 9(1) + b
10.75 - 9 = b
1.75 = b
b = 1.75
y = mx + b
in this case: x = 9a + 1.75
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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I need help solving
This problem
Answers
Weight required to destroy a bridge cable (in ponds) The type of variable is Nominal Categorical
A frequently used category variable is gender. Categorical variables can either be ordinal or numeric.
The closing price (in dollars) of the stock is a quantitative variable, and since the price involves an absolute zero, the scale of measurement is a ratio scale
Pounds is what type of variable?
Weight is a prime example of a ratio variable (e.g., in pounds). With certainty, we may state that 20 pounds weigh twice as much as 10 pounds. Ratio variables also have an important zero-point (e.g., exactly 0 pounds means the object has no weight)..
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Pic includes all informatin
Answers
Answer: 8squares
Step-by-step explanation:
how do you calculate the volume of water in a lake? given is the area of the lake at 1.35 km2 and its depth is 4.0 m
Answers
Given
Area of lake = 1.35 square km
Depth = 4.0m
Find
Volume of water in a lake
Explanation
Volume of water in a lake is given by
[tex]area\times depth[/tex]first we have to make the units same
as we know 1 square km = 1000000
so , 1.35 square km = 1.35 * 1000000= 1350000 square meter
so , volume of water in a lake =
[tex]\begin{gathered} volume=1350000\times4 \\ volume=5400000\text{ }cubic\text{ meter} \end{gathered}[/tex]Final Answer
Therefore , the volume of water in a lake is 5400000 cubic meter
Find the area of a triangle with base 13 ft. and height 6 ft.
Answers
SOLUTION
The area of a triangle is given by the formula
[tex]Area=\frac{1}{2}\times base\times height[/tex]From the question we have been given the base as 13 and the height as 6.
So we will substitute base for 13 and height for 6 into the formula, we have
[tex]\begin{gathered} Area=\frac{1}{2}\times13\times6 \\ 6\text{ divides 2, we have 3, this becomes } \\ Area=1\times13\times3 \\ Area=39ft^2 \end{gathered}[/tex]Hence the answer is 39 square-feet
which numbers are all divisible by 5
Answers
Answer:
numbers that end with 0 or 5.
Answer: 5 35 790 55
Step-by-step explanation:
kekera pere
