Answers
Answer:
a = 84°
b = 21°
c = 48°
Step-by-step explanation:
Step 1.)
The first step is recognizing the angle of 75° is sticking out from a straight-line, PQ. That straight-line represents an angle of 180°
180°-75° = 105 = a° + b°
Step 2.)
We also know that the line RS is 180°. Therefore, it must be true that
75° + 4b° + b° = 180°
or simply
5b + 75 = 180°
Now solve for b. Subtract both sides by 75 and divide the right side by 5
5b = 105°
b = 21°
4b° = 4 x b = 4 x 21° = 84° = 4b°
Step 3)
Since we know that a + b = 105°, we use substitution to get:
a + 21° = 105
Now subtract both sides by 21
a = 84°
Now let's double check if a + b + 75 = 180
84 + 21 + 75 = 180 [check]
Step 4.)
Since we know that PQ is a straight-line that is 180°, we can say:
180° = 4b° + 2c°
Now substitute 4b with 84°
180° = 84° + 2c
Now solve by subtracting 84 from 180 and divide by 2, if needed.
96° = 2c°
48° = c°
Now double check
96° + 84° = 180° [check]
Therefore:
a = 84°
b = 21°
c = 48°
Hope that helps.
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Related Questions
what is the probability of drawing two aces from a standard deck of cards, given that the first card is an ace? the cards are not returned to the deck.
Answers
1/34 is the probability of cards are not returned to the deck.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics is the study of events subject to probability.
A = the first card of ace.
B = Drawing two ace from a standard deck
P(AB) = ²C₄ / ²C₃₂
P(A) = ¹C₄ ¹C₅₁ / ²C₃₂
P(B/A) =P(AB)/P(A)
= ²C₄ / ²C₃₂ * ²C₃₂ / ¹C₄ ¹C₅₁
= ²C₄ /¹C₄ ¹C₅₁
= 1/2 * 17
= 1/34
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which expression is equal to (-2ab)^3 (-a^2b)
Answers
By using exponent, it can be calculated that
[tex](-2ab)^3 (-a^2b)[/tex] = [tex]8a^5b^4[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a .... \times a[/tex] (m times), a is the base and m is the index.
The laws of indices are
[tex]a^m \times a^n = a^{m + n}\\\\a^m\div a^n = a^{m - n}\\\\(ab)^m = a^mb^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}[/tex]
Now,
The given expression is
[tex](-2ab)^3 (-a^2b)[/tex] =
[tex](-8a^3b^3)(-a^2b)\\[/tex]
[tex]8a^{3+2}b^{3+1}[/tex]
[tex]8a^5b^4[/tex]
So, the expression [tex](-2ab)^3 (-a^2b)[/tex] is simplified [tex]8a^5b^4[/tex]
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Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y – 10 = –2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
How much did the bicycle cost?
Answers
Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.
What is an equation?
An equation is written in the form of variables and constants separated by the operation of multiplication and division.
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
According to the given question:
Hugo decided to pay $2 a week to his brother to buy a bicycle.
The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
To pay back to the brother he must owe no money which is y = 0.
∴ The weeks needed is,
0 - 10 = -2(x - 10).
- 10 = -2x + 20.
2x = 30.
x = 15.
He needs 15 weeks to pay back completely.
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If I had 24 assignment and had to get them done in 13 days how many assignments should I do I day
Answers
Answer:
2 per day
Step-by-step explanation:
use distributive property to create an equivalent expression to 40+4x.
Answers
Answer:
4(10+x)
Step-by-step explanation:
find the gcf: 4
divide everything by the gcf: 4(10+x)
Answer:There are 3 answers 4(10+x), 4(10)+4(x), 40+4x
y=3x + 1 if x =-2 then y=?
Answers
Answer:
Step-by-step explanation:
If x equals -2 then you multiply 3 times -2 which equals -6 then add 1. Your total then is -5. Y equals -5
f(x) = 2(3)^x What are the coordinates of the y-intercept of the function? Enter your answer by filling in the boxes.
Answers
Answer: (0,2)
Step-by-step explanation:
to find the y intercept, solve for f(x) when x = 0
f(0) = 2(3)^0 = 2(1) = 2
therefore the coordinates of the y intercept are (0,2)
36. Rapid City is having its annual citywide celebration. The city wants to rent a bumper-car ride. The pieces used to make the floor are 4 foot-by-5 foot rectangles. The ride covers a rectangular space that is 40 feet by 120 feet. a. How many rectangular floor pieces are needed? b. The ride costs $20 per floor piece and $10 per bumper car. How much would it cost Rapid City to rent the floor and the bumper cars? (You will need to decide how many bumper cars will be appropriate.)
Answers
Answer:
a. 240pieces
b. 4800+ 10x
Step-by-step explanation:
a. 40÷4=10, 120÷5=24, 10×24=240
b. (240×20)+ (x×10)= 4800+ 10x ===> x is the number of cars
Here are the shopping times (in minutes) of nine shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 6 .)
Answers
The answer for all 3 of the boxes is 3. The number of observations for each class interval of a variable is shown in group frequency distributions.
Complete the grouped frequency distribution for the data ?DISTRIBUTION OF GROUPED FREQUENCIES
The greatest score is H, while the lowest is L.
By dividing the range by a number of groupings or classes, you can estimate the class width w.
Establish the class intervals.
Add up the scores for each period in the appropriate number.
The shopping time (in minutes) of the nine shoppers are:
15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged everything from least to greatest.)
We can see, that 3 shoppers shopped for 15-20 minutes.
And, 3 shoppers shopped for 21-26 minutes.
And finally, 3 shoppers shopped for 27-32 minutes.
So the answer for all 3 of the boxes is 3.
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Solve your system of equations from part A using elimination. Then, complete the statement. Type the correct answer in each box. Use numerals instead of words. The test has questions worth 2 points and questions worth 4 points
Answers
There are 15 two-point questions and 5 four-point questions.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Let x be two-point questions and y be four-point questions. We know that there are 20 questions so the number of two-point questions plus the number of four-point questions equals 20. So x + y = 20. We also know that the total number of points is 50, so 2x + 4y = 50.
Solving the system:
1) x + y = 20
2) 2x + 4y = 50
Isolate x in 1) to get x = 20-y, then plug into 2)
2(20-y) + 4y = 50
2y=10
y = 5,
It means that there are 5 four-point questions. Plug y = 5 into either equation to get x = 15 so there are 15 two-point questions.
x + y = 20
x + 5 = 20
x = 15
Hence, there are 15 two-point questions and 5 four-point questions.
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Answer:
Step-by-step explanation:
the test ha 65 questions worth points and 5 questions worth 4 points
solve
2(2.1z+4.5)<21.6
Answers
The solution to the given inequality 2(2.1z + 4.5) < 21.6 to solve for the unknown value of z is z < 3
How to solve inequality?Inequality refers to a statement that is of two quantities in which one is specifically less than (or greater than) another.
The symbols of inequality includes;
Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤2(2.1z + 4.5) < 21.6
open parenthesis
4.2z + 9 < 21.6
substract 9 from both sides
4.2z < 21.6 - 9
4.2z < 12.6
divide both sides by 4.2
z < 12.6 / 4.2
z < 3
Hence, z < 3 satisfies the value of z in the inequality 2(2.1z + 4.5) < 21.6
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How can -6.75 + -10.25 be expressed as the sum of its integer and decimal parts
Answers
-17 can be expressed as the sum of its integer and decimal parts.
-6.75+(-10.25)
Remove parentheses: (-a)=-a
=-6.75-10.25
Subtract the numbers: -6.75-10.25=-17
=-17
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
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PLEASE HELP ASAP! (35 POINTS)
Ummi sees an advertisement for her favorite cereal. Then she writes these quotients.
2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1
Part A: What do Ummi's quotients represent in this situation?
Part B: If you were to graph the (weight, cost) pairs for each box, would you be able to draw a straight line through the points? EXPLAIN.
ANSWER ALL PARTS.
Answers
Ummi's quotients in this situation represent the unit rates of the advertisement
You will not be able to draw a straight line through the points
Part A: What do the quotients represent?From the question, we have the following quotients parameters that can be used in our computation:
2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1
These can be rewritten as
2.90/10 = 0.29/1
3.48/12 = 0.29/1
4.48/16 = 0.28/1
The quotients mean that
Unit rate = Total amount spent/Number of adverts
So, the quotient expressions represent the unit rate
Part B: Would you be able to draw a straight line through the points?Recall that
2.90/10 = 0.29/1
3.48/12 = 0.29/1
4.48/16 = 0.28/1
The values of the quotients are not equal
This means that it is not possible to draw a straight line through the points
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need help on this one
Answers
Answer:
19 units
Step-by-step explanation:
You have midline LM marked as 6x+1 and parallel baseline IJ marked as -6x+56 in triangle IJK. You want to know the length of LM.
MidlineThe midline of a triangle is half the length of the parallel base:
LM = 1/2(IJ)
6x +1 = 1/2(-6x +56) . . . . . substitute expressions
6x +1 = -3x +28 . . . . . . . simplify
9x = 27 . . . . . . . . . . . . sdd 3x-1
x = 3
Now, we can find LM:
6x +1 = 6(3) +1 = 19
The measure of LM is 19 units.
Find the difference between (5.5n^2 + 8-3) and (-3n^2-5)
Answers
what i did was 5.5 to the 2nd power and got 30.25n+8-3. then simplified it to 30.25+5.
then got 9n for -3^2. so the remaining equation is 9n-5
30.25n+5
9n-5
the 5s cancel each other out leaving..
30.25n-9n = 21.25.
im not 100% certain tho.
A sales tax is charged on some items at a grocery store but not charged on others. When the
taxable items total t dollars and the non-taxable items total n dollars, the total bill is 1.06t +
n dollars. Malia went shopping yesterday. She spent $20 on taxable items and $8.20 on non-
taxable items.
How much was Malia's total grocery bill?
Answers
Answer:24.90
Step-by-step explanation: My brain
The function below contains ordered pairs of the form (x, y) -
f(x)={(6,5), (2, 3), (1,4)}
What is the range of the function?
Answers
Answer: [tex]\{4, 5, 6\}[/tex]
Step-by-step explanation:
The range of a function is the set of outputs (which is the set of [tex]y[/tex]-coordinates).
find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points. f(x, y)
Answers
The local maxima is(1,0) , local minima is indefinite and the saddle point is (1,0).
As per given in the question ,
f(x,y)=[x2+1 ]
[-2y ]
The critical points are therefore (1,0) and (1,0).
The Hessian is currently
∇²f(x,y)=[−2x 0
0 −2]
2 and 2 are the eigenvalues of the function 2f(1,0).
As a result, (1,0) is a saddle point and 2f(1,0) is indefinite.
Two and two are the eigenvalues of 2f(1,0).
As a result, (1,0) is a maximum and 2f(1,0) is negative definite.
Critical point: If f (p) = 0, then a point p U is f's critical point.
In light of this, the tangent plane to z = f when f is differentiable (x) at (p, f (p)) is horizontal.
Theorem: Assume that f exists and possesses a local extremum at position p. Then, p is a f critical point, with the result that f (p) = 0.
Example: Take into account f (x, y) = x 2 y 2. Once again demonstrating that (0, 0) is the only crucial point of f, fx = 2x = 0 and fy = 2y = 0
However, (0, 0) is not a f local maxima.
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What is the approximate percentage of women with platelet counts between 3 and 4.1?
Answers
The approximate percentage of women with platelet count between 3 and 4.1 is 350
How to solve for approximate percentage?We should know that platelet deals the cells that are found in our body which assemble together when they discover bad blood in the cells.
The range of women is given as 3-4.1
The average of the women is [tex]\frac{3+4.1}{2}=\frac{7.1}{2}[/tex]
Simplifying the expression we have
= 3.5
The appromimate percentage is 3.1*100=350 women
In conclusion the approximate percentage of women with blood platelet is 350 women
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ashley was born on 06/10/1961. how many 8 digit codes could she make using the digits in her birthday
Answers
3360, 8 digit codes could she make using the digits in her birthday.
What is the 4 digit code?
A quick, thorough, and evidence-based method for diagnosing the full range of outcomes seen in people who have had prenatal alcohol exposure is the 4-Digit Code.
Given the date:
Birth date = 12/24/2002 06/10/1961
Number of digits = 8 = 8! = (8*7*6*5*4*3*2*1) = 40320
Repeated digits :
digit 6 = 2 times = 2! = 2*1 = 2
digit 1 = 3 times = 3! = 3*2*1 = 6
Therefore the number of 8 digit codes that can be formed is :
8! / (2! * 3!)
40320 / (2 * 6)
40320 / 12
= 3360
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This morning, Russell took a history test. He got 25 out of 50 problems right. What percentage did Russell get right?
Answers
Answer: 40%
Step-by-step explanation:
What is the result of -21÷(-2-5)+(-14)+6×(8-4×3) ? I need help
Answers
Answer:
[tex]\begin{gathered} \sf - 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 4 \times 3) = \\\sf- 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 12) = \\ \sf- 21 \div( - 3) + ( - 14) + 6 \times ( - 4) = \\ 7 + ( - 14) +( - 24) = \\ \sf 7 - 14 - 24 = \\ \sf - 7 - 24 = \\ \sf \green{ - 31}\end{gathered}[/tex]
When we solve combined calculations, we must first separate into terms when there is an addition or a subtraction.
Then, we solve the operations respecting the hierarchical order of the operations:
First we solve the powers and roots.Then divisions and multiplications.Finally, addition and subtraction.If the calculation has grouping signs, they must be solved in the following order:
Parenthesis.Brackets.Keys.Merry Christmas and Happy New Year
The Alpha.Answer:
negative 36
Step-by-step explanation:
You will useva method known as BODMAS its a principle of combined operations like the one above in mathematics.
B-brackets
O-Of (multipliction) ;commonly used when fractions are involved
D- division
M- multiplication
A- addition
S- subtraction
Working out:
first we will solve the brackets then rewrite the question with the answer obtained
-2-5=-7
8-4×3= minus 4
new question :
-21÷-7+-14+6×minus 4
Next is division since there is no of
-21÷-7=3
Negative divided by negative equals positive
3+minus 14 +6×minus 4
Now do multiplication 6×minus 4= minus24
3+ minus 14+minus 24=minus 36
help help help help help help help help help help help help help help help help help help help help help hel
1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x
A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare
2. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)
A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare
3. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16
4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x
Answers
1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x
2. A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)
3. A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16
4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x
Which value for x makes the sentence true? 4x - 2 = 18 A. x = 5 B. x = 4 C. x = 24 D. x = 20
Answers
Answer: X = 5
Step-by-step explanation:
4x - 2 = 18
+2 +2
4x = 20
/4 /4
x = 5
4(5) -2 =18
20 - 2 =18
18=18
The Beta club sold hot pretzels as a fundraiser. The pretzels normally sold for $2.00, but near the end of the sale, the price was reduced by 25%. What was the new price for a hot pretzel?
Answers
Answer: The new price for a hot pretzel is 1.50
Step-by-step explanation: 200*75/100=150
What is 2 1/4 divided by 4????
1. 5/8
2. 1/10
3. 10
4. 1 3/5
Answers
Step-by-step explanation:
2 1/4 = 9/4
9/4 ÷ 4
9/4 x 1/4
9/16
so neither of these answers?
For the function f(x) = 2x +8, determine f(-3)
A) 2
B) 3
Answers
Answer:
2
Step-by-step explanation:
we replace x with -3
f(-3)=2(-3)+8
f(-3)=-6+8
f(-3)=2
hopes this helps please mark brainliest
Gia is making chocolate truffles. Using the table, find the constant of proportionality
Answers
Using the table we find the constant of proportionality is 15/8
What is constant of proportionality?The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. There are also other names for the constant of proportionality, such as constant ratio, constant rate, unit rate, constant of variation, and even rate of change.
Here,
Since from the table we have to find the constant of proportionality
So, the values of ounces of milk(x) are
30,45
and the values of amount of truffle(y) are
16,24
So for finding the constant of proportionality We take 2 cases,
a)Taking first values of x & y
x/y=30/16
x/y=15/8
b)Taking secondary values of x & y
x/y=45/24
x/y=15/8
Therefore the constant of proportionality is 15/8
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What is the slope of the line that passes through the points (-8, -1) and
(-8, -11)? Write your answer in simplest form.
Answers
Answer:
Step-by-step explanation:
The slope of a line is defined as the change in y-coordinate divided by the change in x-coordinate between two points on the line. In this case, the change in y-coordinate between the two points is -11 - (-1) = -10, and the change in x-coordinate is 0 since both points have the same x-coordinate. Therefore, the slope of the line that passes through the points (-8, -1) and (-8, -11) is -10/0, which is undefined.
Simplify
f(x) = 8x+5 find f(5)
Answers
Answer: To find the value of f(5), we need to substitute 5 for x in the expression f(x) = 8x+5. This gives us:
f(5) = 8*5+5 = 45
So, the value of f(5) is 45.