a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
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A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box. A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall. A diagonal d is drawn from the upper right rear corner to the lowest left front corner.
It is to be noted that the length of the interior diagonal of the box whose dimensions are Height 100cm, Lenght, 80 cm, and width 60 cm, is 140.4cm.
What is the formula for the length of a right rectangular prism?
Recall that the formula for the diagonal length of a right rectangular prism is calculated as √(l² + w² + h²) units. So, the formula for the length of a right rectangular prism's diagonal is √(l²+w²+h²), where l is the length, b is the breadth, and h is the height.
Plugging in the values we have:
d² = 60² + 80² + 100²
Solving for d, we get:
d = √(660² + 80² + 100²)
= √(3600 + 6400 + 10000)
= √(20000)
= 140.4 cm
Thus, the length of the interior diagonal of the box is 140.4 cm.
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An object is attached to a spring that is stretched and released. The equation d= -8cos (pi/6 t) the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.
The time at which the object is 6 inches above the rest position will be 4.62 seconds.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
An item is connected to a spring that is extended and delivered. The condition d= - 8cos [(π/6) t] the distance, d, of the item creeps above or underneath the rest position as an element of time, t, in a flash.
d= - 8cos [(π/6) t]
If d = 6, then the value of the variable 't' is calculated as,
6 = - 8cos [(π/6) t]
- 3/4 = cos [(π/6) t]
cos [(77/100)π] = cos [(π/6) t]
Compare the angle, then we have
(π/6) t = (77/100)π
t / 6 = 77 / 100
t = 4.62 seconds
The time at which the item is 6 crawls over the rest position will be 4.62 seconds.
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in a school walking club, a teacher awards t-shirts to those students who complete their goal of walking 50 miles during a semester. the act of awarding t-shirts to the students is an example of a(n) .
The given statement "a teacher awards t-shirts to those students who complete their goal of walking 50 miles during a semester " is the example for tangible reinforcers.
Tangibles serve as a visual reminder for employees to keep an eye out for desired behaviours and then provide specific positive feedback. . This aided you in completing your assignment quickly and correctly. "You have earned a Tiger Ticket because you followed directions," can improve the student-teacher relationship. You can give the student positive specific feedback without using a tangible (ticket, token, etc.), but a tangible must always be accompanied by positive specific feedback.
Hence, the given statement is an example of tangible reinforcers
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a square room has a floor area of 64 square meters. the height of the room is 9 meters. what is the area of all 4 walls?
Answer:
288 m^2
Step-by-step explanation:
each side of the room is 8 m ( 8x8 = 64)
So you have FOUR walls of widht 8 and height 9
area = FOUR * ( 9 *8) = 288 m^2
Which expression is equivalent to the expression below?
7p+3(2q+9p)
a.7(p+6q+27p)7(p+6q+27p)
b.-2p+12q−2p+12q
c.-p+9q−p+9q
d.34p+6q34p+6q
The equivalent expression will be;
⇒ 34p + 6q
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 7p + 3 (2q + 9p)
Now,
Since, The expression is,
⇒ 7p + 3 (2q + 9p)
Hence, Solve for equivalent expression as;
⇒ 7p + 3 (2q + 9p)
⇒ 7p + 6q + 27p
⇒ 34p + 6q
Thus, The equivalent expression is find as,
⇒ 34p + 6q
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a new washer and dryer set cost $1250 with an annual expenditure of $100 for electricity. The function C(n) =1250+100n/n represents the annual cost of operating the washer-dryer set as a function of n years of owning the set. Which of the following statement(s) about the function is true?
For the question "A new washer and dryer set costs $1250 with an annual expenditure of $100 for electricity..." None of the options are correct
What is annual expenditure?The statement "The annual cost of the washer-dryer set will never exceed $100 during the life of the set" is false because the function C(n) is defined as C(n) = (1250 + 100(n))/n,
A washer-dryer set has an average lifetime of 10ten years
But given the function
C(n) = (1250 + 100(n))/n,
even after 5000 years, the washer-dryer set will still be above $100 as shown below
[tex]C(5000)=\frac{1250+100\left(500000\right)}{500000}[/tex]
C(5000)=100.0025
b) For the given function C(n) = (1250 + 100n) / n, the highest power of x is 1 in both the numerator and denominator. The leading coefficient of the numerator is 100 and the leading coefficient of the denominator is 1, so the horizontal asymptote is the line y = 100.
To find the vertical asymptotes of a rational function, we need to look for values of x that make the denominator equal to 0, but the numerator not equal to 0. These values of x will be the vertical asymptotes of the graph.
For the given function C(n) = (1250 + 100n) / n, the denominator is n, so the vertical asymptotes are x = 0.
Therefore, the asymptotes of the graph of C(n) = (1250 + 100n) / n are the horizontal asymptote y = 100 and the vertical asymptote x = 0.
The statement "The asymptotes of the function are at x = –12.5 and y = 100" is false because a function does not have asymptotes if it is defined for all values of x. In this case, the function C(n) is defined for all positive values of n, so it does not have asymptotes.
c) The statement "The annual cost after 10 years is $225 assuming only purchase and electricity expenses" is false because the annual cost after 10 years is given by
C(10) = (1250 + 100*10)/10
C(10)=225
But
= 225 + 100 (10)
=225000
Therefore, the annual cost after 10 years is $225000, not $225.
Hence given this none of the Options are correct
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CQ
A new washer and dryer set costs $1250 with an annual expenditure of $100 for electricity.
The function C(n) =1250+100n/n represents the annual cost of operating the washer-dryer set (besides the $100 for electricity) as a function of n years of owning the set.
Which of the following statement(s) about the function is true?
I. The annual cost of the washer-dryer set will never exceed $100 during the life of the set.
II. The asymptotes of the function are at x = –12.5 and y = 100.
III. The annual cost after 10 years is $225 assuming only purchase and electricity expenses.
F I only
G I and II only
H I and III only
J I, II, and III
I understand A and B but I do not understand what they are asking for C. I have no idea what the answer is, please help! Thanks
Mike sells grapes at a farmers market. Each pound of grapes sells for the same amount. The table below shows the total prices for different numbers of pounds of grapes sold.
Grapes
Number of Pounds Sold Total Price ($)
2 $4.50
4 $9.00
10 $22.50
A. Write an equation that describes the relationship between the number of pounds of grapes sold(x) and the total price (y), in dollars.
Mike also sells red peppers at the farmers market. The equation below can be used to find the total price (p) in dollars of r pounds of red peppers.
p = 1.80r
B. What is the total price, in dollars, of 17 pounds of red peppers? Explain what the 1.80 represents in the context of the situation.
The farmer decides to increase the price per pound of the grapes. A graph is created to represent both the original equation from Part A and a new equation based on the increased price per pound of the grapes.
C. Thinking about what this graph would look like, explain why the graphs representing the equations will share one point even though the prices per pound are different.
A. The relationship between the number of pounds of grapes sold (x) and the total price (y) can be described by the equation y = 2.25x.
The required details for pounds in given paragraph
This equation can be derived from the data in the table by substituting the values for x and y and solving for the coefficient 2.25. For example, for x = 2 pounds of grapes, we have y = $4.50, so 4.50 = 2.25 * 2. Similarly, for x = 4 pounds of grapes, we have y = $9.00, so 9.00 = 2.25 * 4. We can use this equation to find the total price for any number of pounds of grapes sold.
B. The total price of 17 pounds of red peppers is $31.60. The 1.80 in the equation p = 1.80r represents the price per pound of red peppers. In this case, 1.80 dollars is the price per pound of red peppers, and r is the number of pounds of red peppers that are being purchased. Therefore, the total price of r pounds of red peppers is equal to 1.80 dollars per pound multiplied by the number of pounds of red peppers being purchased.
C. The graphs representing the equations for the original and increased price per pound of grapes will share one point because the two equations will be tangent to each other at that point.
what is pound?
A pound is a unit of weight that is commonly used in the United States and some other parts of the world. It is defined as the weight of a standard reference object, called the international pound, which is kept at the International Bureau of Weights and Measures in France.
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Write Expressions Word Problems 1.
You run a small business and would like to print some business cards.
Staples offers color business cards for a small fee.
The cost is $.75 per card.
A) Write an expression for the total cost (in dollars) if you print b business cards. B) How much does it cost you to print 50 business cards?
Step-by-step explanation:
cost of business card - $.75 ( per card )
I want to print 50
So we will multiply 75 × 50
75
×50
00
355×
=375
$.375 will be the cost of the same
if you want to know the probability that it is a defective bolt (event c), which formula would you use?
The given probability is based on conditions of two events, hence it is called as conditional probability and it's formula according to the events is option.a [tex]p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(C)}{p(A)}[/tex]
Bayes' rule is a mathematical theorem that allows you to modify probability statements in response to new information. With this rule, you can reverse the conditional probability statement and find the probability of the first event occurring given the probability of the second event occurring by using the probability of the second event occurring given the probability of the first event occurring.The first event in this case is that the bolt is defective (event C). The second occurrence is that it was selected from the first machine (event A). As a result, given that the bolt is from the first machine, we can state the conditional probability that it is defective.
Hence, the formula is [tex]p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(C)}{p(A)}[/tex].
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Your question is incomplete , here is the complete question
In a factory that manufactures bolts, the first machine manufactures 70% of the bolts and a second machine manufactures the remaining 20%. The percentage of defective bolts is 3% and 5%, respectively.An employee picks a bolt off a shelf at random and it is from the first machine (event A).If you want to know the probability that it is a defective bolt (event C), which formula would you use?
[tex]a.\ p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(C)}{p(A)}\\\\b.\ p(\frac{A}{C})=\frac{p(\frac{A}{C}).p(A)}{p(C)}\\\\c.\ p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(A)}{p(C)}\\\\d.\ p(\frac{A}{C})=\frac{p(\frac{C}{A}).p(A)}{p(C)}[/tex]
What's the slope of the line connecting (-3, -6) and (-6, -8)? (You may enter your answer as a fraction. Otherwise, round
your answer to 2 decimal places.)
Answer:
Two-thirds
Step-by-step explanation:
slope is
∆y/∆x = (y2-y1) divided by (x2-x1)
= (-8-(-6)) divided by (-6-(-3))
= -2 divided by -3
= 2/3
In a classroom 1/5 student get grade A; 3/10 got grade B and rest get grade C in math. Total number of students in the class is 50. Find how many students got grade C
Answer:
25
Step-by-step explanation:
make 1/5 and 3/10 with equivalent denominator which will give us 2/10 and 3/10 now add them and we get 5/10 5 is the half of ten so we will divide 50 over 2 and we will get 25
Which ordered pair makes both inequalities true? y > -2x + 3 and y < x - 2
(0, 0) (0, -1) (1, 1) (3, 0)
Answer:
Step-by-step explanation:
The answer is (3,0)
You need to plug in the values of x and y to figure it out, because a coordinate is in the form (x,y) so in (3,0) 3 is the x value and 0 is the y value.
If you plug (3,0) into the first inequality y > -2x+3 you get 0 > -3 which is true
steps
-2(3) +3 = -3
And if you plug (3,0) into the second inequality y < x-2 you get 0 < 1 which is also true
So basically just plug in the values of x and y into the inequality and test if it works on one of the inequalities you've been given if it doesn't try the next order pair, if it does try it on the other inequality and check if it works on it to.
The point is located on the x-axis and 10 units to the left of the y-axis
The ordered pair is located at the x-y coordinate at (- 10, 0).
What is an ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Pair in Order = (x, y)
x is the abscissa, the distance measure of a point from the primary axis x
y is the ordinate, the distance measure of a point from the secondary axis y
Given, A point is located on the x-axis which is y = 0, and 10 units to the left of the y-axis which is x = - 10.
So, The location of the ordered pair (x, y) is (- 10, 0).
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Solve the inequality. Enter the answer as an inequality that shows the value of
the variable; for example f> 7, or 6 < w. Where necessary, use <= to write <
and use >= to write 2.
v-(-5) <-9
Solve the inequality. v - (-5) < -9 the solution for the inequality is
v < -14What is inequality?Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
How to solve the inequalityThe given algebraic expression is v - (-5) < -9
This is solved as follows
v - (-5) < -9
v + 5 < -9
v < -9 - 5
v < -14
The value of v is -14
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please help with this
The second price means how much the chips cost per gram. That's what the "/g" part means. Divided by gram. So, the second price of 1000 grams of Nameless chips gets you more chip per cent, because the bag charges $0.002 per gram instead of $0.003 per gram as the other does.
Find an equation that fits this question please
Answer:x-25=y
Step-by-step explanation:
u just subtract and put it into equation form
Could someone pls explain on how to find the 5 number summary, Recall that the 5-number summary is the minimum, lower quartile, median, upper quartile, and maximum.
The numbers are 1 1 1 1 3 3 3 4 4 4 5 5 5 5 6 6 6 13 13 16 16 16 21 22 24 28 28
Maximum = 28, Minimum = 1, Lower Quartile = 3, Median = 5, and Upper Quartile = 16
The Five Number Summary is what?The minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum make up the five-number summary. The median is the middle value; Q1 is the median of the first half of the data, and Q3 is the median of the second half. The lowest is the smallest number, the maximum is the highest, the median is the intermediate value.
The 5 digit summary definition
minimal is a smaller number.
lower quartile: First-half median of the data.
median
upper quartile :Median of the second half of data
greatest number is maximum
The numbers are 1 1 1 1 3 3 3 4 4 4 5 5 5 5 6 6 6 13 13 16 16 16 21 22 24 28 28
minimum = smallest number = 1
lower quartile = Median of the first half of data = 1 1 1 1 3 3 3 4 4 4 5 5 5 = 3
median = median( middle value) = 5
upper quartile = Median of the second half of data = 6 6 6 13 13 16 16 16 21 22 24 28 28 = 16
maximum = largest number = 28
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Given AB CD , what is the m∠ x and m∠ y in this diagram?
Justify your answer using geometry vocabulary.
Answer:
m∠ x is 130° and m∠ y is 130°
Step-by-step explanation:
Based on the drawn example I gave would explain why
So because ∠AGF = ∠CHF that would make these two angles Corresponding angles and corresponding angles are congruent
Thus making ∠AGH or m∠ x equals 130°
Now we look at ∠DHE and ∠AGF these two angles would be classified as Alternate interior angles which would make them congruent to each other aswell
Thus making ∠DHG or m∠ y equals 130°
Reason also includes the fact that m∠ x and m∠ y would be alternate interior angles also
A school dance club is selling bottled water at a football game to raise
funds. The club has raised $26 so far and has the goal of raising $100.
If each bottle of water earns the club an additional $2, which equation can
be used to find the number of bottles of water w that the club needs to sell
to reach their goal?
Step-by-step explanation:
A school dance club is selling bottled water at a football game to raise funds. The club has raised $26 so far and has the goal of raising $100. If each bottle of water earns the club an additional $2, which equation can be used to find the number of bottles of water w that the club needs to sell to reach their goal?
equation:
100 = 2w - 26
solving:
100 = 2w - 26
74 = 2w
w = 37 more bottles
Question
Solve for x.
3/5(x−7/10)=−314
Enter your answer as a mixed number in simplest form in the box.
x =
Answer:
x = -522 19/30
Step-by-step explanation:
To solve for x, distribute the 3/5. This gives us 3/5x - 21/50 = -314. Add over 21/50 to the other side, allowing for 3/5x to equal -313 29/50. Divide by 3/5 on both sides and we get x equal to -522 19/30. This is the final answer as a mixed number and is also in simplest form.
Lin says she has memorized the lengths of a few right triangles, for example, 3, 4, and 5. She is trying to compile a list of several right triangles but needs your help.
Select all the lengths of triangles that are right.
1.) 8, 9, 64
2.) 2,4,6
3.) 1, 1, V2
4.) 7,19,22
5.) 5, 12, 13
Find the equation of a parabola with its vertex at the origin and directrix x = 3.
The equation of a parabola is y²+12x=0.
In mathematics, what is a parabola?A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).
What exactly are the three parabola equations?Parabola functions are classified into three types: standard form, vertex form, and intercept form (also known as factored).
as per the given question:
We have a vertex at (0,0) and the directrix is x = 3, a line parallel to the y-axis, it must have a focus at (3,0).
The parabola equation represents the locus of a point (x, y) that moves so that its distance from x=3 and (3,0) is equal. As a result, the parabola equation is, An equation of the parabola represents the locus of a point (x, y), which moves so that its distance from x=3 and (−3,0) are equal. Hence, the equation of a parabola is
(x−(−3))² + (y−0)² = (x−3)²
or (x+3)² + y² = (x−3)²
or x² + 6x + 9 + y² = x² − 6x + 9
or y² + 12x =0
Hence, The equation of a parabola is y²+12x=0.
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Help please !!!???!!!!
Answer:
the lenth of the court is 78 feet
What is the order from least to greatest of the following: 0.7, −0.2, 2.2, and −2.3?
−2.3, −0.2, 0.7, 2.2
2.2, 0.7, −0.2, −2.3
−0.2, 2.2, 0.7, −2.3
0.7, −0.2, −2.3, 2.2
The order from least to greatest is −2.3, −0.2, 0.7, 2.2. The correct option is A.
What is an ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. We must first compare the numbers before we can arrange them in any order. Compare first, then order. Numbers are arranged in ascending order.
Given that the numbers are 0.7, −0.2, 2.2, and −2.3. The numbers in ascending order will be arranged as,
0.7, −0.2, 2.2, −2.3
-2.3 > -0.2 > 0.7 > 2.2
Hence, the ascending order of the given data is -2.3 > -0.2 > 0.7 > 2.2.
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Which of the following equations is parallel to 8x - 10y = -2 and contains (1, -2)?
1. 4x - 5y = -2
2. 5x - 4y = 6
3. 4x - 5y = 6
4. 4x - 5y = 14
needed as soon as possible
The linear equation that is parallel to 8x - 10y = -2 and contains (1, -2) is:
4x - 5y = 14
So the last option is the correct one.
Which of the following equations is parallel to 8x - 10y = -2?Remember that two linear equations are parallel only if both lines have the same slope (or coefficients if it is written in standard form) and different y-intercept.
Here our line is:
8x - 10y = -2
If we divide all the equation by 2, we will get:
(8x - 10y)/2 = -2/2
4x - 5y = -1
So any equation of the form:
4x - 5y = c, where c ≠ -1
Is parallel to 8x - 10y = -2
Now we want our line to pass through (1, -2), replacing these values in our line we get:
4x - 5y = c
4*1 - 5*-2 = c
4 + 10 = c
14 = c
Then the linear equation is:
4x - 5y = 14
So the correct option is the last one.
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Which method is best for root finding?
Answer:
on the value of the root may produce a value of the polynomial at the approximate root that is of the order of. For avoiding these problems, methods have been elaborated, which compute all roots simultaneously, to any desired accuracy. Presently the most efficient method is Aberth method.
Solve the system of linear equations. -3x+5y=13 x+4y=-10
Answer:
Solve for X: -3x + 5y=13 is x=5/3y + −13/3
(Solve for y: 3/5x + 13/5)
Solve for X: x+4y=-10 is x= −4y−10
(solve for y: y= −1/4x + −5/2)
Step-by-step explanation:
Solve for X in -3x + 5y=13:
Step 1: Add -5y to both sides.
−3x+5y+−5y=13+−5y
−3x=−5y+13
Step 2: Divide both sides by -3.
−3x/−3 = −5y + 13/−3
x = 5/3y + −13/3
Solve for Y in -3x + 5y=13:
Step 1: Add 3x to both sides.
−3x + 5y + 3x = 13 + 3x
5y = 3x + 13
Step 2: Divide both sides by 5.
5y/5 = 3x + 13/5
y = 3/5x + 13/5
Solve for X in x+4y=-10:
Step 1: Add -4y to both sides.
x + 4y + −4y = −10 + −4y
x = −4y −10
Solve for Y in x+4y=-10:
x+4y=−10
Step 1: Add -x to both sides.
x + 4y+ −x = −10 + −x
4y=−x−10
Step 2: Divide both sides by 4.
4y/4 = −x − 10/4
y = −1/4x + −
Hope this helps!!Please help me im trying to finish before deadline
The theorem that proves <DAE=<BAC is Pythagoras theorem.
What is Pythagoras theorem ?The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.To learn more about Pythagoras theorem refer to:
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One angle measures 130°, and another angle measures (8k + 58)°. If the angles are vertical angles, determine the value of k.
Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure, the value of k is 9.
How to find value of k ?Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure. They are formed when two lines intersect, and they are always congruent, or equal in measure.
That if one angle measures 130°, the measure of its vertical angle must also be 130°.
If the other angle has a measure of (8k + 58)°, and it is a vertical angle to the angle that measures 130°, then it must also have a measure of 130°.
We can set up the equation 130 = 8k + 58 and solve for k to find the value of k.
Subtracting 58 from both sides gives us 72 = 8k. Dividing both sides by 8 gives us k = 9.
Therefore, the value of k is 9.
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How many 3/4-cup servings are in 5/12 cups of yogurt?
