(2a) Multiple Choice: Place the letter of the correct answer on the answer line to the right:
For which of the following values of k will the equation have infinite solutions?
4(4x + 1) = k(8x + 2)
(a) 4
(b) 8
(c) 2
(d) 1
(2b) Using your answer from Part (2a) replace the value you selected in the equation below. Then solve the
equation and show that it will, in fact, yield infinite solutions.
4(4x+1)=k(8x + 2)
Answers
For k=2 for infinite solutions.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
4(4x + 1) = k(8x + 2)
Now, the equation should have infinite solutions
In consider the situation then we must put value of k such that LHS part become Equal to RHS.
Now, take k=2
4(4x + 1) = k(8x + 2)
LHS: 4(4x+1)= 16x+ 4
RHS: 2(8x+ 2)= 16x+ 4
Hence, k=2 for infinite solutions.
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Related Questions
12.5% of what number is 24
Answers
Let's begin by listing out the information given to us:
[tex]undefined[/tex]Find the equation of the line through the point (10,-6) that is perpendicular to the line with equation -11x-18y=-2070
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Find the equation of the line through the point (10,-6) that is perpendicular to the line with equation
-11x-18y=-2070
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Given\text{ that:} \\ -11x\text{ - 18y = -2070} \\ We\text{ have that:} \\ -18y\text{ = 11x - 2070} \\ Divide\text{ both sides by -18, we have that:} \\ y\text{ = }\frac{11\text{ x}}{-18}\text{ }\frac{-2070}{-18} \\ Then,\text{ we have that:} \\ y\text{ = }\frac{-11\text{ x}}{18}\text{ + 115} \\ comparing\text{ this with:} \\ y\text{ = mx + c , then m = }\frac{-11}{18} \end{gathered}[/tex][tex]\begin{gathered} For\text{ perpendicular lines, we have that:} \\ m_1m_2=\text{ -1} \\ Then,\text{ we have that:} \\ m_2=\text{ -1 x }\frac{18}{-11}=\text{ }\frac{18}{11} \\ Hence,\text{ m}_2=\frac{18}{11} \end{gathered}[/tex][tex]\begin{gathered} We\text{ have the point:} \\ (\text{ 10 , - 6 \rparen} \\ Using\text{ the formulae:} \\ y\text{ - y}_1=\text{ m}_2\text{ \lparen x - x}_1) \end{gathered}[/tex][tex]\begin{gathered} We\text{ have that:} \\ y\text{ - \lparen-6\rparen =}\frac{18}{11}\text{ \lparen x - 10 \rparen} \\ Multiply\text{ through by 11, we have that:} \\ 11y\text{ + 66 = 18x - 180} \\ Rearranging,\text{ we have that:} \\ 11y\text{ = 18x -180 - 66} \\ 11y\text{ = 18 x -246} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]11\text{ y = 18 x - 246}[/tex]fx) -2 x 14 11 3 5 5 4 -8 Determine the Solution utilizing the Table of Values* (1 Point)
Answers
The domain x with the value of 5 according to the table has a range value of -8.
A. -8
Marques works in a department store selling clothing. He makes a guaranteed salary of $200 per week, but is paid a commission on top of his base salary equal to 10% of his total sales for the week. How much would Marques make in a week in which he made $750 in sales? How much would Marques make in a week if he made x dollars in sales?
Answers
Base salary = $200 per week
Commission = 10% of total sales for that week
In a certain week, he makes sale of = $750
So, commission for that week = 10% of $750 = 10/100 x $750 = $75
In that particular week, Marques earned = base salary + commission = $200 + $75 = $275
For a week, in which he makes x dollars in sales,
Commission = 10% of x = 10/100 x (x) = $x/10
Total earning for that week = base salary + commission = $200 + $x/10
What are Commissions?The payment for goods or services sold in the form of commissions is a type of variable pay. Salesperson motivation and reward frequently involve commissions. Incentives like commissions might be used to promote particular sales techniques. When offering substantial reductions, for instance, commissions might be cut. Alternatively, commissions could go up when a company sells a certain product it wishes to advertise. A sales incentive program's framework, which may comprise one or more commission programs, governs how commissions are normally administered.The principal-agent problem is often solved by businesses by calculating payments as a proportion of revenue in an effort to better align employee interests with those of the business.Creating incentives that take account of an agent's performance is one of the most popular ways to try and balance principal and agent interests. The different forms of compensation systems, such as fixed salaries, straight commissions, or a mix of both, have a wide range of variations.To learn more about Commissions, refer to:
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The length of a rectangle is 3 more than the width. Find the length of the rectangle if the perimeter is 98 in.A.47.5 inB.24.5 inC.26 in.D.23 in.
Answers
Answer
Length of the rectangle = 26 inches
Explanation
Let the length of a rectangle be L
Let the width of the rectangle be W
The length of the rectangle is 3 more than the width.
L = W + 3
But we are provided with the perimeter of the rectangle.
The perimeter of a figure is the sum of the dimensions of its exterior.
For a rectangle,
Perimeter = 2 (L + W)
For this question,
Perimeter = 98 inches
L = W + 3
W = ?
Perimeter = 2 (L + W)
98 = 2 (W + 3 + W)
98 = 2 (2W + 3)
98 = 4W + 6
4W + 6 = 98
4W = 98 - 6
4W = 92
Divide both sides by 4
(4W/4) = (92/4)
W = 23 inches
L = W + 3 = 23 + 3 = 26 inches
Hope this Helps!!!
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, and 2 unit of fat, and will contain 40 calories. Each ounce of nuts will supply 3 units of protein, 2 unit of carbohydrate, and 4 units of fat, and will contain 50 calories. Every package must provide at least 6 units of protein, at least 10 units of carbohydrates, and no more than 16 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories?
Answers
Using a system of inequalities, it is found that:
The quantities that will meet the requirement with the least number of calories is: 2 ounces of fruit and 3 ounces of nuts.The least number of calories is: 230 calories.System of inequalitiesThe variables to the system of inequalities are given as follows:
Variable x: number of ounces of fruit.Variable y: number of ounces of nuts.At least 6 units of protein are needed, hence, considering the amount of protein or each snack, the inequality is:
3y ≥ 6
y ≥ 2.
At least 10 units of carbohydrates are needed, hence, considering the amount of carbohydrates of each snack, the inequality is:
3x + 2y ≥ 10.
At least 16 units of fat are needed, hence, considering the amount of fats of each snack, the inequality is:
2x + 4y ≥ 16
x + 2y ≥ 8.
Hence the system is:
y ≥ 2.3x + 2y ≥ 10.x + 2y ≥ 8.Each ounce of fruit contains 40 calories, and each ounce of nuts contains 50 calories, hence the calories function is:
Calories function = 40x + 50y.
Possible solutions to the system, containing only integers, as units is an integer amount, and their calorie consumption are:
x = 4, y = 2: calories: 40(4) + 50(2) = 260.x = 2, y = 3: calories: 40(2) + 50(3) = 230.x = 1, y = 4: calories: 40 + 50(4) = 240.Hence the quantities with the least calories are: 2 ounces of fruit and 3 ounces of nuts, with a calorie load of 230 calories.
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A survey asks students who walk or ride a bike to school whether they live more than onemile from school. The results are shown in the table. Based on the results, which conclusionis best?Live More Than 1 Mile from SchoolWay to Getto SchoolYesNoTotalWalk103141Bike322759Total4258100of the students who live more than one mileaway, about 76% ride a bike.of the students who ride a bike, about 27% liveless than one mile away.of the students who ride a bike, about 76% livemore than one mile away.of the students who live more than one nabeaway, about 32% ride a bike.
Answers
Answer
Step-by-step explanation
Data is collected from 100 students on whether they walk or bike to school and whether they live more than a mile from school or not is shown in a table.
1 mile or not
Ways Yes No Total
Work 10 31 41
Bike 32 27 59
Total 42 58 100
The question then asks us to examine four options, to obtain the one(s) that are correct.
First Option
Of the students who live more than one mile away, about
what digit is in the
Answers
The decimal number is given 16.837
Convert into fractional form by removing the decimal from the given number.
[tex]16.837=\frac{16837}{1000}[/tex]Hence the fractional notation determined is
[tex]\frac{16837}{1000}[/tex]I don’t understand how to do this can’t oh help me please I’m so struggling
Answers
It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. The answer will be 4.4.
What is division mean?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
At a fundamental level, the process of counting how many times one number is included within another is referred to as the division of two natural numbers. This number of times need not be integer. For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 apples.
When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.
It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. In these expanded number systems, division operates in the opposite direction as multiplication, i.e., a = c / b implies that, if b is not zero, a b = c. This is a division by zero, which is not defined, if b = 0. In the case of the twenty-one apples, there would be no leftovers because each person would get five apples and a quarter of an apple.
Different algebraic structures, or ways of defining mathematical structure, use both modes of division. These are known as Euclidean domains and contain polynomial rings in one indeterminate space where a Euclidean division (with remainder) is defined (which define multiplication and addition over single-variabled formulas). Fields and division rings are those where a division (with a single result) by all nonzero elements is defined. The elements in a ring by which division is always feasible are known as the units; in the ring of integers, this would be 1 and 1. The quotient group is another way to apply division to algebraic structures; in this case, the outcome of "division" is a group rather than a number.
Just divide 3.96 by 0.9
[tex]\frac{3.96}{0.9}[/tex]= 4.4
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find the equation of the line perpendicular to 6y=x-1 that passed through (3,5). write answer in slope intercept form, y=mx+b with all fractions written in lower terms
Answers
You have the following equation:
[tex]6y=x-1[/tex]if you divide by 6 both sides, you obtain:
[tex]y=\frac{1}{6}x-\frac{1}{6}[/tex]the slope of the previous line is m = 1/6.
Take into accout that the relation between the slopes of two perpendicular lines is given by:
[tex]m^{\prime}=-\frac{1}{m}[/tex]For the required perpendicular line you have:
[tex]m^{\prime}=-\frac{1}{\frac{1}{6}}=-6[/tex]Now, use the following general equation for a line:
[tex]y-y_o=m^{\prime}(x-x_o)[/tex]where (xo,yo) is any point on the line.
Replace (xo,yo) = (3,5) and m' = -6 into the previous formula and solve for y:
[tex]\begin{gathered} y-5=-6(x-3) \\ y-5=-6x+18 \\ y=-6x+18+5 \\ y=-6x+23 \end{gathered}[/tex]Hence, the equation of the perpendicular line is, in intercept slope form:
y = -6x + 23
Converting Mixed to Improper
Write the mixed number as an
improper fraction. 8 2/9
Answers
8[tex]\frac{2}{9}[/tex] as improper fraction is [tex]\frac{74}{9}[/tex]
Define improper fraction.A fraction that has the numerator higher than or equal to the denominator is said to be improper. A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances. In fact, using improper fractions in mathematics is simpler than using mixed fractions. However, mixed numbers are easier for individuals to understand in daily life. It is crucial that you understand how to change from one form to another.
Given,
Mixed Fraction
8[tex]\frac{2}{9}[/tex]
Improper fraction:
[tex]\frac{8(9) +2}{9}[/tex]
[tex]\frac{72 +2}{9}[/tex]
[tex]\frac{74}{9}[/tex]
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The science club took a survey to see how many hours each member in the club worked on a science project. The table below
shows the results of the survey.
Students Hours
Greta
16
Juan
14
Mika
20
Paulo
18
Su-Lin
16
Tanika
31
Darnell
13
Wesley
24
What is the mean (average) number of hours the students worked on the science project?
OA. 21
OB. 19
OC. 20
18
Answers
Answer: 19
Step-by-step explanation:
To find an average, you take each of your values, add them, and then divide by the numbers of values you have. There were 8 students interviewed, so your total numbers of values is 8.
Addition: 16 + 14 + 20 + 18 + 16 + 31 + 13 + 24 = 152
Division: 152 ÷ 8 = 19
How much to the nearest penny will we have if he uses this investment? Round to the nearest cent if needed
Answers
Given:
Principal P (Initial amount) =$5100
Rate(R)= 2.75
Time(t) = 16 months = 16/12 ( In years)
We can proceed to calculate the interest using the formula below:
[tex]S\mathrm{}I=\frac{P\times R\times T}{100}[/tex][tex]=\frac{5100\times2.75\times\frac{16}{12}}{100}[/tex][tex]=\frac{5100\times2.75\times16}{100\times12}[/tex][tex]=\text{ \$187}[/tex]The amount he has for the investement = 5100 + 187 = $5287
Help I’m completely lost on this I have no clue what I’m doing. I’ve tried 3 times
Answers
Answer:
Explanation:
Given the equation:
[tex]undefined[/tex]In Richmond, Virginia, the average daily high temperature
was 90°F for July. The average daily low temperature for
the same month was 69°F. If a day's temperature change
is measured by comparing the morning/low temperature
to the afternoon/high temperature, what is the percent of
increase between the average low and high temperatures
in July? Round your answer to the tenths place.
Answers
The percent of increase between the average low and high temperatures
in July would be = 26°F
What is temperature range?Temperature range is defined as the difference between the degree of hotness and coldness of two different places.
The average daily high temperature of the month = 90°F
The average daily low temperature of the month = 69°F
The temperature difference between the two ranges = 90 -69 = 21°F
When both temperature are compared = 90+69/2 = 159/2 = 79.5°F
The percent increase of daily low temperature;
= 21/79.5 × 100/1
= 2100/79.5
= 26.4
= 26°F ( nearest to the tenth place)
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This data shows the height of 10 trees, in metres, after 5 years’ growth.
2.1
2.5
2.2
2.4
2.2
2.7
2.4
2.3
1.9
2.6
Calculate the median, showing your answer to two decimal places and remembering to include units with your answer.
Answers
The median of the given data would be 2.35 meters.
What is the median of data?The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.
The given set of data as:
{2.1, 2.5, 2.2, 2.4, 2.2, 2.7, 2.4, 2.3, 1.9, 2.6}
Arrange the data in ascending order.
1.9, 2.1, 2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.6, 2.7
Since the number of elements in the data set is 10.
Median = [(n/2)th term + ((n/2) + 1)th term]/2
Median = [(10/2)th term + ((10/2) + 1)th term]/2
Median = [5th term + 6th term]/2
Median = [2.3 + 2.4]/2
Median = 4.7/2
Median = 2.35
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Which fraction is equal to 0/03 ?
A. 3/100
B. 1/33
C. 1/11
D.1/3
Answers
Answer:
It depends on what the question is.
Step-by-step explanation:
Your question is unclear.
If the question is the fraction 0/03, then that equals 0, but that is not a choice.
If the question is 0.03, then the answer is 3/100.
If the question is 0.03030303... (repeating 03, then the answer is worked out below.
Let x = 0.030303...
100x = 3.0303030...
- x = 0.0303030...
---------------------------------
99x = 3
x = 3/99
x = 1/33
Miles has 327 action figures and 4 shoeboxes to store them in.Does miles have enough shoe boxes? ,if not, how many action figures are left over?
Answers
Step 1:
Concept
To find out if Miles has enough shoeboxes to fit all 327 of his action figures, we first need to find the amount of action figures his current amount of shoeboxes can store. We can do this by multiplying the amount of shoeboxes Miles has by the amount of action figures each shoebox can hold.
Step 2:
Shoe boxes can contain 80
Total = 4 x 80 = 320
Step 3
There will be 7 left
Left over = 7
What is the correct answer
Answers
In transversal lines, All angles are equal and parallel, so TV ║ WY are parallel lines .
What are transversal lines?
A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. Different sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.A line that crosses other lines is known as a transversal. When transversals intersect parallel lines, such as the two railroad tracks, we often operate with them.∠TUX ≅ ∠UXY ( Alternate angle)
∠SUV ≅ ∠TUX ( Vertically angle)
∠UXY ≅ ∠SUV ( Interior angle )
TV ║ WY ( All angles are equal and parallel, so TV ║ WY
are parallel lines .
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[tex]a ^{2} - 3a + 2 = 0[/tex]put into standard form. identify a,b, and c
Answers
Answer:
a=1,b=-3,c=2
Explanation:
The standard form of a quadratic equation is given as:
[tex]ax^2+bx+c=0[/tex]Comparing with the equation:
[tex]a^2-3a+2=0[/tex]We observe that the equation is already in the standard form.
Furthermore:
[tex]a=1,b=-3,c=2[/tex]Which of the following was included in the procedure that
Flemming used to test his hypothesis? Select the 3 that apply
Answers
Answer:
A,B,C is the answer
e
You rotate the triangle below 180 degrees clockwise about the origin.
What are the coordinates of the new triangle?
P' ( , )
K' ( , )
Y' ( , )
Answers
Answer:
P' = (5, 3) K'= (3,1) and Y'= (1, 4)
Step-by-step explanation:
We currently have the following coördinates:
P = (-5, -3), K = (-3, -1), Y = (-1, -4)
A rotation of 180 degrees (precesily a half turn!) will give us:
P' = (5, 3) K'= (3,1) and Y'= (1, 4)
You can draw a line from K to the origin and extend this line precisely the same distance as from K to the origin. This line will end and the point (3,1). The same method can be used for the other two points.
Safety standards require a pool to add 333 chlorine tablets to every 2,0002,0002, comma, 000 liters of water. Today, the lifeguards at Park Pool added 888 chlorine tablets to their pool's10,00010,00010, comma, 000 liters of water.How does Park Pool's chlorine compare to the safety standards?
Answers
SOLUTION
The standard quantity of water is 2000 liters
The quantity of water in the pool is 10,000
Since 3 chlorine is added to every 2000 liters of water then the number of chlorine added to 10000 liters of water is:
[tex]\begin{gathered} \frac{10000}{2000}\times3 \\ =5\times3 \\ =15 \end{gathered}[/tex]Since 8 tablets is added instead of 15 then:
The park pool has less chlorine than the safety standards require
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
if you could help me with some math bc i am bad at this stuff
Answers
Answer:
57.97 cm²
Step-by-step explanation:
Use the formula for area of a trapezoid
[tex]A = \dfrac{a + b}{2} h\\\\[/tex]
where a and b are the two sides and h is the height
Here a = 7.8, b = 10.8, h = 6.2
Substituting we get
[tex]A = \dfrac{7.9 + 10.8}{2} \times 6.2\\\\A = (7.9 + 10.8) \times \dfrac{6.2}{2}\\\\\\7.9 + 10. 8 = 18.7\\\\\dfrac{6.2}{2} = 3.1\\\\\\A = 18.7 \times 3.1 = 57.97\; cm^2[/tex]
Place a on the number line to illustrate that a+b=0
Answers
To make a+b= 0
Since b is positive ( to the right of zero), a must be positive and must be have the same distance from 0.
So:
which is bigger -4 or 4
Answers
Given data:
The first number is -4.
The second number is 4.
Positive number is always bigger than negative number.
Thus, 4 is bigger than -4.
Kari spent 1 2/3 hours painting a fence. Then he spent 4/5 of an hour walking his dog. How much longer did he spend painting than walking?
Answers
Rewrite x4y2 − 6x3y3 using a common factor.
x2y2(x2 − 6xy)
x2y(xy − 6xy2)
6xy(x3y − x2y)
6xy2(x2 − x2y)
Answers
The common factor of the equation [tex]x^{4}y^{2} -6x^{3}y^{3}[/tex] is [tex]x^{2}y^{2} (x^{2}-6xy)[/tex].
What is a common factor?
A whole number that is a factor of two or more numbers is referred to as a common factor.
The largest factor that will split into two or more integers is known as the highest common factor (HCF).
The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).
The LCM and HCF
when a fraction is added or subtracted.
can be discovered by listing multiple factors. It is more effective to express greater values of a number as the product of prime factors. The Venn diagram is another option.
In finding common factors, the HCF, and LCM need knowledge of how to identify factors, build factor trees, and express integers as the product of their prime factors.
How to locate common factors?
A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10.
A factor that all whole integers share is 1, or 1.
To identify commonalities:
List each number's factors.
To identify the numbers that are the same (or frequent) in both lists, compare the factors.
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Need Help ASAP...PLEASEEEEEEEEEEEEEE HELLPPPPPP
Answers
The value of x would be 70° which is the correct answer would be an option (C).
What is the Exterior Angle?Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
To determine the measure of an Exterior angle of a polygon:
First, we have to find the measure of the supplemental interior angle
Then write the equation: Int. + ext. = 180
Here take an interior angle = 93°, find its Exterior angle
⇒ 93 + ext. = 180 ⇒ ext. = 180 - 93 = 87°
Since the sum of all exterior angles of a convex polygon = 360°
As per the given figure,
⇒ x° + 52° + 87° + (x+3)° + 78° = 360°
Combine the likewise terms to get,
⇒ 2x + 220 = 360
⇒ 2x = 360 - 220
⇒ 2x = 140
⇒ x = 70
Therefore, the value of x would be 70°.
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