Let a be the number of hours that Brian works at Job A in one week and b be the number of hours that he works at Job B .in one week
Since Brian worked 22 hours per week and he made $148.60, we can set the following system of equations:
[tex]\begin{gathered} a+b=22, \\ 6.10a+7.30b=148.60. \end{gathered}[/tex]Subtracting b from the first equation we get:
[tex]\begin{gathered} a+b-b=22-b, \\ a=22-b\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]6.10(22-b)+7.30b=148.60.[/tex]Applying the distributive property we get:
[tex]\begin{gathered} 6.10\times22-6.10\times b+7.30b=148.60, \\ 134.20+1.20b=148.60. \end{gathered}[/tex]Subtracting 134.20 from the above equation we get:
[tex]\begin{gathered} 134.20+1.20b-134.20=148.60-134.20, \\ 1.20b=14.40. \end{gathered}[/tex]Dividing the above equation by 1.20 we get:
[tex]\begin{gathered} \frac{1.20b}{1.20}=\frac{14.40}{1.20}, \\ b=12. \end{gathered}[/tex]Substituting b=12 in a=22-b we get:
[tex]a=22-12=10.[/tex]Answer:
Given F(x) 3x^2+1, G(x) = 2x - 3, H(x) = xF(G(x))
Given
[tex]f(x)=3x^2+1,g(x)=2x-3,h(x)=x[/tex]Answer
[tex]\begin{gathered} f(g(x))=f(2x-3) \\ =3(2x-3)^2+1 \\ =3(4x^2+9-12x)+1 \\ =12x^2+18-36x+1 \\ =12x^2-36x+19 \end{gathered}[/tex]Find the value of k for which x=0 and y=8 is a solution of 3x 6y+k=0
Answer:
(-40)
Step-by-step explanation:
therefore, 3x0=0
(6x8)+k=0
40+k=0
k=0-40
k=(-40)
18. Given J(x. -8) and K(-1,-5) and the graph
of line / below, find the value of x so that
JK \\1.
answer: solutions is x = - 2
Suppose that y varies directly with x and that y=77 when x=7. What is the value of x when y=55? Responses 50 50 11 11 24 24 5
As y varies directly with x, the numerical value of x when y = 55 is 5.
How to solve direct variation problem?Proportional relationships are relationships between two variables where their ratios are equivalent.
A direct variation equation is a linear equation in two variables.
It is expressed as;
y ∝ x
Hence,
y = k(x)
Where k is proportionality constant.
Given that;
y = 77x = 7Proportionality constant k = ?First, we determine the proportionality constant of the direct variation.
y = k(x)
77 = k(7)
Divide both sides by 7
77/7 = k(7)/7
k = 77/7
k = 11
Now, we find the value of x when y = 55
y = k(x)
55 = 11(x)
Divide both sides by 11
55/11 = 11(x)/11
x = 55/11
x = 5
Therefore, the numerical value of x is 5.
Option D)5 is the correct answer.
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Last year, Josh biked b miles. This year, he biked 430 miles. Using b, write an expression for the total number of miles he biked.
Answer:430 + b
Step-by-step explanation:Last year he biked b miles. This year he biked 430 miles. Add the two to get your answer. Hope this helps!
Answer: b+430= total number of miles biked
Step-by-step explanation:
factorise this expression as fully as posaible
5x² + x³
Answer: 625/12
U just have to find the roots then the product then eliminate the exponent.
Mark branliest <3
Solve for x
Your answer must be simplified
-3 < x - 10
The simplified inequality is x > 7.
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: (i)The symbol a b indicates that an is less than b. (ii)A > b indicates that an is greater than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed. In contrast to rigorous inequalities, there are two forms of non-strict inequality relations.
The given inequality -3 < x - 10
or, -3 + 10 < x
or, 7 < x
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If I have .81 gallon and I have 2.41 gallon what is the ratio between the two
Answer:
[tex]\frac{81}{241}[/tex]
Step-by-step explanation:
multiply both numbers by 100. 241 is prime so you cannot reduce it further.
A small publishing company Is planning to publish a new book. The production costs will Include one-time fixed costs (such as editing) and varlable costs (such as printing). The one-time fixed costs will total $49,590. The varlable costs will be $9.25 per book. The publisher will sell the finished product to bookstores at a price of $20.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
4408 books must to be produced so that production costs is equal to sales money.
What is production cost?
Production costs refers to the direct and indirect costs that come from manufacturing a product. Production costs usually include expenses, such as labor, raw materials and manufacturing supplies. Cost of products sold are the production costs incurred on goods that is actually sold in a certain specified period
Let the no. of books= X
Cost = 9.25X + 49590
revenue = 20.50X
20.50X = 9.25X+ 49590
20.50X - 9.25X = 49590
11.25X = 49590
X = 4408
4408 books must to be produced so that production costs is equal to sales money
We can Check by:
cost = 9.25(4408) + 49590
= 40774+ 49590
cost = 90364
revenue = 20.5(4408)
revenue = 90364
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a city planner wants to build a road perpendicular to D street. What is the slope of the new road?
The slope of the new road is zero.
How to find slope?The slope of a line is the change in y with respect to the change in x.
In other words, the slope of a line is rise over run.
Therefore, the new road the city planner wants to build is perpendicular to the the D street.
(5, 1)(5, 4)
slope of D street = 4 - 1 / 5 - 5
slope of D street = 3 / 0
slope of D street = infinity
An infinite slope is simply a vertical line. Therefore, it is only perpendicular to a horizontal line which will have a slope of 0. Hence, the new road should have a slope of 0.
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Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of -2,-1, and 5, and a y-intercept of -10.
Answer:
y = x³ -2x² -13x -10
Step-by-step explanation:
You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.
Polynomial factorsA polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...
p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)
Expanding this gives ...
p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10
This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.
The polynomial function is ...
y = x³ -2x² -13x -10
C(x)=0.08x+9.75
What is the total cost for an order of 30 copies?
Answer:
C^−1 (x) = 12.5 x − 121.875
Step-by-step explanation:
I believe this is the correct answer
According to a candy company, packages of a certain candy contain % orange candies. Suppose we examine random candies. a. What value should we expect for our sample percentage of orange candies? b. What is the standard error? c. Use your answers to fill in the blanks below. We expect ____% orange candies, give or take _____%. Question content area bottom Part 1 a. We should expect 22% of the candies in the sample to be orange. (Type an integer or a decimal.) Part 2 b. What is the standard error? SE 0.021 (Round to three decimal places as needed.) Part 3 c. Use your answers to fill in the blanks below. We expect enter your response here% orange candies, give or take enter your response here%. (Round to one decimal place as needed.)
The sample percentage of orange candies is 0.22, and the standard error is 0.0195 and the expected 22% orange candies, give or take 1.95%.
a) It is assumed that there are 450 random candies with a p=0.22 percentage of orange candies.
As a result, the orange candy sample percentage should be 0.22.
b) Substituting the above data into the standard error formula, compute the needed value as shown below:
SE= √(p × q) ÷ n = √(0.22 × 0.78) ÷ 450 = 0.0195.
Therefore, the answer is 0.0195.
c) Fill in the blanks with the calculated values to get the following:
Therefore, expected 22% orange candies, give or take 1.95%.
We know that if a population proportion, p is drawn from n Bernoulli trials, then the sample proportion, p vector follows an approximately normal distribution, given the sample size is large. The sample proportion's standard error is given by √(p × q) ÷ n.
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Vani needs to order some new supplies for the restaurant where she works. The restaurant needs at least 795 forks. There are currently 315 forks. If each set on sale contains 10 forks, write and solve an inequality which can be used to determine x, the number of sets of forks Vani could buy for the restaurant to have enough forks.
48 sets of forks Vani could buy for the restaurant to have enough forks.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
Given Data
The restaurant needs at least 795 forks. There are currently 315 forks.
If each set on sale contains 10 forks
(10 ×(x)) ≥ (795-315)
10x ≥ 480
x ≥ 48
48 sets of forks Vani could buy for the restaurant to have enough forks.
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Order the function from the least steep slope to the steepest slope.
y=2x-3
y = 4x+0.5
y=-2x+3
y=x+42
y=-0.5x+7
How are the given functions ordered based on their slopes?
1. y = -2x+ 3
slope = m= -2
tanФ = -2 -----(1) Least steep slope
Ф = -63.4°
2. y= 3/4x-3
slope = m = 3/4 ------(3)
tanФ = 3/4
Ф= 36.9°
3. y= 4x+0.5
slope = m = 4 ------(5) Steepest
tanФ = 4
Ф = 75.9°
4. y= x+42
slope = m= 1 ------(4)
tanФ= 1
Ф= 45°
5. y = - 0.5x+ 7
slop = m= -0.5 -----(2)
tanФ = -0.5
Ф = -26.56°
What is a slope?
An indication of how steep a line is is its slope. Nowhere on the line there is a different slope as it is constant. The gradient may be used to refer to it.The ratio of vertical change to horizontal change between any two separate points on a line, or any two points, is used to compute slope.Indicating a steeper line is a slope with a higher absolute value.A line can have upward, downward, horizontal, or vertical directions.To learn more about steep slope, refer:
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Fill in the blanks below.
Find the slope of the line passing through the points (6, 4) and (6, -7).
slope:
Find the slope of the line passing through the points (-9,-5) and (-9, 5).
slope:
The entered points (6,4) and (6,-7) belong to a vertical line, There is no slope and The entered points (-9,-5) and (-9,5)belong to a vertical line. There is no slope.
How to find slope of the coordinates ?The slope, which is essentially how slanted a line is, might be positive, negative, zero, or both (x1,y1) and (x2,y2). The slope equation is (y2 - y1) / (x2 - x1). A vertical line is formed by the points entered. Nothing slopes.Formula: x = 6.
Angle (θ)=90°
Location (d) = 11
(x)=0 Distance between x's
d = (y2 + x2) = (-112 + 02) = 121 = 11 is the distance between y's (y)=11.
A vertical line is formed by the points entered. Nothing slopes.Formula: x = -9.
Location (d) = 10
(x)=0 Distance between x's
Distance between y's (d) = y2 + x2 = 102 + 02 = 100 = 10
A vertical line, on the other hand, will have an ill-defined slope since the x-coordinates are constant. As a result, there will be a division-by-zero error when using the formula.To more learn about coordinates refers to:
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Two more than the quotient of a number and 4 is equal to 9.
The condition "two more than the quotient of a number and 4 is equal to 9" gives the number 28.
What is defined as the term division?Each component of a division equation has its own name.
Dividend: A dividend would be the number divided during the division process.Divisor: The divisor is the number through which the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following describes the relationship between such four parts:
Dividend = Divisor x Quotient + Remainder
For the given problem;
Two more than the quotient of a number and 4 is equal to 9.
Let the number be n;
n/4 + 2 = 9
Simplifying;
n/4 = 9 - 2
n/4 = 7
n = 7×4
n = 28
Thus, the value of the number is found as 28.
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The polynomial passes through the
X-intercepts of (-5, 0), (-3, 0), and (1, 0). The end behavior of the graph is down, up.
Finally, it passes through the point of (3, 14).
The equation of the polynomial is P(x) = 6.86(x + 5) (x + 3) (x - 1)
Given,
x intercepts which the polynomial passes though = (-5, 0), (-3, 0), and (1, 0).
Point = (3, 14).
We have to find the polynomial equation;
A polynomial is defined as;-
P(x) = a(x - c₁) (x - c₂)....(x - cₙ)
Here,
a is a constant
c₁, c₂,...cₙ are the zeros of the polynomial
Here,
-5, -3 and 1 are the zeros of the given polynomial
(x + 5), (x + 3) and (x - 1) are the factors of the given polynomial.
Then the equation of polynomial be like;
P(x) = a(x + 5) (x + 3) (x - 1)
This polynomial passes through point (3, 14)
That is,
14 = a(3 + 5) (3 + 3) (3 - 1)
14 = a x 8 x 6 x 2
14 = 96a
a = 96/14
a = 6.86
Substitute this in equation of polynomial;
That is,
P(x) = 6.86(x + 5) (x + 3) (x - 1)
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A sample of ore is found to be 0.0094 % silver and 0.037 % copper. What is the percentage of matter in the ore that is
neither silver nor copper? Round your answer to the nearest ten thousandth.
The proportion of the ore's composition that is neither silver nor copper is 99.9536 %.
What is percentage ?
Percentage , which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
The ore is found to be 0.0094 % silver and 0.037 % copper.
The percentage of matter in the ore that is
neither silver nor copper is = 100% - 0.0094 % - 0.037 %
= 99.9536 %
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11) Increase 763.685 by 0.1
Answer: its 243
Step-by-step explanation:
Can somebody tell me the answer to 1293/18?
The remainder of the answer to 1293/18 needs to be written as a fraction.
The result of the 1293/18 in mixed fraction is [tex]71\frac{5}{6}[/tex] and 5 is the remainder
The mixed fraction is a fraction that represented with its quotient and remainder. So generally mixed fraction is a combination of a whole number and a simple fraction.
Simple fraction is a fraction that have whole number as numerator and denominator. Top term in the simple fraction is called numerator and bottom term is called denominator
The given expression is
1293/18 = [tex]71\frac{5}{6}[/tex]
Where 71 is the quotient
5 is the remainder
6 is the divisor
Hence, the result of the 1293/18 in mixed fraction is [tex]71\frac{5}{6}[/tex] and 5 is the remainder
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ms. smith sharpened 135 pencils. her students used 88 of them how many sharpened pencils does Ms. smith have left.
Answer: 47
Step-by-step explanation:
Alan is excited to learn how to ski she went to White peaks Mountain rentals pair of skis for $45 and check for hours of group skiing lessons Alan paid 165 an hour which equation can use to find how much white peaks charges for each hour of group skiing lessons
4(h+45)=165
4h+45=165
45(h+4)=165
45h+4=165
Answer:
4h+45=165
Step-by-step explanation:
The cost of the skates does not fluctuate, therefore it always costs $45 no matter how long you use them for.
Answer:
4h + 45 = 165
Step-by-step explanation:
The question was a little hard to understand, but I made some assumptions based off of the answer choices and the information. If any of the assumptions I made sound incorrect, please don't use my answer!
Based off of the question and answer choices, I'm going to assume that Alan paid an initial price of $45 for the skis and then spent 4 hours skiing for an unknown hourly rate. The total amount of money she spent was $165.
Let h represent the hourly rate. Since Alan spent 4 hours skiing, 4 multiplied by h will represent the amount of money Alan paid for her skiing time.
Alan spent a total of $165. This means that the cost of the skis ($45) plus the cost of her ski time (4h) equals $165. This can be represented in this equation:
4h + 45 = 165
:)
What is the rule for 6,8,12,18
Answer: add 2 to the addends and then add that to the number itselx which would be like 6+2=8, 8+4=12, 12+6=18, 18 +8=26, 26+10=36, 36+12=48, so on and so forth
Step-by-step explanation: brainliest please? i could really use it
Answer:
you add 4 each time
Step-by-step explanation:
you need to add 4 to the number you have each time
Distribute the following perfect square: 6x(8x - 9y)² = ?
Answer:
384x² - 486xy²
Step-by-step explanation:
I think this is the answer all I did us first i solved the brackets then I multiplied them by 6x
these five frames show a shapes different positions
From the attached image, we can tell that:
From 1 to 2: There is a shift from left to right along the same plane (x-axis).
From 2 to 3: There is a 90° rotation in the clockwise direction.
From 3 to 4: There is a negative vertical shift. Assuming a y-axis this would be from the top down.
From 4 to 5: There is a 180° rotation in the clockwise direction.
What is a rotation?It is to be noted that a rotation is a sort of transformation that rotates each point in a figure a specific number of degrees around a particular point.
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Full Question:
These five frames (in the attached image_ show shapes of different positions. Describe how the shape moves to get from its position in each frame to the next.
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be emphasized that a relationship is proportional if its graph is a line that passes through its origin.
How should the information be illustrated?
If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to do this, the ratio is not proportional. The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.
If the graph of a relationship is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional. Additionally, if anything is not linear, it is not proportionate.
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Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.
For 47 Go golf and 54 golf game would the cost be the same.
Given that -
Go Golf charges -
Ball and club rental = $2.50
For 1 game = $4.25 and
Golf Games charges -
Ball and club rental =$3.25
For 2 game = $8.50
Find out - For how many games would the cost be the same?
Total charges of Go golf per game = $2.50 + $4.25 = $6.75
Total charges of Golf game for 2 games = $3.25 + $8.50 = $11.75
For per game = $11.75 / 2 = $5.875
For Go golf let game = x and
for golf game let game = y
6.75 x = 5.875y
Transformation of the fraction
27/4 x = 47/8 y
After cross multplication
54x = 47y
x/y = 47 / 54
then x = 47
and y = 54.
Hence, The price would be the same for both the 47 and 54 golf games.
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Which of the following is the graph of (g-f)(x)?
The graph (g-f)(x)=-4x complies with the query.
Graph example: What is it?An edge denotes the connection between the x and y vertices and is represented by the pair (x ,y). In the examples that follow, circles stand in for vertices and lines for edges.
The graph indicates that line generated by function f(x) passes through the points (1,-3) and (0,0) and that line similarly passes through the points (1,1) and (0,0).
With the use of the formula Y-Y1 = y2-y1/x2-x1, we can thus determine the equation of the lines (x-x2)
Therefore, the equation of the line produced by the function f(x) y+3= 3-0/0-1 (x-1)
Function f(x) Equals 3x since y+3=-3x+3 y=-3x.
the line drawn by the function g(x) has the equation y=x, hence function g(x)=x.
We now need to figure out, (g-f) (x) = g(x)- f(x) = -3x-x = -4x
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A turkey casserole (30 servings) uses 3.75 pounds of turkey breast. To scale the recipe for 50 servings, how much turkey would be needed?
A turkey casserole (30 servings) uses 3.75 pounds of the turkey breast. To scale the recipe for 50 servings we need 6.75 pounds turkey.
What is a pound?The currency of the United Kingdom and nine of its affiliated territories is called sterling (stg; ISO code: GBP). The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.
The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, the euro, and the Japanese yen, it is currently the fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with other three currencies and the renminbi. Midway through 2021, sterling is also fourth most-held reserve currency in global reserves.
if 30 servings uses = 3.75 pounds
then, 1 serving = 3.75 pounds/ 30
50 servings = [tex]\frac{3.75}{30} * 50[/tex]= 6.25 pounds
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