We have to solve the following equation for the variable x:
[tex]2ax-b=cx+d[/tex]For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.
[tex]\begin{gathered} 2ax-b-cx=cx+d-cx \\ 2ax-cx-b=d \\ 2ax-cx-b+b=d+b \\ 2ax-cx=d+b \end{gathered}[/tex]Now, we will factor the variable x, as we want to have just one expression with x, thus:
[tex](2a-c)x=d+b[/tex]And lastly, we will divide both sides by 2a-c, and we obtain:
[tex]x=\frac{d+b}{2a-c}[/tex]Which is the asked expression for x.
Al gave correct answers to 11 of the 20 questions on the driving test. What percent of the questions did he get correct?
Given:
Al gave correct answers to 11 of the 20 questions on the driving test.
So, the percent of the correct answers =
[tex]\frac{11}{20}\cdot100=11\cdot5=55\%[/tex]so, the answer will be
the percent of the questions did he get correct = 55%
jon drove an average of 250 miles a day for three days he drove 400 miles on the first dat 125 miles on the second day
Answer:
225 miles on 3rd day
Step-by-step explanation:
400 + 125 + x /3 = 250
multiply each by 3 to get 400 +125 +x = 750
subtract 525 each to get x = 225
Tonya is a real-estate agent with a commission rate of 7%. She wants to earn a commission of $12,900. What is the minimum amount of real estate she needs to sell? Round to the nearest
dollar.
well, she needs to sell $"x", which oddly enough is the 100%.
now, we also know that 7% of "x" is $12900, which is what Tonya takes home.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 12900& 7 \end{array} \implies \cfrac{x}{12900}~~=~~\cfrac{100}{7} \\\\\\ 7x=1290000\implies x=\cfrac{1290000}{7}\implies x\approx 184286[/tex]
PeriodNameDateUsing Tables to Graph Quadratic Functions1. Match the four graphs to the corresponding table.AB10TO105СD105-10D351055-10х-1х-2-101y47014у34.30-5NOХ-3-2-101у-3-4-3AWN-TOXo/w/tw/okalow2
In order to match each plot with its corresponding table, consider the positive and negative values of y respect to the positive or negative values of x.
For example, in the first case (plot A), all values of y-coordinate are positive. The only table with all positive y values if the first one.
Hence, plot A matches with the first table.
For plot B, you can notice that for x=0, y=4. The only table in which you have this result is the second one.
Hence, plot B matches with the second table.
For plot C, you can observe that x=0 for y=0. Moreover, if y=0, x = 4. The only table with this result is the fourth table.
Hence, plot C matches with the fourth table.
Finally, plot D matches with the third table.
A cash register contains $20 bills and $100 bills with a total value of $1260. If there are 23 bills total, then how many of each does the register contain?
$20 bill answer
$100 bill answer
According to the solving Each register held eight $20 bills, thirteen $100 bills.
What is a linear equation?A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
What makes an equation linear?A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from.
According to the given data:x=number of $20bills
y=number of $100 bills
20x+100y
=1460 20x+100(-x+21)
=1460 20x-100x+2100
=1460 -80x
=-640 x
=8
-8+21 =13
y=13
20x+y=21 --&g t;
y=-x+21
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In the year 2016, Ethan was single and had a total income of $58,000. He took a deduction of $9,000 and had a tax credit of $1,500. Calculate the tax owed by Ethan. (Refer to the 2016 Tax Table for Singles for tax rates.)
The tax owed by Ethan is $6,521.25.
Ethan's total income was $58,000. There was a deduction of $9,000. Ethan's net income is $49,000. The tax table is attached below. Now we will calculate the tax as per the table.
From $0 to $9,275, the tax is 10%, i.e., $9,27.5.
From $9,276 to $37,650, the tax is 15%, i.e., $4,256.25.
From $37,651 to $49,000, the tax is 25%, i.e., $2,837.5.
The payable tax is the sum of the above calculated taxes. The payable tax is $8,021.25. There is a tax credit of $1,500. The tax owed is the difference between the payable tax and the tax credit. The tax owed is $8,021.25-$1,500 = $6,521.25.
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6 Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff didnot spend more than $14 on the hot dogs and the bottle of water. Which inequality canbe used to find h, the number of hot dogs that Jeff could have bought?F 3h - 2 s 14G 3h + 2 S 14H h - 2 2 14J 3h + 2 2 14
SOLUTION
Step1: Write out the parameters in the question
Let the number of hot dogs be h
The cost of a hot dog is $3
The cost of the bottle of water is $2
The total amount spent by jeff is $ 14
Step2: Write the inequality
The total amount spend should be less than or equal to the total amount
then
The cost of the hot dog is
[tex]3\times h=3h[/tex]The inequality will be the sum of the cost of the hot dog and the bottle of water
[tex]3h+2\leq14[/tex]Hence option G is the correct op
Suppose sin(A) = 1/4 Use the trig identity sin^2(A)+cos^2(A)=1 to find the cosine in quadrant II. round to ten-thousandth.0.1397-0.9682-0.85720.4630
To find the value f rthe cosine function we will us the identity:
[tex]\sin^2A+\cos^2A=1[/tex]We know that the sine of A i 1/4 then we have:
[tex]\begin{gathered} (\frac{1}{4})^2+\cos^2A=1 \\ \cos^2A=1-\frac{1}{16} \\ \cos A=\pm\sqrt{\frac{15}{16}} \\ \cos A=\pm0.9682 \end{gathered}[/tex]Now, we need to determine which sign to choose. Since the sinA lies in th second quadrant thismeans that tehe coosine als lies in the quadrant; furthermore, we know that the cosine is negative in the second and thirsd quadrants whichmeans that we need to use the negative sign. Therefoore:
[tex]\cos A=-0.9682[/tex]Study the function defined by:f(x)= [tex]x \sqrt{ \frac{x - 1}{x + 1} } [/tex]
So, we have the following function:
To calculate the derivative then, we have to make the following calculation:
So, the result of the equation would be as follows:
The graph of the function would be as follows:
IlusComplete the squareto find the vertexof this parabola.2.yº+4 x - 2y +21=0+([?], []).Enter
Answer
The vertex of the parabola is (-5, 1)
Given the following equation:
y^2 + 4x - 2y + 21 = 0
Explanation:
[tex]\begin{gathered} y^2\text{ + 4x - 2y + 21 = 0} \\ \text{Step 1:} \\ \text{Isolate 4x} \\ 4x=-21+2y-y^2 \\ \operatorname{Re}-\text{arranging the equation} \\ -y^2\text{ + 2y - 21 = 4x} \\ -y^2\text{ +2y - 21 = 4x} \\ -y^2\text{ - }\frac{2}{2}y\text{ -21 = 4x} \\ -(y-1)^2\text{ -21 + 1 = 4x} \\ -(y^{}-1)^2\text{ - 20 = 4x} \\ \text{Divide all through by 4} \\ x\text{ = -}\frac{1}{4}(y-1)^2\text{ - 5} \\ U\sin g\text{ the equation} \\ x\text{ = }a(y\text{ }-k)^2\text{ + h} \\ \text{a = -}\frac{1}{4} \\ \text{h = -5} \\ \text{k = 1} \end{gathered}[/tex]Vertex is (h, k)
Therefore, the vertex is (-5, 1)
Which of the following would be enough information to know that ABC~MNP?
Answer:
[tex]\textsf{(2) \quad $m \angle A=m \angle M$ and $\dfrac{AB}{MN}=\dfrac{AC}{MP}$}[/tex]
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are the same size and the corresponding sides are in the same ratio.
Therefore, if triangle ABC is similar to triangle MNP then their corresponding angles are congruent:
m∠A = m∠Mm∠B = m∠Nm∠C = m∠PSimilarly, if triangle ABC is similar to triangle MNP then their corresponding sides are in the same ratio:
[tex]\implies \dfrac{AB}{MN}=\dfrac{BC}{NP}=\dfrac{AC}{MP}[/tex]
SAS Triangle Similarity
If two sides of one triangle are in the same ratio to the corresponding sides of another triangle, and their included angles are congruent, then the triangles are similar.
∠A is the included angle of sides AB and AC.
∠M is the included angle of sides MN and MP.
Therefore, the only statement that shows that two corresponding sides are in the same ratio and their included angles are congruent is:
[tex]\textsf{(2) \quad $m \angle A=m \angle M$ and $\dfrac{AB}{MN}=\dfrac{AC}{MP}$}[/tex]
Find the perimeter and area of a triangle with a base of 9 cm, height of 9.3 cm, and sides of 12
cm and 19 cm. Round to the nearest hundredth when necessary.
Answer:
P(perimeter) = 40 cm A(area) = 41.85 ≈ 41.9 cm
Step-by-step explanation:
To find the perimeter of any shape, you just add the length of the sides together. Therefore, you would add the base, 9 cm, with the sides, 12 and 19 cm. 9 + 12 = 21 + 19 = 40 cm, so the perimeter is 40 cm.
To find the area, you need to use the formula for the area of triangles, which is [tex]\frac{1}{2} bh[/tex], where b = base and h = height. So, you would plug the numbers in to get [tex]\frac{1}{2} (9)(9.3)[/tex]. This equals [tex]\frac{1}{2} (83.7)[/tex], which equals 41.85 cm. Since the question says to round to the nearest hundredth, the final answer would be 41.85 ≈ 41.9 cm.
Drag each set of coordinates to the correct location on the table.
Calculate the distance between the pairs of coordinates, and classify them according to the distance between them.
The required set of coordinates with the match is shown.
Distance between points can be evaluated from the distance formula,
(3, 4) and (2, 1)
= √[(3-2)² + (4-1)²]
= √ 10
Similarly,
The points whose distance between them is √10 are,
(3, 4) and (2, 1)
(-2, 3) and (1, 2)
(-4, -2) and (-3, 1)
The points whose distance between them is √29 are,
(3, 7) and (5, 2)
(5,-2) and (3, 3)
(4, -1) and (-1, 1)
Thus, the required set of coordinates with the match is shown.
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Reasoning Awat withdraws $17 from his bank account once each day for four days. What integer represents the change in the amount in the account? Use pencil and paper. Find the integer that would represent the change in the amount in the account if Awat deposits $17 into his bank account once each day for four days. Explain the difference between the integer for the withdrawals and the integer for the deposits…
The integer that represents the change in Awat's account is $-68.
The difference between the integers that represents withdrawal and deposits is the integer that represents withdrawals is negative while the integer that represents deposits is positive.
What is the integer that represent withdrawals?In order to determine the total withdrawals in four days, multiply the daily withdrawals by the number of days. Multiplication is the arithmetic operation that is used to determine the product of two or more numbers.
Total withdrawals = daily withdrawal x number of days
$17 x -4 = $-68
When there is a withdrawal, the value of the money in the account would decline. Thus, this would be represented with a negative number. A negative number has a negative sign in front of it. When there is a deposit, the value of the money in the account would increase. Thus, this would be represented with a positive number.
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The yearbook club washes cars to raise at least$600. The club charges $3 for each car (c) thatthey wash. What is inequalities of this situation?
Abdoul, this is the solution to the problem:
Goal of the club : raise at least $ 600
Price of each car : $3
Let c the number of cars that the club has to wash
In consequence, the inequality that represents this situatiion is:
Total money raised ≥ 600
Total money raised = 3c
Thus,
3c ≥ 600
(We use higher and equal symbol because the statement says "at least 600". If the statement would say, "more than 600", we shoould use >)
Carson drove a distance of 120120120 kilometers. He initially had 303030 liters of fuel, and his car's fuel efficiency is 100100100 cubic centimeters per kilometer.
What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters?
If he initially had 30 liters of fuel, and his car's fuel efficiency is cubic centimeters per kilometer. The calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters is: 30- 100/1000×120
How to determine the estimated volume?Given data:
Distance = 120 kilometers
Liters of fuel = 30 liters
Using this formula to find the remaining volume
Remaining volume = I - E × D
Where:
I = Initial volume
E = Fuel efficiency
D = Distance
First step is to formula an equation that will be use to find the remaining volume
Equation = 30- 100/1000 ×120
Now let use the formulated equation to find the remaining volume
Remaining volume = 30- 100/1000 × 120
Remaining volume = 30- 12
Remaining volume = 18
Therefore 30- 100/1000×120 can be used to determine the remaining volume.
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A tennis racket at Sport City costs $180and is discounted 15%. The same modelracket costs $200 at Tennis World and is onsale for 20% off. Which store is offering thebetter deal? Explain.
We can find the discounted price of the tennis racket at Sport City by finding the 100% - 15% = 85% of the total price. We can do this by multiplying the total price by the decimal form of 85%:
[tex]180(85\%)=180(0.85)=153[/tex]then, we have that the price of the racket at Sport City is $153
Doing the same but with the price at Tennis World, we get:
[tex]\begin{gathered} 100\%-20\%=80\% \\ \Rightarrow200(80\%)=200(0.80)=160 \end{gathered}[/tex]since the price of the tennis racket is $160 at Tennis world, we can clearly see that Sport City offers a better deal (since 153 < 160)
Describe the key features of the graph of the quadratic functionf(x) = -5x^2+5.A. Does the parabola open up or down?B. Is the vertex a minimum or a maximum?C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
The graph of the function will be something like this.
To make the graph correctly we can give values to x to find points in the plane
[tex]\begin{gathered} f(x)=-5x^2+5 \\ x\text{ | f(x)} \\ -2|-5(-2)^2+5=-15 \\ -1|-5(-1)^2+5=0 \\ 0|-5(0)^2+5=5 \\ 1|-5(1)^2+5=0 \\ 2|-5(2)^2+5=15 \end{gathered}[/tex]Then the graph passes by the points
[tex]\begin{gathered} (-2,15) \\ (-1,0) \\ (0,5) \\ (1,0) \\ (2,15) \end{gathered}[/tex]From this, you can draw the points in a cartesian plane.
Once we have the graph we can answer the question.
The parabola open down.
the vertex of the parabola is a maximun since all the other points are below it.
Finally, we see that the axis of symmetry is the y axis. Since the left part of the the graph is the reflection of the right part.
the vertex of the parabola is the point (0,5).
the y intercept of the parabola is 5. we see that from the point (0,5).
A line is defined by the equaton y=-x=+3. which shows the graph of this line
The slope and y-intercept of the line whose equation is given as y=(-x+3) is -1 and 3 respectively.
As per the question statement, we are supposed to find the slope and y-intercept of the line whose equation is given as y = -x + 3
We know slope-intercept form of line: y = mx + c, where "m" is the slope of the line and "c" is the y-intercept.
Comparing the given equation with y = mx +c
We get slope, m = -1
and y- intercept, c = 3
Hence, the The slope and y-intercept of the line whose equation is given as y= -x + 3 , is -1 and 3 respectively.
Slope: The value of slope gives an indication of the steepness of a straight line and is calculated by taking the tangent of the angle on x-axis.y-intercept: The graph's intersection with the y-axis is known as the y-intercept of that very line.To learn more about slope and y-intercepts of a line, click on the link given below:
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x 1 2 3 y 16 32 48 Write an equation that represents the proportional relationship. y = 16x y = 2x y equals 1 over 16 times x y equals 1 over 2 times x Question 6(Multiple Choice Worth 2 point
Please HELP ME I WILL GIVE BRAINLYNEST
The equation which represents the proportionality relationship is:
y=16x.
Given, we have the pairs as:
(1,16),(2,32) and (3,48)
calculate the value of y/x for the ordered pairs:
For (1,16), the value of y/x is = 16/1 = 16
For (2,32), the value of y/x is = 32/2 = 16
For (3,48), the value of y/x is = 48/3 = 16
now, compare ratios:
for each ordered pair, y/x = 16
Since, k=y/x, you know that the constant of proportionality , k is 16.
Substitute 16 for k in the equation for a proportional relationship.
y = kx
y = 16x
Hence we get the equation as y=16x.
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how many liters of paint must you buy to paint the walls of a rectangular prism shaped room that is 20m x 15m, with a ceiling height of 8m.. if 1 Liter of paint covers 40m^2? the amount of paint needed is ____ liters. (Round up to the nearest integer as needed)
For this question, we compute the superficial area of a rectangular prism without including the ceiling area nor the floor area. We will use the following formula:
[tex]A=\text{ }(\text{rectangle perimeter)}\cdot\text{ height}[/tex]The rectangle perimeter is 2*(20m+15m)=70m. Substituting in the equation above we get:
[tex]A=\text{ 70m}\cdot8m=560m^2[/tex]Therefore, the amount of paint needed is
[tex]\frac{560}{40}\text{liters}=14\text{liters}[/tex]Answer: 14 liters.
Answer: 14
Step-by-step explanation:
8. Let g(x) = 8 – 2xa) Find g(3)
2
1)In this case, let's plug in 3 from the domain set into the function g(x):
g(3) =8-2(3)
g(3) =8-6
g(3) =2
2) So 2 is the value in the Range when 3 is plugged in from the Domain set.
Answer:
[tex]g(3)=2[/tex]
Step-by-step explanation:
GivensWe are given a function:
[tex]g(x)=8-2x[/tex]
We are asked to find g(3).
SolveFirst, substitute 3 as x in g(x):
[tex]g(x)=8-2x\\\\g(3)=8-2x[/tex]
Then, substitute 3 as x in the function:
[tex]g(3)=8-2x\\\\g(3)=8-2(3)[/tex]
Simplify the function by multiplying 2(3):
[tex]g(3)=8-2(3)\\\\g(3)=8-6[/tex]
Then, simplify by performing the final necessary arithmetic:
[tex]g(3)=8-6\\\\g(3)=2[/tex]
Final AnswerTherefore, g(3) = 2.
Until June 2002 the simple interest rate on Stafford loans to college students was 5.39%% while the students was still in college how much interest would a student pay on a $1,500 loan for 2 years
The amount that a student would pay in interest on a $1,500 loan for 2 years is $161.70
What is simple interest?
Under simple interest loan arrangement, the same amount of interest is paid every year for the entire duration of the loan as the interest is determined as the loan principal multiplied by interest rate as well as multiplied by the loan duration expressed in years as indicated below:
I=PRT
I=the interest on the Stafford loans in dollars=unknown
P=Stafford loans principal=$1500
R=annual rate of interest on the loan=5.39%
T=the loan period in years=2
I=$1500*5.39%*2
I=$161.70
Over the period of 2 years, the interest on the student's loan is $161.70
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2.Make a table & Graph the function f(x) = 2)*х-1012y
We are given the function
f(x) = 2(1/2)^1
Firstly, let f(x) = y
Then, y = 2(1/2)^x
To find y, substitute the value of x into the function.
y = 2(1/2)^x
Find y, when x = -1
y = 2(1/2)^-1
y = 2 ( 1/ 1/2)
y = 2(2 x 1 / 1)
y = 2 x 2
y= 4
When x = -1 , y = 4
find y, when x = 0
y = 2(1/2)^0
In mathematics, anything raise to the power of zero is 1
Therefore, (1/2)^0 = 1
y = 2 x 1
y = 2
When x = 0 , y = 2
find y, when x = 1
y = 2(1/2)^1
y = 2 * 1/2
y = 2/2
y = 1
when x = 1, y= 1
find y, when x = 2
y = 2(1/2)^2
(1/2)^2 = (1/4)
y = 2(1/4)
y = 2x 1/4
y = 2/4
y = 1/2 or 0.5
When x = 2, y= 1/2 or 0.5
The new table becomes
x y
-1 4
0 2
1 1
2 1/2
At soccer practice, 35 minutes are spent playing and 5 minutes are spent on a water break. What percentage of practice time is spent playing?
Answer: 87.5%
Step-by-step explanation:
35/40 = x/100
40 times 2.5 gives you 100 so to find what x is you multiply 35 by 2.5.
An animal food must provide 60 units of vitamins and 65 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 8¢, a gram of meat byproducts 9¢, and a gram of grain 10¢.
(a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost?
(b) What is the minimum cost?
x1 x2 s1 s2 s3 z
2.5 5 1 0 0 0 __
4.5 3 0 1 0 0 __
5 10 0 0 1 0 10
__ __ 0 0 0 1 0
There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual.
When pivoting on the second row of the dual, the mixture would contain __ grams of soybean meal, __ grams of meat byproducts, and __ grams of grain. When pivoting on the third row of the dual, the mixture would contain __ grams of soybean meal, __ grams of meat byproducts, and __ grams of grain.
The minimum cost is $__
Answer: its A i hope this helps <3
Step-by-step explanation:
For this problem, write the numbers in standard form.
19. 1.49 x 102 (1 point)
14.9
149
0 1,490
Answer:
1.49 × 101.
100+40+9
1.49 × 103.
Step-by-step explanation:
is this Right?
Not good at math at all so I rlly don’t know much of anything, could really use the help.
Given
Stack of 39 pennies is exactly as tall as 31 pennies
Find
the correct options
Explanation
No the two stacks will have different volume.
The two stacks will have same height but the area of cross section of the penny stack is smaller than that of nickel stack
Final Answer
option (b) is correct
~(P ∨ (P ⊃ Q))
A.tautology
B.contradiction
C.contingent
D.None of the above
The statement ~(p v (p ^ q)) is classified as follows:
C. contingent
What are tautologies and contradictions?When a logic statement is always true, no matter the inputs, it is called a tautology. Otherwise, when a statement is always false, no matter the inputs, it is called a contradiction.
If the statement can be either true or false, depending on the boolean values of the inputs, the statement is called contingent.
The statement given in this problem is as follows:
~(p v (p ^ q))
From the precedence of operations, it is found that:
p ^ q can be either true or false, true if p = q = 1, false otherwise.p v (p ^ q) is false if p = q = 0 and true otherwise. ~(p v (p ^ q)) is the negation of the above statement, that is, true if p = q = 0 and true otherwise.Since the statement can be either true or false, depending on the boolean values of p and q, it is classified as contingent, and option c is correct.
Missing informationThis problem is incomplete and could not be found on any search engine, hence I will consider that it asks to classify the statement ~(p v (p ^ q)).
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4lemons are bought for RS 40 and sold 3 for RS24 find profit percent or loss percent
Since the buying price is RS 40
Since the selling price is RS 24
If the selling price is less than the buying price, then it is a loss
To find the percent of loss Divide the loss by the buying price, then multiply the answer by 100%
[tex]\begin{gathered} \text{Loss= 40 - }24 \\ \text{Loss = }16 \end{gathered}[/tex]The percent of the loss is
[tex]\begin{gathered} \text{Percent Loss}=\frac{16}{40}\times100\text{ \%} \\ \text{Percent Loss = 40\%} \end{gathered}[/tex]The percent of loss is 40%
