Answer:Let's call the two numbers x and y. We know that:
xy = 72
x + y = -38
We can use the first equation to solve for one of the variables in terms of the other:
x = 72/y
Then, we can substitute this expression into the second equation:
72/y + y = -38
y^2 + 72 = 38y
y^2 - 38y + 72 = 0
This is a quadratic equation that can be solved using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -38, c = 72.
Plugging in these values, we get:
y = (38 ± √(38^2 - 4(1)(72))) / 2(1)
y = (38 ± √(1444)) / 2
y = (38 ± 38) / 2
So, we have two solutions for y:
y = 38 / 2 = 19
y = -38 / 2 = -19
With either of these values for y, we can use the first equation to solve for x:
x = 72/y = 72/19 = 3.8
or
x = 72/-19 = -3.8
So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.
Step-by-step explanation:
Let's call the two numbers x and y. We know that:
xy = 72
x + y = -38
We can use the first equation to solve for one of the variables in terms of the other:
x = 72/y
Then, we can substitute this expression into the second equation:
72/y + y = -38
y^2 + 72 = 38y
y^2 - 38y + 72 = 0
This is a quadratic equation that can be solved using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -38, c = 72.
Plugging in these values, we get:
y = (38 ± √(38^2 - 4(1)(72))) / 2(1)
y = (38 ± √(1444)) / 2
y = (38 ± 38) / 2
So, we have two solutions for y:
y = 38 / 2 = 19
y = -38 / 2 = -19
With either of these values for y, we can use the first equation to solve for x:
x = 72/y = 72/19 = 3.8
or
x = 72/-19 = -3.8
So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.
In trapezoid ABCD, line AC is a diagonal and angle ABC is congruent to angle ACD. Find AC if the lengths of the bases line BC and line AD are 12m and 27m, respectively
Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.
What are Similar Triangles?Similar triangles are triangles with corresponding sides that have the same ratio.
Thus:
AD is parallel to BC (bases of a trapezoid are parallel)
Therefore:
∠ACB = ∠CAD (alternate interior angles)
This implies that, ΔABC ~ ΔACD by AA similarity theorem.
Thus:
AC/DA = CB/AC
Substitute
AC² = 12 × 27
AC = √324
AC = 18 m
Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.
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desk were on sale for $200 the sale is over and they have gone back up to the full price of $300. what was the rate of increase?
The rate of increase is 150%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Desk were on sale for $200 the sale is over,
and they have gone back up to the full price of $300.
The rate of increase,
= 300 x 100 / 200
= 150%
Therefore, the rate is 150%.
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Engberg Company installs lawn sod in home yards. The company’s most recent monthly contribution format income statement follows: Amount Percent of Sales Sales $ 145,000 100 % Variable expenses 58,000 40 % Contribution margin 87,000 60 % Fixed expenses 24,000 Net operating income $ 63,000 Required: 1. What is the company’s degree of operating leverage? 2. Using the degree of operating leverage, estimate the impact on net operating income of a 22% increase in sales. 3. Construct a new contribution format income statement for the company assuming a 22% increase in sales.
The solution is,
* The company’s degree of operating leverage: 1.38;
* The impact on net operating income of a 22% increase in sales: it will increase by 30.4%;
* New contribution format income statement:
Engberg Company
Contribution format income statement
Amount Percentage of sales
Sales $176,900 100%
Variable expenses 70,760 40%
Contribution margin 106,140 60%
Fixed expenses 24,000
Net operating income 82,140
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
* The company’s degree of operating leverage = Contribution / profit = 87,000/63,000 = 1.38
* The impact on net operating income of a 22% increase in sales is calculated as: Degree of operating leverage x % changes in sales revenue = 1.38 x 22% = 30.4%.
* new contribution format income statement is shown in the answer part.
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The variable x represents a value. Which value of x makes 3(x + 6) − 10 = 17 a true statement?
Answer: x=3
Step-by-step explanation:
3(x+6)-10=17
3x+18-10=17
3x+8=17
3x=17-8
3x=9
x=3
If Hayden uses 4 cups of flour and 5 cups of sugar how many cup cakes will he eat?
Proportionately, if Hayden uses 4 cups of flour and 5 cups of sugar to make cupcakes, he will eat 20 cupcakes.
What is proportion?Proportion refers to the relative size or ratio of one value compared to another quantity.
Proportions are represented as fractional values with decimals, percentages, or fractions.
The quantity of flour for 1 cupcake = 1/5 cups
The quantity of sugar for 1 cupcake = 1/4 cups
The quantity of flour Hayden uses = 4 cups
The number of cupcakes from 4 cups = 20 (4 ÷ 1/5)
The quantity of sugar Hayden uses = 5 cups
The number of cupcakes from 5 cups of sugar = 20 (5 ÷ 1/4)
Thus, according to the proportion of cupcake ingredients to the available quantities of ingredients, Hayden will make and eat 20 cupcakes.
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Question Completion:A cupcake requires 1/5 cup of flour and 1/4 cup of sugar to make.
12. Mia must solve the system of equations
3x+4y=8
x-4y=4
As a first step she produces the equation 4x=12 from the system above. What property of equality can be
used to justify this much simpler equation?
The required solution of the given system of equations is x = 5 and y = -1/4.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
3x+4y=8 - - - - - (1)
x-4y=4 - - - - (2)
Put x from equation 2 to equation 1
12y + 12 + 4y = 8
16y = -4
y = -1/4
Now,
Put y in equation 2
x - 4 {1/4} = 4
x = 5
Thus, the required solution of the given system of equations is x = 5 and y = -1/4.
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PLEASE HELP ME AND PLEASEEE PLEASE SHOW YOUR WORK FOR FULL CREDITT!! ILL RATE U 5 STAR AND GIVE U THANKS AND BRAINLIEST ANSWERR
The equation of the horizontal asymptote of f(x) is given as follows:
x = 5/4.
How to obtain the horizontal asymptote of f(x)?The rational function f(x) in the context of this problem is defined as follows:
f(x) = (-4x² + 54x - 47)/(4x - 5).
The horizontal asymptote of a function happens at a value of x which is outside the function's domain.
For a rational function, the denominator cannot be zero, hence the value of x that represents the horizontal asymptote of f(x) is obtained as follows:
4x - 5 = 0
4x = 5
x = 5/4.
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What is the maximum value
of y?
Here are the ingredients needed to make 12 biscuits.
Habib has 400 g of butter
150 g of sugar
675g of flour
Work out the greatest number of biscuits Habib can make.
Optional working
|+
Biscuits
To make 12 biscuits
Answer:
125g of butter
50g of sugar
175g of flour
biscuits
The greatest number of biscuits Habib can make is 25
How to determine the greatest number of biscuits Habib can make.From the question, we have the following parameters that can be used in our computation:
Habib has 400 g of butter
150 g of sugar
675g of flour
Factor each number to determine the GCF
So, we have
400 = 2 * 2 * 2 * 2 * 5 * 5
150 = 2 * 3 * 5 * 5
675 = 3 * 3 * 3 * 5 * 5
So, we have
GCF = 5 * 5
Evaluate
GCF = 25
Hence, the number of biscuits is 25
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HELPPP I need to choose the correct option AND find X?!!!!
Part 1
E. There is a pair of congruent angles and a pair of congruent right triangles, so the triangles are similar by the AA [tex]\sim[/tex] postulate.
Part 2
Note that 4 ft 6 in = 4.5 ft. Using the fact that corresponding sides of similar triangles have proportional side lengths,
[tex]\frac{x}{14}=\frac{4.5}{4} \implies \boxed{x=15.75 \text{ ft}}[/tex]
35%of students wear glasses.There are 14 students who wear glasses.How many pupils are there in the class?
Answer: 40 pupils
Step-by-step explanation:
35 14
------- = --------
100 ?
find the denominator.
multiply 14 and 100:
14 x 100 = 1400
divide 1400 by 35
1400/35 = 40
Therefore there are 40 students
The area of a rectangle is 50ft , and the length of the rectangle is 5 ft less than three times the width. Find the dimensions of the rectangle.
We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.
[tex]50 = w * (3w-5)[/tex]
Expand the multiplication
[tex]50 = 3w^{2}- 5w[/tex]
Subtract 50 from both sides.
[tex]0 = 3w^{2} - 5w - 50[/tex]
We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.
Finally, we can plug this solution into the length formula we found earlier to solve for length.
[tex]l = 3w - 5[/tex]
Plug in the solution to w.
[tex]l = 3(5) - 5[/tex]
Multiply 3 and 5.
[tex]l = 15-5[/tex]
Subtract 5
[tex]l = 10[/tex]
Therefore the width is 5 and the length is 10.
The first row of a bank statement shows:
OA. deposits that have increased the balance.
OB. withdrawals that have decreased the account balance.
C. the account's balance at the end of the period.
D. the account's balance at the beginning of the period.
The first row of a bank statement shows -
Option D : The account's balance at the beginning of the period.
What is bank statement?
A bank statement, also known as an account statement, is a record that summarises all of an account's transactions for a given month and is normally issued by the bank to the account holder each month.
The transactions for a bank account over a specific time period, typically monthly, are listed in a bank statement.
The statement provides the beginning and ending balances for the period along with deposits, charges, and withdrawals.
Every month, account holders typically analyse their bank statements to assist them keep track of their spending and costs and to check for any erroneous or fraudulent charges.
Therefore, the first row shows the balance at the beginning period.
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Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
Answer:
To find the GCF of 2^5·5·11 and 2^3·5^2·7, we first prime factorize each number:
2^5·5·11 = 2^5 x 5 x 11
2^3·5^2·7 = 2^3 x 5^2 x 7
Next, we look for the highest power of each prime factor that they both have in common:
2^3 is the highest power of 2 that both numbers have.
5^2 is the highest power of 5 that both numbers have.
So, the GCF of 2^5·5·11 and 2^3·5^2·7 is 2^3 x 5^2 = 180.
Step-by-step explanation:
With only a part-time job and the need for a
professional wardrobe, Rachel quickly
maxed out her credit card the summer after
graduation.
With her first full-time paycheck in August,
she vowed to pay $250 each month toward
paying down her $8,281 outstanding
balance and not to use the card.
The card has an annual interest rate of 16%.
How long will it take Rachel to pay for her
wardrobe? Should she shop for a new card?
Why or why not?
Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.
How to solve the problem?The length of time it will take Rachel to pay off her credit card balance can be calculated by dividing the outstanding balance by the monthly payment amount and then adding the number of months needed to pay off the balance.
Balance = $8,281
Monthly payment = $250
Annual interest rate = 16%
To calculate the length of time it will take to pay off the balance, we would first need to calculate the monthly interest rate, which can be done by dividing the annual interest rate by 12:
Monthly interest rate = 16% / 12 = 1.33%
Next, we can calculate the monthly payment amount, including the interest:
Monthly payment amount = $250 + ($8,281 * 1.33%)
By continually subtracting the monthly payment amount from the balance and adding the monthly interest, we can determine the length of time it will take to pay off the balance.
Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.
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Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of the river is 2 km per hour, what was her boat speed in still water?
If Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. her boat speed in still water is;3 km/h.
How to find the speed?Let's x represent the Jane's boat speed in still water
Upstream, her speed was x - 2 km/h.
Downstream, her speed was x + 2 km/h.
Let's d represent the distance between the start and end point
Let the time it takes to cover d at a speed of x - 2 km/h= 30 min.
Let the time it takes to cover d at a speed of x + 2 km/h= 10 min.
So we have:
d / (x - 2) = 30 min and
d / (x + 2) = 10 min.
Multiplying both sides of each equation
d * x - 2d = 30 * (x - 2)
d * x + 2d = 10 * (x + 2).
Adding the two equations and solve for x
2d * x = 40 * x + 20
20 * x = 40 * x + 20
20 * x = 60 * x
x= 3 km/h
Therefore Jane's boat speed in still water is 3 km/h.
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Use the definition of continuity and the properties of limits to show that
The given function is continuous at x = 5, RHL = LHL = F(5)
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = [x² - 49]/[x² + 6x -7][x² + 14x + 49]
To check whether it is continuous at x = 3
First taking LHL,
[tex]\lim_{h \to \00 } F(x)[/tex]
[tex]\lim_{h \to \00 }[/tex] [(5-h)² - 49]/[(5-h)² + 6(5-h) -7][(5-h)² + 14(5-h) + 49]
⇒ -24/(48x144)
⇒ -1/288
Now, taking RHL
[tex]\lim_{h \to \00 }[/tex] [(5+h)² - 49]/[(5+h)² + 6(5+h) -7][(5+h)² + 14(5+h) + 49]
⇒ -24/(48x144)
⇒ -1/288
The value at x = 3
F(3) = [(5)² - 49]/[(5)² + 6(5) -7][(5)² + 14(5) + 49]
⇒ -24/(48x144)
⇒ -1/288
Hence Proved, RHL = LHL = F(5)
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Which expression is equivalent to 3x² - 10x -8?
A. (3x-2)(x-4)
B. (3x - 4)(x + 2)
C. (3x-4)(x - 2)
D. (x-4)(3x + 2)
Answer:
working on a answer hold up
Step-by-step explanation:
For the linear expression in X, give the constant term and coefficient of x
7x - x + 9
The constant term is
The coefficient of x is
Answer:
9 and 6
Step-by-step explanation:
7x - x + 9 ← collect like terms
= (7x - x) + 9
= 6x + 9
the constant term is the numeric term, with no variable ( letter) attached
the constant term is + 9
the coefficient of x is the numeric value before x
the coefficient of x is 6
What is Jana’s unit rate if she rides 15 miles in 50 minutes?
Show your work.
The unit rate of Jana's ride is 0.3 Miles per minutes
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
The unit rate of Jane's ride is
= 15miles/50minutes
= 0.3miles per minute
therefore the unit rate of Jane's ride is 0.3 miles per minute.
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1 1/2 x 1 1/2 x 1 1/2
Answer: 3 3/8 or 3.375
Step-by-step explanation:
Answer:
3.375
Step-by-step explanation:
name all of the radii of the circle (help asp pleasee)
Answer:
C) AB, AC, AD
Step-by-step explanation:
All of the line segments stem from point A and connect to a point on the circle.
Hope this helped! :)
Answer:
third option
Step-by-step explanation:
the radius of a circle is a line segment from the centre of the circle A to a point on the circumference of the circle.
the circle shown here with centre A has 3 segments to the circle.
AB , AC and AD
Which expressions are equivalent to 4m+4n+10?
Select all that apply.
Options are in screenshot
Answer: 3 , 4 and 5 are correct options
Step-by-step explanation:
answer please write an equation
The equation of the line that runs through the point (0,-1) and (1,2) in slope-intercept form is y = 3x - 1.
What is the equation of line of the graph?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
From the diagram, the line runs through the point (0,-1) and (1,2).
First, we determine the slope of the line
Slope m = change in y / change in x
Slope m = (2 - (-1)) / (1 - 0)
Slope m = (2 + 1) / (1 - 0)
Slope m = 3/1
Slope m = 3
Next, plug the slope m = 3 and point (0,-1) into the point slope formula.
y - y₁ = m( x - x₁ )
y - (-1) = 3( x - 0 )
y + 1 = 3x - 0
y + 1 = 3x
Subtract 1 from both sides
y + 1 - 1 = 3x -1
y = 3x - 1
Therefore, the equation of the line is y = 3x - 1.
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(9m)^4 without exponits
Answer:
6561m^4
Step-by-step explanation:
(9m)^4 =
(9 * m)^4 =
9^4 * m^4 = ==> distribute the power 4 to 9 and m
6561 * m^4 = ==> simplify
6561m^4
If mZVUW = (4x + 6)° and mZWUT = (6x - 10)°, what
is the measure of ZWUT?
O 32°
O 38°
O 48°
O 76⁰
Based on the definition of an angle bisector, the measure of angle WUT is: B. 38°.
What is an Angle Bisector?An angle bisector is a line, ray or segment that divides an angle into two congruent angles.
Therefore:
m<VUW = m<WUT
Substitute
4x + 6 = 6x - 10
Solve for x
4x - 6x = -6 - 10
-2x = -16
x = 8
m<WUT = 6x - 10
Plug in the value of x:
m<WUT = 6(8) - 10 = 38°
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8 square root x^5 divided by square root x = 5/x^8 divided by 1/x^2
The value of x in the expression is 0.9429
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
8 square root x^5 divided by square root x = 5/x^8 divided by 1/x^2
Express properly
So, we have
8√x⁵/√x = 5x²/x⁸
Evaluate the quotients
So, we have
8x² = 5/x⁶
Cross multiply
This gives
x⁸ = 5/8
Take the 8th root of both sides
x = 0.9429
Hence, the solution is 0.9429
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Graph the line with slope 3/4 and y intercept -9
A graph of the line with a slope of 3/4 and y-intercept of -9 is shown in the image attached below.
What is the slope-intercept form?Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Next, we would write an equation of this straight line based on the slope and y-intercept as follows;
y = mx + c
y = 3x/4 + (-9)
y = 3x/4 - 9
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The phone company charges $19.99 per line for the first 3 phone lines and $15.99 for each additional line. Customer ordered 7 lines, how much will they be charge per month?
The total charge for the month is given as follows:
$123.93.
How to obtain the total charge for the month?The total charge for the month is obtained applying the proportions in the context of the problem.
The costs are given as follows:
$19.99 per line for the first three lines.$15.99 per line for each additional line.For a customer with 7 lines, the charges are given as follows:
$19.99 for each of the first three lines.$15.99 for each of the last four lines.Hence the total charge is then calculated as follows:
3 x 19.99 + 4 x 15.99 = $123.93.
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Please help me, 25 points!
Answer:
Option B
Step-by-step explanation: