Answer:
Slope = -3/4, y-intercept = -4
Step-by-step explanation:
[tex]6x+8y=-32 \\ \\ 3x+4y=-16 \\ \\ 4y=-3x-16 \\ \\ y=-\frac{3}{4}x-4[/tex]
So, the slope is -3/4 and the y-intercept is -4.
For a $250,000 mortgage, with an interest rate of 6% paid over 25 years, the monthly payment is $1,610.75. After one month, what is the balance of the loan?
Round your answer to the nearest dollar.
Do NOT round until you calculate the final answer.
The balance on the loan after a month is $623389.25.
How to calculate the interest?The following can be deduced from the information given:
Principal = $250000
Time = 25
Rate = 6%
Interest = (Principal × Rate × Time) / 100
Interest = (250000 × 6 × 25) / 100
Interest = $375000
The total amount will be:
= Principal + Interest
= $250000 + $375000
= $625000
The balance of the loan will be:
= Amount - One month payment
= $625000 - $1,610.75
= $623389.25
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If < 1 and <2 are complementary, and m< 1 = 42°, find m< 2.
Answer:
m< 2= 48°
Step-by-step explanation:
Complementary angles sum up to 90 degrees
We know that m< 1 = 42°
All we have to do is subtract 90 from 42 to find m< 2:
m< 2= 90 - 42
m< 2= 48°
Hope this answers your question :)
Use the number line below, where RS
I need help with this please help me
leo
toring
29
Due Dec 6 by 11:59pm
Question 13
Ch. 9 Quadratics Homework (Copy)
Score: 12/17 12/17 answered
▼
The width or short side is
The length or long side is
Points 20
Submit Question
The length of a rectangle is 6 feet longer than it is wide. If each side is increased 6 feet, then the area is
multiplied by 2. What was the size of the original rectangle?
<
Submitting an external too
The width or short side is 12 feet
The length or long side is 18 feet
What is Area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.
Let Width= x feet
so, as per question Length = x+6 feet
Area = Length x Width = x(x+6) = [tex]x^{2} +6x[/tex]
According to the question each side is increased 6 feet
New Length = x+12 feet
New Width = x+6 feet
New Area = Length x Width[tex]= 2x(x+6)[/tex] <the area is multiplied by 2>
Length x Width=[tex](x+6)(x+12) = 2x(x+6)[/tex]
x+12=2x
x=12 feet
so, original width = 12 feet
original length = 18 feet
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5. Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay
race. Chris runs his part of the race in 12.35 seconds, Kiona takes
13.12 seconds, and Seiko takes 11.91 seconds.
a. The team wants to break the school record of 48.92 seconds. How
fast will Dwayne have to run?
Dwayne have to complete the race in 11.53 second or the speed of Dwayne is 11.53 second/ 100 meter.
What is speed of an object?
Speed, expressed in terms of meters per second, is the rate at which an object's location changes. An item moves one meter in one second, for instance, if it starts at the origin and moves three meters in three seconds. The formula for speed is straightforward: time divided by distance.
Given that Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay
race. Chris runs his part of the race in 12.35 seconds, Kiona takes
13.12 seconds, and Seiko takes 11.91 seconds.
The total time that is taken by Chris, Kiona, and Seiko is (12.35 + 13.12 + 11.91) seconds = 37.38 seconds.
The team wants to break the record of 48.92 seconds.
To break the record, they should complete the race in 48.91 seconds.
Thus Dwayne have to run 100 meters in ( 48.91 - 37.38) = 11.53 seconds.
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Seth is planning a route for a train that travels at a constant rate of 220 kilometers per hour.
They want to write an equation that shows how many hours (t) a trip takes in terms of the trip's
distance (d).
t = d/220 is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).
Define the relationship between distance, speed, and time.Speed is calculated as follows: speed = distance/time. Calculating the units for speed requires knowledge of the units for both time and distance. Since the distance is measured in meters (m) and the time is recorded in seconds, the units in this example will be meters per second (m/s) (s).
Let the distance be d and the time is t.
The given speed of the train = 220km/hr
Time = d/speed
t = d/220
This is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).
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Answer: t=220/b
Step-by-step explanation: Khan Academy said so
How MANY THOUSANDTHS IN 0.1?
Answer:
100
Step-by-step explanation:
.001*100=.1
Answer:
100 thousandths
Step-by-step explanation:
If cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following. Use fractions and radicals only, no decimals.
sin(x/2)=
cos(x/2)=
tan(x/2)=
please help
According to the trignonmentry of half angles, the value of sin(x/2) is √(1-5/6)/2, cos(x/2) is √(1+5/6)/2 and the value of tan(x/2) is √11/6/(√(1 + 5/6)
Trigonometry of half angles
Trigonometry of half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° that is half of the standard angle 30° and 22.5° that is the half of the standard angle 45 and so on. So if θ is an angle, then the half angle is represented by θ/2.
Given,
Here we need to find if cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following.
sin(x/2), cos(x/2), tan(x/2).
According to the concepts in trigonometry,
We know that the following formulas.
=> sin(x/2) = √(1-cosx)/2
=> cos(x/2) = √(1+cosx)/2
=> tan( x/2)=sin x/1+cosx
Here we know that cos (x) = 5/6
Thus implies that 5 is the opposite and 6 is the hypotenuse, then the adjacent is
Therefore, we can calculate the value of the adjacent a as,
=> a = √(6²-5²)
=> a = √36-25
=> a= √11
Therefore the value of sin x= √11/6
So, the value of sin(x/2)= √(1 - 5/6)/2
And the value of cos(x/2)= √(1 + 5/6)/2
Finally, the value of tan(x/2)=√11/6/(√(1 + 5/6)
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Pratap Puri rowed 18 miles down a river in 2 hours, but the retum trip took him 4 hours. Find the rate Pratap can row in still water and find the rate of the current. Let x=rate Pratap can row in still water and y=rate of the current
What is the rate that Pratap rows in still water?
Pratap can row at a rate of____?
(Type an integer or a decimal)
in still water.
Rate Pratap can row in still water is 6.75 and Rate of current is 2.25
Step: 1
Let's y = speed of water and x = his speed of rowing in still water
Speed = Distance/Time (or)
Rate = Distance/Time
Step: 2
he row downstream in 2 hours
Rate in downstream = 18/2
Rate in downstream = 9
i.e.
x + y = 9
x = 9 - y ---(i)
Now, time taken by min to row in upstream = 4 hours
Rate in upstream = Distance/Time = 18/4
Rate in upstream = 4.5
i.e., x-y = 4.5 ---(ii)
Putting the value of x from equation (i) in equation(ii)
9 - y - y = 4.5
9 - 2y = 4.5
9 - 4.5 = 2y
y = 4.5/2
y = 2.25
Putting the value of y in equation (ii)
x - 2.25 = 4.5
x = 4.5 + 2.25
x = 6.75
x = Rate Pratap can row in still water = 6.75
y = Rate of current = 2.25
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Sam opened a money-market account that pays 4% simple interest. He started the account with $7,000 and made no further deposits. When he closed the account, he had earned $560 in interest. How long did he keep his account open? A. 2 years B. 5 years C. 4 years D. 3 years
the answer is 2 years
Answer:2 years
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer is 2 years
A book sold 41,900 copies it’s first month of release. Suppose this represents 9.2% of the number of copies sold to date. How many copies have been sold to date? Round your number to the nearest whole number.
solve for each proportion
Answer:
r = 20/7
x = 13.5
Step-by-step explanation:
Hello!
7)Solve for r by cross-multiplying:
[tex]\frac r2 = \frac {10}7[/tex][tex]r*7 = 10 * 2[/tex][tex]7r = 20[/tex][tex]r = \frac{20}7[/tex]The value of r is 20/7.
8)Solve for x by cross-multipying:
[tex]\frac 94 = \frac x6[/tex][tex]9*6 = 4*x[/tex][tex]4x = 54[/tex][tex]x = 13 \frac12[/tex]The value of x is 13.5.
Answer:
7) r = 20/7 8) x = 27/2Step-by-step explanation:
7) r/2 = 10/7, value of r?
→ r/2 = 10/7
→ r = (10/7) × 2
→ r = (10 × 2)/7
→ [ r = 20/7 ]
Hence, value of r is 20/7.
8) 9/4 = x/6, value of x?
→ 9/4 = x/6
→ x/6 = 9/4
→ x = (9/4) × 6
→ x = (9 × 6)/4
→ x = 54/4
→ [ x = 27/2 ]
Hence, value of x is 27/2.
NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!
x=-3.645 and x=1.645 is the solution for the given inequality.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given inequality is
y<x²+2x-6
a=1, b=2, c=-6
x=-b±√b²-4ac/2a
=-2±√2²-4(1)(-6)/2(1)
=-2±√4+24/2=
=-2±√28/2=
=-2+√28/2
=-2+5.29/2
=1.645
and -2-5.29/2
x=-3.645
Hence x=-3.645 and x=1.645 is the solution for the given inequality.
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What is does y = 3x - 4
Answer:
x = y/3 + 4/3
Step-by-step explanation:
Solve for x:
y = 3 x - 4
y = 3 x - 4 is equivalent to 3 x - 4 = y:
3 x - 4 = y
Add 4 to both sides:
3 x = y + 4
Divide both sides by 3:
Answer: x = y/3 + 4/3
The sum of four consecutive numbers is thirty-two. Find the largest number. (show work)
9.5 is the largest number
Consecutive numbers are the number will follow each other in order.
The difference between every two numbers is one. if n is the number so, the consecutive number will be n+1,n+2 , . . . . . .
Let four consecutive numbers be a , a+1 , a+2 , a+3
where a+3 will be largest number
Given the sum of these is 32
a + a +1 +a + 2 + a +3 = 32
=> 4a + 6 = 32
=>4a = 26
=> a= 26/4
=> a = 6.5
putting the values,
consecutive number will be = 6.5 , 7.5 , 8.5 , and 9.5
9.5 is the largest number
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This table gives a few (x, y) pairs of a line in the coordinate plane.
x
Y
-54
-21
-40
-14 -26
- 28
What is the y-intercept of the line?
The y-intercept of the line is y = 2
What is an intercept?
A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
Here,
A linear function has the following equation:
y = mx + b
Where m is the slope and b is the y-intercept, which is the value of y when x = 0.
We have given three points:
(-28, -54)
(-21, -40)
(-14, -26)
We use two of them to construct a system, to find values for m and b.
(-28, -54)
This means that when x = - 28 , y = - 54
so, y = mx + b
- 54 = - 28m + b
28m = b + 54
m = (b + 54)/28
Now, we have x = -21, y = -40
so, y = mx + b
- 40 = - 21m + b
we put the value of m here
- 40 = - 21 {(b + 54)/28} + b we get,
7b - 1134 = - 40 × 28
b = 2
Hence, the y-intercept of the line is y = 2
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Answer:
(0,2)
Step-by-step explanation:
khan academy
Anita works a part time job where she makes 9.45$ per hour Anita’s gross pay for the current period is $238.61 her deductions include $28.63 for federal taxes 14.79 for social security 3.46 for Medicare 10.14 for state taxes . How many hours did Anita work and what was her net pay ? Anita works 31 hours next week what is her gross pay total amount of deductions and net pay assuming the same percentage is taken out for each deductions during the next pay period ?
For the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.
When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.
As given in the question,
a. Anita get pay per hour = $9.45
Gross pay received by Anita = $238.61
Deductions :
Federal tax = $28.63
Society tax : $14.79
Medicare : $3.46
State tax : $10.14
Total deduction = $ ( 28.63 + 14.79 + 3.46 + 10.14 )
= $57.02
Net pay = Gross pay - total deduction
= $ ( 238.61 - 57.02 )
= $ 181.59
Let us consider Anita works for 'h' hours at the rate of $9.45,
9.45h = 238.61
⇒ h = 238.61/ 9.45
⇒ h = 25.25 hours
b. When Anita works for 31 hours
Her gross pay = 31 × 9.45
= $ 292.95
Deductions are same
Net pay = $ ( 292.95 - 57.02 )
= $ 235.93
Therefore, for the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.
When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.
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Sarah ran 7/8 of the distance around the school track. Jacob ran 2/3 of Sarah‘s distance what fraction of the total distance around the tractor Jacob run?
Jacob run 7/12 of the total distance around the school track.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
Given: Sarah ran 7/8 of the distance around the school track.
Jacob ran 2/3 of Sarah‘s distance.
To find what fraction of the total distance around the track Jacob ran, we will find when solving 2/3 of 7/8 or symbolically
[tex](\frac{2}{3})(\frac{7}{8}) = \frac{14}{24} = \frac{7}{12}[/tex]
Hence, Jacob run 7 / 12 of the total distance around the school track.
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Can you please help me
How to find the vertex?
The general form of an absolute value function:
y = a|x - h| + k, where (h, k) is vertex and a - coefficientGiven function is:
y = |x + 3| - 2Its vertex is (- 3, - 2), this is our first point to plot, point A.
Step 2How to find x-intercepts?
Set y = 0 and solve for x:
|x + 3| - 2 = 0|x + 3| = 2x + 3 = 2 and x + 3 = - 2x = - 1 and x = - 5So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.
Step 3Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.
graph y= absolute value of 5x
The graph of the absolute value function is attached below.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
The absolute value measures the distance of a point x to the origin, hence, for example, |-4| = |4| = 0, and has vertex(turning point) at (0,0).
We have to grpah the absolute value function of y = 5x.
Thus, the function is linear function.
The graph of the function is attached below.
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for every 4 male birds in a cage there are 6 females what is the ratio of males to females
The ratio of males to females in the cage is 2:3.
According to the question,
We have the following information:
For every 4 male birds in a cage there are 6 females.
The ratio of males to females = Number of males in the cage: number of females in the cage
Ratio of males to females = 4:6
We can convert this ratio into the simplest form by dividing both the numbers by 2 and this will also be the equivalent ratio of this obtained ratio.
Ratio of males to females = 2:3
Hence, the ratio of males to females in the cage is 2:3.
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Find the scale of a map if 4.2 cm on the map corresponds to an actual distance of 6.2 km.
Answer:
21/3100000 ≈ 1/147619
Step-by-step explanation:
You want the scale of a map on which 4.2 cm corresponds to an actual distance of 6.2 km.
ScaleThe scale of a drawing is the ratio of drawing distance to actual distance. It can be expressed a couple of ways. We can write the given scale as ...
4.2 cm : 6.2 km
or, we can reduce it to ...
2.1 cm : 3.1 km
Often, we like to have a single unit of map distance in this ratio, which would make it be approximately ...
1 cm : 1.47619 km
FractionAnother way to write the scale of a map is as a fraction.
(4.2 cm)/(6.2 km) = (0.042 m)/(6200 m) = 21/3100000
When this is expressed as a unit fraction, the denominator is a repeating decimal with a 6-digit repeat. We can round it to ...
≈ 1/147619 . . . . map scale
The scale of the map is ...
21/3100000 ≈ 1/147619 or 2.1 cm : 3.1 km or ≈ 1 cm : 1.47619 km
__
Additional comment
You may need to round the answer to match one of your answer choices.
<95141404393>
There is a pair of natural numbers whose sum is 52 and whose product is 667. The positive difference of their reciprocals is __
The positive difference the numbers is given as 6.
What is the positive difference of their reciprocals ?We are told here that there is a pair of natural numbers whose sum is 52 and whose product is 667. We have to make use of the idea of simultaneous equations to obtain the numbers.
Let the numbers be x and y thus we have;
x + y = 52 ---- (1)
xy = 667 ------ (2)
x = 52 - y ------ (3)
Substituting (3) into (2)
(52 - y)y = 667
52y - y^2 = 667
y^2 - 52y + 667 = 0
Solving the quadratic equation we have;
y=23 or y=29
The difference between the numbers then becomes 29 - 23
= 6
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Which set of fractions is ordered from least to greatest?
A) 5/8, 8/12, 3/4
B) 8/12, 5/8, 3/4
C) 3/4, 5/8, 8/12
D) 5/8, 3/4, 8/12
The arrangement of the fraction from least to greatest is A. 5/8, 8/12, 3/4.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers
The fraction can be changed to percentage to make it easier.
5/8 = 5/8 × 100 = 62.5%
8/12 = 8/12 × 100 = 66.7%
3/4 = 3/4 × 100 = 75%
The arrangement is 5/8, 8/12, 3/4.
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what is the value of f(2) when given f(x)=4x+12
A scale drawing of a rectangular bedroom is shown below. Using a scale of 1cm=4 feet, enter the actual area of the bedroom in square feet.
Answer:
Below
Step-by-step explanation:
Need the drawing but take the two cm measurements and multiply them together then multiply by 4 and then multiply by 4 again to get ft^2
I really need help 30 pointssss
Answer:
2nd one is the best division
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90 %, σ is not known, and the histogram of 52 player salaries (in thousands of dollars) of football players on a team is as shown.
The correct statement regarding the critical value of the t-distribution is given as follows:
a) [tex]t_{\frac{\alpha}{2}} = 1.6753[/tex]
Which distribution should be used?What defines which distribution should be used is whether the population standard deviation is known, as follows:
If the population standard deviation σ is known, then the z-distribution is used.If the population standard deviation σ is not known, then the t-distribution is used.As stated in the problem, the population standard deviation is not known, hence the t-distribution is used, as the sample standard deviation can be calculated from the histogram.
The critical value is obtained using a t-distribution calculator, considering that:
The confidence level is of 90%.The amount of degrees of freedom, which is one less than the sample size, is of 52 - 1 = 51.Hence it is given as follows:
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Translate The product of the quotient of a and b and the quotient of c and d
The product of the quotient of a and b and the quotient of c and d is ac/bd.
What is a quotient?In mathematics, a quotient simply means a quantity produced through the division of two numbers.
From the information, the product of the quotient of a and b and the quotient of c and d.
The product will be:
= a/b × c/d
= ac / bd
The product is ac/bd.
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select all the expressions equivalent to 4^10
The expressions equivalent to 4^10 are 2^20, 4^4 . 4^6, and 4^4 / 4^-6. Option B, option C, and option E are correct.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe need to find all the expressions equivalent to 4^10.
We will use laws of exponents for all the options one by one.
Option A:
2^5 . 2^2 = 2^(5 + 2) = 2^7
This is not equivalent to 4^10.
Option B:
2^10 = 2^(2 * 10) = (2^2)^10 = 4^10
This is equivalent to 4^10.
Option C:
4^4 . 4^6 = 4^(4 + 6) = 4^10
This is equivalent to 4^10.
Option D:
4^7 . 4^-3 = 4^(7 + (-3)) = 4^4
This is not equivalent to 4^10.
Option E:
4^4 / 4^-6 = 4^(4 - (-6)) = 4^10
This is equivalent to 4^10.
So, 2^20, 4^4 . 4^6, and 4^4 / 4^-6 are equivalent to 4^10.
So, option B, option C, and option E are correct.
Thus, the expressions equivalent to 4^10 are 2^20, 4^4 . 4^6, and 4^4 / 4^-6. Option B, option C, and option E are correct.
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