For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the statement we have two points through which the line passes:
[tex](x_ {1}, y_ {1}): (2,2)\\(x_ {2}, y_ {2}): (12, -3)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y- {1}} {x_ {2} -x_ {1}} = \frac {-3-2} {12-2} = \frac {-5} {10 } = - \frac {1} {2}[/tex]
Thus, the equation is of the form:
[tex]y = - \frac {1} {2} x + b[/tex]
We substitute one of the points and find "b":
[tex]2 = - \frac {1} {2} (2) + b\\2 = -1 + b\\2 + 1 = b\\b = 3[/tex]
Finally, the equation is of the form:
[tex]y = - \frac {1} {2} x + 3[/tex]
We write the equation of the standard form[tex]ax + by = c[/tex]
[tex]y-3 = -\frac {1} {2} x\\2y-6 = -x\\x + 2y = 6[/tex]
ANswer:
[tex]x + 2y = 6[/tex]
Find the sum of the first 50 terms in this geometric series 1+10/11+100/121
Answer:
10.91
Step-by-step explanation:
The sum of the first 50 terms in this geometric series is 11.00.
What is a geometric series?When all the terms of a geometric sequence are added, then that expression is called geometric series.
Lets suppose its initial term is f=a , multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
n=50
Series= 1+10/11+100/121
Now,
To find the sum of the first 50 terms in this geometric series, we need to use the formula:
Sum = [tex]a1(1 - r^n) / (1 - r)[/tex]
where a1 is the first term, r is the common ratio, and n is the number of terms. We can identify that the first term is 1, the common ratio is 10/11, and the number of terms is 50. Plugging these values into the formula, we get:
Sum = 1(1 - (10/11)^50) / (1 - 10/11) Sum = (1 - 0.000000000000000000000000000000000000000000000001) / (1/11) Sum = (0.9999999999999999999999) / (0.09090909) Sum = 10.99998
Rounding this result to two decimal places, we get:
Sum = 11.00
Therefore, by the given geometric sequence the answer will be 11.00.
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What is 45 divided by 765
Answer:
.06 rounded to nearest hundreth
Step-by-step explanation:
Answer:
17 I think
Step-by-step explanation:
at a store 20 feet of fencing cost $36 at the rate how much will 15 feet of fencing cost
Answer:
15 feet of fencing costs $27
Step-by-step explanation:
We know 15/20 = 3/4 so...
36 x 3/4 = 27
Another way:
36 divided by 20 = 1.8
1.8 x 15 = 27
answer:
$24
Step-by-step explanation:
36 divided by 15 equals 2.4 then 2.4x5 secne 15 is 5 away from 20 equals 12 then 36 - 12 = 24
Please SHOW me how to complete this problem. 50 points
(10y^3-5y^2-10x+4) ÷(2y-1)
Answer:
10y3 - 5y2 - 10x + 4
————————————————————
2y - 1
Step-by-step explanation:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
Step 2 :
Equation at the end of step 2 :
Step 3 :
10y3 - 5y2 - 10x + 4
Simplify ————————————————————
2y - 1
Checking for a perfect cube :
3.1 10y3 - 5y2 - 10x + 4 is not a perfect cube
Final result :
10y3 - 5y2 - 10x + 4
————————————————————
2y - 1
Answer:
The answer is 10y³-5y²-10x+4 over 2y-1
Step-by-step explanation:
i am pretty sure this the answer because there are no like terms so you can't simplify so you solve it by writing the division as a fraction. but the again im positive this is right but i may be wrong. hope this is right!
Item 13
Factor out the coefficient of the variable.
The expression 14y+38 factored is
Answer:
2(7y+19)
Step-by-step explanation:
14y+38=2(7y+19)
How many like terms are in 3x–2y+7?
Answer:
None.
Step-by-step explanation: 3x does not have the same coefficient as 2y or 7
this year a softball coach raised $1200 for new equipment. that is 4 percent less then last year. how much did he raise last year?
Answer:
The coach raised $1250 last year
Step-by-step explanation:
Let the amount raised last year be $x
Amount raised this year = $1200
Amount raised this year was less by the 4% of x amount last year:
1200 = x - 4% of x
1200 = x - x (x) 4/100 = 96x/100
x = $1250
The coach raised $1250 last year for the equipment.
Which of the following linear equations matches the graph
y = 1/3 x
y = 3/2 x
y = 3x
y = 2x
y = 2/3 x
The only linear equation that matches the graph is: Option E: y = 2/3 x
What is the equation of the line?
The general form for the equation of a Line in slope intercept form is:
y = mx + c
Where:
m is slope
c is y-intercept
We can find the slope between two coordinates using the formula:
m = [tex]\frac{(y_{2} - y_{1}) }{(x_{2} - x_{1})}[/tex]
Using the given coordinates (-3, -2) and (3, 2), we have:
m = (2 - (-2))/(3 - (-3))
m = 4/6 = 2/3
The only equation with slope of 2/3 is Option E
Justin began his walk at 3:05 p.m. He arrived at his destination at 4:32 p.m. How long did Justin walk? Show your work and explain how you found your answer.
PLZZZ HELP!!! 16 POINTS!!!!
Answer:
The answer to this question is it took him an hour and 27 minute
a pet store had a special offer this weekend. for every $120 that customers spend, $3 is donated to a pet rescue program. How much do customers have to spend in order to raise $1000 for the pet rescue program?
$3 donated_____$120 spent
$1,000 donated__X=$40,000 spent
(1,000*120)/3= 40,000
Answer: The Customers have to spend $4000 in order to raise $1000 for the pet rescue program.
Step-by-step explanation:
Hi, to answer this question we have to write a proportion.
Proportion = money spent / money raised for the pet rescue program
For every $120 that customers spend, $3: 120/3
To raise $100 : x / 100
Where x is the money that customers spent to raise $100 for the pet rescue program.
Solving for x:
120/3 = x /100
(120/3)100=x
x =$4000
How much should you invest at 5% simple interest in order to have a balance of 1,200 in two and a half years
Answer:
We should invest 9600 .
Step-by-step explanation:
Interest received in Two and a half year = 1,200
So, Interest that should be received in a year = 1200×[tex]\frac{2}{5}[/tex]
= 480
Interest rate = 5%.
Let we had invested amount X.
Thus 5 % of X we will get in a year as interest
Which is [tex]\frac{5}{100}[/tex]×X = [tex]\frac{X}{20}[/tex].
It is also equal to 480 as calculated above,
So. X = 480×20 = 9600.
Thus,
We should invest 9600 .
Please help me and explain how you got the answer
Answer:
∠NQP = 74°
Step-by-step explanation:
NPQ is a triangle.
We know the sum of 3 angles of a triangle is 180 degrees. So we can write:
N + P + Q = 180
2x + 34 + 2x + 2 = 180
Now, we can solve for x:
[tex]2x + 34 + 2x + 2 = 180\\4x+36=180\\4x=180-36\\4x=144\\x=\frac{144}{4}\\x=36[/tex]
The measure of NQP is "2x+2", we plug in x = 36, and find the measure of NQP:
∠NQP = 2(36) + 2 = 74°
Ohio is the home of two of the world’s largest aluminum smelters, in which metal is separated for recycling. Together, these two facilities process an average of 15 million pounds of aluminum each month. How many pounds of aluminum do the Ohio smelting plants average per week?
3.75 million pounds of aluminium
Step-by-step explanation:
The question requires you to perform division operation
Given that 15 million pounds is processed per month
A month has average 4 weeks.
The aluminium smelted per week will be;
15/4 = 3.75 million pounds of aluminium
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James wants to set aside money each month to save for a down payment on a new home. How much will James need to save each month if he wants to have $30,000 in three years and can earn a 6% interest rate that compounds monthly
Answer:3.80000000000
Step-by-step explanation:
Answer:
$763
Step-by-step explanation:
i got it right on my test
A rectangle has 3 square feet and width 1/2 foot. What is the length of the rectangle
Answer:
We Know, Area = Length * Width
Here, A = 3
W = 1/2
Substitute it into the expression,
3 = L * 1/2
L = 3/ 1/2
L = 3/2 ft²
So, the length of the rectangle would be 3/2 ft²
Hope this helps! :)
The length of the rectangle is found to be 6 feet by using the formula for the area of a rectangle and solving for length.
Explanation:To compute the length of the rectangle, we need to use the formula for the area of a rectangle which is length times width. Given that the area is 3 square feet and the width is 1/2 foot, we can set up the equation length * 1/2 = 3 square feet. From here, solve for length by dividing both sides of the equation by 1/2.
Therefore, the length of the rectangle is 6 feet.
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What is 4,479,621,002 rounded to the nearest ten million
The nearest ten million is 4,480,000,000.
Of the total number of spectators at a circus show, 1/4 are men. 2/5 of the remaining number of spectators are women. There are 132 women at the circus show. How many children are at the circus show?
Answer: There are [tex]198[/tex] children at the circus show.
Step-by-step explanation:
Let be "x" the total number of spectators at the circus show and "c" the number of children at the circus show.
Knowing that [tex]\frac{1}{4}[/tex] of the spectators are men, we can find the remaining:
[tex]x-\frac{1}{4}x=\frac{3}{4}x[/tex]
Since [tex]\frac{2}{5}[/tex] of the remaining number of spectaros are women and there are a total of 132 women, we can write the following equation:
[tex](\frac{2}{5})(\frac{3}{4}x)=132[/tex]
Solving for "x", we get:
[tex]x=(132)(\frac{20}{6})\\\\x=440[/tex]
Therefore, we get that "c" is:
[tex]c=440-\frac{1}{4}(440)-132\\\\c=198[/tex]
General Motors stock fell from 32$ per share in 2006 to 20$ per share during 2008. A) If you bought and then sold 300 shares all these prices what was your loss B) Exress your loss as a percent of the purchase price
Answer:
Step-by-step explanation:
total purchase price = 32*300 = 9600
total selling price = 20*300 = 6000
Net capital loss =total purchase price- total selling price =9600-6000 = 3600. Purchase price of one share is 32
Selling price of one share is 20
Number of shares bought are 300 Net % loss = (3600*100)/9600=37.5%
Final answer:
The total loss from buying and then selling 300 shares of General Motors stock, which fell from $32 to $20 per share, is $3600. Expressed as a percent of the purchase price, the loss is 37.5%.
Explanation:
To calculate the loss when buying and selling shares, we first find the loss per share and then multiply by the total number of shares. For General Motors, the price fell from $32 per share to $20 per share. This results in a loss of $12 per share. If you bought and sold 300 shares at these prices, your total loss would be:
Loss per share = $32 - $20 = $12
Total loss = $12 × 300 shares = $3600.
To express this loss as a percent of the purchase price:
Loss Percentage = (Loss per share / Purchase price per share) × 100
Loss Percentage = ($12 / $32) × 100 = 37.5%.
Goldberg's sleigh currently runs at 203mph, but he needs it to reach 400mph with all the packages he has to deliver.
If Goldberg is delivering presents at an altitude of 5,813.6ft, with the same drag and weight of a 2019 Challenger SRT® Hellcat Redeye, how much HP would he need to reach 400 mph?
Pro Tips:
100% driveline efficiency
P (air density) at 5813.6 ft = .0019 slug/ft^3
A (Area of Challenger front end) = 26.72 ft^2
C(d) (Coefficient of drag) = .398
Goldberg's sleigh required speed, 400 MPH = 587 ft/sec
F(drag) = 1/2 p x v^2 x C(d)A
P = F(drag) x V
Convert to Horsepower = P ( 1HP/550 ft lbf/sec)
Answer:
5,813 HP
Step-by-step explanation:
P=f*v
f=1/2*p*v^2*C*A
HP=(f*v)/550
Answer:
He needed 3747.61 HP to reach 400 mph.
Step-by-step explanation:
Given data :
P (air density) = 0.0019 slug/ft³
A (Area) = 26.72 ft²
C(d) = 0.398
crr = 0.015
V = 400 mph = 587 ft/sec = 178.92 m/sec
weight = 2019 lb = 8980.96 N [1 pound = 4.44822 N]
[tex]P=\frac{Force\times Displacement}{Time}[/tex]
P = Force × Velocity = FV
F = F(sum) = F(drag) + F(rolling resistance)
F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]
F(rolling resistance) = weight × crr
[tex]HP=\frac{P}{1hp}[/tex] 1hp = 745.7 watts
F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]
[tex]=\frac{1}{2}\times 0.0019\times 587^{2} \times 0.398\times 26.72[/tex]
= 3481.23 [tex]\frac{slug\times ft}{sec^2}[/tex]
convert [tex]\frac{slug\times ft}{sec^2}[/tex] to [tex]\frac{kg\times m}{s^2}[/tex]
1 slug = 14.5939 kg
1 ft = 0.3048 m
[tex]\frac{slug\times ft}{sec^2}[/tex] = 14.5939 × 0.3048 = 4.448 [tex]\frac{kg\times m}{s^2}[/tex] or newton
Since F(drag) = 3481.23 × 4.448 N
= 15484.51 N
P = F(drag) × V
= 15484.51 × 178.92 N m/s
= 2770488.529 watts
F rolling resistance = crr × w
= 0.015 × 8980.96 N
= 134.714 N
Power = (Fdrag + Frolling resistance) × V
= (15484.51 + 134.714) × 178.92
= 15619.224 × 178.92
= 279459.558 watts
Power in HP
[tex]HP=\frac{P}{hp}[/tex]
[tex]=\frac{279459.558}{745.7}[/tex]
= 3747.61 HP
He needed 3747.61 HP to reach 400 mph.
A. 141
B. 138
C. 282
D. 69
Answer:
D
Step-by-step explanation:
The measure of x is calculated as
x = 0.5( arc CD - arc BD)
= 0.5(210 - 72) = 0.5 × 138 = 69 → D
Stephan, Gavin and Jim share some sweets in the ratio 1:4:4. Stephen gets 13 sweets. How many more sweets does Gavin get over Stephen?
Final answer:
To find out how many more sweets Gavin gets over Stephan, we use the ratio 1:4:4, knowing that Stephan gets 13 sweets. Gavin, who has 4 times Stephan's amount, ends up with 52 sweets, which is 39 sweets more than Stephan.
Explanation:
To determine how many more sweets Gavin gets compared to Stephan, we need to use ratios. Since Stephan, Gavin, and Jim share sweets in the ratio 1:4:4, and Stephan gets 13 sweets, we can assign variables to the parts of the ratio to make this easier to solve. Let's assign 'x' to the value of one part, so Stephan gets 1x=13 sweets.
Since 1x is equal to 13, that means 4x is the amount Gavin gets. Now we calculate 4x, which is 4 [tex]\times[/tex] 13=52 sweets. To find out how many more sweets Gavin gets we subtract Stephan's 13 sweets from Gavin's 52 sweets to get the difference.
So, Gavin gets 52-13=39 sweets more than Stephan.
4 square meters is equivalent to how many square yards
Answer:
4.8sq. yards
Step-by-step explanation:
Find the probability of obtaining exactly 3 heads when flipping 4 coins
paul has a total of 15 markers and pencil. Each pencil cost $0.30 and each marker costs $1.25 how many pencils does paul have
Answer:
1
Step-by-step explanation:
Jan walks 1/5 of a mile to the bus stop and then gets on the bus and rides 2/3 of a mile to school find the total distance Jan travels to school
Answer:
13/15
Step-by-step explanation:
Hope it is correct
A group of students goes out to lunch. If two have burritos and five have tacos, the bill will be $19.50. If five students have burritos and two have tacos, the bill will be $22.50. Find the price of each taco and burrito
Answer:
The price of the burrito is $3.5 and the price of the taco is $2.5.
Step-by-step explanation:
2x+5y=19.5
5x+2y=22.5
------------------
5(2x+5y)=5(19.5)
-2(5x+2y)=-2(22.5)
-----------------------------
10x+25y=97.5
-10x-4y=-45
-----------------------
21y=52.5
y=52.5/21=2.5
2x+5(2.5)=19.5
2x+12.5=19.5
2x=19.5-12.5
2x=7
x=7/2=3.5
x=3.5, y=2.5
The price of the burrito is $3.5 and the price of the taco is $2.5.
The required price of the burrito is $3.50 and the price of the taco is $2.50.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's represent the price of a burrito b and the price of a taco t.
If two students have burritos, then the cost of the burritos is 2b.
If five students have tacos, then the cost of the tacos is 5t.
The total cost of the meal is 2b + 5t = $19.50.
Similarly, if five students have burritos, then the cost of the burritos is 5b.
If two students have tacos, then the cost of the tacos is 2t.
The total cost of the meal is 5b + 2t = $22.50.
We can set up a system of equations to solve for b and t:
2b + 5t = $19.50
5b + 2t = $22.50
We can solve this system using the elimination method. Multiplying the first equation by 5 and the second equation by 2, we get:
10b + 25t = 97.50
10b + 4t = 45.00
Subtracting the second equation from the first equation, we get:
21t = 52.50
t = $2.50
Substituting this value for t into the first equation, we get:
2b + 5 x $2.50 = $19.50
2b = $7
b = $3.50
Therefore, the price of a taco is $2.50 and the price of a burrito is $3.50.
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write an absolute value inequality that has 3 and -6 as two of its solutions
Final answer:
An absolute value inequality that includes 3 and -6 as solutions is |x + 1.5| ≤ 4.5. Both numbers satisfy the inequality when substituted for x.
Explanation:
To write an absolute value inequality that has 3 and -6 as two of its solutions, we must find an inequality such that both of these numbers satisfy the condition when their absolute values are considered. One such inequality is |x + 1.5| ≤ 4.5.
Let's verify the solutions:
For x = 3: |3 + 1.5| = |4.5| = 4.5, which is less than or equal to 4.5.
For x = -6: |-6 + 1.5| = |-4.5| = 4.5, which is also less than or equal to 4.5.
Therefore, the inequality |x + 1.5| ≤ 4.5 is a valid inequality that includes 3 and -6 as solutions.
Whats 2÷3/4×6&1/2÷4×8÷11=
Answer:
4/9 and 1/64
Step-by-step explanation:
Do PEMDAS:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionThere are no parentheses or exponents, so move onto step 3 Multiplication
[tex]2 \div \frac{3}{4} \times 6[/tex]
[tex] \frac{3}{4} \times \frac{6}{1} = \frac{18}{4} [/tex]
[tex]2 \div \frac{18}{4} = \frac{2}{1} \times \frac{4}{18} = \frac{8}{18} = \frac{4}{9} [/tex]
4/9 is the answer to the first problem
Again there are no parentheses or exponents, so move onto multiplication
[tex] \frac{1}{2} \div 4 \times 8[/tex]
[tex] \frac{1}{2} \div 32 = \frac{1}{2} \times \frac{1}{32} = \frac{1}{64} [/tex]
1/64 is the answer to the second problem
Don’t understand #3 please help quickly
Answer:
the answer is b
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $90 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2350. How long did each mechanic work?
Answer:
The first mechanic worked for 20 hours and the second mechanic worked for 5 hours
Step-by-step explanation:
Let f be the number of working hours of first mechanic
Let s be the number of working hours of second mechanic
Given that they both worked for a combined total of 25 hours
⇒f + s = 25 → equation 1
First mechanic charged $95 per hour and second mechanic charged $90 per hour and they both together charged $2350
⇒95f + 90s = 2350 → equation 2
Using equation 1 in equation 2:
95f + 90(25-f) = 2350
⇒95f + 2250 - 90f = 2350
⇒5f = 100
or f = 20 hours
⇒s = 25 - f ⇒ s = 5 hours
The first mechanic worked for 20 hours and the second mechanic worked for 5 hours