Step-by-step explanation:
Pythagoras :
c² = a² + b²
c is the Hypotenuse (side opposite of the right angle), which is in our case the distance of the 2 cars.
after 2 hours the east car was driving x miles. and the south car was driving x + 2×25 = x + 50 miles.
x² + (x + 50)² = 250²
x² + x² + 100x + 2,500 = 62,500
2x² + 100x = 60,000
x² + 50x = 30,000
x² + 50x - 30,000 = 0
the solution for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 50
c = -30,000
x = (-50 ± sqrt(2500 - 4×1×-30000))/(2×1) =
= (-50 ± sqrt(2500 + 120000)/2 =
= (-50 ± sqrt(122500))/2 = (-50 ± 350)/2 =
= -25 ± 175
x1 = -25 + 175 = 150 miles
x2 = -25 - 175 = -200 miles.
negative distances don't make any sense here in our scenario, so the solution is x = 150 miles.
therefore, the east car was going 75 mph (traveled in 2 hours 150 miles).
and the south car was going 75 + 25 = 100 mph (traveled in 2 hours 200 miles).
Solve the system by graphing. Y=2x-9 y=-2x-1
Answer:
(2,-5)
Step-by-step explanation:
See attachment
One can also solve this by calculation:
y=2x-9
y=-2x-1
-
Rearrange either equation to find x. I'll use the first:
y=2x-9
2x = y+9
x = (y+9)/2
Now use this value of x in the second equation:
y = -2x-1
y =-2((y+9)/2)-1
y = (-2y-18)/2)-1
y = -y -9 - 1
2y = -10
y = -5
Now use -5 for y in the rearranged equation:
y = -2x-1
-5 = -2x-1
-2x = -4
x = 2
Solution is (2,-5)
But the question wants a graph solution, which is also fun when you use DESMOS.
John borrowed $5,000 from his parents to buy a car. He made a one-time payment of $1,500 and then he is going to pay his mother $250 each month. How long will it take for him to pay off the car?
Answer:
14 months
Step-by-step explanation:
5000=1,500+250m
m=months
5000-1500= 3500
3500=250m
3500÷250=14
14=m
Answer:
14 months
Step-by-step explanation:
He already payed $1,500 of the $5,000 payment.
$5,000 - $1,500
So that means he has $3,500 left to pay.
If he is going to pay $250 per month.
Then do $3,500 divided by $250.
$3,500 ÷ $250
Which is 14 months.
Can someone help and explain please!
Answer:
19.56
Step-by-step explanation:
Discount 25% of $24.60 is :
(25/100) x 24.6 = 6.15
$24.60 - 6.15 = $18.45
Tax 4.5% of $24.60 is :
(4.5/100) x 24.6 = 1.107 approx. 1.11
Amount to be paid = $18.45 + $1.11 = $19.56
. If x > 0 and cos 0 = 2/x , what is tan
in terms of x?
Answer:
Explanation:
A)wkt, tanx = perpendicular(p)/base(b) .....(1)
B)We are given tanx=5/12 .....(2)
C)On comparing the quantities we get that p=5 and b=12
D)We require the value of hypotenuse(h),
for this we apply the Pythagoras theorum i.e,
h
2
=
p
2
+
b
2
⇒
h
2
=
5
2
+
12
2
⇒
h
2
=25+144
⇒
h
2
=169
⇒
h=
√
169
⇒
h=13
Step-by-step explanation
well yeah thats the dang answer
Solve for x
-1/5x -25 = -9
Answer:
-80
Step-by-step explanation:
you pass the 25 to the right side adding and the the 1/5 multiplying by -5 to the right side
Can someone help me plsss
Write a function for the line with a slope of 5 that passes through the point (2, 1). Enter the correct equation in the box.
Answer:
brainly
Step-by-step explanation:
if we changed the –0.14 to a 2 in the equation, what would happen to the graph?
If -0.14 is changed to 2, the graph would become a positive graph, or it would be steeper, because it has a positive slope
The equation of the graph is given as:
[tex]y = -0.14x + 3[/tex]
The above equation is a linear equation, which is represented as:
[tex]y =mx + c[/tex]
Where m represents the slope of the linear equation.
By comparison, we have:
[tex]m = -0.14[/tex]
i.e. the slope of the equation [tex]y = -0.14x + 3[/tex] is -0.14
When -0.14 is replaced with 2, the equation becomes
[tex]y = 2x + 3[/tex]
And the slope of the new equation [tex]y = 2x + 3[/tex] is
[tex]m =2[/tex]
2 is greater than -0.14, and 2 is positive.
This means that the graph would become a positive graph, or it would be steeper, because it has a positive slope
Read more linear equations at:
https://brainly.com/question/19045223
Write an equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x−9.
y = -2x + 24
hope this is helpful!
Answer:
y+2x=24
Step-by-step explanation:
the equation of the line: y=1/2x -9
Get the slope by using derivative:
dy/dx= 1/2
dy/dx= slope of the normal line
Since we are looking for slope of the tangent line:
Use Mn=-1/Mt
The slope of the tangent line is -2
Using point slope form:
(y-y1)=m(x-x1) ; where x1=7, y1=10, and m=-2
y-10=-2(x-7)
y-10=-2x+14
ANSWER: y+2x=24
7. One serving of Ms. Scott's tomato soup is 0.75 cup. How many servings are in the 72-cup pot? 104.2. servings 10.42 servings 96 servings O 9.6 servings
Answer:
96 Servings
Step-by-step explanation:
Divide the total 72 cups by the serving, 0.75 cup, which equals 96 servings
Answer:
96 servings
Step-by-step explanation:
Divide the total amount, 72 cups, by each serving, .75 cups, to get the amount of servings, 96.
[tex]\frac{72}{0.75} = 96[/tex]
Find the maturity value of a loan of Php 5,000 at an interest rate of 15% in 2 years
Answer:
Php 6500
Step-by-step explanation:
Assuming simple interest, the value after 2 years is ...
A = P(1 +rt) . . . . . value of loan of principal P at annual rate r for t years
A = 5000(1 +0.15·2) = 5000(1.30) = 6500
The maturity value will be Php 6500.
1+1=3 proof
needs step by step explanation
Answer:
1+1=3, See explenation
Step-by-step explanation:
1+1=2 but thats basically 2.1 because whole numbers are boring, but 2.1 is basically 2.2 because we want it as an even number, but 2.2 is basically 2.3 because 2.3 is the luckiest number, which is basically 2.5 if you think about it because 2.3 looks like 2/3 and two thirds can't be a whole (which is why we say 3/3 instead of 2/3) and 2.5 rounded up is 3. So thats how 1+1=3
Today 60 students rode their bicycles to Coast Middle School. If this is 75% of the students at the school, how many students attend Coast middle School?
Answer:
i think students attend Coast middle School 80 students
Step-by-step explanation:
students attend Coast middle School x students
75%x = 60
x = 60×100/75
x = 80
Answer:
80 students attend
Step-by-step explanation:
75% is the same as 3/4 so you divide 60 by 3 to get 20 then you can multiply that by 4 to get 80
(BRAINLIEST TO THE PERSON WHO HELPS ME WITH THESE FOUR QUESTIONS)
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable.
2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote
4. If Kevin wrote 21 posts, how many did Cheryl write?
Answer:
Cheryl's posts + 7 posts =Kevin Posts
K-C=7 or C+7+K I use them because C is Cheryl and K is Kevin
Operation=subtraction or addition because it could be K-C=7 or C+7+K
Cheryl wrote K-7=C posts
4. Which situation best demonstrates the phrase "correlation is not causation"?
A. As rainfall increases, so does the water level in the river.
B. The hotter the temperature, the faster ice will melt.
C. As the number of people with vision loss increases, the sale of hearing aids increases.
D. The fewer mistakes a student makes on a math test, the better their grade is on the math test.
a
Answer:
C
Step-by-step explanation:
We can solve this by analyzing if the event causes the result. If it does not, then there is correlation but not necessarily causation
A. Event: Rainfall. Result: Water level rises
Does rainfall cause an increase in water level? Yes, so this is incorrect
B. Event: Temperature increase. Result: Ice melting
Does an increase in temperature cause ice to melt faster? Yes, so this is incorrect
C. Event: More people have vision loss. Result: Hearing aids sales increase
Does more people having vision loss cause hearing aids sales to increase? No, vision loss does not cause a need for hearing aids -- hearing loss would, but vision loss does not. This is correct
D. Event: A student makes fewer mistakes. Result: A better grade
Do fewer mistakes cause better grades? Yes, so this is incorrect
Find a quadratic model in standard form for the set of values.
(-2, 18), (0, 4), (4, 24)
4x^2 + 2x - 4
Hope this helps
Find the value of x
SC is the median of QRS
Calculate the distance between the points M=(-1, -2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answer:
nearest hundredth 8.944
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.944
What is the equation of the line passing through the points (Two-fifths, StartFraction 19 Over 20 EndFraction) and (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form
Step-by-step explanation:
Slope-intercept form: y = mx + b
Step 1: Find the slope.Solve for [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]y2-y1 = \frac{11}{12} -\frac{19}{20}[/tex]
[tex]x2-x1 = \frac{1}{3} -\frac{2}{5}[/tex]
To solve for the fractions you need a common denominator.
[tex]y2-y1 = \frac{11*20}{12*20} -\frac{19*12}{20*12} = \frac{220}{240} -\frac{228}{240}=\frac{-8}{240} = \frac{-1}{30}[/tex]
[tex]x2-x1 = \frac{1*5}{3*5} -\frac{2*3}{5*3} = \frac{5}{15} -\frac{6}{15}=\frac{-1}{15}[/tex]
To divide fractions you keep (the first equation), change (the division sign to multiplication), and flip (the second fraction).
[tex]\frac{y2-y1}{x2-x1}=\frac{\frac{-1}{30} }{\frac{-1}{15} } = \frac{-1}{30}*\frac{15}{-1} =\frac{-15}{-30}=\frac{1}{2}[/tex]
Step 2: Plug slope and a point into y=mx+b to solve for b.[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{2}[/tex])*([tex]\frac{1}{3}[/tex])+b
[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{6}[/tex])+b
[tex]\frac{11}{12}-\frac{1}{6}[/tex] = b
[tex]\frac{11*6}{12*6}-\frac{1*12}{6*12}=\frac{66}{72} -\frac{12}{72} =\frac{54}{72}=.75[/tex]
b = .75
y = [tex]\frac{1}{2}+.75[/tex]
Given the points (4, 5) and (-2, 8), find the slope of the line that passes through the points.
Group of answer choices
9/6
-2/1
-1/2
1/2
Answer: c
Step-by-step explanation:
Formula of slope of line :
m=y2-y1/x2-x1
m=8-5/-2-4
=-3/6
m=-1/2
The U.S. Energy Department states that 60% of all U.S. households have ceiling fans. In addition, 29% of all U.S. households have an outdoor grill. Suppose 13% of all U.S. households have both a ceiling fan and an outdoor grill. If a U.S. household is randomly selected, the probability that the household has neither a ceiling fan nor an outdoor grill is
Answer:
Very sorry if this is no help
Step-by-step explanation:
Leo's hair is longer than Wes's hair. Wes's hair is longer than Ella's hair. Whose hair is longer
Answer:
Leo
Step-by-step explanation:
Leo > Wes
Wes > Ella
Leo > Wes > Ella
Answer:
Leo's hair is longer than both Wes's and Ella's hair.
Step-by-step explanation:
Leo's hair> Wes's hair>Ella's hair
max found a car he wants to buy that costs $16,000. He can afford to pay $250 a month for the car. His bank offers him a car loan of 7.3%. The length of his loan should be about 5 years, so he can afford the payments. true or false
Max won't be able to afford the payments.
Since Max found a car he wants to buy that costs $16,000, and he can afford to pay $ 250 a month for the car, and his bank offers him a car loan of 7.3%, and the length of his loan should be about 5 years, to determine if he can afford the payments, the following calculation must be performed:
(16000 x 1.073 ^ 5) / (5 x 12) = X 22,757.187 / 60 = X 379.28 = X
Therefore, each monthly payment will be $ 379.28, so Max won't be able to afford the payments.
Learn more about maths in https://brainly.com/question/25927059
Is (x+2) a factor of f(x) = x3-7x2+2x-8? Use either remainder theorem to explain your reasoning
Answer:
No
Step-by-step explanation:
If (x + h) is a factor of f(x) then f(- h) = 0
Here (x + 2) with h = - 2 , then
f(- 2) = (- 2)³ - 7(- 2)² + 2(- 2) - 8
= - 8 - 7(4) - 4 - 8
= - 8 - 28 - 12
= - 48
Since f(- 2) ≠ 0 then (x + 2) is not a factor of f(x)
What is an equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1)
y= 3x + 1
y=x-3
y=2x+5
y= 2x – 5
What is the equation of the line that passes through the point (-2, 1) and has a
slope of 3/2?
Answer:
Step-by-step explanation:
Given:
x1 = -2
y1 = 1
slope (m) = 3/2
Solution:
y - y1 = m ( x - x1 )
y - 1 = 3/2 ( x - (-2) )
y - 1 = 3/2 ( x + 2 )
y - 1 = 3/2x + 3
y = 3/2x + 3 + 1
y = 3/2x + 4
Shirt Circuit Graphic Tees has fixed expenses of $25,560 for the production of their
t-shirts. They have a variable expense of $4.50 for each t-shirt that they
produce, and they sell their t-shirts for $22.50 each.
How many t-shirts does Shirt Circuit Graphic Tees have to sell to reach their
breakeven point?
Answer:
Step-by-step explanation:
Cost price = fixed expenses + variable expenses× number of products (x)
Selling price = total cost price + profit
At break even point,
Profit = 0
Therefore, total selling price = total cost price
X(22.50)= 25560 + x(4.50)
(22.50 - 4.50)x = 25560
18x= 25560
X = 1420
What is the next term of the geometric sequence?
9/4,-4/3,4
Answer:
-12
Step-by-step explanation:
To find the ration, take the second term and divide by the first term
-4/3 ÷ 4/9
Copy dot flip
-4/3 * 9/4
-3
Multiply each term by -3
4*-3 =-12
hope it helps sorry if it doesn't
sooooooooooooooooooooooooooooo easy
Answer:
11/12..................
Answer:
J) 11/12
Step-by-step explanation:
(5) Arrange the decimals in decreasing order...
(a) 8.6, 0.86, 6.8
(b) 7.005, 5.07 7.05
A) 0.86, 6.8, 8.6
B) 5.07, 7.005, 7.05
hope this is helpful!