Give the equation of a line that goes through the point ( − 24 , 2 ) and is perpendicular to the line 8 x + 3 y = − 6 . Give your answer in slope intercept form
Answer:
[tex]y=\frac{3}{8}x+11[/tex]
Step-by-step explanation:
To find a line that is perpendicular to 8x + 3y = -6 and goes through (-24, 2), lets first find what the line's slope would be.
We can find this by finding the slope of 8x + 3y = -6 and taking the negative reciprocal of it.
We can find the slope of that line by putting it in slope-intercept form:
8x + 3y = -6
Subtract 8x from both sides.
3y = -6 - 8x
Divide both sides by 3.
[tex]y=-\frac{6}{3}-\frac{8}{3}x[/tex]
[tex]y=-\frac{8}{3}x-2[/tex]
So the slope of that line would be -8/3.
The negative reciprocal of -8/3 would be 3/8.
Now we know that the new line would have to pass through the point (-24, 2). We can use this point and write the equation in point-slope form:
[tex]y-2=\frac{3}{8}(x+24)[/tex]
Now lets change this into slope-intercept form. Add 2 to both sides.
[tex]y=\frac{3}{8}(x+24) +2[/tex]
Distribute the 3/8.
[tex]y=\frac{3}{8}x+9+2[/tex]
Simplify.
[tex]y=\frac{3}{8}x+11[/tex]
And now we have our equation in slope-intercept form.
I hope you find this helpful.
Several families are in line to enter a water park. The first family pays $54 for two adult tickets and two child tickets. The second family pays $105 for 3 adults and 5 children. What are the ticket prices for children?
Answer:
adult tickets 15
child tickets 12
Step-by-step explanation:
2x + 2y = 54 L1
3x + 5y = 105 L2
3L1 - 2L2
6x + 6y = 162
-6x - 10y = -210
-4y = -48
y = -48/-4
y = 12
2x + 2y = 54
2x +2(12) = 54
2x + 24 = 54
2x = 54 - 24
2x = 30
x = 15
A coupon subtracts $17.95 from the price p of a pair of headphones. You pay $71.80 for the headphones after using the coupon. Write and solve an equation to find the original price of
the headphones.
Answer:
$89.75
Step-by-step explanation:
p = original price of headphones
$71.80 = p - $17.95 Add $17.95 to both sides
$89.75 = p
Original price is $89.75
What are the domain and range of this function ? Help plz
Answer:
Hey there!
The domain, or possible x values are (-4, -1, 2, 9).
The range, or possible y values are (-3, 0, 6)
Let me know if this helps :)
Answer:
Domain: { -4, -1, 2,9}
Range: {-3, 0, 6}
Step-by-step explanation:
Domain is the x-values and range are the y-values. You can write it out in an x, y table to be able to see it better. Like shown below,
x y
-1 6
2 0
9 -3
-4 6
If you need further explanation let me know, but I hope this helps!
Have a great day!
Two cities are 243 miles apart
It takes a train 4 hours to travel between the two cities at a constant speed.
A car travels between the two cities at a constant speed of 65 miles per hour.
Which is traveling faster, the car or the train? Explain your reasoning.
Answer:
The car is travelling faster.
Step-by-step explanation:
Given that,
Distance between two cities = 243 miles
Time of train = 4 hours
Speed of car = 65 miles/hours
We need to calculate the speed of train
Using formula of speed
[tex]v=\dfrac{d}{t}[/tex]
Where, d = distance
t = time
Put the value into the formula
[tex]v=\dfrac{243}{4}[/tex]
[tex]v=60.75\ miles/ hours[/tex]
Hence, The car is travelling faster.
Solve for x. (Round to the nearest thousandth.)
3x - 8 = 15
Answer:x = 7.667
Step-by-step explanation:
3x - 8 = 15
+ 8 = 23
3x = 23
divide 3 by 3 and 23 so you get x by itself
answer = 7.667
Answer:
x = 7.667
Step-by-step explanation:
3x - 8 = 15 (Rearrange expression)
-8 - 15 = -3x (Combine like terms)
-23 = -3x (Divide)
x = 7.667
I don’t exactly know what the answer is. I would appreciate it if someone could help :)
Answer:
d
Step-by-step explanation:
its inverse so it will be the oppisite of 2/5
the expression as an inequality for the statement above is:
Answer: S > =85000
Reason: its says "atleast"
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes? 6 cups of flour 7 cups of flour 8 cups of flour 9 cups of flour
Answer:
The answer would be b. 7 cups of flour.
Step-by-step explanation:
I took the test.
Decide whether 0 is a solution of the inequality: a.) 2x – 1 9 c.) x – 3 > 1
Step-by-step explanation:
How to check a solution: Just as you can check the solution to an equation, you can check a solution to an inequality. First, you check the end point by substituting it in the related equation. Then you check to see if the inequality is correct by substituting any other solution to see if it is one of the solutions.
How to tell if its true or false: An inequality is a statement that shows the relationship between two (or more) expressions with one of the following five signs: <, ≤, >, ≥, ≠. Like an equation, an inequality can be true or false. 34 - 12 > 5 + 2 is a true statement. 1 + 3 < 6 - 2 is a false statement.
-3 + (-7)
Someone give me an explanation but use another example to show me
-3+-7....The answer is minus 10
4. Solve: 2(5x-2) = 6*
Answer:
x =1Step-by-step explanation:
[tex]2(5x-2) = 6\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\frac{2\left(5x-2\right)}{2}=\frac{6}{2}\\\\Simplify\\5x-2=3\\\\\mathrm{Add\:}2\mathrm{\:to\:both\:sides}\\5x-2+2=3+2\\\\Simplify\\5x=5\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\frac{5x}{5}=\frac{5}{5}\\\\Simplify\\x =1[/tex]
PLEASE HELP WILL MARK AS BRAINLIEST THE QUESTION IS BELOW
Answer:
Step-by-step explanation:
First you have to split the shape into 2. I split the box so that the little one's length is Z and width is x. Find the area of both boxes:
Box 1:
Z x X = ZX
Box 2:
Y x (Z + X) = Y(Z + X)
So the overall area of the box is:
ZX + Y(Z + X)
I'm not quite sure how to explain this without pictures to show you but i hope this helps. Let me know if you have any questions
consider the scatterplot. which data set does the scatter plot represent? a.(7, 8), (2, 12), (8, 5), (8, 4), (9, 5), (4, 14), (5, 9), (6, 7), (2, 15) b.(1, 15), (7, 8), (2, 12), (8, 5), (3, 8), (9, 4), (4, 14), (5, 9), (6, 7) c.(15, 1), (8, 7), (12, 2), (5, 8), (8, 3), (4, 9), (14, 4), (9, 5), (7, 6) d.(1, 2), (15, 12), (3, 4), (8, 14), (5, 6), (9, 7), (7, 8), (8, 5), (9, 4)
Please help me
Which of the following is not equivalent to
3/4
A. 0.75
B. 3:4
С. 75%
D. 4:3
Answer:
C: 75%
D. 0.75
Step-by-step explanation:
Both numbers are the same and they both are equivalent to 3/4.
Given f (x) = 3x - 8 find x if f(x) = -14
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=3x-8[/tex]
And we want to solve for x if f(x) is -14.
So, substitute -14 for f(x):
[tex]-14=3x-8[/tex]
Add 8 to both sides:
[tex]-6=3x[/tex]
Divide both sides by 3:
[tex]x=-2[/tex]
And we're done!
Answer:
The value of x is -2 .
Step-by-step explanation:
You have to solve it by doing comparison :
[tex]f(x) = 3x - 8[/tex]
[tex]f(x) = - 14[/tex]
[tex]3x - 8 = - 14[/tex]
[tex]3x = - 14 + 8[/tex]
[tex]3x = - 6[/tex]
[tex]x = - 6 \div 3[/tex]
[tex]x = - 2[/tex]
What are the coordinates of the point that divides the segment into a 3:2 ratio?
Answer:
(–2.2, –1.2)
Step-by-step explanation:
o divide the segment into a 3:2 ratio, we need to divide the segment into five identical parts, and find the point that divides the segment into 3/5 and 2/5. To do this we have to calculate the distance between the two points of the segment, in x and y, we can do this by just subtracting the two "y" coordinates and the two "x" coordinates:
Δy=║-4-3║=7
Δx=║-1-(-4)║=3
Then we divide those differences by 5.
7/5=1.4
3/5=0.6
and now, we multiply those results by 3 and subtract them or add them from the coordinates of the point G (subtract them from the coordinate y and add it to the coordinate x, because we are moving down and right).
Px=-4+3*0.6=-2.2
Py=3-3*1.4=-1.2
so the coordinates of the point we are looking for (which I called "P") are:
P(-2.2, -1.2).
What is the image of (-7,-1) after a dilation by a scale factor of 4 centered at the origin
Answer: (-28,-4)
Step-by-step explanation:
Multiply the x and y coordinate values by the scale factor to find the image.
-7 * 4 = -28
-1 * 4 = -4
(-28,-4)
please help me i know my shapes but i dont know if this is a square well i know what a square is but i just want to make sure 12.5 point BRAINLYEST.
Answer:
Right now its a parallelogram
Step-by-step explanation:
If you want to make it a square then just move the dots
im pretty sure thats right, if not sorry
Penelope is taking a multiple choice test with a total of 40 points available. Each question is worth exactly 5 points. What would be Penelope's test score (out of 40) if she got 3 questions wrong? What would be her score if she got x x questions wrong
Answer:
see below
Step-by-step explanation:
She got 3 questions wrong
3*5 = 15
She missed 15 points
40-15 = 25
She got 25 points right
25/40 =.625 =62.5%
If she got x questions wrong
5x is the points missed
40 -5x is the points correct
(40-5x)/40 = score
Answer:
25pts
Step-by-step explanation:
Is 17.5 a rational or irrational?
Amanda wants to pay the same amount each month on her car loan. The number of the payment various inversely with the monthly payment amount. If each monthly payment is $175, she makes 48 payments. how much would her monthly payment be if she wanted to pay off the loan in 30 Months?
Answer:
$280
Step-by-step explanation:
175 x 48 = 8400
8400 / 30 = 280
mylar balloons cost $1.25 each, and latex balloons cost $0.75 each. What equations can be used to find the number of each type of balloon in a bunch of 18 balloons that cost $19?
Answer:
Mylar Ballons: 11
Latex Balloons: 7
Step-by-step explanation:
1.25 times 11 equals 13.75
.75 times 7 equals 5.25
5.25+ 13.75 equals 19
11 + 7 equals 18.
Hope this helps you :)
It’s bath time while filling the tub dad used the last capful of bubble bath.after doing quick search for more to buy he notices that he can get 36oz for $3.79 or 24 oz for $2.89. Which of these options is the better deal ?
If you divide the price by the number of ounces, you will get how much you are paying for a single ounce.
[tex]\frac{3.79}{36}[/tex] ≈ 0.11 dollars per ounce
[tex]\frac{2.89}{24}[/tex] ≈ 0.12 dollars per ounce
As you can see, you are paying about 0.01 dollars more for every ounce of bubble bath in the second option. So you are better off buying 36 ounces for 3.79 dollars.
You can also do this buy dividing ounces by dollars.
[tex]\frac{36}{3.79}[/tex] ≈ 9.5 ounces per dollar
[tex]\frac{24}{2.89}[/tex] ≈ 8.3 ounces per dollar
Again, you can see that you get about 1 more ounce for every dollar you pay in the first option. So 36 ounces for 3.79 dollars is the way to go.
Please help! will give brainliest!!
Answer:
c
Step-by-step explanation:
tHE ANSWER IS C
if a number is negative, then its reciprocal will be;
the reciprocal will be negative
Answer:
The reciprocal of a negative number must itself be a negative number so that the number and its reciprocal multiply to 1.
The reciprocal of a positive or negative fraction is obtained by switching its numerator and denominator, the sign of the new fraction remains the same. ... Notice that when you multiply negative fractions with their reciprocals, the product is always 1 (NOT -1).
Need help ASAP
How many cups of water are needed to make 2 servings of soup?
8 cups of water = 10 servings
Answer:
1.6 cups
Step-by-step explanation:
2 servings is 1/5 of 10 servings, so the amount of water needed is 1/5 of 8 cups.
(1/5)(8 cups) = 8/5 cups = 1.6 cups
1.6 cups of water are needed for 2 servings.
5,432 to nearest tens
5430. Since 2 is smaller than 5, we will not round 32 to 40.
Need help with this, thank you
Answer:
65
Step-by-step explanation:
40 + 75 = 115
180 - 115 = 65
Answer:
x=65
Explaination
x+75+40=180
or,x+ 115=180
or, x=180-115
or x= 65
Suppose we get 24 inches of snow tomorrow. Warm weather comes the next day. For the next several days it stays warm and begins to melt the snow. If the snow melts at 2.5 inches a day, how much snow will be left on the ground after 7 days?
Answer:
6.5 inches
Step-by-step explanation:
Suppose we get 24 inches of snow tomorrow
The next day becomes warm.
The weather remains warm for the next several days.
The snow melts at 2.5 inches a day
Therefore the amount of snow that will be left after 7 days can be calculated as follows
= 2.5 ×7
= 17.5
Since the initial amount of snow was 24 inches then,
24 -17.5
= 6.5
Hence the amount of snow that will be left on the ground after 7 days is 6.5 inches