Mrs. Allen a high school teacht is grading quizzes and tests this weekend she has at most 4 hours or 240 minutes to spend grading and she would like to get at least 60 quizzes and tests graded on average it takes her 3 minutes to grade each quiz and 8 minutes to grade each test
Answer:
(55,9)
Step-by-step explanation:
Write one inequality to represent the number of quizzes and tests Mrs. Allen must grade and one inequality to represent the number of minutes it will take her to grade the quizzes and tests.
Mrs. Allen must grade at least 60 quizzes and tests, so the sum of x and y must be greater than or equal to 60.
On average, it takes Mrs. Allen 3 minutes to grade each quiz and 8 minutes to grade each test. So, the total number of minutes it takes her to grade x quizzes is 3x minutes, and the total number of minutes it takes her to grade y tests is 8y minutes. Since she has at most 240 minutes to spend grading, the sum of 3x and 8y must be less than or equal to 240.
The solution set to the system of these linear inequalities represents the numbers of quizzes and tests Mrs. Allen can grade this weekend.
Now, consider each of the coordinate points. In order to be a solution to this system of inequalities, both inequalities must be satisfied by the values of x and y. When x = 55 and y = 9, both inequalities are satisfied. To confirm, substitute these values of x and y into the first inequality.
Now substitute the values into the second inequality.
Therefore, the only point that lies in the solution set is (55,9).
Nathaniel participated in an 18-mile race. He ran 1 2 mile in 1 6 hour. If he ran the entire race at the same pace, how long, in hours, will it take Nathaniel to finish the race?
Answer:
24 hours
Step-by-step explanation:
set up a ratio:
12 miles = 16 hours
------------- ------------
18 miles = x hours
cross multiply
12m * x = 16h * 18 m
solve for x
x=16h * 18m / 12m = 24 hours
What is the midpoint of the line segment with endpoints (-2,-4) and (4,6)?
A. (-6,10)
B. (-3,5)
C. (1,1)
D. (2.2)
E. (3,5)
Answer:
Answer: C. (1,1)
Step-by-step explanation:
Midpoint
Given a segment defined by points (x1,y1) and (x2,y2), the midpoint (xm,ym) is calculated as follows:
[tex]\displaystyle x_m=\frac{x_1+x_2}{2}[/tex]
[tex]\displaystyle y_m=\frac{y_1+y_2}{2}[/tex]
The endpoints are (-2,-4) and (4,6).
Calculating the midpoint:
[tex]\displaystyle x_m=\frac{-2+4}{2}=\frac{2}{2}=1[/tex]
[tex]\displaystyle y_m=\frac{-4+6}{2}=\frac{2}{2}=1[/tex]
The midpoint is (1,1).
Answer: C. (1,1)
Vanessa works 32 hours per week at her job. Her boss offers her a full time job (40 Hours per week) and a 2 dollar per hour raise. She says "this is great now I'll make 200 more per week". What is Vanessa's hourly wage before the raise?
Answer:
$35.75 per hour
Step-by-step explanation:
In order to calculate this, we first need to calculate how much she made with her current hourly wage. We do this by multiplying the hours she worked by her current hourly wage plus her raise.
32 hours * (40+2) = $1,344
Now we subtract $200, since this is how much more she is making with her raise, and then we divide that amount by the 32 hours she is working per week.
(1,344 - 200) / 32 = $35.75 per hour
Finally, we can see that Vanessa's hourly wage before the raise was $35.75 per hour
Factorise 4(x+y)(3a-b)+6(x+y)(2b-3a)
Please solve this fast.
Show your calculation.
Answer:
(-3a+4b) (2x+2y)
Step-by-step explanation:
Expand.
4(x+y)(3a-b)+6(x+y)(2b-3a) = 4(3ax+3ay-bx-by) + 6(2bx+2by-3ax-3ay)
4(3ax+3ay-bx-by) + 6(2bx+2by-3ax-3ay) = 12ax+12ay-4bx-4by+12bx+12by-18ax-18ay
Calculate like terms.
12ax+12ay-4bx-4by+12bx+12by-18ax-18ay = -6ax-6ay+8bx+8by
Factorise.
-6ax-6ay+8bx+8by = -3a(2x+2y) + 4b(2x+2y)
Factorise further.
-3a(2x+2y)+4b(2x+2y) = (-3a+4b) (2x+2y)
Sandra brought 3 pounds of sweet potatoes for $4.41. What is the cost per pound of the sweet potatoes.
Answer:
$1.57
Step-by-step explanation:
Answer:
$1.47 per pound of the sweet potatoes
Step-by-step explanation:
Set up a proportion: [tex]\frac{3}{4.41} = \frac{1}{x}[/tex] Cross multiply, then divide: 1 × 4.41 = 4.41, 4.41 ÷ 3 = 1.47I hope this helps!
Simplify the expression. √-14√-19
Please help!!
On Monday. I bought 3 shirts and 7 pairs of pants for a total cost of $17.25. On
Tuesday, I bought 3 shirts and 9 pairs of pants for a total cost of $20.25. Can you
find the price of each item?
Answer:
Shirt: $2.25. and Pants: $1.50
Step-by-step explanation:
Set up equations with shirts as s and pants as p.
3s+7p=17.253s+9p=20.25Subtract them as there are two variables and two equations:
-2p=-3Make positive, 2p=3Divide, p=1.5To find s:
3s+7(1.5)=3s+10.5=17.25, so 3s=6.75 and s=2.253s+9(1.5)=3s+13.5=20.25, so 3s=6.75 and s=2.25What is the value of x
HELP!!!!
Answer: 7
Step-by-step explanation: This is an equalateral triangle. You can tell by the marks on each angle, marking that they are equal.
This means that the two sides that aren't the hypotenuse are the same.
Therefore,
[tex]4(x+2) = 36[/tex]
Multiply out the 4
[tex]4x + 8 = 36[/tex]
Subtract 8
[tex]4x = 28[/tex]
Divide by 4
[tex]x = 7[/tex]
One study of 91 bald eagle eggs found that the eggs had a mean length of 73.6 millimeters and a standard deviation of 2.9 millimeters.
One of the bald eagle eggs found was 74.9 millimeters long.
Which is closest to the z-score for the egg?
–0.45
0.45
1.02
1.30
Answer: 0.45
Step-by-step explanation:
Answer:
The person above is right and deserves brainliest.
(B), .45
ED2021
A laptop battery has 82 power after 1 hour of use and 46 power after 3 hours of use
Answer:
18 hours
Step-by-step explanation:
18 x 4 = 54 .
t
t
t
t
t
WILL GIVE BRAINLIEST find the value of r (-4,8), (r,12), m=4/3 (show your work pls)
Answer:
r = 13
Step-by-step explanation:
The first step is to find b from y=mx=b using m=4/3 and (-4,8)
[tex]8=\frac{4}{3}(-4)+b[/tex]
After solving the equation, b will equal -16/3 making the final equation be
[tex]y=\frac{4}{3} x-\frac{16}{3}[/tex]
Using the equation, you can solve for r.
[tex]12=\frac{4}{3} x-\frac{16}{3}[/tex]
This will bring the answer being r = 13
How can I put this into an equation?
Answer:
$65m + 125 = 1165
Step-by-step explanation:
will mark brainliest!!
Answer:
175
Step-by-step explanation:
90 + 85 = 175
180 - 175 = 5
180 - 5 = 175 = x
~theLocoCoco
10 POINTS!!!!!! answer quick
Answer:
Thx for the free points! Have a great day
Step-by-step explanation:
Please help me with this question! Will mark brainliest :)
Answer:
The slope is 1 hope this helps
y²-y¹/x²-x¹
6-(-4)/7-(-3)
10/10 =1
bana ran 18.6 miles of a marathon in 3 hours
unit rates
Answer:
6.2
Step-by-step explanation:
try this 18.6 divided by 3
Answer:
6.2
Step-by-step explanation:
Sabrina has 2/4 of a pizza and wants to share it equally between her and kayla.How much of the pizza does each person get?
Answer:
1/4 of the pizza.
Step-by-step explanation:
Since there are 2 people, you would want to divide 2/4 by 2. 2/4*1/2 = 1/4, so your answer is 1/4.
(2x - 4)(x+3) = 2x(x + 5)
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x = −3/2
Decimal Form:
x = −1.5
Mixed Number Form:
x = −1/1/2
Violet used 4 scoops of sugar to make 26cups of lemonade.How many scoops of sugar would violate need to use if she made 234 cups of lemonade?
24
11
31
26
Answer:
Violet used 4 scoops of sugar and mixed it with 26 cups of lemonade and if it makes 234 cups of lemonade then there is 208. 26 scoops of sugar would violate the cups of lemonade.
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
She would need 26 scoops of sugar as in every certain amount she gets 4 which is 26 cups,every 26 cups she needs 4 , equivelent to that is 26.
x^2-8x=-15 solve by completing the square
Answer:
Step-by-step explanation:
The cost of a cab ride is $4.25 plus $0.35 per mile. How many miles did a person travel if the cost of the cab ride was $14.75?
A. 30 miles
B. 35 miles
C. 42 miles
D. 54 miles
Answec 42
Step-by-step explanation:
use a calculater and time 0.35 by each answerd and then you get your annswer
The sum of a whole number and twice the square of the number is 10. Find the number
Answer:
Hey there !
Solution:
Let the number be x
=> x + 2x² = 10
=> 2x² + x - 10 = 0
Factorising the quadratic equation we get,
=> 2x² + 5x - 4x - 10 = 0
=> x ( 2x + 5 ) -2 ( 2x + 5 ) = 0
=> ( x - 2 ) ( 2x + 5 ) = 0
=> x = 2, -5/2
Since x is a whole number, -5 / 2 wont be applicable.
Hence x = 2.
Hence the number is 2.
Hope my answer helped !
Step-by-step explanation:
When are x+3 and 3+x equal? When are they not equal?
Answer:
when x is any real number
Step-by-step explanation:
commutative property
The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units. Which of the following statements is true about the three quadrilaterals? (4 points) a D and E are similar but not congruent. b E and F are similar and congruent. c D and E are similar and congruent. d F and D are similar but not congruent.
for questions 10-11 if l || m, find the values of x and y.
Answer:
10) 9x - 2° = 5x + 54° (corresponding angles are equal)
9x - 5x = 54 + 2
4x = 56
x = 56/4
x = 14°
10y + 6° = 9x - 2° (linear pair)
10y + 6° = 9(14)° - 2°
10y + 6° = 126° - 2°
10y + 6° = 124°
10y = 124° - 6°
10y = 118
y = 118/10
Sorry, i don't know how to do the 11th question
but hope this helps you!
If a 30 foot ladder is positioned so that the bottom of the ladder is 1/4 of its length away from the wall, what angle does the ladder make with the ground
Answer:
[tex]75.52^\circ[/tex]
Step-by-step explanation:
Given that:
The length of the ladder = 30 ft
Distance between bottom of ladder and wall = [tex]\frac{1}{4}^{th}[/tex] of its length
To find:
Angle made between the ladder and ground = ?
Solution:
This situation can be compared with a right angled [tex]\triangle ABC[/tex] as shown in the attached image in the answer area.
Side AC being the hypotenuse has the ladder along it.
AB is the wall.
BC is the distance between the wall and foot of ladder.
Formula for cosine trigonometric ratio:
[tex]cos\theta = \dfrac{Base}{Hypotenuse}[/tex]
In [tex]\triangle ABC[/tex]:
[tex]cosC=\dfrac{BC}{AC}[/tex]
Putting the values:
[tex]BC=\dfrac{AC}{4}[/tex]
[tex]cosC=\dfrac{\frac{AC}4}{AC}\\\Rightarrow cos C = \dfrac{1}{4}\\\Rightarrow \angle C = cos^{-1}(0.25)\\\Rightarrow \angle C =\bold{75.52^\circ}[/tex]
HELP ASAP PLEASE WILL MARK BRAINIEST
Answer:
The correct answer is option A.
Step-by-step explanation:
Hi! Nice to meet you and have a great day.
Answer:
The answer is B.
Step-by-step explanation:
What is StartFraction 8 Over 9 EndFraction divided by two-thirds? A fraction bar labeled 1. Under the 1 are 9 boxes containing one-ninth. Under the 9 boxes are 3 boxes containing one-third. 1 and one-sixth 1 and StartFraction 2 Over 9 EndFraction 1 and one-third 1 and two-thirds
Answer:
C 1 1/3 I got it right in the quiz
2. (0, 3); slope = -2
Answer:
y-3=-2(x-0)
Step-by-step explanation:
i think this is what u needed