Answer:
{y = 1/4x^2 − 2 y = −1/2x}
(0,0)
(-6,3)
Step-by-step explanation:
Rewrite as system of equations
y=-1/2x
1/4x^2-2y=-1/2x
Move expression to left and change its sign
y+1/2=0
1/4x^2-2y+1/2x=0
Multiply both sides of equation by 2
2y+x=0
1/4x^2-2y+1/2x=0
Sum the equation vertically and eliminate variable (2y)
3/2x+1/4x^2=0
Solve the equation
x=0
x=-6
Substitute the value of x into equation
y+1/2*0 = 0
y+1/2*(-6) = 0
Solve equation for y
y=0
y=3
so the solution is
(x1,y1)=(0,0)
(x2,y2)=(-6,3)
If w = -2 and v = -8, which of the following expressions shows the values correctly substituted in for the variables in the expression w2 - v + 1? A) -2 2 - (-8) + 1 B) -2 2 - 8 + 1 C) (-2) 2 - (8) + 1 D) (-2) 2 - (-8) + 1
Answer:
The answer is D.
Answer: D) (-2)*2 - (-8) +1
Step-by-step explanation:
w = -2.
so the w2 is equal to -2*2
v = -8
so -v + 1 = -(-8) + 1
Put it together and you get (-2)*2-(-8)+1
the parentheses are needed for the first -2 because other wise it'd be -(2*2) instead of (-2)*2
please help with this too
Answer:
Step-by-step explanation:
Garden roller is in the shape of cylinder.
So, one revolution = Curved surface area of the cylinder
diameter = 70 cm
radius = 70/2 = 35 cm
h = 100 cm
Curved surface area of the cylinder = 2πrh
= [tex]2*\frac{22}{7}*35*100[/tex]
= 22000 square cm
Area covered in 15 revolutions = 15 * 22000
= 330000 square cm
2) Coin
diameter = 22 mm
r = 22/2 = 11 mm
Volume of coin = 66 mm
πr²h = 66
[tex]\frac{22}{7}*11*11*h=66\\\\\\h=\frac{66*7}{11*11*22}\\h=0.17 mm[/tex]
Figure
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Which combinations of transformations will always produce congruent figures? Check all that apply.
a dilation, followed by a rotation
a reflection, followed by a dilation
a rotation, followed by a translation
a translation, then a rotation, followed by a stretch
O a translation, followed by two reflections
O O O O O
Answer:
a rotation, followed by a translationa translation, followed by two reflectionsStep-by-step explanation:
The rigid motions are the transformations that produce congruent images.
There are three main kinds of rigid motions :
Reflections : Flips a figure across a line of reflection. Rotations : Rotates a figure about some degrees around a center point. Translations : Moves figure on a plane about some distance in a certain direction.But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.
So, the options having dilation and term "stretch" cannot produce congruent figures.
Hence, the correct options are :
a rotation, followed by a translationa translation, followed by two reflectionsWhat is 10^4 in standard notation
Answer:
10,000
Step-by-step explanation:
Standard notation is just the normal way of writing things. 10 x 10 x 10 x 10 = 10,000.
The function h is defined by h (x) = x^2 +5.
Find h (4a).
????
Answer:
16a^2+5
Step-by-step explanation:
What is the measure of Angle X W Y? Triangle X W Y. The exterior angle to angle W is 74 degrees. 16 degrees 74 degrees 106 degrees 116 degrees
The exterior of angle XWY is 74 degrees, so the angle XWY itself is 180-74 = 106 degrees. The two angles form a 180 degree straight line or angle.
Answer:
the answer is 74
Step-by-step explanation:
i did the cumulative test
The function f(x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2,–1)} Which equation is true?
Answer:
y = -6x + 6
Step-by-step explanation:
To make an equation you need to find the slope first
To do that use the expression y2-y1/x2-x1 (-6)
Now plug that in to y = mx + b
Lastly you substitute any coordinate and find b
y = -6x + 6
Answer:C
Step-by-step explanation:
A 2-digit number is increased by 36 when the digits are reversed. The sum of the digits is 10. What is the original number?
====================================================
Work Shown:
T = tens digit of the original number
U = units digit of the original number
U+T = 10 since the digits add to 10. Solve for U to get U = 10-T
10T+U = original number
10U+T = new number where digits are reversed
-----------
new number = (old number) + 36
10U+T = (10T+U)+36
10U+T = 10T+U+36
10(10-T)+T = 10T+10-T+36 ... plug in U = 10-T
100-10T+T = 10T+10-T+36
-9T+100 = 9T+46
100-46 = 9T+9T
54 = 18T
18T = 54
T = 54/18
T = 3 is the tens digit of the original number
U = 10-T
U = 10-3
U = 7 is the units digit of the original number
10T+U = 10*3+7 = 30+7 = 37 is the original number
73 is the reversed number.
73-37 = 36 is the difference, showing that 37 increased by 36 leads to 73. The answer is confirmed.
Answer:
37
Step-by-step explanation:
how do you solve this
Answer:
[tex](a).\:\:\int _1^{-1}3f\left(x\right)dx\:=-12[/tex] is the final answer.
Step-by-step explanation:
See the attachment below.
Best Regards!
SOMEONE PLS HELP I WILL GIVE BRAINLIEST
factor x^(n+2)+x^(2)
pls explain too :>
Answer:
x² (x^n + 1)
Step-by-step explanation:
factor x^(n+2) + x²
= x^(n+2) + x²
= x^n • x² + x² (using law of indices)
= x²(x^n + 1)
*PLEASE ANSWER, NEED HELP* Find the surface area of the rectangular prism below.
Answer:
461.02
Step-by-step explanation:
2 × ( (12.3 × 4.3) + (12.3 × 10.7) + (4.3 × 10.7)) = 461.02 m^2
Answer:
461.02 M^2
Step-by-step explanation:
A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
SA = 2lw+2lh+2hw
2LW = 105.78 M^2 ( 52.89* 2 )
L= 12.3 M^2 , W = 4.3 M^2
LW = 52.89 M^2
2LH = 263.22 ( 131.61 * 2 )
L = 12.3 M^2 , H = 10.7 M^2
LH = 131.61 M^2
2HW = 92.02 ( 46.01 * 2 )
H = 10.7 M^2 , W = 4.3 M^2
HW = 46.01 M^2
SA = 2lw+2lh+2hw
SA = 105.78 M^2+ 263.22 M^2 + 92.02 M^2
SA = 461.02 M^2
Andrew is about to leave for school. if he walks at the speed of 50 meters per minute he will arrive 3 minutes after the bell rings. if he runs at the speed of 80 meters per minute he will arrive 3 minutes before the bell rings. in how many minutes will the bell ring?
================================================
Explanation:
x = time it takes for the bell to ring, time is in minutes
d = distance from his house to the school, in meters
distance = rate*time
If Andrew walks at a speed of 50 meters per minute, then he'll be 3 minutes late. This means he took x+3 minutes to get to class. The x represents the amount of time it takes if he arrived on time, then the +3 is those 3 minutes he is late. We then write
d = 50(x+3)
d = 50x+150
If he runs to school, then he's 3 minutes early. So he took (x-3) minutes to get to class. His rate is 80 meters per minute
d = 80(x-3)
d = 80x-240
We're referring to the same distance (d) value, which allows us to perform substitution to solve the two equations we formed
80x-240 = 50x+150
80x-50x = 150+240
30x = 390
x = 390/30
x = 13
Andrew has 13 minutes to get to class.
-------------------
Checking the answer:
If he walks at a speed of 50 m per minute, then he'll be 3 minutes late. So he really took 13+3 = 16 minutes to arrive. His distance traveled is d = r*t = 50*16 = 800 meters.
If he ran 80 m per minute, and is 3 minutes early, then he took 13-3 = 10 minutes to get to class. His distance is the same as before d = r*t = 80*10 = 800 meters. The fact we get 800 both times helps confirm we have the right answer.
Andrew has 13 minutes to get to class.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.
Now, let x be the time it takes for the bell to ring.
let d be the distance from his house to the school, in meters
distance = speed*time
If Andrew walks at a speed of 50 meters per minute, then he'll be 3 minutes late.
So, Andrew took x+3 minutes to get to class.
Here in the expression +3 shows that she is late.
So,
d = 50(x+3)
d = 50x+150
Now, If he runs to school, then he reached 3 minutes early.
So, toe get in class he will take (x-3) minutes
Here -3 show the child reached early
d = 80(x-3)
d = 80x-240
Since the distance is same.
So, the two equations are equal.
80x-240 = 50x+150
80x-50x = 150+240
30x = 390
x = 390/30
x = 13
Hence, Andrew has 13 minutes to get to class.
Learn more about algebra here:
https://brainly.com/question/953809
#SPJ2
Sam's total expenses last month were $1840. What was his total variable cost for last
month?
Expense
Amount
Rent
$100
Groceries and drinks
$1000
$10
Insurance premiums
Loan interest payment
Clothes
$30
$200
&
Utilities
$300
Home security fee
$200
Answer:
$1500
Step-by-step explanation:
It is given that
Rent = $100
Groceries and drinks = $1000
Insurance premiums = $10
Loan interest payment =$30
Clothes = $200
Utilities = $300
Home security fee = $200
Fixed cost are costs that does not vary and variable cost are costs that vary with goods and services.
In the given problem, rent , insurance premiums, loans interest payment ad home security fee are fixed cost.
Groceries and drinks, clothes and utilities are variable cost.
So, total variable cost for last month is
[tex]\text{Total variable cost}=\$1000+\$200+\$300=\$1500[/tex]
Therefore, total variable cost for last month is $1500.
Answer:
$1500
Step-by-step explanation:
I just took the test and got it right
Can you pleease help ill mark as brainliest
Answer:
Step-by-step explanation:
Rachel made $110 for 5 hours of work. At the same rate, how many hours would she have to work to make $264 ?
Answer: she needs to work 8 hours
Step-by-step explanation:
Graph the following equations and give the slope. Label and (if not using graph paper) mark axis.
14.x=4
15. y = 2
16, 2x - y = 5
17. y - 1 = =(x + 3)
Answer:
Step-by-step explanation:
14. x=4
vertical line(no slope) with one coordinate being (4,0)
15. y=2
horizontal line(no slope) with one coordinate being (0,2)
16. 2x-y=5
slope= 2; two coordinates are (0,-5) and (2,-1)
17. y-1=(x+3)
slope= 1; two coordinates are (-4,0) and (0,4)
HOPE THIS HELPS!!! :)
Select the correct answer from each drop-down menu.
CD is perpendicular to AB and passes through point C(5, 12).
If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x-intercept of CD is ___. The point ____ lies on CD.
Answer:
y = -x + 17
Step-by-step explanation:
A(-10,-3)
B(7,14)
C(5,12)
Need line CD perpendicular to AB through C.
Solution:
slope of AB, m1 = (yb-ya) / (xb-xa) = (14- -3) / (7- -10) = 17/17 = 1
Slope of CD, m2 = -1/m1 = -1 / 1 = -1
Line CD through C, using the point slope form
y-yc = m2(x-xc)
y-12 = -1 (x-5)
rearrange
y = -x + 5 + 12
y = -x + 17
Answer:
x intercept of CD is (17, 0)
Point (-2, 19) lies on CD
Step-by-step explanation:
Convert 18 ft to yards
Answer:
6 yds
Step-by-step explanation:
We know there are 3 ft in 1 yd
Divide by 3 ft
18 ft / 3 ft = 6 yds
Answer:
6 yards
Step-by-step explanation
1 yard= 3 feet
An arithmetic sequence is represented in the following table. Enter the
missing term of the sequence.
Answer:
387
Step-by-step explanation:
we can use the formula y=-81+(x-1)13, because 13 is the common difference
then plug 37 in for x
you get y=-81+36(13)
which simplifys down to 387
Which relation is a function? Coordinate grid with graph of a vertical line at x equals 3. A coordinate grid with graph of a curve that increases through the third quadrant through the origin and exits the first quadrant A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair. A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
Answer:
the answer is "A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin"
I took the test. Good luck!
A function is a coordinate grid containing a U shape with arrows on both ends that opens to the right, and in which the bottom portion of the U passes through the origin.
A function is a rule that connects outputs to each value. The relationship between value and output is often described with a mathematical formula, where the value is represented by one or more variables, alternatively by a table or graphically by a graph, a relationship diagram or an arrow diagram.
An important property of functions is that they are deterministic (that is, consistent, so that each value always gives the same value). This means that the function can be seen as a machine, which systematically delivers output values as soon as input values are inserted.
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Write a linear equation in point-slope form for the line that goes through
(-1,1) and (1,-5).
A. y+1 = -3(x+1)
B. y-1 = 3(x+1)
C. y+ 1 = 2(x - 1)
D. y-1=-3(x + 1)
Answer:
y -1 = -3(x+1)
Step-by-step explanation:
First find the slope
(-1,1) and (1,-5)
m = (y2-y1)/(x2-x1)
= (-5-1)/(1--1)
=-6/ (1+1)
= -6/2
= -3
We are using point slope form
y-y1 = m(x-x1) where m is the slope
y - 1 = -3( x - -1)
y -1 = -3(x+1)
Answer:
The answer is option D.
Step-by-step explanation:
Equation of a line is y= mx + c
where m is the slope
Slope of the line using points
(-1,1) and (1,-5) is
[tex] \frac{ - 5 - 1}{ 1 + 1} = \frac{ - 6}{2} = - 3[/tex]
Therefore the equation of the line using point (-1,1) is
y - 1 = - 3( x + 1)Hope this helps you
A prism has a volume of 238 cubic millimeters. Which is the correct substitution for finding the length of the prism?
Answer:
D. V = l w h. 238 = l times 8 and one-half times 3 and one-half
Step-by-step explanation:
A prism has a volume of 238 cubic millimeters.
A prism has a length of l millimeters, height of 3 and one-half millimeters, and width of 8 and one-half millimeters.
Which is the correct substitution for finding the length of the prism?
A. V = l w h. 238 = l + 8 and one-half + 3 and one-half
B. V = l w h. V = 238 times 8 and one-half times 3 and one-half
C. V = l w h. l times 8 and one-half times 3 and one-half
D. V = l w h. 238 = l times 8 and one-half times 3 and one-half
From the question
V=lwh
Volume of a prism=length)(width)(height)
Volume=238
l= l mm
w= 8 1/2
h= 3 1/2
Substituting all the values
V=lwh
238= l * 8 1/2 * 3 1/2
D. V = l w h. 238 = l times 8 and one-half times 3 and one-half
Answer:
D
Step-by-step explanation:
got it right on edge 2020
Gary runs a recycling centre for a local charity.
New staff have to take part in 7 hours of training before they can
work at the centre,
Gary needs to arrange a training programme for new staff.
The training programme will start on Monday 5th September
Each training day:
1) starts at 10 am and must finish by 5 pm
2)has sessions in 2 hour blocks which include a 15 minute
break
3)has a 1 hour break for lunch
The 15 minute breaks and
lunch do not count towards the 7 hours of training
At the end of the training there will be a 90 minute assessment.
Gary needs to know the least number of days he needs to allocate
for the 7 hours of training and the assessment.
Plan a training programme for Gary.
Show the start and finish times for the sessions on your plan.
Answer:
Just use 2 days
Step-by-step explanation:
Train for 2
Break
Train for 2
Break
Lunch
Day 2:
Train for 2
Break
Lunch
Exams
One student ate 3/20 of all candies and another 1.2 lb. The second student ate 3/5 of the candies and the remaining 0.3 lb. What weight of candies did they each eat? PLEASE HELP!!
Let the total weight of the candy = x
We know the total weight is:
X = 3/20x + 1.2 + 3/5x+ 0.3
Simplify:
X= 3/20x + 1.2 + 12/20x + 0.3
X = 15/20x + 1.5
Subtract 15/20x from both sides:
5/20x = 1.5
Divide both sides by 5/20:
X = 1.5 / 5/20
X = 6
Total = 6 pounds.
Can someone answer a-c please!
solve for x -7x+1≥22 or -10x+41≥81
Answer:
The answer to the union of the two sets is: [tex]x\leq -3[/tex]
Step-by-step explanation:
Since they are asking for an "OR" condition, we need to find the set of solutions for each inequality, and then use the union of those two sets.
First inequality:
[tex]-7x+1\geq 22\\1-22\geq 7x\\-21\geq 7x\\-3\geq x\\x\leq -3[/tex]
so this is the set of all real numbers smaller than or equal to -3 (visualize the numbers on the number line to the left of -3 and including -3 itself)
Second inequality:
[tex]-10x+41\geq 81\\41-81\geq 10x\\-40\geq 10x\\-4\geq x\\x\leq -4[/tex]
So, this sets consists of all real numbers smaller than or equal to -4 (visualize the numbers on the number line to the left of -4 and including -4 itself.
Then, when we do the union of these two sets, we get:
[tex]x\leq -3[/tex]
since the number -4 is located to the left of -3 on the number line, so the set defined by the second inequality is in fact a subset of the one defined by the first inequality.
Please help me fast!
Answer:
39.5
Step-by-step explanation:
Let's figure out the equations of l and m first.
For line l, we see that the coordinates (0, 5) and (3, 0) are on the line. The equation of a line is y = mx + b where m is the slope and b is the y-intercept.
We can find the slope, which is the difference in the y-coordinates divided by the difference in the x-coordinates:
m = slope = (5 - 0) / (0 - 3) = 5/-3 = -5/3
The y-intercept of a line is the place where the line crosses the y-axis. For line l, it is at (0, 5), so b = 5. Our equation is thus: y = (-5/3)x + 5.
For line m, we see that the coordinates (0, 2) and (7, 0) are on the line. The slope is:
m = slope = (2 - 0) / (0 - 7) = 2/-7 = -2/7
The y-intercept is at (0, 2), so b = 2. Our equation is hence: y = (-2/7)x + 2.
Taking the two equations, let's set 15 equal to y and solve for x:
y = (-5/3)x + 5 ⇒ 15 = (-5/3)x + 5 ⇒ 10 = (-5/3)x ⇒ x = -6
y = (-2/7)x + 2 ⇒ 15 = (-2/7)x + 2 ⇒ 13 = (-2/7)x ⇒ x = -91/2
Let's find the difference:
-6 - (-91/2) = 39.5
The answer is thus 39.5.
~ an aesthetics lover
Please help me on this question
Answer:
x = [tex]\frac{k(a+r)}{7}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{7x}{k}[/tex] - r ( add r to both sides )
a + r = [tex]\frac{7x}{k}[/tex] ( multiply both sides by k to clear the fraction )
k(a + r) = 7x ( divide both sides by 7 )
[tex]\frac{k(a+r)}{7}[/tex] = x
Answer:
ak - kr k(a - r)
x = -------------- or x = ------------
7 7
Step-by-step explanation:
1. Multiply all three terms by k to eliminate the fraction:
ak = 7x - kr
2. Subtract kr from both sides:
7x = ak - kr
3. Divide both sides by 7:
ak - kr k(a - r)
x = -------------- or x = ------------
7 7
Scanning the road can be thought of as a
A. way to improve your mileage
B. way to reduce your mileage
C. comprehensive drive test
D. systematic search process
Answer:
D
Step-by-step explanation:
Well scanning the road for mileage wouldn't be the correct formula for "scanning" but looking for a gas station sounds more right.
Answer: d
Step-by-step explanation: i did it and got it right
describe the y-intercept in terms of knots and rope length
Answer:
what is the y-intercept sorry i can't help there isn't enough information
Step-by-step explanation: