A large rectangle is made up of nine identical rectangles whose longer side equals 10. What is the area of the large rectangle?
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Explanation:
Refer to the diagram below.
A small rectangle has its longer side equal to 10 and its shorter side is x, which is some real number on the interval 0 < x < 10.
Across the top, the two sides of length 10 add to 20. So the larger rectangle has a horizontal dimension of 20 units.
The vertical side of the larger rectangle is x+10+x = 2x+10 units
The area would be
area = length*width = 20(2x+10) = 40x+200
Each of the nine smaller rectangles has area of length*width = 10x. Since we have 9 identical copies, the smaller rectangle areas must add to 9*10x = 90x
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Equate those two expressions and solve for x
90x = 40x+200
90x-40x = 200
50x = 200
x = 200/50
x = 4
So each smaller rectangle has area of 10*x = 10*4 = 40 square units. In total, the nine smaller rectangles combine to an area of 9*40 = 360 square units
Note how x = 4 leads 40x+200 to result in 360 as well.
Help me, please!!!
Lesson 3-8. Write an equation for the line perpendicular to the given line through the given point.
Answer:
y = -3x + 14Step-by-step explanation:
Given line:
y = 1/3x - 2/5Perpendicular lines have negative-reciprocal slopes.
We will have a line:
y = -3x + bUse the coordinates of the given point to find the value of b:
-1 = -3(5) + b-1 = - 15 + bb = 14So the line is:
y = -3x + 14Evaluate |-6| + 3|4| + |-5| -0×6.
O 0
O 25
O 23
O 18
Plz help! A,B,C OR D
Answer:
c
Step-by-step explanation:
Answer:
Option DStep-by-step explanation:
All steps correct apart from the last one.
The student worked out the value of b = 4.4 but when finalizing the equation he subtracted 4.4 instead of adding:
y = -2x + 4.4 ⇒ correcty = -2x - 4.4 ⇒ wrongCorrect answer choice is D
Some help PLZ make sure it’s right will mark brainiest:)
Answer:
y= 7/9x -17/9
Step-by-step explanation:
(5,2) (-4,-5)
slope intercept of a line is
y = mx +b
m = y2-y1/ x2-x1
= -5-2/ -4-5 = -7/-9
=7/9
if the line is passing through (5,2)
2= 7/9(5)+ b
2=35/9 +b
b = 2-35/9
b= -17/9
y= 7/9x -17/9
2(x-y)(x+y)+(x+y)^2+(x-y)^2
A list of numbers is given below. If x is a number in this list, which inequality could represent x? {-5, -12, -2, -9}
Answer:
x<-1
Step-by-step explanation:
All of the numbers on/in the set are below -1. That means for that any of them to be x, the inequality would be x<-1.
plz help me solving me math questions
Write the slope-intercept form of the equation for each line.
Answer:
y = x + 2
Step-by-step explanation:
Slope = 1x
y-intercept = 2
y = x + 2
Exit
What is the decimal equivalent of 4/5
Answer:
0.8
Step-by-step explanation:
to find the decimal equivalent we must get the denominator to 100
to do that we must multiply it by 20, 4/5 * 20/20 is 80/100
80/100 is also 80%, which is also 0.80 (which can be simplified to 0.8)
the mean of eight numners is 41 the mean of two of the numbers is 29 work out the mean of the other six numbers
Answer: 270/6 =45
Step-by-step explanation:
There are 3 different sets of numbers involved here.
A set of six, a set of two and the set of all eight.
Each set has its own mean.
ILL GIVE BRAINLIEST PLS HELP
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 9.5?
A.
It is the graph of y = x translated 9.5 units to the right.
B.
It is the graph of y = x translated 9.5 units up.
C.
It is the graph of y = x where the slope is increased by 9.5.
D.
It is the graph of y = x translated 9.5 units down.
Answer:
Im pretty sure is B but it might be C.
Step-by-step explanation:
Need Helpp!!!
Line segment CD is shown on a coordinate grid:
The line segment is reflected about the y- axis to from C’D’.
Which statement describes C’D’
C’D’ is perpendicular to CD
C’D is half the length of CD
C’D’ is greater than twice the length of CD
C’D’ and CD are equal in length
Thanks!
Answer: -1.56i^ +1.07j^
Step-by-step explanation:Vector C = -1.56i^ +1.07j^
This question requires that we use the properties of the scalar product of two vectors to find the required x and y component.
The dot product of two perpendicular vectors is equal to and the product of two vectors that are not parallel is equal to a nonzero value.
These are the properties that have been used in solving this problem alongside solving the simultaneous questions generator.
Explanation:
The full solution can be found in the attachment below.
Thank you for reading and I hope this post is helpful to you.
The manager of a food court estimates that he needs 7 pretzels for every 20 people who attend a hockey game. What constant of proportionality relates the number of pretzels to people?
A. 0.35
B. 2.86
C. 35
D. 140
Answer:
a) 0.35
Step-by-step explanation:
The manager of a food court estimated that he needed 7 pretzels for every 20 people who attend that hockey game. This means that 20 people need/require to have 7 pretzels. 20 people= 7 pretzels.
The Candela brothers own two pizza restaurants, one on Park Street and one on Bridge Road.
The computer output below summarizes the distribution of weekly revenues at each
restaurantâ€"26 weeks for Park Street and 40 weeks for Bridge Avenue.
The mean, median and mode are measures of central tendency, that is they tend to indicate the location middle of the data
Required values;
(a) The performance for the week for Park Street
Revenue is Q₂ < $7,500 < Q₃The sales for the week is better than 72.91% of all salesThe performance for the week for Bridge Road
Revenue; Q₂ < $7,100 < Q₃The sale for the week is better than 59.87% of all sales(b) The mean is $3611
The median is $3,600
The standard deviation is $3250
The Interquartile range is $6075
Reason:
The table of values that maybe used to find a solution to the question is given as follows;
[tex]\begin{array}{|l|l|l|}\mathbf{Variable} &\mathbf{Park}&\mathbf{Bridge}\\N&36&40\\Mean&6611&5989\\SE \ Mean&597&299\\StDev&3580&1794\\Minimum&800&1800\\Q_1&3600&5225\\Median&6600&6000\\Q_3&9675&7625\\Maximum&14100&8600\end{array}\right][/tex]
(a) Park Street revenue = $7,500
Bridge Road's revenue = $7,100
The two stores sold close to but below the 75th percentile
Bridge Road revenue;
The z-score is given as follows;
[tex]Z = \dfrac{x - \mu }{\sigma }[/tex]
[tex]Z = \dfrac{7100 - 5,989 }{1794 } \approx 0.6193[/tex]From the Z-Table, we have;
The percentile= 0.7291
Therefore, the sale for the week for Park Street is better than 72.91% of all the salesPark Street revenue;
The z-score is given as follows;
[tex]Z = \dfrac{7500 - 6611}{3580} \approx 0.25[/tex]From the Z-Table, we have;
The percentile = 0.5987
Therefore, the sale for the week is better than 59.87 % of all the sales(b) Given that the operating cost is $3,000, frim which we have;
The subtracted value is subtracted from the mean and median to find the new value
Profit = The revenue - Cost
New mean = 6611 - 3000 = 3611
The new mean = $3,611The new median = 6600 - 3000 = 3600
The new median = $3,600The standard deviation and the interquartile range remain the same, therefore, we have;
The standard deviation = $3,580The interquartile range = 9675 - 3600 = 6075
The interquartile range = 6075Learn more here:
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Question 15
5 pts
Nicole babysits on the weekends. She charges a
flat fee of $10 and then $5 per hour. If she made
$40 on Friday night, how many hours did she
babysit?
Choose the equation to represent this situation.
O
o 10h + 40 = 5
10h + 5 = 40
o 5 + 10 = 40h
o 5h + 10 = 40
-
wins some money on the lottery. She uses 1/3 of her lottery win to buy a house
and she gives 1/8 of her lottery win to charity. Molly then shares the remainder of her
lottery win equally among her four children. Work out the fraction of Molly's lottery
win that each of her four children receives.
Answer:11/96
Step-by-step explanation:
1-(1/3)=2/3=14/24
(2/3)-(1/8)=(14/24)-(3/24)=11/24
11/24 divided into 4 again is 11/96
is 1/3 more than the number 3?
Answer:
1/3 is less than 3
Step-by-step explanation:
1/3 = 0.3333 which is less than 3
636/526 pls answer and you get points
Answer:
1.20912547529
Step-by-step explanation:
Find an equation of the line with slope 3 that
contains the point (7.11).
y = mx + b
−4 + 20 > −8 what the answers
Answer: -20
Step-by-step explanation: plz mark me brainliest please?
Select ALL that could take P to Q:
Answer:
No question.
Step-by-step explanation:
Solve for c. 2a + 3b = c
Please help as soon as possible. Thanks! =D
Answer:
a = c - 3b/2
Step-by-step explanation:
2a + 3b - 3b = c - 3b
2a = c - 3b
2a/2 = c/2 - 3b/2
therefore your answer is a = c - 3b/2
Don’t understand I’ll give u a brainly
The answer is the second one
yis inversely proportional tox.Wheny=50,x=4Work outywhenx=8
Answer:
55555
Step-by-step explanation:
8th grade algebra pleas help
y=-2/3x + 7 what is the slope?
Answer:
Lucky for you i'm good at algebra:)
Step-by-step explanation:
Slope: -2/3
Y-intercepts: (0,7)
Answer:
Slope = -1.333/2.000 = -0.667
x-intercept = 21/2 = 10.50000
y-intercept = 21/3 = 7
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(-2/3*x+7)=0
Step 1:
Simplify 2/3
Equation at the end of step 1:
y - ((0 -(2/3• x)) + 7) = 0
Step 2: Rewriting the whole as an Equivalent Fraction
Rewrite the whole as a fraction using 3 as the denominator :
7 = 7/1 = 7 · 3 /3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
-2x+7·3/3 = 21-2x/3
Equation at the end of step 2:
y-(21-2x)/3=0
Step 3:
Rewriting the whole as an Equivalent Fraction :
Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
y=y/1=y·3/3
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
y • 3 - ((21-2x)) 3y + 2x - 21
————————————————— = ————————————
3 3
Equation at the end of step
3
:
3y + 2x - 21
———————————— = 0
3
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
3y+2x-21
———————— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
3y+2x-21 = 0
Equation of a Straight Line
4.2 Solve 3y+2x-21 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3y+2x-21 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000
y-intercept = 21/3 = 7
Calculate the X-Intercept :
When y = 0 the value of x is 21/2 Our line therefore "cuts" the x axis at x=10.50000
x-intercept = 21/2 = 10.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 5.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.667 - 7.000 = -1.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -1.333/2.000 = -0.667
Geometric figure: Straight Line
Slope = -1.333/2.000 = -0.667
x-intercept = 21/2 = 10.50000
y-intercept = 21/3 = 7
Please help with this question
work out the value of 3^2 + 2^3
Answer:
17
Step-by-step explanation:
3² + 2³
= 9 + 8
= 17
Answer:
3/2 can be written as 3*1/2.
Now in 3*1/2 apply PEDMAS
3*0.5
Now multiply 3 with 0.5
The answer is 1.5…
3/2 means half of a three that is 1.5…it is fraction form of 1.5…
Step-by-step explanation:
A water tank in Stewart's
home had a small, steady
leak.
Loss of 1 3/5 mL in 10 min.
a. Use a complex fraction to
represent the change in the
volume of water in 1 minute.
___ milliliters
10 minutes
b. Simplify the complex fraction to find the change in the volume of water in the tank in 1 minute.
The change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
Since a water tank in Stewart's home had a small, steady leak loss of 1 3/5 mL in 10 min, to find the change in the volume of water in 1 minute, the following calculation must be performed:
The total leak must be calculated and divided by the 10 minutes duration. 3/5 = 0.6 1 + 0.6 = 1.6 1.6 / 10 = 0.16
Therefore, the change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
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