Answer:
Step-by-step explanation:
(4x+3)²÷(x-10)
=(16x²+24x+9)÷(x-10)
x-10) 16x²+24x+9 (16x+184
16x²-160x
- +
------------------
184x+9
184x-1840
- +
----------------
1849
----------------
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
Which equation will solve the following word problem? There are 36 tables and 7 booths in the family restaurant. Each table seats 4 people. If the restaurant can seat up to 184 people, what is the capacity of each booth?
(B * 7 ) - (36 * 4) = 184
7B + (36 * 4) = 184
184 - (36 * 4) = B/7
184/4 = B * 7
Answer:
7B + (36 * 4) = 184
Step-by-step explanation:
In a family restaurant there are 36 tables and 7 booths.
Each table can seat 4 people.
Let the number of people who can be seated in a booth be represented by B.
Total seating capacity of the restaurant is 184 people.
Expressing this as an equation:
Among the given options, this relation is expressed in the second option, namely, 7B + (36 * 4) = 184
A car with a passenger of mass 56 kg can travel a distance of 120 km using 10 l of petrol. If the number of passengers increases to 4 people with a total mass of 224 kg, the distance travelled decreases by 10%.
What is the total distance that the car carrying 4 passengers can travel using 10 l of petrol?
Answer:
120 * 0.90 = 108 km
Step-by-step explanation:
Answer:
108km
Step-by-step explanation:
HELP ASAP!!!
The circle graph shows the percentage of visitors at a
convention who ordered various flavors of juice. There were 700
visitors at the convention.
About how many visitors ordered grape juice or apple juice?
Enter your answer in the box.
Step-by-step explanation:
40+24+11+8+17= 100
100 - 700
24 - ?
24×700/100
= 168 visitors ordered apple juice
100-700
11-?
11×700/100
=77 people ordered grape juice
Help!!
Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result?
StartFraction S Over 2 pi r EndFraction equals h. – r = h
StartFraction S minus r Over 2 pi r EndFraction equals h. = h
S – S minus StartFraction r Over 2 pi EndFraction equals h. = h
S – S minus StartFraction 2 pi Over r EndFraction equals h. = h
Answer:
(S-2πr^2)/ 2πr = h
Step-by-step explanation:
S = 2πrh + 2πr^2
Subtract 2 pi r^2 from each side
S-2πr^2 = 2πrh + 2πr^2 -2πr^2
S-2πr^2 = 2πrh
Divide each side by 2 pi r
(S-2πr^2)/ 2πr = 2πrh/2πr
(S-2πr^2)/ 2πr = h
It is given that,
→ S = 2πrh + 2πr²
Now subtract 2πr² from the both sides,
→ S - 2πr² = 2πrh + 2πr² - 2πr²
→ S - 2πr² = 2πrh
Then divide both sides by 2πr,
→ (S-2πr²)/2πr = 2πrh/2πr
→ (S-2πr²)/2πr = h
Hence, (S-2πr²)/2πr = h is the result.
Need help on this!! 10 points!!!
Answer:
The answer is B
Jacob Sketched a floor plan for a new two room clubhouse . In his sketch each centimeter was equal to 1.5 feet . The largest room on his clubhouse plan measured 6.2 cm by 7.4 cm. How many square feet would the actual room be? Round you answer to the nearest hundredth.
Answer:
103.23 square feet
Step-by-step explanation:
Area of the largest room = length × width
Each centimeter was equal to 1.5 feet
7.4 cm = 1.5 × 7.4 = 11.1 feet
6.2 cm = 1.5 × 6.2 = 9.3 feet
Length = 11.1 feet
Width = 9.3 feet
Area of the largest room = length × width
= 11.1 feet × 9.3 feet
= 103.23 square feet
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
A.
10
B.
89
C.
118
D.
208
Answer:
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice
Step-by-step explanation:
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
What is the line of best fit?
A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.
To learn more about the data visit:
https://brainly.com/question/19243813
#SPJ2
Solve 3 - x/2 > 15..
Answer:
x ≥-24
Step-by-step explanation:
3 - x/2 ≥ 15
Subtract 3 from each side
3-3 - x/2 ≥ 15-3
-x/2 ≥12
Multiply by -2
-x/2 * -2 ≥12 *-2
x ≥-24
Answer:
A. x ≤ 24
Step-by-step explanation:
[tex] \small \sf \: 3 - \frac{x}{2} ≥ 15 \\ [/tex]multiply both side by 2 . Since 2 is the positive the inequality direction remains the same.
6 - x ≥ 30subtract 6 from both sides
6 - 6 - x ≥ 30 - 6 -x ≥ 24Divide both side by - 1. Since -1 is negative, the inequality direction remains the change.
x ≤ -24Multiplicar:
a. (– 6) (– 7) =
b. – 12 x – 5 =
c. (+ 10) (– 6) =
d. (– 15) (+ 5) =
e. (+ 11) (+6) =
f. (– 3) (– 5) (– 6) =
g. (– 8) (+6) (-3) =
h. (- 5) (+ 3) (+9) =
Answer:
a. 42
b. -12x-5
c. -60
d. -75
e. 66
f. -90
g. 144
h. -135
Can someone help me with this math homework please!
Answer:
-1
Step-by-step explanation:
we match the input to the output to find that f(3) points towards -1
m-2n = 8
n = m - 2
The value of m in the system of equations is:
What is the word form of 0.604
Answer:
zero point six hundred and four
Step-by-step explanation:
2. A rectangle has length 13 and width 10. The length and the width of the rectangle are each
increased by 2. By how much does the area of the rectangle increase? *
50
20
38
35
f(x)=2^x by a factor of five
Tamisha's shampoo bottle holds 1/2 bottle of shampoo.She used 5/6 of the bottle.How many gallons of shampoo has Tamisha used?
Answer:
5/12
Step-by-step explanation:
1/2 x 5/6 = 5/12
Can someone please help me! Big ideas number 22 8.4
Answer:
26
Step-by-step explanation:
the whole area is the sum of the area of the rectangle in the middle and the 2 triangles on either side of the rectangle.
sBC = distance between (0,3) and (4,-1)
and that is the Pythagoras calculation with the coordinate differences
sBC² = (4-0)² + (-1 - 3)² = 16 + 16 = 32
sBC = sqrt(32) = sFE
to get the area of the rectangle we need also FB (or CE).
sFB² = (0 - -2)² + (3-1)² = 4 + 4 = 8
sFB = sqrt(8) = sCE
area of rectangle is
sBC×sFB = sqrt(32)×sqrt(8) = sqrt(32×8) = sqrt(256) = 16
the area of a right-angled triangle is
a×b/2
we have sFB and need sAF
sAF² = (-5 - -2)² + (4-1)² = 9 + 9 = 18
sAF = sqrt(18)
the area of the left triangle is
sFB×sAF/2 = sqrt(8)×sqrt(18)/2 = sqrt(8×18)/2 = sqrt(144)/2 = 12/2 = 6
for the right triangle we have sCE and need sED.
sED² = (2 - 4)² + (-3 - -5)² = 4 + 4 = 8
sED = sqrt(8)
the area of the right triangle is
sCE×sED/2 = sqrt(8)×sqrt(8)/2 = 8/2 = 4
so in total we have for the area
16 + 6 + 4 = 26
Can you help with 7-10
Answer:
7.Mean=Ex/n
= 88+96+92+84+86+92+98/7
=90
(b). Median = {84,86,88},92,{92,96,98}
=92
(C).Mode=92 ; it is the number with the highest frequency
9.Mean=Ex/n
=28+26+32+24+27+32+29/7
=28
(b).Median={24,26,27},28,{29,32,32}
=28
(c).Mode=32;it is the number with the highest frequency.
8.Mean=Ex/n
=3.5+5.7+9.8+7+12.4+10.2/6
=8.1
(b).Median={3.5,5.7},7,9.8,{10.2,12.4}
=7+9.8/2
=8.4
(c).Mode=no mode
10.Mean=Ex/n
=2+6+9+8+8+2+8+7+5+4/10
=5.9
(b).Median={2,2,4,5},6,7,{8,8,8,9}
=6+7/2
=6.5
(c).Mode= 8;it is the number with the highest frequency.
I hope this helps.
Graph and identify image coordinates rx=2
Answer:
Step-by-step explanation:
Rule defining the reflection across the line x = -2 has been given as,
[tex]r_{x=-2}[/tex]
Line x = -2 will work as a mirror for the given triangle J, K, L.
That means distance of the vertices J, K and L and image points J', K' and L' will be equidistant from the line x = -2,
Vertices of the image triangle J'K'L' will be,
J' → (-5, 2)
K' → (-3, 2)
L' → (-4, 1)
Flying against the wind, a jet travels miles in hours. Flying with the wind, the same jet travels miles in hours. What is the rate of the jet in still air and what is the rate of the wind
Answer:
Velocity in still air: 760 mi/ hr
Velocity against the wind: 210 mi/ hr
Step-by-step explanation:
Given
See attachment for complete question
Required
The rate in still air
The rate of the wind
From the question, the velocity (v) against the wind is:
[tex]v =\frac{distance}{time}[/tex]
[tex]v =\frac{3040}{4}[/tex]
[tex]v_1 =760mi/hr[/tex]
The velocity with the wind is:
[tex]v_2 = \frac{8260}{7}[/tex]
[tex]v_2 = 1180mi/hr[/tex]
Let:
[tex]x \to[/tex] velocity in still air
[tex]y \to[/tex] velocity of the wind
So, we have:
[tex]x - y = 760[/tex]
[tex]x + y = 1180[/tex]
Add both equations
[tex]x + x -y + y = 760 + 1180[/tex]
[tex]2x = 1940[/tex]
Divide by 2
[tex]x = 970[/tex]
Substitute [tex]x = 970[/tex] in [tex]x - y = 760[/tex]
[tex]970 - y= 760[/tex]
Make y the subject
[tex]y = 970 - 760[/tex]
[tex]y = 210[/tex]
The Marked price, inclusive of GST, of a notebook computer is $1679.90.it is sold at a discount of 10%.
a) find its marked price before GST
b)Find the GST before discount.
c)What is the selling price of the computer
d) find the GST after the discount
e)what is the percentage decrease in the GST
Answer:i don’t know
Step-by-step explanation:i don’t know
This year, Carlos planted 6 more than one-third of the cucumber plants he planted last year. How many cucumber
plants did he plant this year if last year he planted 12 plants?
6
9
10
12? PLEASE HELP SMB
Answer:
10 plants
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
He planted 10 this year because last year he planted 12, and 1/3 of that is 4. He planted 6 more than that this year, so 4+6=10.
I need help please!!!
Answer:
40 degrees
Step-by-step explanation:
Question 1: Use the image and your knowledge of the isosceles triangle to find the value of x
Answer:
35 degrees
Step-by-step explanation:
since both sides are equal, so are the angles involved.
What are the steps in order of operations
How is mathematical thinking established? How can we have mathematical thinking?
修改翻译结果
Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.
数学思维是如何建立的？ 怎样才能有数学思维？
Complete the remainder of the
table for the given function rule:
y = 3x - 8
X | -4 -2 0 2 4
y -20 [?] [ ] [ ] [ ]
The values that complete the table are -14, -8, -2 and 4
Function ruleGiven the function y = 3x - 8, we are to complete the given table.
If x = -2
y = 3(-2) - 8
y = -14
If x = 0
y = 3(0) - 8
y = -8
If x = 2
y = 3(2) - 8
y = -2
If x = 4
y = 3(4) - 8
y = 4
Hence the values that complete the table are -14, -8, -2 and 4
Learn more on table of functions here: https://brainly.com/question/3632175
Find the area of the parallelogram
Answer:
The answer is 32.
Step-by-step explanation:
Just multiply the height by the base length. 4*8=32
in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.
Given:
In a two digit number the tens digit is 6 more than the units digit.
If the digits are interchanged, the sum of the new and the original number is 132.
To find:
The original number.
Solution:
Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:
[tex]m=(x+6)\times 10+x\times 1[/tex]
[tex]m=10x+60+x[/tex]
[tex]m=11x+60[/tex]
If we interchange the digits, then the value of new number is:
[tex]n=x\times 10+(x+6)\times 1[/tex]
[tex]n=10x+x+6[/tex]
[tex]n=11x+6[/tex]
The sum of the new and the original number is 132.
[tex]m+n=132[/tex]
[tex]11x+60+11x+6=132[/tex]
[tex]22x+66=132[/tex]
[tex]22x=132-66[/tex]
[tex]22x=66[/tex]
Divide both sides by 22.
[tex]x=\dfrac{66}{22}[/tex]
[tex]x=3[/tex]
So, the unit digit of the original number is 3 and the tens digit is:
[tex]x+6=3+6[/tex]
[tex]x+6=9[/tex]
Therefore, the original number is 39.
Which property would allow you to use mental computation to simplify the problem 27 + 15 + 3 + 5?
Answer:
commutative property of addition.
a sequence of additions can be done in any order and the total remains the same.
Step-by-step explanation:
so, we can actually do
27 + 3 + 15 + 5
and now it is easy to combine 27+3 to 30 and 15+5 to 20, and to make the final calculation of 30 + 20 = 50 in our minds.