Answer: one solution; that solution is x = -7/2 which is the same as x = -3.5
====================================================
Work Shown:
The idea is to get all the x terms to one side, and the other stuff to the other side. We follow PEMDAS in reverse to help isolate x
12x+24 = 6x+3
12x+24-24 = 6x+3-24 .... subtract 24 from both sides
12x = 6x-21
12x-6x = 6x-21-6x ...... subtract 6x from both sides
6x = -21 ...... now the x terms are all on one side
6x/6 = -21/6 ...... dividing both sides by 6
x = -21/6
x = (-7*3)/(2*3)
x = -7/2
x = -3.5
This is the only solution. Whenever we have different coefficients for the x terms like this, we can see right off the bat we have exactly one solution. Consider graphing y = 12x+24 and y = 6x+3. The two lines will intersect at the point (x,y) where the x coordinate is the solution to the original equation. There is only one point of intersection which corresponds to exactly one solution.
The thing to notice about y = 12x+24 and y = 6x+3 is that the slopes are not the same, so the lines aren't parallel. Parallel lines always have equal slopes but different y intercepts. If your teacher gave you 12x+24 = 12x+3, then the two lines to graph would be y = 12x+24 and y = 12x+3. At this point, we would get two parallel lines that don't intersect, and therefore we wouldn't get any solutions here.
3.
Select all the true statements.
A
-6.1 +-7.8 is positive.
B.
-3.2--19) is positive.
C.
12+(-3.5) is negative.
D.
4+-4 is equal to zero.
E.
82 - (-28) is negative.
Answer:
B & D
Step-by-step explanation:
B & D
Which expression is not equivalent to 2/3 x4
Answer:
I don't know I need the answer choices
Step-by-step explanation:
(4x + 24)/x
since the expression is an integer, x
How many different integer values are there?
Step-by-step explanation:
this is an integer of the interior comes from into juice
Answer:
x= -8
Step-by-step explanation:
4x+ 24= x
4x - x = -24
3x = -24
x = -24/3
x = -8
A football team has 40 players. One of the players is a kicker. The coach randomly selects a player to perform a conditioning exercise. What is the probability that the player selected is the kicker? Write your answer as a fraction.
Answer:
1/40
Step-by-step explanation:
7. A quadratic function has the form y-ax' for
some nonzero value of a and (4, 48) is on the
graph. What is the value of a?
The height of the triangle is 3 meters longer than twice its base. Find the base and height if the area is 8 square meters. Round to the nearest hundreth.
9514 1404 393
Answer:
base: 2.18 mheight: 7.35 mStep-by-step explanation:
Let b represent the base of the triangle in meters. Then the height is ...
h = 3 +2b
and the area is ...
A = 1/2bh
8 = 1/2(b)(3 +2b)
16 = 3b +2b^2 . . . . . . . multiply by 2 and eliminate parentheses
2(b^2 +3/2b + (9/16)) = 16 + 9/8 . . . . . . complete the square
2(b +3/4)^2 = 17.125
(b +3/4)^2 = 8.5625 . . . . . divide by 2
b + 0.75 = √8.5625 ≈ 2.9262
b = -0.75 +2.9262 = 2.1762
h = 3 +2b = 7.3523
The base is about 2.18 meters and the height is about 7.35 meters.
Charlotte walks home from school every day at a rate of
4 miles per hour. It takes her 30-minutes to reach
home. Her brother, Noah, runs home from the same
school every day at a rate of 6 miles per hour. How
many fewer minutes does it take Noah than Charlotte
to reach home from school each day? Be sure to
SHOW your WORK!
Answer:
It takes 10 fewer minutes for Noah than for Charlotte to home from school each day.
Step-by-step explanation:
We use the following relation to solve this question:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
Finding the distance:
Charlotte walks home from school every day at a rate of 4 miles per hour. It takes her 30-minutes to reach home.
This means that [tex]t = 0.5, v = 4[/tex]. Time is 0.5 because as the velocity is in miles per hour, the time has to be in hours. We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]4 = \frac{d}{0.5}[/tex]
[tex]d = 4*0.5 = 2[/tex]
The distance is of 2 miles.
Her brother, Noah, runs home from the same school every day at a rate of 6 miles per hour.
We have to find t, in hours, for which [tex]v = 6, d = 2[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]6 = \frac{2}{t}[/tex]
[tex]6t = 2[/tex]
[tex]t = \frac{1}{3}[/tex]
A third of an hour. In minutes, this is a third of 60, that is 60/3 = 20 minutes.
How many fewer minutes does it take Noah than Charlotte to reach home from school each day?
Noah: 20 minutes
Charlotte: 30 minutes
30 - 20 = 10
It takes 10 fewer minutes for Noah than for Charlotte to home from school each day.
Courtney is ordering nachos at a restaurant, and the server tells her that she can have up to three toppings: pico de gallo, onions, and steak. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Courtney gets just onions and steak
Answer:
[tex]Probability = \frac{1}{9}[/tex]
Step-by-step explanation:
Given
Toppings: Pico de gallo, Onions and Steak
Required
The probability of getting Onions and Steak
The probability is calculated using:
[tex]Probability = P(Onion)\ and\ P(Steak)[/tex] --- because the events are independent
[tex]P(Onion) = \frac{n(Onion)}{Total}[/tex]
[tex]P(Onion) = \frac{1}{3}[/tex]
[tex]P(Steak) = \frac{n(Steak)}{Total}[/tex]
[tex]P(Steak) = \frac{1}{3}[/tex]
So, we have:
[tex]Probability = P(Onion)\ and\ P(Steak)[/tex]
[tex]Probability = P(Onion)\ *\ P(Steak)[/tex]
[tex]Probability = \frac{1}{3} * \frac{1}{3}[/tex]
[tex]Probability = \frac{1}{9}[/tex]
What is 21/1 divided by 1/4
Answer:
84
Step-by-step explanation:
To divide two fractions we turn the second fraction upside down and multiply two fractions
21/1 ÷ 1/4 ➡ 21/1 × 4/1 = 84/1
This can be written as 84
the ratio of boys to girls is 15:11 .if boys are 435 find the number of girls
Answer:
[tex]Girls = 319[/tex]
Step-by-step explanation:
Given
[tex]Boys: Girls = 15:11[/tex]
Required
Find Girls, when Boys = 435
Substitute 435 for Boys
[tex]435: Girls = 15:11[/tex]
Express as fraction
[tex]\frac{Girls}{435} = \frac{11}{15}[/tex]
Multiply through by 435
[tex]435 * \frac{Girls}{435} = \frac{11}{15}* 435[/tex]
[tex]Girls = \frac{11}{15}* 435[/tex]
[tex]Girls = \frac{11* 435}{15}[/tex]
[tex]Girls = \frac{4785}{15}[/tex]
[tex]Girls = 319[/tex]
Can someone
Please
Help me
Answer:
First let's calculate the area of the bottom part
diameter is 34 m
so the radius (r) is 1/2 * 34 m = 17 m
bottom part is 1/2 of a circle
circle surface area formula is πr²
so surface area of our bottom part is 1/2 * πr²
1/2 * πr² = 1/2 * 3,14 * 17² = 453,73
so it's 453,73 m²
Triangle part consists of 2 smaller rectangular triangles
surface area for rectangular triangle is 1/2 * a * h
in our case a = r = 17 m and h = 30m
so one smaller rectangular triangle is 1/2 * r * h = 1/2 * 17 * 30 = 255
so it's 255 m²
and because our entire triangle part consists of 2 smaller rectangular triangles it's area is 2 * 255 m² = 510 m²
Surface area of the entire figure is a sum of 510 m² and 453,73 m²
510 m² + 453,73 m² = 963,73 m²
What number makes the equation true ? 5*2/5= ? * 1/5
Answer:
10
Step-by-step explanation:
Answer:
5*2/5= 10*1/5
Step-by-step explanation:
Pls answer correctly I’ll give you brainliest
Answer:
Step-by-step explanation:
y=mx+b
so inset the first point into the equation
-3 for x and 7 for y.
7=m(-3)+b
y=mx+b
1 for x and -1 for y
-1=m(1)+b
now put them together and solve for m and b.
-1=m+b
7=-3m+b
--------------------
-1-b=m
7=-3m+b
inset m into the equation
7=-3(-1-b)+b
7=3+3b+b
4=4b
b=1
--------------
insert b back in for -1=m+b
-1=m+1
m=-2
---------------------------------------
Now insert it back into y=mx+b
y=(-2)x+1
so this line contains those points that were given
Hope this helps :)
Ronald is calculating the density of oranges in a crate. He knows the number of oranges in the crate and the volume of the crate. Which of the following formulas can be used to calculate the density of oranges in the crate? (6 points) Density = volume of crate over number of oranges Density = number of oranges over volume of crate Volume of shelf = density over number of oranges Number of books = density over volume of crate
Answer:
B. Density = number of oranges over volume of crateStep-by-step explanation:
The density would be the number of oranges per unit of volume:
Density = number of oranges / volume of crateCorrect choice is B
Density = number of oranges over volume of crate Volume of shelf is right formula
10 points pls answer!
Answer:
a
Step-by-step explanation:
8x-20 and 3x together will equal 90
Answer:
The answer is D
Step-by-step explanation:
I NEED AN ANSWER WITHIN LIKE 10 MINUTES-
Which expression is equivalent to -2 1/4 over -2 2/3
A. 9/4 Divided by 3/2
B. -9/4 divided by (-2/3)
C. -9/4 divided by 2/3
D. 9/4 divided by (-3/2)
Answer:
I think the option B is the answer -9/4 divided by (-2/3)
I hope this might help u
your cell phone plan is by the minute. each minute of use cost $0.10. create a relation that represents the amount spent, A, per minute, m, of call time. Then, use the relation to find the amount spent if you talk 65 minutes.
Answer:
Talking 65 minutes, $ 6.50 must be paid.
Step-by-step explanation:
Since your cell phone plan is by the minute, and each minute of use cost $ 0.10, to create a relation that represents the amount spent, A, per minute, m, of call time, and then use the relation to find the amount spent if you talk 65 minutes, the following calculations must be performed:
0.10 x M = A
0.10 x 65 = A
6.50 = A
Thus, talking 65 minutes, $ 6.50 must be paid.
Help with 1-2 please
Answer: 1) 70° 2) x = 55
Step-by-step explanation:
1) If m∠1 = 70°,then m∠8 = 70°.
Because m∠8 is the vertical angle of m∠5, and m∠5 is the corresponding angle of m∠1, which means that m∠8 = m∠1 = 70°. And also m∠1 and m∠8 are alternate exterior angles, they equal to each other.
2) m∠4 = 70°, and m∠7 = 2x, then m∠4 + m∠7 = 180°,because they are consecutive interior angles.
m∠4 + m∠7 = 180°
70 + 2x = 180
2x = 110
x = 55
Find the lateral surface area of the following prism: 5 cm 4 cm 5 cm 8 cm 6 cm LSA = [?] cm2 Enter
Answer:
Step-by-step explanation:
I was using 6×8 rectangle as a base of the triangular prism (as shows on the picture.
Let use the definition of a triangular prism and LSA = (5 + 5 + 6) × 8 = 128 cm²
The lateral surface area of the triangular prism is 128 square cm.
What is triangular prism?A triangular Prism is a pentahedron. It is a 3-D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The edges and vertices of the bases are joined with each other via three rectangular sides.
For the given situation,
The sides of the triangle are 5 cm, 6 cm, 5 cm.
The length of the prism = 8 cm
The formula for lateral surface area of triangular prism is
[tex]LSA=(perimeter)(length)[/tex]
On substituting the above values,
⇒ [tex]LSA=(5+6+5)(8)[/tex]
⇒ [tex]LSA=(16)(8)\\[/tex]
⇒ [tex]LSA=128[/tex]
Hence we can conclude that the lateral surface area of the triangular prism is 128 square cm.
Learn more about triangular prism here
https://brainly.com/question/15070306
#SPJ2
MEMO
To: All businesses in Simpsons Square Mall
From: Louise Pembrooke, Simpsons Square Mall Manager
Re: New garbage collection rules
Simpsons Square Mall has hired a new waste collection company. Quick Clean, Inc., will be collecting garbage and recycling from all businesses starting next Monday. Collection days will not change, nor will the types of garbage and recycling that are acceptable to dispose of. The pickup time will be two hours later, so please adjust your schedules accordingly.
Each business will be given one blue garbage can and one green recycling bin. Full garbage cans must weigh no more than 40 pounds. Recycling bins must weigh no more than 20 pounds. Do not overfill the garbage cans. Debris that is not in cans must weigh no more than 10 pounds. Items put in the compactor should weigh no more than 60 pounds, except in December when it may weigh up to 70 pounds. Put your garbage in the alley behind your business’s back door.
You own a store in Simpsons Square Mall. Each garbage can must weigh no more than:
10 pounds.
20 pounds.
40 pounds.
60 pounds.
70 pounds.
Answer:
hhhhhh
Step-by-step explanation:
i think it is 40
Which of the following functions is graphed below ?
Answer:
A. y = |x + 4| - 2.
Step-by-step explanation:
The graph of y = |x| is V shaped and passes through the origin and the slope is 1 (like the given graph).
y = |x + 4) moves the V shaped graph 4 units to the left so the tip of the V is at x = -4.
Now subtracting 2 from this graph will bring the graph to the point where x = -4 and y = -2.
So the given function is y = |x + 4| - 2.
which statement best explains how Italian society was affected by the Renaissance?
italian society entered a new era of artistic and academic achievement
A positive integer is 4 less than another. If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer, then the result is −67. Find all pairs of integers that satisfy this condition.
Answer:
(0.0147, 4.0147) and (-4.04, 0.04)
Step-by-step explanation:
Let the smaller number be x
Let the larger number be y
If a positive integer is 4 less than another, then;
x = y - 4 ...1
If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer and result is -67, then;
1/y - 3(1/x) = -67
1/y -3/x = -67 ...2
Substitute 1 into 2
1/y - 3/y-4 = -67
y-4-3y/y(y-4) = -67
-4-2y = -67(y^2-4y)
- 4-2y = -67y^2 +268y
-67y^2 +268y+2y + 4 = 0
-67y^2 +270y + 4 =0
67y^2 -270y - 4 = 0
Factorize
-270±√270² - 4(-4)(67)/2(67)
= -270±√72,900+1072/134
= -270±271.97/134
= -270 -271.97/134 and -270 +271.97/134
= -541.97/134 and 1.97/134
x = 0.0147 and -4.04
y = x+4
y = 0.0147+4
y = 4.0147
If x = -4.04
y = -4.04 + 4
y = 0.04
Hence the pair of values are (0.0147, 4.0147) and (-4.04, 0.04)
The scientist measured the wingspans of another random sample of hawks in the national park. There were 100 hawks in the sample, and the number of hawks in the park is about 2,750. There were 82 hawks in the random sample that had a wingspan less than 50 inches. Which value best estimates the number of hawks in the national park that have a wingspan less than 50 inches?
Answer:
Step-by-step explanation:
a
I NEED HELP AND FAST WITH A PROBLEM
Answer:
Volume ≈ 15.63 ft³
Step-by-step explanation:
V=a³=2.5³=15.625ft³
Hope this helpz
Determine the mean, standard deviation, and five number summary of each data set round to the nearest hundredth, if necessary
I'll do problem 3 to get you started.
---------------------------------------------------------
Part 1) Finding the mean:
The mean is found by adding up all the numbers and dividing by n, where n is the number of items in the set.
We sum the numbers to:
5+8+5+9+6+15+9+3+8+7+10+12 = 97
Then we divide over n = 12
mean = sum/n = 97/12 = 8.083333 approximately
This rounds to 8.08
---------------------------------------------------------
Part 2) Finding the standard deviation:
I'm assuming your teacher is talking about the population standard deviation, as opposed to the sample standard deviation.
First subtract each value from the mean. It helps to make a table as shown in the attachment below.
Column A is the original data set. Column B is when we subtract each data item x from the mean M.
Column C is where we square each item in column B.
Adding up everything in column C leads to 118.916666666667 which is approximate. This value is highlighted in the table diagram. Divide this over n = 12 to get 9.90972222222222 which is also approximate
The last step is to apply the square root to that and we get 3.1479711279
This rounds to 3.15
---------------------------------------------------------
Part 3) Finding the min:
From here on out, we have fairly simple calculations and don't need to involve a spreadsheet or any complicated formulas.
The min value is the smallest value of the set. So that would be 3
---------------------------------------------------------
Part 4) Finding the value of Q1, first quartile:
Sort the items in ascending order, ie from smallest to largest.
You should get this set: {3, 5, 5, 6, 7, 8, 8, 9, 9, 10, 12, 15}
There are n = 12 items here, so the median is between slot 12/2 = 6 and slot 7. The values in slot 6 and 7 are the two copies of '8'. That must mean the median is (8+8)/2 = 8.
Now break up the set into two equal halves
L = {3, 5, 5, 6, 7, 8} = lower half of six items
U = {8, 9, 9, 10, 12, 15} = upper half of six items
The median of set L is exactly the value of Q1, so that would be (5+6)/2 = 11/2 = 5.5; note how this is exactly between the two middle most values of 5 and 6.
---------------------------------------------------------
Part 5) Finding the median:
We found that earlier in part 4. The median is 8.
---------------------------------------------------------
Part 6) Finding the value of Q3, third quartile:
Focus on set U = {8, 9, 9, 10, 12, 15}, which was the upper set of values, ie values larger or equal to the median.
The middle two values here are the '9' and '10'. The median is at the midpoint of these values: (9+10)/2 = 19/2 = 9.5
We have Q3 = 9.5
---------------------------------------------------------
Part 7) Finding the max:
The max is the largest item in the original set
Refer to the sorted set {3, 5, 5, 6, 7, 8, 8, 9, 9, 10, 12, 15} and we see that 15 is the max.
---------------------------------------------------------
Part 8) Finding the IQR (interquartile range):
Subtract the values of Q3 and Q1 to get the IQR
IQR = Q3 - Q1
IQR = 9.5 - 5.5
IQR = 4
---------------------------------------------------------
Part 9) Finding the range:
The range is a similar idea as the IQR; however, we'll subtract the max and min this time.
Range = max - min = 15 - 3 = 12
The range is 12.
The range, IQR and standard deviation all help us determine the spread of the data. The larger the value gets, the more spread out the data is.
---------------------------------------------------------
Summary:
Mean = 8.08 (approximate)Standard Deviation = 3.15 (approximate)Min = 3Q1 = 5.5Median = 8Q3 = 9.5Max = 15IQR = 4Range = 12Side note: The phrase "five number summary" refers to the five values of: min, Q1, median, Q3, max. All of which are needed to form a box-and-whisker plot.
PLEASE HELP ME!!!!!
sin(a-28)=cos4
a=?
Answer:
sin(a−28)=cos(4)
sin(a−28)=−0.653644
Step-by-step explanation:
Which rule describes the x-coordinates in the translation below?
Answer:
It's either x-6 or x+6 I wanna say that it is x-6 because they moved the shape down, but it could also have been moved up. I was assuming that the green one was the original, which would make the answer x-6.
Step-by-step explanation:
Answer:he is wiring the answer would be x+6 and the bike is the original because it does not have primes on the numbers
Step-by-step explanation:learn your mad bro
Pls help i will put brainlyist if you don’t answer correctly i will report
Answer:
23.04
Step-by-step explanation:
length×width
4.8×4.8
correct me if im wrong:)
one more question whats 6/8 times 40
Answer:
30
Step-by-step explanation:
hope it helps <3