Hi!
[tex]2x-1=\frac{3}{4x+9}[/tex]
[tex]2x(4x+9)-1*(4x+9)=\frac{3}{4x+9}(4x+9)[/tex]
[tex]2x(4x+9)-(4x+9)=3[/tex]
[tex]2x(4x+9)-(4x+9)=3[/tex]
[tex]x=\frac{\sqrt{145-7} }{8},x=-\frac{7+\sqrt{145} }{8}[/tex]
[tex]x=\frac{\sqrt[]{145-7} }{8}, or x=-\frac{7+\sqrt{145} }{8}[/tex]
Explanation: First you had to multiply by 4x+9 from both sides. Then simplify, it gave us 2x(4x+9)-(4x+9)=3. Next you can also solve 2x(4x+9)-(4x+9)=3. And the answer it gave us is x=√145-7/8 or x=-7+√145/8 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie
which of the following are functions
A. [(-2,3)], [(-1,5)], [(0,7)], [(1,9)]
B. [(-3,3)], [(3,3)], [(0,0)], [(1,1)], [(-1,1)]
C. [(-2,5)], [(-1,4)], [(0,3)], [(-1,2)], [(-2,1)]
Both A and B represent functions, as the same x value is not used twice.
However, with option C, the x value -2 is used twice, and thus it is not a function.
The concept of functions in mathematics is determined by whether each input (or 'x' value) corresponds to exactly one output (or 'y' value). Upon examination, the sets of ordered pairs in option A qualify as functions, while the sets in options B and C do not.
Explanation:A function in Mathematics is a relation between a set of inputs and a set of outputs where each input is related to exactly one output. In your question, you have three different sets of ordered pairs. Let's examine them.
A. [(-2,3)], [(-1,5)], [(0,7)], [(1,9)]
Here every 'x' value is paired with only one 'y' value, so this one is a function.
B. [(-3,3)], [(3,3)], [(0,0)], [(1,1)], [(-1,1)]
For this one, we see that 'x' values -1 and 1 are both paired with 'y' value 1. This implies that a single 'x' value has more than one 'y' value which is not allowed for a function. So this one is not a function.
C. [(-2,5)], [(-1,4)], [(0,3)], [(-1,2)], [(-2,1)]
This one is similar to the second case where 'x' values -1 and -2 are both paired with multiple 'y' values. So, this one is not a function either.
So, only the first set constitutes a function.
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What is the slope of this graph?
−1/4
1/4
4
−4
The slope of a graph is the rate of change of the graph
The slope of the graph is that passes through (0,2) and (1,-2) is (d) -4
Start by selecting any two points on the line of the graph
[tex](x_1,y_1) = (0,2)[/tex]
[tex](x_2,y_2) = (1,-2)[/tex]
The slope (m) of the graph is simply the average rate of change of the graph.
It is calculated as follows:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substitute values for x and y
[tex]m = \frac{-2-2}{1 - 0}[/tex]
Simplify
[tex]m = \frac{-4}{1}[/tex]
Divide
[tex]m = -4[/tex]
Hence, the slope of the graph is -4
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the sum of a number 9 is multiplied by -2 and the answer is -8
find the number.
-2(x + 9) = -8
Distributive property.
-2x - 18 = -8
Add 18 to both sides.
-2x = 10
Divide both sides by -2.
x = -5
Antoine and Angela both like to walk for exercise. Today they are walking together. Antoine walks every 3 days and Angela walks every 5 days. Circle all the days on which they will walk together again. Choices are 8, 12, 15, 25, 45.
15 and 45 becuase bith 3 and 8 can go into them.
Students in Mr. Smith's class want to find out how far they can jump. Which of the following will help give a valid conclusion about the data?
1. Five students are chosen randomly to jump.
2. All 25 students are measured.
3. Students who want to jump are measured.
4. Students playing during recess are measured.
Answer:
2 student who want to jump are measured
At a chess tournament, the number of competitors in each round is 50% of the number of competitors in the previous round. What type of relationship most appropriately models this situation?
A. linear increase
B. exponential decay
C. exponential growth
D. linear decrease
Answer: Option B. exponential decay
Solution:
If initially the number of competitors is n
If the number of round is "r" and the number of competitors after "r" rounds is N(r)
1) After the first round (r=1), the number of competitors is:
N(r)=N(1) = n * 50% = n * 50/100 →N(r)=N(1)=n*0.5=n*0.5^1
2) After the second round (r=2), the number of competitors is:
N(r)=N(2) = N(1) * 50% = (0.5 n)*(50/100)=(0.5n)*(0.5)→N(r)=N(2)=n*0.5^2
3) After the third round (r=3), the number of competitors is:
N(r)=N(3)=N(2)*50%=(n*0.5^2)*(50/100)=(n*0.5^2)*(0.5)→N(r)=N(3)=n*0.5^3
Then:
For r=1→N(r)=N(1)=n*0.5^1
For r=2→N(r)=N(2)=n*0.5^2
For r=3→N(r)=N(3)=n*0.5^3
In general: N(r)=n*0.5^r
This is an exponential function because the independent variable "r" is in the exponent, and because the number of competitors (funcion N(r) )decrease with the number of rounds the type of relationship most appropiately models this situation is an exponential decay
The reduction by 50% of competitors each round in a chess tournament is modeled by an exponential decay relationship, not a linear decrease, as it depends on the current number of competitors.
The chess tournament with the number of competitors decreasing by 50% each round is best modeled by a exponential decay relationship. This is because with each round, the number of competitors is halved, which is a rate that depends on the current number of competitors. (A) linear decrease would imply a constant decrease irrespective of the current number of competitors, which is not the case here.
Exponential relationships can be represented by mathematical functions where the rate of change is proportional to the current value. In contrast to exponential growth, where the quantity increases at a rate proportional to its current value, exponential decay describes a situation where the quantity is reduced by a certain factor over equal successive periods.
abigail has 16 shoes use repeated subtraction to show how many pairs of shoes Abigail has
Hello!
Here is how we solve this question.
We know that 2 shoes = 1 pair
So we subtract 2 from 16 until we reach 0, and count how many times we subtracted.
16-2=14
14-2=12
12-2=10
10-2=8
8-2=6
6-2=4
4-2=2
2-2=0
After we do repeated subtraction we find that Abigail has 8 pairs of shoes!
Hope this helps you with your question.
Since shoes comes in pairs, then the number of shoes Abigael has would be obtained by subtracting 2 from 16 until we obtain 0. Hence, the number of shoes she has is 8.
The total number of shoes = 16
Shoes are in pairs ; Hence 1 pair of shoe = 2 shoes
Using repeated subtraction :
1 ; 16 - 2 = 14
2 ; 14 - 2 = 12
3; 12 - 2 = 10
4; 10 - 2 = 8
5; 8 - 2 = 6
6; 6 - 2 = 4
7; 4 - 2 = 2
8; 2 - 2 = 0
Therefore, the Number of shoes Abigael has is 8
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Number 21 help me with this one
Answer:
175 %
Step-by-step explanation:
7/4 = (7/4)* 100
= 700 / 4
= 175 %
The answer is 175% I think
A dress normally cost $62. The dress is on sale for 20% off. What is the sale price of the dress
[tex]\$62\cdot0.2=\$12.40[/tex]
[tex]\$62-\$12.40=$49.60[/tex]
a wallet containing 5 five-dollar bills, 7 ten-dollar bills, and 8 twenty-dollar bills Is found and returned to its owner. the wallets owner will reward the finder with 1 bill drawn randomly from the wallet. what is the probability that the bill drawn will be a twenty-dollar bill?
The formula for probability is [tex]\frac{number of ideal outcomes}{number of possible outcomes}[/tex]. Because there are 8 $20 bills, there are 8 ideal outcomes and 20 possible outcomes. THis gives us [tex]\frac{8}{20}[/tex] which can be simplified to [tex]\frac{2}{5}[/tex].
The answer is 2/5 or 0.4 or 40%.
Answer:
2/5
Explanation:
There are 5+7+8 = 20 total bills.
Out of these, 8 are twenty-dollar bills.
The probability of choosing 1 twenty-dollar bill is then 8/20, which simplifies to 2/5.
A 275 inch pipe is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.
Since one piece is four time the length x, we can represent that as 4x.
Thus making the equation:
4x+x=275
5x=275
x=55
4(55)=220
220+55=275
So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.
In order to find the length of the shorter piece of pipe, we can set up and solve the equation x + 4x = 275. When simplified, we get 5x = 275, and by dividing both sides of the equation by 5, we find that x = 55. This tells us that the length of the shorter piece is 55 inches.
Explanation:To solve this problem, let's denote the shorter piece as x. Because the other piece is four times the length of the shorter one, it can be denoted as 4x. We know that these two pieces put together make the total length of the initial pipe, which is 275 inches. Therefore, we can set up the equation: x + 4x = 275.
Simplifying this equation, we get 5x = 275. To get the value of x, we need to divide both sides of this equation by 5, resulting in x = 55. Hence, the length of the shorter piece is 55 inches.
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Confused can someone help me...
Answer,
- 1 1/4
Hope this helps :-)
Two numbers have an absolute value of 16. Which of the two numbers is greater than 12?
if the sum of 5 consecutive multiples of 6 is 930, what is the smallest multiple?
x + x+6 +x+12+x+18+ x+24 = 930
5x + 90 = 930
5x = 930 - 60
5x = 870
x = 174 (which is the smallest consec multiple of 6)
174 is answer.
Given that sum of 5 consecutive multiples of 6 is 930
To find the smallest multiple
The consecutive multiples of 6 would be of the form
6(k-2), 6(k-1), 6k, 6(k+1), 6(k+2) for some natural number k.
The sum would be
6(k-2)+ 6(k-1)+ 6k+ 6(k+1)+ 6(k+2)= 6(5k) = 930
Divide by 30
k = 930/30 = 31
Smallest number = 6(k-2) = 6(31-2)
= 6(29) = 174
-------------------------------------
Verify:
174+180+186+192+198 = 930
Hence verified
How is subtracting integers related to adding integers
We can use the number line as a model to help us visualize adding and subtracting of signed integers. Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations.
To add integers having the same sign, keep the same sign and add the absolute value of each number.
To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest.
Subtract an integer by adding its opposite.
answer: well i thing subtracting and adding integers are related because they both can be solved using an number line
Find the equation of the line in slope-intercept form.through (−5, 6) with slope = 3
y = 3x + 21 that's the answer
What special marks are used to show that segments are congruent
1). Solve for x 3x-6=7x+18
2) Simplify the expression
65-4^2 (10-2)+37
Please show the work for both.
1) The solution of expression is, x = - 6
2) The solution is, - 26
We have to give that,
1) An expression is,
3x - 6 = 7x + 18
2) An expression,
65 - 4² (10 - 2) + 37
Now, Simplify the expressions as,
1) 3x - 6 = 7x + 18
Add 6 on both sides,
3x - 6 + 6 = 7x + 18 + 6
3x = 7x + 24
Subtract 7x on both sides,
3x - 7x = 24
- 4x = 24
Divide both sides by - 4,
x = - 24/4
x = - 6
Hence, Solution is, x = - 6
2) 65 - 4² (10 - 2) + 37
Apply the BODMAS rule,
65 - 16 (8) + 37
65 - 128 + 37
65 + 37 - 128
102 - 128
- 26
Therefore, the Solution is, - 26
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Chen rode his stake board 3 3/4 miles of an hour. What was his average speed in miles per hour?
3 3/4 miles as a decimal is 3.75 miles. He rode for one hour. Average speed within an interval is (distance made) / (interval duration). So the average speed = 3.75 miles / 1 hour, or 3.75 mph.
What is the coefficient in the expression 3x13+4 ? Enter your answer in the box.
Answer:
3
Step-by-step explanation:
Its the number immediately before x
Answer:
What is the coefficient in the expression 3x13+4?
3/13
Step-by-step explanation:
2 11/32 divide by 1 1/2
2 11/32 / 1 1/2 = 25/16 hope this helps you
5n+30-17n-(-12)
[tex]5n + 30 - 17n - ( - 12)[/tex]
Hey there!!
Given equation :
... 5n + 30 - 17n - ( -12n )
... 5n + 30 -17n + 12n
... 5n + 30 - 5n
... 30
The answer is 30...
Hope my answer helps!!
Solving for n, we find that n equals 3.5 or 7/2.
Simplify the equation by removing the parentheses,
5n + 30 - 17n - (-12)
5n + 30 - 17n + 12.
5n - 17n =30 + 12.
-12n + 42 = 0.
-12n = -42.
n = 42 / 12.
n = 7 / 2 or n = 3.5.
Name the parallel segment.
[tex]\overline{NP}\ ||\ \overline{AB}\\\\\overline{JI}\ ||\ \overline{PN}[/tex]
m<3 is (3x + 4) and m<5 is (2x +11)
Angles 3 and 5 are _____
A. Alternate interior angles
B. Corresponding angles
C. Same side interior angles
D. Alternate exterior angles
The equation ___ can be used to solve for x.
A. (3x+4) + (2x+11) = 180
B. (3x+4) = (2x+11)
C. (3x+4) - (2x+11) = 180
m<5= __
A. 33
B. 77
C. 103
Answer:
Part 1) Option C. Same side interior angles
Part 2) Option A. [tex](3x+4)+(2x+11)=180\°[/tex]
Part 3) Option B. [tex]m<5=77\°[/tex]
Step-by-step explanation:
Part 1) we know that
If p and q are parallel
then
m<3 and m<5 are consecutive interior angles or Same side interior angles
and
[tex]m<3+m<5=180\°[/tex]
Part 2) we know that
[tex]m<3+m<5=180\°[/tex] -----> by consecutive interior angles (supplementary angles)
we have that
[tex]m<3=(3x+4)[/tex]
[tex]m<5=(2x+11)[/tex]
so
substitute
[tex](3x+4)+(2x+11)=180\°[/tex]
Part 3) Find the measure of angle 5
we know that
[tex](3x+4)+(2x+11)=180\°[/tex]
Solve for x
[tex]5x+15\°=180\°[/tex]
[tex]5x=180\°-15\°[/tex]
[tex]x=165\°/5\°=33\°[/tex]
[tex]m<5=(2x+11)[/tex]
substitute the value of x
[tex]m<5=(2(33)+11)=77\°[/tex]
Answer: C, A, B
Step-by-step explanation:
Jim Smith is a world processor. He is paid $3.50 a page. A normal job has 500 pages and requires about 250 words per page. About how much will jim receive for his work?
If a page costs 3.50 and there are 500 pages, all you have to do to get your answer is multiply these 2 numbers,
The answer is 1750
35 POINTS!!!
What is the solution to the inequality?
-2/3 (2x - 1/2)<= 1/5x - 1
-2/3(2x-1/2) ≤1/5x-1
Simplify the left side:
-4/3x+1/3 ≤1/5x-1
Subtract 1/5x from each side:
-23/15x + 1/3≤-1
Subtract 1/3 from each side:
-23/15x ≤-4/3
Divide both sides by -23/15:
X = -4/3 / -23/15
X ≥ 20/23
Convert to interval notation:
[ 20/23 , ∞)
what is 2.85 as a fraction in simplest from
In Simplest form your answer is: [tex]\frac{57}{20}[/tex] and as a mixed number is 2 [tex]\frac{17}{20}[/tex]
Francis heard that a car stereo system was on sale for 30% off. If the sale price was 57.75, what was the original price of the stereo?
Answer:
$82.5
Step-by-step explanation:
We can calculate it with a direct rule of 3. As it has a 30% off, the remaining price is the 70% and we want to know how much is the 100%
[tex]70\% -\!\!\!-\!\!\!- \$57.75\\ 100\% -\!\!\!-\!\!\!- \$ x[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {100/100*57.75}{70/100} \\ \\ x = \frac {57.75}{70/100}\\ x = 57.75 * 100/70[/tex]
x = 82.5
The original price of the stereo was $82.5
The original price of the stereo is 82.5
Since the car stereo system was on sale for 30% off, this means that it was sold for 100% - 30% = 70% of the original price.
Let the original price be represented by x
Therefore, 70% of x will be 57.75
70/100 × x = 57.75
0.7 × x = 57.75
0.7x = 57.75
Divide both side by 0.7
0.7x/0.7 = 57.75/0.7
x = 82.5
The original price of the stereo is 82.5
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Determine the volume of a rectangle box with a link of 5 inches height of 7 inches and the width of 9 inches
A number between 200 and 300 with 7 in the thousandths place and a 2 in the hundredthsplace
The question is asking for a decimal number between 200 and 300 with '7' in the thousandths place and '2' in the hundredths place. One possible answer is 250.027, but other variations exist based on the whole number part as long as it is between 200 and 300.
Explanation:The student's question is asking for a specific decimal number between 200 and 300. The conditions set are that the number should have '7' in the thousandths place, and '2' in the hundredths place. Since there are no conditions for the other places, these digits could be any whole number.
One possible answer could be 250.027. We have '2' in the hundredths place (right after the decimal point), '7' in the thousandths place (two spots after the decimal point), and the whole number part is between 200 and 300. Other possibilities exist too, like 267.327 or 280.217.
This question could relate to a topic like Place Value Decomposition where students learn to read, write, and understand the value of each digit in a decimal number.
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