In solving the inequality, 3x+8/x-4 <= 0, we identify critical points and assign intervals based on them. The solution offers two possible scenarios: x is less than or equal to -8/3 or x is greater than 4.
Explanation:The inequality 3x+8/x-4 =< 0 can be divided into two possible scenarios by clarifying the critical points. To solve this inequality, you first need to identify where the expression equals zero, that's where 3x+8=0 and x=4. Solving 3x+8=0 yields x=-8/3, which is the first
possible solution. Another critical point is where the denominator is zero, which is x=4.
Next, we need to check the signs of these intervals: (-inf, -8/3), (-8/3, 4) and (4, inf). Testing these intervals on the given inequality gives us the
solution that x is less than or equal to -8/3 or x is greater than 4 . Remember, x cannot be equal to 4 because it makes denominator zero in the origin expression which is undefined in mathematics.
Therefore, the correct solution is 'x less than or equal to -8/3 or x greater than 4'.
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A rectangular room is 8 feet long and 12 feet wide. How many tiles would be needed to cover the floor if the tiles are six inches by six inches?
Answer: 192
Step-by-step explanation: 6 inches times 2 is a foot. 12 times 2 is 24 tiles across the top times 8 rows. 24 times 8 is 192
16
Because 8x12=96 and 96/6= 16
$4386 + 25% of the amount over $31850 1) 3986 2) 426.25 3) 4650 4) 7750
Answer:
3.)
Step-by-step explanation:
PLEASE HELP!!!!
The table shows which color boys and girls from 8th grade picked as their favorite color
Answer:
It should be B I me
Step-by-step explanation:
To determine which percentage is higher, we need to calculate the percentage of boys who prefer green and the percentage of girls who prefer red.
Percentage of boys who prefer green:
Total number of boys = 2 + 4 + 4 + 5 = 15
Number of boys who prefer green = 5
Percentage of boys who prefer green = (5/15) x 100% = 33.33% (rounded to the nearest whole number, this is 33%)
Percentage of girls who prefer red:
Total number of girls = 4 + 3 + 1 + 3 = 11
Number of girls who prefer red = 4
Percentage of girls who prefer red = (4/11) x 100% = 36.36% (rounded to the nearest whole number, this is 36%)
Therefore, the percentage of girls who prefer red (36%) is higher than the percentage of boys who prefer green (33%).
The answer is B. At 36%, the percentage of girls who prefer red is higher.
Which sequences are arithmetic? Select three options.
Answer:
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Step-by-step explanation:
Arun Decided to walk 7 1/3 miles to his friend house . After he had gone 3 5/8 miles , he stopped to rest . How much farther does he have to walk to reach the friend house ?
Answer:
3.71 miles farther.
Step-by-step explanation:
To answer this, subtract 3 5/8 miles from 7 1/3 miles:
22/3 - 29/8 (miles)
Here the LCD is 24. Thus, we have:
176 87 89
------ - ------ (miles), or ------- (miles)
24 24 24
Arun has to walk another 89/24 miles, or 3.71 miles.
Check: do 3 5/8 miles and 3.71 miles add up to 7 1/3 miles? Yes, approximately.
Arun has 89/24 miles left to walk to reach his friend's house.
Arun decided to walk 7 1/3 miles to his friend's house. After walking 3 5/8 miles, he stopped to rest. To calculate how much farther Arun has to walk to reach his friend's house, we subtract the distance he has already walked from the total distance he needs to walk.
The total distance to his friend's house: 7 1/3 miles = 7 + 1/3 = (7 × 3 + 1)/3 = 22/3 miles.
Distance already walked: 3 5/8 miles = 3 + 5/8 = (3 × 8 + 5)/8 = 29/8 miles.
To find the remaining distance, we subtract 29/8 miles from 22/3 miles:
First, find a common denominator for the fractions, which is 24. Convert both fractions: 22/3 × 8/8 = 176/24 and 29/8 × 3/3 = 87/24.
Now subtract the distances: 176/24 - 87/24 = 89/24 miles.
Therefore, Arun has 89/24 miles left to walk to reach his friend's house.
11. Kara's credit card had a balance of $209.53 on July
1. On July 8, she made a payment of $50. On July
16, she made a charge of $20. On July 24, she
made another charge of $35 and did not use the
credit card the rest of the month. What was her
average daily balance?
$159.53
$179.53
$214.53
$190.18
$190.78
190.18 is the average balance
Answer:
The answer is $190.18
Step-by-step explanation:
When we calculate the average daily balance, we total the balance from each day in the billing cycle and divide the total by the number of days in the cycle. Here the billing cycle is given for July that has 31 days.
Lets calculate each days amount.
Opening balance from 1st July to 7th July = $209.53
So, it is a total of 7 days; amount is [tex]209.53\times7=1466.71[/tex]
On 8th July a payment of $50 is made making the amount
[tex]209.53-50=159.53[/tex]
So, from 8th July to 15th July (8 days), the balance was $159.53 making a total of [tex]159.53\times8=1276.24[/tex] dollars
On 16th July a charge of $20 was added, so from 16th July to 23 July (8 days), the amount became = [tex](159.53+20)\times8=1436.24[/tex] dollars
On 24th July additional charge of $35 was added and the period it remained same was till 31st July, making it 8 days.
So, amount is = [tex]214.53\times8=1716.24[/tex] dollars
Now adding all the charges we get;
[tex]1466.71+1276.24+1436.24+1716.24= 5895.43[/tex] dollars
Now we will divide this by 31 days to get the average daily balance.
[tex]\frac{5895.43}{31}=190.175[/tex] ≈ $190.18
If the number of bacteria in a colony doubles every 25 hours and there is currently a population of 10,000 bacteria, what will the population be 75 hours from now
Answer:
The population of 75 hours from now would be 40,000.
Step-by-step explanation:
The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.
The population of a bacterial colony that doubles every 25 hours will increase exponentially. In this case, starting from a population of 10,000 bacteria, after 75 hours, we will have 80,000 bacteria. This demonstrates the concept of exponential growth commonly seen in bacteria.
Explanation:The population of a bacterial colony that doubles every 25 hours follows an exponential growth model. This process is where the increasing rate is proportional to the current scope, leading to continued growth. If we start with a colony of 10,000, after 25 hours, we will have 20,000 bacteria. After another 25 hours, this will double again to 40,000. And after a final 25 hours, we double the number again to 80,000.
Here are the calculations:
After 25 hours, the number of bacteria doubles, so the population is 10,000 * 2 = 20,000 bacteriaAfter another 25 hours (50 hours total), the number of bacteria doubles again, so we have 20,000 * 2 = 40,000 bacteriaAfter the final 25 hours (75 hours total), the number of bacteria doubles once more, so we end up with 40,000 * 2 = 80,000 bacteriaThis demonstrates the concept of exponential growth commonly seen in the bacteria populations. The growth rate increases over time due to the characteristic of bacteria to divide and reproduce, leading to a rapid increase in their numbers.
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Graph the line y=-1/5x-2
Answer:
Can't really show a graph but I'll explain how to:
Step-by-step explanation:
Plot the point (0,-2) since -2 is the y=intercept. After, just count-down 1 unit and count 5 units to the right. I hoped this helped!
Erica has a monthly budget of $300 to spend on all of her expenses. She uses 2/3 on rent, and 1/4 on food. How much money remains for her expenses
Answer: $25
Step-by-step explanation: 2/3 of $300 is $200. 1/4 of $300 is $75. The total money she used is $275. $300-$275= $25.
Answer:
$75
Step-by-step explanation:
2/3 of 300 is 200 which means $100 bucks is left and 1/4 on food is $25 so what is left over is $75
Gracie baked 4 apple pies. She cuts the pies into halves and will give them to her neighbors. How many neighbors will get 1/2 of an Apple pie?
Answer:
8
Step-by-step explanation:
If you cut one apple pie in half, then you have two halves. Do the same with the other 3 pies and you will have 8 halves of the pie to give to neighbors.
What are the solutions to the system of equations? y=− x 2 +5x+6 −6x+y=6
(0,−1) and (6, 0)
(−1, 0) and (0, 6)
(0, 6) and (1, 2)
(−1, 0) and (6, 0)
Answer:
option B
(−1, 0) and (0, 6)
Step-by-step explanation:
Given in the question two equations,
Equation 1
y =−x² + 5x + 6
Equation 2
−6x + y = 6
plug value of y in second equation
−6x −x² + 5x + 6 = 6
-x² -6x + 5x +6 - 6 = 0
-x² - x + 0 = 0
-x² -x = 0
-x(x+1) = 0
x = 0
and
x = -1
plug value of x in second equation to find y
x = 0
−6(0) + y = 6
0 + y = 6
y = 6
and
x = -1
−6(-1) + y = 6
6 + y = 6
y = 0
Answer:
(−1, 0) and (0, 6)
Step-by-step explanation:
The given system of equations is
[tex]y=-x^2+5x+6[/tex]
and
[tex]-6x+y=6[/tex]
Solve for y in this second equation
[tex]y=6x+6[/tex]
We equate the two equations to get;
[tex]-x^2+5x+6=6x+6[/tex]
[tex]x^2+x=0[/tex]
[tex]x(x+1)=0[/tex]
x=0,x=-1
When x=0,
y=6(0)+6
y=6
When x=-1
y=6(-1)+6
y=0
What is an equivalent expression to x^-3
Answer:
1
---------
x^3
Step-by-step explanation:
The proper way to write this is with parentheses: x^(-3).
If you wish to eliminate the negative exponent, rewrite this x^(-3) as
1
---------
x^3
Kate sets a goal to walk 3 miles every day for a year. How many miles more or less than 1,000 miles will she walk in the year? A. 95 miles more B. 33 miles less C. 33 miles more D. 95 miles less
Answer:
95 miles more.
Step-by-step explanation:
There are 365 days in the normal year.
Walking 3 miles daily for a year thus comes to (3 miles/day)(365 days) =
1095 miles total per year. This is Answer A: 95 miles more than 1000 miles.
Answer:
95 miles
Step-by-step explanation:
what value of x makes this equation true? justify your solution.
6x + 12 = -6x + 12
Answer
0
Solution
6x+6x=12-12
12x=0
X=0
Find the volume of the rectangular prism
To find the volume of a rectangular prism, we use the formula
Volume = length × width × height.
Since the rectangular prism has a length of 4 m, a width of 2 m, and a height of 1 m we can plug this information into the formula.
(4 m) (2 m) (1 m)
4 m × 2 m = 8 m
8 m × 1 m = 8 m³
Therefore, the volume of the rectangular prism is 8 m³.
Answer:
8
Step-by-step explanation:
L=Length
W=Width
H=Height
L=4
W=2
H=1
4 x 2 x 1
4 x 2 = 8
8 x 1 = 8
Rearranging to check my work:
1 x 4 x 2
1 x 4 = 4
4 x 2 = 8
I was right.
Hope this answers your question.
What is the price of one pound of strawberries
Answer:
$3
Step-by-step explanation:
4 / 12 = 3
Answer:
3
Step-by-step explanation:
You Divide $12.00 / 4 And Get You Answer As 3 :)
Graph the linear equation. Find three points that solve the equation, then plot on the graph. -3y=x-6
The linear equation -3y=x-6 can be graphed using the slope-intercept form y = -1/3x + 2. By choosing different values for x and solving for y, we can find three points that solve the equation. Plotting these points on a graph and connecting them with a line represents the linear equation.
Explanation:The linear equation -3y=x-6 can be rewritten in slope-intercept form as y = -1/3x + 2. This form allows us to easily determine the slope and y-intercept of the equation. The slope is -1/3, which means for every increase of 1 in x, y decreases by 1/3. The y-intercept is 2, which indicates that the line crosses the y-axis at the point (0, 2).
To find three points that solve the equation, we can choose different values for x and substitute them into the equation to solve for y. Let's choose x = 0, x = 3, and x = -3. Plugging these values into the equation, we get y = 2, y = 1, and y = 3, respectively.
Therefore, the three points that solve the equation are (0, 2), (3, 1), and (-3, 3). When we plot these points on a graph, we can then connect them with a straight line to represent the linear equation.
find the area. please show steps!
Answer:
96 in²
Step-by-step explanation:
The surface area of the square pyramid is the area of the square base plus the area of the four triangular faces. The slant length is the height of each triangle.
A = s² + 4 (½ sL)
A = s² + 2sL
Given s = 6 and L = 5:
A = (6)² + 2(6)(5)
A = 36 + 60
A = 96
The area that needs to be painted is 96 in².
What is the equation parallel to y= -1/5x + 3 and goes through the point (7,4)? Please show steps.
Answer:
Step-by-step explanation:
If it's parallel, that means it has the same slope: -1/5.
Use point-slope form to write the equation:
y - 4 = -1/5 (x - 7)
If you wish to write in point-intercept form:
y - 4 = -1/5 x + 7/5
y = -1/5 x + 27/5
If two lines are parallel, it means that they will have the same gradient:
And remember, the equation of a line is y = mx +c
-----------------------------------
So we know that the equation of the parallel line is:
y = - [tex]\frac{1}{5}[/tex]x + c through point (7, 4)
All we need to do now is to work out what c is
Note: at point (7, 4) x = 7 , and y = 4.
So to work out c, we substitute in the values of x and y, and solve:
y = - [tex]\frac{1}{5}[/tex]x + c
4 = - [tex]\frac{1}{5}[/tex] * 7 + c
4 = -1.4 + c
5.4 = c
----------------------------------
Finally, we just put the value of c back into the original equation
y = - [tex]\frac{1}{5}[/tex]x + 5.4
------------------------------------------
Answer:
The equation of the a line parallel to y = - [tex]\frac{1}{5}[/tex]x + 3 through point (7,4)
is: y = - [tex]\frac{1}{5}[/tex]x + 5.4
Sharon suspects that her brother's penny is unfair. She flips it 50 times and heads comes up 40 times. Based on these trials, the probability that a flip of this coin comes up TAILS is A) 1/5 B) 4/5 C) 4/9 D (5/9)
The correct answer is B. 4/5. Hope this helps! : )
Answer:
1/5
Step-by-step explanation:
it said so in usa testprep and i hope this helps you! ^-^
HELP PLEASE!!
What is the value of 18^2?
A) 36
B) 324
C) 360
D) 9
18² is the same as saying 18 * 18, which is 324
Joelle bought 20 lollipops and 6 bags of Doritos for a total cost of $8.20. She knows that each lollipop cost 25 cents and reasoned that two bags of chip must cost a little more than $1.00. Is this a reasonable guess? Why or why not?
I mean... I think it's a reasonable guess because not gonna lie- chips can get expensive. BUT- It doesn't really make sense because like, she bought so many lollipops. My brain isn't really functioning to do the math- but my best guess would beeeee... UNreasonble. I'm super super sorry if it's wrong. Math isn't my strong point, sorry. Have a nice day!
Answer:
no
Step-by-step explanation:
because 20×.25 = 5 so the lollipop cost $5.00 and then you only have 3.20 left over
A chef has 6 cups of berries and will use 2/3 cups of berries for each serving of fruit salad how many servings can be made
Answer:
6*2/3 = 12/3 = 4
Step-by-step explanation:
For this case we have a total of 6 cups of berries and per serving of salad we use [tex]\frac {2} {3}[/tex]of cups.
Let "x" be the variable that represents the portions of fruit salad that can be made, then, to find it we divide the number of cups of berries among the amount that is used for a portion:
[tex]x = \frac {6} {\frac {2} {3}} = \frac {6 * 3} {2 * 1} = \frac {18} {2} = 9[/tex]
Thus, 9 portions of salad can be prepared.
Answer:
9 portions
Evaluate 1/3m-1-1/2n, when m=21 and n
=12
Answer:
0
Step-by-step explanation:
= 7 - 1- 6
= 6 - 6
=0
To evaluate the expression 1/3m - 1 - 1/2n with m=21 and n=12, you perform a series of arithmetic operations, resulting in an evaluated expression of 0.
Explanation:To evaluate the expression 1/3m - 1 - 1/2n when m=21 and n=12, we substitute the given values of m and n into the expression.
Firstly, calculate 1/3 of m: (1/3) × 21 = 7.Secondly, subtract 1 from the result of the first step: 7 - 1 = 6.Thirdly, calculate 1/2 of n: (1/2) × 12 = 6.Finally, subtract the result of the third step from the result of the second step: 6 - 6 = 0.A kitchen drawer has a Volume 1,125 cubic inches. The drawer is 15 inches long and 5 inches deep. What is the width of the drawer? Please show work so I can understand
Answer:
The width of the drawer is [tex]15\ in[/tex]
Step-by-step explanation:
we know that
The volume of the drawer is equal to
[tex]V=LWH[/tex]
we have
[tex]L=15\ in[/tex]
[tex]H=5\ in[/tex] -----> the deep of the drawer
[tex]V=1,125\ in^{3}[/tex]
substitute the given values in the formula and solve for W
[tex]1,125=(15)(W)(5)[/tex]
[tex]1,125=(75)(W)[/tex]
[tex]W=1,125/(75)[/tex]
[tex]W=15\ in[/tex]
Base your answer to the following question on the diagram shown and the given information.
Answer:
A
Step-by-step explanation:
1. Line l is cut by line a (let it be named a, because the figure doesn't show its name). Angles 1 and 6 are vertical, so they are congruent.
2. Line m is cut by line a. Angles 3 and 8 are vertical, so they are congruent.
3. Parallel lines l and m are cut by transversal a. Angles 6 and 3 are congruent as alternate interior angles.
Hence,
[tex]3x+25=4x-17,\\ \\3x-4x=-17-25,\\ \\-x=-42,\\ \\x=42^{\circ}.[/tex]
4. The measure of angle 6 is
[tex]3x+25=3\cdot 42+25=126+25=151^{\circ}.[/tex]
5. Angles 6 and 2 are supplementary angles, so they add up to 180°:
∠2=180°-∠6=180°-151°=29°
find the area of the shape
Answer:
A = 12.5 units ^2
Step-by-step explanation:
This figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 (b1+b2) * h where b1 and b2 are the lengths of the bases and h is the height
b1 = 7.5 and b2 = 2.5 and h = 2.5
A = 1/2( 7.5 + 2.5) * 2.5
A = 1/2(10) * 2.5
A = 12.5
2.5x2.5=6.25
7.5-2.5=5/2=2.5
(1/2)x2.5x2.5=3.125x2=6.25
6.25+6.25=12.5
The answer is: 12.5 units^2
can u plz help i need the unser right now!!
Answer:
C
Step-by-step explanation:
Solving the inequality
[tex]\frac{1}{2}[/tex] x - 2 > 0 ( add 2 to both sides )
[tex]\frac{1}{2}[/tex] x > 2 ( multiply both sides by 2 )
x > 4
Since greater than 4 we want a number line with an open circle at 4, indicating x is not equal to 4 and arrow pointing to the right.
Hence C
If a spinner is spun 5 times then each event is independent
True or false?
Answer:
True
Step-by-step explanation:
Each time a spinner is spun, there is an equal chance that each result will occur, thus each of these spins are independent.
The answer is true
Hope this helped
Identify GCF and LCM (1)
Identify the GCF or LCM for each pair of numbers.
2205
3570
1100
1576
1100
1576
456
4680
456
4680
Choices to choose from
GCF = 24
GCF = 4
LCM = 433400
LCM = 74970
LCM = 88920
Answer:
2205
3570
LCM = 74970
1100
1576
GCF = 4
1100
1576
LCM = 433400
456
4680
GCF = 24
456
4680
LCM = 88920
Step-by-step explanation:
18837429928373829193