What is the graph of the solution to the following compound inequality? –6x – 1 < –25 or 3x + 4 ≤ –5
Answers
Answer:
[tex]x>4[/tex] or [tex]x \leq -3[/tex]
Step-by-step explanation:
Given :[tex]-6x -1 < -25[/tex] or[tex]3x + 4 \leq -5[/tex]
Solving first inequality :
[tex]-6x-1<-25[/tex]
Add 1 to both sides
[tex]\Rightarrow -6x-1+1<-25+1\\\Rightarrow -6x<-24\\\Rightarrow 6x>24[/tex]
Divide both sides by 6
[tex]\Rightarrow \frac{6}{6}x>\frac{24}{6}\\\Rightarrow x>4[/tex]
Solving second inequality:
[tex]3x + 4 \leq -5[/tex]
Subtract 4 from both sides
[tex]\Rightarrow 3x+4-4 \leq -5-4\\\Rightarrow 3x \leq -9[/tex]
Divide both sides by 3
[tex]\Rightarrow \frac{3}{3}x \leq \frac{-9}{3}[/tex]
[tex]\Rightarrow x \leq -3[/tex]
So, [tex]x>4[/tex] or [tex]x \leq -3[/tex]
Refer the attached graph
Related Questions
Drag the tiles to the correct box?
Answers
Answer:
1. (3,-1) and (5,4)
[tex]Distance\ = 5.39[/tex]
2. (2,3) and (4,5)
[tex]Distance\ = 2.83[/tex]
3. (-5,7) and (8,5)
[tex]Distance = 13.15[/tex]
4. (-2,4) and (3,-1)
[tex]Distance = 7.07[/tex]
Step-by-step explanation:
Given
The attached
Required
Calculate the distance between each points;
Distance between points is calculated using;
[tex]d =\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
1. (3,-1) and (5,4)
Here; [tex]x_1 = 3; x_2 = 5; y_1 = -1; y_2 = 4[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(3 - 5)^2 + (-1 - 4)^2}[/tex]
[tex]d =\sqrt{- 2^2 + (-5^2)}[/tex]
[tex]d =\sqrt{4 + 25}[/tex]
[tex]d =\sqrt{29}[/tex]
[tex]d = 5.39[/tex] (Approximated)
2. (2,3) and (4,5)
Here; [tex]x_1 = 2; x_2 = 4; y_1 = 3; y_2 = 5[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(2 - 4)^2 + (3 - 5)^2}[/tex]
[tex]d =\sqrt{- 2^2 + (-2^2)}[/tex]
[tex]d =\sqrt{4 + 4}[/tex]
[tex]d =\sqrt{8}[/tex]
[tex]d = 2.83[/tex] (Approximated)
3. (-5,7) and (8,5)
Here; [tex]x_1 = -5; x_2 = 8; y_1 = 7; y_2 = 5[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(-5 - 8)^2 + (7 - 5)^2}[/tex]
[tex]d =\sqrt{- 13^2 + 2^2}[/tex]
[tex]d =\sqrt{169 + 4}[/tex]
[tex]d =\sqrt{173}[/tex]
[tex]d = 13.15[/tex] (Approximated)
4. (-2,4) and (3,-1)
Here; [tex]x_1 = -2; x_2 = 3; y_1 = 4; y_2 = -1[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(-2 - 3)^2 + (4 - (-1))^2}[/tex]
[tex]d =\sqrt{- 5^2 + (4+1)^2}[/tex]
[tex]d =\sqrt{- 5^2 + 5^2}[/tex]
[tex]d =\sqrt{25 + 25}[/tex]
[tex]d =\sqrt{50}[/tex]
[tex]d = 7.07[/tex] (Approximated)
Evaluate 3x + 12 when x = 9
Answers
Answer:
The answer is 39.
Step-by-step explanation:
You have to substitute the value of x into the expression :
[tex]3x + 12[/tex]
[tex]let \: x = 9[/tex]
[tex]3(9) + 12 = 27 + 12 = 39[/tex]
Answer:
39
Step-by-step explanation:
To solve your question we must replace x with the given number which is 9 so,
3 (9) +12 =
We can now solve it by multiplying 3 * 9 which will give us 27. Then we can add 27 to 12.
27 + 12 = 39
Hope this helps!!
help me pls
Tell whether lines m and n must be parallel from the given
Information. If they are, state your reasoning.
Answers
Answer:
The first one isn't the second one is.
Step-by-step explanation:
In the first one, they have to be equal because they're corresponding angles so m and n are parallel.
In the second one, m<2 and m<3 would be supplementary and add up to 180 degrees if the lines were parallel and since they don't add up to 180, the lines are not parallel.
Function f is given by the table of values shown.
x|0|1|2|3
f(x)|7|0|-5|-8
If function fis reflected across the x-axis to obtain function g, complete the table of values which represents function g.
Answers
Answer:
x | 0 | 1 | 2 | 3
f(x) | - 7 | 0 | 5 | 8
Step-by-step explanation:
When you reflect a point say across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). Therefore if the function f( x ) is reflected across the x - axis, it's new function would be y = - f( x ). This new function is function g, so you can also say y = - g( x ).
Given the following table ...
x | 0 | 1 | 2 | 3
f(x) | 7 | 0 | - 5 | - 8 ... we can keep the x - values constant, but take the opposite of each y - value, or " f( x ). " Doing so the new table should be the following -
x | 0 | 1 | 2 | 3
f(x) | - 7 | 0 | 5 | 8 ... note that 0 remains constant as you can't take it's opposite, it remains zero. Therefore, the function g is represented by the above table.
The values of g(x) are as follows:
x | 0 | 1 | 2 | 3
g(x) | -7 | 0 | 5 | 8
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
As per the given data:
We are given a function f(x) and a table where the values of f(x) at different values of x is given.
The table for the values is as follows:
x | 0 | 1 | 2 | 3
f(x) | 7 | 0 |-5 | -8
We have to find the values for the function g(x) which is obtained when f(x) is reflected about the x-axis.
When any function is reflected about the x-axis, the values of the y-axis will have their signs changed, i.e. the y-axis values will become -ve if they are positive and +ve if they are -ve.
For g(x):
x | 0 | 1 | 2 | 3
g(x) | -7 | 0 | 5 | 8
Hence, the values of g(x) are as follows:
x | 0 | 1 | 2 | 3
g(x) | -7 | 0 | 5 | 8
To learn more about Function, click:
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Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?
Answers
Answer:
600 blocks
Step-by-step explanation:
Well this question is asking us to find the volume of the rectangular prism.
Dimensions)
L: 12
W: 10
H:5
The formula for the volume of a rectangular prism is l*w*h or B*h.
So 12*10 = 120
120 * 5 = 600 blocks
Thus,
the fort contains 600 blocks.
Hope this helps :)
Answer:
[tex]\boxed{280\ blocks}[/tex]
Step-by-step explanation:
The blocks at the base are:
Length * Width = 10 * 12 = 120 blocks
On the 2nd Layer:
=> 9+11+9+11 = 40 blocks
There are 3 more layers as the 2nd layer:
So, the blocks of these 4 layers are => 4 * 40 = 160 blocks
Total Blocks = Base Blocks + Layer Blocks
=> 120 + 160
=> 280 blocks
Help with the question attached, thank you!!
Answers
Answer:
the third one
Step-by-step explanation:
try to factor them and if it cannot be factored then it is prime
the only one that cannot be factered is the one you have highlighted so that is correct.
Write the following decimals as fractions.
Answers
Answer:
5a. 0.2823 = 2823/10000 5b. 0.5474 = 2737/5000
6a. 0.3484 = 871/2500 6b. 0.5 = 1/2
7a. 0.11 = 1/9 7b. 0.1224 = 153/1250
Which expression can you simplify by combining like terms?
CLEAR CHECK
12b2+4ab−3ba−6
17a2−6b2a+4ba−9
5b2−5a2+8a−b
14a2+6ab−3b−3a
Answers
Which of the following is a valid reason why the quadrilateral shown below is
a parallelogram?
A. Both pairs of opposite sides are parallel.
B. The diagonals bisect each other.
C. The diagonals are congruent.
D. Both pairs of opposite sides are congruent.
Answers
A parallelogram is a quadrilateral with two pairs of parallel sides.
Option A is the correct answer.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
A parallelogram is a quadrilateral with two pairs of parallel sides.
So, option A is a valid reason for the given quadrilateral to be a parallelogram.
The other options do not necessarily hold true for all parallelograms. For example, the diagonals of a parallelogram bisect each other and are congruent, but not all quadrilaterals with bisecting diagonals are parallelograms.
Similarly, not all parallelograms have congruent diagonals or congruent opposite sides.
Thus,
A parallelogram is a quadrilateral with two pairs of parallel sides.
Learn more about parallelograms here:
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Brad wants to open a new savings account. He finds one that returns 3% on his investment each year.
Question 1
Assign a variable to each of the following płeces of information:
• final balance
• initial investment
• return rate
use the variable to write a formula for the final balance after 2 years
Answers
Answer:
1.03x
Step-by-step explanation:
1 year b would be the inital investment added with interest
i believe this is the equation
b = x + r(x)= (1 + r)x
and since it says 3% each year we know its 0.03 (r)
and when you solve it out you get that answer
Micah is handing out miniature chocolate bars and butterscotch hard candies for Halloween. He wants tohave a total of 7 pounds of candy, but he doesn't want to spend more than $11.00 total on the candy. If miniature chocolate bars costs $1.80 per pound, and butterscotch hard candies costs $1.00 per pound, how many pounds of each type of candy should he buy?
Answers
Answer:
5 pounds of miniature chocolate and 2 butterscotch hard candies
Step-by-step explanation:
5 x $1.80 =$9 for 5 pounds of candy
2 x $1.00 =$2 for 2 pounds of candy
2 + 5 =7 pounds
7 pounds of candy using $11.00
Which method correctly solves the equation using the multiplication property of equality and the reciprocal of One-third?
Answers
Answer: -third
Step-by-step explanation:
How is everyone doing today? Here is a problem for the day! Problem - 10 + 8 x 119
Answers
Answer:
..
-10 + 8× 119
= -10 + 952
= 942. .....
Answer:
236 (i think)
Step-by-step explanation:
cuz 0-10= -10+8= -2 X 119=236 (sorry if you cant read this my keyboard sucks
Write an ordered pair for each point graphed below.
Answers
Answer:
[tex]\boxed{(-1,4)}[/tex]
Step-by-step explanation:
The point is located in Quadrant II of the graph, where x-values are negative and y-values are positive.
Each marking on the graph represents one unit of distance. The two axes meet at the origin, where the coordinate point is equal to [tex](0,0)[/tex].
So, you can count backwards once from the origin to get your x-value ⇒ [tex]-1[/tex] and count up upwards four times from [tex]x=-1[/tex] to get your y-value ⇒ [tex]4[/tex].
Finally, place these in a coordinate point [tex](x,y)[/tex] ⇒ [tex]\boxed{(-1,4)}[/tex].
Answer:
(-1, 4)
Step-by-step explanation:
The point lies on the line x = -1.
The point lies on the line y = 4.
Where both lines intersect, that is the coordinate.
(x, y)
(-1, 4)
If a store is selling packs of gum at 3 for $0.99, how much would 12 packs cost?
Answers
Answer:
$3.96.
Step-by-step explanation:
3 cost $0.99, so 12 packs would cost 12/3 = 4 times as much.
0.99 * 4 = 3.96.
12 packs would cost $3.96.
Hope this helps!
Hello! The answer will be below! :3
The answer to your question is 3.96.
Because we have to take the info that’s given like we first have to divide.
12 divided by 3 is 4
Now we multiply.
0.99 * 4 = 3.96
So the answer is 3.96
Hope this helps! :)
⭐️Have a wonderful day!⭐️
Select the decimal that is greater than 1/3 and smaller than 1/2. A 0.299 B 0.300 c. 0.415 d 0.501
Answers
Answer:
C, 0.415
Step-by-step explanation:
Convert the fractions to decimals:
1/3 = 0.3333333...
1/2 = 0.5
So the decimal must be greater than 0.3333333... and smaller than 0.5,
from the options,
only 0.415 matches with the requirements.
Answer:
c.415
Step-by-step explanation:
1/3 = 0.333333...
1=2 = 0.5
Therefore the "c option - 0.415" as it is greater than 1/3 and lesser than 1/2
Hope ths helps....
Pls mark my ans as brainliest :)
PLS PLS PLS
I want to rank up....
Dat y pls mark my ans as brainliiest :)
There were 3 bands that
performed at the talent show.
What percent of the 16 group acts
were band performances?
Answers
Answer:
18.75%
Step-by-step explanation:
(round answer if needed)
Answer: 18.75%
Step-by-step explanation:
divide 100 by 16
100/16=6.25
6.25x3=18.75
Write an equation of the line that satisfies the given conditions. Give the equation (a) in slope-intercept form and (b) in standard form.
Through (-2,4): perpendicular to x=8
(a) The equation of the line in slope-intercept form is_____.
Answers
Answer:
y = 4
Step-by-step explanation:
The line x=8 is a vertical line. The perpendicular line will be horizontal, with a slope of 0. In order for it to go through the given point, the y-intercept must match the y-value of the point. The equation is ...
y = 0x +4 . . . . . slope-intercept form with slope explicitly shown as 0
This simplifies to ...
y = 4
Plz help me 3(x + 1) = 5 + x
Answers
Answer:1
Step-by-step explanation:distribute 3 through the parentheses, move variable to the left hand side and change it’s sign, move constant to the right hand side and change its sign , collect like terms , subtract the numbers and then divide .
That will bring our equation to:
3x + 3 = 5 + x
Now we have to move around so the like terms are separated from each other
That will bring our equation to:
2x = 2
Now we can divide by 2 to get x alone
That will bring us to our answer:
x = 1
A. Plot the data for the functions f(x) and g(x) on a grid (SHOWN ABOVE)
B. Identify each function as a linear, quadratic, or exponential, and uses complete sentences to explain your choices.
C. Describe what happens to the function values in each function as x increases from left to right.
D. At what value(a) of x are the function values equal? If you cannot give exact values for x, give estimates.
Answers
Katrina owns a dance studio and offers four classes a day for $28.00 each, with 10 people maximum per class. If she decides to offer a 25% discount on the two morning classes offered one day, and all four classes reach the maximum number of people attending, how much money will Katrina make that day?
Answers
Answer:
$980
Nvm you have to multiply 98 by 10 since there are 10 participants. :)
Step-by-step explanation:
Well, first we wanted to find how much the morning classes cost together. You have to $28 multiplied with 75/100. I am multiplying it with 75/100 instead of 25/100 because the discount cuts off the 25% and the 75% is what you still have to pay. This will give you 2100/100 which is $21. Now you have to multiply $21 with 2 since there are two morning classes. $21 x 2 equals $42. Total for Morning Classes is $42.
Now the other two classes don't have a discount. So all you have to do is $28 x 2 or $28 + $28. This gives you $56. Total for The Other Classes is $56.
Last Step:
Total for Morning Classes + Total for the Other Classes = $56 + $42
= $98
Hope that helped! :)
Answer:
$ 980
Step-by-step explanation:
Discount for morning session = 25 % of 28 = 0.25 * 28 = $ 7
Fees for morning class = 28 - 7 = $ 21
Maximum people in one session = 10
Money earned in the morning sessions = 2 * 21 * 10 = $ 420
Money earned in the evening sessions = 2 * 28 * 10 = $ 560
Total money earned that day = 420 + 560 = $ 980
Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.
Use the polygon tool to graph the dilated figure.
Answers
Answer:
(2,4), (6,4), (2,-2), (6,-2)
Step-by-step explanation:
To dilate a figure multiply 2(x,y)
2(1,2) = (2,4)
2(3,2) = (6,4)
2(1,-1) = (2,-2)
2(3,-1) = (6,-2)
Hope this helps! Ξ
Pls help xDDDDD thx!
Answers
Answer:
-25
Step-by-step explanation:
Tell me if you need an explanation :)
why is it important to break down the radical into its prime factor?
Answers
Answer:
The prime factors of a number are all the prime numbers that, when multiplied together, equal the original number. You can find the prime factorization of a number by using a factor tree and dividing the number into smaller parts.
Step-by-step explanation:
Given: P∈ BC , Pabc = 45, Pabp = 30, Papc = 35. Find AP.
Answers
Answer:
10
Step-by-step explanation:
Pabp = AB +BP +AP
Papc = AP +PC +CA
So the sum of perimeters of the two smaller triangles is ...
Pabp +Papc = AB +BP +AP + AP +PC +CA
= (AB +BP +PC +CA) +2AP
= Pabc +2AP
Filling in numbers, we have ...
30 +35 = 45 +2AP
20 = 2AP . . . . subtract 45
10 = AP . . . . . . divide by 2
The length of AP is 10 units.
This is question 18 for the recent post please help!!
Answers
Answer: D) 6
Step-by-step explanation:
Because this triangle's legs are x and x*root(3), it is a 30-60-90 triangle. Thus, the hypotenuse equals 2x, or 6.
Hope it helps <3
Find the median of the data in the dot plot below.
Answers
Explanation: the easiest way to find the medium is by one by one crossing out both sides till you get to the last standing middle number. Which in this case is 5
HOPE THIS HELPED
Help me ASAP for this question the picture are the answers
If triangle BAT is similar to triangle ROD (ABAT AROD), which of the following statements is incorrect?
Answers
Answer:
I'm pretty sure it's the last one that is incorrect
Step-by-step explanation:
Answer:
The first one - “line segment TA is congruent to line segment DO” is incorrect
Step-by-step explanation:
Since the triangles are similar, the angle measurements would be the same (congruent), but the line segments are are only similar, not congruent, as they have different lengths. So the first statement is incorrect.
30 points high school geometry question
Answers
Answer:
x = 5
Step-by-step explanation:
9/15 = 3/x
x = 5
X would equal 5
I did this test in high school. smh
What is the volume of the following rectangular prism?
Answers
Answer:
Step-by-step explanation:
The Volume is given by the following equation: V= Base x Height
Therefore, [tex]V = 16\frac{1}{4} * \frac{1}{2} = \frac{65}{4} * \frac{1}{2} = \frac{65}{8} = 8\frac{1}{8}[/tex] units