Inequality shows a relationship between two numbers or two expressions.
The number is between -7 and -2.
i.e
-7 < M < -2
What is inequality?Inequalities show a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
Example:
2x > 4
3x < 7
We have,
Let the number be = M
If the product of -5 and a number is greater than 35 or less than 10.
The product of -5 and a number greater than 35 can be written as
-5M > 35 _____(1)
The product of -5 and a number less than 10 can be written as
-5M < 10 _____(2)
From (1) we get,
M > 35/-5
M > -7 _____(3)
From (2) we get,
M < 10/-5
M < -2 ______(4)
From (3) and (4) we get,
-7 < M < -2
Thus
The number is between -7 and -2.
i.e
-7 < M < -2
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Final answer:
The question asks to solve two inequalities resulting from the product of -5 and a number being greater than 35 or less than 10. The solution reveals the number must be either smaller than -7 or greater than -2.
Explanation:
The student's question relates to an inequality involving multiplication with a negative number. The statement 'the product of -5 and a number is greater than 35 or less than 10' can be translated into two separate inequalities because of the 'or.' They are as follows:
-5x > 35
-5x < 10
To solve these inequalities, you would divide each side by -5. Remember the rule: when you divide or multiply an inequality by a negative number, you must flip the inequality sign.
For -5x > 35:
x < -7
For -5x < 10:
x > -2
Therefore, the number must be either smaller than -7 or greater than -2.
Factor 5n2 - 12n - 9 A) (n + 3)(5n - 3) B) (2n - 5)(n - 8) C) (3n - 1)(n + 2) D) (5n + 3)(n - 3)
Answer:
A. 2n-5
Step-by-step explanation:
Your dog eats 7/8 lb of food in 4 meals , how many meals will it take your dog to eat 1 lb of food
Answer:
The dog needs eat 4.6 meals
Step-by-step explanation:
Due to:
7/8 lb ----> 4 meals
1 lb --------> X meals
X = [(1 lb)*(4 meals)] / [7/8 meals]
X = 4.6 meals
Best regards
Graph the following system of equations. Click on the graph until the correct graph appears.
y < -x
y ≤ x - 2
please quick 20POINTS
Answer:
See explanation
Step-by-step explanation:
1. Draw the dotted line y=-x. This line must be dotted, because the inequality y<-x is with sign < (without notion "or equal to"). Then shade the region that contains all values of y that are less than -x (bottom part that is shaded in red on the attached diagram).
2. Draw the solid line y=x-2. This line must be solid, because the inequality y≤x-2 is with sign ≤ (with notion "or equal to"). Then shade the region that contains all values of y that are less or equal to x-2 (bottom part that is shaded in blue on the attached diagram).
3. Their common part (region that is shaded in both red and blue colors) represents both inequalities.
It's this one, just did the test.
37) What is the value of x? 1/6 (3 - 2x)< 1/3 x
A) x > 3 4
B) x < 3 4
C) x > - 4 3
D) x < - 3 4
Answer:
A: x > 3/4
Step-by-step explanation:
First you simplify the equation.
Simplify 1/3x
Then Simplify the left side.
1/2-x/3<x/3
Move x/3 to the left side of the equation by subtracting it from both sides.
1/2-x/3-x/3<0
Now simplify the left side.
1/2-2x/3<0
Find the LCD of the terms of the equation. In this case it's 6.
Multiply each term by 6 and simply.
3-2x<2x
Move all terms that contain a x to the left side of the inequality.
3-4x<0
Subtract 3 from both sides.
-4x<-3
Now divide each term by -4 and simplify.
This gives us our answer of x > 3/4.
Hope this helps. :)
Which description can represent the surface area of this trunk
Answer:
It's B.
Step-by-step explanation:
A trunk has six faces . The total surface area will be the sum of the areas of these faces.
The surface area of a rectangular prism (like a trunk) is the total area of the surface of the object and can be found using the formula A = 2lw + 2lh + 2wh, where 'l' represents length, 'w' represents width and 'h' represents height.
Explanation:The surface area of a trunk, or any three-dimensional object, refers to the total area that the surface of the object occupies. In the case of a trunk, if we consider it as a rectangular prism (a box shape), that surface area can be found by adding the areas of all six faces of the prism. The formula to calculate the surface area (A) of a rectangular prism is A = 2lw + 2lh + 2wh where l denotes length, w width, and h height. Let's say, for example, that your trunk has a length of 3 units, a width of 4 units, and a height of 2 units. The surface area would then be 2*(3*4) + 2*(3*2) + 2*(4*2) = 24 + 12 + 16 = 52 square units.
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Evaluate f(3) divided by g(2) using functions f(x)=x^+1 and g(x)=x .
ANSERWS
A.4
B.5
C.8
D.10
Answer:
[tex]\large\boxed{B.\ 5}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2+1\\\\f(3)\to\text{put x = 3 to the equation of the function}\ f(x):\\\\f(3)=3^2+1=9+1=10\\\\g(x)=x\\\\g(2)\to\text{put x = 2 to the equation of the function}\ g(x):\\\\g(2)=2\\\\f(3):g(2)=10:2=5[/tex]
Don’t know what to do
Answer:
104.65 km/hour
Step-by-step explanation:
We need to convert miles to kilometers. The miles cancel so
65 miles 1.61 kilometers 104.65km
--------------- * ------------------- = -----------------
hour 1 mile hour
The speed limit is 104.65 km/hour
What is the value of sine of begin argument 45 degrees end argument?
Question 1 options:
fraction numerator square root of 2 over denominator 2 end fraction
fraction numerator square root of 3 over denominator 2 end fraction
square root of 2
square root of 3
Answer:
Option A
fraction numerator square root of 2 over denominator 2 end fraction
Step-by-step explanation:
The answer can be obtained using a calculator.
It corresponds to a notable identity
sin (45) = [tex]\sqrt{2}[/tex] / 2
sin (45) = 0.7071
[tex]\sqrt{2}[/tex] / 2 = 0.7071
Please see attached picture
A trapezoid has a height of 10 feet, and base measurements of 20 feet and 8 feet.
What is the area?
what is the answer to number 15 p.s. show how u got this ANSWER PLEASE
Answer:
The volume of the rectangular prism is [tex]V=442.341\ cm^{3}[/tex]
The surface area of the rectangular prism is [tex]SA=384.62\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(12.7)(8.1)(4.3)=442.341\ cm^{3}[/tex]
The surface area of the rectangular prism is equal to the area of its six faces
so
[tex]SA=2(8.1)(4.3)+2(12.7)(8.1)+2(12.7)(4.3)=384.62\ cm^{2}[/tex]
Mia did a study for a health class about the effects of the length of a person's foot and their shoe size. Based on a graph of her data, she found that there was a relationship between the length of a person's foot and their shoe size. Which of the following is a valid conclusion? A. The length of a person's foot is a cause of their shoe size, which implies that there is also a correlation between the length of a person's foot and their shoe size. B. There is no correlation between a person's shoe size and the length of their foot. C. A person's shoe size is a cause of the length of their foot. D. No conclusion can be drawn about the correlation or causation between a person's shoe size and the length of their foot.
Answer: The answer is A.
Step-by-step explanation: The only valid conclusion that is listed in the options is choice A. The correct one is that the length of a person’s foot is a cause of their shoe size, which implies that there is also a correlation between the length of a person’s foot and their shoe size.
what is z if 6 = 1/2 z
Answer:
z = 12
Step-by-step explanation:
12 divided by .5 = 6.
Christy rode her bike 60 miles in 5 hours. (A) what was her average speed in miles per hour?
Answer:
12mph
Step-by-step explanation:
Christy rode 60 miles in 5 hours.
60/5 = 12 miles per hour
Answer:
The answer is 12mph.
Step-by-step explanation:
If she rode her bike 60 miles in 5 hours, in order to find 1 hour, you divide 60/5. Every hour, she rode 12 miles per hour.
250 people were asked to name their favorite fruit.
Berries/ 44%
Peaches 32%
Cherries 24%
A: Of those surveyed, how many people prefer peaches?
B: Which type of fruit did more than 100 people prefer
Answer:
Step-by-step explanation:
A. 250 x .32 = 80
B. 250 x .44 = 110 So, the answer is berries.
Final answer:
Out of 250 surveyed individuals, 80 people prefer peaches. Berries are the preferred choice of more than 100 people.
Explanation:
A total of 250 people were surveyed about their favorite fruit. To find out how many people prefer peaches, we calculate 32% of 250 people. This calculation is done by multiplying the total number of people by the percentage of those who prefer peaches:
250 people x 32% = 250 x 0.32 = 80 people
Therefore, 80 people prefer peaches.
To determine which type of fruit more than 100 people prefer, we apply the same calculation method. Here are the calculations:
Berries: 250 x 44% = 110 people
Peaches: 250 x 32% = 80 people
Cherries: 250 x 24% = 60 people
More than 100 people prefer berries.
PLEASE HELP ASAP ILL REALLY APPRECIATE IT
Answer:
see below
Step-by-step explanation:
2.5 = 2 5/10 = 250%
40% = .40 = 40/100 = 4/10 =2/5
220% = 220/100 = 2 20/100 = 2 2/10 = 2 1/5
1/4 = 25/100 = 25%
4% = 4/100 = .04
2.5 =2/5
0.004 =4%
220% = 2 1/5
1/4 =25%
Which of the following expressions is equivalent to -3(-x+12)
Answer:
the correct answer is 3x-36
what is the horizontal asymptote of the function f(x)= -2x/x+1
Answer:
-2
Step-by-step explanation:
We have been given a function f(x)=\frac{-2x}{x+1} and we are asked to find the horizontal asymptote of our given function.
Recalling the rules for a horizontal asymptote:
1. If the numerator and denominator have equal degree, the horizontal asymptote will be the ratio of the leading coefficients.
2. If the polynomial of denominator has larger degree than the numerator, then the horizontal asymptote will be the x-axis or y=0.
3. If the polynomial of numerator has larger degree than denominator, then the function has no horizontal asymptote.
Here, the numerator and denominator are of the same degree. So the horizontal asymptote will be the ratio of the coefficients.
Horizontal asymptote = [tex]-\frac{2}{1}[/tex] = -2
help me quick please look at the pic
It’s 140 degrees. The angles are congruent from their pair.
a is 35 because vertical angles
b is 55 because triangle sum
90(right angle)+35(a)+b=180
180-90=90-90+35+b
90=35+b
-35 -35
55=b
c is 110 because linear pairs
180-70=c
Suppose that in 20% of all traffic accidents involving an injury, driver distraction in some form (for example, changing a radio station or texting) is a factor. Find the probability that in a random sample of 275 such accidents between 15% and 25% involve driver distraction in some form. Assume the sample is large enough that the normal distribution applies
To find the probability that between 15% and 25% of a random sample of 275 traffic accidents involving an injury involve driver distraction, calculate the z-scores for both percentages and use the standard normal distribution.
Explanation:To find the probability that between 15% and 25% of a random sample of 275 traffic accidents involving an injury involve driver distraction, we need to calculate the z-scores for both percentages and use the standard normal distribution.
First, calculate the z-score for 15%:Which value is the solution to the equation? -3(t-7) = 24
Answer:
-3(t - 7) = 24
t - 7 = -8
t = -1
Final answer:
The correct solution to the equation -3(t-7) = 24 is t = -1, which contradicts the reference indicating solutions for a different quadratic equation.
Explanation:
The equation presented, -3(t-7) = 24, does not yield the solutions t = 3.96 and t = -1.03 as the provided reference indicates. Instead, those solutions seem to be related to a different quadratic equation. To solve the given linear equation for t, you need to perform the following steps:
Distribute the -3 across the parenthesis: -3t + 21 = 24.Subtract 21 from both sides of the equation: -3t = 3.Divide both sides of the equation by -3: t = -1.Therefore, the solution to the equation -3(t-7) = 24 is t = -1.
what percent is 18 out of 30?
Answer:
60%
Step-by-step explanation:
p/100 = 18/30
Multiply each side by 100
p/100 *100 = 18/30 *100
p = 60
18 is 60 percent of 30
The number 18 out of the number 30 is 60 percent.
We need to find what percent is 18 out of 30.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, 18/30
= 9/15
= 3/5
= 0.6
In percentage 0.6×100
= 60%
Therefore, the number 18 out of the number 30 is 60 percent.
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 57 kilograms. A delivery of 8 large boxes and 3 small boxes has a total weight of 126 kilograms. How much does each type of box weigh?
Final answer:
The large box weighs 13.5 kilograms and the small box weighs 6 kilograms.
Explanation:
To solve this problem, we can assign variables to represent the weight of each type of box. Let's say the weight of a large box is L and the weight of a small box is S.
From the given information, we can set up a system of equations:
2L + 5S = 57 (Equation 1)
8L + 3S = 126 (Equation 2)
We can solve this system of equations using the method of substitution or elimination. Let's use elimination:
Multiply Equation 1 by 8 and Equation 2 by 2 to eliminate the S variable:
16L + 40S = 456 (Equation 3)
16L + 6S = 252 (Equation 4)
Subtract Equation 4 from Equation 3:
34S = 204
Solve for S: S = 6
Substitute the value of S into Equation 1:
2L + 5(6) = 57
2L + 30 = 57
2L = 27
Solve for L: L = 13.5
Therefore, the large box weighs 13.5 kilograms and the small box weighs 6 kilograms.
The planets close to the sun are
A)
small and rocky.
B)
large and rocky.
C)
small and gaseous.
D)
large and gaseous.
Answer:
small and gaseous.
It would be A small and rocky and the planets names are Mercury, Venus, Earth, and Mars
Rounded to the nearest whole number, how many 2ft by 2 ft squares will fit into circle that has a diameter of 20 feet
Answer:
79
Step-by-step explanation:
A square that has side length [tex]l=2 ft[/tex] has area [tex]2^2=4ft^2[/tex].
A circle that has a diameter 20 feet has area [tex]A=\frac{\pi d^2}{4}[/tex]
We substitute the diameter into the formula to obtain;
[tex]A=\frac{\pi \times 20^2}{4}=100\pi ft^2[/tex]
The number of squares that has area 4 feet square that can fit into a circle with area [tex]100\pi ft^2[/tex] is
[tex]=\frac{100\pi}{4}=25\pi=78.5398[/tex]
When we round to the nearest whole number; we have 79 squares.
Approximately 79 squares of size 2 ft by 2 ft can fit into a circle with a diameter of 20 feet.
To accurately determine how many 2ft by 2ft squares can fit into a circle with a diameter of 20 feet, let's perform a step-by-step calculation:
1. Calculate the area of the circle:
[tex]\[ \text{Area of the circle} = \pi r^2 \][/tex]
Given the diameter is 20 feet, the radius r is 10 feet:
[tex]\[ \text{Area of the circle} = \pi \times 10^2 = 100\pi \approx 314.16 \text{ square feet} \][/tex]
2. Calculate the area of one 2ft by 2ft square:
[tex]\[ \text{Area of one square} = 2 \times 2 = 4 \text{ square feet} \][/tex]
3. Calculate the theoretical maximum number of squares that can fit into the circle by dividing the area of the circle by the area of one square:
[tex]\[ \text{Theoretical number of squares} = \frac{\text{Area of the circle}}{\text{Area of one square}} = \frac{314.16}{4} \approx 78.54 \][/tex]
4. Round to the nearest whole number:
[tex]\[ \text{Rounded number of squares} = 79 \][/tex]
Helaine graphed the equation 12x – 4y = 3. What was the slope of Helaine’s line?\
Answer:
[tex]\large\boxed{\text{The slope}\ m=3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line in the standard form:
[tex]12x-4y=3[/tex]
Convert to the slope-intercept form:
[tex]12x-4y=3[/tex] subtract 12x from both sides
[tex]-4y=-12x+3[/tex] divide both sides by (-4)
[tex]y=\dfrac{-12}{-4}x+\dfrac{3}{-4}\\\\y=3x-\dfrac{3}{4}[/tex]
Answer: The required slope of the given line is 3.
Step-by-step explanation: Given that Helaine graphed the following equation :
[tex]12x-4y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the slope of the line.
We know that
the slope-intercept form of a straight line is given by
[tex]y=mx+c,[/tex] where m is the slope of the line.
From equation (i), we have
[tex]12x-4y=3\\\\\Rightarrow 4y=12x-3\\\\\Rightarrow y=\dfrac{12x-3}{4}\\\\\\\Rightarrow y=3x-\dfrac{3}{4}.[/tex]
Comparing with the slope-intercept form, we get
slope, m = 3.
Thus, the required slope of the given line is 3.
What I the slope of the equation of the line below.
Answer:
the slope m = 3Step-by-step explanation:
Look at the picture.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (0, 4) and (-2, -2). Substitute:
[tex]m=\dfrac{-2-4}{-2-0}=\dfrac{-6}{-2}=3[/tex]
Answer:
-3
Step-by-step explanation:
area- compound shapes
Answer:
Step-by-step explanation:
Hello, you need to divide that form into two forms: a triangle and a square.
For square:
A1 = 7in X 7in = 49 in2
For triangle:
A2 = [(7in) X (11in-7in)]/2 = 10.5 in2
So, the total area is the sum of A1+A2
Area = 59.5 in2
Best regards
Classify each number as rational or irrational. Drag the choices into the boxes to correctly complete the table.
rational irrational
3√
−1/16
0
2√
Answer:
3 = irrational
-1/16 = rational
0 = rational
2 =irrational
Answer: - 1/16 and 0 are rational. 3 and 2 are irrational.
Step-by-step explanation:
suppose the circumference of a crop circle is 150.7968 hectometers (hm) what's the radius of the circle? (usett=3.1416)
Answer:
The radius of the circle is [tex]24\ hm[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
In this problem we have
[tex]C=150.7968\ hm[/tex]
[tex]\pi=3.1416[/tex]
substitute and solve for r
[tex]150.7968=2(3.1416)r[/tex]
[tex]r=150.7968/(2(3.1416))=24\ hm[/tex]
Answer:
24 hm
Step-by-step explanation:
I got the question.
Bill is doing a fundraiser for school. He needs to sell at least $100 dollars worth of items. Candy bars cost $2 each and shirts cost $10 each. He must sell more than 4 candy bars.
Answer:
bill can sell 5 candy bars and 9 shirts
Step-by-step explanation:
5x2=10
9x10=90
90+10=100