Match each compound inequality on the left to the graph that represents its solution on the right.
Note that equation 1 matches the Line Graph in option (B), equation 2 matches option (C), and equation 3 matches option (A).
How would you define a Line Graph?It is a graph that depicts a line connecting many points or a line indicating the relationship between the points. The graph depicts quantitative data between two changing variables by connecting a sequence of succeeding data points with a line or curve.
With regard to the above-given graphs,
The inequalities are given as
1. 4x + 3 > 15 or —6x ≥ 12
2. —8x > —24 and —10 ≤ 2x -6
3. -29 ≤ 9x -2 < 16
Note that the way to identify the plots on the line graphs is by solving the above equations.
1) 4x + 3 > 15 or —6x ≥ 12
4x + 3 > 15 can be solved by subtracting 3 from both sides, resulting in 4x > 12. Dividing both sides by 4 gives x > 3.-6x ≥ 12, can be solved by dividing both sides by -6, resulting in x ≤ -2.2) —8x > —24 and —10 ≤ 2x -6
To solve for x in —8x > —24, divide both sides by -8
x > 3;
So solve for —10 ≤ 2x -6; add 6 from both sides and divide by 2
-4/2 ≤ x
-2 ≤ x or x ≥ -2
3) -29 ≤ 9x -2 < 16
To solve this inequality, you can start by isolating the variable on one side of the inequality. To do this, you can add 2 to both sides to get:
-29 + 2 ≤ 9x < 16 + 2
-27 ≤ 9x < 18
Now divide both sides by 9 to get:
-3 ≤ x < 2
This means that x can be any number that is greater than or equal to -3 and less than 2.
Given the above results, it is correct to state that equation 1 matches option (B), equation 2 matches option (C), and equation 3 matches option (A).
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Full Question:
See the attached.
Someone HELPPppp for tmr
Answer:
y=1x-6
Step-by-step explanation:
First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.
-Hope this helped
Rosa sold lemonade at a baseball game. She sold 101 cups for $2.00 each.
She spent $40.50 on supplies. How much money did she make?
Answer: it’s 161.50
Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides
of 12 centimeters. He will make the "X" by stretching red ribbon diagonally from corner to corner.
How many centimeters of ribbon will Peter need to make the "X"?
Round your answer to the nearest centimeter.
Answer:
34 centimetres
Step-by-step explanation:
Since the flag is made of a square white flags, then all its sides are equal in length. a diagonal of a square would divide it into two equal triangle.
Let the length of the diagonal be represented by t, such that;
[tex]/hyp/^{2}[/tex] = [tex]/adj 1/^{2}[/tex] + [tex]/adj 2/^{2}[/tex]
[tex]t^{2}[/tex] = [tex](12)^{2}[/tex] + [tex](12)^{2}[/tex]
= 144 + 144
[tex]t^{2}[/tex] = 288
t = [tex]\sqrt{288}[/tex]
t = 16.9706
t = 17 centimetres
The length of a diagonal of the flag is 17 centimetres.
So that,
The centimetres of ribbon required to make the "X" = 2 x diagonal
= 2 x 17
= 34
The centimetres of ribbon required to make the "X" is 34 centimetres.
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 units
Answer:
A
Step-by-step explanation:
refer the sketch for step by step answer
question 12 to find the shaded portion
12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.
9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,
= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].
= [8×8 - 4×4] cm².
= 64 - 16 cm².
= 48 cm².
10. Similarly the figure in (10) is twice the area of the two trapezoids.
11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.
12. The total area is the sum of the areas of the trapezoid and the parallelogram.
13. The larger figure is a rectangle with a right-angle triangle on top.
We have to subtract two rectangles from this to obtain the area of the shaded region.
14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.
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Find the area of the figure.
plz i give brainliest.
Answer:
23.5 inches^2
Step-by-step explanation:
Area of triangle = 1/2 * base * height
area = 1/2 * (5+2) * (5+4)
area = 31.5 in^2
Area of rectangle = length * breadth
area = 4 * 2
area = 8 in^2
Area of figure = area of triangle - area of rectangle
area = 31.5 - 8
area =23.5 in^2
What is 507 less than 607
Which of the following functions represent exponential decay?
O y=-2X
Oy
0 7 = 20.5x
Oy=2
Answer:
Im guessing the top one?
Step-by-step explanation:
not sure since the questions are a bit janky, but the exponential decay formula is y=a(1-r)^x
compare the function rule f(x) = 3x +2 and the graph of g(x)
which statements are true? select two that apply.
-g(x) increases at a faster rate over the interval (-1,0)
-g(x) increases at a faster rate over the interval (1,2)
-g(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (2,3)
-f(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (1,2)
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x)
[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]
from the graphs n f (x) and g( x) are 1 and 5 .
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Can someone help me with this please
Helpp me pleasee! No fake people or responses
Answer:
The first statement and the 3rd statement are true. :)
For future reference, cosine is ratio of the adjacent side to the hypotenuse
An appliance store sells 373 vacuum
cleaners in the month of August. If it
sells 300 more vacuum cleaners in the
next month, how many vacuum
cleaners does it sell in September?
Use the distributive property to write an equivalent expression.
16+32
Hint: find the gcf.
Answer:
2( 4+4) = 16
Step-by-step explanation:
The gcf of 16+32 is 16
Can y’all help me on question 35?!
Quadratic polynomial which has zeros at 7 and 3?
Answer:
x^2 - 10x + 21
Step-by-step explanation:
Sum of zeros
= 7 + 3
= 10
Product of zeros
= 7 x 3
= 21
x^2 - ( sum of zeros )x + product of zeros
= x^2 - 10x + 21
The Quadratic polynomial is x^2 - 10x + 21.
if the zeroes of a quadratic polynomial are a and b, then the polynomial can be written as :
[tex] \boxed{{x}^{2} - (a + b)x + ab}[/tex]
So,
[tex] \hookrightarrow \: {x}^{2} - (7 + 3)x + (7 \times 3)[/tex]
[tex]\hookrightarrow \: {x}^{2} - 10x + 21[/tex]
A book publisher find production cost associated 30 and fixed cost 25000 if each book is sold for 50 find cost function and profit function
The cost function is a function that describes the total cost of producing x number of books. The fixed cost of 25000 is a constant cost that does not depend on the number of books produced, so it is not included in the cost function. The cost function is therefore:
Cost function: C(x) = 30x
The profit function is a function that describes the profit made from selling x number of books. The profit is equal to the revenue from selling the books minus the cost of producing the books. The revenue from selling x number of books at a price of 50 each is 50x, so the profit function is:
Profit function: P(x) = 50x - 30x = 20x
This profit function tells you that for every book you sell, you will make a profit of 20.
can you help me find this solution if you can explain it to me please also
If point C is between points A and B, AB=43, AC= -12x -9, BC = 24x + , what is the value of X? please help
Answer:
equation: 43+(-12x-9)+24x=X
Step-by-step explanation:
Select all the values of r that make the inequality r>4.6 true.
A. 4.60
B. 5.05
C. 3.7
D. 4.9
E. 4.08
Construct the requested confidence interval. A meteorologist was interested in the average speed of a thunderstorm in his area. He sampled 13 thunderstorms and found that the average speed at which they traveled across the area was 15 miles per hour with a sample standard deviation of 1.7 miles per hour. Assuming the speed of a thunderstorm is approximately normal, construct a 99% confidence interval for the true average speed of a thunderstorm in his area.
Answer:
The 99% confidence interval for the true average speed of a thunderstorm in his area is between 13.56 miles per hour and 16.44 miles per hour.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 13 - 1 = 12
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 12 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 3.0545
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.0545\frac{1.7}{\sqrt{13}} = 1.44[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.44 = 13.56 miles per hour
The upper end of the interval is the sample mean added to M. So it is 15 + 1.44 = 16.44 miles per hour.
The 99% confidence interval for the true average speed of a thunderstorm in his area is between 13.56 miles per hour and 16.44 miles per hour.
Goran wants to build a square picture frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?
After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.
What is a square?A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.
given,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.
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What is equivalent to " two more than three times a number is seven
Answer:
if it’s asking for a numerical answer it would be 1.67
(Rounded to the nearest two)
Step-by-step explanation:
Please help solve the equation using cos(no links)
Answer:
cos 52 = 11/alpha ---> alpha = 11/cos52 = 17.9
Help pleaseeeeeee, I need help
Answer:
15, 60, and 61
Step-by-step explanation:
First we have to find the 3rd side length from 2 side length chosen. So let’s pick 8 meters and 11 meters, to find the third side length we use the Pythagorean theorem: c^2 = a^2 + b^2
c = 11^2 + 8^2 = 121 + 64 = 185 = 13.6
13.6 isn’t one of the answers so we can’t pick 11 & 8. Let’s try 11 & 15:
c = 15^2 + 11^2 = 225 + 121 = 346 = 18.6
18.6 isn’t one of the answers either. Let’s try 15 & 60:
c = 60^2 + 15^2 = 3600 + 225 = 3825 = 61.85
61.85 might be it but let’s try one more just in case:
c = 60^2 + 61^2 = 3600 + 3721 = 7321 = 85.6
Nope! That means 15, 60, and 61 are the answer. I hope this is correct!
3x • 3y + 8 when x = 3, y = 2
Answer:
62
Step-by-step explanation:
Substitute x by 3 and y by 2
3*3*3*2+8=62
Please HELP!!!!! Will give brainlyest!!! (Image attached.)
Answer:
18 because you use the middle section which explains how many rolls are needed
Sharon created a rectangular prism with cubes that have a side length of 1 inch. The prism is shown below.
What is the volume of Sharon’s prism? A. 18 cubic inches B. 27 cubic inches C. 36 cubic inches D. 54 cubic inches
Answer:
6 x 2 x 3 = 36
Step-by-step explanation:
C is answer :)
Answer:
lets look at the width and the height and the length!
your width is: 6
your height is: 2
your length is: 3
Now lets multiply all given lengths to find the volume!
6 x 2 x 3 = 36 cubic inches!
1/3m = 12-m
Please explain step by step to get marked as brainliest.
Step-by-step explanation:
cross multiply
12-m(3m)= 1
12-3m²-1=0
multiply by -1
3m²+1-12=0
3m²= 11
m²= 11/3
m=√11/3.
How much is 2a + b greater than a - 2b
Answer:
2a + b>a-2b( just an inequality solution)
hope this helps
have a good day :)
Step-by-step explanation: