Given:
The graph of an inequality.
To find:
The inequality for the given graph.
Solution:
From the given graph it is clear that the boundary line passes through two point (0,3) and (2,4). So, the equation of boundary line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-3=\dfrac{4-3}{2-0}(x-0)[/tex]
[tex]y-3=\dfrac{1}{2}(x)[/tex]
[tex]y=\dfrac{1}{2}x+3[/tex]
The shaded area lies below the boundary line and the boundary line is a solid line. So, the sign of inequality must be ≤.
The required inequality is
[tex]y\leq \dfrac{1}{2}x+3[/tex]
Therefore, the correct option is B.
Question 4 (10 points)
(05.06 MC
The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph:
Motion of Ant
10
Distance
from Holes
o
P
R
2
1 2 3 4 5 6 7
Time (sec)
Part A is the graph linear or nonlinear? Explain your answer. (2 points)
Part B: In which segments is the graph increasing decreasing and constant? (3 points)
Part C: In your own words, describe the motion of the ant, as shown on the graph (5 points)
Answer:
I need Help on this one too.
Step-by-step explanation:
PLease Help
Answer:
Part A: it is linear because it is not curving and it consists of straight lines.
Part B: in side A it is increasing because it has a positive slope. In side b it is constant because the slope is 0 since it is straight. Finally, side C is decreasing because the slope is negative.
Part C: during side A the ant is crawling out of the hole in 2 seconds. After that, the ant stops for 2 more seconds as shown in side B. Then, he crawls back into the hole as shown by the decrease in distance due to the slope.
Step-by-step explanation:
can I have some help with this please?
Answer:
Is this Trig? If so I recommend using SOHCAHTOA, if not i have No way of helying you sorry
Step-by-step explanation:
Find the inverse of f (x) = x + 2 + 9
Answer:
y = x - 11
Step-by-step explanation:
First, turn the f(x) into a y:
y = x + 2 + 9
Now, switch the x and y.
x = y + 2 + 9
Add like terms.
2 + 9 = 11
x = y + 11
Now, solve for y. Subtract 11 on both sides.
y = x - 11
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
Answer: The first table
Step-by-step explanation:
1:16
2:32
4:64
8:128
Answer:
The first one that goes 1-8 under the cups.
Step-by-step explanation:
Since theres 16 tablespoons in 1 cup, it goes up by 16 per cup. So, for 2 cups, it's 2 x 16, for 3 cups, its 3 x 16, and so on. If you were to do that the first table is the only one that matches.
i need help plzzzzzzz
Answer:
12
Step-by-step explanation:
25-13= 12
A recipe for pie dough calls for a ratio of butter to flour of 23 : 134. If you plan to use 7 cups of flour, how much butter should you use to keep the same ratio?
Answer:
You might have to round, but ≈1.2015
Step-by-step explanation:
butter: flour
23 : 134 is really just a:b
b = 7, so: a : 7
Divide both sides by 134, so
≈0.172 : 1
Multiply by 7 to get 7 cups of flour
≈1.2:7
2
Select all the correct answers.
HELP PLS! ASAP
Which expressions are equivalent to this exponential expression?
Answer:
A and C
Step-by-step explanation:
Bill drove 240 miles in 4 hours. On another day, he drove 480 miles in 8 hours. What is the constant of proportionality?
Answer:
12
Step-by-step explanation:
This is a fraction equal to
30 miles ÷ 2.5 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2.5
30 miles ÷ 2.5
2.5 hours ÷ 2.5
=
12 miles
1 hour
=
12 miles
hour
= 12 miles per hour
Write the equation of the exponential function using two points. (-3,8)(0,1)
Answer:
m= −7/3
(x1,y1)=(−3,8)
(x2,y2)=(0,1)
Use the slope formula:
m=
y2−y1
x2−x1
=
1−8
0−−3
=
−7
3
=
−7
3
9. Which is a true statement about dilations?
A. A dilation will always enlarge a figure.
B. A dilation will always produce congruent figures.
C. A dilation will always produce similar figures.
D. A dilation will always change the orientation of a figure.
A dilation will always produce similar figures. Therefore, option C is the correct answer.
We need to find the which is a true statement about dilation.
What is a dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
After the dilations an image and original shape look same, so they are similar.
A dilation will always produce similar figures. Therefore, option C is the correct answer.
To learn more about the dilation visit:
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Please look at picture
A 3-foot-wide wood deck will be built around a rectangular-shaped pool that measures 15 feet by 30 feet. The resulting shape is also rectangular. If the lumber costs $10 per square yard, If the lumber costs 10 dollars per square yard, what is the cost of the wood for the deck?
Answer:
$340
Step-by-step explanation:
We are told that the pool measures 15 feet by 30 feet,
Since the cost of the wood around it is per yards, let's convert this measurement to yards.
15 ft = 5 yards
30 ft = 10 yards
The deck is 3 ft wide. Converting to yards it is 1 yard.
Since the deck is round the pool, it means when we add it to the pool dimensions, we now have a dimension of; width: 7 yards by length: 12 yards
Thus, total area of pool and deck is;
A_t = 7 × 12 = 84 Sq.yds
Area of only pool is;
A_p = 5 × 10 = 50 Sq.yds
Finally, area of the deck will be;
A_d = 84 Sq.yds - 50 Sq.yds = 34 Sq.yds
We are told that the costs of the wood is $10 per Sq.yds
Thus, total cost is;
C = 10 × 34
C = $340
Dhanraj spent $204.20 purchasing volleyballs and basketballs.
He bought 3 more basketballs than volleyballs. If each volleyball cost $8.20 and each basketball cost $12.60, how many of each type did he buy?
Answer:
Number of volleyballs bought = 8
Number of basketballs bought = 11
Step-by-step explanation:
Given that:
Total amount spent = $204.20
Let,
x be the number of volleyballs
y be the number of basketballs
According to given statement;
y = x+3 Eqn 1
8.20x+12.60y=204.20 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
8.20x + 12.60(x+3) = 204.20
8.20x + 12.60x + 37.80 = 204.20
20.80x = 204.20 - 37.80
20.80x = 166.40
Dividing both sides by 20.80
[tex]\frac{20.80x}{20.80}=\frac{166.40}{20.80}\\x=8[/tex]
Putting x=8 in Eqn 1
y = 8+3 = 11
Hence,
Number of volleyballs bought = 8
Number of basketballs bought = 11
Find the simple interest payable on a deposit of ₹20,000 at 12% per annum over a period of 4 years.
Answer:
The simple interest accumulated on a principal of ₹20,000 at a rate of 12% per year for 4 years is ₹9600.
Step-by-step explanation:
Given
Principle P = ₹20,000
Rate r = 12% per annum = 0.12 per annum
Time period t = 4 years
To determine
Simple Interest I = ?
Using the simple interest formula equation
I = Prt
substituting P = 20000, r = 0.12, t = 4
I = 20000 × 0.12 × 4
I = ₹9600
Therefore, the simple interest accumulated on a principal of ₹20,000 at a rate of 12% per year for 4 years is ₹9600.
A)
lo
Absolute value of 8/7,-8/7
Answer:
8/7, 8/7
Step-by-step explanation:
A straight line is divided into two angles. If the first angle is 88 degrees, what is the measure of the second angle?
PLEASE HELP EEP-
Answer:
i think its going to be 180* degreas! sorry if im wrong
Step-by-step explanation:
3. Find the value of y.
w
(4y - 4)
N
52
Зу"
х
Answer:
hi how you doing
Step-by-step explanation:
bye have a great day 12
PLEASE HELP ! worth 18 points :)
Using the Law of Cosines Given SAS
Information
Z
Find the value of x to the nearest tenth.
Which of the following equations correctly sets up
the law of cosines to solve for x?
552 - 52 +82-25)(8)· cos(X)
2-52 +82-2(5)(8).cos(559)
O * - (5+8) -2(5)(8).cos(559)
552 - 52 +82-2(5)(8) cos(x)
5
55°
Y
DONE
8
The equations correctly set up the law of cosines to solve for x will be x² = 5² + 8² - 2 (5)·(8) cos 55°. Then the correct option is B.
What is the cosine law?The squared of the size of any solitary side of either a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, times by the cosine of something like the angle they are a part of.
Let the triangle ΔABC, then the cosine law is given as,
c² = a² + b² - 2 a·b cos C
From the graph, the measure of the length 'x' is calculated as,
x² = 5² + 8² - 2 (5)·(8) cos 55°
The equations correctly set up the law of cosines to solve for x will be x² = 5² + 8² - 2 (5)·(8) cos 55°. Then the correct option is B.
More about the cosine law link is given below.
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Rosita’s mom is 42 years old. She is six times as old as Rosita. The equation 6a = 42 can be used to find Rosita’s age, a. A model of the equation is shown. What is the solution to the equation?
Answer:
7
Step-by-step explanation:
All you have to do is divide 42 by 6 and you get 7!
I hope this helps and have a great day!
find the least common multiple of 36,6 ,3
-- least common multiple of 36, 6, 3 = 36
- it is the smallest number divisible by all three.
7 one is equivalent to how many hundreds?
1400 tenths is equivalent to how many tens?
Answer:
(i) 7 one is equivalent is equivalent to [tex]\frac{7}{100}[/tex] hundreds, (ii) 1400 tenths is equivalent to 14 tens.
Step-by-step explanation:
We proceed to find the equivalent number in rational form:
(i) 7 one is equivalent to how many hundreds? In this case, we know that 7 one is equivalent to [tex]x[/tex] hundreds. That is:
[tex]7\times 1 = x \times 100[/tex]
Then, we solve the expression for [tex]x[/tex]:
[tex]x = \frac{7\times 1}{100}[/tex]
[tex]x = \frac{7}{100}[/tex]
7 one is equivalent is equivalent to [tex]\frac{7}{100}[/tex] hundreds.
(ii) 1400 tenths is equivalent to how many tens? In this case, 1400 tenths is equivalent to [tex]x[/tex] tens. That is:
[tex]1400\times \frac{1}{10} = x\times 10[/tex]
Then, we solve for [tex]x[/tex]:
[tex]x = \frac{1400}{10\times 10}[/tex]
[tex]x = \frac{1400}{100}[/tex]
[tex]x = 14[/tex]
1400 tenths is equivalent to 14 tens.
If the area of a rectangle is 30 cm what can the possible length and breadth of the rectangle be?
(Hint: The area of a rectangle = length x breadth)
Answer:
The length could be 6, 10, or 15 and the breadth; 5, 3 and 2 respectively
This is because, length x breadth = area
6x5=30
10x3=30
15x2=30
What is 4 to the -2 power divided by 4 to the 4th power
Answer:
4 to the -2 power divided by 4 to the 4th power
[tex] \frac{ {4}^{ - 2} }{ {4}^{4} } = \frac{1}{( {4}^{2} \times {4}^{4} ) } = \frac{1}{ {4}^{(2 + 4)} } = \frac{1}{ {4}^{6} } = \frac{1}{4096}\\ [/tex]
(1/4096) is the right answer.Select the correct answer from the drop down menu
The last one , because I will now solve it for you and prove therefore.
x²–4x+5=0;
D=(–4)²–4•5=16–20= –4= (2i)².
So:
x1= (4–2i)/2= 2–i
x2= (4+2i)2= 2+i.
This is the whole answer....
Three other u will solve by yourself and have roots which will not be suitable.
Solve for x: 0.03x - 1.2 = 0.24
Answer:
920
Step-by-step explanation:
After the point B(2, 3) is translated along the vector <5, 7> the image will be located at ?
Answer:
(7, 10)
Step-by-step explanation:
The vector has an x component of 5 and a y component of 7, so we can add each of these components to the coordinates of B to get its image:
B(2,3)
B'(2 + 5, 3 + 7) = B'(7, 10)
The image will be located at (7, 10).
What is vector?Vectors, in Maths, exist as objects which have both, magnitude and direction. Magnitude determines the size of the vector. It exists described by a line with an arrow, where the length of the line exists the magnitude of the vector and the arrow displays the direction.
The vector has an x component of 5 and a y component of 7, so we can add each of these components to the coordinates of B to get its image:
B(2,3)
B'(2 + 5, 3 + 7) = B'(7, 10)
To learn more about vector refer to:
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write 5.3 x 5.3 x 5.3 x 5.3 as a power.
I need an answer, please. thanks. -Furreto
Answer:
5.3 to the 3rd power
Step-by-step explanation:
The expression 5.3 x 5.3 x 5.3 x 5.3 can be expressed as (5.3)⁴.
To express 5.3 x 5.3 x 5.3 x 5.3 as a power, we can use the exponentiation property.
When we multiply a number by itself multiple times, we can simplify it using an exponent.
In this case, we have four instances of multiplying 5.3 by itself. So we can write it as:
5.3 x 5.3 x 5.3 x 5.3 = (5.3)⁴
The exponent 4 indicates that we are multiplying 5.3 by itself four times.
It represents the number of times the base (5.3) is multiplied by itself.
So, (5.3)⁴ means 5.3 raised to the power of 4, which is equivalent to multiplying 5.3 by itself four times.
Therefore, 5.3 x 5.3 x 5.3 x 5.3 can be expressed as (5.3)⁴.
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1.) The soccer field at Trey's school is 110 --- long
a) millimeter
b) centimeter
c) meter
d) Kilometer
Answer:
c) meter
Step-by-step explanation:
Millimeters and Centimeters are too short of units for a soccer field, and kilometers are too big.
Answer:
meter
Step-by-step explanation:
centimeters are way to small and millimeter is also way to small kilometer Is to big so it has to be a meter
Can someone please answer this
I really need help with this Triangle problem.
Answer:
x = 10
y = 20
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{x}{10 \sqrt{3} } \\ \\ \frac{1}{ \sqrt{3} } = \frac{x}{10 \sqrt{3} } \\ \\ \sqrt{3} x = 10 \sqrt{3} \\ \\ x = \frac{10 \sqrt{3} }{ \sqrt{3} } \\ \\ x = 10 \\ \\ \cos 30 \degree = \frac{10 \sqrt{3} }{y} \\ \\ \frac{ \sqrt{3} }{2} = \frac{10 \sqrt{3} }{y} \\ \\ y = 10 \sqrt{3} \times \frac{2}{ \sqrt{3} } \\ \\ y = 10 \times 2 \\ \\ y = 20[/tex]