Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 In which section of the graph does the actual solution to the system lie?
A. 1
B. 2
C. 3
D. 4
Answers
The actual solution lie in region 4.
EXPLANATION
The given system of inequalities are
[tex]y \leqslant - 0.75x \: and \: y \leqslant 3x - 2[/tex]
Choose a point from each region and substitute in to the system of inequalities, the one that satisfies the system simultaneously is the actual solution.
Region 2: We test for
[tex](0,2)[/tex]
Thus,
[tex]2 \leqslant - 0.75(0)\: and \: 2 \leqslant 3(0)- 2[/tex]
[tex]2 \leqslant 0\: and \: 2 \leqslant- 2[/tex]
The above statement is false.
For region 1: We test for
[tex](-2,0)[/tex]
[tex]0 \leqslant - 0.75( - 2)\: and \: 0 \leqslant 3( - 2) - 2[/tex]
[tex]0 \leqslant 1.5\: and \: 0 \leqslant - 8[/tex]
The first statement is true but the second statement is false, so the whole thing is false.
For Region 3: We test
[tex](2,0)[/tex]
[tex]0 \leqslant - 0.75(2) \: and \: 0 \leqslant 3(2)- 2[/tex]
[tex]0 \leqslant - 1.5 \: and \: 0 \leqslant 4[/tex]
The first statement is false and the second is true so the whole statement is not true.
For region 4: We test
[tex](0,-4)[/tex]
[tex]0 \leqslant - 0.75( - 4)\: and \: - 4 \leqslant 3( 0) - 2[/tex]
[tex]0 \leqslant 3\: and \: - 4 \leqslant - 2[/tex]
Both statements are true, region 4 represents the actual solution to the system.
Answer:
4
Step-by-step explanation:
trust me
Related Questions
A , O and B lie on a straight line segment
Evaluate x the diagram is not drawn to scale
Answers
if A , O and B lie on a straight line segment
then
∡AOY+∡YOZ+∡ZOB=180°
so
3x+x+x=180-----> 5x=180--------> x=180/5--------> x=36°
the answer is
x=36°
The value of x from the given diagram is; 36°
Sum of angles on a straight line.The sum of angles on a straight line is 180°.
In this scenario, the sum of angles on the straight line: AOB is 180°.
Therefore, we have
3x + x + x = 180°5x = 180x = 36°
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A total of 327 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Answers
109 Adults
Let x = adults
Let 2x = students
Add together and set equal to the total number.
109 adult tickets were sold for the school play.
Explanation:Let's assume the number of adult tickets sold is x.
According to the given information, the number of student tickets sold is 2 times the number of adult tickets sold. So, the number of student tickets sold is 2x.
Since the total number of tickets sold is 327, we can write the equation x + 2x = 327. Simplifying this equation gives us 3x = 327. Dividing both sides by 3, we get x = 109.
Therefore, 109 adult tickets were sold.
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The cost of gasoline is expected to increase by 2.5% next year. If p represents the current cost of gasoline, which experession represents the expected gasoline price next year?
Answers
[tex]y = x \times 0.025[/tex]
Jason eats 10 ounces of candy in 5 days. a. How many pounds does he eat per day?
b. How long will it take Jason to eat 1 pound of candy?
Answers
B. It would take him a total of 8 days to eat a pound of candy.
A. Since he ate 10 ounces in 5 days, you divide 10 by 5 to find he ate 2 ounces per day. Since there are 16 ounces in a pound that would be your denominator (bottom of fraction) and 2 would be the numerator (top of your fraction). You will get 2/16 which if you simplify (divide by 2) you get 1/8.
B. Knowing that there are 16 ounces per pound and he ate 1/8 pound ( 2/16 pound or 2 ounces) a day, you can either look at the simplified denominator to get the answer, or, divide 16 by 2 to get your answer.
I hope this helps!
Use the Distributive Property to multiply 9 and 37 in your head. What is the answer?
270 + 7 = 277
27 + 63 = 90
30 + 63 = 93
270 + 63 = 333
Answers
If you did it in your head, it would look like this:
9(30) + 9(7)
270 + 63 = 333
Write the equation for a parabola that has x− intercepts (−1.6,0) and (−3.2,0) and y−intercept (0,25.6).
Answers
(x-x1)(x-x2)=(x+1.6)(x+3.2)=x² +1.6x+3.2x+5.12=x²+4.8x+5.12
y=x²+4.8x+5.12, but the y-int. is (0, 25.6),
So, our parabola should look like
y=5(x²+4.8x+5.12)
y=5x²+24x+25.6
∞∞∞∞∞∞∞∞
Explanation:
∞∞∞∞∞∞∞∞
x-intercept = (-1.6, 0) and (-3.2, 0)
=====> y = a(x + 1.6)(x + 3.2)
Given y-intercept = (0, 25.6)
=====> 25.6 = a( 0 + 1.6)(0 + 3.2)
=====> 25.6 = 5.12a
=====> a = 5
Plug in a = 5 into the equation
=====> y = 5(x + 1.6)(x + 3.2)
write the standard form of the line that passes through the given point. include your work in your final answer. (-8,0) and (1,5)
Answers
The points are (-8,0) and (1,5). The slope(m) of the line will be:
[tex]m= \frac{5-0}{1+8} = \frac{5}{9} [/tex]
Using the slope and a point (-8,0) we can write the equation in point slope form as:
[tex]y-0= \frac{5}{9}(x+8) \\ \\ y= \frac{5x}{9} + \frac{40}{9} \\ \\ 9y=5x+40[/tex]
In standard form, the equation will be:
5x - 9y = - 40
Could someone please help with this question!
Answers
Part (A):
Since the two figure are similar, therefore, we will use the similarity proportionality to get the unknown side as follows:
[tex] \frac{16}{8} = \frac{x}{2} [/tex]
x = [tex] \frac{2*16}{8} = 4 units[/tex]
Part (B):
Since the two figures are similar, therefore, we will use similarity proportionality to get the unknown sides as follows:
[tex] \frac{y}{8} = \frac{12}{4} = \frac{18}{x} [/tex]
x = [tex] \frac{18*4}{12} = 6 units[/tex]
y = [tex] \frac{12*8}{4} = 24 units[/tex]
Hope this helps :)
A large pizza has a diameter of 18 inches. How many square inches of pizza does the large pizza have?
Answers
the area of a pizza is equal to the area of a circle
so
area of a circle=pi*r²
diameter=18 in
radius=diameter/2-----> r=18/2------> r=9 in
area of a circle=pi*9²------> 254.34 in²
the answer is
254.34 in²
Two ships leave a harbor at the same time. one ship travels on a bearing upper s 12 degrees upper w at 18 miles per hour. the other ship travels on a bearing upper n 75 degrees upper e at 12 miles per hour. how far apart will the ships be after 2 hours?
Answers
Between E and S there are 90°
Between South and S12°W there 12°
Applying cosine rule
Another way is to measure all angles clockwise from north (called azimuth) The ship at S12°W is at 180+12 = 192°
The ship at N75°E is at 75°
Angle between them is 192-75 = 117°
Applying cosine rule:
c=√(36²+24²-2×36×24cos117)
c=√2656.496
c=51.54 mi
Which of following equations is equivalent to the slope formula?
Answers
A researcher reports that mean ratings of liking for some food are m = 0.8, sd = 2.4. if the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated cohen's d?
Answers
The scatterplot shows a linear relationship between the distance traveled and the time elapsed. What is the rate of change of the linear relationship?
For every increase in time by 1 hour, the distance increases
36 miles.
54 miles.
72 miles.
90 miles.
Answers
slope,m=(change in y-values)/(change in x-values)
taking 2 points (1.25, 90) and (0.75,54) we get:
slope,m=(90-54)/(1.25-0.75)=36/0.5=72
The answer is:
72 miles
Answer:
The answer is C. 72 miles.
Step-by-step explanation:
Anyone know? Will give brainiest
Answers
THE FIRST ANSWER GETS BRAINIEST The total height of the Statue of Liberty and its pedestal is 153 feet more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.
WRITE THE EQUATION !!
Answers
The complete question is :
The total height of the Statue of Liberty and its pedestal is 305 feet. This is 153 more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.
Question says 153, so we add 153 with the height of the statue
The total height of the Statue of Liberty = Height of the statue + 153
305 = h + 153
To find out h we subtract 153 on both sides
305 - 153 = h + 153 - 153
h = 152
The height of the statue = 152 ft
The height of the statue is 152 feet.
Let's call the height of the statue "h" in feet. According to the problem, the total height of the Statue of Liberty and its pedestal is 305 feet, and this is 153 more than the height of the statue. So, you can write the equation as:
Total Height = Statue Height + Pedestal Height
305 feet = h + 153 feet
Now, to find the height "h" of the statue, you can isolate it on one side of the equation. To do that, subtract 153 feet from both sides of the equation:
305 feet - 153 feet = h
152 feet = h
So, the height of the statue is 152 feet.
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The complete question is:
The total height of the Statue of Liberty and its pedestal is 305 feet. This is 153 more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.
Kali earns $8 per hour. She worked x hours on both Monday and Tuesday. She also worked 5 hours on Thursday. The expression which represents Kali’s earnings for the week is shown.
Image in screenshot!
Which number should go into the box to complete the expression?
Answers
It is given that:
Kali earns $ 8 per hour.
This means that if she works for n hours then this earning for n hours will be given by: $ 8n
She works x hours on both Monday and Tuesday.
This means that the earning of x hours is: $ 8x
and hence the earning for both Monday and Tuesday is:$ 2(8x)
She also worked for 5 hours on Thursday.
Hence, the earning for Thursday is: 5×8=40
The total earning of the week is given by:
2(8x)+5(8)
find the surface area of a sphere with a radius of 0.8 ft
Answers
Sphere Surface Area = 4 * PI * .8^2
Sphere Surface Area = 8.0424771932 square feet
Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?
Answers
x candies -----100%
x=(147*100)/70= 210
Total were sold 210 candies.
Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?
Solution:
Candles Emily sold=70% of Total Number of Candles
Emily sold 147 candles.
So, We have,
147=70% of Total Number Of Candles
Let, Total Number Of Candles=x
147=70% of x
147=[tex] \frac{70}{100} [/tex] *x
147=[tex] \frac{70x}{100} [/tex]
Let us multiply by 100 on both sides
147*100=[tex] \frac{70x*100}{100} [/tex]
14700=[tex] \frac{70x*1}{1} [/tex]
14700=70x
To solve for x, Let us divide by 70 on both sides
[tex] \frac{70x}{70}=\frac{14700}{70} [/tex]
x=14700/70
x=210
Total Number of Candles=210
Find 2004-04-02-04-00_files/i0340000.jpg. Round the answer to the nearest tenth.
A.
46.1°
B.
47.2°
C.
54.9°
D.
79.0°
Answers
The problem is to calculate the angles of the triangle. However, it is not clear which angle you have to calculate, so we are going to calculate all of them
we know that
Applying the law of cosines
c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]
a=12.5
b=15
c=11
so
cos C=[a²+b²-c²]/[2*a*b]---> cos C=[12.5²+15²-11²]/[2*12.5*15]
cos C=0.694------------> C=arc cos (0.694)-----> C=46.05°-----> C=46.1°
applying the law of sines calculate angle B
15 sin B=11/sin 46.1-----> 15*sin 46.1=11*sin B----> sin B=15*sin 46.1/11
sin B=15*sin 46.1/11-----> sin B=0.9826----> B=arc sin (0.9826)
B=79.3°
calculate angle A
A+B+C=180------> A=180-B-C-----> A=180-79.3-46.1----> A=54.6°
the angles of the triangle are
A=54.6°
B=79.3°
C=46.1°
Can someone help me please!!!!
Answers
Right triangle DEF right-angled at F.
ED=97 (hypotenuse)
DF=72 (opposite side of angle E)
FE=65 (adjacent side of angle E)
Cosine of angle E
=(adjacent side)/(hypotenuse)
=FE/ED
=65/97
=0.6701 (to four decimal places)
George purchased a new car with the special 2.9% financing. If the car's price was $19,999 and he financed it for five years, find his monthly payment.
A. $357.46
B. $358.47
C. $199.99
D. $343.25
Answers
P = C*{(i/12)/[1-(1+i/12)^-12t}
C = Cost of the car = $19,999; i = financing rate = 2.9% = 0.029; t = time of payment in years = 5 years
Therefore,
P = 19999*{(0.029/12)/[1-(1+0.029/12)^-12*5} = $358.47
B. is the correct answer.
Correct Answer is B which is $ 358.47 for monthly payment
A tangent-tangent angle intercepts two arcs that measure 124 and 236. what is the measure of the tangent-tangent angle?
Answers
The measure of the external angle is the semi difference of the arcs that it covers.
let
x-----> the measure of the tangent-tangent angle
∠ x=(1/2)*[236-124]----> 56°
the answer is
the measure of the tangent-tangent angle is 56 degrees
Answer:
the measure of the tangent-tangent angle is 56 degrees.
Step-by-step explanation:
apex
Consider the square root of 25. Is it rational or irrational? Explain your reasoning.
Answers
The square root of 25 is rational. This is because it is equal to the product of 5 x 5. Since 5 is a rational number and 25 is equal to 5 x 5, the square root of 25 is rational.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
YO! I WILL MAKE YOU LOOK GOOD IF YOU ANSWER MY QUESTION!!!!!!!
Answers
Since the turning points are two and the first line came from the negative side and the second is in the positive side, so there for if you will multiple it negative times positive will give you negative.
This is the hint that this is an odd degree. Since if you raise thw power to an odd degree, it wi give you a negative answer. So it will have two different sides, points in the negative and points on the positive side.
If you will consider it an even degree, the graph's shape must be either up, up or down, down. But the graph shows down, up which indicstes its an odd degree. Hope you understand.
A ball is thrown downward from the top of a 190-foot building with an initial velocity of 21 feet per second. the height of the ball h after t seconds is given by the equation h equals negative 16 t squared minus 21 t plus 190. how long after the ball is thrown will it strike the ground?
Answers
1- You have the following information give in the problem above:
- The ball is thrown downward from the top of a 190-foot building with an initial velocity of 21 feet per second.
- The height of the ball h after t seconds is given by this equation: h=-16t²-21t+190.
2- h=0 when the ball strikes the ground, then you have:
-16t²-21t+190=0
3. When you solve the quadratic equation shown above, you obtain:
t=2.85 seconds
The answer is: 2.85 seconds.
The ball hits the ground after approximately 4.16 seconds.
To find the time at which the ball strikes the ground, we need to determine when h(t) = 0. Given the equation for height:
[tex]\[ h(t) = -16t^2 - 21t + 190 \][/tex]
we can set h(t) to 0 and solve for t:
[tex]\[ -16t^2 - 21t + 190 = 0 \][/tex]
Using the quadratic formula, we can find the roots of this equation:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where a = -16 , b = -21, and c = 190. Plugging in the values, we get:
1. Find the discriminating value [tex]\( \Delta = b^2 - 4 \times a \times c \)[/tex]:
[tex]\[ \Delta = (-21)^2 - 4 \times (-16) \times 190 = 441 + 12160 = 12601 \][/tex]
2. Calculate the roots:
[tex]\[ t = \frac{-(-21) \pm \sqrt{12601}}{2 \times -16} \\ \[ t = \frac{21 \pm \sqrt{12601}}{-32} \][/tex]
Since we're interested in the positive value (representing the time when the ball hits the ground), we'll only consider the root with the "minus" sign:
[tex]\[ t = \frac{21 - \sqrt{12601}}{-32} \approx \frac{-21 + \sqrt{12601}}{32} \approx \frac{21 - \sqrt{12601}}{32} \][/tex]
Using a calculator, let's approximate the result:
[tex]1. Compute \( \sqrt{12601} \approx 112.24 \),\\2. Then calculate \( 21 + 112.24 \approx 133.24 \),\\3. Divide by 32 to get \( t \approx \frac{133.24}{32} \approx 4.16375 \).[/tex]
Rounding to a more readable result, we can say that the ball hits the ground after approximately 4.16 seconds.
What is the length of a garden hose that is stretched diagonally corner-to-corner across a yard that measures 72 meters long and 60 meters wide? Round to the nearest meter.
Answers
length = sqrt (72^2 + 60^2)
= 94 meters to nearest meter
Here, we need to find the length of the hose which is diagonally placed in the rectangular garden.
The length is given as = 72 meters
The width is given as = 60 meters
We will use Pythagoras theorem here.
Hypotenuse² = Perpendicular² + Base²
Hypotenuse² = 72² + 60²
Hypotenuse² = √8,784 meters²
Hypotenuse = 93.72 meters
Thus, the length of diagonal hose will be = 93.72 meters
please help but only answer if you're going to show work please!!!!
Answers
4[3(-2) - 6]
---------------
1 + (-2)
4[-6 - 6]
= ---------------
-1
4[-12]
= ---------------
-1
-48
= ----------
-1
= 48
1. You have the following expression given in the problem above:
4(3h-6)/(1+h)
2. Then, if h is h=-2, you have to substitute this value into the expression given above, as below:
4(3h-6)/(1+h)
4(3(-2)-6)/(1+(-2))
3. Then, you have
4(-6-6)/(1-2)
4(-12)/-1
-48/-1
48
What is the approximate area of the shaded sector in the circle below
Answers
so plug in the numbers A= (3.14)(4.5)(4.5)= 63.62 is the total area
150*63.62=9543 9543/360=26.5
So the answer is 26.5 cm ^2
What is the value of ø for the acute angle in a right triangle?
sim (ø)= cos (48 degrees)
Ø=??????
Answers
sin (90 - θ) = cos(θ)
The value of θ in the given case is 48, so the equation becomes:
sin(90 - 48) = cos(48)
sin (42) = cos(48)
Thus, in the given question value of ø will be 42 degrees.
Mike is going to a ball game on saturday. he will pay $8.00 admission, plus $1.50 per item he buys at the concession stand. which of the equations represents this information?
Answers
x: number of items that he buys at the concession stand
y: total payment
We now write the equation that represents this problem.
We have then:
y = 1.50x + 8
Answer:
An equation that represents this information is:
y = 1.50x + 8
The equation that represents this information will be y = 1.5x + 8.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Mike is going to a ball game on Saturday.
He will pay $8.00 for admission, plus $1.50 per item he buys at the concession stand.
Let x be the number of items and y be the total cost.
Then we have
y = 1.5x + 8
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