The given point (−7,1) is a solution to the inequality.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.
We have been given inequality is:
⇒ y < 0.5x + 9
To determine the point (−7,1) a solution to the inequality
Substitute x = -7 and y = 1 in the inequality, we get
⇒ y < 0.5x + 9
⇒ 1 < 0.5(-7) + 9
⇒ 1 < -3.5 + 9
Apply the subtraction operation in the above inequality, we get
⇒ 1 < 5.5
This is true.
Hence, the given point (−7,1) is a solution to the inequality.
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A rectangular room is three times as long as it is wide, and its perimeter is 48 meters. Find the length of the room.
there are 6 grams of fat per serving of granola. each serving provides 180 calories. what percentage of these calories is from fat?
This may make me look dumb but idk what to do. I need answers please
The number of timeshare condos available at sunset beach is 3/5 the number of timeshare condos available at playa del mar. if the total number of timeshare condos available at the two beaches combined is 240, what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar?
To find the difference between the number of condos available at Sunset Beach and Playa Del Mar, we need to set up an equation and solve for the unknown. The number of timeshare condos available at Sunset Beach is 3/5 of the number available at Playa Del Mar. By solving the equation, we find that the difference is 60 condos.
Explanation:To solve this problem, we can set up an equation. Let's say the number of timeshare condos available at Playa Del Mar is x. According to the question, the number of condos available at Sunset Beach is 3/5 of x, or 3/5x.
So, the total number of condos available at both beaches is x + 3/5x = 240. We can combine the like terms to get 8/5x = 240.
To solve for x, we divide both sides of the equation by 8/5, which is the same as multiplying by its reciprocal, 5/8. Simplifying, we get x = 240 * 5/8 = 150.
Therefore, the number of condos available at Sunset Beach is 3/5 * 150 = 90, and the difference between the number of condos available at Sunset Beach and Playa Del Mar is 150 - 90 = 60.
5(x+2)7x+4 plz help idk what to do
An item is regularly priced at $65 . it is on sale for 80% off the regular price. how much (in dollars) is discounted from the regular price?
if two angles are supplementary, then it adds up to 180 degrees True or false?
starting from 105 feet away a person on a bicycle rides toward a checkpoint and then passes it.the rider is traveling at a constant rate of 35 feet per second.The distance between the bicycle and the checkpoint given by the equation is D=|105-35t|.at what times is the bike 60 feet away from the checkpoint?
A.1.3 sec and 2.6 sec
B.1.3 sec and 4.7 sec
c.1.1 sec and 2.6 sec
d.4.7 sec and 9.4 sec
WHO EVER ANSWERS IT FIRST AND RIGHT GETS BRAINIEST
Answer:
The correct option is B.
Step-by-step explanation:
It is given that starting from 105 feet away a person on a bicycle rides toward a checkpoint and then passes it.the rider is traveling at a constant rate of 35 feet per second.
The distance between the bicycle and the checkpoint given by the equation
[tex]D=|105-35t|[/tex]
We have to find the times at which the bike 60 feet away from the checkpoint.
Substitute D=60 i the given equation.
[tex]60=|105-35t|[/tex]
[tex]\pm 60=105-35t[/tex]
Case 1:
[tex]60=105-35t[/tex]
Subtract 105 from both the sides.
[tex]60-105=-35t[/tex]
[tex]-45=-35t[/tex]
Divide both sides by -35.
[tex]1.2857=t[/tex]
[tex]t\approx 1.3[/tex]
Case 2:
[tex]-60=105-35t[/tex]
Subtract 105 from both the sides.
[tex]-60-105=-35t[/tex]
[tex]-165=-35t[/tex]
Divide both sides by -35.
[tex]4.71428=t[/tex]
[tex]t\approx 4.7[/tex]
The bike is 60 feet away from the checkpoint at 1.3 sec and 4.7 sec. Therefore the correct option is B.fore the correct option is B.
is it possible to have three points that would not fit on the same plane 2 dimensional surface? Why or why not
if you cross multiply 10 over 2.4=15 over x
Find three consecutive integers such that the sum of the first and twice the second is equal to the third plus four.
How do u you a irrantional number from a rational number?
What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ? Enter your answer in the box. ___units²
HELP PLEASE!!!
A wheel makes 20 revolutions per minute. Find the angular velocity.
10π rad/min
20π rad/min
40π rad/min
Answer:
Angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min
Step-by-step explanation:
Angular velocity, ω = 2πf , where f is the frequency.
Here frequency, f = 20 revolutions per minute
Substituting frequency value in angular velocity equation,
Angular velocity, ω = 2πf = 2 x π x 20 = 40π rad/min
So angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min
Cards numbered 1 through 30 are shuffled in a bin one card is randomly selected what is the probability of selecting a number that is a multiple of 11 ? please help
Is the value a an improper fraction less than 1 or greater than 1
A cookie factory uses 3/8 of a barrel of oatmeal in each batch of cookies with the factor uses 3/4 of a barrel of oatmeal yesterday how many batches of cookies did the factory make
The cookie factory made 2 batches of cookies yesterday. This is found by dividing the total amount of oatmeal used (3/4 of a barrel) by the amount used per batch (3/8 of a barrel).
Explanation:To find the number of batches of cookies the factory made, we would divide the total amount of oatmeal used by the amount used per batch.
The factory used 3/4 of a barrel of oatmeal yesterday, and each batch uses 3/8 of a barrel. So, we divide 3/4 by 3/8.
Before doing that, remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/8 is 8/3.
So, 3/4 divided by 3/8 is equivalent to 3/4 multiplied by 8/3, giving us a result of 2.
Therefore, the cookie factory made 2 batches of cookies yesterday using 3/4 of a barrel of oatmeal.
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If y varies directly as x and y is 18 when x is 5 which expression can be used to find the value of y when x is 11?
Answer:
The value of y is [tex]\frac{198}{5}[/tex] or 39.6.
Step-by-step explanation:
It is given that y varies directly as x and y. It means y is directly proportional to x.
[tex]y\propto x[/tex]
[tex]y=kx[/tex] .... (1)
where, k is constant of proportionality.
It is given that y is 18 when x is 5.
Substitute y=18 and x=5 in equation (1).
[tex]18=k(5)[/tex]
Divide both sides by 5.
[tex]\frac{18}{5}=k[/tex]
The value of k is [tex]\frac{18}{5}[/tex]. So, the relation between x and y is
[tex]y=\frac{18}{5}x[/tex] .... (2)
We need to find the value of y when x=11.
[tex]y=\frac{18}{5}(11)[/tex]
[tex]y=\frac{198}{5}[/tex]
[tex]y=39.6[/tex]
Therefore the value of y is [tex]\frac{198}{5}[/tex] or 39.6.
angle efg and angle gfh are a linear pair, the measure of angle efg equals 4n+20, and measure of angle gfh equals 3n+13. what are the measures of angle efg and angle gfh?
Answer:
∠EFG=104° and ∠GFH=76°
Step-by-step explanation:
Given information:∠EFG = (4n+20)°, ∠GFH = (3n+13)° and ∠EFG and ∠GFH are a linear pair.
If two angles are a linear pair, then the sum of those angles is 180°.
It is given that ∠EFG and ∠GFH are a linear pair.
[tex]\angle EFG+\angle GFH=180^{\circ}[/tex]
Substitute the given values.
[tex](4n+20)+(3n+13)=180[/tex]
Combined like terms.
[tex](4n+3n)+(20+13)=180[/tex]
[tex]7n+33=180[/tex]
Subtract 33 from both sides.
[tex]7n+33-33=180-33[/tex]
[tex]7n=147[/tex]
Divide both sides by 7.
[tex]n=21[/tex]
The value of n is 21.
[tex]\angle EFG=4n+20=4(21)+20=104^{\circ}[/tex]
[tex]\angle GFH=3n+13=3(21)+13=76^{\circ}[/tex]
Therefore, the measure of ∠EFG and ∠GFH are 104° and 76° respectively.
Jan scored 539,178 points in a video game what is Jans score rounded to the nearest ten thousand?
ALGEBRAAA
1. A square has the side measurement of s= 2 3/2,
Using the formula A=s^2, find the area of the square.
2 3/2 = 3 1/2 ( 3/2 = 1 1/2 + 2 = 3 1/2)
so area = 3 1/2 ^2
3 1/2 x 3 1/2 = 12 1/4
Area = 12 1/4
1. What is the value of x in the triangle?
Enter your answer in the box. Round your final answer to the nearest hundredth.
x = cm
2. What are the values of the trigonometric ratios for this triangle?
Drag the answer into the box to match each ratio.
sinθ-----
cosθ-----
tanθ-----
OPTIONS YOU CAN DRAG
5/4
3/4
3/5
4/3
4/5
5/3
3. What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
x = °
4. What is the value of θ for the acute angle in a right triangle?
sin(θ)=cos(58°)
Enter your answer in the box.
θ= °
5. A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle the rope makes with the floor is 55°.
What is the height of each pole?
Enter your answer in the box. Round only your final answer to the nearest tenth.
6. What is the exact value of sin 60° ?
Enter your answer, as a simplified fraction, in the box.
Answer: Took the test correct :)
Step-by-step explanation:Problem 1
cos(angle) = adjacent/hypotenuse
cos(18) = x/25
25*cos(18) = x
x = 25*cos(18)
x = 23.7764129073789
x = 23.78
Answer: x = 23.78
=====================================================
Problem 2
theta = greek letter that looks like a "zero" or the letter O with a horizontal line through it
With the reference angle of theta, the opposite side is 3. This side is the leg furthest from the angle theta. In contrast, the side 4 is the closest leg to theta. The longest side 5 is the hypotenuse. The hypotenuse is always the lonest side
sin(theta) = opposite/hypotenuse
sin(theta) = 3/5
cos(theta) = adjacent/hypotenuse
cos(theta) = 4/5
tan(theta) = opposite/adjacent
tan(theta) = 3/4
---------------------------
In summary:
sin(theta) = 3/5
cos(theta) = 4/5
tan(theta) = 3/4
=====================================================
Problem 3
cos(angle) = adjacent/hypotenuse
cos(x) = 15/29
x = arccos(15/29) .... inverse cosine or cos^(-1) also works
x = 58.852610078491
x = 58.85
Answer: x = 58.85
=====================================================
Problem 4
The rule we'll use is
sin(x) = cos(90-x)
sin(theta) = cos(90-theta)
cos(90-theta) = cos(58)
90 - theta = 58
90 - theta+theta = 58+theta
90 = 58+theta
90-58 = 58+theta-58
32 = theta
theta = 32
Answer: 32
=====================================================
Problem 5
x = height of pole
the vertical side is the side we want, which is the opposite side compared to the angle 55 degrees
sin(angle) = opposite/hypotenuse
sin(55) = x/25
25*sin(55) = x
x = 25*sin(55)
x = 20.4788011072248
x = 20.5
Each pole is roughly 20.5 feet tall.
=====================================================
Problem 6
The exact value is the fraction sqrt(3)/2 which can be written as \frac{\sqrt{3}}{2}
"sqrt" is shorhand for "square root"
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What is the equation of the line in slope-intercept form?
Cristina Suarez has insured her home for 80% of its replacement value of $155,000. Use the chart to determine the amount of coverage for her personal property, to the nearest dollar.
The final answer is 55,800
A car travels at an average speed of 64 miles per hour. how many miles does it travel in 4 hours and 45 minutes?
Final answer:
The car travels 304 miles in 4 hours and 45 minutes at an average speed of 64 miles per hour.
Explanation:
To find the distance the car travels in 4 hours and 45 minutes, we need to convert the time to hours and minutes. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours. Therefore, the total time is 4 + 0.75 = 4.75 hours.
To calculate the distance, we can use the formula:
Distance = Speed x Time
Given that the average speed is 64 miles per hour and the time is 4.75 hours, we can plug these values into the formula:
Distance = 64 mph x 4.75 hours = 304 miles.
A: What is the real part of the complex number? B: What is the imaginary part of the complex number? Select one answer for part A, and select one answer for part B. A: i B: 3 A: 3 A: 2i B: i B: 2i B: 2 A: 2
There are 2 4/5 pounds of bricks in a bag. each brick weighs 2/5 of a pound. how many bricks are in the bag?
Which of these statements about the two triangles is true?
There is not enough information to determine whether the triangles are congruent or not congruent.
The triangles are congruent by the SAS Congruence Postulate.
The triangles are not congruent.
What is the reference angle for a 240° angle
The reference angle for a 240° angle is 60 degree.
What is a Reference Angle?Reference Angle is the acute angle between the terminal side and the x axis. The value of reference angle is always positive and less than 90 degree.
The angle is 240 degree, for which the reference angle has to be determined.
The angle 240 degree lies in the third quadrant between 180 and 270 degree.
To determine the reference angle, the given angle will be subtracted by 180 degree.
=> 240 - 180
=> 60 degree
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15 coins worth $3.15. if the coins are all quarters and dimes, how many quarters and dimes does she have?