Answer:
y = 0.5 cosine (4 (x - pi/2)) - 2
Step-by-step explanation:
two owls leave the same tree at 9:00 p.m. One owl flies west at 7 miles per hour and the other flies east at 13 miles per hour. In how many hours will they be 60 miles apart?
Answer:
3 hours.
Step-by-step explanation:
Trust me...
A doctor has found that the number of hours students sleep each night is inversely related to the amount of time they spend playing video games. He collected the data below.
If the trend the doctor has observed holds true, how many hours of sleep would you expect of a student who plays video games for 6 hours?
A. 6.5 hours
B. 7.5 hours
C. 7.25 hours
D. 6.25 hours
Answer: 6.25
Step-by-step explanation:
Find the area of the trapezoid shown below and choose the appropriate result.
Answer:
13.5 in²
Step-by-step explanation:
We can use the area formula for a trapezoid.
Area = [tex]\frac{1}{2}(b_{1}+b_{2} )h[/tex]
To solve, we find and plug in the variables. According to the trapezoid, we know
h (height) = 3 in
[tex]b_{1}[/tex] (base 1) = 4in
[tex]b_{2}[/tex] (base 2) = 5in
1/2(4 + 5) ·3 = 13.5 in²
The area of a trapezium is 13.5 in².
Option B is the correct answer.
We have,
The area of a trapezium.
= 1/2 x (sum of the parallel sides) x height
Now,
height = 3 in
Parallel sides = 5 in and 4 in
Now,
Substituting the values.
The area of a trapezium.
= 1/2 x (sum of the parallel sides) x height
= 1/2 x (5 + 4) x 3
= 1/2 x 9 x 3
= 27/2
= 13.5 in²
Thus,
The area of a trapezium is 13.5 in².
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Find the area of the rectangle.
square feet:
Answer:
4x9=36
Step-by-step explanation:
36
Answer:
36 sq ft.
Step-by-step explanation:
To solve for the area of a rectangle, all you need to do is multiply the length by the width which gives you:
4×9= 36 sq ft.
1. In a sample of 300 high school
seniors, 78 reported that they do not
have a driver's license. What is the
sample proportion?
Answer:
13 to 50
Step-by-step explanation:
1). 78 / 300 = 13 / 50 or 26 %
For a project, Gabrielle made a model of an Egyptian pyramid. The square base has a side length measuring 10 inches.
The pyramid is 12 inches tall.
What is the surface area of the model?
240
260
340
360
Select the number that completes the sentence. 20 is 1/10 of
0.02
O 0.2
2
200
O2,000
Answer:
the answer is 200
Step-by-step explanation:
We can write 1/10 of 200 in the form of equation as follows:
\frac{1}{10} * 200 = x
Where x represents that number we want to find.
so the answer is 20
What is the average rate of change for ƒ(x) = 2^x + 10 over the interval 2 ≤ x ≤ 4?
A.) 4
B.) 6
C.) 8
D.) 12
Johnny prepares a solution by mixing sodium acetate and water. To calculate the molarity of the solution, Johnny should calculate the moles of which substance, and why? *
sodium acetate, because it is the solvent
sodium acetate, because it is the solute
water, because it is the solvent
water, because it is the solute
Answer is B, sodium acetate, because it is the solute .
Which figure has a greater volume, and how much greater is it?
361
Figure 1
Figure 2
The volume of figure 1 is 97213 greater than the volume of figure 2.
The volume of figure 2 is 9721? greater than the volume of figure 1.
The volume of figure 1 is 1.134 ft greater than the volume of figure 2.
The volume of figure 2 is 1.134f greater than the volume of figure 1.
Mark this and retum
Save and Exit
TER
Submit
Answer:
the last one
Step-by-step explanation:
Approximate the value of 11−−√ to the nearest tenths place. Plot the approximation on the number line.
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Approximate the value of [tex]\sqrt{11}[/tex] to the nearest tenths place. Plot the approximation on the number line.
(Please have a look at the attached photo)
My answer:
The value nearest tenths place of [tex]\sqrt{11}[/tex] is: 3.3
Hope it will find you well.
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
in feet after t seconds is given by the function h=-16t^2 + 120t + 10. How long does it take to
reach maximum height? What is the boulder's maximum height? Round to the nearest
hundredth, if necessary.
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
b. Reaches a maximum height of 10.00 feet in 7.50 seconds.
c. Reaches a maximum height of 7.58 feet in 3.75 seconds.
d. Reaches a maximum height of 15.16 feet in 7.5 seconds.
Answer:
The boulder's maximum height is:
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
Step-by-step explanation:
The easiest way to solve the unknown is to replace the time in the given equation, with the values given in the answer, look for the highest value and check if the height value decreases as the time increases or decreases.
First the equation provided is taken:
h = -16t ^ 2 + 120t + 10The time values in the options are 3.75 seconds and 7.5 seconds, therefore we proceed to replace this formula with those values:
h (3.75) = - 16 (3.75) ^ 2 + 120 (3.75) + 10 = 235 h (7.5) = - 16 (7.5) ^ 2 + 120 (7.5) + 10 = 10Since a higher height value is obtained with 3.75 seconds (235 feet), this time will be taken as appropriate, however, it is best to check that by using more time and less time, the height decreases from that value, so we will take two very close times: 3.74 seconds and 3.76 seconds:
h (3.74) = - 16 (3.74) ^ 2 + 120 (3.74) + 10 = 234.9984 h (3.76) = - 16 (3.76) ^ 2 + 120 (3.76) + 10 = 220.5884As you can see, if slightly higher or lower time values are taken, the height of the rock still decreases from 235 feet, so we can be sure that the time in which it reaches its maximum height is 3.75 seconds.
What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places
Answer:
r ≈ 6.71
Step-by-step explanation:
The distance from the centre of the circle to a point on it is the radius.
Calculate the radius r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (8, 2) and (x₂, y₂ ) = (14, - 1)
r = [tex]\sqrt{(14-8)^2+(-1-2)^2}[/tex]
= [tex]\sqrt{6^2+(-3)^2}[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex] ≈ 6.71 ( to 2 dec. places )
Final answer:
The radius of the circle with the center at (8, 2) and a point on the circle at (14, -1) is 6.71 units, after rounding to two decimal places.
Explanation:
To find the radius of a circle with a given center and point on the circle, we need to calculate the distance between these two points. This distance represents the radius. The center of the circle is at (8, 2) and the point on the circle is at (14, -1).
Using the distance formula, which is d = √((x_2 - x_1)^2 + (y_2 - y_1)^2), where (x_1, y_1) is the first point and (x_2, y_2) is the second point:
[tex]d = √((14 - 8)^2 + (-1 - 2)^2) = √((6)^2 + (-3)^2) = √(36 + 9) = √45[/tex]
When using a calculator that has an eight-digit output, √45 is approximately 6.70820393. However, if we are to report the answer with only two decimal places, we get the radius as 6.71 units.
It's important to note that significant figures play a role in determining the precision of our result. Even though the calculator can give us many decimal places, we often round the number to either preserve significant figures or because the extra precision is not materially important for estimation purposes. In this case, the radius to two decimal places is 6.71, despite the calculator's eight-digit output.
A worker makes a ramp by placing one end of an 8-foot-long board on the bed of a pickup truck and the other end on the ground. The bed of the truck is 3 feet above
the ground. Which expression could be used to determine the angle between the board and the ground?
The expression sin^-1(3/8) can be used to determine the angle between the board and the ground in this scenario. This utilizes the sine function in trigonometry, which involves the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angle triangle.
Explanation:The subject of this question is Mathematics, specifically trigonometry. In such a problem, we can utilize the concept of trigonometric functions, in this case is the sine function. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse. In this scenario, the board acts as the hypotenuse, the height of the truck is the side opposite the angle, and the angle we're trying to determine is between the ground (which we can consider as the adjacent side) and the board.
So, to determine the angle, we would use the expression: sin^-1(opposite/hypotenuse) = sin^-1(3/8).
The sine inverse or 'sin^-1' is used to find the angle when we know the sine value. Also, note that the answer will be in radians and can be converted into degrees by multiplying by 180/pi if necessary.
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pls helppp this is so urgent:
The 7th graders at DEMS are going to help set the playground for the kindergartners at the new school. School Safety regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started.
The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches.
How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing sets?
Answer:
90 bags of sand
Step-by-step explanation:
9 feet × 1.5 = 13.5
12 feet × 1.5 = 18
Large pit area= 13.5 × 18 = 243ft squared
The small pit area=9 × 12 = 108ft squared
243 / 108 = 2.25 times larger
This means the large pit needs 2.25 times more sand.
40 × 2.25 = 90 bags of sand
Answer 114.8
A triangle has side lengths 1.5 cm, 2 cm, and 3 cm. Is this a right triangle? Explain.
Answer:
No
Step-by-step explanation:
To figure out whether a triangle is a right triangle using only the side lengths, you can use the Pythagorean theorem:
a^2 + b^2 = c^2
1.5^2 + 2^2 = 3^2
2.25 + 4 = 9
Since this equation isn't true, these numbers cannot be the side lengths of a right triangle.
After applying the Pythagorean theorem to the triangle with sides 1.5 cm, 2 cm, and 3 cm, it is determined that the triangle is not a right triangle because the squares of the shorter sides do not sum up to the square of the longest side.
Explanation:To determine if a triangle with sides measuring 1.5 cm, 2 cm, and 3 cm is a right triangle, we can apply the Pythagorean theorem. The theorem states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In mathematical terms, this is expressed as c² = a² + b².
Let's check if our triangle meets this condition:
Assume the longest side, 3 cm, is the hypotenuse (c).Square the lengths of the shorter sides: 1.5² + 2² = 2.25 + 4 = 6.25 cm².Square the length of the assumed hypotenuse: 3² = 9 cm².Since 6.25 cm² does not equal 9 cm², the sides do not satisfy the Pythagorean theorem, so the triangle is not a right triangle.
At the store Jason finds the total volume of soda in a pack is 50.24 cubic inches . If each cylinder -shaped can has a height of 4 inches and a diameter of 2 inches , how many soda cans are in a pack ? (Use 3.14 for pi)
A) 4
B) 5
C) 13
D) 2
Explain:
Answer: A) 4
Step-by-step explanation:
Hi, to answer this, first, we have to calculate the volume of each can:
Volume of a cylinder: π x radius^2 x height
Since:
Diameter: 2 radius
2 = 2r
2/2 =r
r=1
Back with the volume formula:
V = 3.14 ( 1)² 4 =12.54 cubic inches
Now, we have to divide the total volume of soda by the volume of each can:
50.24/12.54= 4 soda cans
Feel free to ask for more if needed or if you did not understand something.
34 more than the quotient of a number and 15 is 53
Answer:
x=285
Step-by-step explanation:
34 more than ( +34)
quotient of number and 15 (x/15)
is 53 (=53)
(-34)x/15+34=53(-34)
(15)x/15=19(15)
x=285
Which expression can be used to find the surface area of the following rectangular prism?
O 4+4+8+8+1+1
O 8+8+4+4+2+2
O 8+8+8+8
O 2+4
Answer:
8+8+4+4+2+2
Step-by-step explanation:
4×2=8
4×1=4
1×2=2
A student graphed the line y = 3x + 2 plotting and connecting points A, B, and C. How can the student use points A, B, and C to find the graph of y =3x - 5?
Answer:
The student has to translate the points A, B and C 7 units down to create points A', B' and C', and then connect these points
Step-by-step explanation:
The slope of the lines is the same (3). The difference between the lines is their y-intercept (from the first line is 2 and for the second one is -5). This means that the lines are parallel and separated by 2 - (-5) = 7 units
Which expression is equivalent to StartFraction 4 a + 4 Over 2 a EndFraction times StartFraction a squared Over a + 1 EndFraction? StartFraction 2 (a + 1) squared Over a cubed EndFraction 6a 2a StartFraction 6 a squared Over a + 1 EndFraction
Answer:
C. 2a
Step-by-step explanation:
i did this because I love you- angelo (junior 11th grade) CCHS 2021
The expression that is equivalent to (4a + 4)/2a × a²/(a + 1) is: 2a.
What are Equivalent Expressions?Equivalent expressions are expressions that have the same value when simplified.
Thus:
(4a + 4)/2a × a²/(a + 1)
Multiply
[(4a + 4)(a²)] / [(2a)(a + 1)]
(4a³ + 4a²) / (2a² + 2a)
2a(2a² + 2a) / 2a(a + 1)
(2a² + 2a) / (a + 1)
2a(a + 1) / (a + 1)
= 2a
Therefore, the expression that is equivalent to (4a + 4)/2a × a²/(a + 1) is: 2a.
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Please help with steps
Answer:
what is the question
Step-by-step explanation:
Determine is the following set is a function or not: (-3,5) (1,3) (4,5 (3,5) (-3,5)
Answer:
It is
Step-by-step explanation:
The reason being is both times you imputed -3 you got an output of 5.
can someone please help me?
Answer:
The answer is 27
Step-by-step explanation:
The reason being, you can solve this 2 ways.
1) Combine like terms, 7a-4a = 3a.
Now just substitute (a=9) into 3a.
3 * (9) = 27.
2) Or just substitute a = 9 into the original expression.
7 * (9) - 4 * (9)
= 63 - 36 = 27
Hello!
Answer:The correct answer is option four, 27.
Explanation:We know that a = 9.
Because the a is right next to the 7 and the 4, this indicates that it is being multiplied.
7a - 4a
Substitute for the 'a'.
= 7(9) - 4(9)
= 63 - 36
= 27
Which choices are in the solution set of the equation below? Check all that
apply.
25x = 40
The solution set for the equation 25x = 40 is {1.6}, obtained by dividing both sides by 25 and verifying the solution by substitution.
Explanation:To find the solution set of the equation 25x = 40, we need to isolate the variable x by performing algebraic operations. The goal is to get x by itself on one side of the equation. This involves dividing both sides of the equation by the coefficient of x, which in this case is 25. Following this step, we arrive at the equation x = 40 / 25.
By simplifying 40 / 25, we find that x = 1.6. Therefore, the solution set for the equation 25x = 40 is {1.6}. It’s important to check the solution by substituting it back into the original equation to ensure that it satisfies the equation:
25(1.6) = 40
40 = 40
This indeed confirms that x = 1.6 is the correct solution. In mathematics, solving linear equations such as this one is a fundamental skill that involves understanding algebraic manipulation and the properties of equality.
The solution set for the equation 25x = 40 is x = 8/5. In other words, the only value for x that satisfies the equation is 8/5.
The solution set for the equation 25x = 40, we can isolate the variable x by dividing both sides of the equation by 25:
x = 40/25
Simplifying the right side gives:
x = 8/5
So, the solution set for this equation is {8/5}. In other words, the only value for x that satisfies the equation is 8/5. To understand this, you can substitute this value back into the original equation:
25 * (8/5) = 40
Simplifying the left side:
200/5 = 40
Indeed, the equation holds true.
In summary, the only choice in the solution set for the equation 25x = 40 is x = 8/5. This means that when you substitute 8/5 for x in the equation, both sides will be equal.
Which fraction shows the number of hours Amy's dog slept sleeps for every 2 hours in the day? Complete the Fraction
Answer: 1/2
Step-by-step explanation:12 is divided by 2
fraction that shows the number of hours Amy's dog sleeps is 1/2.
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator and the bottom part is numerator.
Given is Amy's dog who sleeps for every 2 hours in the day.
Since Amy's dog sleep for 2 hours a day, then in a complete day he would sleep for 12 hours out of 24 hours. So, we can write the fraction as-
12/24 = 1/2
Therefore, fraction that shows the number of hours Amy's dog sleeps is 1/2.
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The function f(x) = 3(1.9)x gives the length (in inches) of an image after being enlarged by 10% x times. What is the length of the image after it has been enlarged 3 times? Round your answer to the nearest hundredth.
The length of the image is how many
inches?
Answer:
20.58 inches
Step-by-step explanation:
As the variable x represents the number of times the figure is enlarged, to find the length of the image after it has been enlarged 3 times, we just need to use the function f(x) with the value of x = 3:
f(x) = 3 * (1.9)^x
f(3) = 3 * (1.9)^3
f(3) = 3 * 6.859
f(3) = 20.577 inches
Rounding to nearest hundredth, we have f(3) = 20.58 inches
So the length of the image after being enlarged 3 times is 20.58 inches
How do the temperatures compare? Order the temperatures from coldest to warmest. 42, -36.3, -15, 41.4, 36.1, -41.5
Answer:
-41.5, -36.3, -15, 36.1, 41.4, 42
Step-by-step explanation:
Final answer:
To order temperatures from coldest to warmest, place negative values first from smallest to largest, followed by positive values from smallest to largest. The correct order is -41.5, -36.3, -15, 36.1, 41.4, 42.
Explanation:
When comparing temperatures and ordering them from coldest to warmest, we need to recognize that negative temperatures are colder than positive temperatures. In °C or °F, lower negative values represent colder temperatures, and higher positive values represent warmer temperatures. Thus, to order the given temperatures from coldest to warmest: -41.5, -36.3, -15, 36.1, 41.4, 42.
ILS
What type of triangle is shown below?
630
4.50
O
A. Acute
O
B. Obtuse
O
c. right
hich is the graph of the linear function that is represented by the equation y= 1/2x-2 ?
Answer:
this is the best way i could explain
Step-by-step explanation:
remember that the equation of a line is y = mx +b, where m is the slope and b is the y-intercept.
Start with your first point on the y-axis at -2. Your slope is 1/2 (rise/run), so go up 1 and over 2 for your next point. Keep going with this and you'll find your points.
Another way to find your y-values is to plug in the x's you have. y = 1/2(2) - 2 = 1 - 2 = -1, so your first point is (2,-1). This should show up on your graph, as well.
What do you get when you plug in the 0? Your answer should be your first point on your graph, since along the y-axis, x = 0.
The graph of the equation given is attached to the solution.
Given that, an equation y = 1/2 x - 2, we need to graph it,
So, for the same, we will first find the coordinates points,
Therefore,
y = 1/2 x - 2
Put y = 0,
1/2 x - 2 = 0
x = 4
The point = (4, 0)
Put x = 0,
y = -2
The point = (-2, 0)
Put the coordinates in the graph and join the points, we will have a straight line, this straight is the graph of the linear equation given,
That mean the equation is a linear equation.
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