Hey there! I’m having a bit of trouble with this one, I think I’ve been looking at this for too long. If you could give me an explanation, I would be appreciate it! Thanks in advance! This is a practice test.
no lo sé, pero como necesito puntos, ¿sí?
Terry just bought a used car with only 28,500 miles on it and it cost $8,200. Every year Terry expects to put another 14,000 miles on the car. Unfortunately, the car’s value will depreciate by 15% per year. How much will the car be worth when it has 100,000 miles on it? Explain your work.
The sum of two consecutive even integers is at most 400. Find the pair of integers with the greatest sum
The largest pair of consecutive integers are 198 and 200.
Explanation: hope it helpsIf the sum of two equal even numbers is 400, the numbers will be 200+200.
Therefore the largest possible consecutive even numbers which have a sum of 400 or less are 198 and 200 which have a sum of 398.
Any pair of consecutive numbers less than these will have a sum of less than 400.
Centered 7 meters above the ground, a Ferris wheel of radius 6 meters is rotating with angular speed
24 degrees per second.
a. Assuming that you begin at time t = 0 seconds at the lowest point on the wheel, find a formula
that describes the distance h (in meters) from you to the ground after t seconds of riding.
b. At what times are you 10 meters above the ground? Please explain clearly how you got your
solution.
a)[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.
b) you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.
Let's break down this problem step by step:
a. To find a formula for the distance ( h ) (in meters) from you to the ground after ( t ) seconds of riding, we can use trigonometry and the properties of circular motion.
1. The Ferris wheel has a radius of 6 meters and is centered 7 meters above the ground. This means that at the lowest point, you are ( 7 + 6 = 13 ) meters above the ground, and at the highest point, you are ( 7 - 6 = 1 ) meter above the ground.
2. The angular speed of the Ferris wheel is given as 24 degrees per second. Since the Ferris wheel completes one full rotation (360 degrees) in[tex]\( \frac{360^\circ}{24^\circ/\text{sec}} = 15 \)[/tex] seconds, its angular velocity is[tex]\( \omega = \frac{2\pi}{15} \)[/tex]radians per second.
3. Let [tex]\( \theta \)[/tex] be the angle in radians that the Ferris wheel has rotated through at time ( t ) seconds. The height ( h ) above the ground can be expressed as:
[tex]\[ h = 13 - 6\cos(\theta) \][/tex]
To relate[tex]\( \theta \) to time \( t \)[/tex], we use the formula for angular displacement in circular motion:
[tex]\[ \theta = \omega t \][/tex]
Substitute [tex]\( \omega = \frac{2\pi}{15} \)[/tex] into the equation above to get:
[tex]\[ \theta = \frac{2\pi}{15} t \][/tex]
Now, substitute [tex]\( \theta \)[/tex]back into the equation for height \( h \):
[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.
b. To find the times when you are 10 meters above the ground, we set \( h(t) = 10 \) and solve for \( t \):
[tex]\[ 10 = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
First, subtract 10 from both sides:
[tex]\[ -3 = -6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
Divide both sides by -6:
[tex]\[ \frac{1}{2} = \cos\left(\frac{2\pi}{15} t\right) \][/tex]
Now, take the inverse cosine (arccos) of both sides:
[tex]\[ \frac{2\pi}{15} t = \cos^{-1}\left(\frac{1}{2}\right) \][/tex]
Solve for \( t \) by dividing both sides by [tex]\( \frac{2\pi}{15} \)[/tex]:
[tex]\[ t = \frac{15}{2\pi} \cos^{-1}\left(\frac{1}{2}\right) \][/tex]
Using the fact that [tex]\( \cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} \)[/tex], substitute this value into the equation:
[tex]\[ t = \frac{15}{2\pi} \times \frac{\pi}{3} \]\[ t = \frac{5}{2} \][/tex]
So, you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.
One number is 5 greater than another. the product of the numbers is 150. find the numbers. one pair of numbers, both of which are positive, is nothing.
What is the sum of the polynomials (7x^3-4x^2)+(2x^3-4x^2)
Answer:
9x3 (B)
Step-by-step explanation:
i just took the unit test, it was correct
The sum of the polynomial function is 9x^3 - 8x^2
Sum of polynomial functionsPolynomial functions area function with a leading degree of 3 and above. Given the sum;
(7x^3-4x^2)+(2x^3-4x^2)
Expand
(7x^3-4x^2)+(2x^3-4x^2)
= 7x^3-4x^2 + 2x^3-4x^2
Collect like terms
7x^3 + 2x^3 - 4x^2 -4x^2
9x^3 - 8x^2
Hence the sum of the polynomial function is 9x^3 - 8x^2
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PLEASE HELP ASAAAAPPPPPPP
Can you please help me with this that’ll you so much
Ms. Jones is ordering pizzas for the school dance. To keep things simple, she plans on only ordering two types, cheese and pepperoni. Each cheese pizza costs $10 and each pepperoni pizza costs $13. The number of cheese pizzas should be more than twice the number of pepperoni pizzas. The school dance budget will allow for no more than $200 to pay for the pizzas. This situation can be modeled by the following system of inequalities.
You didn't add the system of inequalities. But when you are posting a question and you don't know how to type the question or the answer or if you don't feel like it. Hold down shift, ctrl (control), and the button that divides/spaces each tab out, amd you're screen if go dime so you can highlight a part of the screen so it will take a picture and you can post it.
___________________________
I posted the question and answer below.
!!Hope this helped!!
Please rate "excellent"
Step-by-step explanation:
Answer: In the picture below the correct answer is
D. The system represents the minimum amount that Ms. Jones can spend on cheese pizzas, x, and pepperoni pizzas, y, and the relationship between the number of cheese pizzas and pepperoni pizzas.
Which is the graph of f(x)= square root of x
Quadrilateral ABCD is inscribed in circle O.
What is m∠C?
Enter your answer in the box.
____°
Please show how to solve this question. Thanks again.
To solve this question we will have to make use of one of the properties of the inscribed quadrilateral. That property is: "Opposite angles in any quadrilateral inscribed in a circle are supplements of each other".
Thus, as we can see from the diagram given, [tex] \angle B+\angle D=180^{\circ} [/tex]
[tex] (2x+3)+(4x+3)=180^{\circ} [/tex]
[tex] \therefore 6x+6=180^{\circ} [/tex]
[tex] 6x=174^{\circ} [/tex]
[tex] \therefore x=\frac{174^{\circ}}{6} =28^{\circ} [/tex]
Thus, now that we know the value of x, we can easily find the value of the [tex] \angle C [/tex] because we know that:
[tex] \angle C=2x+1 [/tex]
[tex] \therefore \angle C=2(29^{\circ})+1=59^{\circ} [/tex]
Thus, [tex] \boldsymbol{59^{\circ}} [/tex] is the correct answer.
PLEASE HELP QUICK
HURRRY!!!!!
In circle K, what is the value of x?
x = 30°
x = 25°
x = 20°
x = 15º
Answer:
The correct option is 4.
Step-by-step explanation:
Given information: K is the center of the circle. AB is the diameter of the circle.
Angle subtended by a diameter is always a right angle. It the means the measure of that angel is 90 degree.
[tex]\angle C=90^{\circ}[/tex]
According to the angle sum property, the sum of interior angles of a triangle is 180 degree.
Using angle sum property in triangle ABC, we get
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]75^{\circ}+x+90^{\circ}=180^{\circ}[/tex]
[tex]x=15^{\circ}[/tex]
Therefore the measure of x is 15 degree. Option 4 is correct.
Which of these is equal to sin 21°?
A) cos 21°
B) cos 69°
C) sin 69°
D) tan 69°
Answer:
B. Cos 69°
Step-by-step explanation:
Given : sin 21°
Solution : To show how Cos 69 ° = Sin 21 °
we will use sine and cosine trigonometric identity
i.e. Cos (90 °-x) = Sin x ---(A)
We are given Sin 21 °
So, putting x =21 ° in (A)
We are getting : Cos(90 °-21 °) = Sin 21 °
⇒Cos 69 ° = Sin 21 °
Hence it is shown that Cos 69 ° = Sin 21 °
can someone check my answer please HELP!
Sonji paid $25.00 for two scarves, which were different prices. When she got home she could not find the receipt. She remembered that one scarf cost $3 more than the other. What was the price of the more expensive scarf?
i believe i got 14 for the most expensive scarf am i correct?
how do i solve this?
Which of the points are solutions to the inequality?
y > 2x -4
Check all that apply.
(–2, –5)
(0, –4)
(1, 1)
(3, 5)
(5, 5)
the real answer is (1) (3) (4) on edgen.
The points that are solutions to the inequality below are (–2, –5), (1, 1) and (3, 5)
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We need to replace the values of x and y of the point into the inequality, and if all conditions are respected, they are solutions.
Given inequality is
y > 2x -4
The points that are solutions given as follow:
1. (–2, –5)
y > 2x -4
-5 > -4 -4, True
2. (0, –4)
y > 2x -4
-4 > -4 False
3. (1, 1)
y > 2x -4
1 > -2 True
4. (3, 5)
y > 2x -4
5 > 2 True
5. (5, 5)
y > 2x -4
5 > 6 False
Hence, The points that are solutions to the inequality below are (–2, –5), (1, 1) and (3, 5)
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Determine, for vectors u = i + 2j − k, v = −i + j + k, w = i + k (a) a unit vector in the direction u + 2v − 3w
Derek's phone number, $336$ - $7624,$ has the property that the three-digit prefix, $336,$ equals the product of the last four digits, $7 \times 6 \times 2 \times 4.$ how many seven-digit phone numbers beginning with $336$ have this property?
To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits. The number of different seven-digit phone numbers that satisfy the given property is 7.
Explanation:To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits.
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Clare's teacher has a box of 180 stickers for a group of students to share equally. Does each student get more stickers if there are 6 students or if there are 9 students
How can you use factoring to solve quadratic equations in standard form?
The shortest distance from a point to a straight line is
A duck has two legs. Write a conditional statement based on the given statement. A. An animal is a duck if it has two legs. B. If an animal has two legs, then it is a duck. C. If an animal is a duck, then it has two legs. D. If an animal is not a duck, then it does not have two legs.
Answer:
C
Step-by-step explanation:
8.42 x 10^3, Between which of the following pairs of numbers does the above number lie? A. .0083 and .0084 B. .0084 and .0085 C. 8300 and 8400 D. 8400 and 8500
The number 8.42 x 10³ lies in between pairs of numbers 8400 and 8500.
Option D is correct.
What is PEDMAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations.
PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
We have the number 8.42 x 10³.
Now, expanding the exponents we get
= 8.42 x 10³
= 8.42 x 1000
= 84.2 x 100
= 842 x 10
= 8420
Thus, the values lie between 8400 and 8500.
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jackie set up a lemonade stand
1 question need help thank you!!
Evaluate the series 8 simga 5n n=3.In this image, the lower limit of the summation notation is n=3
Answer:
The value of [tex]\sum_{n=3}^{8}5n[/tex] is 165.
Step-by-step explanation:
We have to evaluate sigma 5n from n=3 to 8 taht is:
[tex]\sum_{n=3}^{8}5n[/tex]
Thus, substituting the value of n from 3 to 8 in the above equation, we get
=[tex]5(3)+5(4)+5(5)+5(6)+5(7)+5(8)[/tex]
=[tex]15+20+25+30+35+40[/tex]
=[tex]165[/tex]
Thus, the value of [tex]\sum_{n=3}^{8}5n[/tex] is 165.
(3c2 + 2d)(–5c2 + d) Select all of the partial products for the multiplication problem above.
Answer:
2d^2
-15c^4
-10c^2 d
3c^2d
Step-by-step explanation:
Just had the question, good luck lovelies! :)
The partial products for the expression (3c² + 2d)(-5c² + d) are -15c⁴, 3c²d, -10c²d, and 2d².
The multiplication of the expression (3c² + 2d)(-5c² + d) step by step,
(3c² + 2d)(-5c² + d)
To find the partial products, we'll use the distributive property, which states that for any numbers a, b, and c:
a(b + c) = ab + ac
Now, applying this to your expression:
3c² × -5c²:
Multiply 3c² by -5c².
Result: -15c⁴
3c² × d:
Multiply 3c² by d.
Result: 3c²d
2d × -5c²:
Multiply 2d by -5c².
Result: -10c²d
2d × d:
Multiply 2d by d.
Result: 2d²
Therefore, these are the partial products obtained when multiplying the given expressions.
-15c⁴
3c²d
-10c²d
2d²
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The above question is incomplete , the complete question is:
(3c² + 2d)(–5c² + d) Select all of the partial products for the multiplication problem above.
2d²
3cd³
-15c⁴
-10c²d
-15c²
3c²d
what transformation changes the graph of y= x^3-x-6 into the graph of y=x^3-x?
What is the measure of AE?
No explanation is needed, also, sorry if the picture is blurry!