Answer:
Option A
amplitude = 3 feet; period = 16 hours; midline: y = 5 amplitude = 3 feet;
Step-by-step explanation:
Given that The saginaw bay tides vary between 2 feet and 8 feet.
When we correspond these to sine curve we can say minimum 2 ft max 8 ft middle value being 5 ft
Period = 16 hours (since it completes one full cycle in 16 hours_
Amplitude = maximum - middle value or middle value-minimum
=[tex]8-5 = 5-2 = 3 ft[/tex]
Thus the equation would be as[tex]y = 3sin \frac{8}{\pi}+5[/tex]
Thus we find that minimum =2, max =8 middle line y=5
Amplitude = 3 ft and period = 16
Hence option A is right.
What is the distance between points A and B?
___ units
we know that
the distance's formula between two points is equal to
[tex]d=\left|xB-xA\right|[/tex]
substitute
[tex]d=\left|1-(-5)\right|[/tex]
[tex]d=6\ units[/tex]
therefore
the answer is
[tex]6\ units[/tex]
The distance between two point [tex]A{\text{ and }}B[/tex] is [tex]\boxed{{\mathbf{6 units}}}[/tex].
Further explanation:
The distance between two points is the modulus of difference of the given two points.
The distance between two points can be found by the distance formula as,
[tex]\left| {B - A} \right|[/tex]
Here, [tex]A{\text{ and }}B[/tex] are the points on the number line.
The distance cannot be negative therefore modulus is applied in the formula.
Step by step explanation:
Step 1:
First we determine the points from the given number line.
It can be observed from the given number line that there are two points one is on the left side of the origin and the second is right side of the origin.
The point [tex]A[/tex] is [tex]- 5[/tex] and the point [tex]B[/tex] is 1.
Step 2:
Now use the distance formula to obtain the distance between the two points [tex]A{\text{ and }}B[/tex].
Here, the value of A is [tex]-5[/tex] and B is 1.
Substitute the value of [tex]A{\text{ and }}B[/tex] to obtain the distance as,
[tex]\begin{aligned}d&= \left| {B - A} \right| \\&= \left| {1 - \left( { - 5} \right)} \right|\\&= 6{\text{ units}}\\\end{aligned}[/tex]
Therefore, the distance between two point [tex]A{\text{ and }}B[/tex] is [tex]6{\text{ units}}[/tex].
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Number line
Keywords: Integers, distance, point, number line, units, measurement, origin, negative numbers, positive numbers, right side, left side, difference.
3.Cornelia spends 2 2/3 hours studying for her big science test. She spent 2/3 of an hour finishing her writing assignment and 1/4 of an hour playing outside. How much time did she spend overall on the three activities?
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divide total distance by time
7.5 miles / 3 hours = 2.5 miles per hour is his speed
Help please pre calculus
put 7.6*10^-1 into the equation to get:
10log(1/7.6*10^-4) = 31.19
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In Indianapolis, the Market Tower has 2/3 as many stories as the Chase Tower. If the Market Tower has 32 stories, how many stories does the Chase Tower have?
the ordered pair (2 36) is a solution to which equation(s)
A. y=2x^2
B. y=(3x)^2
C. y=7x^2+2
D. y=(x+4)^2
(2, 36) → x = 2, y = 36
Substitute the value of x and y to the equations of the functions:
A. y = 2x^2
36 = 2(2)^2 → 36 = 8 FALSE
B. y = (3x)^2
36 = (3 · 2)^2 → 36 = 6^2 → 36 = 36 CORRECT
C. y = 7x^2 + 2
36 = 7(2)^2 + 2 → 36 = 7 · 4 + 2 → 36 = 30 FALSE
D. y = (x + 4)^2
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Two angles that are complementary __________ form a right angle. 2. angles with a common side and a common vertex ______ form a linear pair. 3. two angles that are supplementary are _______ complementary.
1. Factor the expression 3x^3 + 4x^2 - 15x - 20 Please show work!
The expression 3x^3 + 4x^2 - 15x - 20 can be factored into the form (3x + 4)(x^2 - 5) by grouping terms, factoring out common components, and simplifying.
Explanation:The provided expression to be factored is [tex]3x^3 + 4x^2 - 15x - 20.[/tex]Factoring this involves finding common factors and breaking the terms down until we cannot do so any further.
Group terms that look like they might have common factors: [tex](3x^3 + 4x^2) - (15x + 20).[/tex]Factor out the common factors: [tex]x^2(3x + 4) - 5(3x + 4).[/tex]Notice that we have the binomial of (3x + 4) common between both terms. We can now factor that out: [tex](3x + 4)(x^2 - 5).[/tex]
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True
False
true
Step-by-step explanation:
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One car rental company charges $30 per day plus $0.25 per mile driven. a car company charges $40 per day plus $0.10 per mile driven. how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company? write an inequality to solve.
Answer:
66.667 miles
Step-by-step explanation:
Given: One car rental company charges $30 per day plus $0.25 per mile driven.
Second car company charges $40 per day plus $0.10 per mile driven.
To find: how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company?
Solution: Let the distance driven on a day be x miles.
As per question,
The first rental company will charge [tex]=30+0.25x[/tex]
The second rental company will charge [tex]=40+0.10x[/tex]
Now, we want the rental charges of second company to be less expensive then the first.
So we get the inequality,
[tex]30+0.25x>40+0.10x[/tex]
[tex]0.25x-0.10x>40-30[/tex]
[tex]0.15x>10[/tex]
[tex]x>\frac{1000}{15}[/tex]
[tex]x>66.667[/tex] miles
Hence, at least 66.667 miles should be driven on a day.
1. The equation of a circle is x ^2 + y ^2 – 4 x + 2 y = 11 .
What are the coordinates of the center of the circle?
Question 1 options
(2, –1)
(4, –2)
(–4, 2)
(–2, 1)
2. What is the equation of the circle with center (4, -3) and radius 2?
Question 2 options:
(x + 4)^2 + (y – 3)^2 = 4
(x + 4)^2 – (y – 3)^4 = 4
(x – 4)^2 + (y + 3)^2 = 2
(x – 4)^2 + (y + 3)^2 = 4
3. What is the equation of this circle? (has picture)
(x – 2)^2 + (y – 7)^2 = ½
(x + 2)^2 + (y + 7)^2 = ¼
(x + 7)^2 + (y + 2)^2 = ¼
(x + 2)^2 + (y + 7)^2 = ½
4. What are the center and radius of the circle described by the equation x2 + y2 – 18x + 12y + 68 = 0?
Question 4 options:
Center (-9, 6); radius 7
Center (9, -6); radius 7
Center (-6, 9); radius 7
Center (6, -9); radius 7
5. Select the equation of a circle with center (-3, 7) and radius 5.
Question 5 options:
(x - 3)^2 + (y + 7)^2 = 25
(x + 3)^2 + (y - 7)^2 = 25
(x + 3) + (y - 7) = 25
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15.5 units
21.0 units
21.6 units
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Answer: Terry passed 16 science tests.
Step-by-step explanation: Given that by the end of the school year, Terry had passed 80% of his science tests and Terry failed 4 science tests.
We are to find the number of science tests that Terry passed.
Let x represents the total number of science tests that Terry appeared in.
Since he failed 4 science tests, so the number of science tests that Terry passes is given by
[tex](x-4).[/tex]
Since he passed 80% of his tests, so we get
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So, total number of science tests = 20.
Therefore, the number of science tests that Terry passed is given by
[tex]n=20-4=16.[/tex]
Thus, Terry passed 16 science tests.
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B. 8/15
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D. 2/3
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