$50 per day x 6 days = 300
20% = 0.2, times t = 0.2t
The equation would be: f(t) = 300 + 0.2t
Answer:
Option D:[tex]f(t)=300+0.2 t[/tex]
Step-by-step explanation:
We are given that Mikayla is a waitress
She makes a guaranteed per day =$50
Her tips per day =20 % of weekly tips t
We have to find a function that represents the amount of money makes by Mikayla in one week
[tex]20% of t=\frac{20}{100}t=0.2t[/tex]
She works per week=6 days
She earns in 6 days=[tex]50\times 6[/tex]=$300
Total earning of Mikayla in one week =[tex]300+0.2t[/tex]
[tex]f(t)=300+0.2 t[/tex]
Hence, option D is true.
Change -25.49 to degrees,minutes,and seconds A -25 29' 24'' B -25 31' 32'' C -25 29' 31'' D -25 32' 40''
Answer:
A. -25° 29' 24"
Step-by-step explanation:
It is easier to talk about this by considering the magnitude of the angle, then applying the sign to the result.
The fractional part, 0.49°, can be multiplied by 60' per degree to get the number of minutes:
0.49° × 60'/1° = 29.4'
The fractional part of this, 0.4', can be multiplied by 60" per minute to get the number of seconds:
0.4' × 60"/1' = 24"
Then the angle is ...
-25.49° = -25° 29' 24"
_____
Alternate solution
You can recognize this is 0.01° less than 25° 30', so is ...
0.01° × 60' = 0.6' = 0.6 × 60" = 36"
When 36" is subtracted from 25.5° = 25° 30', the result is 25° 29' 24". Of course, your angle is negative: -25° 29' 24".
_____
Comment on base-60 arithmetic
In base-10 arithmetic, when you borrow 1 from the next higher place in the number, you are borrowing ten of the current place. For example, when you are doing arithmetic with hundreds, and you borrow 1 from the thousands place, you have effectively borrowed 10 hundreds.
In base-60 arithmetic, when you borrow one from the next higher place, you borrow 60 of the current unit. That is, borrowing one minute gives you 60 seconds. Thus, 30 minutes is the same as 29 minutes and 60 seconds. Subtracting 36 seconds from this value gives 29 minutes and 24 seconds.
The term "borrowing" was used when I learned arithmetic. More recently, I've seen it called "rewriting" the number. I also think of it as "making change": changing a higher unit to an equivalent number of smaller units.
Line segment XY is a directed line segment beginning at point X(9, 2) and ending at point Y(-6, 2). Find the point Z on the line segment that partitions the line segment into the segments XZ and ZY at a ratio of 5:3.
Answer:
[tex](-\frac{3}{8},2)[/tex]
Step-by-step explanation:
Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y. That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8). Our k value is 5/8. Now we will find the rise and run values which is the slope of this line segment:
[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]
Coordinates are found in this formula:
[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]
Filling that in:
[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]
which simplifies to
[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]
which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The graph of a polynomial function of degree 5 has three x-intercepts, all with multiplicity 1. Describe the nature and number of all its zeros.
The answer is C: Three real zeros and 2 imaginary zeros
Answer: C) 3 real zeros & 2 imaginary zeros
Step-by-step explanation:
Since the function has a degree of 5, then there must be 5 zeros.
If each of the 3 given zeros crosses the x- axis (which is what happens when it has an odd-numbered multiplicity), then there are 2 zeros missing.
The missing zeros are imaginary.
(3 zeroes × multiplicity of 1) + (2 imaginary)
3 + 2 = 5 [tex]\large\checkmark[/tex]
The table show whether a bus pass is a child’s or adult’s pass and whether it is a daily or monthly pass
(it’s a lot of different answers, like 50.8% or 60% or 60.8%)
do anybody have a for sure answer?
Answer:
50.8%
Step-by-step explanation:
That is the one my friend and I chose. It is 31/61 when all the stuff is added together and that is put to 50.8 as a percentage..
A vendor sells three types of watches. Of the watches in stock 20% are mens watches, 40% are ladies watches and the rest are childrens watches. There are 250 all together how many childrens watches are there math
Answer:
100.
Step-by-step explanation:
The percentage of children's watches = 100 - 20 - 40 = 100-60
= 40%.
40% = 0.40 as a decimal fraction.
So the number of children's watches
= 0.40 * 250
= 100.
Consider a triangle with side lengths of 10 ft, 17.32 ft, and 20 ft. By examining the side lengths, what can you conclude about the measurement of the angles? Explain your reasoning. A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3 . B) The angles are 60-60-60. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3. C) The angles are 45-45-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3. D) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 2.
Answer:
A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.
Step-by-step explanation:
The answer choice speaks for itself.
The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.
The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.
Clearly, the given leg lengths match the second set of ratios more closely:
10 : 17.32 : 20 ≈ 1 : √3 : 2.
x^2−1.78x, if x=2.78
Answer:
2.78
Step-by-step explanation:
We are given the expression [tex]x^2-1.78x[/tex]
As we know that x=2.78, we can plug that value into the expression and simplify it
[tex](2.78)^2-1.78(2.78)\\\\7.7284-4.9484\\\\2.78[/tex]
What is the area of a triangle with vertices at (–2, –1), (4, –1), (6, 5)?
6 square units
9 square units
18 square units
36 square units
The calculated area of the triangle is 18 square units
How to calculate the area of the triangle in square units?
From the question, we have the following parameters that can be used in our computation:
(–2, –1), (4, –1), (6, 5)
The area of the triangle in square units is calculated as
Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * |-2 * -1 - 4 * -1 + 4 * 5 - 6 * -1 + 6 * -1 - 5 * -2|
Evaluate the sum and the difference of products
Area = 1/2 * 36
So, we have
Area = 18
Hence, the area is 18 square units
Please please help me
Answer:
151.4496 cm²
Step-by-step explanation:
The area of a trapezoid is found using the formula ...
A = (1/2)(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases and h is the distance between them. Fill in the numbers and do the arithmetic.
A = (1/2)(22.2 cm + 8.52 cm)(9.86 cm) = 151.4496 cm²
Diego's family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Write an inequality that represents the number of days Diego's father can drive the car without the warning light coming on. Explain each part of your inequality
Answer:
The inequality is [tex]0.6x < 12.5[/tex]
The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days
Step-by-step explanation:
14 gallons-1.5 gallons=12.5 gallons
we know that
If the remaining fuel is greater than 1.5 gallons Diego's father can drive the car without the warning light coming on
so
Let
x ----> the number of days
[tex]0.6x < 12.5[/tex] ----> inequality that represent the situation
Solve for x
[tex]x < 12.5/0.6[/tex]
[tex]x < 20.8\ days[/tex]
The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days
An inequality is similar to an equation in that they both describe the relationship between two expressions.
The inequality represents the number of days Diego's father can drive the car without the warning light coming on is [tex]\rm x<20.8[/tex].
GivenDiego's family car holds 14 gallons of fuel.
Each day the car uses 0.6 gallons of fuel.
A warning light comes on when the remaining fuel is 1.5 gallons or less.
What is inequality?An inequality is similar to an equation in that they both describe the relationship between two expressions.
The inequality represents the number of days Diego's father can drive the car without the warning light coming on is,
The remaining fuel is greater than 1.5 gallons Diego's father can drive the car without the warning light coming on.
Here, x represents the number of days.
Therefore,
The inequality represents the number of days Diego's father can drive the car without the warning light coming on is,
[tex]\rm 0.6x<12.5\\\\x < \dfrac{12.5}{0.6}\\\\x<20.8[/tex]
Hence, The inequality represents the number of days Diego's father can drive the car without the warning light coming on is [tex]\rm x<20.8[/tex].
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Find the greatest common factor of 8m 3 and 6m 4
The greatest common factor of 8m^3 and 6m^4 is 2m^3. This is found by determining the highest number or term that can divide both terms exactly, considering both the coefficients and the power of the variable.
Explanation:The question asks for the greatest common factor of the terms 8m3 and 6m4. The greatest common factor (GCF) is the highest number or term that divides both numbers exactly. Ignoring the coefficients (8 and 6), we can easily see that these terms both contain the variable 'm', raised to the powers 3 and 4, respectively.
The rule for dealing with variables when finding the GCF is to take the variable to the power which is the lesser of the two. In this case, that would be m3. Now, looking at the coefficients (8 and 6), the highest number that can divide them both exactly is 2. Therefore, the greatest common factor of 8m3 and 6m4 is 2m3.
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The greatest common factor of 8m³ and 6m⁴ is 2m³, which is found by identifying the shared prime factors and the lowest power of 'm' present in both terms.
To find the greatest common factor (GCF) of 8m³ and 6m³, we need to find the highest power of each prime number and the variable that is contained in both terms. The prime factorization of 8 is 23, and for 6, it is 2 × 3. Since both have at least one factor of 2, we'll use that in our GCF. Additionally, since the lowest power of 'm' that appears in both terms is m3, we will also use that.
The GCF is the product of these shared factors. So, we have:
2 (the common prime factor)
m3 (the lowest power of 'm' in both terms)
Therefore, the GCF of 8m³ and 6m⁴ is 2m³.
A used car is priced at $2,695. If you borrow the money for the car, your payments will be $122 a month for 30 months. How much will you save by paying cash? A. $333 B. $1,075 C. $965 D. $233
Answer: $965
Step-by-step explanation:
The used car is priced at $2,695.
If you borrow the money for the car, your payments will be $122 a month for 30 months. This means that the total amount of money that you would have paid at the end of 30 months at a rate of $122 per month is the amount paid per month multiplied by the total number of months. It becomes
Total payment = 122×30 = $3660
This means that you ended up paying higher than you would have paid if you paid cash.
Amount that you would have saved = amount paid over 30 months - cost of the car
Amount that you would have saved
= 3660 - 2695 = $965
By paying cash for the used car priced at $2,695, you will save $965. Option C is correct.
The total amount paid when financing the car can be found by multiplying the monthly payment by the number of months:
Total amount paid when financing = Monthly payment × Number of months
= $122 × 30
= $3,660
To find the savings, we subtract the total amount paid when financing from the total cost of the car when paying cash:
Savings = Total cost of the car when paying cash - Total amount paid when financing
= $2,695 - $3,660
= -$965
Since the result is negative, it means you would actually be paying more when financing the car compared to paying cash.
Absolute value of savings = |- $965|
= $965
Therefore, the correct answer is $965.
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A rectangle prism has a length of 1 1/4 cm a width of 4 cm and a height of 3 1/4 cm what is the volume of this prism
Answer:
65/4 cm³, or 16.25 cm³
Step-by-step explanation:
Here, Volume V = (length)(width)(height). Those measurements are included here:
V = (1 1/4 cm)(4 cm)(3 1/4 cm), or
V = (5/4 cm)(4 cm)(13/4 cm)
V = (5 cm²(13/4 cm) = 65/4 cm³, or 16.25 cm³
The equation for a circle is x^2 − 8x + y^2 - 2y - 8 = 0
.
What is the equation of the circle in standard form?
(x−16)^2+(y−1)^2=16 (A)
(x−4)^2+(y−1)^2=25 (B)
(x−16)^2+(y−1)^2=25 (C)
(x−4)^2+(y−1)^2=16 (D)
Answer:
B
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
To obtain this form use the method of completing the square
Given
x² - 8x + y² - 2y - 8 = 0 ( add 8 to both sides )
x² - 8x + y² - 2y = 8
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 8 + 16 + 1
(x - 4)² + (y - 1)² = 25 → B
Final answer:
The standard form of the given circle equation is (x - 4)^2 + (y - 1)^2 = 25, which is option (B).
Explanation:
To rewrite the given equation of a circle in standard form, we need to complete the square for both x and y terms. The equation is given as:
x² − 8x + y² - 2y - 8 = 0
We organize the equation by grouping x and y terms:
(x² − 8x) + (y ² - 2y ) = 8
To complete the square, we add to each side (½ the coefficient of x) ² for the x-terms and (½ the coefficient of y) ² for the y-terms:
For the x terms: (½ × -8)² = (-4)² = 16. Add 16 to both sides.
For the y terms: (½ × -2)² = (-1)² = 1. Add 1 to both sides.
Our equation becomes:
(x² − 8x + 16) + (y² - 2y + 1) = 8 + 16 + 1
Which simplifies to:
(x - 4)² + (y - 1)² = 25
Therefore, the standard form of the given equation is (x - 4)² + (y - 1)² = 25, and the correct answer from the options is (B).
Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C, Checked) C w = 5 \times 15w=5×15w, equals, 5, times, 15
Answer:
Option C. w=5×15
Step-by-step explanation:
Let
w ----> the amount of dollars to buy 5 tickets
we know that
The variable w is equal to multiply the numbers of tickets by the cost of each ticket
so
The equation that represent this situation is
w=5(15)
Answer:
Thus, the required equation is W=15×5
Step-by-step explanation:
Consider the provided information.
Gina wants to go to the water park with her friends. They have a total of w dollars.
W represents the total money they have.
They buy 5 tickets and each ticket cost 15 dollars.
Thus the total cost for 5 tickets is:
15×5
She had W dollars. That means the above expression is equal to W.
W=15×5
Thus, the required equation is W=15×5.
Anyone willing to help me?
Answer:
I think it's the last one, BD/AE
Step-by-step explanation:
Will give brainliest answer. Simplify and select the answer with the appropriate restrictions for the variable.
Answer:
4:The denominator can't be equal to 0, therefore - 5
5: 4)The denominator can't equal to 0 -4
Answer:
Question 4:
(x² - 25) / (x - 5)
= (x² - 5²) / (x - 5)
= [(x - 5) · (x + 5)] / (x - 5)
= x + 5
The denominator can't be equal to 0, therefore:
x - 5 ≠ 0 ⇔ x ≠ 5
Question 5:
(3x² - 6x) / (x² - 2x - 8)
= [3x (x - 2)] / (x² + 4x - 2x - 8)
= [3x (x - 2)] / [x (x + 4) - 2 (x + 4)]
= [3x (x - 2)] / [(x - 2) (x + 4)]
= 3x / (x + 4)
The denominator can't equal to 0, therefore:
x + 4 ≠ 0 ⇔ x ≠ -4
Which choice is equivalent to the expression below when x is greater than or equal to 0?
Answer:
Choice A is the correct answer
Step-by-step explanation:
[tex]2x\sqrt{2x}[/tex]
Find the attachment below for the explanation
For this case we must indicate an expression equivalent to:
[tex]\sqrt {18x ^ 3} - \sqrt {9x ^ 3} +3 \sqrt {x ^ 3} - \sqrt {2x ^ 3}[/tex]
So, rewriting the terms within the roots we have:
[tex]18x ^ 3 = (3x) ^ 2 * (2x)\\9x ^ 3 = (3x) ^ 2 * (x)\\x ^ 3 = x ^ 2 * x\\2x ^ 3 = (2x) * x ^ 2[/tex]
So:
[tex]\sqrt {(3x) ^ 2 * (2x)} - \sqrt {(3x) ^ 2 * (x)} + 3 \sqrt {x ^ 2 * x} - \sqrt {(2x) * x ^ 2} =[/tex]
Removing the terms of the radical:
[tex]3x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} -x \sqrt {2x} =[/tex]
We simplify adding terms:
[tex]3x \sqrt {2x} -x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} =\\2x \sqrt {2x} + 0 =\\2x \sqrt {2x}[/tex]
Answer:
Option A
Jackie has set up a lemonade stand this summer. The line plot represents how many liters she has sold during her first 13 days in business. How much lemonade has Jackie sold in all? A) 5 8 L B) 70 8 L C) 13 8 L D) 33 8 L
Answer the answer is c
Step-by-step explanation:
I also got C for this answer
Scores on a standardized test are normally distributed with a mean of 228 and a standard deviation of 18. Students who score at least 2.3 standard deviations above the mean receive a certificate.
What is the minimum score required to receive the certificate?
Answer:
270
Step-by-step explanation:
The mean is 228 and the standard deviation is 18.
2.3 standard deviations above the mean is:
228 + 2.3×18
228 + 41.4
269.4
Since scores are usually integers, we round up to 270.
Jeremy is recording the weights, in ounces, of different rock samples in a lab. The weights of seven rocks are listed below.
11, 13, 14, 6, 10, 9, 10
The eighth rock that he weighed was 5 ounces. How would the interquartile range of the data be affected if Jeremy includes the weight of the eighth rock?
A.
The interquartile range does not change.
B.
The interquartile range cannot be determined.
C.
The interquartile range increases.
D.
The interquartile range decreases.
CCCCCCCCCCCCCCCCCCCCCC
Answer:
The correct answer is option "C"
"The interquartile range increases"
The value of the (RIC) will increase from 4 to 5.75, that is, 44%
Step-by-step explanation:
The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin
The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.
Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%
Describe the roots of the equation shown below.
[tex]3x^2+4x+2=0[/tex]
A. There are two complex roots.
B. There is one real, double root.
C. There are two real, rational roots.
D. There are two real, irrational roots.
Answer A becaus descriminant =16-4*3*2=-8
ANSWER
A. There are two complex roots.
EXPLANATION
The given quadratic equation is
[tex]3x^2+4x+2=0[/tex]
when we compare this to
[tex]a {x}^{2} + bx + c = 0[/tex]
we have a=3,b=4 and c=2.
We use the discriminant to determine the nature of roots.
[tex]D= {b}^{2} -4ac [/tex]
[tex]D= {4}^{2} -4(3)(2) [/tex]
[tex]D= 16-24[/tex]
[tex]D= - 8[/tex]
Since the discriminant is less than zero, the equation will have 2 complex roots.
PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
51
Step-by-step explanation:
Given
P(x) = 2x³ + 4x² - 10x - 9, then
P(a) = 2a³ + 4a² - 10a - 9 ← substitute x = a into P(x)
To evaluate P(3) substitute a = 3 into P(a)
P(3) = 2(3)³ + 4(3)² - 10(3) - 9 = 54 + 36 - 30 - 9 = 51
Since P(3) ≠ 0 then (x + 3) is not a factor of P(x)
Answer:
51
Step-by-step explanation:
2(3)³ + 4(3)² - 10(3) - 9
= 51
The result of subtracting two or more numbers is called
Answer:
Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.
Step-by-step explanation:
The result of subtracting two or more numbers in mathematics is called the difference. In vector subtraction, this applies as we add the first vector to negative of the vector that needs to be subtracted, resulting in a difference vector. This is equivalent to subtracting scalar values.
Explanation:In mathematics, the result of subtracting two or more numbers is known as the difference. This concept also applies to vectors in a process called Vector Subtraction.
For instance, if we have two vectors A and B, and we wish to subtract B from A (usually written as A - B), we do so by adding the first vector, A, to the negative (-) of the second vector, B (written as A + (-B)). Here, -B (negative B) represents the same vector as B but in the opposite direction. The subtraction of A and B results in a difference vector, D, i.e., D = A - B.
The same principle is true for ordinary numbers. Take the numbers 5 and 2 for example. If we subtract 2 from 5 (5 - 2), it's equivalent to adding 5 and -2 (5 + (-2)). Here, the difference is 3.
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Question 4(Multiple Choice Worth 2 points) (09.06) For two functions, m(x) and p(x), a statement is made that m(x) = p(x) at x = 7. What is definitely true about x = 7? Both m(x) and p(x) cross the x-axis at 7. Both m(x) and p(x) cross the y-axis at 7. Both m(x) and p(x) have the same output value at x = 7. Both m(x) and p(x) have a maximum or minimum value at x = 7.
Answer:
See below.
Step-by-step explanation:
The 2 functions have the same output value when x = 7 ( that is what m(x) = p(x) at x = 7 means).
A roller coaster starts from a deck at an elevation of 20 feet above the ground. On the first hill it climbs 78 feet and then drops 85 feet. On the second hill the coaster climbs 103 feet and then drops 110 feet. How far below or above the deck is the coaster after the completion of the two hills?
Answer:
14 feet below. the deck.
Step-by-step explanation:
That would be (20 + 78 - 85 +103 - 110 ) feet above the ground
= 6 feet above the ground.
That is 20 - 6 = 14 feet below the deck.
r=14costheta in rectangular form
Answer:
x² +y² = 14x
Step-by-step explanation:
Making the usual substitution x = r·cos(θ) and r² = x² +y², we can get there this way:
Substitute cos(θ) = x/r:
r = 14·x/r
Multiply by r:
r² = 14x
Substitute for r²:
x² + y² = 14x
_____
The original equation is shown dotted; the rectangular version is shown as a solid line. The graphs are identical.
x2 + y3 = 14x is the soulution of your answer (sorry for bad grammar)
If a circle with a diameter of 20 m is inscribed in a square, what is the probability that a point picked at random in the square is in the shaded region?
A. 1/5
B. 43/200
C. 86/314
D. 314/400
I used 3,14 for pi since it was only way it made sense based on the answers.
The question probably provided you with this.
If you have any more questions do not hesitate :)
The probability that a point picked at random in the square is in the shaded region will be 86/314. Thus option C is correct.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given:
A circle with a diameter of 20 m is inscribed in a square .
Thus side of square = 20 m
Now, area of square = 20 x 20
= 400 sq m
The radius of circle = 10 m
Area of circle
[tex]A = \pi r^2\\\\A = 3.14 \times 10^2\\\\A = 314 m^2[/tex]
Now, Area of shaded region = Area of the square - an area of circle
Area of shaded region = 400 - 314
= 86
The probability that a point picked at random in the square is in the shaded region will be 86/314. Thus option C is correct.
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A line through which two points would be parallel to a line with a slope of 3/4?
F. (0,5) and (-4,2)
G. (0,2) and (-4,1)
H. (0,0) and (0,-2)
J. (0,-2) and (-4,-2)
Answer:
F. (0, 5) and (-4, 2)
Step-by-step explanation:
We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:
F. (0,5) and (-4,2) As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4. This is the line with slope 3/4.
The height of a rocket launched upward from a 160 foot cliff is modeled by the function h(t)= -16t^2+48t+160, where h is height in feet and t is time in seconds. Find the time it takes the rocket to reach the ground at the bottom of the cliff.
Answer:
5 seconds
Step-by-step explanation:
In order to find the time when it landed, we will have to find the x-intercepts.
Equation given to us : -16t² + 48t + 160
Let's take the GCD, which is -16.
-16( t² - 3t - 10 )
Factoring what's inside the brackets, we get the x-intercepts.
What multiples to -10 but adds up to -3? The numbers are -5 and 2
-16 ( t - 5 ) ( t - 2 )
X-intercepts are t - 5 and t - 2
Which is 5 and 2 seconds. But one of this is an extraneous solution and that is 2.
If we substitute the value of 2 in the equation, we will not get 0.
During the x-intercept, the x has a value and y is 0. If we substitute 5 ans x. we will get y as 0.
Hence, the answer is 5 seconds.