Kerry wants her stopping distance to not exceed 75ft. At what range of speeds can she travel?
Answers
The range of speeds that she can travel is determined as 30 mph or less.
Range of speed of KerryThe range of speed of Kerry is calculated as follows;
d = v + (v²)/20
d = (20v + v²)/20
75 = (20v + v²)/20
20(75) = 20v + v²
1500 = 20v + v²
v² + 20v - 1500 = 0
v² + 50v - 30v - 1500 = 0
v(v + 50) - 30(v + 50) = 0
(v + 50)(v - 30) = 0
v = 30 mph or - 50 mph
Thus, the range of speeds that she can travel is determined as 30 mph or less.
The complete question is below:
For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the following formula, where d is measured in feet. Kerry wants her stopping distance not to exceed d = 75 ft. At what range of speeds can she travel?
d =v+(v^2)/20
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Related Questions
9n^2 - 24 + 16
please help
Answers
Answer:
lol the answer is the second one
Write the equation for the trigonometric graph.y= 8cos(pi/40x)y= –8sin(pi/40x)y= –8cos(pi/40x)y= 8sin(pi/40x)
Answers
Solution
For this case we can verify the answer using the point x= 0 if we replace we got:
y=8 cos (pi/40* 0) = 8 cos (0) = 8
y= -8 sin (pi/40 *0)= -8 sin(0) = 0
y= -8cos(pi/40*0)= -8 cos (0)= -8
y= 8 sin (pi/40 *0)= 8 sin(0) = 0
Then the correct option would be:
y= -8cos(pi/40*0)
190 is what percent of 360
Answers
Answer:
190 / 360 = 0.52777777
0.527777 x 100 = 52,78%
If f(1) = 5 and f(n) = 5f(n-1) + 5 then find the value of f(3)
Answers
The value of function for f(5) is 3125.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given that, f(1) = 5 and f(n) = 5f(n − 1)
Now, for finding the the 5th term we have to find the remaining four term before the 5th term.
So, n=2
f(2) = 5f(1)
f(2)= 5(5)
f(2)= 25
Now, n=3
f(3) = 5f(2)
f(3)= 5(25)
f(3)= 125
Now, n=4
f(4) = 5f(3)
f(4)= 5(125)
f(4)= 625
Now, n=5
f(5) = 5f(4)
f(5)= 5(625)
f(5)= 3125
Hence, the value of function for f(5) is 3125.
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Identify the next number in the following sequence
25 49 97 ?
Select only one answer
- 124
- 171
- 139
- 193
Answers
Answer:
the correct answer is 193
Step-by-step explanation:
25×1-0=25
25×2-1=49
49×2-1=97
97×2-1=193
In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Answers
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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1) Which pair of lines are parallel? Using the measurements of a given pair of angles,state a Theorem that supports your choice 2) Determine the measurements of angles x,y, and zM
Answers
For this part of the exercise, we can use the Alternate Exterior Angles Converse theorem, which says that if two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.
Therefore, lines C and D are parallels since the alternate exterior angles of 95° are equal.
Part 2
From the above, we know that the angles 124° and x° are alternate exterior angles. Then, we have:
\($$\boldsymbol{m\angle x=124}$$\text{\degree}\)For angle y, we can use the Triangle Sum Theorem, which says that the sum of the three interior angles in a triangle is always 180°. Then, we have:
\(\begin{gathered} m\angle y+53\text{\degree}+39\text{\degree}=180\text{\degree} \\ m\angle y+92\text{\degree}=180\text{\degree} \\ \text{ Subtract 92\degree from both sides of the equation} \\ m\angle y+92\text{\degree}-92\text{\degree}=180\text{\degree}-92\text{\degree} \\ $$\boldsymbol{m\angle y=88}$$\text{\degree} \end{gathered}\)Finally, for angle z, we know that angles y and z are supplementary angles, that is, angles that add up 180°.
Then, we have:
\(\begin{gathered} m\angle y+m\angle z=180\text{\degree} \\ 88\text{\degree}+m\angle z=180\text{\degree} \\ \text{ Subtract 88\degree from both sides of the equation} \\ 88\text{\degree}+m\angle z-88\text{\degree}=180\text{\degree}-88\text{\degree} \\ $$\boldsymbol{m\angle z=92}$$\text{\degree} \end{gathered}\)
Find the slant height of the pyramid.
7 mm
6 mm
8 mm
5 mm
Answers
Answer:
5 mm
Step-by-step explanation:
Given:
A rectangular pyramid
h (height) = 4 mm
l (side length) = 6 mm
Find: s (slant height) - ?
There is a right triangle in the middle
The bottom leg is 3 mm, because it's half the side length of the square
According to that, we can find x by using the Pythagorean theorem:
\( {x}^{2} = {3}^{2} + {4}^{2} = 9 + 16 = 25\)
\(x > 0\)
\(x = \sqrt{25} = 5\)
A 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider.
What is the sample size? Give only the number:
The margin of error for this data set is 2.5%. What is the 95% confidence interval for those who say they felt fully engaged with their mortgage provider (rounded to 1 decimal place)?
Answers
The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.
First, let's calculate the margin of error:
Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055
Next, we can calculate the lower and upper bounds of the confidence interval:
Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%
Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%
Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
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Help help help help help hell
Answers
Answer:
19c + 30
Step-by-step explanation:
PLEASE ANSWER THIS I HAVE 5 MINS WILL MARK BRAINLIEST IF CORRECT (PICTURE)
Answers
A= 36 * 3.14
A = 113.04 but after rounding the answer will be 113 cm^2
Answer:
Step-by-step explanation:
diameter = 12 cm
r = 12/2 = 6 cm
\(Area \ of \ semicircle = \dfrac{1}{2}\pi r^{2}\\\\\\=\dfrac{1}{2}* 3.14*6*6\\\\\\= 56.52 \ cm^{2}\)
Which is the correct trigonometric substitution for evaluating
Answers
The correct trigonometric substitution for evaluating integral ∫√(x² + 64) dx is option B. x = 8 tan θ.
How did we get the correct trigonometric substitution?To evaluate the integral ∫√(x² + 64) dx using trigonometric substitution, use the substitution x = 8 tan θ.
Let's go through the steps to see how this substitution leads us to the solution:
1. Substitute x = 8 tan θ.
This implies dx = 8 sec² θ dθ.
2. Substitute the expression for x and dx in the integral:
∫√(x² + 64) dx becomes ∫√((8 tan θ)² + 64) * 8 sec² θ dθ.
3. Simplify the expression:
∫√(64 tan² θ + 64) * 8 sec² θ dθ = ∫√(64(sec² θ - 1)) * 8 sec² θ dθ.
4. Further simplify:
∫√(64sec² θ - 64) * 8 sec² θ dθ = ∫√(64sec² θ) * 8 sec² θ dθ.
5. Simplify the expression inside the square root:
∫8sec θ * 8 sec² θ dθ = ∫64sec³ θ dθ.
6. Integrate with respect to θ:
∫64sec³ θ dθ = 64∫sec³ θ dθ.
Now, this integral can be evaluated using standard trigonometric integral identities or integration techniques. However, it's worth noting that the original integral did not involve the variable θ, so we would eventually need to convert the result back to x by substituting x = 8 tan θ.
The correct answer is B. x = 8 tan θ.
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How many inches are in 4 1/2 feet ?
Answers
Answer:
54 in
Step-by-step explanation:
12 x 4= 48
1/2 ft= 6in
48 +6= 54
There are 54 inches in 4 1/2 feet.
We have,
To convert feet to inches, we know that 1 foot is equal to 12 inches.
To find the number of inches in 4 1/2 feet, we multiply the number of feet by 12 and add the number of inches.
4 feet multiplied by 12 inches/foot = 48 inches.
1/2 foot equals 1/2 multiplied by 12 inches/foot = 6 inches.
So,
4 1/2 feet is equal to 48 inches + 6 inches, which equals 54 inches.
Therefore,
There are 54 inches in 4 1/2 feet.
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Which linear function is graphed on the grid?
90
80
70
60
8
50
30
20
10
-9-8-7-6-5- -3 -2 -1
-10
20
у
-30
-40
-50
-60
-70
-80
88
-90
1234
56789
X
Answers
The linear function that is graphed on the grid is g(x) = (15/2)x + 45 , the correct option is (d) .
In the question ,
a linear function graph is shown ,
we have to find that linear function .
So , From the given graph we can see that
the graph passes from the points (2 , 60) and (6 , 90)
in order to find the equation , we first need to find the slope .
slope = (90 - 60)/(6 - 2)
= 30/4
= 15/2
So , the equation of the line passing through the points (2 , 60) and slope 15/2 is
(y - 60) = 15/2(x - 2)
y - 60 = (15/2)x - 15
Adding 60 to both the sides ,
we get
y - 60 + 60 = (15/2)x - 15 + 60
y = (15/2)x - 15 + 60
y = (15/2)x + 45
function is (15/2)x + 45
Therefore , The linear function that is graphed on the grid is g(x) = (15/2)x + 45 .
The given question is incomplete , the complete question is
Which linear function is graphed on the grid shown below ?
(a) g(x) = (2/15)x - 6
(b) g(x) = (2/15)x + 45
(c) g(x) = (15/2)x - 6
(d) g(x) = (15/2)x + 45
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Guysss help mee i dont get it !!
Answers
Answer:
A. 2, 160 R2
Step-by-step explanation:
8642 ÷ 4 = 2160 R2
(2160 × 4 = 8640) (8642 - 8640 = 2)
Which statement may not be true about a rhombus?
a.) The diagonals of a rhombus bisect its four angles.
b.) The diagonals of a rhombus are perpendicular.
c.) The diagonals of a rhombus are congruent.
d.) The diagonals of a rhombus bisect each other.
Answers
Answer:
B i believe! Hope thats not wrong may wanna check with the Mewoo guy he is AWESOME wish I could tag ppl
Solve for p.
p + 36 = 73
p =
Answers
Answer:
p=37
Step-by-step explanation:
to get p by its self, you would do:
p+36=73
-36=-36
p=37
Answer:
37
Step-by-step explanation:
Write the inverse of g(x)=x²-7
Answers
Answer:
\(\± \sqrt{x + 7}\)
Step-by-step explanation:
y = x² - 7
Add 7 to both sides.
y + 7 = x²
Take square root on both sides.
±√(y + 7) = x
Switch variables.
±√(x + 7) = y
You are going to the movies with your family. Adult tickets cost $12.50 each. Children's tickets cost $9 each. The other expenses come to $25. Which expression can be use to figure out how much is spent, regardless of how many children and adults come?
A. 12.50 + 9 + 25
B. 12.50c + 9a + 25
C. 12.50a + 9c = 25
D. 12.50a + 9c + 25
Choose one answer.
Answers
3/4x = 1/5 .x =
Pls help I will give brainliest
Answers
Answer:
x= 4/16 stan
x=0.26 dec
Step-by-step explanation:
⬇ Hello! The answer would be down below! :) ⬇
x = 0 will be the answer.
Step-by-step explanation:
So, we start with \(\frac{3}{4} x = \frac{1}{5} x\) .
For step 1 we should subtract \(\frac{1}{5} x\) on both sides.
\(\frac{3}{4} x - \frac{1}{5} x = \frac{1}{5} x - \frac{1}{5} x\)
= \(\frac{11}{20} x = 0\)
For step 2 we will multiply both sides by \(\frac{20}{11}\).
\((\frac{20}{11})\) x \((\frac{11}{20} x ) = (\frac{20}{11})\) x \(\ (0)\)
= x = 0
Write an equation of the line that passes through (2, -5) and has a slope of 4
Answers
Step-by-step explanation:
(y-(-5))/(x-2) = 4
(y+5)/(x-2) = 4
y+5 = 4x - 8
y = 4x - 13
Coordinates are (2,-5) so x = 2, and y = -5. Since the slope is 4, m = 4
Plugging them in, we get:
-5 = 2(4) + b
-5 = 8 + b
-13 = b
The y intercept is -13. So the equation is:
y = 4x - 13.
Hope this helps
Pythagorean Theorem in Cones.
Find h.
13 cm
8cm
First we must set up our equation
using the Pythagorean Theorem.
a2 + b2 = c2
42 + b2 = 132
16 + b2 = 169
b2 = 153
b= [?]
Hint: Enter the number that belongs under the radical.
Answers
Answer:
c2 = a2 + b2 ('c' = hypotenuse of the right triangle whereas 'a' and 'b' are the other two legs.).
Step-by-step explanation:
Image result for Pythagorean Theorem in Cones. Find h. 13 cm 8cm First we must set up our equation using the Pythagorean Theorem. a2 + b2 = c2 42 + b2 = 132 16 + b2 = 169 b2 = 153 b= [?] Hint: Enter the number that belongs under the radical.
Pythagoras theorem equation helps you to solve right-angled triangle problems, using the Pythagoras equation:
The value of b for the given data is b =13 cm.
What is the Pythagorean theorem?The Pythagorean theorem is a fundamental concept in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
c²= a² + b² ('c' = hypotenuse of the right triangle whereas 'a' and 'b' are the other two legs.).
Image result for Pythagorean Theorem in Cones. Find h. 13 cm 8cm First we must set up our equation using the Pythagorean Theorem.
a² + b² = c²
4² + b² = 13²
16 + b² = 169
b² = 153
b = [12.36] or 12 cm
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Directions - Evaluate the following exponential function for the x-values in the table. Complete the table with y-values.
�
=
9
⋅
(
1
3
)
�
y=9⋅(
3
1
)
x
Answers
Sure, here's a complete table of y-values for different x-values:
x y = 9*(13)^x
0 9
1 117
2 1521
3 19773
4 256809
5 3335777
6 43363161
7 562002993
8 7304038917
9 94852405821
What is function?In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. Functions are often represented using function notation, where the input is the independent variable and the output is the dependent variable. Functions are used to model relationships between different quantities or variables, and are an essential tool in many areas of mathematics, science, engineering, economics, and more. They allow us to make predictions, analyze data, and understand complex systems.
Here,
The exponential function y = 9*(13)^x means that for any given value of x, we can calculate the corresponding value of y by plugging in x and performing the calculation. The base of the exponential function is 13, which means that the function will increase rapidly as x gets larger.
For example, if x = 0, then y = 9*(13)⁰ = 91 = 9.
If x = 1, then y = 9(13)¹ = 913
= 117.
If x = 2, then y = 9(13)² = 9*169
= 1521.
And so on.
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5 is greater than or equal to 3+2 it is true or false statement ?
Answers
Answer:
True Statement
Step-by-step explanation:
The inequality \(\geq\) means that the number can be equal or greater than the end number. In this case, the 5 is equal to 3+2, so the inequality is true.
The ratio of boys to girls at Louisiana Middle School is 3:5. There are currently 1,600 students enrolled. How many students at Louisiana Middle School are boys?
Answers
Which equation demonstrates the distributive property?-0)A)20 + 36 = 56B)20 x 36 = 36 x 2020 + 36 = 4(5 + 9)D)(5 +9)4 = 4(5 +9)
Answers
The distributifve property implies that the product of a number and a sum is the sum of the products. With this in mind we can say that the correct option is the one that states: "4*(5+9)=20+36".
Which one is it
a
b
c
d
Answers
The solution is b. (-3,0).
What is a system of equations?
Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.
The given system of equations is:
y=x+3...................(1)
2x+y=-6...............(2)
We will substitute (1) in two to find the solution for the given system of equations.
2x+x+3=-6
3x=-9
x=-3
Now we will substitute x=-3 in (1), and we will get y=-3+3=0
so y=0
Therefore the solution is b. (-3,0).
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What are the factors of 42 to find it’s prime numbers and how do I put it in a factor tree
Answers
To create a factor tree for 42, we start by finding a pair of factors of 42, such as 2 and 21 and factor each branch until we have prime numbers.
Answer:
See below
Step-by-step explanation:
Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.
Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.
The Cardinality of this set {7,8,9) includes
a. n(P) = 3
b. n(P) = 6
c. n(P) = 24
d. n(P) = 2
Answers
Answer:
The Cardinality of this set {7,8,9} is n(P) = 8.
Step-by-step explanation:
Because:
n(P) = {{}, {7}, {8}, {9}, {7, 8}, {8, 9}, {7, 9}, {7, 8, 9}}
Hence by the formula 2^k.
where, k = number of elements in the set.
The cardinality is 8.
sin
\( \sin( \binom{ - 11\pi}{3} ) \times \tan( \frac{35\pi}{6} ) \times \sec( - ) \)
Answers
Answer:
solve it :)
Step-by-step explanation: