Which is the equation of a line that has a slope of 5 and passes through point (2, -3)?
To all
o y = -x-4
o y = 1/2 X-2
To y = 1/8 x + 3
Answer:
y = 5x - 13
Step-by-step explanation:
Use the formula y = mx + b to solve for b. Then plug in known values.
Answer:
y=5x-13
Step-by-step explanation:
Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = √x 2 + y 2 and bounded above by the sphere x 2 + y 2 + z 2 = 8. Evaluate the integral to find the volume.
Answer:
Evaluate The Integral To Find The Volume. This problem has been solved! See the answer. Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = \sqrt{x^2+y^2} and bounded above by the sphere x2 + y2 + z2 = 8. Evaluate the integral to find .
Step-by-step explanation:
took it
The clocks radius is 10m. What is the circumference of the clock
Answer:
20π or 62.8 roughly
Step-by-step explanation:
Hello!
The formula for finding the circumference of a circle is 2rπ:
In that case, all we have to do is substitute 10m for our r.
2 × 10 = 20.
So circumference will be 20π.
Using 3.14 for π:
We get that 62.8 is a rough estimate for the circumference.
Really, it's 62.831..... going on forever since π is irrational.
Thus, the answer exactly is [tex]\boxed{20\:\pi}}[/tex].
Hope this helps!
Final answer:
The circumference of a clock with a radius of 10m is calculated using the formula C = 2πr, resulting in a circumference of 20π m or approximately 62.83185 m when using the approximate value of π (3.14159).
Explanation:
The circumference of a clock can be calculated using the formula for the circumference of a circle which is C = 2πr, where C is the circumference and r is the radius of the clock. Given that the radius of the clock is 10m, we substitute the value into the formula to get the circumference.
So, the circumference of the clock is C = 2π(10m) = 20π m.
The exact value of π (π is approximately 3.14159) would allow us to find the numerical value for the circumference, which would be approximately C ≈ 62.83185 m.
Elijah wants to know the cross-sectional area of the circular pipe. He measures the diameter which he finds, to the nearest millimeter, to be 5 centimeters. To find the area of the circle, Elijah using the formula A=πr^2, where A is it the area of the circle and r is the radius. he uses 3.14 for π. what value does Elijah get for the area of circle? type is that number. (Hint:3 decimal points!)
Answer:
The area is 0.002m² to 3 dp
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes(I.e cross sectional area of pipe ) , this time the a circle.
It requires us to look for the area of the shape
Given data
Diameter d = 5cm
Converting to mm = 5/100= 0.05m
Radius of circle r=d/2=0.05/2 =0.025mm
Given the area of the circle
A=πr²
A=3.14*0.025²
A=0.0019m²
To 3 dp we have area as 0.002m²
What is the amplitude of the graph of the equation y=3cos2x?
A jar lid has a diameter of 32
millimeters. What is the
circumference of the lid to the
nearest tenth?
Answer:
32pi cm or 100.530964915 mm
Step-by-step explanation:
To find this answer you will need to use the equation 2*pi*r or pi*d.
Your value 32 can be plugged in as your value of d which can then be substituted to make 32 pi or if you use a calculator you get 100.530964915.
hope this helps!
Answer: 100.5 mm
Step-by-step explanation: The formula to find the circumference of a circle is 2(pi)r
Since we know the diameter is 32, divide 32 by 2 to get the radius: 16
2(pi)(16) = 100.5309
To the nearest tenth, that would be 100.5
A child who is 58 inches tall is standing next to the woman who is 5 feet and 4 inches tall casts a shadow that is 40 inches long. How long is the child’s shadow?
Final answer:
To find the length of the child's shadow, set up a proportion comparing the woman's height and shadow length to the child's height and unknown shadow length. Solving the proportion 64/40 = 58/Child's shadow, we find that the child's shadow is approximately 36.25 inches long.
Explanation:
The question involves using proportions to calculate the length of the child’s shadow. Since the child is shorter than the woman, we can expect that the child’s shadow will also be shorter in proportion to her height. The woman is 5 feet and 4 inches tall, which converts to 64 inches. The shadow to height ratio is the same for both individuals because they are standing under the same lighting conditions.
We can set up a proportion using the woman’s height and shadow length to find the child’s shadow length:
Woman’s height / Woman’s shadow = Child’s height / Child’s shadow
64 inches / 40 inches = 58 inches / Child’s shadow
To solve for the child’s shadow, we cross-multiply:
64 * Child’s shadow = 58 * 40
Child’s shadow = (58 * 40) / 64
Child’s shadow = 2320 / 64
Child’s shadow = 36.25 inches
Therefore, the child’s shadow is roughly 36.25 inches long.
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75 of the distance fallen.
(a) After jumping and rebounding 10 times, how far has the jumper traveled downward? How far has
the jumper traveled upward? What is the total distance traveled downward and upward?
(b) Approximate the total distance, both downward and upward, that the jumper travels before coming to rest.
In this scenario, a bungee jumper's total distance traveled can be calculated using a geometric series. The initial drop is the bridge's total height, and each following jump is 75% of the previous one. Summing this series gives the total downward and upward travel.
Explanation:This problem is a classic example of a geometric series used in mathematics. The first downward travel is the entire height of the bridge, 876 feet. Each consecutive downward travel will be 75% of the previous downward travel, as the question specifies that the jumper rebounds 75% of the distance fallen.
For the downward distance after 10 jumps, you sum the geometric series with first term (a) of 876 feet, common ratio (r) of 0.75, and n terms (n) being 10. The sum S of such a series can be calculated as: S = a * (1 - r^n) / (1 - r). The upward travel distance will be 75% of the total downward distance.
To find out the total distance before the jumper comes to rest, we look at the situation when the sum of the geometric series tends to infinity (i.e., as the number of terms n approaches infinity) which can be calculated as S = a / (1 - r).
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If the point ( x , √3/2) is on the unit circle, what is x?
A. √3/2
B. 1/2
C. - √3/2
D. 2/√3
Answer:
B. 1/2
Step-by-step explanation:
This problem involves the use of the Pythagorean theorem. In the unit circle, the hypotenuse of any right triangle formed is 1 while the coordinates of the point are then the two legs that make up the triangle.
a = 1 (given)
b = √3/2 (given)
a² = b² + c² (Pythagorean Theorem)
1² = (√3/2)² + c² (Substitute information)
Now, we need to solve for c
1 = (3/4) + c² (square the hypotenuse and one of the legs)
1 - (3/4) = (3/4) + c² - (3/4) (subtract 3/4 on both sides)
1/4 = c² (combine like terms)
√(1/4) = √(c²) (square root both sides)
√1 / √4 = c (square root both sides)
1/2 = c (final answer)
Therefore the other leg of the right triangle is 1/2, this also means that the other coordinate, or x, is 1/2, so the answer is B. 1/2.
Final answer:
The x-coordinate for the point (x, √3/2) on the unit circle is determined using the Pythagorean theorem for a unit circle. After substituting √3/2 for y and solving for x, the x-coordinate can be ±1/2. The correct option from the given choices is B. 1/2.
Explanation:
If the point (x, √3/2) is on the unit circle, we must use the Pythagorean theorem that applies to the unit circle, which states that x² + y² = 1, where x and y are the coordinates of a point on the circle. For a unit circle, the radius is 1. Since the y-coordinate is given as √3/2, we can substitute this value into the equation and solve for x:
x² + (√3/2)² = 1
x² + (3/4) = 1
x² = 1 - 3/4
x² = 1/4
x = ±√(1/4)
x = ±(1/2)
Therefore, x could be either 1/2 or -1/2. Since the question doesn't specify which quadrant the point is in, both answers are correct. However, within the given options, the correct answer is B. 1/2.
10) Stephanie spent half of her weekly
allowance buying pizza. To earn more
money her parents let her weed the garden
for $4. What is her weekly allowance if
she ended with $8?
Answer:
$16
Step-by-step explanation:
-Given that her balance after buying one pizza is half her weekly allowance.
#We multiply her balance times 2 to determine her total weekly allowance:
[tex]Total \ Allowance=Balance \times 2\\\\=8\times 2\\\\=\$16[/tex]
Hence, her total weekly allowance is $16
What is 6 times 0 ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Answer:
6 x 0 = 0
Step-by-step explanation:
Tell if the measures 10, 12, and 16 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
Answer:
Yes, acute
Step-by-step explanation:
Because 10 and 12 add up to more than 16, it is possible to construct an acute triangle with these side lengths. Since 10^2 + 12^2 ≠ 16^2, we know that any triangle so constructed will not be a right triangle.
The measures 10, 12, and 16 can be the side lengths of a triangle because the sum of the two shorter sides must be greater than the longest side for a triangle to exist.
In this case, 10 + 12 is greater than 16, 16 + 10 is greater than 12, and 12 + 16 is greater than 10, satisfying the triangle inequality theorem. Therefore, a triangle can be formed.
Classifying the triangle: Using the Pythagorean theorem, we can determine that the triangle with side lengths 10, 12, and 16 is a scalene triangle, and since 10^2 + 12^2 is less than 16^2, it is an obtuse triangle.
What is the sum of -20 and 4?
Answer:
-16
Step-by-step explanation:
-20 + 4 Equals -16. Try it on a number line.
Answer:-16
Step-by-step explanation:
-20+4=-16
Which ordered pair is a solution of the equation ? y + 1 = 3(x - 4) Choose 1 answer: Only * (4, - 1) ) Only (5, 2) Both (4, - 1) ) and (5, 2) ) Neither
Replacing the ordered pairs into the equation, we find that the correct option is:
Both (4, - 1) and (5, 2)
The equation is:
[tex]y + 1 = 3(x - 4)[/tex]
Ordered pair:An ordered pair (x,y) is a solution to the equation if we replace (x,y) in the equation and get an identity.
Test if (4,-1) is a solution:
[tex]-1 + 1 = 3(4 - 4)[/tex]
[tex]0 = 0[/tex]
Identity, so it is.
Test if (5,2) is a solution:
[tex]2 + 1 = 3(5 - 4)[/tex]
[tex]3 = 3[/tex]
Identity, so it is.
Hence, both is the correct option.
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PLEASE HELP, ASAP! PLEASE AND THANK YOU!
Answer:
The answer to your question is 6.- B 7.- D
Step-by-step explanation:
Data
Parallelogram ACFG
6.-
m∠GAC = 112°
m∠ACF = ?
Process
These angles are supplementary, they measure the same.
∠GAC + ∠ACF = 180
-Substitution
112 + ∠ACF = 180°
-Solve for ∠ACF
∠ACF = 180° - 112°
-Result
∠ACF = 68°
7.-
m∠AGF = 2a + 10
m∠ACF = a + 20
The angles ∠GAC and ACF are equal, they measure the same.
∠GAC = ∠ACF
-Substitution
a + 20 = 2a + 10
-Solve for a
a - 2a = 10 - 20
-Result
-a = -10
a = 10
-Find ∠AGF
∠AGF = 2(10) + 10
20 + 10
= 30°
a bag of pretzels contains approximately 17 1/2 ounces. one serving of pretzels is 1 1/4 ounces. how many servings of pretzels are in the bag?
Answer:
14
Step-by-step explanation:
Answer: The answer is: 14
Step-by-step explanation: I just took that test!
Have a great day!
-Sunny
Students in a club are selling flowerpots to raise money each flowerpot sells for $15. Write an expression that represents the total amount of money in dollars, the students raise from selling x flowerpots.
Answer:
The expression that represents the total amount of money raised from selling [tex]\(x\)[/tex] flowerpots is [tex]\(15x\)[/tex].
Explanation:
The total amount of money raised from selling [tex]\(x\)[/tex] flowerpots can be represented by the expression:
[tex]\[ \text{Total amount of money} = \text{Price per flowerpot} \times \text{Number of flowerpots sold} \][/tex]
Given that each flowerpot sells for $15, and [tex]\(x\)[/tex] represents the number of flowerpots sold, the expression would be
[tex]\[ \text{Total amount of money} = 15x \][/tex]
So, the expression that represents the total amount of money raised from selling [tex]\(x\)[/tex] flowerpots is [tex]\(15x\)[/tex].
She Elle has 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width "w" (in meters) is modeled by: A(w) = -(w-25)^2+625 What is the maximum area possible in square meters?
Answer:
[tex]625 m^2[/tex]
Step-by-step explanation:
In this problem, we are told that the area of the garden is given by the expression
[tex]A(w)=-(w-25)^2+625[/tex]
where
w is the width of the garden (in meters)
Here we want to find the maximum possible area.
The maximum of a function f(x) can be found by requiring that its first derivative is zero:
[tex]f'(x)=0[/tex]
Therefore, here we have to calculate the derivative of [tex]A(w)=0[/tex] and find the value of w for which it is equal to zero.
Let's start by rewriting the area function as
[tex]A(w)=-(w^2-50w+625)+625=-w^2+50w[/tex]
Now we calculate the derivative with respect to w:
[tex]A'(w)=-2w+50[/tex]
Now we require this derivative to be zero, so
[tex]-2w+50=0\\w=-\frac{50}{-2}=25 m[/tex]
So now we can substitute this value of w into the expression of A(w) to find the maximum possible area:
[tex]A(25)=-(25-25)^2+625 = 625 m^2[/tex]
This value is allowed because we know that the maximum length of the perimeter of the fence is 100 meters; If the garden has a square shape, the length of each side is [tex]L=\frac{100}{4}=25 m[/tex], and the area of the squared garden is
[tex]A=L^2=(25)^2=625 m^2[/tex]
Which is equal to what we found earlier: this means that the maximum area is achieved if the garden has a squared shape.
Answer:
Step-by-step explanation:
To find the surface area of the figure shown Mia found the surface area and the rectangular prism and the rectangular prism from this Mia subtracted 6ft did mia make an error
Answer:
The answer is b
Step-by-step explanation:
Because i just did it and got it right
Answer:
B
Step-by-step explanation:
just got it right
The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. If the scores at this school have the same distribution as national scores.
(a) What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?(b) What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?(c) What is the sampling distribution of the sample mean score for a random sample of 36 students?
Answer:
a. mean=18.6
b. standard deviation=1.0
c. The distribution is a symmetry and mound-shaped but nowhere near normal.
Step-by-step explanation:
a. let [tex]\mu_x[/tex] be the sample mean.
-For a normal distributed sample, the population mean is equal to the sample mean:
[tex]\mu_x=\mu\\\\=18.6[/tex]
Hence, the sample mean is 18.6
b. Let s denote the sample standard deviation.
-For a normally distributed population, the sample standard deviation is calculated using the formula;
[tex]s=\frac{\sigma}{\sqrt{n}}\\\\=\frac{6}{\sqrt{36}}\\\\=1.0[/tex]
Hence, the sample standard deviation is 1.0
c. The sample has a mean of 18.6 and a standard deviation of 1.0
-Since it's derived from a normally distribted population, it will be symmetrical and have an almost normal shape.
-Hence, it is a symmetry and mound-shaped, but Not Normal.
The mean of the sampling distribution is 18.6. The standard deviation of the sampling distribution is 1.0. The sampling distribution of the sample mean score for a random sample of 36 students is normally distributed with a mean of 18.6 and standard deviation of 1.0, according to the central limit theorem.
Explanation:The mean and standard deviation of the population, which are given as 18.6 and 6.0 respectively, are used to calculate the mean and standard deviation of the sampling distribution.
(a) According to the central limit theorem, the mean of the sampling distribution of the sample mean score for a random sample of 36 students (µx-bar) is equal to the mean of the population (µ), so µx-bar = µ = 18.6.
(b) The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students (σx-bar) is the standard deviation of the population (σ) divided by the square root of the sample size (n), so σx-bar = σ/√n = 6.0/√36 = 1.0.
(c) The sampling distribution of the sample mean score for a random sample of 36 students is a normal distribution with mean µx-bar = 18.6 and standard deviation σx-bar = 1.0, according to the central limit theorem, since the sample size is sufficiently large (n > 30).
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Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately.
Answer:
These equations are in slope-intercept form. I can use the y-intercept and slope to graph both lines. I plot the y-intercept and use rise over run to locate another point on the line. Then, I can draw a line through the two points.
Step-by-step explanation:
Which of the following statements is NOT true about the graph of a system of
equations with infinitely many solutions?
The lines will have the same slope.
The lines will have one positive y-intercept and one negative
y-intercept.
The lines will have the same y-intercept.
The lines will share all of the same points.
Answer:
The lines will have one positive y-intercept and one negative y-intercept is NOT true.
Step-by-step explanation:
If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.
The lines will have one positive y-intercept and one negative y-intercept that is not true.
What is the graph?The graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.
Determining:The lines will have one positive y-intercept and one negative y-intercept is NOT true.
If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, and y-intercept, and will share all of the same points. Answer b is the only choice left.
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How high is the toy after 1 second , what is the toy’e maximum height ? , how long is the toy in the air ?
Answer:
i.)12 feet
Step-by-step explanation:
ut+1/2gt^2
7×1+1/2×10×1^2 =12
There are three children in the McComb family. Which sample space represents the gender order, M (Male) or F(Female), in which the children could have been born?
Answer:
d
Step-by-step explanation:
{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}
Use a tree diagram to list the possibilities.
Answer:
The answer is D
Step-by-step explanation:
Your college fund has $56,000. It is currently in an account which pays 3.4% compounded quarterly. How much money will you have in 11 years
Answer:
$81,269.53
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 3.4% into a decimal:
3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034
Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:
[tex]A=56,000(1+\frac{0.034}{4})^{4(11)}[/tex]
[tex]A=81,269.53[/tex]
After 11 years, you will have $81,269.53
Which is the solution set for (z+4)>15
Answer:
Sol set = {12, 13, 14, 15, 16, 17,....... ".}
Step-by-step explanation:
[tex](z + 4) > 15 \\ z + 4 > 15 \\ z > 15 - 4 \\ z > 11 \\ z = \{12, \: 13, \: 14, \: 15, \: 16, \: 17, ........... \}[/tex]
Can anyone help??????
Answer:
C) 109.5
Step-by-step explanation:
Use cosine of 64°
cos 64° = 48/x
Put x on one side
x = 48/ cos 64°
x = 109.4962576
Answer:
The answer is C or 109.5 units
Step-by-step explanation:
We have to use the trig function cosine to find the answer.
cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
cosine of 64 = 0.438371147
the equation is: cos 64 = [tex]\frac{48}{hypotenuse}[/tex]
So using this equation,
we must divide 48 by the cosine of 64 to get the hypotenuse
this equals 109.5
The hypotenuse is our length that we need to find so the question is solved.
Hope This helps
Branliest is appreciated!
To play basketball with her friends, Evangeline needs to pump air in her ball, which is completely deflated. Before inflating it, the ball weighs 0.615 kilograms. Afterwards, it weighs 0.624 kilograms. The diameter of the ball is 0.24 meters.Assuming the inflated ball is perfectly spherical, what is the air density within it.
Answer:
1.24 kilograms per cubic meter.
Step-by-step explanation:
The air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]"
Air density:The initial weight of 7 ball [tex]= 0.615 \ kg\\\\[/tex]
weight of 7 inflated balls[tex]= 0.624 \ kg\\\\[/tex]
Calculating the mass (weight) of 7 air:
[tex]\to 0.624-0.615\ kg\\\\ \to 0.009\ kg\\\\[/tex]
Calculating the diameter of 7 balls:
[tex]\to 0.24 \ m\\\\[/tex]
Calculating the Radius of the ball:
[tex]\to \frac{\text{diameter}}{2}\\\\ \to \frac{0.24}{2}\\\\ \to 0.12\ m\\\\[/tex]
Calculating the volume of air in the ball:
[tex]\to \frac{4}{3} \pi r^3\\\\\to \frac{4}{3} \pi (0.12)^3 \\\\ \to 1.333333 \times 3.14 \times 0.001728 \\\\ \to 0.00723456\\\\[/tex]
Calculating the density of air:
[tex]\to \text{Air density}=\frac{\text{Mass}}{\text{volume}}\\\\[/tex]
[tex]=\frac{ 0.009}{0.00723456}\ \frac{kg}{m^3}\\\\ =1.244\ \frac{kg}{m^3} \\\\=1.24\ \frac{kg}{m^3}[/tex]
Therefore, the air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]".
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Please Help!!!!! 25 Points!!!!!!
Answer: 7 yards will be your answer.
Step-by-step explanation: I tried. Sorry if the answer is wrong!
Answer:
8 yards
Step-by-step explanation:
The small triangle is inside the big triangle and shares two of it's legs which means it is similar to the big triangle.
12:15
x:10
4:5
x must be 8
What are the surface area and volume ratios of a cylinder change if the radius and height are multiplied by 5/4 ?
Answer:
The ratio of the surface areas and volume is 8((5y+5x) /25xy)
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes.
Let us assume that the radius =x
Radius r=5x/4
And the height =y
Height h= 5y/4
We know that the total surface area of a cylinder is
A total = 2πrh+2πr²
We can factor out 2πr
A total = 2πr(h+r)
The volume of a cylinder is given as
v= πr²h
The surface area and volume ratios
Can be expressed as
2πr(h+r)/πr²h= 2(h+r)/rh
= (2h+2r)/rh= 2h/rh + 2r/rh
= 2/r + 2/h
= 2(1/r + 1/h)
Substituting our value of x and y
For radius and height we have
= 2(1/5x/4 + 1/5y/4)
=2(4/5x + 4/5y)
=2*4(1/5x + 1/5y)
= 8 (5y+5x/25xy)
Answer:
Ratio of surface area = 25/16
Ratio of volume = 125/64
Step-by-step explanation:
The surface area and volume of a cylinder are given by the formulas:
Surface area = 2*(pi*r^2 + pi*r*h)
Volume = pi*r^2*h
If we increase the radius and height by 5/4, we have that:
New surface area = 2*(pi*(5/4*r)^2 + pi*(5/4)*r*(5/4)*h) = (5/4)^2 * 2*(pi*r^2 + pi*r*h) = (5/4)^2 * Surface area
New volume = pi*(5/4*r)^2*(5/4)*h = (5/4)^3 * pi*r^2*h = (5/4)^3 * Volume
So the ratios are:
ratio of surface area = New surface area / Surface area = (5/4)^2 = 25/16
ratio of volume = New volume / Volume = (5/4)^3 = 125/64