Answer:
C. (-5,0) and (3,0)
Step-by-step explanation:
y= x² + 2x-15
y = 0
x² + 2x-15 = 0
(x - 3) (x + 5) = 0
x = 3 or x = -5
The x-intercepts of the graph of the function are (-5,0) and (3,0).
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the x-intercepts of the graph of the function,
We need to set y = 0 and solve for x.
So we have:
x² + 2x - 15 = 0
Factoring this quadratic equation.
(x + 5) (x - 3) = 0
Setting each factor equal to zero.
x + 5 = 0 or x - 3 = 0
Solving for x.
x = -5 or x = 3
Therefore,
The x-intercepts of the graph of the function are (-5,0) and (3,0).
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Can you help me plss!
(1/3) × the cone's volume = The cylinder's volume.
Step-by-step explanation:
Step 1:
The volume of any cone is obtained by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius ([tex]r^{2}[/tex]) and the height ([tex]h[/tex]).
So the volume of the cone, [tex]V=\pi r^{2} \frac{h}{3}[/tex].
Step 2:
The cylinder's volume is nearly the same as the cone but instead by multiplying [tex]\frac{1}{3}[/tex] we multiply with 1.
So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder ([tex]r^{2}[/tex]) and the height of the cylinder ([tex]h[/tex]).
So the the cone's volume, [tex]V = \pi r^{2} h[/tex].
Step 3:
Now we equate both the volumes to each other.
The cone's volume : The cylinder's volume = [tex]\pi r^{2} \frac{h}{3}: \pi r^{2} h[/tex] = [tex]\frac{1}{3} : 1[/tex].
So if we multiply the cone's volume with [tex]\frac{1}{3}[/tex] we will get the cylinder's volume with the same dimensions.
This table shows how many sophomores and juniors attended two school events. What is the probability that the student attended the jazz concert, given
Answer:
A. 0.60
Step-by-step explanation:
make a proportion so
36 over 60 = x over 100
36*100= 3600
3600/60
60
.60
The probability that the student attended the jazz concert is 0.60. The correct answer is option A.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
It is given from the table that the student who attended the jazz concert is 36 out of 60 students. Then the probability that the student attended the jazz concert is calculated as below:-
Probability = Number of favorable outcomes / Number of sample
Probability = 36 / 60
Probability = 0.60
Therefore, the probability that the student attended the jazz concert is 0.60. The correct answer is option A.
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Rewrite the following in the form log(c).
log(4)+log(5)
Yo sup??
by the property of log we can say that
laga+logb=logab
log4+log5=log4*5
=log20
Hope this helps
Determine the center and radius of the following circle equation:
22 + y2 + 8x – 12y + 3 = 0
Please help :)
Answer:
center(8x,12y) radius 3
Step-by-step explanation:
If i am doing this correct
question 1: find the volume of a cube whose total surface area is 486cm^2
Solution:
The surface area of cube is given as:
[tex]Surface\ area = 6a^2[/tex]
Where, "a" is the length of side of cube
Given that, surface area = 486 square centimeter
[tex]486 = 6a^2\\\\a^2 = \frac{486}{6}\\\\a^2 = 81\\\\a = 9[/tex]
Find the volume of cube:
[tex]volume\ of\ cube = a^3\\\\volume\ of\ cube = 9^3\\\\volume\ of\ cube = 9 \times 9 \times 9\\\\volume\ of\ cube = 729[/tex]
Thus volume of cube is 729 cubic centimeter
Which of the following equations is equivalent to x - y = 5?
x - 2y = 30
4x - 3y = 30
3x - 4y = 30
Answer:
[tex]6x-6y=30[/tex]
Step-by-step explanation:
The complete options are
a) x - 2y = 30
b) 4x - 3y = 30
c) 3x - 4y = 30
d) 6x - 6y = 30
The given equation is
[tex]x-y=5[/tex]
Verify option d
we have
[tex]6x-6y=30[/tex]
Divide by 6 both sides
[tex](6x-6y)/6=30/6[/tex]
[tex]\frac{6x}{6}-\frac{6y}{6}=\frac{30}{6}[/tex]
[tex]x-y=5[/tex]
therefore
[tex]x-y=5[/tex] and [tex]6x-6y=30[/tex] are equivalent
Answer:
3x -4y = 30
Step-by-step explanation:
What is the result when the number 22 is decreased by 9.1%?
Answer:
19.998
Step-by-step explanation:
Take the number and decrease (subtract) by 9.1% of the original number
22 - 22*9.1%
Change the percent to decimal form
22 - 22*.091
22 -2.002
19.998
Final answer:
The result when the number 22 is decreased by 9.1% is 20.0, after calculating 9.1% of 22, which is 2.002, and subtracting it from 22 and rounding to the nearest tenths place.
Explanation:
To find the result when the number 22 is decreased by 9.1%, you can use the following steps:
Calculate the decrease amount by finding 9.1% of 22: (9.1/100) × 22.
Subtract the decrease amount from the original number: 22 - (9.1% of 22).
Using a calculator, the decrease amount is:
(0.091) × 22 = 2.002.
Then subtract this from the original number:
22 - 2.002 = 19.998.
However, we need to report our final answer to the nearest tenths place since that is the precision of the number 9.1%. Therefore, we round 19.998 to 20.0 to reflect the proper significant figures.
So, the result when the number 22 is decreased by 9.1% is 20.0.
In triangle ABC, a = 12, _ B= 25°, and
C= 45°. Find b.
The value of b is 5.4
Explanation:
Given that ABC is a triangle.
It is also given that [tex]a=12[/tex] , [tex]\angle B=25^{\circ}[/tex] and [tex]\angle C=45^{\circ[/tex]
We need to find the value of b.
The value of b can be determined using the law of sine formula, which is given by
[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C}[/tex]
First, we shall find the angle of A.
Since, ABC is a triangle and all the angles in a triangle add up to 180°
Thus, we have,
[tex]\angle A+\angle B+\angle C=180[/tex]
[tex]\angle A+25+45=180[/tex]
[tex]\angle A+70=180[/tex]
[tex]\angle A=110^{\circ}[/tex]
Thus, the value of angle A is 110°
Let us substitute these values in the law of sine formula.
Hence, we get,
[tex]\frac{12}{sin \ 110^{\circ}} =\frac{b}{sin \ 25^{\circ}}[/tex]
Simplifying, we get,
[tex]\frac{12}{0.9397} =\frac{b}{0.423}[/tex]
Multiplying both sides of the equation by 0.423, we get,
[tex]\frac{12\times 0.423}{0.9397} =b[/tex]
Simplifying, we get,
[tex]\frac{0.5076}{0.9397} =b[/tex]
Dividing, we have,
[tex]5.4=b[/tex]
Thus, the value of b is 5.4
Neil has 3 partially full cans of white paint . They contain 1/3 gallon , 1/5 gallon and 1/2 gallon of paint. About how many paint does Neil have in all
Answer:
31/30 gallons
Step-by-step explanation:
finding the lowest common denominator for all three numbers. so 1/3 becomes 10/30, 1/5 becomes 6/30, and 1/2 becomes 15/30. 10/30+6/30+15/30=31/30
Answer:31/30
Step-by-step explanation:
you have to first find a common denominator. Which in this case is 30 so then you have to multiply by the same number for both bottom and top number of the fraction. 1/3 = 10/30 1/5=6/30 1/2=15/30. Then, you just have to add JUST THE TOP NUMBERS. You get 31/30 then divide that and i will leave that last part to you. Hope this helps!
the perimeter of a rectangle is 400 meter. The length is three times the width. Which of the following best describes the length of the rectangle?
Length of the rectangle is 150 m.
Step-by-step explanation:
Step 1:
Let the width of the rectangle be x. Then the length = 3x. Given that perimeter = 400 m, find the length.
Perimeter of the rectangle = 2 (length + breadth)
400 = 2 (3x + x)
400 = 8x
∴ x = 400/8 = 50
⇒ Width is 50 m
∴ Length = 3x = 150 m
Craig has the following data: 14,14,16,b,1 If the range is 25, what is the value of b?
Final answer:
The student needs to find the missing number 'b' in a data set, given that the range is 25. Since we know the smallest value is 1, adding the range to that value gives us the largest possible number, which in this case is 26. Therefore, 'b' must be 26 to achieve the specified range.
Explanation:
The student is asking about finding a missing value in a set of numbers given the range of the data set. To find the value of b, we must remember the definition of range: Range is the difference between the largest and smallest values in a set.
With the knowledge that the range is 25, and having the numbers 14, 14, 16, and 1, we identify 1 as the smallest value.
If we add the range to the smallest number (1 + 25), we get the largest number the set could contain, which is 26.
Since the other numbers in the set are all smaller than 26, b must equal 26 for the range to be 25.
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi, and make certain to show your work. Hint: you may need to find the volume of the component shapes.
The volume of the prop is calculated to be 2,712.96 cubic inches.
Step-by-step explanation:
Step 1:
The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.
Step 2:
The volume of a cone is determined by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.
The volume of the cone : [tex]V=\pi r^{2} \frac{h}{3}[/tex] = [tex]3.14 \times 9^{2} \times \frac{14}{3}[/tex] = 1,186.92 cubic inches.
Step 3:
The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying [tex]\frac{4}{3}[/tex] with π and the cube of the radius (r³).
Here the radius is 9 inches. We take π as 3.14.
The volume of a full sphere = [tex]V=\frac{4}{3} \pi r^{3}[/tex] = [tex]\frac{4}{3} \times 3.14 \times 9^{3}[/tex] = 3,052.08 cubic inches.
The volume of the half-sphere = [tex]\frac{3,052.08}{2}[/tex] = 1,526.04 cubic inches.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.
Which is the most accurate way to estimate 52% of 71?
To estimate 52% of 71, you can use either the proportion method or the multiplication method by setting up a proportion or multiplying 0.52 by 71.
Explanation:To estimate 52% of 71, you can use either proportion or multiplication. Here's how:
Proportion method: Set up the proportion 52/100 = x/71, where x represents the unknown value. Cross-multiply and solve for x. Multiplication method: Multiply 52% (or 0.52) by 71.Using the proportion method:
52/100 = x/71
71 * 52 = 100 * x
x = 36.92 (rounded to 37)
Using the multiplication method:
0.52 * 71 = 36.92 (rounded to 37)
The area of a rectangle is 33 m-, and the length of the rectangle is 5 m less than twice the width. Find the dimensions of the rectangle.
Answer:
x = 9.25
y = 13.5
Step-by-step explanation:
area = 33
let length be y and width be x
2x - 5 = y
area of rectangle = length * breadth
(2x-5)(x)=33
2x²-5x=33
2x²-5x-33=0
solving quadratic equation
x = 9.25
y = 13.5
Samantha Vega's gross weekly salary is $600. Her weekly federal withholding is $35.00. The Social Security
tax is 6.2% of the first $97,500. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay.
Each week she pays $12.40 for medical insurance. What are Samantha's total deductions?
Answer:
$102.30
Step-by-step explanation:
Answer:
2600
The gross pay $2,600 if $572 is the tax amount.
Step-by-step explanation:
Ty puts 9 Sports cards each on the front and back of each page in his cars album. How many pages are in Ty’s album if he has 144 cards?
SHOW WORK
grusi lob ze cruz?masi pa koi foitaitua leo leone fatua fatui?
Select all that apply. A coin is flipped and a number cube is rolled. Which of the following are true?
The sample space has 12 different outcomes.
The sample space has 8 different outcomes.
Each result is equally likely.
Heads and an even number are very likely.
Answer:
1. True
2. False
3.True
4.False
In a study of crime, the FBI found that 13.2% of all Americans had been victims of crime during a 1-year period. This result was based on a sample of 1,105. Estimate the LOWER LIMIT of the confidence interval of the percentage of victims at the 99% confidence level.
Please round to the nearest whole number.
Answer:
11%
Step-by-step explanation:
The margin of error is the standard error times the critical value.
For a proportion, the standard error is:
σ = √(pq / n)
σ = √(0.132 × 0.868 / 1105)
σ = 0.0102
Since n is large, we can approximate the critical value using a normal distribution. For 99% confidence, the critical value is 2.576.
The margin of error is:
ME = 0.0102 × 2.576
ME = 0.026
The confidence interval is 0.132 ± 0.026. So the lower limit is 0.106, or 10.6%. Rounded to the nearest whole number, that's 11%.
a rectangle is 68 inches by 42 inches. Find the angles that a diagonal makes with each side of the rectangle.
Answer:
90⁰
Step-by-step explanation:
The diagonal of the rectangles forms two angles with the sides, about 32 degrees and 58 degrees respectively. These are found using the Pythagorean theorem to find the length of the diagonal, and then the arctan function to find the angles.
Explanation:To find the angle that the diagonal makes with the sides of the rectangle, first calculate the length of the diagonal which can be found using the Pythagorean Theorem. 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. We can write this as: c² = a² + b². In this case, the length and width of the rectangle are the two sides (a and b) and the diagonal is the hypotenuse (c).
So a = 68 inches, b = 42 inches. Plugging these into our formula gives: c² = 68² + 42², so c = √[(68²) + (42²)] which approximates to 80 inches.
Next, calculate the angles using the inverse tangent (or arctan) function: θ = arctan(opposite/adjacent). In this case, the angles are = arctan(42/68) and arctan(68/42). This gives us angles of approximately 32 degrees and 58 degrees.
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Noah wants to clean his second story windows and plans to buy a ladder that will reach at least
22
feet high. If he leans the ladder against the house so that the base of the ladder makes a
51.5
∘
angle with the ground, how long of a ladder should he buy? Please round to one decimal place
Answer:
Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.
Step-by-step explanation:
Given:
Noah has to reach at least 22 ft height.
Angle made by the base of ladder with the ground = 51.5°
To find the length of the ladder.
Solution:
On drawing the situation, we get a right triangle. The hypotenuse of the triangle represents the length of the ladder.
In triangle ABC.
∠C = 51.5°
AB = 22 ft
Applying trigonometric ratio to find AC (length of the ladder).
[tex]\sin\theta = \frac{Opposite\ side}{Hypotenuse}[/tex]
[tex]\sin C=\frac{AB}{AC}[/tex]
Plugging in values.
[tex]\sin 51.5\°=\frac{22}{AC}[/tex]
Multiplying AC both sides.
[tex]AC\sin 51.5\°=\frac{22}{AC}\times AC[/tex]
[tex]AC\sin 51.5\°=22[/tex]
Dividing both sides by [tex]\sin 51.5\°[/tex]
[tex]\frac{AC\sin 51.5\°}{\sin 51.5\°}=\frac{22}{\sin 51.5\°}[/tex]
[tex]AC=\frac{22}{\sin 51.5\°}[/tex]
[tex]AC=28.1\ ft[/tex]
Thus, Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.
15,35,40 will it make a right triangle
Answer:
NO.
Step-by-step explanation:
If it is a right triangle then by the Inverse of the Pythagoras Theorem:
40^2 = 35^2 + 15^2
Testing:
40^2 = 1600
35^2 + 15^2 = 1225 + 225 = 1450
So the answer is NO>
Answer:
NO.15, 35, 40 it will make an obtuse triangle.Step-by-step explanation:
If a ≤ b ≤ c are sides of a triangle, then a + b > c.
We have a = 15, b = 35, c = 40.
Check:
15 + 35 = 50 > 40 CORRECT
These sides can be the sides of a triangle.
If a ≤ b ≤ c are sides of a triangle, then
if a² + b² = c², then it's a right triangle
if a² + b² < c², then it's an obtuse triangle
if a² + b² > c², then it's an acute triangle
Check:
15² + 35² = 225 + 1225 = 1450
40² = 1600
1450 < 1600 ⇒ 15² + 35² < 40²
Therefore it's an obtuse triangle
a car rental company charges $75.00 rental fee plus $30.00 per day. Selena paid $225.00 to rent car
Answer:
5 days
Step-by-step explanation:
First subtract the flat fee so that you know you just have the price of the days
225-75
150 Then divide by 30, the day rate so you know how many days it was
150/30= 5
Selena had the car for 5 days
PLEASE HELP ME WITH THIS ASAP
Answer:
1900 ft
Step-by-step explanation:
To find the area where roses will be planted, find the area of the 2 triangles. 60×38 divided by 2 = 1140ft. 40×38 divided by 2 = 760. 760+1140=1900
Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $195,000 at 6.6% interest, compounded monthly?
Answer:
$195P00*0.0055(1+0.0055)^360
____________________________
(1+0.0055)^360-1
what is equivalent to 3/12 and 1/6
Answer:
1/4 and 2/12
Step-by-step explanation:
If you mulitply both the numerater and denominator by 2 (or any number) it will be equivelent.
1/6 is equivelient to 2/12, 3/18, etc.
However, if you divide 3/12, you get 0.25, which is equivelent to 1/4
A circle with circumference 6 has an arc with a 60° central angle.
What is the length of the arc?
Answer:
length of an arc = 1unit
Step-by-step explanation:
given that the circumference of a circle = 6
central angle = 60
length of the arc =?
recall that the circumference of a circle = 2πr
6 = 2πr
r = 6/2π
now to calculate the length of an arc
recall,
length of an arc = 2πr(Ф/360)
length of an arc = 2π(6/2π) × 60/360
length of an arc = 6 × 60/360
length of an arc = 360/360
length of an arc = 1unit
therefore the length of the arc whose circumference is 6 and arc angle is 60° is evaluated to be 1unit
The elevation of the surface of the Dead Sea is -424.3 meters. In 2005, the height of Mt. Everest was measured as 8,844.43 meters. How much higher was Mt. Everest?
Answer:
8,420.43 meters higher im pretty sure
Step-by-step explanation:
If you do 8,844.43-424.3, you get 8,420.83
Answer:
9,268.73 meters higher
Step-by-step explanation:
Add the elevation of Mt.Everest to the absolute value of the elevation of the Dead Sea. That equation looks like: 8,844.43 + |-424.3| = 9,268.73
Mt.Everest was 9,268.73 meters higher than the Dead Sea in 2005.
Roshanda bought pound of ham and pound of roast
beef. How much more roast beef than ham did she buy?
Write in simplest form
Final answer:
Roshanda bought the same amount of roast beef as ham, 0 pounds.
Explanation:
To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the weight of the ham from the weight of the roast beef. Roshanda bought 1 pound of ham and 1 pound of roast beef, so the difference is 1 pound minus 1 pound, which equals 0 pounds. Therefore, Roshanda did not buy more roast beef than ham, they bought the same amount.
Roshanda bought 1/4 pound more roast beef than ham.
To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the amount of ham from the amount of roast beef.
Given:
Ham = 5/8 pound
Roast beef = 7/8 pound
To find the difference:
Roast beef - Ham
= (7/8) - (5/8)
To subtract fractions, we need a common denominator, which is 8 in this case.
= (7/8) - (5/8)
= (7 - 5)/8
= 2/8
Now, simplify the fraction:
2/8 = 1/4
So, Roshanda bought 1/4 pound more roast beef than ham.
Question
Roshanda bought 5/8 pound of ham and 7/8 pol 11 d of roast beef. How much more roast beef than ham did she buy? Write in simplest form.
An opaque bag contains 3 green marbles, 3 red marbles. If two consecutive marbles are drawn without replacement what is the probability that they will both be green?
Final answer:
The probability of drawing two green marbles consecutively without replacement from a bag containing 3 green and 3 red marbles is 1/5 or 20%.
Explanation:
The probability that both marbles drawn consecutively from an opaque bag without replacement will be green is calculated by multiplying the probability of the first event by the probability of the second event. Here, we have 3 green marbles out of a total of 6 marbles. So, the probability of drawing the first green marble is 3/6 or 1/2. After drawing one green marble, there are now 2 green marbles left out of 5 total marbles. Therefore, the probability of drawing a second green marble is now 2/5. To find the combined probability, we multiply these two probabilities together: (1/2) × (2/5) which equals 1/5 or 0.2. Hence, there is a 20% chance that both marbles drawn will be green.
1 2/5 hours in minutes
Answer:
84 minutes
HOPE THIS HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
An hour is 60 minutes
60 x 2/5 = 24
24 minutes plus an hour (60 minutes)
= 84