Answer:
[tex]\pm11,\pm1,\pm\frac{11}{5},\pm\frac{1}{5}[/tex]
Step-by-step explanation:
The given polynomial function is
[tex]f(x)=5x^3-7x+11[/tex]
According to the Rational Roots Theorem, the ratio of all factors of the constant term expressed over the factors of the leading coefficient.
The potential rational roots are
[tex]\pm\frac{11}{1}=\pm11[/tex]
[tex]\pm\frac{1}{1}=\pm1[/tex]
[tex]\pm\frac{11}{5}[/tex]
[tex]\pm\frac{1}{5}[/tex]
In the Stoneridge apartment complex, 35% of apartments have one bedroom. If there are 49 one-bedroom apartments, what is the total number of apartments at Stoneridge?
Answer:
140
Step-by-step explanation:
35/ 100 = 49/?
49 times 100 equals 4900
4900/35 is 140
Answer:71 Apartments
Step-by-step explanation: 35/49=x/100
49x=3500
x=71
The number of tourists at the beach per weekend in July was 55,000. In November, the number of tourists per weekend was 18,000. Find the percent change from July to November?
Answer:
32.7 percent
Step-by-step explanation:
18000 divided by 55000
Ray Company received a shipment of 25 cartons of stereos. In each carton were five stereos. Each stereo sells for $80 and has a $30 cost to Ray. Assuming Ray sells all the stereos, what would the company's profit be?
A. $2,560 B. $560 C. $6,250 D. $625
Answer:
C ($6,250)
Step-by-step explanation:
25 cartons with 5 stereos per carton=125 stereos total
profit for one stereo=80-30=50
125*50= 6250
After selling all the stereos, the company's profit will be $ 6250.
What is Profit?Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.
Here, Ray have 25 cartons with 5 stereos per carton
So total Ray have, 25 X5 = 125 stereos
profit on one stereo = 80 - 30 = $50
Total profit on 125 stereos = 125*50= $ 6250
Thus, after selling all the stereos, the company's profit will be $ 6250.
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Which ordered pair represents a solution to f(x)=-5 if f(-1)?
A. (-1, -6)
B. (-4, -1)
C. (-1, -5)
D. (-6, -1)
Answer:
C
Step-by-step explanation:
Given
f(x) = - 5
This will result in a value of - 5 for any value of x, hence
f( - 1) = - 5
Thus (- 1, - 5) ← represents a solution
50 points Item 15 Simplify the expression. (15k)2 The simplified expression is
30k just multiply the 2 by 15 and get 30k
Find the exact circumference of a circle with the given radius. x/2 miles C =
¼x miles x miles 2x miles
Answer:
[tex]\pi[/tex] x miles
Step-by-step explanation:
Circumference, C= 2[tex]\pi r[/tex]
r=radius = x/2
C= 2×[tex]\pi[/tex] × x/2
C=[tex]\pi[/tex] x
Answer:
πx miles
Step-by-step explanation:
Given in the question,
radius of a circle = x/2 miles
To find circumference of a circle we will use following formula
2π * r
where π is constant = 3.14
r is radius of circle
Plug values in the formula
2(3.14)(x/2)
2 will cancel out
So we are left with 3.14x miles or πx milesQuotient to a Power Rule (4c^3/7b^4)^2 Enter the result.
Answer:
The result is 16c^6/49b^8.
The figure ABCD is made up of two different triangles.ABD is a right-angled triangle.AB=25 cm,AD=60 cm,BD=65 cm and CE=45 cm.Find the area of figure ABCD.
the area of ABCD is 135
Answer:
2212.5 cm²
Step-by-step explanation:
ABCD is constructed from 2 right triangles ABD and BCD
The area (A ) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
In ΔABD, b = AD = 60 and h = AB = 25, hence
A = [tex]\frac{1}{2}[/tex] × 60 × 25 = 30 × 25 = 750 cm²
-----------------------------------------------------------------------------
In ΔBCD, b = BD = 65 and h = CE = 45, hence
A = [tex]\frac{1}{2}[/tex] × 65 × 45 = 1462.5 cm²
----------------------------------------------------------------------------
The area of figure ABCD = area of ΔABD + area of ΔBCD
A = 750 + 1462.5 = 2212.5 cm²
Find the volume of the cylinder. Use 3.14 for (π Pi) 34 m on top and 27 m down on the right.
Is 34 the diameter or radius?
find the slope of the line shown
Answer:
The slope m = -1Step-by-step explanation:
Look at the picture.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (-5, 2) and (-3, 0). Substitute:
[tex]m=\dfrac{0-2}{-3-(-5)}=\dfrac{-2}{2}=-1[/tex]
How many 1 3 ounce servings are available in 6 ounces? A) 10 servings B) 14 servings C) 18 servings D) 24 servings
Answer:
Step-by-step explanation:
the answer is 18
How to do multiplication
To do multiplication is to take (usually) two sets on numbers and put them together to make them one.
For example: let’s say you want to multiply 5 and 3
This means you do 5➕5➕5
Your answer would be 15.
5✖️3= 15
Now let’s say you want to multiply a two digit number
10✖️12
This means you add 10 together 12 times.
10. First do 0✖️2 which is 0 so put it at the bottom. Then 1✖️2 which is 2
x 12. Then do 1✖️0 and 1✖️1
——————
20
➕11x. You put a place holder in this case (x) which equals 0
———————
120
Then you are left with your answer
Hope this helps! :3
Multiplication is like adding but with less work.
For example 9x9 is equal to
9+9+9+9+9+9+9+9+9.
Another example would be 15x3
which is equal to
15+15+15
Or
3+3+3+3+3+3+3+3+3+3+3+3+3+3+3z
Of the 300 students in a home room, 120 play a school sport. What percent of students play a school sport?
Equation:
Solution:
Answer:
40%
Step-by-step explanation:
120/300 is 0.4 convert to percentage it is 40%
QUICKKK
What is the image of (-1,-6) after a reflection over the x-axis ?
Answer:
I don't actually have an image but i think the coordinate point is (-6,1)
I hope this helps
3 A classroom is arranged with 8 seats in the front row, 10 seats in the middle row, and 12 seats in the back row. The teacher randomly assigns seats to students as they enter the classroom. What is the probability that the first student who enters the classroom will be assigned a seat in the front row? 2 5 A 2 3 B 4 11 4 15
Answer:
0.266
Step-by-step explanation:
Total No of seats in class = 8+10+12 = 30
probability that first student will be assigned first row will be: 8/30 = 0.266
because there are 8 front row seats and total seats are 30.
The probability that the first student who enters the classroom will be assigned a seat in the front row is; Option D; 4/15
We are told;
Number of front row seats = 8 seats
Number of middle row seats = 10 seats
Number of back row seats = 12 seats
Thus;
Total number of seats in classroom = 8 + 10 + 12
>> 30 seats
Now, we want to find the probability that the first student who enters the classroom will be assigned a seat in the front row.
Thus;
P(1st student sits in front row) = 8/30
This can be reduced to get;
P(1st student sits in front row) = 4/15
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Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has oil and the test predicts it?
A. 0.09
B. 0.11
C. 0.36
D. 0.44
Answer: A. 0.09
Step-by-step explanation:
So if you subtract 45% from 80% and thats when you get 0.09
Minh is packing books into boxes. The mass of one of the boxes is 20 kilograms. If the box holds 10 books that each have the same mass, what is the mass of each book in grams?
The mass of each book in the box is 2000 grams.
Explanation:In this question, we are given the total mass of the books in a box and the number of books in that box. We are being asked to determine the mass of each book in grams.
We know that there are 10 books in the box and the total mass for all the books is 20 kg. As 1 kilogram is equal to 1000 grams, the total mass of the books in the box is 20 kg x 1000 g/kg = 20000 grams.
Now, to find the mass of each book, we divide this total mass by the number of books. Therefore, the mass of each book is 20000 g / 10 books = 2000 grams per book.
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Each book has a mass of 2,000 grams.
Explanation:To find the mass of each book in grams, we need to convert the mass of the box from kilograms to grams by multiplying it by 1000.
So, 20 kilograms is equal to 20,000 grams.
Since there are 10 books in the box, we can divide the mass of the box by the number of books to find the mass of each book.
Therefore, each book has a mass of 2,000 grams.
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Q is the midpoint PR.If PQ =2x and QR= x+8.What is PQ?
2x=x+8
Subtract x on both sides
X=8
So PQ=8
A rectangular prism has a height of 8 meters and a volume of 640cubic meters. What is the area of the base of the prism?
Can you help me find the answer for number 2
Here is the work along with the answer to the problem.
Find the area of triangle AOB
Answer:
9√3 unit^2.
Step-by-step explanation:
The area = 1/2 6^2 sin 60
= 1/2 * 36 * √3/2
= 9√3
The area is [tex]9\sqrt{3}un^2.[/tex]
Note that: triangle AOB is an equilateral triangle because:
OA = OB (both are radius)
So ∠OAB = ∠OBA
Given that ∠AOB=60 degree.
The sum of three angles of a triangle is 180 degrees.
So,
∠OAB + ∠OBA + ∠AOB = 180
∠OAB + ∠OBA + 60 = 180
∠OAB + ∠OBA = 120
∠OAB + ∠OAB = 120
2∠OAB = 120
∠OAB = 60
It means ∠OAB = ∠OBA =60.
Since all the angles of these triangle is 60 degree, so triangle AOB is an equilateral triangle.
Given: side length = a = 6.
The area of the triangle is: [tex]\frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{3}}{4}\left(6^{2}\right)=\frac{\sqrt{3}}{4}\left(36\right)=9\sqrt{3}[/tex]
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Angelina drew a net of a container in the shape of a triangular pyramid. The base is an isosceles triangle with sides measuring 24 cm, 20 cm, and 20 cm.Which statement about the area of the pyramid is true?
A. The base cm is 384cm
B.The Lateral area is 692cm
C.The surface area is 740cm
D. The area of each congruent face is 264cm
Answer:
Option B. The Lateral area is 692 cm2
Step-by-step explanation:
Verify each statement
case A) The area of the base is 384 cm2
The statement is False
Because
The area of the base is
[tex]B=\frac{1}{2}(24)(16)=192\ cm^{2}[/tex]
case B) The Lateral area is 692 cm2
The statement is True
Because
we know that
The lateral area is equal to the area of its three triangular lateral faces
so
[tex]LA=2(\frac{1}{2}(20)(22))+ \frac{1}{2}(24)(21)=692\ cm^{2}[/tex]
case C) The surface area is 740 cm2
The statement is False
we know that
The surface area is equal to the lateral area plus the area of the base
so
[tex]SA=LA+B[/tex]
we have
[tex]LA=692\ cm^{2}[/tex]
[tex]B=192\ cm^{2}[/tex]
substitute
[tex]SA=692+192=884\ cm^{2}[/tex]
case D) The area of each congruent face is 264 cm2
The statement is False
The area of each congruent face is equal to
[tex]A=\frac{1}{2}(20)(22)=220\ cm^{2}[/tex]
State 1 positive and 1 negative coterminal angle for 1250 degrees
Answer:
[tex]\large\boxed{530^o\ and\ -190^o}[/tex]
Step-by-step explanation:
[tex]\text{Coterminal angle with}\ \alpha:\\\\\alpha+360^o\ and\ \alpha-360^o.\\\\\text{Firs\ step}\\\\1250^o:360^o=3\ and\ 170^o\ rest\\\\1250^o=170^o\\\\170^o+360^o=530^o\\\\170^o-360^o=-190^o[/tex]
Answer the question present in the picture
Translate this sentence into an equation. The product of Mabel's score and 6 is 90 . Use the variable m to represent Mabel's score.
product is the answer to a multiplication problem mx6=90
The sentence 'The product of Mabel's score and 6 is 90' translates into the equation 'm * 6 = 90' in mathematics, where m represents Mabel's score.
Explanation:The sentence provided can be translated into an equation. In mathematics, the phrase 'the product of' means to multiply. Here, Mabel's score is represented by the variable m. The 'product of Mabel's score and 6' is the same as saying 'm multiplied by 6'. This is said to be equal to 90. Therefore, the equation that represents this sentence is m * 6 = 90.
To translate the sentence 'The product of Mabel's score and 6 is 90' into an equation using the variable m to represent Mabel's score, we can write:
6m = 90
This equation states that the product of Mabel's score (m) and 6 is equal to 90.
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What is the measure of angle 4
Answer:
35 degress
Step-by-step explanation:
Answer: 108 degress
Step-by-step explanation:
A local grocer cut his marketing budget by 38% last year. He spent only $650 on marketing this year and is happy with his decision. How much did the grocer spend on marketing last year?
Answer:
the amount the grocer spend on marketing last year = $ 1048.38
Step-by-step explanation:
To find the budget we will subtract the current marketing budget number from 100
As 38% = 0.38
i.e, 100 - 0.38= 0.62
Now divide the previous year budget amount percentage found by the amount spent this year
=650 / 0.62
= 1048.38
Final answer:
To find out how much the grocer spent on marketing last year, divide the current amount he spent by the remaining percentage of the original amount before the cut.
Explanation:
To find out how much the grocer spent on marketing last year, we need to determine the original amount before the 38% cut. Let's assume the original amount is x. If the grocer cut the marketing budget by 38%, it means he spent 100% - 38% = 62% of the original amount. The equation can be set up as: 0.62x = $650. To solve for x, divide both sides of the equation by 0.62. So, x = $650 ÷ 0.62 = $1048.39.
a cake recipe call for 2 1/2 cups of sugar. how many cups of sugar are needed to bake 5 cakes
The number of sugar cups required will be 12.5.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a cake recipe calls for 2¹/₂ cups of sugar. The number of cups of sugar for 5 cakes will be calculated as,
Number = 5 x ( 2¹/₂ )
Number = 5 x 2.5
Number = 12.5 cups
Therefore, the number of sugar cups required will be 12.5.
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To bake 5 cakes, you would need 12 1/2 cups of sugar by multiplying 2 1/2 cups, the amount needed for one cake, by the number of cakes.
Explanation:To calculate how many cups of sugar are needed to bake 5 cakes when a single cake recipe calls for 2 1/2 cups of sugar, you can simply multiply the amount of sugar needed for one cake by the number of cakes you plan to bake. Therefore, you have:
2 1/2 cups of sugar/cake × 5 cakes = 12 1/2 cups of sugar.
Here's the step-by-step calculation:
First, convert the mixed number to an improper fraction: 2 1/2 cups = 5/2 cups.Multiply the amount needed for one cake by the number of cakes: (5/2 cups) × 5 = 25/2 cups.Convert the improper fraction back to a mixed number: 25/2 cups = 12 1/2 cups.Therefore, you need 12 1/2 cups of sugar to bake 5 cakes.
PLEASE HELP!!Select the expressions that are equivalent to 3/4x^3 . Select all that apply.
Answer:
c.) (3x^ -3)/4
Step-by-step explanation:
when you move something from the top to the bottom or vice versa, it becomes negative or in this case, changes the sign
Answer:
im pretty sure its c
Step-by-step explanation:
You and another person are sunbathing on the beach near a lifeguard station. The other person chooses a spot that is the same distance from the shoreline but 11 feet closer to the station than you. The angles of elevation from you and the other person to the top of the lifeguard station are 36 degrees and 46 degrees, respectively. Estimate the height of the lifeguard station to the nearest tenth of a foot.
Answer: 26.8 feet
Step-by-step explanation:
In the figure attached you can see two right triangles triangle ABD and a triangle ACD.
You are located at point B and the other person at point C.
The approximate height of the lifeguard station is x.
Keep on mind that:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
Therefore:
For the triangle ABD:
[tex]tan(36\°)=\frac{x}{DC+11}[/tex] [EQUATION 1]
For the triangle ACD:
[tex]tan(46\°)=\frac{x}{DC}[/tex] [EQUATION 2]
Solve from DC from [EQUATION 2]:
[tex]DC=\frac{x}{tan(46\°)}[/tex]
Substitute into [EQUATION 1] and solve for x:
[tex]tan(36\°)=\frac{x}{(\frac{x}{tan(46\°)}+11)}\\tan(36\°)(\frac{x}{tan(46\°)}+11)=x\\11*tan(36\°)=x-\frac{xtan(36\°)}{tan(46\°)}\\7.991=0.298x[/tex]
[tex]x=26.81ft[/tex]≈26.8ft