Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
find the coordinates of the point whose ordinate is -7 and lies on y axis
Answer:
(0,-7)
Step-by-step explanation:
If nay point is form (x,y)
x is abscissa can be also called x axis coordinate
y is ordinate can be also called y axis coordinate
ordiantes are points lying on y axis.
For any point lying on y axis, its x-axis coordinate will be 0
given that ordinate is -7. it means that value of y coordinate is -7
Thus, coordinates of the point is (0,-7)
Haley works at a candy store. There are 10 types of bulk candy. Find the probability that one type of candy will be chosen more than once in 10 trials.
Answer:
Probability that one type of candy will be chosen more than once in 10 trials = 0.2639
Step-by-step explanation:
This is a binomial experiment because
- A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
- It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (10 trials, with the outcome of each trial being that we get the required candy or not)
- The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 10 trials
x = Number of successes required = number of times we want to pick a particular brand of candy = more than once, that is > 1
p = probability of success = probability of picking a particular brand of candy from a bulk with 10 different types of candies = (1/10) = 0.10
q = probability of failure = Probability of not picking our wanted candy = 1 - p = 1 - 0.1 = 0.90
P(X > 1) = 1 - P(X ≤ 1)
P(X ≤ 1) = P(X = 0) + P(X = 1)
P(X = 0) = ¹⁰C₀ (0.10)⁰ (0.90)¹⁰⁻⁰ = 0.3486784401
P(X = 1) = ¹⁰C₁ (0.10)¹ (0.90)¹⁰⁻¹ = 0.387420489
P(X ≤ 1) = 0.3486784401 + 0.387420489 = 0.7360989291
P(X > 1) = 1 - 0.7360989291 = 0.2639010709 = 0.2639
Hope this Helps!!!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Indicate in standard form the equation of the line through the given points. P(0, -4), Q(5, 1)
Answer:
x -y =4
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
= (1- -4)/(5 - 0)
= (1+4)/(5-0)
5/5
= 1
Then we can use slope intercept form
The slope is 1 and the y intercept is -4
y = mx+b
y = 1x-4
We want it in standard form
Ax + By = C where A is a positive integer
Subtract x from each side
-x +y = -4
Multiply by -1
x -y =4
Answer:
x -y =4
Step-by-step explanation:
1
If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term
If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].
We're given
[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]
So the first five terms in the GP are
3, 6, 12, 24, 48
Adding up the first four gives a sum of 45.
If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:
[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]
Multiply both sides by 2:
[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]
Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:
[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]
Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].
u can look this up here on brainly for an answer source if you want but do the one that has the greatest points... its on google
Answer:
First one is 41
Second one is 87
Step-by-step explanation:
Make the shaded part as a trapezoid which is (3+6)*10/2 you just have to get rid of 2*2. So you get 41 as the answer.
The unshaded part will be 16*8 then subtracts the shaded part which is 41. Then you get the answer 87.
quadratic equation grade :9
10 points;)
Answer:
Step-by-step explanation:
put (x+2)/(x-2)=a
a-1/a=5/6
[tex]multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\\frac{x+2}{x-2} =\frac{3}{2} \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\[/tex]
[tex]or~3a+2=0\\a=-2/3\\\frac{x+2}{x-2} =-\frac{2}{3} \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5[/tex]
2.
put (x+3)/x=a
a+1/a=4 1/4
[tex]a+\frac{1}{a} =\frac{17}{4} \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\\frac{x+3}{x} =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\\frac{x+4}{x} =\frac{1}{4} \\4x+16=x\\3x=-16\\x=-16/3[/tex]
A group of students made trees out of paper for a scene in a school play. The trees are shaped like square pyramids. The base is 70 cm and the height 140 cm. How much paper will it take to make each tree, including the bottom?
Answer:
26.4ft²
Step-by-step explanation:
I first converted the centimeter values to feet
140Cm x 30.48 = 4.59
70cm x 30.48 = 2.3
the paper required is approximately equal to the area of the pyramid.
area of pyramid is equal to area of triangle + base²
Are of triangle = 1/2 x b xh
= 4 x 1/2 x4.59x2.3 + (2.3)²
= 2 x 4.59 x 2.3 + 5.29
= 26.4 feet²
therefore it will take 26.4 feet² paper to make each tree, including the bottom.
Answer:
It is actually 24500
Step-by-step explanation:
Hope this helped! I had the same lesson.
Find the distance between the points (0, 10) and (–9, 1).
The distance between the points (0, 10) and (–9, 1) is 12.73 units.
Given the following data;
Points ([tex]x_1, x_2[/tex]) = 0, -9
Points ([tex]y_1, y_2[/tex]) = 10, 1
To find the distance between the points;
In Mathematics, the distance between two points on a plane is calculated by using the formula;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 }[/tex]
Substituting the points into the formula, we have;
[tex]Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}[/tex]
Distance = 12.73 units
Therefore, the distance between the points is 12.73 units.
Find more information: https://brainly.com/question/13272812
Solve for x Your answer must be simplified. 2x<15 Khanacademy
Answer:
[tex]\boxed{x < 7.5}[/tex]
Step-by-step explanation:
=> 2x < 15
Dividing both sides by 2
=> x < 15/2
=> x < 7.5
Answer:
[tex]\boxed{x<\frac{15}{2}}[/tex]
Step-by-step explanation:
[tex]2x<15[/tex]
Divide both parts by 2.
[tex]\displaystyle \frac{2x}{2} <\frac{15}{2}[/tex]
[tex]\displaystyle x<\frac{15}{2}[/tex]
someone plz help !
A town currently has a population of 1,000,000, and the population is increasing 6 percent every year. Write a recursive function in now-next form to predict the population at any year in the future.
Answer:
Y=x(t)(0.06) + x
Y =predicted population
X= population currently
t= number of years
Y= 60000(t) + 1000000
Step-by-step explanation:
Let the current population be x
X= 1000000
The rate of increase= 6% each year
Let the the predicted population= y
If the population is to increase by 6% each year the function predicting the population at the future will be
Y=x(t)(0.06) + x
The only changing value in the above formula is the time.
Y= 1000000(0.06)(t) +1000000
Y= 60000(t) + 1000000
Answer: The actual answer is:
next = now x 1.06, starting at 1,000,000
what is the range of the function: h(x)=x+1/x^2 - 7x+10
Answer:
(-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)
Step-by-step explanation:
To make it easier to differentiate, we'll rewrite the function as ...
h(x) = 2/(x-5) -1/(x-2)
Then the derivative is ...
h'(x) = -2/(x-5)^2 +1/(x-2)^2
This will be zero when ...
-2(x-2)^2 +(x-5)^2 = 0
-2(x^2 -4x +4) +(x^2 -10x +25) = 0
-x^2 -2x +17 = 0
x^2 +2x +1 = 17 +1
x +1 = ±√18 = ±3√2
x = -1 ±3√2
The values of the function at these locations are ...
h(-1-3√2) = -1 +(2/3)√2 ≈ -1.9428
h(-1+3√2) = -1 -(2/3)√2 ≈ -0.0572
Then the range of h(x) is ...
(-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)
Please answer this question now
Answer:
397.7 m²
Step-by-step Explanation:
Step 1: find m < W
W = 180 - (33+113) (sum of ∆)
W = 34°
Step 2: find side UV using the law of sines
[tex] \frac{UV}{sin(W)} = \frac{VW}{sin(U)} [/tex]
[tex] \frac{UV}{sin(34)} = \frac{29}{sin(33)} [/tex]
Multiply both sides by sin(34)
[tex] \frac{UV}{sin(34)}*sin(34) = \frac{29}{sin(33)}*sin(34) [/tex]
[tex] UV = \frac{29*sin(34)}{sin(33)} [/tex]
[tex] UV = 29.8 m [/tex] (approximated)
Step 3: find the area using the formula, ½*UV*VW*sin(V)
area = ½*29.8*29*sin(113)
Area = 397.7 m² (rounded to the nearest tenth.
As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:
f(x)=-14 cos(720(t-10))+14
Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?
Answer:
a) 28 units
b) 0.0262 seconds
c) Minimum height of the nail = 1.923 units
Step-by-step explanation:
a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)
Where:
d = The mid line
a = The amplitude
The period = 2π/b
c/b = The shift
Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28
b) Given that three revolution = 6×π, we have;
At t = 0
cos(720(t-10) = cos(720(0-10)) = cos(7200) = 1
Therefore, for three revolutions, we have
720(t - 10) = 720t - 7200
b = 720
The period = 2π/b = 6·π/720 = 0.0262 seconds
c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;
f(x) = -14×cos(720(t - 10)) + 14
At t = 0 gives;
f(x) = -14×cos(720(0 - 10)) + 14
Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923
Minimum height of the nail = 1.923
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m30.35\text{ m}^30.35 m30, point, 35, start text, space, m, end text, cubed of fluffy material. What is the length of the pillow? Give an exact answer (do not round).
Complete question is;
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m³ of fluffy
material. The Height is 0.5 m and the
Base is 1 m.
What is the length of the pillow?
Give an exact answer (do not round)
Answer:
length of Pillow = 1.4 m
Step-by-step explanation:
This wedge will be the shape of a triangular prism. The volume of a triangular prism is given as;
V = area of base x length = ½ × base × height × length
Thus;
Volume of Wedge = ½ × base × height × length
We are given;
base = 1 m
height = 0.5 m
Volume = 0.35m³
And we want to find the Length(L)
Thus;
½ × 0.5 × 1 × L = 0.35
L/4 = 0.35
Multiply both sides by 4 to give;
L = 0.35 × 4
L = 1.4 m
length of Pillow = 1.4 m
Answer:
1.4
Step-by-step explanation:
Khan
$70 discounted to $63
Answer:
10% off
Step-by-step explanation:
When $70 is discounted to $63, you can multiply 70 times 0.1 to get 7 which 70-63=7. To make 0.1 to a percentage, multiply by 100 to get 10%.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Maria rotated the triangle 90 degrees clockwise about the origin. What is the new triangle?
Answer:
A’B’C’
Step-by-step explanation:
Well if triangle ABC is rotated 90 degrees clockwise around the origin it will turn right to create triangle A’B’C’.
A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number. cubic inches
Answer:
927 cubic inches
Step-by-step explanation:
The area of the octagonal base is ...
A = (1/2)Pa
where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...
A = (1/2)(8·4)(4.83) = 77.28 . . . square inches
The volume of the prism is given by ...
V = Bh
where B represents the area of the base, and h is the height.
V = (77.28 in^2)(12 in) = 927.36 in^3
The volume of the prism is about 927 cubic inches.
the answer on edg is 927
Which statement are true about the solution 2
Answer:
¿De que solución habla?
Step-by-step explanation:
Answer:
B, D, F
Step-by-step explanation:
edge 2020
Caisha has a circular garden with a radius of 4 ft. She needs to put a layer of soil on top. Each bag of soil covers 9.42 square feet. How many bags of soil will she need to buy? 5 bag 6 bags 7 bags 8 bags
Answer:
6 bags
Step-by-step explanation:
Hey there!
Well first we need to find the area of the circle using,
π r^2
4*4 = 16
16 * pi ≅ 50.27
So now to find how much bags needed we do,
50.27 ÷ 9.42 = 5.34
Meaning 6 bags of soil is needed.
Hope this helps :)
Answer:
Caisha will need 6 bags of soil.
(B.) 6 bags :)
Instructions: Find the missing length indicated.
I
Answer:
x = 12 units
Step-by-step explanation:
In the picture attached,
Since, DE and BC are the parallel lines,AC and AB are the transverse.
Therefore, ∠AED ≅ ∠ABC [Alternate angles]
∠ADE ≅ ∠ACB [Alternate angles]
ΔADE ~ ΔACB [By AA postulate of similarity]
By the property of similarity,
If two triangles are similar then their corresponding sides will be proportional.
[tex]\frac{\text{AB}}{\text{AE}}=\frac{\text{AC}}{\text{AD}}[/tex]
[tex]\frac{(4+8)}{4}=\frac{(6+x)}{6}[/tex]
[tex]3=1+\frac{x}{6}[/tex]
x = 12
Therefore, length of missing segment is 12 units.
7 (42 ÷ 3) + 4 (72 + 53) + 8 (-3) 4
Answer:
Step-by-step explanation:
7(42 ÷ 3) + 4 (72 + 53) + 8 (-3)4
7(14) + 4(125) + 8(-12)
98 + 500 - 96
598 - 96
502
Answer:
502Step-by-step explanation:
[tex]7(42 \div 3) + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]
Divide the numbers
[tex] = 7 \times 14 + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]
Add the numbers
[tex] = 7 \times 14 - 4 \times 125 + 8 \times ( - 3) \times 4[/tex]
Calculate the product
[tex] = 7 \times 14 + 4 \times 125 - 96[/tex]
Multiply the numbers
[tex] = 98 + 500 - 96[/tex]
Add the numbers
[tex] = 598 - 96[/tex]
Subtract the numbers
[tex] = 502[/tex]
Hope this helps..
Best regards!!
look at pic to see question
Answer:
1/2*base*height
Step-by-step explanation:
All triangles have the area of 1/2*base* height.
Answer:
1/2 * b * h
Step-by-step explanation:
A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flat screen TV makes. Each sound bar and TV must be processed by cutting machine (A), A fitting machine (B), and a polishing machine (C). each sound bar must be processed on machine A for one hour, Machine B for one hour machine C for four hours. each TV must be processed on machine A for two hours, machine B for one hour, machine C for one hour. Machine A is available for 16 hours, machine B for nine, machine C for 24. Using the information in the problem, right the constraints. Let X represent the number of sound bars made, and Y represent the number of TVs
Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]
Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C
Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C
So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]
Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]
Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]
More for reference : https://brainly.com/question/9405925?referrer=searchResults
Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130130130 new words per month when he lived in Portugal and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did Wolfrich live in Portugal, and how long did he live in Brazil
Answer:
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
Step-by-step explanation:
Given;
Total Months = 14
Total Words = 1920
Required
Find the time spent in Portugal and time spent in Brazil
Let P represent Portugal and B represent Brazil; This implies that
[tex]P + B = 14[/tex] ---- Equation 1
Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that
[tex]130P + 150B = 1920[/tex] --- Equation 2
Make P the subject of formula in equation 1
[tex]P = 14 - B[/tex]
Substitute 14 - B for P in equation 2
[tex]130(14 - B) + 150B = 1920[/tex]
Open Bracket
[tex]1820 - 130B + 150B = 1920[/tex]
[tex]1820 + 20B = 1920[/tex]
Subtract 1820 from both sides
[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]
[tex]20B = 100[/tex]
Divide both sides by 20
[tex]\frac{20B}{20} = \frac{100}{20}[/tex]
[tex]B = 5[/tex]
Substitute 5 for B in [tex]P = 14 - B[/tex]
[tex]P = 14 - 5[/tex]
[tex]P = 9[/tex]
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
.....................
Answer:
B. √16 × √6
C. √96
Step-by-step explanation:
4√6
4 can be written as a square root.
4 = √16
√16 × √6
The square roots are multiplied, they can be written under one whole square root.
√(16 × 6)
√96
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75
(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75
(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10
(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs
Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.
The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713
Given that:
[tex]Entrance\ Fee = \$18[/tex]
[tex]Rate = \$0.08[/tex] per ball
Let:
[tex]B \to Balls[/tex]
The amount (A) Carolina can spend on B balls is:
A = Entrance Fee + Rate * B
This gives:
[tex]A = 18 + 0.08 * B[/tex]
[tex]A = 18 + 0.08B[/tex]
To get $10, Carolina must spend $75 or more.
This means:
[tex]A \ge 75[/tex]
So, the inequality is:
[tex]18 + 0.08B \ge 75[/tex]
The smallest number of balls is calculated as follows:
[tex]18 + 0.08B \ge 75[/tex]
Collect like terms
[tex]0.08B \ge 75 - 18[/tex]
[tex]0.08B \ge 57[/tex]
Divide both sides by 0.08
[tex]B \ge 712.5[/tex]
Round up
[tex]B \ge 713[/tex]
Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713
Learn more about inequalities at:
brainly.com/question/20383699
Using a linear function, it is found that:
1. [tex]18 + 0.08B \geq 75[/tex], given by option B.2. She has to buy at least 713 paintballs.-----------
The linear function for the cost of B paintballs has the following format:
[tex]C(B) = C(0) + aB[/tex]
In which
C(0) is the fixed cost.a is the cost per paintball.-----------
Question 1:
Entrance fee of $18, thus [tex]C(0) = 18[/tex].Cost of $0.08 per ball, thus, [tex]a = 0.08[/tex]Thus:
[tex]C(B) = 18 + 0.08B[/tex]
The promotion is valid if the cost is of at least 75, thus:[tex]C(B) \geq 75[/tex]
[tex]18 + 0.08B \geq 75[/tex], given by option B.
-----------
Question 2:
The smallest number is the solution of the inequality for B, thus:[tex]18 + 0.08B \geq 75[/tex]
[tex]0.08B \geq 57[/tex]
[tex]B \geq \frac{57}{0.08}[/tex]
[tex]B \geq 712.5[/tex]
Rounding up, she has to buy at least 713 paintballs.
A similar problem is given at https://brainly.com/question/24583430
PLEASE HELP ME GUYS!! Write and solve equations based on the angle relationships in the diagram below to find the measure of ∠EKC and ∠CKA
Answer:
x = 65°
y = 25° (equations in explanation)
Step-by-step explanation:
We know that EKD is 25° and we know that DKB is 90°.
EKD, DKB, and BKF are supplementary. This means that their angle measures add up to 180°.
So, since we know two, we can find the other very easily.
[tex]180 - (25+90)\\180 - 115\\65[/tex]
This means that BKF is 65°.
Now, BKF and EKC are alternate interior angles, so they have the exact same measurement. Therefore, EKC, x, is 65°.
Again, EKC, CKA, and AKF are supplementary. AKF is 90° and EKC is 65°, so we can find the measure of CKA easily.
[tex]180 - (65+90)\\180-155\\25[/tex]
Therefore y is 25° and x is 65°.
Hope this helped!
The area of a rectangular dining room is 20 square meters. It is 5 meters long. How wide is it?
Answer:
4 meters
Step-by-step explanation:
To do this you would need to know what the area of a rectangle is, it is base times width. So you already know the area so you would just divide it by 5 and you would get the width, which is 4 meters
If we increase the number 100 by 10% and then reduce the resulting number by 20% what would the answer be plz show how u did it and I will mark brainliest for the best explanation
Answer:
88
Step-by-step explanation:
The original number ⇒ 100
100 is increased by 10%
The result is 20% reduced.
Calculate increase.
100 × (1 + 10%)
100 × (1.1)
= 110
Calculate decrease.
110 × (1 - 20%)
110 × 0.8
= 88
How many terms are in the arithmetic sequence 7, 0, –7, …,–175?
Answer:
27 terms
Step-by-step explanation:
a1 = 7
nth term is -175
common difference d= 0-7 = -7 or -7 - 0 = -7
nth term = first term + ( n-1) * common difference
-175 = 7 + ( n - 1 ) * (- 7)
-175 = 7 - 7n + 7
-175 = 14 - 7n
-175-14 = -7n
-189 = - 7n
n= -189 /-7
n=27