Answers
The value of x is 5. The correct option is the second option- 5
Proportionality theoremFrom the question, we are to determine the value of x
By the proportionality theorem, we have that
If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
Considering the diagram, we can write that
[tex]\frac{12}{28 }= \frac{35-4x}{35}[/tex]
Then, we get
12 × 35 = 28(35-4x)
420 = 980 -112x
112x = 980 - 420
112x = 560
x = 560/ 112
x = 5
Hence, the value of x is 5. The correct option is the second option- 5
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Related Questions
At a basketball game, 6% were supporting the visiting team. If total number of people attending the game was 2500, how many people were supporters of the home team?
Answers
There were 2350 people supporting the home team
How to determine the number of supporters?The given parameters are:
Total = 2500
Proportion that supports the visiting team= 6%
Let the number of people that supports the team be x.
So, we have:
x = (1 - Proportion that supports the visiting team) * Total
This gives
x = (1 - 6%) * 2500
Evaluate
x = 2350
Hence, there were 2350 people supporting the home team
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An eight-sided die is tossed. Determine the odds against rolling an 8.
Answers
Reason:
There are 7 outcomes we don't want vs 1 outcome we do want
outcomes we don't want = rolling one of the following {1,2,3,4,5,6,7}
outcome we want = rolling an 8
Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill Two years ago she has been at the hospital for twice as long How long has each been at r=the hospital
Answers
Answer:
Hoang has been at the hospital for 12 years while Bill has worked for 7 years.
Step-by-step explanation:
Let the years Hoang has worked as a nurse equal h and let the years Bill has worked as a nurse equal b.
Since Hoang has worked 5 years longer, h is five more than b:
h = b + 5
Now we move onto the situation 2 years ago. 2 years ago, Hoang had worked at the hospital two less than h or h-2 years while Bill has worked for b-2 which is two years less than b. We are also told that at the time, Hoang worked twice as longs, so
h - 2 = 2(b - 2)
This can be simplified:
h - 2 = 2b - 4
h = 2b - 2
We can use substitution. Since h = b + 5 and h = 2b - 2,
b + 5 = 2b - 2
b = 7
Therefore, since Hoang has worked five more years, h = 12. So, Hoang has been at the hospital for 12 years while Bill has worked for 7 years.
Please help I will give the most points
Answers
Which option is an even function?
Answers
The correct answer is option D. Which is the even function is f (x) = x⁴.
What is an even function?The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).
let us check the given four options:-
A f(x) = √x ; f(-x) = √-x here f(x) ≠ f(-x)
B f(x) = x ; f(-x) = -x here f(x) ≠ f(-x)
C f(x) = x³ + 1 ; f(-x) = -x³ + 1 here f(x) ≠ f(-x)
D f(x) = x⁴ ; f(-x) = (-x)⁴ = x⁴ here f(x) = f(-x)
We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).
Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.
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If √ 24 + √ 96 7 √600 = y√ 6, find the value of y. -
Answers
28) Which of the following sets of ordered pairs does not represent a linear function?
(a) {(1, 2), (3, 4), (4, 5), (6, 7)}
(b) {(0, 3), (1, 5), (3, 9), (1, 13)}
(c) {(2, 2), (3, 3), (4, 4), (5,5)}
(d) {(1, 2), (2, 2), (3, 5), (4, 8)}
Answers
Answer: D
Step-by-step explanation:
Answer: Choice D
Plot the points given for choice D. See below.
It is impossible to draw a single straight line through all of the points.
Therefore, this set of points do not represent a linear function.
You are asked to prepare a prescription for an Antihistamine 12.5mg/5ml elixir. What is the percent strength of the medication?
Answers
Answer:
1) 0.25%
Step-by-step explanation:
Ratio= weight in g/ volume in ml
1. percent strength = 12.5× 10-³g /5ml × 100%
=0.25%
Answer:
0.25%
Step-by-step explanation: Convert mg to g (1g = 1000mg)
12.5mg/1000mg = 0.0125g/5ml ( 0.0025) x 100 = 0.25%
If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value of a, where a > 0.
Answers
The value of a using integration is 2, such that the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units
How to determine the value of a?The given parameters are:
Curve, y² = 4ax
Line, x = 4a
Substitute x = 4a in y² = 4ax
y² = 4a * 4a
Take the square root of both sides
y = ±4a
This means that the point of intersection between the line and the curve is (4a, -4a) and (4a, 4a)
Remove the negative interval
So, we have: (4a, 0) and (4a, 4a)
The area is then calculated as
[tex]A =2 \int\limits^{4a}_0 {\sqrt y} \, dx[/tex]
This gives
[tex]A =2 \int\limits^{4a}_0 {\sqrt {4ax}} \, dx[/tex]
Remove the constant
[tex]A = 2\sqrt{4a}\int\limits^{4a}_0 {\sqrt {x}} \, dx[/tex]
Integrate
[tex]A = 2\sqrt{4a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]
Evaluate the exponent
[tex]A = 4\sqrt{a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]
Expand
[tex]A = 4\sqrt{a} * \frac 23 (4a)^\frac32[/tex]
Rewrite as:
[tex]A = 4 * a^\frac12 * \frac 23 * 4^\frac32 * a^\frac32[/tex]
Evaluate the exponents by the laws of indices
[tex]A = 4 * \frac 23 * 8 * a^2[/tex]
Recall that the area is:
A = 256/3
So, we have:
[tex]\frac{256}3 = 4 * \frac 23 * 8 * a^2[/tex]
Evaluate the quotients
[tex]256 = 4 * 2 * 8 * a^2[/tex]
Divide both sides by 64
4 = a²
Take the square root of both sides
2 = a
Rewrite as:
a = 2
Hence, the value of a is 2
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-6>2x+6 ≤18
graph the inequality
Answers
Answer:
y= x + b
-6 > 2x+6- graph a doted line that crosses through -6, and 2 shade below the dotted line going to the negative
18 >< 2x+6 graph a solid line through 18 and 2 and shade everything above the line going positive
have a good day hope this helped
Step-by-step explanation:
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS!!! EVEN IF IT IS WRONG!!!!! Mariano is standing at the top of a hill when he kicks a soccer ball up into the air. The height of the hill is h feet, and the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of the hill after t seconds is given by the polynomial −16t2 + vt + h. Find the height of the ball after 4 seconds if it was kicked from the top of a 25 foot tall hill at 72 feet per second.
Answers
Answer:
57 feet
Step-by-step explanation:
A formula is given for the height of the ball, and all of the values necessary to evaluate the formula are also given. The height of the ball after 4 seconds is found by substituting the given values into the formula and doing the arithmetic.
__
height = -16t² +vt +h . . . . . for t=4, v=72, h=25
height = -16(4²) +72(4) +25 = -256 +288 +25 = 57
The height of the ball is 57 feet above the bottom of the hill 4 seconds after it was kicked.
_____
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The numbers of pages in the books in a library follow a normal distribution. If the mean num
pages, what can you conclude?
O A. About 60% of the books have fewer than 150 pages.
OB.
About 16% of the books have fewer than 150 pages.
OC.
About 95% of the books have more than 150 pages.
About 16% of the books have more than 150 pages.
O D.
Reset
Next
Answers
Answer:
For the answer to the question above, the numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30 pages, you can conclude that about 16% of the books have fewer than 150 pages.
what is -23/6 - 7/3
A -37/6
B -30/9
C -16/6
D 37/6
Answers
Answer:A
Step-by-step explanation:
-23/6 - 7/3 =-6.16666666667
-37/6 = -6.16666666667
Answer:
[tex] \frac{ - 37}{6} [/tex]
Step-by-step explanation:
[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]
Evan picks up a cantaloupe that weighs 3.24 pounds. Suppose Evan
could buy 100 cantaloupes that are all this weight. Without using the
multiplication algorithm, explain how Evan could figure out the total
weight of all 100 cantaloupes.
Answers
The total weight of the 100 cantaloupe is 324 pounds
How to determine the total weight?The given parameters are:
Weight of each = 3.24 poundsNumber of cantaloupe = 100Since the number of zeros in 100 is 2;
All Evans needs to do is to move the decimal point in 3.24 two places forward.
i.e. 3.24 becomes 324 when the decimal point is moved
Hence, the total weight of the 100 cantaloupe is 324 pounds
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Question 1 of
Select the correct answer.
A rectangular sheet of steel is being cut so that the length is four times the width. The perimeter of the sheet must be less than
100 inches.
length (/)
width (w)
Which inequality can be used to find all possible lengths, I, of the steel sheet?
5/2L > 100
10L < 100
5/2L< 100
10L > 100
Answers
Answer:
5L/2 < 100
Step-by-step explanation:
Let's get started!
Let :
⇒ Length = L
⇒ Width = L/4
It mentions the perimeter must be less than 100 inches.
Perimeter Formula :
Perimeter (Rectangle) = 2(Length + Width)
Then, the inequality formed will be :
⇒ 2 (L + L/4) < 100
⇒ 2 (5L/4) < 100
⇒ 10L/4 < 100
⇒ 5L/2 < 100
Length be L
width be L/4
Now
Perimeter=2(Length+Breadth)
2(L+L/4)<1002(5L/4)<1005L/2<100 y = 12•3x for x = -2
Answers
Answer:
y=12×3(-2)
y=-72
Step-by-step explanation:
please mark me as brainlest
A={j,a,c,k,p,o,t} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′.
Answers
Answer:
Answer: {b,d,e,f,g,h,i,l,m,n,q,r,s,u,v,w,x,y,z}
Step-by-step explanation:
A' = U-A
={b,d,e,f,g,h,i,l,m,n,q,r,s,u,v,w,x,y,z}
Help me please I been trying to figure out how to do this problem
Answers
sin 30 = x/4
sin 30 = 0.5
0.5 = x/4
x = 2
Find the value of x.
x = [?]
Answers
Answer:
x = 14 units
Step-by-step explanation:
Distance of both the chords from the center of the circle is 9 units.-> Both the chords are equal. (Chords equidistant from the center of the circle are equal)Perpendicular drawn from the center of the circle bisects the chord.-> Measure of one chord = 7 + 7 = 14 unit-> Measure of the other chord = 14 units-> x = 14 unitsWhich of the following statements must be true about parallelogram ABCD?
Options are below
Answers
Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]
Step-by-step explanation:
Adjacent angles of a parallelogram are always supplementary.
A circular garden has a circumference of 42.3 feet. Find the approximate diameter of the garden. Use 3.14 for π.
Answers
Answer:
13.5
Step-by-step explanation:
c = 2πr
42.3 = 2(3.14)r
42.3 = 6.28r
6.74 = r
d = r + r
d = 6.74 + 6.74
d = 13.5
WILL MARK BRAINLIEST 50 POINTS Find the area of the regular pentagon if the apothem is 7 ft and a side is 10 ft. Round to the nearest whole number.
175 ft2
350 ft2
35 ft2
70 ft2
Answers
Answer:
175 ft^2
Step-by-step explanation:
split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2
then the pentagon has an area 35*5 = 175 ft^2
What is the minimum value of the following function f(x)=(x-1)^2 +1
Answers
Answer:
1
Step-by-step explanation:
f(x)=(x-1)²+1
f(1)=(1-1)²+1
f(1)=0²+1
f(1)=0+1
f(1)=1
The discussion in this lesson offers two tips for saving money. Write 1-2 paragraphs that describe the following: 1. state the two money saving tips 2. tell why these tips work
Answers
The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.
What is saving?Saving is the method of saving your money for the future. We can not predict the future if anything bad happens and we need a large amount of money these savings will help us.
The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.
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Question 1 Complete the missing reasons for the proof. Given: 4(x - 2) = 6x + 18 Prove: x= -13 Statements Reasons 1.4(x - 2) = 6x +18 given 2. 4x8= 6x +18 distributive property 3.-2-8-18 4.-2x = 26 addition property of equality 5.x = -13 O 3. subtraction property of equality; 5. multiplication property of equality O 3. subtraction property of equality; 5. division property of equality 3. addition property of equality; 5. division property of equality O 3. addition property of equality; 5. multiplication property of equality
Answers
Looking at the problem statement, the question is asking us to determine what the missing reasons are. The information that is given to us is a step-by-step process of solving an expression for an unknown. There are also two blanks in the reasons column for steps 3 and 5 which we will need to determine.
For step #3, we can see that they subtracted 6x from both sides which means that options 3 and 4 are automatically out since they reference addition in the first part. The correct reasoning for this part would be Subtraction Property of Equality which states that we subtract the same item from both sides of the expression.
We can see this being done in the following actions
[tex]4x - 8 = 6x + 18[/tex][tex](4x - 6x) - 8 = (6x - 6x) + 18[/tex][tex](4x - 6x) - 8 = 18[/tex][tex]-2x - 8 = 18[/tex]For step #5, we can see that they divided both sides by -2 which means that option 1 is out since it references the multiplication property of equality. The correct reasoning for this part would be Division Property of Equality which states that we divide both sides by the same item.
We can see this being done in the following actions
[tex]-2x = 26[/tex][tex]\frac{-2x}{-2} = \frac{26}{-2}[/tex][tex]x= \frac{26}{-2}[/tex][tex]x= -13[/tex]Therefore, the option that would best fit the description that we provided during our work would be option 2 (3. subtraction property of equality; 5. division property of equality).
Answer:
b) 3. addition property of equality; 5. division property of equality.
Step-by-step explanation:
Given: 4(x - 2) = 6x + 18
Prove: x = -13
Algebraic Properties:
Addition: If a = b, then a + c = b + cSubtraction: If a = b, then a - c = b - cMultiplication: If a = b, then ac = bcDivision: If a = b, then a ÷ c = b ÷ cDistributive: a(b + c) = ab + acSteps:
1. Given:
⟹ 4(x - 2) = 6x + 18
2. Distribute property:
4(x) + 4(-2) = 6x + 18 [distribute 4]
⟹ 4x - 8 = 6x + 18
3. Subtraction property of equality:
4x - 6x - 8 = 6x - 6x + 18 [subtract 6x from both sides]
⟹ -2x - 8 = 18
4. Addition property of equality:
-2x - 8 + 8 = 18 + 8 [add 8 to both sides]
⟹ -2x = 26
5. Division property of equality:
-2x ÷ -2 = 26 ÷ -2 [divide both sides by -2]
⟹ x = -13
In conclusion, the missing reasons are the subtraction and division properties of equality.
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Five times a number decreased by nine is equal to twice the number increased by 23 which equation could be used to solve the problem
Answers
Answer:
(5 • x) - 9 = 2x + 23
Use the following table of Registered Voters at Kensington College, Registered Voters at Kensington College 2009 2010 640 790 Democrats Republicans 960 410 Independents 320 300 11) What is the probability that a voter registered in Kensington College in 2009 was not a Republican?
Answers
Step-by-step explanation:
remember, a probability is ultimately always
desired cases / total possible cases
what are the total possible cases for our question here ?
all registered voters in 2009 :
640 + 960 + 320 = 1920
the desired cases (not republican) out of all these 1920 possibilities are
640 + 320 = 960
so, the probability for a registered voter to not be republican was
960 / 1920 = 1/2 = 0.5
The base of an isosceles triangle is half
as long as each of the two equal sides.
Write the area of the triangle, A(x), as a
function of the length of the base, x.
A(x) =
Answers
Answer:
X * H
-----------
2
Step-by-step explanation:
Base of the triangle (X) times height of triangle, divided by 2
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
The area of the isosceles triangle will be A(x) = √15(x² / 4).
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.
The base of an isosceles triangle is half as long as each of the two equal sides.
Let the base length be x. Then the length of each other legs will be 2x.
A(x) = √[s(s - x)(s - 2x)(s - 2x)]
The value of s is half of the perimeter.
s = (x + 2x + 2x) / 2
s = 5x / 2
Then the area of the isosceles triangle will be
A(x) = √[5x / 2(5x / 2 - x)(5x / 2 - 2x)(5x / 2 - 2x)]
A(x) = √[5x / 2(3x / 2)(x / 2)(x / 2 )]
A(x) = √(15x⁴ / 16)
A(x) = (x² / 4)√15
The area of the isosceles triangle will be A(x) = √15(x² / 4).
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Which expression correctly shows 2x³y - 2y factored completely?
O 2xy(x - 1)(x² + x + 1)
O 2y(x - 1)(x² + x + 1)
O 2(x - y) (x² + xy + y²)
O-2y(x + 1)(x² - x + 1)
Answers
Answer:
[tex]2y(x-1)(x^2+x+1)[/tex]
Step-by-step explanation:
[tex]~~~2x^3y-2y\\\\=2y(x^3-1)\\\\=2y(x-1)(x^2+x+1)~~~~~~~~~~;[a^3-b^3 = (a-b)(a^2 +ab+b^2)][/tex]
X 49°
14
i will give points!!
Answers
In the given diagram, the length of the side marked x is 21.34
TrigonometryFrom the question, we are to determine the value of the side marked x
In the given diagram,
Hypotenuse = x
Adjacent = 15
Included angle = 49°
Using SOH CAH TOA
We can write that,
cos 49° = 14 / x
∴ x = 14 / cos 49°
x = 21.34
Hence, the length of the side marked x is 21.34.
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