Answers
Answer: Choice D
[tex]\frac{-19}{\text{x}-5}[/tex]
=================================================
Work Shown:
[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]
[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]
This matches with choice D as the final answer.
Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]
Related Questions
The price of a jacket is $500 and the price of a pair of jeans is $250.
(a) The price if the jacket is ____% if the pair of jeans.
(b) The price of the pair of jeans is ___% or the price of the jacket.
Answers
Answer:(a) 50% (b)5%
Step-by-step explanation:
For a, it's not really difficult because the price of a jacket is 1/2 more than jeans. So it's 50%.
For b, it's similar to no. (a) because the price of the jean is 1/2 less than a jacket. So u need to divide 250 by 500 and u will get 0.5 so if u want to put in % u need to multiply with 10, so u will get 5%.
the selling price of a mobile after discount is 10000.if the discount is 10% find the mp
Answers
Answer:
Rs.11,111.11 (2 d.p.)
Step-by-step explanation:
The original price of the mobile is 100% of the price.
Therefore, the price of the mobile after a discount of 10% is 90% of the original price.
Let x be the original price.
If the price of the mobile after the discount is Rs.10000 then:
⇒ 90% of x = Rs.10000
⇒ 0.9x = 10000
⇒ x = 10000 ÷ 0.9
⇒ x = 11111.11 (2 d.p.)
M.P. =Rs 11111.1111
Answer:
Solution Given:
Selling price (S.P.) = Rs 10,000.
Discount =10%
Marked Price (M.P.)=?
we have
M.P. = S.P. + discount% of M.P.
keeping M.P. on same side
M.P. - discount% of M.P=S.P.
substituting value
M.P. - 10% of M.P.= Rs 10,000
taking common M.P.
M.P.(1-10%)=Rs. 10,000
we know that %=1/100
M.P.(1-10/100)=Rs 10,000
(9/10)M.P.= Rs 10,000
M.P.= Rs 10,000*10/9
M.P.=Rs11111.1111
How many ways can a 2 person subcommittee be selected from a comittee of 6 people?
Answers
Answer: 15 ways
Step-by-step explanation: 5+4+3+2 + 1 = 15
Answer:
15.
Step-by-step explanation:
That would be the number of combinations of 2 from 6.
6C2
= 6! /4!2!
= 6*5/2*1
= 15.
The table above shows four numeric expressions. Which expression is an integer when it's evaluated?
Question 6 options:
A)
G
B)
F
C)
H
D)
E
Answers
Answer: H
Step-by-step explanation:
[tex]9(-3)=-27[/tex], which is an integer.
Write 304.9% as a decimal.
Answers
Answer:
3.049
Step-by-step explanation:
Move the decimal place in 304.9% to the left two places in order to convert from a percentage to a decimal. 3.049 is the answer.
Brainliest, please :) Hope this helps!
The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of
the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches
Answers
Answer:
15
Step-by-step explanation:
12 / 2 = 6
5 / 2 = 2.5
6 x 2.5 = 15
15 inches²
number 7 please and don t care abt others lol
Answers
Answer:
The question does not make a lot of sense to me but I think this is how its supposed to be done
so there are 15 shirts
2 are sold at 3.90, 2 x 3.90 = 7.8
15-2= 13 t shirts
13 sold at 4.70, 13 x 4.70 = 61.1
amount of money made is = 7.8 + 61.1
= 68.9
Area=
Help Me asap pleaseee thanks
Answers
The area of the shaded region shown in the image is 14π unit²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Area of semicircle = π*diameter² / 4
The area of the shaded region is the sum of the area of the individual semi circles shown in the diagram.
Area of shaded region = area of SR + area of QR + area of PQ
Area of shaded region = (1/2) * π(4²/4) + (1/2) * π(2*4²/4) + (1/2) * π(2 * 2 * 4²/4) = 14π
The area of the shaded region shown in the image is 14π unit²
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can someone please help mee ( will give brainliest 20 points!!!)
Answers
The piecewise function graphed below is given as follows:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex][tex]f(x) = x + 2, -2 < x \leq 3[/tex][tex]f(x) = -1, 3 < x \leq 5[/tex]What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex]
For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:
[tex]f(x) = x + 2, -2 < x \leq 3[/tex]
For x greater than 3 until 5, the function is constant at -1, hence the definition is:
[tex]f(x) = -1, 3 < x \leq 5[/tex]
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In need of help for answers
Answers
The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
From the diagram using the point (-6, 0.5) and (-1, 5):
y - 0.5 = [(5 - 0.5)/(-1 - (-6))](x - (-6))
y = (9/10)x + 5.9
Also, using the point (2, 1) and (4, -4):
y - 1 = [(-4 - 1)/(4 - 2)](x - 2)
y = -(5/2)x + 6
The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]
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Please help!!!!! Please explain too, I want to understand it!
Answers
Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
Answers
The total number of integral solutions of x + y + z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and z ≥ 3 is; 59 integer solutions
How to find the number of Integral Solutions?We are given the condition that;
−3 ≤ x ≤ 4
Thus, we will use x values of -3, -2, -1, 0, 1, 2, 3, 4
When;
x = -3 and y = 2, in x + y + z = 12, solving for z gives z = 13
x = -3 and y = 3, in x + y + z = 12, solving for z gives z = 12
x = -3 and y = 4, in x + y + z = 12, solving for z gives z =11
x = -3 and y = 5, in x + y + z = 12, solving for z gives z = 10
x = -3 and y = 6, in x + y + z = 12, solving for z gives z = 9
x = -3 and y = 7, in x + y + z = 12, solving for z gives z = 8
x = -3 and y = 8, in x + y + z = 12, solving for z gives z = 7
x = -3 and y = 9, in x + y + z = 12, solving for z gives z = 6
x = -3 and y = 10, in x + y + z = 12, solving for z gives z = 5
x = -3 and y = 11, in x + y + z = 12, solving for z gives z = 4
Thus, there are 10 solutions with x =-3
Repeating the above with x = -2, we will have 10 solutions
Similarly, with x = -1, we will have 9 more solutions
Similarly, with x = 0, we will have 8 more solutions.
Similarly, with x = 1, we will have 7 more solutions.
Similarly with x = 2, we will have 6 more solutions.
Similarly with x = 3, we will have 5 more solutions.
Similarly with x = 4, we will have 4 more solutions.
Thus,
Total number of solutions = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 10
= 59 integer solutions
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PLEASE HELP ME QUICK!! I"M BEING TIMED
Carter and Ari had $240 altogether. Ari had twice as much as Carter after Carter gave him $16. How much more money did Ari have than Carter in the beginning?
Answers
Answer: $48 more
Step-by-step explanation: We use algebra. Let c = Carter and a = Ari. C+A = 240. A+16 = 2(C-16). 2C-32 + C-16 = 240. 3C - 48 is 240. 240+48 is 288. So, C is 96 and a is 144. 144- 96 = 48 more.
What are the solutions to this quadratic equation x2+6x-5=0
Answers
Answer:
See Below.
Explanation:
Quadratic Form:
[tex]a {x}^{2} + bx + c[/tex]
Quadratic Formula:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
Based on the information given from the question, we can deduce:
a = 1
b = 6
c = -5
Now we can substitute all these values into the formula to find x.
[tex]x = \frac{ - 6 + - \sqrt{ {6}^{2} - 4(1)( - 5)} }{2(1)} \\ = - 3 + \sqrt{14} \: or \: - 3 - \sqrt{14} [/tex]
write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-6,6) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of -15
Answers
Answer:
[tex]y=-\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
Slope of line with given x and y intercepts
The x-intercept is when y = 0.
Therefore, if the x-intercept is 5 ⇒ (5, 0).
The y-intercept is when x = 0.
Therefore, the y-intercept is -15 ⇒ (0, -15).
Inputting these two points into the slope formula to find the slope of this line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]
Slope of function f(x)
If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.
[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]
Equation of f(x) in point-slope form
Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]
Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:
[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]
[tex]\implies y=-\dfrac{1}{3}x+4[/tex]
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Find all numbers whos absolute value is 8
Answers
Answer:
8 and -8.
Step-by-step explanation:
Absolute value is the magnitude of quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as |8| or |-8| is equal to 8.
The absolute value of number a:
⇒ |a| = a for a ≥ 0⇒ |a| = -a for a < 0|a| = 8 ⇔ a = 8 or a = -8
The graph f(x) = (x + 2) ^ 2 - 7 is translated 3 units up, resulting in the graph g(x) . Which equation represents the new function, g(x) ?
Answers
Step-by-step explanation:
x^2 +4x +4 -7 is
y=x^2+4x-3
Answer: g(x)=(x+2)²-4.
Step-by-step explanation:
g(x)=f(x)+3
g(x)=(x+2)²-7+3
g(x)=(x+2)²-4.
Select the correct answer. which of these organizations provides help to the friends and families of an alcoholic? a. national clearing house for alcohol and drug information b. american council on alcoholism c. alateen
Answers
Alateen, also called Al-Anon, provides meetings and services for young people age 13 to 18 who’ve been affected by the drinking of other people.
Answer: C
Step-by-step explanation:
For 17-20, Find the value of each variable.
Answers
The unknown angles are as follows;
x = 180 degrees
r = 90 degrees.
How to find the angles of each value in a circle?The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.
Therefore,
x = 2(90)
x = 180
Therefore, the sum of angle in a circle is 360 degrees.
Hence, the 2 angles of the arc are the same.
Therefore,
360 - 180 = 2r
2r = 180
divide both sides by 2
2r / 2 = 180 / 2
r = 90 degrees.
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I really don't know what to do for this question! :( help?
Answers
The amount of money she should deposit is 6131.14 dollars.
How to find the compound interest ?The amount she should deposit can be found as follows:
[tex]p = \frac{A}{(1+\frac{r}{n} )^{nt} }[/tex]
where
A = amount to depositr = raten = number of timest = timep = principalTherefore,
p = [tex]\frac{20000}{(1+\frac{0.12}{4}{} )^{40} }[/tex]
[tex]p=\frac{20000}{(1+0.03)^{40} }[/tex]
[tex]p = \frac{20000}{1.03^{40} }[/tex]
[tex]p=\frac{20000}{3.262037792}[/tex]
Hence,
p = $6,131.14
Therefore, she should deposit 6131.14 dollars.
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A ribbon is 5 m long. A piece of length 3 4/5 m is cut from it. What is the length of the remaining piece?
Answers
Answer:
1.2 meters long
Step-by-step explanation:
3(4/5)m=3.8m
5m-3.8m=1.2m
Which of the following is a monomial? O A. 11x-9 OB. 20x9 OC. 20x⁹ - 7x O D.9/x
Answers
Answer:
B. 20x⁹
Step-by-step explanation:
A monomial is a polynomial with just one term.
Example: 3x²
A. 11x - 9
INCORRECT, this has two terms 11x and 9
B. 20x⁹
CORRECT, this only has one term!
C. 20x⁹ - 7x
INCORRECT, this has two terms 20x⁹ and 7x
D.9/x
INCORRECT, this is not a polynomial
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find the perimeter of the figure below, composed of a rectangle and two semicircles
.
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's consider the shape given to us:
⇒ a rectangle with two semicircles cutout on the edges
⇒ perimeter/circumference of the two semicircles can count as one
circle
Let's solve:
Circumference = circumference of two semicircle[tex]\hookrightarrow \text{Total circumference} =\frac{1}{2} *\pi *\text{ diameter} +\frac{1}{2} *\pi * \text{diameter}\\= \pi *\text{diameter}=10\pi =10 * 3.14 = 31.4[/tex]
Total Perimeter = 31.4 + 14 + 14 = 31.4 + 28 = 59.4Answer: 59.4 square units
Hope that helps!
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.A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500?
Answers
Answer:
given,
final interest = Prt
p = 7500
r = 15%
t= 8 yrs
Fi= 7500 x 0.15 x 8
= 1125 x 8
=9000
total savings = 9000 + 7500 = 16500
PLEASE HELP ME PLEASE
WHICH EQUATION DOES THE GRAPH REPRESENT
Answers
Answer:
Step-by-step explanation:
B is the best answer
There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing do they need if the radius of the circle is 40 feet, and the arc takes up 45°? Use 3.14 for pi.
Answers
The length of the railing needed is 31.4 feet
Calculating the length of an arcFrom the question, we are to determine the length of railing needed
To determine the length of railing needed, we will determine the length of the arc formed by the balcony
Using the formula,
l = θ/360° × 2πr
Where l is the length of the arc
θ is the angle subtended by the arc
and r is the radius
From the given information,
θ = 45°
r = 40 feet
Putting the parameters into the equation, we get
l = 45°/360° × 2 × 3.14 × 40
l = 1/8 × 2 × 3.14 × 40
l = 2 × 3.14 × 5
l = 31.4 feet
Hence, the length of the railing needed is 31.4 feet
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Solve the equation in the image (yr 8 maths, 50pts)
Answers
4x - 20 = -x
5x -20 = 0
5x = 20
x = 4
Answer: x = 4
Step-by-step explanation:
Given equation
4x - 20 = -x
Add x on both sides
4x - 20 + x = -x + x
5x - 20 = 0
Add 20 on both sides
5x - 20 + 20 = 0 + 20
5x = 20
Divide 5 on both sides
5x / 5 = 20 / 5
[tex]\Large\boxed{x=4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
70 POINTS !! Charlotte has a map of the village. The scale on the map is such that 1cm represents 25m.
a) On the map, the church is 7cm from the village store. What is the real distance from the church to the village store?
b) Charlotte calculates her car is parked approximately half a kilometer from the church. On the map, how many cm would represent this distance?
Answers
Answer:
A. 175 m
B. 20 cm
Step-by-step explanation:
[tex]\frac{1 cm}{25 m} =\frac{7 cm}{x m}[/tex]
x = 175 m
[tex]\frac{25 m}{1 cm} = \frac{500 m}{x cm}[/tex]
x = 20 cm
Answer:
No1. 175 m
no2. 20 cm
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week.
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answers
Answer:
The answer is C- Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Use the discrete probability distribution to find the probability that x exceeds 5. (note that it is not required to find the missing probability. )
Answers
The discrete probability distribution that finds the probability that x exceeds 5 is 0.38
Opportunity provides records approximately the likelihood that something will manifest. Meteorologists, for instance, use weather patterns to are expecting the chance of rain. In epidemiology, the probability idea is used to recognize the connection between exposures and the risk of fitness consequences.
Finding the possibility of a simple event happening is fairly straightforward: upload the changes collectively. For example, if you have a 10% chance of triumphing $10 and a 25% threat of triumphing $20 then your normal odds of prevailing something is 10% + 25% = 35%.
If there is no ambiguity within the occurrence of an occasion, then the chance of such an occasion is equal to 1. In other phrases, the chance of a sure occasion is 1. If an occasion has no probability of taking place, then its chance is zero.
We want to find the probability for x exceeding 5 means for x>5
Consider,
P(X>5)=P(x=6)+P(X=8)
=0.18+0.2
=0.38
Hence, the probability is 0.38
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