Answer:
Value of a is:
[tex]x^4+10x^3+100x^2+1000x+10000[/tex]
Step-by-step explanation:
we know that:
[tex]x^n-a^n=(x-a)(x^{n-1}+ax^{n-2}+a^2x^{n-3}+...+a^{n-2}x+a^{n-1})[/tex]
Here, a=10 and n=5
[tex]x^5-10^5=(x-10)(x^4+10x^3+100x^2+1000x+10000)[/tex]
[tex]x^5-10^5=(x-10)a[/tex]
⇒ [tex]a=x^4+10x^3+100x^2+1000x+10000[/tex]
Hence,Value of a is:
[tex]x^4+10x^3+100x^2+1000x+10000[/tex]
Show that (2-√x)^2 divided by √x can be written as 4x^(-1/2)-4+x^1/2
A washer and a dryer cost $942 combined. The washer costs $42 more than the dryer. What is the cost of the dryer?
Last year shantell bought a car for $24,000 the current value of the car is $21,000 find the percent decrease in the value of the car
For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula d = v + v2 20 where d is measured in feet. kerry wants her stopping distance not to exceed 75 ft. at what range of speeds (in mi/h) can she travel? (enter your answer using interval notation.) c
The range of speeds in miles per hour Kerry can travel is [tex]-50\ge v\le30[/tex] .
Given that, a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula [tex]d = v + \frac{v^2}{20}[/tex].
Here,
[tex]75=v+\frac{v^2}{20}[/tex]
[tex]75=\frac{(20v+v^2)}{20}[/tex]
[tex]v^2+20v=20\times75[/tex]
[tex]v^2+20v=1500[/tex]
[tex]v^2+20v-1500=0[/tex]
[tex](v+50)(v-30)=0[/tex]
[tex]v-30=0[/tex]
[tex]v=30[/tex]
First thing is to realize what 'not to exceed' means. More than 75 feet exceeds 75 feet, but exactly 75 feet or anything less does not. So you want to determine v such that [tex]d\le75[/tex].
[tex]d=v+\frac{v^2}{20}[/tex]
is the given model. This is a reasonably good model presuming you have a better than average reaction time, dry pavement, new tires, etc. Be that as it may, you need to determine v such that:
[tex]v+\frac{v^2}{20} \le75[/tex]
Multiply by 20, we get
[tex]20v+v^2\le1500[/tex]
Add -1500 to both sides
[tex]v^2+20v-1500\le0[/tex]
[tex](v+50)(v-30)\le0[/tex]
So, [tex]v\le-50[/tex] or [tex]v\le30[/tex]
Thus, the range is [tex]-50\ge v\le30[/tex]
Therefore, the range of speeds in miles per hour Kerry can travel is [tex]-50\ge v\le30[/tex] .
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Kerry can travel at speeds in the range [tex]{(-\infty, 30]} mi/h[/tex].
To find the range of speeds Kerry can travel while ensuring her stopping distance doesn't exceed 75 feet, we need to solve the inequality [tex]v + \frac{v^2}{20} \leq 75[/tex], where v represents her speed in miles per hour.
First, we rearrange the inequality:
[tex]v^2 + 20v - 1500 \leq 0[/tex]
Next, we factor the quadratic equation:
[tex](v - 30)(v + 50) \leq 0[/tex]
This gives us two critical points: v = 30 and v = -50.
Since speed cannot be negative, we discard v = -50.
Now we test the intervals created by the critical point:
- For v < 30, the inequality holds.
- For v > 30, the inequality does not hold.
One number is 5 more than another number. their sum is −15 . what are the numbers?
Which is the best simplification of (24 x 32) / (2 x 3)?
To simplify (24 x 32) / (2 x 3), perform the multiplication operations first. Then perform the division operation. This results in the simplification of the given expression to 128.
Explanation:To simplify the expression (24 x 32) / (2 x 3), we'll first carry out the multiplication operations because of the BIDMAS or PEMDAS rule that gives the order of operations in maths. B or P stands for brackets, I or E stands for Indices or Exponents, D/M for Division/Multiplication and A/S for Addition/Subtraction. According to this rule, Division or Multiplication is performed from left to right. Therefore, we first multiply 24 x 32 which gives 768, and secondly multiply 2 x 3 which gives 6. Thus, the expression now becomes 768 / 6. This division gives us the final answer of 128.
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An airplane descends at a rate of 300 feet for every 5000 horizontal feet that the plane travels. What is the slope of the path of descent?
Answer:
slope=-3/50
Step-by-step explanation:
slope= y/x
y=-300
x=5000
substituting into the equation:
slope=-300/5000
caryssa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost $45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for $5. What is the minimum number of braclets she must sell to make a profit?
what is the answer to this problem?
Barbie is thinking of s number. Twenty less than one third of the number is 72. Find barbies number
Look at the diagram. Which of the following is another name for < 1
A. < CBA
B. < ACB
C. < CAB
D. < BAC
Answer: A. ∠CBA
Step-by-step explanation:
We need three points to write a name of an angle. One point on each ray with the vertex lies in the middle.
There are total three ways to write a name of an angle.
For example :- M and N are points on each ray of an angle with vertex O.
Then, the name of angle can be ∠O, ∠MON or ∠NOM.
From the given picture , it can be observe that A and C are points on each ray of ∠1 with vertex B.
Then, the possible name of ∠1 will be ∠B , ∠ABC or ∠CBA.
Since, ∠CBA in given in option A.
Thus OPTION A is the correct option.
Manda uses the recipe shown to make punch for a family party. amanda’s punch recipe 7 parts mixed fruit juice 2 parts lemonade how much lemonade will she need to make 180 fluid ounces of punch
Answer:
40 fluid ounces of lemonade.
Step-by-step explanation:
Amanda uses the recipe shown to make punch for a family party.
Amanda's punch recipe 7 parts mixed fruit juice 2 parts lemonade.
7 + 2 = 9 parts
She will need to make 180 fluid ounces of punch.
she will need lemonade = (180/9) × 2
= 20 × 2
= 40 fluid ounces lemonade
She will need fruit juice = (180/9) × 7
= 20 × 7
= 140 fluid ounces fruit juice.
Amanda will need 40 fluid ounces lemonade to make 180 fluid ounces of punch.
Find the circumference of a circle with a radius of 6. Leave your answer in terms of
Indicate the equation of the given line in standard form.
The line through (2, -1) and parallel to a line with slope of 3/4
A flower store has 42 carnations and 21 pansies. It puts the same number of flowers in each of 7 bouquets.
How many flowers are in each bouquet?
What is 3a-2b if a=-1 and b=-2
The product of a number and 7 is at most the difference of the number and 5. write an inequality and solve for the variable
The quotient of y and 3 is 25
Help please !! It’s geometry credit recovery
Suppose you are building a rectangular pen for your goats. You use 400 feet of fencing for the pen.
What is 23% of 256? please help
Calculate f (-3) f (x)=-2x+3
Ramona is ordering carpet for a room that is 19.5 feet by 41.6 feet. the carpet is $9.50 per square foot. about how many square feet of carpet will ramona need to order to cover the entire room
Algebra expression ; Nine more than the product of 51 and the number T
one week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091. find the cost of a trumpet, a clarinet would, and a violin.
One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091.
Let x be the cost of trumpets
y be the cost of clarinets
z be the cost of violins
Now we frame equations
2x +3y + 5z = 1240 ---> equation 1
3x + 1y + 4z = 1027---> equation 2
5x + 7y + 2z = 2091 ---> equation 3
Now we solve for x,y and z using elimination method
Multiply the second equation by -3 and with first equation
2x +3y + 5z = 1240
-9x - 3y -12z = -3081
--------------------------------
-7x - 7z = -1841 ( divide both sides by -7)
x + y = 263 ----------> equation 4
Multiply the second equation by -7 and add it with third equation
-21x - 7y - 28z = -7189
5x + 7y + 2z = 2091
------------------------------------
-16x - 26z = -5098 (divide the whole equation by -2)
8x + 13z = 2549 --------> equation 5
Now use equation 4 and 5 to eliminate x. Multiply equation 4 by 8
-8x - 8z = -2104
8x + 13z = 2549
------------------------------
5z = 445
z = 89
We know x + z = 263, replace z with 89
x + 89 = 263 ( subtract 89 on both sides)
x = 174
2x +3y + 5z = 1240 ---> equation 1 ( substitute the values of x and z)
2(174) + 3y + 5(89) = 1240
348 + 3y + 445 = 1240
793 + 3y = 1240 ( subtract 793 on both sides)
3y = 447 ( divide by 3 on both sides)
y = 149
The cost of trumpets = $174
The cost of clarinets = $149
The cost of violins = $89
Using a system of equations, it is found that:
The cost of a trumpet is of $174.The cost of a clarinet is of $149.The cost of a violin is of $89.------------------
For the system of equations, i will say that:
The cost of a trumpet is x.The cost of a clarinet is y.The cost of a violin is z.------------------
2 trumpets, 3 clarinets, and 5 violins for $1240, thus:
[tex]2x + 3y + 5z = 1240[/tex]
3 trumpets, 1 clarinet, and 4 violins for $1027, thus:
[tex]3x + y + 4z = 1027[/tex]
5 trumpets, 7 clarinets, and 2 violins for $2091, thus:
[tex]5x + 7y + 2z = 2091[/tex]
------------------
From the second equation:
[tex]y = 1027 - 3x - 4z[/tex]
Replacing into the other two:
[tex]2x + 3y + 5z = 1240[/tex]
[tex]2x + 3(1027 - 3x - 4z) + 5z = 1240[/tex]
[tex]-7x - 7z = -1841[/tex]
Simplifying by 7:
[tex]x + z = 263 \rightarrow z = 263 - x[/tex]
Also:
[tex]5x + 7y + 2z = 2091[/tex]
[tex]5x + 7(1027 - 3x - 4z) + 2z = 2091[/tex]
[tex]-16x - 26z = -5098[/tex]
[tex]16x + 26z = 5098[/tex]
------------------
Solving for x:
[tex]16x + 26z = 5098[/tex]
[tex]16x + 26(263 - x) = 5098[/tex]
[tex]10x = 1740[/tex]
[tex]x = \frac{1740}{10}[/tex]
[tex]x = 174[/tex]
The cost of a trumpet is of $174.
------------------
Solving for z:
[tex]z = 263 - x = 263 - 174 = 89[/tex]
The cost of a violin is of $89.
------------------
Solving for y:
[tex]y = 1027 - 3x - 4z = 1027 - 3(174) - 4(89) = 149[/tex]
The cost of a clarinet is of $149.
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△R′S′T′ is the image of △RST under a dilation through point C. RS=5 and R′S′=8 . What scale factor was used in the dilation?
Answer:
1.6
Step-by-step explanation:
To find the scale factor, we compare the image size to the pre-image size.
R'S' = 8 and RS = 5; this makes the scale factor 8/5, which is 1.6.
Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. The scale factor that was used in the dilation is 1.6.
What is dilation?Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.
Scale factor = Dimension of the new shape/Dimension of the original shape
Given that △R′S′T′ is the image of △RST under a dilation through point C. Also, given that RS=5 and R′S′=8. Therefore, the scale factor that was used in the dilation is,
Scale factor = Dimension of the new shape/Dimension of the original shape
Scale factor = R′S′ / RS = 8/5
= 1.6
Hence, the scale factor that was used in the dilation is 1.6.
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what does the y-intercept mean in terms of the graph? Select all that apply.
a. the x-value at a y-value of 0.
b. the y-value at an x-value of 0.
c. where the function crosses the y-axis
d. where the function the x-axis
What is the equation of a horizontal line passing through the point (-7,5)
The simplified version of what you’re asking, and by simolified i mean solved, is Y= 5
Write the domain of the function given in the graph in set builder notation.
a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}
I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.
You are considering leasing one of two store sites of equal size. The first site features a percentage lease of 4% of sales per month. The second site features a triple net lease with these monthly terms: rent is 3% of sales, insurance is $175, maintenance is $50, utilities total $345, and property tax is $165. Your business plan estimates your monthly sales to average $85,000. Which lease is better for you financially?
The amount due for the first term of payment is the product of the total sales and the percentage.
(1) Amount due = ($85,000)(0.04) = $3,400
The total amount due for the second term of payment is the product of the total sales and the percentages together with all the fees specified in the item (insurance, maintenance, and utilities).
(2) Amount due = ($85,000)(0.03) + $175 + $50 + $345 = $3,120
If we are to compare the two amounts, using the second term of payment, lesser amount will be paid. Thus, the answer to this item is the second choice.
Answer: Second site
Step-by-step explanation:
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