9514 1404 393
Answer:
a) 7
b) 20
c) 14
d) 24
Step-by-step explanation:
The desired number is found by subtracting the given number from the square of the integer just higher than the root of the given number.
a) √42 ≈ 6.5, so the desired number is 7² -42 = 49 -42 = 7
__
b) √101 ≈ 10.05, so the desired number is 11² -101 = 121 -101 = 20
__
c) √470 ≈ 21.7, so the desired number is 22² -470 = 484 -470 = 14
__
d) √1000 ≈ 31.6, so the desired number is 32² -1000 = 1024 -1000 = 24
if the total value of the coins is 71$ and she has 9 rolls of dimes, how many rolls of nickels does she have?
Answer:
18 rolls of nickles
Step-by-step explanation:
One roll of dimes would be the same value as 2 rolls of nickles. If she has 9 rolls of dimes, she would have 18 rolls of nickles.
Dont forget to thanks and rate!
Alysha has 13 nickel rolls.
Let x be the number of dime rolls and y be the number of nickel rolls.
What are linear equations?A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.
Each dime roll has 50 dimes, then x dime rolls are worth 50×10×x=500x cents or $5x.
Each nickel roll has 40 nickels, and then y nickel rolls are worth 40×5×y=200y cents or $2y.
A. The total value of Alysha's rolls is 500x+200y cents or $(5x+2y).
If the total value of the coins is $71 and she has 9 rolls of dimes, then x = 9 and 5×9+2y=71.
⇒45+2y=71
⇒2y=71-45
⇒2y=26
⇒y=13
Therefore, Alysha has 13 nickel rolls.
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Alysha has a collection of dime and nickel rolls that she'd like to take to the bank. Each dime roll has 50 dimes and each nickel roll has 40 nickels.
a) Write an equation to represent the total value of
b) If the total value of the coins is $71 and she has 9 rolls of dimes, how many does she have?
Lola pulls two marbles fro. A bag that contains four red marbles four blue marbles and 12 yellow marbles without replacing them what is the probability that she pulled out a red marble first and a yellow marble second ?express your answer in decimal form rounded to the nearest hundreth
[tex]|\Omega|=20\cdot19=380\\|A|=4\cdot12=48\\\\P(A)=\dfrac{48}{380}\approx0.13[/tex]
Write the equation of the line with a slope of -1 and a y-intercept of -6
y=-1x-6 is your answer
The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d?
Answer:
6
Step-by-step explanation:
The approximate distance in km between her house and her job is 9 km.
What is scaling ?
It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles
It is given that :
The distance on a map between a student’s house and her job is 6 cm.
also, on the same map, the distance between her house and her school is 8 cm.
The scale of the map = 8cm : 12km
Therefore, Distance between the house and the job = (12 x 6) / 8 = 9m
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.Perform each operation. Check by using the inverse operation. a. 769 – 362 = b. 502 + 17 = c. 7,802 – 3,461 = d. 1,432 + 2,568 =
a.) [tex]769-362 = 407[/tex]
Checking: Since, [tex]407+362 = 769[/tex]
Therefore, our answer is correct.
b.) [tex]502+17 = 519[/tex]
Checking: Since, [tex]519-17 = 502[/tex]
Therefore, our answer is correct.
c.) [tex]7802-3461 = 4341[/tex]
Checking: Since, [tex]4341+3461 = 7802[/tex]
Therefore, our answer is correct.
d.) [tex]1432+2568 = 4000[/tex]
Checking: Since, [tex]4000-2568 = 1432[/tex]
Therefore, our answer is correct.
Answer:
Consider the numbers:
a) 769 - 362 = ?
Subtract the numbers.
769 - 362 = 702
Therefore, the value is 702.
Now, check using the inverse operation.
407 + 362
Add the numbers.
407 + 362 = 769
Thus, the answer is correct.
Consider the numbers:
b) 502 + 17 = ?
Add the numbers.
502 + 17 = 519
Therefore, the value is 519.
Now, check using the inverse operation.
519 - 17
Subtract the numbers.
519 - 17 = 502
Thus, the answer is correct.
Consider the numbers:
c) 7802 - 3461 = ?
Subtract the numbers.
7802 - 3461 = 4341
Therefore, the value is 4341.
Now, check using the inverse operation.
4341 + 3461
Add the numbers.
4341 + 3461 = 7802
Thus, the answer is correct.
d) 1432 + 2568 = ?
Add the numbers.
1432 + 2568 = 4000
Therefore, the value is 4000.
Now, check using the inverse operation.
4000 - 2568
Subtract the numbers.
4000 - 2568 = 1438
Thus, the answer is correct.
Here we will study the function f (x) = e ^ x sin (x), where x ∈ [0, 2π]. a) Determine where the function is decreasing and increasing. b) Find all local maximam and minimam. Does the absolute (global) maximam / minimam have? c) Determine where f (x) curves up and down. Also find any turning points.
we are given
[tex]f(x)=e^x sin(x)[/tex]
(a)
Firstly, we will find critical numbers
so, we will find derivative
[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]
now, we can set it to 0
and then we can solve for x
we get
[tex]x=\frac{3\pi }{4} ,x=\frac{7\pi }{4}[/tex]
now, we can draw a number line and then locate these values
and then we can find sign of derivative on each intervals
increasing intervals:
[tex][0,\frac{3\pi}{4} )U(\frac{7\pi}{4} , 2\pi][/tex]
Decreasing interval:
[tex](\frac{3\pi}{4} ,\frac{7\pi}{4} )[/tex]
(b)
Local maxima:
It is the value of x where function changes from increasing to decreasing
so, local maxima is at
[tex]x=\frac{3\pi}{4}[/tex]
Local minima:
It is the value of x where function changes from decreasing to increasing
so, local minima is at
[tex]x=\frac{7\pi}{4}[/tex]
now, we will plug critical numbers and end values into original function
and we get
At x=0:
[tex]f(0)=e^0 sin(0)[/tex]
[tex]f(0)=0[/tex]
At [tex]x=\frac{3\pi}{4}[/tex]:
[tex]f(\frac{3\pi}{4})=e^{\frac{3\pi}{4}} sin(\frac{3\pi}{4})[/tex]
[tex]f(\frac{3\pi}{4})=7.46049[/tex]
At [tex]x=\frac{7\pi}{4}[/tex]:
[tex]f(\frac{7\pi}{4})=e^{\frac{7\pi}{4}} sin(\frac{7\pi}{4})[/tex]
[tex]f(\frac{7\pi}{4})=-172.640[/tex]
At [tex]x=2\pi [/tex]:
[tex]f(2\pi)=e^{2\pi} sin(2\pi )[/tex]
[tex]f(2\pi )=0[/tex]
Global maxima:
It is the largest value among them
so, we get
[tex]f(\frac{3\pi}{4})=7.46049[/tex]
Global minima:
It is the largest value among them
so, we get
[tex]f(\frac{7\pi}{4})=-172.640[/tex]
(c)
now, we can find second derivative
[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]
[tex]f''(x)=\frac{d}{dx}\left(e^x\sin \left(x\right)+e^x\cos \left(x\right)\right)[/tex]
[tex]=\frac{d}{dx}\left(e^x\sin \left(x\right)\right)+\frac{d}{dx}\left(e^x\cos \left(x\right)\right)[/tex]
[tex]=e^x\sin \left(x\right)+\cos \left(x\right)e^x+e^x\cos \left(x\right)-e^x\sin \left(x\right)[/tex]
[tex]f''(x)=2e^x\cos \left(x\right)[/tex]
now, we can set it to 0
and then we can solve for x
[tex]f''(x)=2e^x\cos \left(x\right)=0[/tex]
so, we get
[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]
now, we can draw number line and locate these values
and then we can find sign of second derivative on each intervals
concave up intervals:
[tex][0,\frac{\pi}{2})U(\frac{3\pi}{2}, 2\pi][/tex]
Concave down intervals:
[tex](\frac{\pi}{2} ,\frac{3\pi}{2})[/tex]
Turning points:
All values of x for which concavity changes
so, we get turning points at
[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]
fff
[tex]f(x) = e^x sin (x)[/tex]
To find increasing and decreasing intervals we take derivative
[tex]f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)[/tex]
Now we set the derivative =0 and solve for x
[tex]e^x(sinx+cosx)=0[/tex]
sinx + cosx =0
divide whole equation by cos x
[tex]\frac{sinx}{cosx} + \frac{cosx}{cosx} =0[/tex]
tanx +1 =0
tanx = 1
[tex]x=\frac{3\pi }{4}[/tex] and [tex]x=\frac{7\pi}{4}[/tex]
Now we pick a number between 0 to [tex]\frac{3\pi }{4}[/tex]
Lets pick [tex]\frac{\pi }{2}[/tex]
Plug it into the derivative
[tex]f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))[/tex]
= 4.810 is positive
So the graph of f(x) is increasing on the interval [0, [tex]x=\frac{3\pi }{4}[/tex])
Now we pick a number between [tex]\frac{7\pi}{4}[/tex] to 2pi
Lets pick [tex]\frac{11\pi}{6}[/tex]
Plug it into the derivative
[tex]f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))[/tex]
= 116 is positive
So the graph of f(x) is increasing on the interval [tex](\frac{7\pi }{4}, 2\pi)[/tex]
Increasing interval is [tex](0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)[/tex]
Decreasing interval is [tex](\frac{3\pi}{4}, \frac{7\pi}{4})[/tex]
(b)
The graph of f(x) increases and reaches a local maximum at [tex]x=\frac{3\pi}{4}[/tex]
The graph of f(x) decreases and reaches a local minimum at [tex]x=\frac{7\pi}{4}[/tex]
(c)
f(0) = 0
[tex]f(2\pi)=0[/tex]
[tex]f(\frac{3\pi }{4})=7.46[/tex]
[tex]f(\frac{7\pi}{4})=-172.64[/tex]
Here global maximum at [tex]x=\frac{3\pi}{4}[/tex]
Here global minimum at [tex]x=\frac{7\pi}{4}[/tex]
Courtney has $50 to spend at the county fair. She spends $10 on admission and $15 on snacks. The games at the fair cost $1.25 each. Which inequality could be used to find the maximum number of x games that Courtney can play while at the fair?
$1.25x + $10 + $15 (less than or equal to) $50
Answer:
So, with the reaming 25 dollars she can play at max 20 games.
Step-by-step explanation:
Given that
Amount Courtney has to spend = $ 50
Amount Spent on Admission = $ 10
Amount Spent on Snacks = $ 15
Price of a Game at Share = $ 1.25
Now, lets find the total amount spent by her already
Amount Spent = 50 - 10 - 15 = $ 25
Suppos x represent the number of games so, we can represent the remaining amount and in term of games that can be purchased by using it
[tex]1.25x\leq25[/tex]
the above inequality can be simplified as follows
[tex]x\leq\frac{25}{1.25}[/tex]
[tex]x\leq20[/tex]
So, with the reaming 25 dollars she can play at max 20 games.
HELP PLS math equation!
b represents rate of change
Answer:
rate of change
Step-by-step explanation:
Daniel biked to the park. On the way, he stopped for a soda, then continued to the park. After playing a game of catch, Daniel biked home. Between which two points did Daniel more than likely stop for a soda?
A) between points B and C
B) between points C and D
C) between points D and E
D) between points E and F
the distance from home would not change while he was stopped, so it would be a flat line. the two possibilities are B and C or D and E. He stopped for a soda then played catch (which would also be a flat line since he would be the same distance from home) so it must be B and C
Choice A
Answer:
A
Step-by-step explanation:
because D and E is when he's playing catch and right after he went home.
I need help with this Algebra question
Step 1 = Distributive Property ( multiplying the 2 by each term in parenthesis)
Step 2 = Addition Property ( adding like terms)
Step 3 = Addition Property (adding 34x to each side)
Step 4 = Division Property. ( dividing both sides by 17)
PLEASE HELP RATIOS TABLES DUE TOMARROW!!!!!!
Since the ratio is as simple as 1:2, just double each Euro value.
1:2, 2:4, 5:10, 10:20.
Answer:
$4,$10,$20.
Step-by-step explanation:
If 1 Euro=$2 then,2 euro=2*2=$4 5 euro=5*2=$1010euro=10*2=$20Find the dilated coordinates with the given center and scale factor (k). NEED ANSWER ASSAP
Do you need all the coordinates or just A' and B'
What is the square root of r^64
Answer:
The answer is 8.
Step-by-step explanation:
If is
[tex]\sqrt{r^{64}}=\sqrt{r^{32\cdot2}}=\sqrt{(r^{32})^2}=r^{32}[/tex]
Used:
[tex](a^n)^m=a^{nm}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]
If is
[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]
I have to Express 34.5 ÷ 15
You can solve this using long division. The answer should end up being 2.3.
Answer:
2.3
Step-by-step:
To make it easier,break it down first;35.5 also means 345/10(after the point,the number of digits is the number of 0’s behind the 1 that was used to divide a whole number.e.g;784.25=78425/100 e.t.c).You can then make the divided by 15 which also means 15/1 to multiplication by reversing it to *1/15(an example is division of 17/4 reversed to multiplied by 4/17).Note;After reversing the sign would change from division to multiplication.From there,we have an easier decimal;345/10*15/1=23/10 which is then equal to 2.3What are the 6 trigonometry functions
Sine, Cosine, Tangent, Cosecant (opposite of Sine), Secant (opposite of Cosine), and Cotangent (opposite of Tangent)
explain how ba+ca can be rewritten as a(b + c)
with the distributive property of multiplication you can take ba+ca and rewrite it as a(b+c)=ab+ac=ba+ca
Can someone help please
6=x+2/3
x=16/3 or 5.33333333
Answer:
Step-by-step explanation:
multiply by 3 the whole equation
6×3 = (x)×3 + (2/3) ×(3)
18 =3x + 2
subtracting 2 both sides
18-2 = 3x +2-2
16= 3x
dividing by 3 both sides
16/3 = 3x / 3
16/3 = x
(0,1)(4,2) find the slope and y-intercept using the point slope formula
Hello, Jssoyg! I've solved the problem for you below. I hope it helps.
Slope equation is[tex]\frac{y2 - y1}{x2 - x1}[/tex]. The two points are (0,1) and (4,2), so the equation becomes [tex]\frac{2 - 1}{4 - 0} = \frac{1}{4}[/tex]. We now know that the slope is 1/4, so now let's write it in the [tex]y = mx + b[/tex] format. Plug in the m, x, and y values:[tex]2 = 4*\frac{1}{4} + b[/tex].
This becomes [tex]2 = 1 + b[/tex] which means b = 1.
Your answer is y = 1/4x + 1. Hope this was helpful. :D
Five classmates came to Dan’s birthday party.Thus is as many as the number of friends from his summer camp,and one third as many as the number of his relatives that were there.How many people were at Dan’s birthday party
I think it is 25 sorry if im wrong
Answer:
There were 25 guest in Dan's party.
Step-by-step explanation:
We are given the following information in the question:
Number of classmates came to Dan’s birthday party = 5
Number of friends from his summer camp = Number of classmates came to Dan’s birthday party = 5
Number of relatives in Dan's party =
Let x be the number of relatives, then,
[tex]\displaystyle\frac{x}{3} = 5\\\\x = 15[/tex]
Total number of guest in Dan's party =
[tex]\text{Number of classmates came to Dan’s birthday party} +\\ \text{Number of friends from his summer camp } + \\\text{Number of relatives}\\= 5 + 5 + 15\\=25[/tex]
Hence, there were 25 guest in Dan's party.
what is the slope of -4x - 3
Hey there!
The slope of the equation is -4.
This is because each time x increases by 1, y increases by -4.
You can typically find the slope right in front of the x value in equations that look like this one.
Hope this helps!
An insurance agent receives 16% commission on every premium paid. How much commission is paid on a policy with a premium of $497.69?
Here we are given the information that an insurance agent receives 16% commission on every premium paid.
Now we are given that a premium of $497.69 is paid.
Let us say $x is the commission paid on the policy with a premium of $497.69.
Let us try to find the amount x here.
So we have to find 16% of 497.69 to get the commission amount x.
So finding 16% of 497.69.
x= 16% of 497.69 = 0.16*497.69 = 79.63
Answer: Commission of $79.63 is paid on a policy with a premium of $497.69.
Answer:
$ 79.6304 of commission was paid on policy with a premium of $497.69.
Step-by-step explanation:
Percentage on amount received on every premium = 16% of the premium
So, when the premium of the $ 497.69 was paid , the commission received by an agent will be: 16% of the $497.69 .
[tex]\$497.69\times \frac{16}{100}=\$79.6304[/tex]
$ 79.6304 of commission was paid on policy with a premium of $497.69.
Find the equation of a circle with center at the origin and x intercepts 10 and -10
Serena simplify the expression 3 (2x - 6 - x + 1 )^2 - 2 + 4x in step 1 she simplified within the parentheses in step 2 she expanded the exponent witch is a possible next step
Answer:
For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x
Step-by-step explanation:
step 1: 3(x - 5)² - 2 + 4x
step 2: 3(x - 5)(x - 5) - 2 + 4x
For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x
d. distribute the 3 to each term in the parentheses by multiplying.
First, simplify within parentheses: [tex]\(3(2x - 6 - x)^2 = 3(x - 6)^2\)[/tex]. Next, expand the exponent to get [tex]\(3x^2 - 36x + 108\)[/tex].
Sure, let's break down the steps:
Given expression:
[tex]\[ 3(2x - 6 - x)^2 - 24x \][/tex]
Step 1: Simplify within the parentheses.
[tex]\[ 3(2x - 6 - x)^2 = 3(x - 6)^2 \][/tex]
Step 2: Expand the exponent.
[tex]\[ 3(x - 6)^2 = 3(x^2 - 12x + 36) \][/tex]
[tex]\[ = 3x^2 - 36x + 108 \][/tex]
Now, combine this result with the given expression:
[tex]\[ 3x^2 - 36x + 108 - 24x \][/tex]
Step 3: Combine like terms.
[tex]\[ = 3x^2 - 60x + 108 \][/tex]
So, the simplified expression is:
[tex]\[ 3x^2 - 60x + 108 \][/tex]
The correct question is:
sharina simplified the expression 3(2x – 6 – x 1)^2 – 2 4x. in step 1 she simplified within the parentheses. in step 2 she expanded the exponent. which is a possible next step?
a. simplify the expression by adding and subtracting from left to right.
b. combine like terms within the parentheses.
c. combine all x-terms.
d. distribute the 3 to each term in the parentheses by multiplying.
if f(x)=3(x+5)+4/x what is f(a+2) ?
[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]
Estimate the product by rounding 9x54
9*54=486
10x50=500
So, either 450 or 500.
Is the digit in hundreds place 1/10 the value of the digit in the thousands place 8,556 yes or no
No, it is not.
Hope it helped! :)
If Raul rides his bike 3 miles for 10 minutes how many mile would he ride for 60 minutes at the same speed
60 divided by 10 =6
3x6=18
Raul would ride 18 miles.
Hope this helped :)
Raul would ride 18 miles for 60 minutes at the same speed.
Explanation:To find out how many miles Raul would ride for 60 minutes at the same speed, we can set up a proportion. If Raul rides 3 miles for 10 minutes, then we can say that 3 miles is to 10 minutes as x miles is to 60 minutes. Setting up this proportion, we get: 3/10 = x/60. To solve for x, we can cross multiply and then divide both sides by 10. This gives us: x = (3/10) * 60 = 18 miles.
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Error Analysis. Find and Correct ALL 3 of the errors in the proof.( 3 points)
Answer: The correct reason for [tex]\angle4\cong \angle7[/tex] is property of corresponding angles and the reason for [tex]\angle4+\angle6=180[/tex] is substitute [tex]\angle7=\angle4[/tex] and the third error is the forget the property that the sum of consecutive interior angles is 180.
Explanation:
It is given that m is parallel to n.
When two parallel lines intersected by a transversal eight angles are produced as shown in the given figure, where m and n are parallel and l is the transversal line.
In this case corresponding angles are congruent. Example [tex]\angle1\cong \angle5[/tex],[tex]\angle2\cong \angle6[/tex] etc.
So, [tex]\angle4\cong \angle7[/tex] by the property of corresponding angles.
[tex]\angle7+\angle6=180[/tex] because these are supplementary angles.
Substitute [tex]\angle7=\angle4[/tex]
[tex]\angle4+\angle6=180[/tex]
So, the correct reason is substitution.
Hence proved [tex]\angle4+\angle6=180[/tex]
The third error is the forget the property that the sum of one side interior angles is 180. Since the alternate interior angles are congruent therefore the consecutive interior angles are supplementary angles around the sum of consecutive interior angles is 180 degree.
Find the product of (3x − 4)(2x2 + 2x − 1).
Solve:
(3x − 4)(2x^2 + 2x − 1)
Simplify:
(3x − 4)(2x^2 + 2x − 1)
= (3x + −4)(2x^2 + 2x + −1)
= (3x)(2x^2) + (3x)(2x) + (3x)(−1) + (−4)(2x2) + (−4)(2x) + (−4)(−1)
= 6x^3 + 6x^2 − 3x − 8x^2 − 8x + 4
Answer = 6x^3 − 2x^2 − 11x + 4
Hope that helps!!!! : )
Final answer:
The product of (3x - 4) and (2x² + 2x - 1) is calculated by multiplying each term in the first polynomial by each term in the second and combining like terms, resulting in the final expression 6x³ - 2x² - 11x + 4.
Explanation:
The product of the polynomials (3x − 4) and (2x2 + 2x − 1) is obtained by applying the distributive property, otherwise known as FOIL (First, Outer, Inner, Last) method in this context. Each term in the first polynomial is multiplied by each term in the second polynomial and then the results are summed together. The step-by-step calculation is as follows:
Multiply the First terms: (3x) × (2x2) = 6x3.
Multiply the Outer terms: (3x) × (2x) = 6x2.
Multiply the Inner terms: (− 4) × (2x2) = − 8x2.
Multiply the Last terms: (− 4) × (− 1) = 4.
Once these calculations are done, we combine like terms:
6x3 (no like terms to combine here)
6x2 − 8x2 = -2x2
(3x) × (2x) = 6x2 (already accounted for in the previous step)
(3x) × (−1) = -3x
(− 4) × (2x) = − 8x
4 (no like terms to combine here)
So, adding all these up, we get:
6x3 − 2x2 − 3x − 8x + 4
Combining the x terms, we have:
− 3x − 8x = − 11x, so the final answer is:
6x3 − 2x2 − 11x + 4
A music store gives every 20th customer a $5 gift card. Every 50th customer gets a $10.00 gift card. Which customer will be the first to receive both types of gift cards?
100th customer is your answer
Find the first number that shows up on both answers when they are added
Add 20 each time for $5 gift card:
20, 40, 60, 80, 100
Add 50 each time for $10 gift card:
50, 100
------------------------------------------------------------------------------------------------------------
As seen above, the first number that shows up on both is 100, therefore, 100 is your answer
hope this helps