The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108
Evaluation of ExpressionThe given expression is:
[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]
Simplifying the expression, we have:
[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]
Substitute y = 7 into the simplified expression
[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]
Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108
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Answer: -1
Step-by-step explanation: khan academy
10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined
them. After how many days was the whole job done?
A. 8days
B. 12days
C. 16days
D. 18days
Answer:
C. 16 days
Step-by-step explanation:
Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.
If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.
2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.
4 more workers join to complete the job, so we now do 12 work each day.
150 - 54 = 96
96 work is left to do, which would be done in 8 days by 12 workers.
8 days + 8 days = 16 days
use the sum to product formula to find exact values: if cos255 - cos195 = squrtroot a/ 2 then a=
By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2
How to analyze a trigonometric expression
In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:
[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]
Then,
cos 255° - cos 195° = - 2 · sin 225° · sin 30°
cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°
cos 255° - cos 195° = 2 · sin 135° · sin 30°
cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)
cos 255° - cos 195° = √2 / 2
Then, by direct comparison we find that a = 2.
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At some department store, all suits are reduced 20% from the retail price. If a man purchased a suit that originally retailed for 231.20 how much did he save?
well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]
find the slope of this line
6m + 2 - 4m =
help with this please
The answer is: 2(m+1)
First combine like terms.
we do 6m-4m which is 2m
2m+2=?
Second we factor. We notice that both terms have 2.
2(m+1)
by distributive law, the 2 is distributed to m and 1.
Please help! Solve this
The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1
How to solve the equation?The equation is given as:
[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]
Split the equation as follows:
[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]
[tex]y = 1 + x^2[/tex]
Next, we plot the graph of both equations (see attachment)
From the attached graph, the intersection point is (1, 2)
Remove the y value
x = 1
Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1
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What is the measure of arc RT
The measure of arc RT is 156 degree.
Measure of arc RTGiven:
arc TRM=102°
Hence:
arc RST=2×1O2°
arc RST=204°
Measure of arc RT
arc RT= 2(180° - 102°)
arc RT = 2(78°)
arc RT = 156 degrees
Therefore the correct option is B.
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the graph shown below expresses a redical function that can be written in the form f(x)= a(x+k)^1/n + c. what does the graph tell the value of a in this function?
The value of n given the form of the function is (b) positive odd number
How to interpret the graph?The form of the graph is given as:
f(x) = a(x + k)^1/n + c
For the given graph, we have the following features:
a > 0 --- a is positive
k > 0 --- k is positive
c < 0 --- c is negative
If n is an even number, the function would be undefined because the even root of a number is undefined
However, the function is defined if n is an odd number,
Hence, the value of n given the form of the function is a positive odd number
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A retailer buys a table costing £95 and sells it for £114 what is the name percentage change
Answer:
20% increase
Step-by-step explanation:
To find the percent increase, use this formula
New value - original value
----------------------------------------
original value
114-95
-----------
95
19
---- = .2
95
.2 is 20%, so it is a20% increase
help me pleaseeeee (20 points)
what is the volume of this solid?
Answer:
A) 39
Step-by-step explanation:
If you calculate the volume of the cube which is the V=a^3 you get 27, then calculating the pyramid, the Length is 3, and the Width is also 3. Then the height is 4. so you put that into the formula to calculate the volume which is V=L*W*H
--------
3
you get 12. Now its simple, you just add the 2 volumes, so you do 27+12 and its 39.
39 is the answer by calculating the volume using formula!
Find the sum of the first five terms using the geometric series formula for the sequence 1/2, -1,2,-4…
The sum of the first five terms is 11/2
How to determine the sum?The series is given as:
1/2, -1,2,-4…
Calculate the common ratio of the series using
r = -4/2
Evaluate
r = -2
The sum is then calculated as:
[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]
This gives
[tex]S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}[/tex]
Evaluate
[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]
Evaluate
[tex]S_n =\frac{11}{2}[/tex]
Hence, the sum of the first five terms is 11/2
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5660 and his stock in Company B was worth $2500. The stock in Company A has increased 5% since last year and the stock in Company B has increased 9%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary)
Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The values of the stocks of Company A and Company B, after the increase are given, respectively, by:
Company A: 5660 x 1.05 = $5,943.Company B: 2500 x 1.09 = $2,725.The total values are given as follows:
Before the increase: 5660 + 2500 = 8160.After the increase: 5943 + 2725 = 8668.The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:
P = (8668 - 8160)/8160 x 100% = 6.2%.
The total percentage increase in the investor's stock account was of 6.2%.
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Preeta’s book has 300 pages. Each day she reads 10 more pages than the day before. She finishes her book in 6 days. How many pages does she read?
Step-by-step explanation:
1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;
2. if the sum of all the pages is 300, then it is possible to make up the equation:
x+x+10+x+20+x+30+x+40+x+50=300;
3. x=25, it means:
1st day - 25;
2d day - 35;
3d day - 45;
4th day - 55;
5th day - 65;
6th day - 75 pages.
what would be your return on the investment if you bought when rates were 7% and sold when rates were 10%
The return on the investment is 3%
How to determine the return on investment?The given parameters are:
Buying rate = 7%
Selling rate = 10%
The return on the investment is
ROI = Selling - Buying
So, we have:
ROI = 10% - 7%
Evaluate
ROI = 3%
Hence, the return on the investment is 3%
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Please help me answer this question, 20 POINTS!
Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
It's 4 buns & 5 cakes
Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.
E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p
Given AB=10cm, CD=11cm, and AD=39cm, find the length of BC
Answer:
BC = 18 cm
Step-by-step explanation:
As we can see from the diagram:
AB + BC + CD = AD
⇒ 10 cm + BC + 11 cm = 39 cm
⇒ BC + 21 cm = 39 cm
⇒ BC = 39 cm - 21 cm
⇒ BC = 18 cm
In the following diagram, line m is parallel to line n and line q intersects the parallel lines at
Answer:
108°
Step-by-step explanation:
We know for a theorem that A = B, so:
4x + 28 = 2x + 68
Isolating the x:
2x = 40
x = 20
Now let's plug in the equation for A:
4(20) + 28 = 108°
a green grocer has 180 mangoes to sell. she has to arrange them in piles of 9,10,and 12 mangoes. in which ways would she arrangfe them without a reminder?
It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.
What are the different ways the mangoes can be arranged?The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.
Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:
9 mangoes piles: 180/ 9 = 20 piles (9 x 20 = 180 with no remainders)10 mangoes piles: 180/10 = 18 piles (10 x 18 = 180 with no remainders)12 mangoes piles: 180/12 = 15 piles (12 x 15 = 180 with no remainders)Learn more about division in https://brainly.com/question/369266
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find the product xy if
2^(x)+3^(y)=5,
2^(x+2)+3^(y+1)=18
The solution to the system of equation is (0, 1)
System of equationsGiven the following system of equation as shown below
2^(x)+3^(y)=5,
2^(x+2)+3^(y+1)=18
Rewrite
2^(x)+3^(y)=5,
2^x*2^2 + 3^y*3^1 = 18
___________
2^(x)+3^(y)=5,
4(2^x) + + 3(3^y) = 18
Let a = 2^x and b = 3^y
Substitute
a + b = 5
4a + 3b = 18
a = 5 - b
Substitute
4(5-b) + 3b = 18
20 - 4b + 3b = 18
-b = -2
b = 2
since a = 5 - b
a = 5 - 2
a = 3
Recall that a = 2^x and b = 3^y
2^x = 2
x = 0
Similarly
3^y = 3
y =1
Hence the solution to the system of equation is (0, 1)
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he parallelogram on the left was dilated by a scale factor of 2 about point P . It was then transformed in another way to produce the parallelogram on the right. On a coordinate plane, parallelogram P has points (negative 4, 0), (negative 2, 0), (negative 3, negative 3), (negative 5, negative 3). Parallelogram P prime has points (3, 0), (7, 0), (5, negative 6), (1, negative 6). Which identifies the transformation that occurred after the dilation?
The transformation that occurred after the dilation of the parallelogram is a translation of 9 units to the right.
What is a parallelogram?A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a parallelogram.
The initial parallelogram was dilated by a scale factor of 2 about point P.
The points of the initial parallelogram are: (-4, 0), (-2, 0), (-3, -3), (-5, -3).
The parallelogram obtained on dilation will have the points: (-6, 0), (-2, 0), (-4, -6), (-8, -6).
The points of the final parallelogram are: (3, 0), (7, 0), (5, -6), (1, -6).
(-6,0) →(3,0) ⇒ (x,y)→(x+h , y+k)
x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9
y = 0 , y+k = 0 ⇒ k = 0
The transformation rule is (x,y)→( x+9 , y )
That is, a translation of 9 units to the right.
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Answer:
A. a translation of 9 units to the right
Step-by-step explanation:
Edge 2023
the volume formula for a cylinder is v=nr^h. isolate for the variable r in this formula .
Answer:
[tex]r=\sqrt{\frac{V}{\pi h}}[/tex]
Step-by-step explanation:
[tex]V = \pi r^{2} h \\ \\ r^{2} =\frac{V}{\pi h} \\ \\ r=\sqrt{\frac{V}{\pi h}}[/tex]
Henry wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?
A trapezoid with a height of 3 feet and bases of 6 feet and 10 feet is shown.
The total cost to laminate the tabletop is $96.
What is the total cost to laminate the tabletop?The first step is to determine the area of the trapezoid.
Area of the trapezoid = 0.5 (sum of parallel sides) x height
0.5 x (6 + 10) x 3 = 24 feet²
The total cost of laminating = cost per square feet x area
$4 x 24 = $96
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One solution to the problem below is 3.
What is the other solution?
b²-9=0
By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.
How to find the remaining root of second order polynomial
Herein we have a quadratic equation, that is, a second order polynomial, of the form b² - a² = 0. By algebra we know that the polynomial of such form have the following equivalence:
b² - a² = (b - a) · (b + a), which means that the roots of the interval are x₁ = a and x₂ = - a.
If we know that a² = 9, then the roots of the second order polynomial are:
b² - 9 = (b - 3) · (b + 3)
By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.
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After flying at an altitude of 500m, a helicopter starts to descend when its ground distance from the landing pad is 11 kilometers. What is the angle of depression for the flight?
Answer:
2.603 degrees
Step-by-step explanation:
This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.
Height = 500
Base = 11,000
The hypotenuse ends up being 11,011.35777
in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!
question 3 of 8. Step 1 of 1
1/8
Correct
-
1
Incorrect
Adairy needs 385 gallons of milk containing 6 % butterfat. How many gallons each of milk containing 7 % butterfat and milk containing 2 % butterfat must be used to
obtain the desired 385 gallons?
308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.
CombinationSince a dairy needs 385 gallons of milk containing 6% butterfat, to determine how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 385 gallons, the following calculation must be performed:
385 x 0.06 = 23.1300 x 0.07 + 85 x 0.02 = 22.7310 x 0.07 + 75 x 0.02 = 23.2308 x 0.07 + 77 x 0.02 = 23.1Therefore, 308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.
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I need help with b and c please and thank you!!
Answer:
rjdjdj shiejd shsuisis shusisos
On 1st January 2014, Rs1,000,000 was invested and on 1st January of each
successive year Rs500,000 was added to it. What sum will be accumulated by
31st December 2018 if interest is compounded each year at 10% per annum?
The sum accumulated by 31st December 2018 is Rs 4,163,060.00
What is future value?
Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.
Note in this case that Rs500,000 would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)
We can determine the future value of each investment using the future value formula shown below:
FV=PV*(1+r)^N
PV=amount invested
r=interest=10%
N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)
Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1
Total FV=Rs 4,163,060.00
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32. What is the perimeter of a regular octagon with a side length of 7 units?
11 units
35 units
49 units
56 units
Answer:
56
Step-by-step explanation:
solution
Here
P=8a=8·7=56
Answer:
56 units
Step-by-step explanation:
the perimeter of a rectangular octagon with sides of length a
is equal to: 8 × a
Then
the perimeter of a regular octagon with a side length of 7 units
is equal to: 8 × 7 = 56 units
Which is the only state that uses to calculate its area
Answer:
The answer is circle.
Step-by-step explanation:
For all the rest of the shapes, we use certain base x height formulas. Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula [tex]\pi r^{2}[/tex] where r= radius.
A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/5 for pink, 1/25 for blue, 1/10 for yellow, and 1/15 for black. What is the probability of pulling a blue or yellow card,
The probability of pulling a blue or yellow card, written as a reduced fraction is 7/50
How to determine the probability of pulling a blue or yellow card, written as a reduced fraction?From the question, we have the following probabilities:
P(Pink) = 1/5
P(Blue) = 1/25
P(Yellow) = 1/10
P(Black) = 1/15
The probability of pulling a blue or yellow card, written as a reduced fraction is the calculated as:
P(Blue or yellow card) = P(Blue card) + P(Yellow card)
Substitute the known values in the above equation
P(Blue or yellow card) = 1/25 + 1/10
Express 1/25 as 2/50 and 1/10 as 5/10
P(Blue or yellow card) = 2/50 + 5/50
Take the LCM
P(Blue or yellow card) = (2+ 5)/50
Evaluate the sum
P(Blue or yellow card) = 7/50
Hence, the probability of pulling a blue or yellow card, written as a reduced fraction is 7/50
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