Answer:
The product of exponents is equal to the sum of the exponents.
Step-by-step explanation:
(x^2)*(x^2)=x^4, as it can be written as x*x*x*x, which is also x^4.
(x^3)(x^3)(x^3) does NOT equal x^27
(x^3)(x^3)(x^3) equals x^9
in the triangle shown determine j to the nearest degree
Answer:
63
Step-by-step explanation:
Tan x = 3.5/1.8
Tan X=1.94444
x=62.78
The admission fee at an amusement park is $4.00 for children and $6.40 for adults. On a certain day,
301 people entered the park, and the admission fees collected totaled $1504. How many children
and how many adults were admitted?
number of children equals
number of adults equals
On solving the given equation, we have - 125 adult tickets and 179= children tickets.
What exactly is an equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
301= 104
6.40 =2.25
4.00=1.75
Suppose the number of adult ticket bought =x
And number of children tickets bought = (301-x).
equation is
6.40(x) + 4(301-x) = 1504
6.40x + 1204 - 4x = 1504
2.40x = 300
x= 125
125 adult tickets and 179= children tickets.
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Calculate the distance between the points J=(-3, -2) and G=(3, 1) in the coordinate plane.
Give an exact answer (not a decimal approximation).
Answer:
√45
Step-by-step explanation:
Hope this helps! Pls give brainliest!
This is the most accurate answer I can give otherwise you have to round.
HELP ME please. i dont understand this.
Answer:
Step-by-step explanation:
Perimeter add all the sides.
so let's walk around and combine like terms:
starting on the bottom moving to the left.
3x^2 + x^2= 4x^2 (there are no other squared terms)
back to the bottom moving left again:
-11x-3x+3x+x = -10x (-3x + 3x =0)
so -11x + x = -10x
now add all of the constants
-1 + 2 = 1
so your answer is
4x^2 -10x + 1
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answer: 180 gallons needed
Step-by-step explanation:
Zykeith,
Assume x gallons of 50% antifreeze is needed
Final mixture is x + 60 gallons
Amount of antifreeze in mixture is 0.4*(x+60)
Amount of antifreeze added is .5x + .1*60 = .5x + 6
so .5x + 6 = .4(x + 60)
.5x -.4x = 24 -6
.1x = 18
x = 180
Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:
\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)
Simplifying the equation:
\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)
\(\qquad\quad\implies 0.1x = 21\)
\(\qquad\qquad\implies \bold{x = 210}\)
\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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you purchase a tight sealed container for your sugar cubes to keep the ants away. The container is a rectangular prism with dimensions 6 in by 4 in by 3. The sugar cubes have 0.5 in sides. Is your container big enough to store 560 sugar cubes?
The container is indeed big enough to store 560 sugar cubes.
To determine if the container is big enough to store 560 sugar cubes, we need to calculate the volume of the container and compare it to the total volume occupied by the sugar cubes.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the dimensions of the container are:
Length (l) = 6 inches
Width (w) = 4 inches
Height (h) = 3 inches
Using the formula, the volume of the container is calculated as follows:
V = 6 inches * 4 inches * 3 inches
V = 72 cubic inches
Now, let's calculate the volume occupied by a single sugar cube:
The side length of a sugar cube is 0.5 inches, so the volume of a single sugar cube is:
V_cube = 0.5 inches * 0.5 inches * 0.5 inches
V_cube = 0.125 cubic inches
To determine the number of sugar cubes that can fit in the container, we divide the volume of the container by the volume of a single sugar cube:
Number of sugar cubes = V_container / V_cube
Number of sugar cubes = 72 cubic inches / 0.125 cubic inches
Number of sugar cubes = 576
Since the number of sugar cubes that can fit in the container is 576, which is greater than the required 560 sugar cubes, we can conclude that the container is indeed big enough to store 560 sugar cubes.
Therefore, the container can comfortably accommodate the desired quantity of sugar cubes while providing a tight seal to keep ants away.
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William leaves his home at 15:03 and walks for 12 minutes to Euston station.
He spends 4 minutes buying a ticket and then catches the next train to Bletchley.
What time will he arrive at Bletchley?
Train timetable
Euston
14:49 15:18 15:29
14:52
15:32 15:35
Harrow
Watford 15:01
15:30
15:41 15:44 16:11
Hemel
15:39 15:50
15:53
16:20
Tring
15:31
16:00
Q
16:14 16:41
Bletchley 15:47
16:16
16:30
Bedford 15:54 16:23 16:34 16:37 17:04
15:32 15:59
*Answer*
15:47
Step-by-step explanation:
He left; 15:03
Walk for; 12mins
Spends extra;4min
So by my side,
I'll sum up those values we're having to find the total time that was spent
12+4= 16mins
So, at that time when he reached at the station it was 15:19 when we add those extra mins
And so I think it'll 15:47
My thought told me so though
Dana has driven her car 95,598 miles. She estimates she can
drive the car another 5000 miles before the mileage reaches
100,000 miles. Use the rules for estimating differences to
explain if Dana is correct.
Answer: Dana estimation is incorrect because difference = 598 miles
Step-by-step explanation:
Given data,
Dana has driven her car 95,598 miles.
She estimates she can
drive the car another 5000 miles.
she can,
drive the car another 5000 miles before the mileage reaches
100,000 miles.
Estimated Mileage of the car is equal to 100,000 miles.
That is,
Estimated Mileage of the car is = 100,000 miles.
So,
We can write,
Total distance Dana has to travel = already driven + additional miles to cover
Total distance Dana has to travel = 95,598 + 5,000 miles
Total distance Dana has to travel = 1,00,598 miles.
As per mileage of car is 100,000 miles.
So, Dana has to travel = 1,00,598 miles.
So, Dana estimation is incorrect because difference is = 100,598 - 100,000
Therefore,
Dana estimation is incorrect because difference = 598 miles
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Find the slope and y-intercept
b. y = 1/4x - 6
Step-by-step explanation:
the slope is 1/4
the y-int is (0, -6)
F(x)=0.25x-2;H(x)=-F(x)
The solution to the function's operation of h(x) is -0.25x + 2.
What is a function?A function connects an element x to an element f(x) also known as (y) in another set. The domain of a function refers to the x-values and the range of the function is the set of values of f(x) i.e. (the y-values) that are produced by the values in the domain of the function, which is the set of values of x.
Given that:
f(x) = 0.25x - 2
h(x) -f(x)
We are going to simply replace the value of f(x) with h(x), i.e.
h(x) = -(0.25x - 2)
h(x) = -0.25x + 2
Therefore, we can conclude that the solution to the function's operation of h(x) is -0.25x + 2.
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Please help! No one literally ever answers me so please I'm begging ya'll!
Write the coordinates of the vertices after a translation 1 unit left and 7 units down.
R(-8, 2) → R′( , )
S(1, 2) → S′( , )
T(-7, 9) → T′( , )
Answer:
Simply subtract 1 from each x value and subtract 7 from each y value
Step-by-step explanation:
R'=(-9,-5)
s'=(0,-5)
T'=(-8,2)
Kindly solve the following with the cirrect method .SOLVE ALL . I'll give brainliest + thanks + follow
The following percentages are listed below:
12.5 %40 %6.25 %6.667 %41.667 %75 %How to use percentages in real life situationsIn this question we have seven cases of real life situations in which percentages are used. Mathematically speaking, percentages are represented by the following expression:
x = r / r' × 100 (1)
Where:
r - Real quantityr - Maximum quantityNow we proceed to determine quantities related to percentages:
2.8 mm as a per cent of 2.24 cm
x = (2.8 mm / 22.4 mm) × 100 %
x = 12.5 %
What per cent of 1.5 m is 60 cm?
x = (60 cm / 150 cm) × 100 %
x = 40 %
What per cent of 2 kg is 125 g?
x = (125 g / 2000 g) × 100
x = 6.25 %
What per cent of R 6 to 40 p?
x = (40 / 600) × 100
x = 6.667 %
What per cent of a day is 10 h?
x = (10 h / 24 h) × 100
x = 41.667 %
What per cent of 7 1 / 3 m in 5 1 / 2 m ?
x = [(11 / 2) / (22 / 3)] × 100 %
x = 75 %
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Pls help me I really nee it pls pls pls pls
A university's freshman class has 3000 students. 21% of those students are majoring
in Engineering. How many students in the freshman class are Engineering majors?
Answer: 630
Step-by-step explanation:
\(3000 * 21 /100 = 3000 * 0.21 = 630\)
Which equation represents the sentence, "The sum of three times p and twenty-five is q"?
A. (3 + 25) = q
B. 3(p + 25) = q
C. 3p – 25 = q
D. (3p + 25) = q
Answer:
D. (3p + 25) = q
f(x)=(x-1)(x-2)(x-3)(x-4)(x-3)(x-2)(x-2)/[(x-2)(x-4)(x-2)]
Answer:
Step-by-step explanation:
(x-2)(x-2)(x-4)
When Xander arranges his pennies into a rectangle with more than one row, he always has some leftover pennies. When he uses two equal rows or three equal rows, he has one leftover penny. When he arranges them into a rectangle with four equal rows, he has three leftover pennies. Remember he has between 10 and 40 pennies total. How many pennies does Xander have?
Answer:
20
Step-by-step explanation:
hope this was right and helpful
a triangle has one side length of 9cm and another side of .12cm what are 3 possible answers for the third side
If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side are: 17, 20, and 21.
What are the possible lengths for the third side?To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:
9 + 12 > x
9 + x > 12
12 + x > 9
Simplifying these inequalities, we get:
x > -3 (always true)
x > -9 (always true)
x > -3 (always true)
Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).
The possible lengths for the third side are:
9 + 12 > x, so x < 21
9 + x > 12, so x > -3
12 + x > 9, so x > -3
Therefore, the possible lengths for the third side of the triangle are:
17 (9 + 12 = 21, which is greater than 17)
20 (9 + 12 = 21, which is greater than 20)
21 (9 + 12 = 21, which is equal to 21)
So, the three possible lengths for the third side of the triangle are 17, 20, and 21.
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The complete question is:
A triangle has one side length of 9
centimeters (cm) and another side length of 12
cm.
Which answers are possible lengths for the third side?
Select three that apply
17
22
9
21
20
3
Find the solution of the system for which
Answer:
3,0,-6,0
Step-by-step explanation:
x1=3 because 3+0+0=3
since x2 and s2=0.
Vincent is going to frame a rectangular picture with the dimensions shown. Write a polynomial for the parameter of the frame, and then simplify.
1) Examining that rectangular picture, we can write out its Perimeter (2P) as the sum of its sides.
2) Since a rectangle has two pairs of parallel and congruent sides we can write out:
2P = 2a -2b + 2a -2b + 5a +3b +5a +3b Combine like terms
2P = 4a + 10a + 6b - 4b
2P = 14a +2b
3) Hence, the Perimeter (2P) of this rectangular frame is 14a + 2b
There are 25 girls and 20 boys in class 7. 7/15of the students in the class are fond of cricket and the remaining students are fond of football. How many students are fond of football?
Step-by-step explanation:
this is you're answer thanks for point
Answer:24
Step-by-step explanation:
7/15×45=21
45-21=24
Ronnie made a scale drawing of a shopping center. A bakery in the shopping center is 7 inches wide in the drawing. The actual bakery is 42 feet wide. What is the scale of the drawing?
Answer:
1:72
Step-by-step explanation:
The scale of a drawing is the ratio of the length in the drawing to the real length.
Drawing length: 7 inches
Real length: 42 ft × 12 in. / ft = 504 in.
Scale:
7 in. to 504 in.
Divide both numbers by 7:
1 in. to 72 in.
Scale: 1:72
What’s the probability that a randomly selected sheet will be blue if there are only 2 out of 12?
Answer:1/6
Step-by-step explanation:
đạo hàm của y= x^(x+1)
Answer:
-1
Step-by-step explanation:
Simplify 6 - 23 + (-9 + 5) · 2.
6 - 23 + (-9+5) * 2
-17 + (-4)*2
-17 + (-8)
-17 - 8
-25
Answer:
-25
Step-by-step explanation:
follow the order for pemdas which is (parenthesis,exponent,multiplication/division, and then addition/subtraction)
Compute the quadratic form xTAx for A = [3 2 0, 2 2 1, 0 1 0].
A. x = [x1 x2 x3].
B. x = [-2 -1 5].
C. x = [1/2 1/2 1/2].
Answer:
(a)\(x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\)
(b) 12
(c)\(2\frac{3}{4}\)
Step-by-step explanation:
\(G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\)
We are to compute the quadratic form \(x^TAx\) for A.
Part A
\(x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\)
\(x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\)
\(= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right]\)
\(= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)\)
\(= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\)
Part B
\(x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12\)
Part C
\(x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}\)
A box of matches measures 1 cm by 4 cm by 5 cm. Boxes of matches are packed in a cardboard box measuring 15 cm by 32 cm by 40 cm. How many boxes of matches fit into the cardboard box?
PLEASE HELP
Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 81 = 0
Rochelle deposited $500 in a bank account at a rate of 2.5% simple interest. How much interest did the money earn in 3 years?
Answer:
450
Step-by-step explanation:
500×2.5%×36=450
hope it helps