Answer:
0.7.
Step-by-step explanation:
x^2 = 0.7x
x^2 - 0.7x = 0
x(x - 0.7) = 0
x = 0, 0.7.
After solving the quadratic equation x² = 0.7x , we get that the original number is 0.7
What is a quadratic equation?
Quadratic equation is an equation which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the standard quadratic equation in x is given by
ax²+bx+c =0, where a, b, c are constants and a≠0
We can solve this equation by factorizing ax²+bx+c and putting those factors equal to zero to solve for x.
Let a non zero number be x, x≠0 and given that the square of a non zero number is equal to the 70% of the original number.
As 70 % of the original number = 70/100(x) = 0.7 x
⇒ x² = 0.7 x
⇒x²-0.7 x = 0
⇒ x(x -0.7)= 0
⇒ x =0 and x - 0.7 = 0
⇒ x = 0.7, as we have given that x is a non zero number
Therefore, the original number is 0.7
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Solve ax + by = a-b and bx – ay = a+b
Answer: x=1 y=1
Step-by-step explanation:
ax+by=a−b .......... (1)
bx−ay=a+b .......... (2)
Multiply equation (1) with a and equation (2) with b ,
a
2
x+aby=a
2
−ab ..........(3)
b
2
x−aby=ab+b
2
......... (4)
Adding (3) and (4), we get,
(a
2
+b
2
)x=a
2
+b
2
⇒x=1
Now, from (1),
ax+by=a−b
a+by=a−b
by=−b
y=−1
A car driving at 20m/s accelerates at 3m/s2 for 3s. What is its final velocity? How far will it travel during this time?
Answers:
Final velocity = 29 m/s
Distance traveled = 73.5 meters
========================================================
Work Shown:
The given data is
[tex]v_i = 20 \text{ m}/\text{s} = \text{initial velocity}\\\\a = 3 \text{ m}/\text{s}^2 = \text{acceleration}\\\\t = 3 \text{ s} = \text{time duration}\\\\[/tex]
This leads to
[tex]v_f = v_i + a*t\\\\v_f = 20 + 3*3\\\\v_f = 20 + 9\\\\v_f = 29\\\\[/tex]
The final velocity is 29 m/s.
----------
We can use that final velocity to find the distance traveled.
[tex]x = 0.5*(v_i+v_f)*t\\\\x = 0.5*(20+29)*3\\\\x = 0.5*(49)*3\\\\x = 24.5*3\\\\x = 73.5\\\\[/tex]
The distance traveled is 73.5 meters.
----------
An alternative way to calculate the distance is to do this
[tex]x = \frac{(v_f)^2 - (v_i)^2}{2a}\\\\x = \frac{(29)^2 - (20)^2}{2*3}\\\\x = \frac{841 - 400}{6}\\\\x = \frac{441}{6}\\\\x = 73.5\\\\[/tex]
Or you could do this
[tex]x = v_i*t + 0.5*a*t^2\\\\x = 20*3 + 0.5*3*3^2\\\\x = 20*3 + 0.5*3*9\\\\x = 60 + 13.5\\\\x = 73.5\\\\[/tex]
For more information, check out the Kinematics equations.
Which pattern is a characteristic of a graph of exponential growth?.
Answer:
rises sharply on the right
Step-by-step explanation:
A regular decagon has a radius of 8 cm. what is the approximate area of the decagon? recall that a decagon is a polygon with 10 sides.
The approximate area of the decagon with a side of 8cm comes to be 492.40 cm².
The side of the regular decagon = 8cm
What is a regular decagon?A regular decagon is a polygon with 10 sides that are equal to each other.
The area of a regular decagon with side a is:
[tex]A=\frac{5}{2} a^{2} \sqrt{5+2\sqrt{5} }[/tex]
So, the area A of the regular decagon with a side of 8cm:
[tex]A=\frac{5}{2} 8^{2} \sqrt{5+2\sqrt{5} }[/tex]
[tex]A=160\sqrt{5+2\sqrt{5} }[/tex]
A=492.40 cm²
Therefore, the approximate area of the decagon is 492.40 cm².
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just this one
What percent of your budget is food if your monthly income is $6000 and you spend 900 on food each month?
Answer:
15%
Step-by-step explanation:
900/6000
which is the same as 900÷6000
900÷6000= 0.15
0.15 as a percent in 15%
A university has 34,350 students. In a random sample of 255 students, 17 speak three or more languages. Predict the number of students at the university who speak three or more languages.
Tori is throwing a pool party to kick off the summer. Her pool is empty, so she starts filling it with water from a garden hose. There is a proportional relationship between the time Tori has been filling up the pool (in minutes), x, and the volume of water in the pool (in gallons), y.
Answer:
y/x
Step-by-step explanation:
Answer: y/x
water/time = unit rate = y/x
transtle (-2,-2) up 1 unit then reflect the result over the x axis what are the coordinates of the final point
Answer:
(-2,1)
Step-by-step explanation:
1 unit up will change the y-value as it is moving vertically. Will make it (-2,-1)
Then, reflecting over x-axis means x-value stays the same and the sign of y-value switches.
so,
(-2,1)
Curtis has two bags of marbles the first bag contains 7 blue 2 yellow 6 red and 5 green marbles the second bag contains 4 blue 2 yellow 2 red and 2 green marbles soda hd have a greater probability of choosing a blue marble from the first or second bag
Answer:
Step-by-step explanation:
First Container.
Total = 7 + 2 + 6 = 15
Probility blue = 7 / 15 = 0.467
Second Container
Total = 4 + 2 +2 = 8
Probability Blue = 4/8 = 1/2 = 0.5
Answer: You are much better off drawing from the Second Container.
For what value of x is the equation 2(x-12)+x=36
[tex]~~~~~~2(x-12)+x=36\\\\\implies 2x-24+x = 36\\\\\implies 3x = 36+24\\\\\implies 3x = 60\\\\\implies x = \dfrac{60}3\\\\\implies x = 20[/tex]
2(x+12)+x=36
or,2x+24+x=36
or,3x+24=36
or,3x=36-24
or,3x=12
or,x=12/3
or,x=4
Thus, 20 is your answer
Part B
Based on your research, which of the three stocks would have been the best investment option over the past year? Explain the reason for your
choice.
Answer:The J C Penney Company stock would have been the best investment option, because the stock provided a rate of return of 18.82 percent to investors during the past year. The Apple stock offered a lower return of 13.29 percent. The Ford Motor Company gave a negative return of 0.51 percent, which means investors in this stock lost a small amount of their investment over the past one year.
Step-by-step explanation: ANSWER FOR EDMENTUM/PLATO
(Answers may vary.)
The J C Penney Company stock would have been the best investment option, because the stock provided a rate of return of 18.82 percent to investors during the past year. The Apple stock offered a lower return of 13.29 percent. The Ford Motor Company gave a negative return of 0.51 percent, which means investors in this stock lost a small amount of their investment over the past one year.
Step-by-step explanation: edmentum/ plato exact
Which statement best describes how to determine whether f(x) = x4 – x3 is an even function? determine whether (–x)4 – (–x)3 is equivalent to x4 – x3. determine whether (–x4) – (–x3) is equivalent to x4 x3. determine whether (–x)4 – (–x)3 is equivalent to –(x4 – x3). determine whether (–x4) – (–x3) is equivalent to –(x4 x3).
Since f(x) ≠ f(- x) then f(x) is not an even function. (–x)^4 – (–x)^3 is equivalent to x^4 – x^3.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
We need to find f(x) = x^4 – x^3 is an even function
If 2 functions are even, then
f(x) = f(- x)
f(x) = [tex]- x^3[/tex]
f(- x) = [tex]- (- x)^3 = + x^3[/tex]
Since f(x) ≠ f(- x) then f(x) is not an even function.
Learn more about function;
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Answer:
A
Step-by-step explanation:
The volume of a number cube is 27 cm^3. What is the length of each side of a cube?
Answer:
Side = 3 cm
Step-by-step explanation:
Given:
[tex]\text{Volume of cube} = 27 \ \text{cm}^{3}[/tex]
The formula to calculate the volume is (Side)³.
Thus, we obtained the following equation:
[tex](\text{Side})^{3} = 27 \text{cm}^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Side}^{3} = \text{Volume of cube}][/tex]
Cube root both sides to obtain the side length of the cube:
[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]
Evaluate the side of the cube:
[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]
[tex]\implies \sqrt[3]{\text{(Side)}\text{(Side)(Side})} = \sqrt[3]{3 \times 3 \times 3 \times \text{(cm)(cm)(cm)}}[/tex]
[tex]\implies \text{Side = 3 cm}[/tex]
Answer:
3 cm
Step-by-step explanation:
Formula
Volume of a cube = [tex]a^3[/tex] (where a is the side length)
Given that the volume of the cube is 27 cm³, to find the side length, substitute the given volume into the equation and solve for [tex]a[/tex]:
[tex]\implies 27\: \sf cm^3=a^3[/tex]
Cube root both sides:
[tex]\implies \sqrt[3]{27\: \sf cm^3} =\sqrt[3]{a^3}[/tex]
[tex]\implies \sqrt[3]{27}\sqrt[3]{\sf cm^3} =\sqrt[3]{a^3}[/tex]
[tex]\implies 3\: \sf cm=a[/tex]
[tex]\implies a=3\: \sf cm[/tex]
Therefore, the length of each side of the cube is 3 cm.
At 7 P.M., the temperature was 0.6°C. Over the next 3 hours, the temperature decreased by 1.9º. What was the temperature at 10 P.M.?
Answer:
2.5
Step-by-step explanation:
3 hours after 7 is 10 so add 1.9 to 0.6
Hello"! Need Help!
Question 1) Given 15 cot A = B. Find sin A and sec A .
Notes:-
• Kindly Don't spam
• Need Genuine Answer
• Don't copy from other website.
• Answer will be step-by-step explanation otherwise answer will be report...
↪Given 15 cot A = 8. Find sin A and sec A
Hope this helps...☆
In this polygon all angles are right angles what is the area of this polygon
Answer:
please check photo for detailed explanation
Which shows one way to determine the factors of 4x3 x2 – 8x – 2 by grouping? x2(4x 1) – 2(4x 1) x2(4x – 1) 2(4x – 1) 4x2(x 2) – 1(x 2) 4x2(x – 2) – 1(x – 2)
An expression has numbers, variables, and mathematical operations. The factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The factors of the expression by grouping can be done as,
[tex]4x^3+x^2-8x-2[/tex]
Take x² as the common factor from the first two terms while -2 from the last two terms,
[tex]4x^3+x^2-8x-2\\\\=x^2(4x+1)-2(4x+1)[/tex]
Thus, the factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).
Learn more about Expression:
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ILL GIVE BRAINLIEST
Type the correct answer in the box.
Answer:
1 (one)
Step-by-step explanation:
Answer:
1
----------------------------------------------------------------------------------------------------------
SolveFirst things first, evaluate all square roots in order, starting with the square root of 12
3.4641016151377553.1622776601683792.236067977499792.449489742783178The next step is to divide, despite multiplication always coming before division, you cannot multiply without first knowing the values of the division.
[tex]3.5 / 3.2 = 1.09\\\\2.2 / 2.4 = 1.09[/tex]
Now, you can multiply.
[tex]1.09 * 1.09 = 1.1881[/tex]
That said, 1.1881 is closest to 1 because it has a 1 in the tenths place, the greatest place in a decimal number.
Sam is planning to start a pool cleaning business from his home. he has developed the following cost analysis for the set-up and operation for the first year of his business. he has $9,000 in savings and $23,000 in credit that he can use for the business. approximately what percent of the initial set-up and operation costs will sam need to finance with a lender or investor? item cost truck $9,000 pool cleaning supplies $6,000 payroll $23,000 advertising $1,500 a. 19% b. 23% c. 33% d. 78%
The percent of the initial set-up and operation costs that Sam needs to finance with a lender or investor is A. 19%.
How to illustrate the percentage?From the information given, Sam is planning to start a pool cleaning business from his home. he has developed a cost analysis for the set-up and operation.
Here, the percent of the initial set-up and operation costs that Sam need to finance with a lender or investor is simply 19%.
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What is the fraction of the repeating decimal?
it's 46/99
whenever you get a question like this, you need to think: what would those fractions even be?
well it sure is not a bc 3/6 is already 0.5 and you need a lower number
it's not b either bc 4/16= 1/4 and that is 0.25
and well it can't be d either bc 13/16 is that not far away from 1
====================================================
Explanation:
Let x = 0.464646...
Multiplying both sides by 100 gets to 100x = 46.464646... which moves the decimal point over two spots to the right.
Then subtract the two equations
100x - x = 46.464646... - 0.464646...
99x = 46
x = 46/99
Notice how the decimal portions cancel out when we subtract. This is because they line up perfectly.
To confirm the answer, your calculator should show that
46/99 = 0.46464646
The "46"s going on forever.
At some point, your calculator may round the last '4' to a 5 to have it read something like 0.464646465 but this is of course rounding error.
On some calculators I tried, I noticed it displayed 0.46464646464647 which is even more strange considering the next digit (4) isn't five or larger. So that 6 shouldn't have bumped up to the 7.
To convert 27 kg to mg, you would move the decimal point _____ places to the _____.
Answer:
To convert 27 kg to mg, you would move the decimal point 6 places to the right.
hope that's helpful to you!
Pt2 check first one for the question
Answer:
what how
Step-by-step explanation:
find the area of given trapezium which save height is 3 cm and p1 is 12 cm and p2 is 24 cm
Answer:
Hope the picture will help you.......
A large rectangular card measures 80 centimetres by 90 centimetres.
Maria uses all this card to make small rectangular cards measuring 40 millimetres
by 15 millimetres.
Calculate the number of small cards.
1200 cards
All measurements should be taken in centimeters
Calculate the area of large rectangular card:
Length * Width 80 * 907200 cm²Calculate the area of each small cards:
Length * Width4 * 1.56 cm²Divide the area of large card by area of small card
7200 cm² ÷ 6 cm²1200Number of small cards: 1200 cards
For bigger rectangle:-
L=90cmB=80cmArea:-
LB90(80)7200cm²720000mm²For smaller rectangle
L=40mmB=15mmArea:-
LB40(15)600mm²Total cards:-
720000/6001200cardsA bag contains 5 red crayons, 4 blue crayons, and 6 green crayons. A crayon is randomly selected, its color is recorded, and it is returned to the bag. This is repeated 750 times.
How many times is it expected that a blue crayon will be selected?
Answer:200
Step-by-step explanation: There are 15balls and the probability of picking a blue ball once is 4/15
The ball is returned and repeated 750 Times. Multiply 4/15 by 750
A 200Answer:
Step-by-step explanation:
Marcus is buying a car. He borrows $10,000 from the bank at a 9% rate for 5 years. At the end of the 5 years, how much interest does Marcus pay?
Answer:
$4500 in interest.
Step-by-step explanation:
9% of 10,000 is 900, 900 x 5 is 4500
Calculate the following unit rates.
The cookie recipe calls for 2/3 cup of brown
sugar for 1/2 batch of cookies.
Using proportions, it is found that the unit rate is of 1.33 cups of brown sugar for a batch of cookies.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
2/3 cups of brown sugar are used for half a batch of cookies. The unit rate is the amount used for one batch. Hence, the rule of three is given by:
2/3 cups - 1/2 batch
x cups - 1 batch.
Applying cross multiplication:
[tex]\frac{1}{2}x = \frac{2}{3}[/tex]
[tex]x = \frac{4}{3}[/tex]
The unit rate is of 1.33 cups of brown sugar for a batch of cookies.
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A backyard has an area of 64 square feet. What is the smallest possible perimeter of the backyard?
I have been having trouble with width, and perimeter! I cant memorize it all. I need help on that question, and I know I wont get an answer back immediately so, please help me out!
What is the first step in solving the system shown below using substitution? 2x=y-1 y=3x
Answer:
you have to solve the first equation for y
Step-by-step explanation:
Step-by-step explanation:
At first put the value of y that is 3x in equation 2x=y-1.
Then put the value of x in equation y=3x that comes from the first solving part.
can anyone please teach me how to do this
Answer:
I will not give in answer but will give an example
Step-by-step explanation:
The area of irregular shapes can be determined by dividing the given shape into smaller regular shapes. The area of irregular shapes can be determined by dividing the given shape into smaller regular shapes.
In real life figures are often irregular shapes - a little bit messy. Think of your messy bedroom once more ‐ is it a perfect rectangle?
The trick is to break these figures into shapes that you know well and whose area you know how to find.
1. Find the area of this room:
3- 2 -4 -6 irregular shape
This can be done in two different ways but ill only give one example on how to find an area.
Method #1
Divide the figure into two rectangles and find all missing lengths.
The larger rectangle has an area of
4cm x 7cm = 28cm2
The smaller rectangle has an area of
4cm x 2cm = 8cm2
If we combine these we will find the total area:
28cm2 x 8cm2 = 36cm2
hope this helps :)