Answer:
Step-by-step explanation:
Take the square root of both sides
[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{25}[/tex]
x=±5
What is the smallest distance between the origin and a point on the graph of y = 1/2*(x^2 - 8)?
The smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Given, a function
y = 1/2(x² - 8)
We have to find the smallest distance between origin and a point on the graph of y = 1/2(x² - 8).
Now, the point on the graph be,
( x , 1/2(x² - 8) ) and origin be (0 , 0)
Let the function of the distance between both the points be,
D = √(x - 0)² + (1/2(x² - 8) - 0)²
D = √x² + 1/4(x² - 8)²
D² = x² + 1/4(x² - 8)²
On differentiating, we get
2DD' = 2x + x(x² - 8)
x³ + 2x - 8x = 0
x³ - 6x = 0
x(x² - 6) = 0
So, x = 0 , √6 , -√6
and the distance is minimum for x = √6
Therefore, using distance formula, we get
Distance = √(x1 - x2)² + (y1 - y2)²
Distance = √(0 - √6)² + (0 - (-1))²
Distance = √6 + 1
So, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Hence, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
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What is the constant of proportionality, ?
I
y
30+
28+
26+
-24+
22+
20+
18+
16+
14+
12+
10+
8+
6+
4+
2+
2
3
4
5
6
7
8
I
Answer:50.8%
Step-by-step explanation:
Which of the following is a rational expression?
1) 2
2) 6/x-20
3) 20x^2+2/9x^3+x
4) All of them are rational expressions?
Answer:
All of them
Step-by-step explanation:
A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.
Help to solve this question attached below###
Which fraction has the same value as 44.4¯%?
Answer: 111/250
Step-by-step explanation:
Step 1: Write down the percent divided by 100 like this:
44.4% = 44.4/100
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,
44.4/100 = (44.4 x 10)/(100 x 10) = 444/1000.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(444,1000) = 4. So,
Simplify.
-6√7.4√5
-2√35
24√√35
-24 √√35
The simplified form of the expression is -24√35
Expression
Basically, an expression is the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
Here we have the expression -6√7.4√5
Now, we have to simplify the expression.
While we looking into the given expression, we have identified that the expression is in the form of multiplication,
So, the first step in solving the expression is to group the similar element,
So, the grouped form of the expression is,
=> (-6 x 4).(√7 x √5)
Now, we have to perform the multiplication on it, then we get,
=> -24√35
Therefore, the simplified form of the expression is -24√35
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100 pointers! pls answer ASAP!!!!
find the measure of angle A show all your work
Thx
The value of ∠A in triangle ABC is 40°
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given triangle ABC,
∠A=7x-16°, ∠B=81°
By alternate segment theorem,
∠C=4x+27°
The sum of all the angle of a triangle is 180°.
∠A+∠B+∠C=180°
⇒7x-16+81+4x+27=180
11x=180-92
11x=88
x=8
So the value of ∠A=7×8-16 = 40°
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Answer:
The value of ∠A in triangle ABC is 40°
Pretty much the same as the person that posted before.
The farmer has 8.9kg of animal feed. In a day, he used 350g for the chickens, 675g for the cows and 1.3kg for the horses. How much feed will he have left?
Answer:
-1027.4
Step-by-step explanation:
that is the answer i got from my calculations. I hope this is right
There are 8 roses and 7 daisies in a vase.
(a) What is the ratio of roses to all flowers in the vase?
(b) What is the ratio of daisies to all flowers in the vase?
A tourist from the U.S. is vacationing in Greece. One day, he notices that gasoline costs 1.28 euro per liter. On that same day, euro is worth 1.09 dollars. How much does the gas cost in dollars per gallon? First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of the equation.
The cost of the gas in dollars per gallon would be = $5.3 per gallon.
What is the conversation of liters to gallon?Liters can be converted to gallon as 1 liter = 0.264 gallon.
On the first day, the cost of gasoline = 1.28 euro per liter
On the first day, the worth of £1 = $ 1.09
Which means, if £1 = $1.09
£ 1.28 = $x
Make $x the subject of formula;
$x = 1.28 × 1.09/1
$x = $1.40
Which means that on the first day, the cost of gasoline in dollars = $1.40
To convert liters to gallon;
1 liter = 0.264 gallon
If $1.40 = 0.264 gallon
$x = 1 gallon
make $x the subject of formula;
$x = 1×$1.40/0.264
$x = 5.3
Therefore, the cost of gasoline in dollar per euro = $5.3 per gallon.
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Multiply.
1,000 x 550.343978
Answer:
1,000 x 550.343978 = 550343.978
a magician charges a $30 fee to cover travel and expenses, plus $19.99 per hour. Write an equation to represent the relationship between h, the number of hours, and t, the total charge for the magician.
The equation to represent the relationship between h and t is
t = 30 + 19.99h.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the magician charges a $30 fee one time and a $19.99 fee per hour.
The total charge, t, for the magician for h hours is,
t = 30 + 19.99h
Hence, the equation to represent the relationship between h and t is
t = 30 + 19.99h.
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(x+1)² using identity
please help on this question
Answer:
[tex]x^2+2x+1[/tex]
Step-by-step explanation:
Note that [tex](a+b)^2=a^2+2ab+b^2[/tex].
Let [tex]a=x[/tex] and [tex]b=1[/tex].
[tex](x+1)^2=x^2+2(x)(1)+1^2=x^2+2x+1[/tex]
How many units are in 10 lots
A standard lot is an amount of currency which is the same as 100,000 units of a base currency .
What are the types of lot sizes?There are three lot sizes;
The standard lotThe mini lotThe micro lotIn finance, a lot indicates a measure or increment of a commodity that can be transacted. Products are bought and sold using different lot sizes. Products such as spot forex are sold in lots of 100,000, 10,000, 1,000, or 100 units.
Competition and brokerage online has resulted in the introduction of various lot sizes and forms.
A change of $10 corresponds to a pip movement of a standard lot.
By buying $100,000 at ¥110.00 and the price increases to ¥110.50, which indicates a 50 pip movement and a gain of $500 and vice versa.
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Joyce paid $120.00 for an item at the store that was 40 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
Two tracking stations are on the equator 163 miles apart. A weather balloon is located on a bearing
of N 43°E from the western station and a bearing of N 17°E from the eastern station. How far, to the
nearest mile, is the balloon from the western station? i got 322 miles
If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
Suppose the selling price of a towel is x, according to the given condition,
5 = x - 15% of x
5=x-0.15x
5=0.85 x
x=5/0.85
x=5.88
Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
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what is the ancer to 50+50
Answer: 100 is the ancer m
Step-by-step explanation: my man
A little help please i dont know how to do this
Find a polynomial function of degree 4 with -1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Step-by-step explanation:
a polynomial of degree 4 must have 4 zeroes.
when we know these zeroes, we can define the polynomial by the factors defining these zeroes.
after all, a multiplication of several factors can only be zero, if at least one of the factors is zero.
we have 3 zeroes at x = -1. and 1 zero at x = 0.
so,
f(x) = (x + 1)(x + 1)(x + 1)x
you see ? this will only be zero, if x = -1 or x = 0. and -1 is built in as zero 3 times.
let's do the multiplications :
(x + 1)(x + 1) = x² + 2x + 1
(x + 1)x = x² + x
(x² + 2x + 1)(x² + x) = x⁴ + x³ + 2x³ + 2x² + x² + x =
= x⁴ + 3x³ + 3x² + x
f(x) = 1x⁴ + 3x³ + 3x² + 1x
Consider two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
The value of the consecutive numbers are 7 and 8.
What are consecutive integers?Consecutive integers simply means the numbers that follow each others. It should be noted that such numbers have the same difference between them.
From the information given, we want to find two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
Let the numbers be x and x+1.
Therefore, 6x + (x + 1)² = 106
6x + x² + 2x + 1 = 106
Collect like terms
x² + 8x + 1 - 106
x² + 8x - 105
x² + 15x - 7x - 105
x(x + 15) - 7(x - 15) = 0
Therefore x - 7 = 0
x = 0 + 7
x = 7
Therefore x + 1
= 7 + 1
= 8
The numbers are 7 and 8.
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Jay and Ted observed two points, P and Q, on a number line.
A number line is shown from negative 1 to positive 1 with increments of 1 over 8. The numbers negative 1, negative 6 over 8, negative 4 over 8, negative 2 over 8, 0, 2 over 8, 4 over 8, 6 over 8 are labeled on the number line. A point P is shown at the first tick mark to the left of 0, and a point Q is shown at the first tick mark to the right of 0.
Jay said that the absolute values of the numbers represented by the two points are the same.
Ted said that the absolute values of the numbers represented by the two points are different.
Which of the following explains who is correct? (1 point)
Jay, because each point is fraction 1 over 8 unit from 0
Jay, because the distance between the points is fraction 1 over 8 unit
Ted, because the points are on different sides of 0
Ted, because the points are at different locations on the number line
Jay, because each point is fraction 1 over 8 unit from 0.
What is absolute length?
One way to think about a number's absolute value is as its distance from zero on the real number line.In addition, the distance between two real numbers is the absolute value of their difference.For instance, the absolute value of 12:
Since each number is 12 units away from zero, it is clear that 12 and -12 both have the same absolute value, which is 12. In order to determine the absolute value of a negative number, simply remove the minus sign. Absolute value is always positive.Absolute value is the length from which the number is from 0 in this they are adding two so it would mean that they are both 1/8 away from 0.
Hence, Jay, because each point is fraction 1 over 8 unit from 0.
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15. Tim can finish painting his barn in 10 hours. It takes
his wife JoAnn only 8 hours to do the same job. If they
work together, how long will it take them to complete the
job?
Answer:
4 4/9
is the time it will take
Heather and her friends want to buy tickets to the Harry Styles concert. Each ticket cost 85$ and parking cost 25$. Write an equation to represent if Heather spends 280$
answer: 85+85+85+25
what is 500,000x100=
The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]
We have,
The product of 500,000 multiplied by 100.
= 500,000 x 100
= 50,000,000
This can be written as:
= 5 x [tex]10^7[/tex]
Therefore,
The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]
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Ted is a freshman attending a 4-year college. He has been approved for an $8,000 subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of
Education subsidize in interest costs during his 4.5-year non-payment period?
Answer:
$1544.40
Step-by-step explanation:
You want to know the amount of interest cost subsidized by the Department of Education during the 4.5-year non-payment period on an $8000 subsidized federal loan at 4.29%.
InterestThe interest accrued on the loan amount is found by the simple interest formula:
I = Prt
The principal is $8000, the rate is 4.29%, and the time period is the non-payment period, 4.5 years. The interest is ...
I = $8000·0.0429·4.5 = $1544.40
The DoE will subsidize $1544.40 in interest during the non-payment period.
__
Additional comment
For the purpose of this problem, the 10-year period of the loan is irrelevant, as we're only concerned with the 4.5 year period before repayment starts. Because the loan is subsidized, that interest is never "capitalized" and is not due to be repaid by the borrower.
<95141404393>
. Which equations are true? Choose all that apply.
A. 2 x 0 = 2
B. 5x0=9×0
D.) 1 x 3 = 3
C. 6 x 1= 3x2
Suppose an investment account is opened with an initial deposit of $18,500 earning 6.25% interest, compounded continuously. How much will the account be worth after
25 years? (Round your answer to two decimal places.)
$
The amount in the account after 25 years be $ 84,216.11
Given, an investment account is opened with an initial deposit of $18,500 earning 6.25% interest, compounded continuously.
We have to find the amount in the account after 25 years.
Now, on using the compound interest amount formula, we get
Amount = P(1 + r/100)^t
Amount = 18500(1 + 6.25/100)^25
Amount = 18500(1.0625)^25
Amount = 18500(4.55)
Amount = 84,216.1137
Hence, the amount in the account after 25 years be $ 84,216.11
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Add.
(-x³-x)+(6x² + 6x -7)
Answer:
[tex]-x^{3}+6x^{2} +5x-7[/tex]
Step-by-step explanation:
-x^3-x+6x^2+6x-7
Order the polynomial from exponent order to make it easier
-x^3+6x^2+6x-x-7
-x^3+6x^2+5x-7
Hopes this helps please mark brainliest
Answer:
-x^3+6x^2+5x-7
Step-by-step explanation:
open parentheses, collect like terms.
A department store buys 400 shirts at a cost of $3,200 and sells them at a selling price of $10 each. What is the percent markup?
A waterskier skis over the ramp shown in the figure at a speed of 30 ft/s. How fast is she rising as she leaves the ramp?
The waterskier has a final speed of approximately 25.350 feet per second.
What is the final speed of the waterskier?
In this question we need to determine the final speed of the waterskier, that is, the final speed of the waterskier when she leaves the ramp. This can be done by means of the principle of energy conservation, where the total energy is the result of combining translational kinetic energy (K), in pounds-feet per second, related to the speed of the waterskier, and gravitational potential energy (U), in pounds-feet per second.
The equation that represents the situation is described below:
K = U + K'
0.5 · m · v² = m · g · h + 0.5 · m · v'²
0.5 · v² = g · h + 0.5 · v'²
v'² = v² - 2 · g · h
Where:
K' - Final translational kinetic energy, in pounds-feet per second.K - Initial translational kinetic energy, in pounds-feet per second.m - Mass of the waterskier, in pounds.v - Initial speed of the waterskier, in feet per second. v' - Final speed of the waterskier, in feet per second.g - Gravitational acceleration, in feet per square second. h - Final height of the waterskier, in feet.If we know that v = 30 ft / s, g = 32.174 ft / s² and h = 4 ft, then the final speed of the waterskier is:
v' = √[(30 ft / s)² - 2 · (32.174 ft / s²) · (4 ft)]
v' ≈ 25.350 ft / s
The final speed of the waterskier is approximately 25.350 feet per second.
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