Answer:
The answer is
[tex]\sqrt{101} \: \: \: or \: \: \: 10.05 \: \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(4,-9) and (-6,-10)
The distance between them is
[tex]d = \sqrt{ ({4 + 6})^{2} + ( { - 9 + 10})^{2} } \\ = \sqrt{ {10}^{2} + {1}^{2} } \\ = \sqrt{100 + 1} \: \: \\ = \sqrt{101} \: \: \: \: \: \: \: \: \: \\ = 10.04987...[/tex]
We have the final answer as
[tex] \sqrt{101} \: \: \: or \: \: \: 10.05 \: \: \: \: units[/tex]
Hope this helps you
Identify the coefficients in the expression . Check all that apply
3a-6b + 11
A . 3
B . 6
C . -6
D . 11
E. -11
Answer:
A and C
Step-by-step explanation:
Because coeficcients are numbers that come before a variable
Amy spent $6.00 for 2 gallons of gas. Bobby paid $15.00 for 6 gallons of gas. Carlos paid $32.00 for 8 gallons of gas. List the people in order of how much they paid for one gallon of gas, from the cheapest to the most expensive cost per gallon.
Answer:From cheapest to most expensive: Bobby, Amy, Carlos
-Hope this helped!
Step-by-step explanation:
Amy pays $3. 6/2=3
Bobby pays $2.50. 15/6=2.5
Carlos pays $4. 32/8=4
Company earns S dollars by selling y items per week. According to the equation S(y)=−2y^2+60y+10, how many items does company need to sell to maximize earnings.
Answer:
[tex]Max = 15[/tex]
Step-by-step explanation:
Given
[tex]s(y) = -2y^2 + 60y + 10[/tex]
Required
Determine number of items that gives maximum earnings;
The general form of a quadratic equation is:
[tex]s(y) = ay^2 + by + c[/tex]
And the maximum is calculated as:
[tex]Max = \frac{-b}{2a}[/tex] If a<0
Comparing [tex]s(y) = ay^2 + by + c[/tex] to [tex]s(y) = -2y^2 + 60y + 10[/tex]
We have that:
[tex]a = -2[/tex] [tex]b = 60[/tex] [tex]c = 10[/tex]
Substitute these values to
[tex]Max = \frac{-b}{2a}[/tex]
[tex]Max = \frac{-60}{2 * -2}[/tex]
[tex]Max = \frac{-60}{-4}[/tex]
[tex]Max = 15[/tex]
The number of item that maximizes the function is when y = 15
Let the Universal set be the letters a through J:
Answer:
{a, b, d}Step-by-step explanation:
A= {a, b, d, e}B = {a, d, h, j}C = {a, b, g, h}A ∩ (B ∪ C) = {a, b, d, e} ∩ {a, b, d, g, h, j} = {a, b, d}
evaluate [(30+6)-3^2] ÷ by 9·2
Answer:
PEMDAS
[(30+6)-3^2] ÷ by 9·2
[(30+6)-9] ÷ by 9·2
[(36)-9] ÷ by 9·2
(27) ÷ by 9·2
Division comes first in this equation. Multiplication & Division goes from left to right when using PEMDAS. Same thing goes for Addition & Subtraction.
[(27) ÷ 9] · 2
(3) · 2
Answer: 6
Hopefully that made sense!
Step-by-step explanation:
_
Step-by-step explanation:
hello..................
As an object falls through Earth's atmosphere, which of the following statements correctly describes the energy change (assume no friction or drag)
a. The potential energy of the object decreases while the thermal energy increases
b. The kinetic energy of the object increases while the elastic energy increases
c. The potential energy of the object decreases while the kinetic energy increases(THIS ANSWER IS CORRECT)
d. The thermal energy of the object decreases while the kinetic energy increases
Answer:
(c) The potential energy of the object decreases while the kinetic energy increases.
Step-by-step explanation:
Given that, an object falls through Earth's atmosphere.
As there is no friction of drag, this is the case of free fall.
So, there is no restriction in the motion of the object due to the air molecule. i.e there is no rubbing of air molecule with the object, so there is no possibility of heat (thermal energy) generation. So, the thermal energy of the object remains constant. So, options (a) and (d) are incorrect.
The only force that acts on the body is the gravitational force, as there is no drag. This force causes only the acceleration of the body. The shape of the body remains unaffected. So, there is no strain in the body. Hence, the elastic energy of the body is zero and there is no change in it. Option (b) is also incorrect.
Now, due to gravitational force, the object falls towards the earth, and its velocity increases. As the object moves towards the center of the Earth, so, the distance between the center of the earth and the object is decreases, which leads to a decrease in the potential energy of the object (as the potential energy of any object due to another body is directly proportional to the distance between the center of both the body).
While, the velocity of the object increases, so the kinetic energy of the object increases (as the kinetic energy of any object of directly proportional to the square of the velocity of the object).
Hence, the potential energy of the object decreases while the kinetic energy increases.
Therefore, option (c) is correct.
Answer:
C) The potential energy of the object decreases while the kinetic energy increases.
1. A student says that the zeros of y = (x - 2)(x + 7) are -2 and 7. Is the student correct? If not, describe and correct the error the student made.
2. Explain why x^2 + 25 is not equal to (x + 5)^2?
3. Describe how the factoring can help you find the x-intercepts of the graph of the quadratic function y = x^2 - 4x + 3.
Answer: 1) NO. the zeros are: 2 and -7
2) (x + 5)² has a middle term when in expanded form
3) Factoring provides the Intercept form: y = a(x - p)(x - q)
Step-by-step explanation:
1) y = (x - 2)(x + 7)
To find the zeros, set the factors equal to zero:
0 = x - 2 0 = x + 7
x = 2 x = -7
The zeros are 2 and -7.
The student did not set the factors equal to zero.
2) (x + 5)² = (x + 5)(x + 5)
= x² + 5x + 5x + 25
= x² + 10x + 25 ≠ x² + 25
3) The Intercept form of a quadratic equation is: y = a(x - p)(x - q) where p and q are the x-intercepts. Notice that the intercept form IS the factored form. Set the factors equal to zero to find the x-intercepts.
y = x² - 4x + 3
y = (x - 1)(x - 3) --> Intercept form
0 = (x - 1)(x - 3) --> finding the zeros (aka x-intercepts)
0 = x - 1 0 = x - 3
x = 1 x = 3 --> zeros are 1 and 3
1.The zeroes are 2,-7
2.[tex]x^2 + 25\neq ( x + 5)^{2}[/tex]
3. So, factoring can help to find the x-intercepts
1.We have y = (x - 2)(x + 7)
For zeroes of y , Put y=0
(x - 2)(x + 7) =0
x=2,-7
So, the zeroes of y = (x - 2)(x + 7) are 2 and -7.
2. We have [tex]x^2 + 25[/tex]
[tex]x^2 + 25= x^2 + 5^{2}[/tex]
And
[tex](x+ 5)^{2} \\=x^{2} +5^{2} +10x\\=x^{2} +25 +10x\\\neq x^{2} +25[/tex]
So, [tex]x^2 + 25\neq ( x + 5)^{2}[/tex]
3.We have the quadratic function [tex]y = x^2 - 4x + 3[/tex]
[tex]y=x^2 - 4x + 3\\=(x-3)(x-1)\\[/tex]
For x-intercept put y=0, we get
[tex](x-3)(x-1)=0\\x=3,x=1[/tex]
So, factoring can help to find the x-intercepts of the graph of the quadratic function [tex]y = x^2 - 4x + 3.[/tex]
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How to solve?
-7k-4K=8-2k-8k
Answer:
-7k-4K=8-2k-8k
-11K = 8-10K (combine like terms)
8 = -11k+10k (move the -10 to combine like term with -11)
8 = -1k
k = 8/-1 (isolate the k to find its value by dividing the 8)
k = -8
What's the first step to solve this equation? *
h - 18/10 = –14
Answer:
multiply by 10 on both sides
that is to get rid of the denominator
A health study tracked a group of person for five years. At the beginning of the study, 20% were classified as heavy smokers, 30% as light smokers, and 50% as nonsmokers. Results of the study showed that light smokers were twice as likely as nonsmokers to die during the five-year study, but only half as likely as heavy smokers. A randomly selected participant from the study died during the five-year period. Calculate the probability that the participant was a heavy smoker. g
Answer: 0.421
Step-by-step explanation:
Heavy smoker = 20%
Light smoker = 30%
Non smokers = 50%
We can assume that the probability that a non-smoker is going to die in the next 5 years be y.
Since light smokers were twice as likely as nonsmokers to die during the five-year study, the probability will be:
= 2 × y = 2y
Probability for the Heavy smokers will be:= 2 × 2y = 4y
The expected number of people that will die for each in the next 5 years will be:
Non smoker:
= 50% × y
= 0.5 × y
= 0.5y
Light smoker:
= 30% × 2y
= 0.3 × 2y.
= 0.6y
Heavy smoker:
= 20% × 4y.
= 0.2 × 4y
= 0.8y
Total = 0.5y + 0.6y + 0.8y = 1.9y
The probability that the participant was a heavy smoker will be:
= 0.8y/1.9y
= 0.421
A farmer has 5 cartons of eggs for sale. Each carton contains 12 eggs.
if 5/6 of the eggs are brown, what is the total number of eggs that are not brown
Answer:
10 eggs
Step-by-step explanation:
5 cartons multiplied by 12 eggs each equals 60 eggs in total.
Therefore 5/6 would be equal to 50/60 since we multiply the denominator and numerator by 10
As a result 10 of the eggs are not brown
The total length of wires a b and c is 445 cm wire a is 45 cm longer then wire b and wire b is half as long as wire c how long is wire a
Answer:
[tex]a = 145\ cm[/tex]
Step-by-step explanation:
Given
[tex]a + b + c = 445[/tex]
[tex]a = 45 + b[/tex]
[tex]b = \frac{1}{2}c[/tex]
Required
Determine the length of a
Solve for c in [tex]b = \frac{1}{2}c[/tex]
[tex]2 * b = \frac{1}{2}c * 2[/tex]
[tex]2b = c[/tex]
[tex]c = 2b[/tex]
Substitute [tex]c = 2b[/tex] and [tex]a = 45 + b[/tex] in [tex]a + b + c = 445[/tex]
[tex]a + b + c = 445[/tex]
[tex]45 + b + b + 2b = 445[/tex]
[tex]45 + 4b = 445[/tex]
Solve for 4b
[tex]4b = 445 - 45[/tex]
[tex]4b = 400[/tex]
Solve for b
[tex]b = 400/4[/tex]
[tex]b = 100[/tex]
Recall that: [tex]a = 45 + b[/tex]
[tex]a=45+100[/tex]
[tex]a = 145\ cm[/tex]
The graph shows the costs of two types of fruit at a store. A graph measuring cost and amount. Two lines, labeled Cherries and Apples, exit the origin to show that cost increases as amount increases Drag and drop the appropriate symbol to the box to compare the rates of the fruits. cost of apples per lb Response area cost of cherries per lb
The cost of apples per lb is less than cost of cherries per lb.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the graph shows the costs of two types of fruit at a store. Two lines, labeled Cherries and Apples, exit the origin to show that cost increases as amount increases.
Slope of the line representing apples is smaller than slope of the line representing cherries. This means that the unit rate for cherries is greater than that of apples. So, cost of apples per lb is less than cost of cherries per lb.
Therefore, the cost of apples per lb is less than cost of cherries per lb.
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what are the steps to finding the distance between two points on a coordinate grid using pythagorean theorem
Answer:
Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem, a2+b2=c2 a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse.
Step-by-step explanation:
Answer:
Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem, a2+b2=c2 a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse.
Step-by-step explanation:
Simplify 3√6 − 10√2 ⋅ √3
−13√6
−13√2
−7√6
−7√3
Answer:
4
Step-by-step explanation:
Answer:
-7√6Step-by-step explanation:
Simplify 3√6 − 10√2 ⋅ √3
3√6 − 10√2 ⋅ √3=3√6 - 10√6 =(3-10)√6 =-7√6What is the sun of the equation 9 + 9+9
-18= 5-(6k - 19) i have the answer but i need help on how to get the answer 7?
Answer:
k = 7
Step-by-step explanation:
Step 1: Write equation
-18 = 5 - (6k - 19)
Step 2: Solve for k
Distribute negative: -18 = 5 - 6k + 19
Combine like terms: -18 = -6k + 24
Subtract 24 on both sides: -42 = -6k
Divide both sides by -6: k = 7
Step 3: Check
Plug in k to verify it's a solution.
-18 = 5 - (6(7) - 19)
-18 = 5 - (42 - 19)
-18 = 5 - 23
-18 = -18
Triangle ABC was translated to form triangle A'B'C'. Which describes the transformation? Check all that apply.
A.
It is non rigid
B.
The size is preserved
C.
It is rigid
D.
The angles are not preserved
E.
It is isometric
Answer:
B, C, E
Step-by-step explanation:
Translation is a rigid transformation. As such, it preserves sizes and angles. "Isometric" is another way to say "the size is preserved."
nine times a number y subtracted from 85 is seven times the sum of four and y
Answer:
85-9y= 7(4+y)
solve for y if you need to simplify
A bag of popcorn contains 483 calories and serves 3.5 people. How many calories are in each serving?
Answer:
U simply multiply 483 by 3.5
=1690.5
Step-by-step explanation:
(01.05 MC)Taylor bought 6 tickets to a movie. The price of each ticket was
the same. After he bought the tickets, his account balance showed a change
of -$68.04. What would have been the change to Taylor's account balance
had he only bought 1 ticket to the movie?
Answer:
-$11.34
Step-by-step explanation:
Each of these tickets have been said to have the same costs of buying them.
If 6 tickets = -68.04 dollars
1 ticket = ?
We cross multiply to get the unknown
6 x ? = 1 x -68.04
Such that
? = -68.04/6
= -$11.34
So in conclusion if Taylor had not bought these 6 tickets and had only gotten 1 for the movie, the change to his account balance would be $-11.34
Please answer this correctly without making mistakes my homework is due today I have to finish this as soon as possible I want genius expert and ace people to answer this correctly without making mistakes
Answer:
18 practices
Step-by-step explanation:
9.63 / 9 = 1.07
19.26 - 1.07 = 18
How does one find the inverse function of f(x)= [tex]\frac{1}{3x-1}[/tex]
Answer:
[tex]\displaystyle f^{-1}(x)=\frac{1+x}{3x}[/tex]
Step-by-step explanation:
The Inverse of a Function
The procedure to find the inverse of the function is:
* Write the function as a two-variable equation:
[tex]\displaystyle y=\frac{1}{3x-1}[/tex]
* Solve the equation for x.
Multiply by 3x-1
[tex]y(3x-1)=1[/tex]
Divide by y:
[tex]\displaystyle 3x-1=\frac{1}{y}[/tex]
Sum 1:
[tex]\displaystyle 3x=\frac{1}{y}+1[/tex]
Operate the right side:
[tex]\displaystyle 3x=\frac{1+y}{y}[/tex]
Divide by 3:
[tex]\displaystyle x=\frac{1+y}{3y}[/tex]
* Swap the variables:
[tex]\displaystyle y=\frac{1+x}{3x}[/tex]
Write back into function form:
[tex]\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}[/tex]
A moderately active 140 pound person will use 2100 calories per day to maintain that body weight, how many calories per day are necessary to maintain a moderately active 145 pound person
Answer:
2,175 calories
Step-by-step explanation:
140 pound person will use 2100 calories per day
145 pounds person will use x calories per day
Find x
Pounds : calories
140 : 2100 = 145 : x
140/2100 = 145/x
Cross product
140 * x = 2100 * 145
140x = 304,500
Divide both sides by 140
x = 304,500 / 140
= 2,175
Therefore,
145 pounds person will use 2175 calories per day
Solve the absolute value equation. If no solution write NO SOLUTION.
-{2x + 3] + 8
12
Answer:
If problem is "-|2x+3|+8=12"
then there is (no solution.)
Step-by-step explanation:
Let's solve your equation step-by-step.
−|2x+3|+8=12
Step 1: Add -8 to both sides.
−|2x+3|+8+−8=12+−8
−|2x+3|=4
Step 2: Divide both sides by -1.
−|2x+3|=4
-1 -1
|2x+3|=−4
Step 3: Solve Absolute Value.
|2x+3|=−4
No solutions Because absolute value is less than 0.
From 1960 to 1980, the consumer price index (CPI) increased from 29.6 to
82.4. If a pound of grapes cost $0.14 in 1960 and the price of grapes
increased at the same rate as the CPI from 1960 to 1980, by approximately
how much did the price of a pound of grapes increase from 1960 to 1980?
A. $0.82
B. $0.25
C. $0.39
D. $0.30
The price of pound of grapes increased from 1960 to 1980 is $0.25.
What is a consumer price index?The Consumer price index (CPI) may be a measure of the typical change overtime within the prices paid by urban consumers for a market basket of goods and services.The CPI is one amongst the foremost popular measures of inflation and deflation. The CPI report uses a special survey methodology, prices sample and index weights than the producer index number (PPI), which measures change within the prices received by producers of products and services.Given:
CPI in 1960 = 29.6
CPI in 1980 = 82.4
Price of pound of grapes in 1960 = $0.14
We have to find the increase in the price of pound of grapes from 1960 to 1980.
Now, the rate of increase in the CPI from 1960 to 1980 is given by:
⇒ Rate = (CPI in 1980) / (CPI in 1960)
⇒ Rate = 82.4/29.6
⇒ Rate = 2.78
Now, the price of pound of grapes in 1980 will be calculated as:
⇒ Price of pound of grapes in 1980 = (rate of increase in the CPI from 1960 to 1980) × (Price of pound of grapes in 1960)
⇒ Price of pound of grapes in 1980 = 2.78 × $0.14
⇒ Price of pound of grapes in 1980 = $0.389
Increase in the price of pound of grapes from 1960 to 1980 will be calculated as:
⇒ Increase in the price = (Price of pound of grapes in 1980) - (Price of pound of grapes in 1960)
⇒ Increase in the price = $0.389 - $0.14
⇒ Increase in the price = $0.249
⇒ Increase in the price ≈ $0.25
Therefore, the approximate increase in the price of pound of grapes from 1960 to 1980 is $0.25.
Hence, Option (B) is correct.
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b) 4 meter 20 centimeter to cm
Answer:
4 meters and 20 centimeters will be 420 centimeters
Step-by-step explanation:
Answer:
420 (cm)
Step-by-step explanation:
1 meter = 100 centimeters.
so,
4 meters = 400 centimeters
400 + 20 equals 420cm
THIS IS DUE SOON!!! Multiple-step equation. Please help ASAP.
Which of the following represents a true statement?
A. 19^21 x 19^3 = 19^63
B. (24^8)^5 = 24^40
C. 20^1 x 20^0 = 20^0
D. 16^40 / 16^20 = 16^2
(LOOK AT THE PICTURE PLEASE)
When you raise an exponential expression to another exponent, you multiply the exponents. We have 8*5 = 40 as the final exponent. The rule is (x^y)^z = x^(y*z). The base stays the same.
Statement A is not true because we should be adding the exponents. The rule is x^y*x^z = x^(y+z). Note how the bases are all the same. We'll use this rule for statement C to show that it is also false.
A similar rule is (x^y)/(x^z) = x^(y-z). We subtract the exponents this time. This rule is used to show that statement D is false.
How many solutions are there to the equation
8x - 7 = 2 (2x + 7) - 5
Answer:
x=4
Step-by-step explanation:
8x - 7 =2(2x +7) - 5
8x - 7 =4x +14 - 5
8x - 7 =4x +9
8x - 4x =9 +7
4x =16
x=16 :4
x=4
