The shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units
The coordinates of the point = (9,1)
The equation of the line is
y = 2x + 3
Here the slope of the line is 2
The shortest distance between the point and the second line will be the perpendicular distance between the point and line
The perpendicular line slope will be -(1/m)
= -(1/2)
This perpendicular line will pass through the point (9, 1)
The point slope form is
y - 1 = -(1/2)(x - 9)
y - 1 = -(1/2x) + 9/2
y = -(1/2)x + 9/2 + 1
y = -(1/2)x + 11/2
Solve the equation
y = 2x + 3
y = -(1/2)x + 11/2
0 = (2 + 1/2)x -5/2
5/2 x = -5/2
x = -5/2 / 5/2
x = -1
Then
y = 2(-1) + 3
y = -2 + 3
y = 1
The distance between the point (9,1) and (-1, 1)
= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-1-9)^2+(1-1)^2}[/tex]
= [tex]\sqrt{100}[/tex]
= 10 units
Hence, the shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units
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can someone please help me with problem, thank u.
Answer:
D
Step-by-step explanation:
First, we should find the equations of the two lines. The red line is just horizontal, and represents y = 4 while the blue line intersects the y-axis at -4 and every time it goes right one, it goes up 4, so it has a slope of four(also it looks kinda steep, so it cannot have a slope of 1/4). This means the equation is y = 4x - 4.
Notice the red line is dashed, that means the inequality is either less than or greater than. Also, the shaded part is below the vertical line, enclosing all the values of y less than 4, so the first inequality would be y < 4.
The blue line is solid, so it is either greater than or equal to or less than or equal to. To find out which one, we check to se where the point (0, 0) fits in:
y ? 4x - 4
0 ? 0 - 4
0 ? -4
Only a greater than or equal to sign would fit in: 0 ≥ -4
This means the answer is:
y < 4
y ≥ 4x - 4
which is option D
Answer:
Step-by-step explanation:
1)
The equation of a straight line:
y = k·x + b
x = 0
b = y = - 4
k = (y - y₀) / (x - x₀) = ( 4 - (-4)) / (2 - 0) = 8 / 2 = 4
y = 4·x - 4
2)
The equation of a straight line:
y = 4
3)
Shaded area:
y ≤ 4
y ≥ 4x - 4
Right answer:
D.
y ≤ 4
y ≥ 4x - 4
A shopkeeper compares the income from sales of a laptop in July and August. August 1/3 Price Number sold 2/5 more than July less than July By what fraction does the income from these sales decrease in August? Answer: Decreases by ....
The fraction that illustrates the decrease in sales is 15.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, August 1/3 and this was 2/5 more than what was sold earlier. Therefore the decrease will be:
= 2/5 - 1/3
= 6/15 - 5/15
= 1/5
The fraction is 1/15.
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Find the x value that makes the lines parallel.
2x°
80°
Answer:
x = 40
Step-by-step explanation:
for m and n to be parallel then
2x and 80 are alternate angles and congruent , so
2x = 80 ( divide both sides by 2 )
x = 40
Write a linear function f with the values f(0) = −5 and f(1) =−3.
A function is f(x)=¯
Answer:
[tex]y=2x-5[/tex]
Step-by-step explanation:
We want to find a linear function [tex]f(x)[/tex] with the values
[tex]f(0)=-5\\f(1)=-3[/tex]
These mean that when x is 0, y is -5, and when x is 1, y is -3.
This means that we want to find the equation of a line that goes through the ordered pairs below:
[tex](0,-5)\\(1,-3)\\[/tex]
Let's find the slope between the two ordered pairs. The slope is the rise over the run. The rise is the change in y-values.
[tex]-3--5=-3+5=2[/tex]
The change in y-values is 2.
The run is the change in x values.
[tex]1-0=1[/tex]
The change in x-values is 1.
The slope is the rise divided by the run, so:
[tex]slope=\frac{2}{1}=2[/tex]
Now that we know the slope, let's find the y-intercept! This is when x equals 0. Luckily, that number is already given! We know that when x equals 0, y equals -5!
[tex]intercept=-5[/tex]
Now that we have the slope and intercept, we can plug these numbers into slope-intercept form!
[tex]y=2x-5[/tex]
How do you write 6 hundredths as a decimal?
Answer:
.06
Step-by-step explanation:
6 hundredths
We want to write this as a decimal.
Writing decimals
This means write 6/100
There are two zeros so we need two numbers.
06/100
Then there are two numbers before the decimal.
We can write 06 before the decimal.
.06
6 hundredths can be written as 0.06 as a decimal.
What is fraction?
All fractions consist of a numerator and a denominator, separated by horizontal bars called fraction bars.
The denominator indicates the number of parts into which the whole is divided. Placed at the bottom of the break below the break bar. The
counter indicates how many sections of the fraction are displayed or selected. Placed at the top of the break above the break bar.
A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent.
6 hundredths means that when you divide "something" into a hundred equal parts, 6 hundredths are six of the newly divided parts.
When you divide 6 by hundreds, you get 6 hundredths as a decimal, which is 0.06.
Therefore, 6 hundredths can be written as 0.06 as a decimal.
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Barrett works at an ice cream shop. The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 4
g of x equals the square root of the quantity 3 x cubed
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of f(g(x)) is 6x³ + 4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
3x + 4 = 5 is an equation.
2x + 4x = 4 is an equation.
We have,
The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes.
The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works.
f(x) = 2x² + 4
g(x) = √(3x³)
Now,
f(g(x)):
= f(√(3x³))
= 2{√(3x³)}² + 4
= 2(3x³) + 4
= 6x³ + 4
Thus,
The value of f(g(x)) is 6x³ + 4.
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13. Find the measure of
(5x +27)°
(2x + 10)°
(4x + 2)°
Check the picture below.
Let f and g be differentiable functions such that f(3)=5,g(3)=7,f
′
(3)=13,g
′
(3)=6,f
′
(7)=2, and g
′
(7)=0. If h(x)=(fog)(x), then h
′
(3)= ?? A. 14 B. 6 C. 12 D. 10
If h(x)=(fog)(x) then h'(3) = 12.
Given:
Let f and g be differentiable functions such that f(3)=5,g(3)=7,f'(3) = 13, g'(3) = 6,f'(7) = 2 and g'(7) = 0
h(x)=(fog)(x)
h(x) = f(g(x))
h'(x) = f'(g(x)) * g'(x)
h'(3) = f'(g(3) * g'(3)
= f'(7) * 6
= 2*6
= 12
Therefore If h(x)=(fog)(x) then h'(3) = 12.
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is 25 3/8 bigger than 25 2/5
best answer = brainliest
Answer:
2/5 is greater than 3/8, so 25 2/5 is greater
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 5 and 8 is 40
Next, find the equivalent fraction of both fractional numbers with denominator 40
For the 1st fraction, since 5 × 8 = 40,
2/5
=
2 × 8
5 × 8
=
16/40
Likewise, for the 2nd fraction, since 8 × 5 = 40,
3/8
=
3 × 5
8 × 5
=
15/40
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
16/40 > 15/ 40 or 2/5 > 3/8
Simplify. Express your answer using positive exponents.
(7tuv7)(4t3u4v2)
Answer:
[tex]28t^4u^5v^9[/tex]
Step-by-step explanation:
I will answer this a few different ways depending on whether there are supposed to be exponents in the question.
As written
As written, the product is:
[tex](7tuv7)(4t3u4v2)[/tex]
All of the coefficients can be multiplied together. This is what that looks like:
[tex]4704tuvtuv[/tex]
Now, each variable multiplied by itself gets the exponent of 2.
[tex]4707t^2u^2v^2[/tex]
Assuming exponents and coefficients
Assuming exponents, the product is:
[tex](7tuv^7)(4t^3u^4v^2)[/tex]
Again, the coefficients can be multiplied, and the like variables written next to each other:
[tex]28tt^3uu^4v^7v^2[/tex]
When multiplying like terms with exponents, add the exponents. Variables without an exponent have an exponent of 1.
[tex]28t^4u^5v^9[/tex]
Given h(x) = -2x - 5, solve for a when h(x) = 9.
X
Answer:
-23
Step-by-step explanation:
h(x) = -2x - 5
Let x = 9
h(9) = -2*9 - 5
h(9) = -18 - 5
= -23
Answer:
h(9) = -23
Step-by-step explanation:
Given explanation,
→ h(x) = -2x - 5
Then the value when h(x) = 9 is,
→ h(x) = -2x - 5
→ h(9) = -2(9) - 5
→ h(9) = -18 - 5
→ h(9) = -23
Hence, the value of h(9) is -23.
a rectangle is 6cm wide two different expressions are used to state it's length
Answer:
The length is 12
The area is 72[tex]cm^{2}[/tex]
Step-by-step explanation:
3x + 7 = 5x -17 Subtract 3x from both sides
7 = 2x -17 Add 17 to both sdies
24 = 2x Divide both sides by 2
12 = x
Area = length times witdth
Area = 6(12) = 72
Answer:
Step-by-step explanation:
part a):
6(3x+7)=6(5x-17)
part b):
18x+42=30x-102
42+102=30x-12x
144=12x
x=144/12
x=12
area = l x b
area = 6x{5(12)-17}
=6x(60-17)
=6x43
area=258cm2
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The amount of money raised at a fundraiser is directly proportional to the number of attendees. The amount of money raised for 12 attendees is $300. How much money is raised for 75 attendees?.
Answer:
900
Step-by-step explanation:
300/12=25
75*12=900
Calculate the area of a circular ring, whose internal and external radii are 3 cm and 10 cm respectively.
Step-by-step explanation:
area of circle = πr²
internal radii - 3 cm = r1
external radii - 10 cm = r2
internal + external radii = πr1² + πr2²
= 22/7×3² + 22/7×10²
= 28.28 + 314.28
= 342.56 cm²
At a candy store, Eva bought 2 pounds of jelly beans and 2 pounds of gummy worms for $26.
Meanwhile, Mimi bought 3 pounds of jelly beans and 2 pounds of gummy worms for $31. How
much does the candy cost per pound?
start with
m: cost per pound for Jelly Beans
n: cost per pound for Gummy Worms
Answer:
cost per pound for Jelly Beans is 5$
cost per pound for Gummy Worms is 8$
The Bartolotti family took out a loan to have a garage built next to their house. The 10-year, 10.4% loan was for $56,188. The monthly payment was $475, but the promissory note stated that there was a balloon payment at the end. what is the sum of all but the last monthly payment?
If the promissory note stated that there was a balloon payment at the end. The sum of all but the last monthly payment is: $56,525, $57,000.
How to find the monthly payment?Total payment = $475 × [(10 years × 12 months) -1]
Total payment = $475 × 119 payment
Total payment = $56,525
Total payment = $475 × [(10 years × 12 months) ]
Total payment = $475 × 120 payment
Total payment = $57,000
Therefore the monthly payment is; $56,525, $57,000.
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please help i need this quick asap
A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
The value of [tex]x_{11}[/tex] is 8
The value of [tex]x_{21}[/tex] is -1
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
[tex]\left[\begin{array}{ccc}3&-8\\1&1\\\end{array}\right] X=\left[\begin{array}{ccc}32\\7\\\end{array}\right][/tex] _____(1)
Now,
[tex]X = \left[\begin{array}{ccc}x_{11}\\x_{21}\\\end{array}\right][/tex] ________(2)
Multiplication of matrix.
From (1) and (2) we get,
[tex]3x_{11} - 8x_{21}[/tex] = 32 ____(a)
[tex]x_{11} + x_{21}[/tex] = 7 ______(b)
From (b) we get,
[tex]x_{11}[/tex] = 7 - [tex]x_{21}[/tex] ______(3)
Substitute (3) in (a)
Now,
3 (7 - [tex]x_{21}[/tex]) - 8[tex]x_{21}[/tex] = 32
21 - 3[tex]x_{21}[/tex] - 8[tex]x{21}[/tex] = 32
-11[tex]x_{21}[/tex] = 32 - 21
[tex]x_{21}[/tex] = -1
Now,
[tex]x_{11}[/tex] = 7 - (-1) = 7 + 1 = 8
Thus,
The value of [tex]x_{11}[/tex] is 8
The value of [tex]x_{21}[/tex] is -1
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PLEASE HELP, I WILL GIVE BRAINLY!!!
Compare the scenarios to determine which represents a greater speed. Explain your choice including a written description of each scenario. Be sure to include the rates in your explanation.
For every 50 y, there is 1 hour
A survey shows that 2/3 of all homeowners have a pet. Of those, 3/4 have either a dog or a cat. Of the homeowners, what fraction has either a dog or a cat ?
Answer:
Of the homeowners, half have either a dog or a cat.
Step-by-step explanation:
Since 2/3 of all homeowners have a pet, and 3/4 of those have dogs or cats, we simply need to multiply 2/3 and 3/4 to see what fraction of all homeowners have a dog or a cat.
2/3 x 3/4 = 6/12
6/12 = 1/2
We can double check this. If there are 60 homeowners, and 2/3 have a pet, that would mean that 40 of those homeowners have a pet.
If 3/4 of the 40 homeowners have either a dog or a cat, that would equate to 30 homeowners having either a dog or a cat.
Since 30 is half of 60, this would mean that 1/2 of the 60 homeowners have a dog or cat!
Hope this answer helped you!
The estimate number of cars that can be produced (C in thousands) at a manufacturing plant over the course of time (x in years) can be modeled by the polynomial function
The average rate of change between year 1 and year 10 is given as follows:
4.3 thousand cars a year.
How to obtain the average rate of change of a function?The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In this problem, the function is presented as follows:
C(x) = 0.15x³ - 3.28x² + 23.75x - 2.1.
The interval is:
[1,10], hence a = 1, b = 10.
At x = 1, the numeric value is found replacing each instance of x by 1, hence:
C(1) = 0.15(1)³ - 3.28(1)² + 23.75(1) - 2.1 = 18.52 thousand cars.
At x = 10, the numeric value is found replacing each instance of x by 10, hence:
C(10) = 0.15(10)³ - 3.28(10)² + 23.75(10) - 2.1 = 57.4 thousand cars.
Then the average rate of change is obtained as follows:
r = (57.4 - 18.52)/(10 - 1) = 4.3 thousand cars a year.
Missing InformationThe problem is given by the image shown at the end of the answer.
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ANSWER ASAP A basketball team played six games. In those games, the team won by 8 points, lost by 8, won by 7, won by 10, lost by 2, and won by 9. What was the mean difference in game scores over the six games?
The average difference or mean in game scores across six games is 5.67
MeanThe mean is the average of a data set. The mode is the most common number in a data set. The median is the middle of the set of numbers. The mean is the average or the most common value in a collection of numbers. the mean is one of the measures of b, apart from the mode and median. Mean is nothing but the average of the given set of a data.
To solve this problem, we have to write the wins and loss separate and then find the mean.
Wins = 8 points, 7 points, 20 points, 9 points
Loss = 8 points, 2 points
The sum of win points = 8 + 7 + 20 + 9 = 44 points
The sum of lost points = 8 + 2 = 10 points
The mean difference = (win - loss)/ total number of games
The mean difference = ( 44 - 10) / 6
The mean difference = 34 / 6 =5.67
The mean difference in the game scores over six games is 5.67 points
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5 divided by 1 and 2/3
Answer: The answer to that would be 3.
Step-by-step explanation: So 5 / 1 2/3 = 3
Sorry my handwriting is so sloppy! Hope it helps!
What is the slope of the line passing through the points (-1, 0) and (0, - 7)?
Answer:
1/-7
Explanation:
rise/run so up 1 down 7
8-(-4f-3)≤ -f-8+2f
solve for f
Answer:
f ≤ - [tex]\frac{19}{3}[/tex]
Step-by-step explanation:
8 - (- 4f - 3 ) ≤ - f - 8 + 2f ← distribute parenthesis on left side by - 1
8 + 4f + 3 ≤ f - 8
4f + 11 ≤ f - 8 ( subtract f from both sides )
3f + 11 = - 8 ( subtract 11 from both sides )
3f ≤ - 19 ( divide both sides by 3 )
f ≤ - [tex]\frac{19}{3}[/tex]
x + 25/-8 = -6 Solve for x.
Simplify your answer as much as possible.
Step-by-step explanation:
if there is nothing missing, we have
x + 25/-8 = -6
in order to compare or add or subtract fractions, we need to bring them all to the same denominator (bottom part).
remember, integer numbers are fractions too. like here
-6 = -6/1
25/-8 = -25/8
so, how can we bring -6/1 to .../8 ?
by multiplying 1 by 8.
but we cannot multiply only the denominator by 8. otherwise we would suddenly have
-6/8
and is -6/8 = -6/1 ? no, certainly not.
to keep the original value of the fraction we have to do the same multiplication also with the numerator (top part).
so, we actually do
-6/1 × 8/8 = -48/8
with this little trick we have now .../8 to operate with, and our transformed fraction has still the same value
-6/1 = -48/8 indeed.
so, we have
x + -25/8 = -48/8
x - 25/8 = -48/8
x = -48/8 + 25/8 = -23/8
which postulate or theorem can be used to prove <RPQ = <RNM
Answer:
alternate interior angles theorem
Step-by-step explanation:
alternate interior angles theorem states that, if 2 parallel lines and a transversal form alternate interior angles, then, said angles are congruent.
your calculations indicate that you will need 20.8 cubic yards of concrete for a slab floor. which of the following quantities would be the best amount to order accounting for waste?
Answer:
Step-by-step explanation:Your calculations indicate that you will need 20.8 cubic yards of concrete for a slab floor. Which of the following quantities would be the best amount to order accounting for waste
What does b represent in the equation of a line in the form y = mx + b?The y-intercept
The value of x when y = 0
The slope
The x-intercept
Answer:
The y intercept
Step-by-step explanation:
g(x)=-2x-1 find g(-1)
A car travels 37 km in 25 minutes.
What is its average speed in km/h?
Give your answer rounded to 1 decimal place.
Answer:
88.8 km/h
Step-by-step explanation: