use the point-slope formula to write an equation of the line that passes through (6,- 3) and (3,1).
Write the answer in slope-intercept form (if possible).
The slope of the line is
[tex]\frac{-3-1}{6-3}=\frac{-4}{3}[/tex]
Substituting into point-slope form using the point (3,1),
[tex]\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}[/tex]
Answer: The equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex] +5.
Step-by-step explanation:
Point-slope formula : (y - y1) = m(x - x1)
y = y coordinate of second point
y1 = y coordinate of first point
m = slope
x = x coordinate of second point
x1 = x coordinate of first point
slope (m) = [tex]\frac{1-(-3)}{3-6}[/tex]
m = [tex]\frac{4}{-3}[/tex] or [tex]\frac{-4}{3}[/tex]
now put values in point-slope formula : (y - 1) = [tex]\frac{-4}{3}[/tex](x - 3)
y - 1 = [tex]\frac{-4x}{3\\}[/tex] + 4
y = [tex]\frac{-4x}{3}[/tex] +5
So the equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex]+5.
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Line m passes through the points (-4,3) and (-4,7). What is the slope of the line that is parallel to line m?
Answer:
undefined
Step-by-step explanation:
Since line m passes through two points that have the same x-value but different y values, line m is horizontal to the y-axis which has an undefined slope.
Suppose the measures of the interior angles of a convex quadrilateral are four consecutive odd numbers. Find the measure of the third angle.
Answer:
91 degrees
Step-by-step explanation:
Sum of angles in a quadrilateral: 360 degrees
87, 89, 91, 93 are four consecutive odd numbers that add up to 360
third angle is 91 degrees
Calculus. Please answer question attached.
(a) Given [tex]f(x) = x^3[/tex], the derivative is
[tex]f'(x)=3x^2[/tex]
which is exists for all [tex]x[/tex] in the domain of [tex]f[/tex], so [tex]]f[/tex] is differentiable everywhere and satisfies the mean value theorem. There is some number [tex]c[/tex] in the open interval (0, 2) such that
[tex]f'(c) = \dfrac{f(2) - f(0)}{2-0} \iff 3c^2 = \dfrac{8-0}2 = 4[/tex]
Solve for [tex]c[/tex] :
[tex]3c^2 = 4 \implies c^2 = \dfrac43 \implies \boxed{c = \dfrac2{\sqrt3}}[/tex]
We omit the negative square root since it doesn't belong to (0, 2). Graphically, the MVT tells us the tangent line to the curve [tex]f(x)=x^3[/tex] at [tex]x=\frac2{\sqrt3}[/tex] is parallel to the secant line through the endpoints of the given interval.
(b) [tex]f(x)=1+x+x^2[/tex] has derivative
[tex]f'(x)=1+2x[/tex]
By the MVT,
[tex]f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff 1+2c = \dfrac{7-1}2 \implies \boxed{c = 1}[/tex]
(c) [tex]f(x) = \cos(2\pi x)[/tex] has derivative
[tex]f'(x) = -2\pi \sin(2\pi x)[/tex]
By the MVT,
[tex]f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff -2\pi \sin(2\pi c) = \dfrac{0-0}2 \implies \sin(2\pi c) = 0 \\\\ \implies 2\pi c = n\pi \implies c = \dfrac n2[/tex]
where [tex]n[/tex] is any integer. There are 3 solutions in the interval (0, 2),
[tex]\boxed{c = \dfrac12, c = 1, c = \dfrac32}[/tex]
(Pictured is the situation with [tex]c=\frac12[/tex])
Solve the following multiplication problem.
9 cu yd 17cu in
× 135
−−−−−−−−−−−−−−−−−−−
The multiplication of the expression will be 1215 cubic yd 2295 cubic inches.
What is multiplication?It is also known as the product. If the object n is given to m times, then we just simply multiply them.
The expression is given below.
(9 cubic yd and 17 cubic in) × 135
On multiplication, we have
135 × 9 cubic yd and 135 × 17 cubic in
1215 cubic yd and 2295 cubic inches
1215 cubic yd 2295 cubic inches
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The multiplication is 56,689,335 cu in
What is Number system?A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
9 cu yd 17cu in
1 cu yard = 46656 cu inches
9 cu yard = 9*46656 = 419904 cu inches
Now, total inches
= 419904 cu inches + 17 cu in
= 419,921 cu inches.
and, the multiplication is
=56689335
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f(x) = 3x² + 7x + 2, what is f(5)?
Answer:
112
Step-by-step explanation:
find the perimeter: (use 3.14 for pi):
Answer:
10.676 mm
Step-by-step explanation:
The perimeter of a circle (circumference) formula is 2*(3.14)*r. Therefore since r is 1.7, 2*3.14*1.7 = 10.676 mm.
Hope this helps!!! Please mark me as brainliest!!!
A giant tortoise can travel 0.11 miles in 1 hour. At this rate, how long would it take the tortoise to travel 3 miles?
Answer:
about 27.27 hours.
Step-by-step explanation:
If it can travel 0.11 miles in 1 hour, we need to divide 3 miles by 0.11 miles to get the number of hours it would take to travel 3 miles. 3/0.11 is 27.27 repeating.
Hope this helps!
Answer:
27.27 hours
Step-by-step explanation:
You need to set up a proportion. I did distance over time.
[tex]\frac{.11 mi }{1 hr} = \frac{3 mi}{x hr}[/tex]
Cross multiply
.11x = 3
Divide by .11
x = 27.27
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Big Oil, Inc. has a preferred stock outstanding that pays an $7 annual dividend. If
investors' required rate of return is 10 percent, what is the market value of the shares?
If the required return declines to 6 percent, what is the change in the price of the stock?
The change in the price of the stock is $46.67.
How to calculate the change in price?From the information given, the current price will be:
= Annual dividend / Required rate
= 7/0.1
= $70
The market value of the shares will be:
= 7/6%
= 7/0.06
= $116.67
Therefore, the change in the price of the stock will be:
= $116.67 - $70
= $46.67
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Please help!!! I will give 20 points to the correct answer!! Thanks so much
Answer:
either it's 7 and 3 but not sure
Step-by-step explanation:
7x3 =21
now for the negative -10 it would basically be -7+-3=-10
Does this relation represent a function?
Answer:
No
Step-by-step explanation:
There are multiple coordinates with the same x coordinate
The frequency table below represents the 30 best batting averages for a
semi-pro baseball league. Which ranges of batting averages were least
common among the players?
Batting Average Frequency
1
2
12
14
1
0.320-0.329
0.330 0.339
0.340 0.349
0.350-0.359
0.360-0.369
A. 0.340 0.349 and 0.350 - 0.359
B. 0.330
0.339 and 0.360 - 0.369
C. 0.320
0.329 and 0.330 -0.339
D. 0.320 0.329 and 0.360 -0.369
The ranges of batting averages were least common among the players is 0.320-0.329 and 0.360-0.369 , Option D is the correct answer.
What is meaning of Average ?Average is the middle value of a set of data points , calculated by summing all the data points and then dividing by the number of points.
It is given that , 30 best batting averages for a semi-pro baseball league.
The ranges of batting averages were least common among the players
To find this , it has to be observed that which range has the lowest frequency
The range 0.320-0.329 and 0.360-0.369 has frequency of 1 which is the least among all
Hence Option D is the correct answer.
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what is the measure of < ABC ?
Answer:
I believe its A. 37
Step-by-step explanation:
That seems to be the measure of B
Please answer this and I will give u a cookie ;)
Answer:
m∠BAC = 40°
Step-by-step explanation:
Note that line BD passes through A, so ∠BAC and ∠CAD form a linear pair. By the Linear Pair Postulate, ∠BAC and ∠CAD are supplementary angles, and by definition their measures add to 180°:
m∠BAC + m∠CAD = 180°
Since the diagram gives us that m∠CAD = 140°, we can substitute and solve:
Starting supplementary angles definition equation ...
m∠BAC + m∠CAD = 180°
Substituting the known value of m∠CAD ...
m∠BAC + (140°) = 180°
Subtracting 140° from both sides of the equation...
(m∠BAC + 140°) - 140° = (180°) - 140°
Simplifying/evaluating...
m∠BAC = 40°
6. Five years ago, Ross was N times as old as
Amanda was. If Amanda is now 19 years old,
how old is Ross now in terms of N?
Answer:
14N+5
Step-by-step explanation:
Five years ago; Rose Nx
Amanda x
Now; Rose Nx+5
Amanda x+5=19
x=19-5=14years
Rose(NOW) =14N+5
The mean diastolic blood pressure for a random sample of 80 people was 100 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 millimeters of mercury, find a 95% confidence interval for the true mean diastolic blood pressure of all people. Then give its lower limit and upper limit.
The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41
How to determine the confidence interval?We have:
Mean = 100
Sample size = 80
Standard deviation = 11
At 95% confidence interval, the critical z value is:
z = 1.96
The confidence interval is then calculated as:
[tex]CI = \bar x \pm z \frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]CI = 100 \pm 1.96 \frac{11}{\sqrt {80}}[/tex]
Evaluate the product
[tex]CI = 100 \pm \frac{21.56}{\sqrt {80}}[/tex]
Divide
[tex]CI = 100 \pm 2.41[/tex]
Split
CI = (100 - 2.41,100 + 2.41)
Evaluate
CI = (97.59,102.41)
Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41
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i tried can you help me
Answer:
question 1
the ticket price which results in the greatest revenue is 14+8=22$
question 2
the greatest revenue we get is 22*(7500-250*8)= 22*5500=121000$
Step-by-step explanation:
the cost of a ticket to music concert is 14$
capacity of people for concert = 7500
for every increase in price attendance decreases by 250
so the required equation for getting revenue is
y = (14+x)(7500-250x)
= 105000+7500x-3500x-250x^2
by differentiating the above equation with respect to x we can find the local maxima which gives us the price for getting more revenue
dy/dx = 7500 -3500 - 500x =0
4000=500x
x= 8
from the above equation we got that if the increase in price was 8$ we will be getting the most revenue out of the concert
question 1
the ticket price which results in the greatest revenue is 14+8=22$
question 2
the greatest revenue we get is 22*(7500-250*8)= 22*5500=121000$
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A snowstorm started on
Tuesday at 2:12 P.M. and
ended on Wednesday at
5:46 A.M. How long did it snow in hours and minutes?
(A) 15 hours, 24 minutes
(B) 15 hours, 34 minutes
(C) 16 hours, 14 minutes
(D) 16 hours, 44 minutes
B) 15 hours, 34 minutes
2:12 + 15 hours = 5:12 A.M
5:12 + 34 minutes = 5:46 A.M
The length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°. What is the approximate length of the radius of the circle?
The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
Length of the arc of a circle:
s = 7.34 units
The measure of central angle:
θ = 81 degrees = 1.413 radians
s = rθ
r is the radius of the circle
7.34 = r(1.413)
r = 5.19 ≈ 5.2 units
Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°
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Answer:
The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°
Step-by-step explanation:
ก
3
The graphs below show measurements from cubes with
different side lengths.
Perimeter of 1 Face
24
2
10
2
40
36-
32-
8 28-
2
Side Length
Which pairs of variables have a linear relationship?
Select two options.
side length and perimeter of 1 face
perimeter of 1 face and area of 1 face
O surface area and volume
area of 1 face and surface area
Oside length and volume
The pairs of variables that have a linear relationship is: A. side length and perimeter of 1 face.
What is the Graph of a Linear Equation?The graph of a linear equation that shows a linear relationship between two variables are straight line graphs.
The graph shown is a straight line graph, therefore, it shows a linear relationship. Therefore, the pairs of variables that have a linear relationship is: A. side length and perimeter of 1 face.
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Which value is a solution to the inequality x – 4 > 15.5? A) x = 21.4 B) x = 17.3 C) x = 15.5 D) x = 19.3
Answer:
A.) x = 21.4
Step-by-step explanation:
When solving the inequality, you can treat the sign like an equal sign. To isolate the "x" variable, you can add "4" to both sides. This eliminates the -4 from the right side.
You are left with the inequality:
x > 19.5
If "x" must be greater than 19.5, the only answer that satisfies this is A.) x = 21.4. All of the other answers are less than 19.5.
[tex]\bf{x -4 > 15.5}[/tex]
[tex]\bf{Add \ 4 \ to \ both \ sides.}[/tex]
[tex]\bf{x-4+4 > 15.5+4 }[/tex]
[tex]\bf{x > 19.5 === > Answer }[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
what steps do you need to do to evaluate the following expression? Select two options. –5(–2) Drag 5 sets of –2 tiles to the window. Drag zero pairs to the window. Remove the 5 groups of –2 tiles. Remove 5 negative tiles from the window.
To solve the expression given , Drag zero pairs to the window and then Remove the 5 groups of –2 tiles , Option b and c is the right answer
What is an Integer Tile method ?It is a teaching method in which materialistic representation is done for concepts like addition and subtraction .
It is used for kids who find it difficult to understand adding a negative integer etc.
For the expression given
-5 (-2)
Drag zero pairs to the window and then Remove the 5 groups of –2 tiles.
Therefore Option B and C is the right answer.
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8 cm
6 cm
2 cm
Find the surface area of the rectangular prism.
Surface Area = [?]cm²
Answer:
152cm²
Step-by-step explanation:
math and stuff and things
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.1 and a standard deviation of 1.47. Using the empirical rule, what percentage of American women have shoe sizes that are greater than 5.16?
97.5% of American women have shoe sizes that are no more than 11.47.
Lets try to solve the question,
Given values ,
Dev (u) = 8.47
Standard deviation (x) = 1.47
So we e have to find the percentage of American women whose shoe size's are not more than 11.47 P(x<11.47).
Lets find z score by using empirical formula.
=> [tex]z= (x-u) / a[/tex]
=> [tex]11.47-8.47/1.5[/tex]
=> [tex]z= 2[/tex]
Now we have to find [tex]P(z < 2)[/tex] . Using the empirical rule, we know that 97.5% data lies below 2 standard deviations above mean.
Therefore the 97.5% of American women have shoe sizes that are no more than 11.47.
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Kira plans to buy a used van that costs $14,000. The dealer requires a 20% down payment. The rest of the cost is
financed with a 4-year, fixed-rate amortized auto loan at 3.5% annual interest with monthly payments.
22
Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent
if necessary. If necessary, refer to the list of financial formulas.
(a) Find the required down payment.
S
▷
$ 0
(b) Find the amount of the auto loan.
Aa
(c) Find the monthly payment.
A: 2800
B: 11200
C: 250.39 per month
can I get a help please
Answer:
middle graph
Step-by-step explanation:
Soluton
The second (middle ) graph is the only one that works.
First of all when you simplicity the right, you get y = x^2 - 1). That means that x does not go through 0,0. If you put x = 0 into x^ - 1 = 0, you get - 1. So on that basis alone both the first and third graphs are incorrect.Second, both xs in the factors are plus, so x^2 is plus, which means the graph opens upward.Toyota manufactures most of the vehicles it sells in the United Kingdom in Japan. The base platform for the Toyota Tundra truck line is ¥1,650,000. The spot rate of the Japanese yen against the British pound has recently moved from ¥197/£ to ¥190/£. How does this change the price of the Tundra to Toyota's British subsidiary in British pounds? Explain.
When the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
Prices = 1,650,000
Exchange rates = ¥197/£
Change in exchange rate = ¥190/£
So, here Original price of the Toyota tundra is
= 1,650,000 ÷ 197
= 8375.63
New import price is = 1,650,000 ÷ 190
= 8,684.21
Percentage change in the price of the imported trucks should be
= ( New price - Old price) / old price *100 = (8,684.21 - 8375.63) ÷ 8375.63 = 3.68%
Hence , when the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
(This is the percentage change in the Japanese yen as the price of the truck remains unchanged).
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Which of the numbers below are whole numbers?
A. 0
B. 0.388
C. 2454
D. 602.49
E. 996
F. 719557
Answer:
a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal
whole: a,c,e&f
not:b&d
Question 11 (5 points) ✓ Saved Solve x² + 4x + 12 = 0 by completing the square. Ox= -2 + 2√2i, x=-2-2√/2i Ox= -2 +2i, x=-2-2/ O x = 0, -4 Ox= -2+ √2i, x=-2-√2i
The solution of the equation is x = -2±2i√2. The solution to the equation is found in the Sridharacharya formula.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation;
x² + 4x + 12 = 0
The solution to the equation is found as;
x² + 4x + 12 = 0
The solution to the equation is;
[tex]\rm x=-b \pm \frac{\sqrt{b^2-4ac}}{2a} \\\\ \rm x=-4 \pm \frac{\sqrt{4^2-4\times 4 \times 1}}{2\times 4} \\\\[/tex]
x = -2±2i√2
Hence the solution of the equation is x = -2±2i√2.
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