Answer:
See explanation
Step-by-step explanation:
1) Equation of line through (3, 2) with slope -2.
y = mx + b
2 = -2(3) + b
2 = -6 + b
8 = b
y = -2x + 8
2) Equation of the line through the points (4, 2) and (3, 1)
m = (1 - 2)/(3 - 4) = -1 / -1 = 1
y = mx + b
1 = 1(3) + b
1 = 3 + b
-2 = b
y = x - 2
Answer:
y=-2x+8
y=x-2
Step-by-step explanation:
y=-2x+b
2=-2(3)+b
2=-6+b
8=b
Plug it into your expression
y=-2x+8
(1-2)=m(3-4)
-1=m(-1)
-1=-m
1=m
Plug it into your expression
y=1x+b
1=1(3)+b
-2=b
Plug it into your expression
y=x-2
Find the volume of a cylinder that has the following dimensions. Do not round your answer.
(Use 3.14 for pi.)
Radius = 5 cm
Height = 0.25 m
Volume = __ cm3
Answer:
19.625 cm^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 * 5^2 * .25
V =19.625 cm^2
Simplify:$$\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}$$
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]
All Done!
Answer:
Your correct answer is 8.660254
Step-by-step explanation:
√2√82 + 152 + √92 + 402 = 8.660254
Use the following data set to find the sample statistics for the following data set. 1. (N) or (n) 2. (x-bar) or (μ) 3. (σ) or (s) Thanks!
Answer:
(1) N or n = 20
(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4
(3) σ = 9.78 and s = 10.04.
Step-by-step explanation:
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;
Mean = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]
= [tex]\frac{868}{20}[/tex] = 43.4
So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.
(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;
Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]
= 10.04
Can someone help me solve this?
Answer:
(a) y = -3/5 x + 13/5
(b) y = 5/3 x + 1/3
Step-by-step explanation:
(a) The slope of the tangent line is dy/dx. Use implicit differentiation:
x² + y² + 4x + 6y − 21 = 0
2x + 2y dy/dx + 4 + 6 dy/x = 0
2x + 4 + (2y + 6) dy/dx = 0
x + 2 + (y + 3) dy/dx = 0
(y + 3) dy/dx = -(x + 2)
dy/dx = -(x + 2) / (y + 3)
At the point (1, 2), the slope is:
dy/dx = -(1 + 2) / (2 + 3)
dy/dx = -3/5
Using point-slope form of a line:
y − 2 = -3/5 (x − 1)
Simplifying to slope-intercept form:
y − 2 = -3/5 x + 3/5
y = -3/5 x + 13/5
(b) The normal line is perpendicular to the tangent line, so its slope is 5/3. It also passes through the point (1, 2), so point-slope form of the line is:
y − 2 = 5/3 (x − 1)
Simplifying to slope-intercept form:
y − 2 = 5/3 x − 5/3
y = 5/3 x + 1/3
Which of the following is the correct scientific notation for 0.00566 meters?
A. 566 x 10-5 m
B. .566 x 10-3 m
C. 5.66 x 10-3 m
D. 5.66 x 103 m
The least of 3 consecutive integers is a, and the greatest is z. What is the value of a + 2z/ 2 in terms of a?
Answer:
The value of a + 2z/ 2 in terms of a is (3a+4)/2
Step-by-step explanation:
least of 3 consecutive integers is a, and the greatest is z
if a is the least one
we know that integers differ by value of 1.
example -2, -1, 0, 1,2
they all differ by
then next consecutive integer will be a+1
third integer will be second integer +1 = a+1 + 1 = a+2
Thus, 3 consecutive integer
a , a+1, a+2
but given that greatest is z
thus, a+2 is greatest and hence
a+2 = z
we have to find value of a + 2z/ 2 in terms of a
a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.
The value of a + 2z/ 2 in terms of a is (3a+4)/2
Billy has three times as many llamas as lambs.
Milly has twice as many lambs as llamas.
They have 17 animals in total.
How many of the animals are llamas?
Answer:
There are 9 llamas.
Step-by-step explanation:
For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.
As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.
If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.
If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.
We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.
9 ÷ 3 = 3.
This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6, because she has twice the amount of lambs.
Billy has 2 lambs and 6 llamas.
Milly has 6 lambs and 3 llamas.
The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.
Answer:
Billy: Has 4 lots of animals
Milly: Has 3 lots of animals
17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total
How is the graph of y = 2 (3)^x+1 -4 translated from the graph of y = 2(3)^x
Answer:
f(x - n) - shift the graph n units right
f(x + n) - shift the graph n units left
f(x) - n - shift the graph n units down
f(x) + n - shift the graph n units up ----------------------------------------------------------------------------
Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.
Which inequality is equivalent to \-41 <9?
0-9 > X-4 < 9
-9 < x-4 < 9
O X-4<-9 or x – 4 < 9
hry 4 > -9 or x - 4<9
please help i dont understand it
30 POINTS
Answer:
0.16 P(Yellow or Brown)=0.16
Answer: 0.44
Step-by-step explanation:
0.4 + 0.28 = 0.68
1.00 - 0.68 = 0.32
0.32 divided by 2.0 = 0.16
Total answer is 0.44
GLAD TO HELP:)
HAVE A NICE DAY!
BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)
PLEASE BRAINLEST ME!
I NEED HELP ASAP!!!! WILL MARK BRAINLIEST
Answer: 5x + 1
Step-by-step explanation:
f(x) - g(x)
(3x + 2) - (-2x + 1) Here you distribute the negative sign to (-2x + 1)
3x + 2 + 2x - 1 Here you combine like terms
5x + 1 This is the answer.
1 Point
Which of the following best describes a random event?
A. The number of doctor visits a person makes in a year
B. The winner of an election
C. The age at which a baby will get her first tooth
D. The age at which a person is legally allowed to drive in the state of
California
SEBNI
Answer: B
Step-by-step explanation:
Makes the most sense out of all the options because it’s the most random or unpredictable
Juan did a survey in four butterfly parks and wrote the following observations: Butterfly Park Survey Park Number of Pink Butterflies Total Number of Butterflies P 25 53 Q 35 64 R 37 75 S 23 55 Based on the survey, which park had the greatest percentage of pink butterflies? Park P Park Q Park R Park S
Answer:
Park Q has greatest percentage of pink butterflies.
Step-by-step explanation:
Butterfly Park Survey Park P Q R S
No, of Pink Butterflies 25 35 37 23
Total Number of Butterflies 53 64 75 55
Now we are supposed to find which park had the greatest percentage of pink butterflies
So, Percentage of pink butterflies in park P =[tex]\frac{25}{53} \times 100=47.169\%[/tex]
Percentage of pink butterflies in park Q =[tex]\frac{35}{64} \times 100=54.68\%[/tex]
Percentage of pink butterflies in park R= [tex]\frac{37}{75} \times 100=49.33\%[/tex]
Percentage of pink butterflies in park S= [tex]\frac{23}{55} \times 100=41.81\%[/tex]
So, Park Q has greatest percentage of pink butterflies.
So, Option B is true
Hence Park Q has greatest percentage of pink butterflies.
Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5. Pls help ASAP btw, the answer isn't -12/19 or 12/19
Answer:
The found values are:
A = 1/3
B = -8/3
Step-by-step explanation:
We know that general equation is given by:
y = mx + c
where m is the slope and c is a constant.
x + 3y = -5
y = -(1/3)x - 1/3(5)
Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:
Ax + By = 3
By = -Ax - 3
By = (1/3)x - 3
Hence, A = 1/3
Substitute point (-7,2) into the equation:
B(2) = (1/3)(-7) -3
B(2) = -7/3 - 3
B(2) = -16/3
B = -16/6
B = -8/3
59. A car dealership has SUVs and sedans in a ratio of
5:9. How many sedans does the car dealership
have if there are 140 SUVs?
Answer:
The car dealership has 252 sedans.
Step-by-step explanation:
Number of SUVs = 140
Ratio of SUVs to sedans = 5:9
Sum of ratios = 5+9 = 14
Total number of cars = 14/5 × 140 = 392
Number of sedans = 9/14 × 392 = 252
On which number line do the points represent negative seven and one over two and +1? Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of 0.
Answer:
A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers
I hope that is what your asking...
Answer:
On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of
Step-by-step explanation:
When solving the following system of equations, which variable would be the easiest to solve for?
Answer:
the y is the second equation.Answer:
The y in the second equation
Step-by-step explanation:
hope this helps
Simplify (*x* +2x? - 5x)+(-3x + x +1)+(3+* + 2x).
A. 3x + 2x* - 3x2 – 3x² +1
B 4x*- 3x + x2 + 4x +2
C. 4x4 - 3x + 3x² + 4x +2
D. 4x*- 3x + 3x? - 3x + 1
Answer:
D
Step-by-step explanation:
4x^4+3x^2-3x^3-3x+1
The perpendicular bisector of the line segment connecting the points (-3,8) and (-5,4) has an equation of the form y = mx + b. Find m+b. BTW, the answer is not 16...
Answer:
Step-by-step explanation:
find the slope
[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]
take a coordinate to fill in
[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]
this means that the equation is y=2x-13
and if you add m and b
you get :-11
I HOPE THIS HELPS
Answer:
7/2
Step-by-step explanation:
Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.
The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by
\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find
\[y = -\frac{1}{2} x + 4.\]
Does this table represent a function? why or why not?
Answer:
I think it's A but I could be wrong
Answer: B
Step-by-step explanation:
A graph or table is a function if it passes the vertical line test. That means, each x and only 1 y. One x cannot have more than 1 y because, that means it does not pass the veritcal line test. In the vertical line test, the vertival line only passes through 1 point, not 2. Since we know that this graph does not pass the vertical in test, we can eliminate C and D. We can eliminate A because 2 y-values can be the same as lone as there have different x. B fits the description of what we see on the table. Therefore, the answer is B.
Find the area ratio of a cube with volume 125m3 to a cube with volume 64m3.
Answer:
25:16
Step-by-step explanation:
i think its right
Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
Answer:
The third and fourth options.
Step-by-step explanation:
You simplify the inequality first...
-6x + 15 < 10 - 5x
-x < -5
x > 5
The first option is incorrect since it is less than.
The second option is basically -5x < 15; x > -3; that's incorrect.
The third option is basically -x < -5; x > 5; that is correct!
The fourth option is correct since it shows more than 5.
The fifth option is incorrect because it shows less than -5.
Hope this helps!
Answer: The answer is C and E
Step-by-step explanation:
Hope this helps;)
Need help with trig problem in pic
Answer:
a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]
b) [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]
c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]
d) [tex]\alpha\approx 53.1^o[/tex]
Step-by-step explanation:
a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.
We can use the Pythagorean identity:
[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]
Where we have used that the secant of an angle is the reciprocal of the cos of the angle.
Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:
[tex]cos(\alpha)=-\frac{3}{5}[/tex]
b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:
[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]
where we took the positive value, since we know that the angle is in the first quadrant.
c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:
[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]
Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:
[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]
Then:
[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]
d)
Since [tex]sin(\alpha)=\frac{4}{5}[/tex]
then [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]
What are the first three terms of the Arithmetic Sequence an=11-3(n-1)?
a. 1, 2, 3
b. 0, 8, 16
c. 8, 5, 2
d. 11, 8, 5
Answer:
11,8,5
Step-by-step explanation:
an=11-3(n-1)
Let n=1
a1 = 11 - 3(1-1)
= 11 -0
=11
Let n=2
a2 = 11-3(2-1)
= 11 -3(1)
= 8
Let n=3
a3 = 11-3(3-1)
= 11 -3(2)
= 11 -6
=5
Answer:
The answer is 11,8,5
Step-by-step explanation:
that's the correct answer
Please help me match these formulas . :)
Answer:
1. equilateral triangle
2. rectangle
3. circle area
4. trapezoid
5. circle circumference
6. parallelogram
7. regular polygon
8. triangle
Hope that helps.
Help help please.....Thanks
Hey there! :)
Answer:
56.7 kg.
Step-by-step explanation:
Use the density formula to solve for the mass:
D = m/V.
Rearrange in terms of mass, or 'm':
DV = m.
Solve for the volume:
0.06 × 0.9 × 1.5 = 0.081 m³.
Plug this into the equation along with the density:
700 × 0.081 = 56.7 kg.
What is the slope of the line shown below? A. -1/3 B. 1/3 C. -3 D. 3
Answer:
C. -3
Step-by-step explanation:
Plugging both of those points into the slope formula gets you a slope of -3.
ΔHFG is dilated by a scale factor of 2 with the center of dilation at point F. Then, it is reflected over line a to create ΔEFI. Based on these transformations, which statement is true? Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F. segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI segment FG = segment FI, segment FH = segment FE, and segment HG = segment EI; ΔHFG ~ ΔEFI segment FG = one half segment FE, segment FH = one half segment FI, and segment HG = one halfsegment EI; ΔHFG ~ ΔIFE segment FG = segment FE, segment FH = segment FI and segment HG = segment EI; ΔHFG ~ ΔIFE
Answer:
segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI
Step-by-step explanation:
In the picture attached, the triangles are shown.
After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG and segment EI. More specifically:
FG = 1/2*FIFH = 1/2*FEHG = 1/2*EIAnswer:
segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI
Step-by-step explanation:
In the picture attached, the triangles are shown.
After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG and segment EI. More specifically:
FG = 1/2*FI
FH = 1/2*FE
HG = 1/2*EI
This answer is right! took the test on FLVS and confirmed it :)
please help me and hurry
Answer:
median: 90
mode: 91
mean: 84.2 or round it to 84
Step-by-step explanation:
Let me know if this helps! have a great day! :)
Answer:
a) Median = 91
b) mode = 91
c)Mean 84.2
Step-by-step explanation:
a) Median is the middle term. So, 6th term
Median = 91
b) Mode is the score which occurs more number of times
91 occurs 3 times
Mode = 91
c) Mean= sum of all data's/Number of data's
= 85 + 91 + 48 +98 + 99 /5
= 421/5
Mean = 84.2
Miracle Maid Service charges a $30 house visit fee plus $5 per room to clean a house. What is the independent variable? A) The price per room B) The number of rooms C) The house visit fee D) The Miracle Maid Service
Answer:
B
Step-by-step explanation:
The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.