write an equation of the line in slope-intercept form: A(-1,3) and b(2,-1)
Answer: y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
First we will find the slope, then we will find the y-intercept.
Slope is change in y over change in x:
[tex]\frac{-1-3}{2--1}=\frac{-4}{3}[/tex]
Now we will solve for the y-intercept:
y = [tex]\frac{-4}{3}[/tex]x + b
(-1) = [tex]\frac{-4}{3}[/tex](2) + b
-1 = [tex]\frac{-8}{3}[/tex] + b
[tex]\frac{5}{3}[/tex] = b
b = [tex]\frac{5}{3}[/tex]
Final equation:
y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
Solve one half ÷ 8 = ___.
one seventh
one sixteenth
one twenthieth
one thirtieth
Answer:
one sixteenth
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
A glass holds 189 milliliters of juice. How many liters will 36 glasses hold?
Answer:
1 glass - 189 mm
thn 36 - 189 x 36
6804mm - 0.6 littre is holded by 36 glass
a student needs to fill a tank with 9 liters of waters how many 1/3 liters of water will it take to fill the tank
It will take 27 containers of 1/3 liter to fill the tank.
Since you need 3 containers of 1/3 to have a full liter, and 9 liters for the tank, 9*3=27.
Answer:
27
Step-by-step explanation:
1= 1/3x3
3x9=27
Will give Brainly!!
5 Questions
Financial Mathematics
Questions Attached
Which expression is equivalent to z+z+z+z+3?
A. 7z
B. 4z + 3
C. 3z +4
D. z3
Answer:
4z+3
Step-by-step explanation:
multiply the z's giving four z's and we don't know the value of z so we can't add 3 to it
Point R divides PQ in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?
A. -1/3
B. 3
C. 5
D. 6
E. -9
The x-coordinate of Q if the x-coordinate of R is -1 and the x-coordinate of P is -3 is 5
Here, we have,
given that,
Point R divides PQ in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3,
Midpoint of a line
The formula for calculating the midpoint of a line divided in the ratio m:n is expressed as:
M(x,y) = (mx₂ + nx₁) / (m + n) , (my₂ + ny₁) / (m + n)
For the x-coordinate
X = (nx₁+mx₂/m+n)
let, the x-coordinate of Q = a
Substitute the given parameters
-1 = 3(-3) + 1(a) / 1+3
or, -1 = -9 + a/4
or, -4 = -9 + a
or, a = 5
Hence the x-coordinate of Q if the x-coordinate of R is -1 and the x-coordinate of P is -3 is 5
Learn more on coordinate here:
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I need help with this question step by step
Z-scores are used to determine the probability of data. The z-score for the given parameters in normal distribution is -6.35
How to calculate z-score for a normal distribution?
The formula given to calculate the z-score is expressed as:
[tex]z = \dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Given the following parameters:
Mu = 1.36
n = 28
[tex]\sigma = 5[/tex]
Mean = 130
Substitute into the formula
[tex]z = \dfrac{130-136}{\frac{5}{\sqrt{28}} }\\ x = \frac{-6}{0.9449} \\z = -6.35[/tex]
Hence the z-score for the given parameters in normal distribution is -6.35
Learn more on z-score here: https://brainly.com/question/25638875
Solve the system of equations.
2x−9y=14
x=−6y+7
Step-by-step explanation:
[tex]put \: x \: into \: equation \: 1[/tex]
[tex]2( - 6y + 7) - 9y = 14[/tex]
[tex] - 12y + 14 - 9y = 14[/tex]
[tex] - 21y + 14 = 14[/tex]
[tex] - 21y = 14 - 14[/tex]
[tex] - 21y = 0[/tex]
[tex] \frac{ - 21y}{12} = \frac{0}{21} [/tex]
[tex]y = 0[/tex]
[tex]put \: y = 0 \: into \: equation \: 2[/tex]
[tex]x = 6y + 7[/tex]
[tex]x = 6(0) + 7[/tex]
[tex]x = 0 + 7[/tex]
[tex]x = 7[/tex]
Answer:
y = 0
x = 7
Step-by-step explanation:
2x − 9y = 14 ⇒ ( 1 )
x = − 6y +7 ⇒ ( 2 )
First, let us find the value of y.
For that, replace x with ( - 6y + 7 ).
Let us take equation 1 for that.
2x − 9y = 14
2 ( - 6y + 7 ) - 9y = 14
-12y + 14 - 9y = 14
21y = 14 - 14
21y = 0
Divide both sides by 21.
y = 0
And now let us take equation 2 to find the value of x by replacing y with 0.
2x − 9y = 14
2x - 9 × 0 = 14
2x - 0 = 14
2x = 14
Divide both sides by 2.
x = 7
What is the smallest positive integer n such that n! ends in at least 2019 zeros?
Answer:
I think there's 502
Step-by-step explanation:
if this is a olunomical question that should be it I believe, because you have to write in standered form then when it equals zero, then factor it
Following is the probability distribution for age of a student at a certain public high school.
X
13
14
15
16
17
18
P(x) 0.09 0.22 0.24 0.28 0.15 0.02
(a) Find the variance of the ages. Round the answer to at least four decimal places.
The variance of the ages is
Considering the given discrete distribution, the variance of the ages is of 1.5844.
What is the mean and the variance of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The variance is given the sum of the difference squared between each outcome and the mean, multiplied by it's respective probability.In this problem, considering the distribution given in the table, the mean is given by:
[tex]E(x) = 13(0.09) + 14(0.22) + 15(0.25) + 16(0.28) + 17(0.15) + 18(0.02) = 15.39[/tex]
Hence, the variance is given as follows:
[tex]Var(x) = 0.09(13-15.39)^2 + 0.22(14-15.39)^2 + 0.25(15-15.39)^2 + 0.28(16-15.39)^2 + 0.15(17-15.39)^2 + 0.02(13-15.39)^2 = 1.5844[/tex]
More can be learned about discrete distributions at https://brainly.com/question/24855677
a 5 1/2 quart pot is filled 2/3 of the way with water. How many quarts of water can the pit hold?
Answer:
4 5/6 quarts or 4.83 quarts
Step-by-step explanation:
5 1/2 quart pot has an equal value to 11/2 quart pot
it is filled with 2/3 quarts of water
Therefore, the quarts of water the pot can hold is;
11/2 - 2/3
LCM = 6
11/2 - 2/3 ÷ 6
33 - 4 ÷ 6
29/6
:. 29/6 quarts(4 5/6 quarts or 4.83 quarts) of water is the amount needed to fill the 5 1/2 quart pot
Find the measure of the missing angle.
Answer:
You see that 73 degrees and angle 'a' must add up to be = to 180 degrees since both angles form that straaight line on the left. So 180 degrees - 73 = 107 degrees which is measure of angle 'a'
Step-by-step explanation:
Answer:
107°
Step-by-step explanation:
The two angles below form a linear pair.
They are characterized by forming a sum of 180°, which is the standard angle measure of any line.
⇒ a + 73° = 180°
⇒ a = 107°
Kim has a cube that is 1 unit long, 1 unit wide, and 1 unit high. What is the
volume of Kim's cube?
Answer:
Volume of cube is width times length times height. So it's simply 1 unit × 1 unit × 1 unit = 1 unit³. Final answer: 1 unit³ (or 1 cubed unit).
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
multiply the length, width, and the height for the answer
is this is right please make it brainlyest!
PLEASE HELP PLEASE HELP
Answer:
B
Step-by-step explanation:
please help asap and please leave a real answer thank you
Answer:
[tex] \frac{0.75x - 3}{x - 1} [/tex]
Step-by-step explanation:
Equation of a rational function is
[tex] \frac{p(x}{q(x)} [/tex]
where q(x) isn't zero.
There is a vertical asymptote at
[tex]x = 1[/tex]
So this mean that our denomiator must have a zero that occur at x=1.
That zero is
[tex]x - 1[/tex]
So our denomiator is
[tex] \frac{p(x)}{x - 1} [/tex]
Since our horinzontal asymptote is a non zero value, the numerator must be a linear equation as well.
So our rational function is
[tex] \frac{ax + b}{x - 1} [/tex]
We know the graph pass through (0,3)
So if we apply that logic,
[tex] \frac{a(0) + b}{0 - 1} = 3[/tex]
[tex] \frac{b}{ - 1} = 3[/tex]
[tex]b = - 3[/tex]
And it passes through (4,0)
[tex] \frac{a(4) + b}{3} = 0[/tex]
[tex]4a + b = 0[/tex]
[tex]4a + ( - 3) = 0[/tex]
[tex]4a = 3[/tex]
[tex]a = \frac{3}{4} [/tex]
So our rational equation is
[tex] \frac{0.75x - 3}{x - 1} [/tex]
is 0.304 meters less than 1 meter
Answer:
yes!
Step-by-step explanation:
because it is 0.
if it is was 1.304, it would be more than 1 meter.
Hope this makes sense! If you have further questions, let me know!
- profparis
please help me!!!!!!!
I'll do part 1 to get you started
================================================
Answers:
D) 90, 45, 45A) centroidB) vertex of right triangleB) 41C) 5^4*3^5================================================
Explanations:
In an isosceles triangle, the base angles are congruent. Let's call them x. When dealing with a right triangle, those bases angles are also complementary and they add to 90 degrees. This means x+x = 90 solves to x = 45. Therefore we have a 45-45-90 triangle.This is something to memorize. There's not much explanation I can think of. The altitudes intersect at the orthocenter. For a right triangle, the altitude for the base is the height, and vice versa. The base and height intersect at the vertex point that's the 90 degree angle.The number 41 is prime because the only factors are 1 and itself. Something like 81 is not prime because 3 is a factor. We consider 81 to be composite.Rewrite 5^4*3^5 as 5*(5^3*3^5) to see that 5^3*3^5 is a divisor or factor of 5^4*3^510 men can do the work in 8 days. how many men should be reduced to finish the work in 10 days
If Reducing 2 men will bbe enough too finish the work in 10 days
For rate of work use the formualar
rate of work = quantity of work / duration
10 men can do the work at a rate of = 1 / 8
x men can do same work at a rate of = 1 / 10
x * ( 1 / 8 ) = 10 * ( 1 / 10 )
x = 1 * 8 = 8
therefore 8 men can do the work in 10 days
number of men reduced = 10 men - 8 men = 2 men
Hope it helped
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
please show work!!
Answer:
f(0)=6
Step-by-step explanation:
It should be the third one because it is the only one that has the x-value in the parentheses and equals the y-value. (I think please someone back me up)
Natasha's uncle has a rectangular field that has an area of 5/8 square miles. The width of the field is 1/4 mile. How long is the field? Show your work.
Answer:
5/2 or 2 1/2
Step-by-step explanation:
You divide the area by the width to get the length
5/8 / 1/4 and do keep change flip to get:
5/8 * 4/1 = 20/8 which you then simplify and get 5/2
Is it possible that someone could help me with this?
(I tried to take the best picture a can)
Answer:
Below.
Step-by-step explanation:
There are 2 outliers:
234, 880.
All the other values range from 485 to 510.
how can we use a "line of best fit" to make a prediction?
Step-by-step explanation:
To draw a line of best fit, balance the number of points above the line with the number of points below the line.
Your puppy dug up two-thirds of the flowers in the flower bed that contained 18 flowers. How many flowers were dug up?
flowers
Answer:
12 :)
Step-by-step explanation:
18/3 = 6
Now we multiply :)
6 x 2 = 12
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
12
Step-by-step explanation:
2/3 of 18 =
1/3 of 18 = 6
(because 18 divided by 3 = 6)
2/3 of 18 = 1/3 + 1/3
therefore 2/3 of 18 = 6 + 6 = 12 (or 6 x 2)
Hope this makes sense! If you have further questions, let me know!
- profparis
a brainliest would be appreciated if i helped you! :D
Grady rode his bike 910 of a mile. Which of the following show this distance using decimal notation?
The distance Grad rode his bike 9 / 10 miles is represented in decimal as 0.9 miles.
What are decimal numbers?Decimal number are number whose whole number part and the fractional part is separated by a decimal point. Example of decimal numbers are 0.345, 7.45, 6.72 etc.
The distance Grad rode his bike is represented in fraction. The distance can be converted to decimal number as follows:
Distance in fraction = 9 / 10 miles
Therefore, the distance in decimal = 0.9 miles
learn more on decimal here: https://brainly.com/question/1645285
What is the ratio of the surface areas of two cones if the radius of one is 3 en and the slant height is 7 cm, and the other has a radius of 5 cm and a slan Height of 9 cm?
Given Information :-
⠀
A cone with dimensions :-
Radius = 3 cmSlant height ( l ) = 7 cm⠀
Another cone with dimensions :-
⠀
Radius = 5 cmSlant height = 9 cm⠀
To Find :-
⠀
The ratio of their total surface area⠀
Formula Used :-
⠀
[tex] \qquad \diamond \: \underline{ \boxed{ \red{ \sf T.S.A._{Cone}= \pi r(r+l) }}} \: \star[/tex]
⠀
Solution :-
⠀
For the first cone,
⠀
Since, we don't really have to find the exact values of the surface area, we will let pi remain as a sign itself, this will make the calculations easier.
⠀
[tex] \sf \longrightarrow T.S.A. = \pi \times 3(3 + 7) \\ \\ \\ \sf \longrightarrow T.S.A. = \pi \times 3 \times 10 \: \: \: \\ \\ \\ \sf \longrightarrow T.S.A. =30 \pi \: {cm}^{2} \: \: \: \: \: \: \: \: \\ \\ [/tex]
Now, for the second cone,
⠀
[tex] \sf \longrightarrow T.S.A. = \pi \times 5(5 + 9) \\ \\ \\ \sf \longrightarrow T.S.A. = \pi \times 5 \times 14 \: \: \: \: \\ \\ \\ \sf \longrightarrow T.S.A. =70 \pi \: {cm}^{2} \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Now, we just have to calculate the ratio of their surface areas, thus,
⠀
[tex] \sf \longrightarrow Ratio = \dfrac{Surface ~area~of~first~cone}{Surface ~area~of~second~cone} \\ \\ \\ \sf \longrightarrow Ratio = \frac{30 \pi \: {cm}^{2} }{70 \pi \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \qquad \qquad \qquad \\ \\ \\ \sf \longrightarrow Ratio = \frac{ 3 \cancel{0 \pi \: {cm}^{2}} }{ 7 \cancel{0 \pi \: {cm}^{2} } } \qquad \qquad \qquad \qquad \\ \\ \\\sf \longrightarrow Ratio = \frac{3}{7} = 3 : 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio between the surface areas of the cones is 3 : 7.
⠀
[tex] \underline{ \rule{227pt}{2pt}} \\ \\ [/tex]
What is the amplitude of the function?
Answer:
2
Step-by-step explanation:
Take the absolute value of the lowest y value.
So
[tex] | - 1| = 1[/tex]
Take the absolute value of highest y value.
[tex] |3| = 3[/tex]
Add those two together and divide by two.
[tex] \frac{1 + 3}{2} = 2[/tex]
So the amplitude is 2
Compare the integers.
-14
-23
A)
B)
> Greater than
O
= Equal to
D
Neither
Answer:
-14 > -23
Step-by-step explanation:
-14 is greater than -23 since it is closer to 0 than -23.
hope this helps!! p.s. i really need brainliest :)
A cardboard box, which has the shape of a parallelepiped, has the following sizes: 35 cm by 27 cm
(rectangular base). The height of the box is - 27 cm. Calculate the volume of the box.
Answer:
25,515
Step-by-step explanation:
35 x 27 x 27
945 x 27
25,515
A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude
Answer:
Area of given triangle is 939.15cm² and smallest altitude is 30.8cm
Solution:We are given three sides of a triangle, Let the sides be :
( a ) = 35 cm( b ) = 54 cm( c ) = 61 cmWe can find the area of the triangle with its three sides using Heron's Formula
Heron's FormulaHeron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:
[tex] \sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}[/tex]
where ( s ) :
[tex] \sf \longrightarrow s = \dfrac{a + b + c}{2} [/tex]
Therefore, for the given triangle first we will calculate ( s )
[tex] \begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}[/tex]
Now, Area of triangle will be:
[tex] \begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}[/tex]
Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,
[tex] \begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}[/tex]
Answer:
Area = 939.15 cm² (2 d.p.)
Shortest Altitude = 30.79 cm (2 d.p.)
Step-by-step explanation:
Heron's Formula allows us to find the area of a triangle in terms its side lengths.
Heron's Formula
[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
where:
a, b and c are the side lengths of the triangles is half the perimeterGiven values:
a = 35 cmb = 54 cmc = 61 cmFind the value of s:
[tex]\sf \implies s=\dfrac{a+b+c}{2}=\dfrac{35+54+61}{2}=75\:cm[/tex]
Substitute the values into the formula and solve for area:
[tex]\begin{aligned}\implies \sf Area & =\sf \sqrt{75(75-35)(75-54)(75-61)}\\& = \sf \sqrt{75(40)(21)(14)}\\& = \sf \sqrt{882000}\\& = \sf \sqrt{176400 \cdot 5}\\& = \sf \sqrt{176400}\sqrt{5}\\& = \sf 420\sqrt{5}\\& = \sf 939.15\:\:cm^2\:\:(2\:d.p.)\end{aligned}[/tex]
The altitude of a triangle is a perpendicular line segment drawn from a vertex of the triangle to the side opposite to it.
The shortest altitude of a triangle is drawn to the longest side.
Therefore, the shortest altitude will be the height of the triangle when the longest side is the base:
[tex]\begin{aligned}\textsf{Area of a Triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \sf 420\sqrt{5} & = \sf \dfrac{1}{2} \times 61 \times altitude \\\implies \sf Altitude & = \sf \frac{2 \cdot 420\sqrt{5}}{61}\\& = \sf \dfrac{840\sqrt{5}}{61}\\ & = \sf 30.79\:\:cm\:\:(2\:d.p.)\end{aligned}[/tex]