Answers
Answer:
[tex]\sf y= \dfrac{1}{2}x-5[/tex]
Explanation:
coordinates taken: (0, -5), (6, -2)slope:
[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{-2--5}{6-0}[/tex]
[tex]\rightarrow \sf \dfrac{1}{2}[/tex]
equation in slope intercept form:
y = m(x) + b [ where "m is slope", "b is y-intercept" ][tex]\sf y= \dfrac{1}{2}x-5[/tex]
Answer:
[tex]y=\frac{1}{2}x-5[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
To find slope, we use points on the line.
Here, I will be suing (-6, -8) and (8, -1)
[tex]m=\frac{1-(-8)}{8-(-6)} \\\\m=\frac{-1+8}{8+6} \\\\m=\frac{7}{14}\\\\m=\frac{1}{2}[/tex]
[tex]y=mx+b[/tex]
[tex]y=\frac{1}{2} x+b\\[/tex]
Now, we use either of our points (-6, -8) OR (8, 1) to find b.
I will be using (8, -1):
[tex]y=\frac{1}{2}x+b\\\\-1=\frac{1}{2}(8)+b\\\\-1=4+b\\\\-4-4\\\\-5=b[/tex]
[tex]y=\frac{1}{2}x+b== > y=\frac{1}{2}x-5[/tex]
Check your answer manually: (-6, -8)
[tex]y=\frac{9}{14}x-\frac{29}{7}\\\\-8=\frac{9}{14}(-6)-\frac{29}{7}\\\\-8=\frac{9}{7}(-3)-\frac{29}{7}\\\\-8=-\frac{27}{7}-\frac{29}{7}\\\\-8=-\frac{56}{7}\\\\-8=-8[/tex]
This statement is correct.
*You can also view the attached graph to verify the answer, meaning that those two points should lie on the same line.*
Hope this helps!
Related Questions
What is the area of the shape below?
Answers
Answer:
A = 192 units²
Step-by-step explanation:
the figure is a trapezium.
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the bases and b₁, b₂ are the bases
here h = 12 , b₁ = 12 , b₂ = 20 , then
A = [tex]\frac{1}{2}[/tex] × 12 × (12 + 20) = 6 × 32 = 192 units²
2.1
For her science project Manuerted into degrees Newton by multiplying the number of
is exploring different temperature scales. She has found
degrees Celsius by Suppose she constructed a graph, with degrees Celsius along the
that degrees Celsius can
horizontal axis and degrees Newton along the vertical axis. If she plotted some points
and drew a line through them, which of these statements would be true about the line?
Answers
Answer:
123 this is a good idea to make sure you have the best time ever.
is 56/72 and 7/9 proportional
Answers
Answer:
Yes.
Step-by-step explanation:
7 x 8= 56
9 x 8= 72
56/72 is proportional to 7/9
Answer:
[tex]\frac{56}{72}[/tex] and [tex]\frac{7}{9}[/tex] are indeed proportional
Step-by-step explanation:
In order to confirm that [tex]\frac{7}{9}[/tex] is proportional to [tex]\frac{56}{72}[/tex], you need to make sure both fractions share the same denominator. In this case, it is better to multiply 9 by a value that causes the product to be 72 than to divide 72 by a number to get to 9. 72 is eight times greater than 9, so you multiply [tex]\frac{7}{9}[/tex] by [tex]\frac{8}{8}[/tex] (This is important as you need to make sure you aren't changing the value of the fraction when multiplying a number to it, so you must be sure to multiply your fraction by the number over itself - which is essentially one - to ensure that you are keeping the value of the fraction the same) and you will get [tex]\frac{7*8}{9*8} =\frac{56}{72}[/tex], this means the fractions [tex]\frac{7}{9}[/tex] and [tex]\frac{56}{72}[/tex] are proportional.
Let $a_1 a_2 a_3 \dotsb a_{10}$ be a regular polygon. A rotation centered at $a_1$ with an angle of $\alpha$ takes $a_4$ to $a_8$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees
Answers
Answer:
72°
Step-by-step explanation:
The required angle of rotation can be found by considering the regular polygon to be inscribed in a circle. Each of its 10 vertices will be separated by a central angle of 360°/10 = 36°. So, the vertices a8 and a4 will be separated by a central angle of (8 -4)(36°) = 144°.
The angle a4-a1-a8 is an inscribed angle, so will have half the measure of the central angle intercepting the a4-a8 arc. The desired angle of rotation to map a4 to a8 is ...
α = 144°/2 = 72°
The value of angle α is 72° if the regular polygon is inscribed in a circle and rotation centered at a_1
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. A polygon's sides or edges are made up of straight-line segments that are joined end to end to form a closed shape. The vertices or corners are the points where two line segments meet, and an angle is generated as a result.
Consider the regular polygon to be inscribed in a circle to get the required angle of rotation.
A center angle of 360°
=360°/10 = 36°
It will separate each of its 10 vertices.
The central angle:
= (8 - 4)×(36°) = 144°
An inscribed angle is a4-a1-a8:
So α will be:
α = 144/2 ⇒ 72°
Thus, the value of angle α is 72° if the regular polygon is inscribed in a circle and rotation centered at a_1
Learn more about the regular polygon here:
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What is the square root of 25
Answers
Answer: 5
Step-by-step explanation:
5*5 is equal to 25
Answer:
5
Step-by-step explanation: The square root of 25 is 5 because 5x5=25 or [tex]5^{2}[/tex]=25
BIG IDLAS MATH
#19 i
Evaluate the expression. Write your answer in scientific notation.
(6 x 10-3) + 0.23 – (5 x 10-2) =
Answers
Answer:
Step-by-step explanation:
9.23
The function I = $19n represents the amount of income from ticket
sales for a single theater performance. The letter n represents the
number of tickets sold. The theater's maximum capacity is 400
people. What is a reasonable domain for this function?
Answers
The function I = 19n is a linear function
The reasonable domain of the function is [0,21]
How to determine the domain?The function is given as:
I = 19n
The smallest value of n is 0 i.e. the smallest number of ticket sold is 0
The maximum capacity is 400.
So, we have:
19n = 400
Divide both sides by 19
n = 21.05
Remove the decimals
n = 21
Hence, the reasonable domain of the function is [0,21]
Read more about domain at:
https://brainly.com/question/1770447
help me w this question please
Answers
Answer:
2560000 or 2.56*10^6
Step-by-step explanation:
[tex]\frac{((-4)^6)^2*(-5^2)^3}{(-4)^6*(-5)^2}[/tex]
[tex]\frac{(-4)^1^2*(-5^6)}{(-4)^6*(-5)^2}[/tex]
[tex]\frac{16777216*15625}{4096*25}[/tex]
[tex]\frac{262144000000}{102400}[/tex]
[tex]2560000[/tex]
Find the critical t-value that corresponds to % confidence. Assume degrees of freedom
Answers
Using a t-distribution, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.
How to find the critical value for a t-distribution confidence interval?It is found with the help of a calculator, having two inputs:
The confidence level.The number of degrees of freedom, which is one less than the sample size.Hence, using a calculator, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.
More can be learned about the t-distribution at https://brainly.com/question/16162795
John, Cindy, and Isaiah went to the store to buy school supplies. John bought 2 pens, 3 folders, and 4 notebooks for a total of $20. Cindy bought 5 folders and 5 notebooks for a total of $25. Isaiah bought 3 pens, 1 folder, and 2 notebooks for a total of $11
Answers
Using a system of equations, it is found that:
Each pen costs $0.6.Each folder costs $0.4.Each notebook costs $4.4.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: The cost of a pen.Variable y: The cost of a folder.Variable z: The cost of a notebookJohn bought 2 pens, 3 folders, and 4 notebooks for a total of $20, hence:
2x + 3y + 4z = 20.
Cindy bought 5 folders and 5 notebooks for a total of $25, hence:
5y + 5z = 25.
x + z = 5.
x = 5 - z.
Isaiah bought 3 pens, 1 folder, and 2 notebooks for a total of $11, hence:
3x + y + 2z = 11.
y = 11 - 3x - 2z
Replacing the second and the third equation on the first, we have that:
2x + 3y + 4z = 20.
2(5 - z) + 3(11 - 3x - 2z) + 4z = 20.
10 - 2z + 3[11 - 3(5 - z) - 2z] + 4z = 20.
2z + 3(11 - 15 + 3z - 2z) = 10
2z + 3(z - 4) = 10
5z = 22.
z = 4.4
x = 5 - z = 5 - 4.4 = 0.6
y = 11 - 3x - 2z = 11 - 3(0.6) - 2(4.4) = 0.4.
Hence:
Each pen costs $0.6.Each folder costs $0.4.Each notebook costs $4.4.More can be learned about a system of equations at https://brainly.com/question/24342899
If the probability of a basketball player making a shot is 5/12, what is the probability of him not making a shot
Answers
Answer:
5 percent of 12 is 0.6
Step-by-step explanation:
Answer:
7/12
Step-by-step explanation:
total = 12/12
p(shot) = 5/12
p(not making shot) = 7/12
because
12/12 - 5/12 = 7/12
Hope this helped!
The greenhouse pictured below can be modeled as a rectangular prism with a half-cylinder on top. The rectangular prism is 20 feet wide, 12 feet high, and 45 feet long. The half-cylinder has a diameter of 20 feet.
To the nearest cubic foot, what is the volume of the greenhouse?
Answers
The volume of the greenhouse made from a rectangular prism with a half-cylinder on top is 17869 ft³
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
The volume of the rectangular prism = length * width * height = 20 * 12 * 45 = 10800 ft³
The volume of the half cylinder = (1/2) * π * (diameter/2)² * height = 0.5 * π * (20/2)² * 45 = 7069 ft³
Volume of the greenhouse = 10800 ft³ + 7069 ft³ = 17869 ft³
The volume of the greenhouse made from a rectangular prism with a half-cylinder on top is 17869 ft³
Find out more on volume at: https://brainly.com/question/12410983
Look at the chart and complete the function rule.
y = 5x + ?
Answers
Answer:
Step-by-step explanation:
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
5
b
=
0
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
5
y-intercept:
0
Logarithms
Please do not answer with a link, not only can I not access it (nor would I be comfortable doing so) but the answer will be immediately deleted.
Answers
Answer:
[tex]\huge\boxed{\sf -2.280}[/tex]
Step-by-step explanation:
Finding value of log₃(4/49):
[tex]\displaystyle = log_{3}\frac{4}{49} \\\\= log_{3} (\frac{4}{7^2} )\\\\\underline{Using \ log \ rule \ :} \ log( \frac{a}{b} )= log \ a - log \ b \\\\= log_{3}4 - log_{3}7^2\\\\\underline{Using \ log \ rule \ : } \ log \ a ^m = m \ log \ a \\\\= log_{3}4 - 2(log_{3}7)\\\\[/tex]
Given that:
log₃4 ≈ 1.262, log₃7 ≈ 1.771
Put the values in the above expression
[tex]= 1.262-2(1.771)\\\\= 1.262 - 3.542\\\\= \bold{-2.280}\\\\\rule[225]{225}{2}[/tex]
Lodine-131 is a very useful radioactive isotope that is used to locate and treat cancerous tumors in the body and has a half life of 8 days. If a radiologist were to use 64 mg of this isotope, how much of it would still be left after 32 days?
Answers
Using an exponential function, it is found that 4 mg of the substance would still be left after 32 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, considering that the initial amount if of 64 mg, and we are working with half-lifes, the equation is given by:
[tex]A(t) = 64(0.5)^t[/tex]
32 days is 32/8 = 4 half-lifes, hence the amount remaining in mg is given by:
[tex]A(4) = 64(0.5)^4 = 4[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
(h+1)^2=16 solve using square root property
Answers
Answer: h = 3
Step-by-step explanation:
(h+1)² = 16
h+1 = √16
h+1 = 4
h = 3
Hope this helped :)
Answer:
[tex]h=3, \ h=-5[/tex]
Step-by-step explanation:
[tex](h+1)^2=16[/tex]
[tex](h+1)^2=16[/tex]
[tex]\sqrt{(h+1)^2} = \±\sqrt{16}[/tex] <== you take the square root of both sides
[tex](h+1) = \±\ 4[/tex] <== you take the square root of both sides
[tex](h+1) = +\ 4, \ (h+1) = -\ 4[/tex] <== separate into 2 equations and solve
[tex]h+1 = 4, \ h+1 = -\ 4\\\\. \ -1 -1, \ \ \ \ -1\ \ \ \ -1\\\\h=3, \ h=-5[/tex]
Hope this helps!
In a student union election of a school, 91% of boys and 84% of girls voted. It is kwon
Answers
Answer:
If there are 350 kids for example your answers would be:
Boys: 182
Girls: 168
Step-by-step explanation:
If you add those numbers together you'll get 350 again
Find the length of x in the 45 degree, -45 degree, -90 degree triangle. Show work
Answers
Answer:
Option A
Step-by-step explanation:
Given:
Angle=45°Base= 9hypotenuse = x[tex] \sf \therefore \: cos \: 45 \degree = \frac{base}{hypotenuse} = \frac{9}{x} [/tex]
[tex] \sf \cos(45 \degree) = \frac{1}{ \sqrt{2} } [/tex]
[tex] \sf \frac{1}{ \sqrt{2} } = \frac{9}{x} [/tex]
[tex] \therefore \: \rm \: x = 9 \sqrt{2} [/tex]
Bill drove 605 miles in 11 hours. At the same rate, how many miles would he drive in 5 hours?
Answers
Answer:
Step-by-step explanation:
605/11 = x/5
11x = 3025
x = 275 miles
Answer:
275 miles
Step-by-step explanation:
Bill drove 605 miles in 11 hours , so by the formula , Speed = Distance/ time
We can find that ,
Speed = 55 miles/hours
So , In 5 hours he will drive
Distance = Speed × Time
Distance = 55 × 11
Distance = 275 miles
Which equation can be used to find x, the length of the hypotenuse of the right triangle? a triangle has side lengths 63, 16, x. 16 63 = x 16 squared 63 = x (16 63) squared = x squared 16 squared 63 squared = x squared
Answers
The Pythagoras is the sum of the square of two sides equal to the square of the longest side. The equation is x² = 16² + 63² then the correct option is D.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
The dimensions of the triangle are 16, 63, and x.
Where x is the hypotenuse.
By the Pythagoras theorem, we have
x² = 16² + 63²
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
Answer:
D. 16 squared + 63 squared = x ^2 is the answer.
Step-by-step explanation:
Find the length of the wire
Answers
Answer:
Step-by-step explanation:
It could be 32m. Maybe, I'm not positive though.
Answer:
Hope you like the answer
Step-by-step explanation:
Mark me as Brilliant if you like the answer
hello, can someone answer this question, please show work
Answers
Answer:
It's 10(10+3)
Step-by-step explanation:
10x10 is 100 and 3x10 is 30 which gives you 100+30
Answer:
a) 10(10 + 3)
Step-by-step explanation:
Which expresison is equivalent to 100 + 30 (130)?
a) 10(10 + 3)
10(10) + 10(3)
100 + 30 <== equivalent
130
b) 10(10 + 2)
10(10) + 10(2)
100 + 20 <== NOT equivalent
120
c) 5(20 + 25)
5(20) + 5(25)
100 + 125 <== NOT equivalent
225
d) 10(10 + 4)
10(10) + 10(4)
100 + 40 <== NOT equivalent
140
Therefore, the correct answer is 10(10 + 3)
Hope this helps!
f(x)=-2(x-4)^2 for x=2 evaluate
Answers
What is the value of f(g(3))?
Answers
F(-1)=1+5/2
F(-1)= 6/2
F(-1)=3 or D
What percentage of take-home pay is spent on expenses? (round to nearest whole percent)
A) 67% B) 68% C) 84% D) 85%
Answers
c) 84%
hope this helps :)
85% of take-home pay is spent on expenses option (D)85% is correct.
It is given that in the chart there are various expenses.
It is required to find the percentage of take-home pay is spent on expenses.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We have a total take-home salary = $5388
Total expenses = $4558
In percentage it can be expressed as follows:
[tex]=\frac{4558}{5388}\times100[/tex]
[tex]=0.84595\times100\\\\= 84.595 \ \%[/tex]
or ≈ 85% (round to nearest whole)
Thus, 85% of take-home pay is spent on expenses.
Learn more about the percentage here:
https://brainly.com/question/8011401
Please help! WILL GIVE BRAINLIEST! George and Sarah were building a cone-shaped sand castle. After some time, the diameter of the sand shaped cone was 12 in. and the height was 14 in. What is the approximate volume of the sand cone rounded to the nearest hundreth? (Show your work. Remember you can draw a picture to help you solve the problem). Label your answers with the correct units.
Use 3.14 to approximate pi
Answer:
They kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. What is the approximate volume of the sand cone now? Label your answers with the correct units. (Show your work) Use 3.14 to approximate pi
Answers
Answer:
volume = 527.52 in³
volume increased by 30% = 685.776 in³
Step-by-step explanation:
Volume of a cone
[tex]V=\dfrac13\pi r^2h[/tex]
(where r is the radius and h is the height)
Given:
diameter = 12 in ⇒ radius = 6 inheight = 14 in[tex]\pi =3.14[/tex][tex]\implies V=\dfrac13 \cdot 3.14 \cdot 6^2 \cdot 14[/tex]
[tex]\implies V=527.52 \ \sf in^3[/tex]
---------------------------------------------------------------------------
If the volume increases by 30% then it will now be 130% of the original volume.
130% as a decimal = 130/100 = 1.3
Therefore, to find the new volume, multiply the original volume by 1.3.
[tex]\implies V=527.52 \cdot 1.3[/tex]
[tex]\implies V=685.776 \ \sf in^3[/tex]
What is x in this equation -3x+7 = 1
Answers
help me please‼️‼️ har har har har har
Answers
Answer: -63.5 feet per mintue
Step-by-step explanation:
We can look at what the problem is asking for, and solve. It says average change in altitude per minute:
[tex]\frac{altitude}{minute}[/tex] = [tex]\frac{1,524}{24}[/tex] = 63.5 feet per mintue
Since she is hiking down the mountainside, this will be negative. We arrive at our final answer of:
-63.5 feet per mintue
ASAP GIVING 5 STARS AND A LIKE AND BRAINLIEST 412 ÷ 10¹
Answers
Answer:
Your answer would be:
41.2
10¹ = 10
412 / 10 = 41.2
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Jack rides in a motorboat against a river current for 36 km. Then he returns to his starting point by floating down river on a raft. Tommy travels 9 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 15 km/h.
Answers
Answer:
3 km/h
Step-by-step explanation:
You want to know the speed of the river current if floating 36 km downstream takes 9 h longer than the trip upstream in a boat with a speed relative to the current of 15 km/h.
TimeThe relation between time, speed, and distance is ...
time = distance / speed
If c represents the speed of the current, then 15-c is the speed upstream. The relation between the travel times is ...
36/(15 -c) = 36/c -9
SolutionMultiplying by c(15-c), we have ...
36c = 36(15 -c) -9(c)(15-c) . . . . . . . multiply by c(15-c)
36c = 540 -36c -135c +9c² . . . . . eliminate parentheses
9c² -207c +540 = 0 . . . . . . . collect terms
c² -23c +60 = 0 . . . . . . . . divide by 9
(c -20)(c -3) = 0 . . . . values that make the factors zero are c=20, c=3
The speed of the current is 3 km/h.
__
Additional comment
The speed of the current cannot be greater than 15 km/h, or the boat could not go upstream. The speed of the current cannot be greater than 4 km/h, or the trip downstream would take less than 9 hours.
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