The solution to the system of equations is (2,0)
The equation is given as:
[tex]y = 0.5x - 1[/tex]
The other equation passes through the points (3,1) and (-5,-7).
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{-7 - 1}{-5 -3}[/tex]
[tex]m = \frac{-8}{-8}[/tex]
[tex]m =1[/tex]
The equation is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
So, we have:
[tex]y = 1(x -3) + 1[/tex]
[tex]y = x -3 + 1[/tex]
[tex]y = x -2[/tex]
Substitute x - 2 for y in [tex]y = 0.5x - 1[/tex]
[tex]x- 2 =0.5x - 1[/tex]
Collect like terms
[tex]x-0.5x= 2 - 1[/tex]
[tex]0.5x= 1[/tex]
Divide both sides by 0.5
[tex]x= 2[/tex]
Substitute 2 for x in [tex]y = 0.5x - 1[/tex]
So, we have:
[tex]y = 0.5\times 2 - 1[/tex]
[tex]y = 1 - 1[/tex]
[tex]y = 0[/tex]
So, we have:
[tex](x,y) =(2,0)[/tex]
Hence, the solution to the system of equations is (2,0)
Read more about systems of equations at:
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Can you plsssssssssssssssssssssssssssss help me with this.
Answer: (-1, 7) should be the answer
Step-by-step explanation:
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A system of equations is shown: 2x = â’y 6 â’4x 3y = 8 What is the solution to this system of equations? (â’1, â’4) (1, 4) (4, 1) (â’4, â’1).
The correct option is B. (1,4).
Given equations,
[tex]2x=-y+6....(1)\\-4x+3y=8....(2)[/tex]
We have to find the solution of the given system of equations.
Equation 2 can be written as,
[tex]-2\times(2x)+3y=8\\[/tex]
Now by substitution method, putting the value of [tex]2x[/tex] from Equation (1) in above equation, we get
[tex]-2\times(-y+6)+3y=8\\2y-12+3y=8\\5y-12=8\\5y=20\\y=4[/tex]
Now putting the value of y in equation 1 we get,
[tex]2x=-4+6\\2x=2\\x=1[/tex]
Hence the solution of the given system of equation will be (1,4).
For more details follow the link:
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What is the correct classification of the system of equations below?
14x + 2y= 10
y+ 7x=-5
A.
parallel
B.
coincident
C.
intersecting
Answer:
parallel
B.
coincident
C.
intersecting
Answer:
I think it's parallel, because they have the same gradient. parallel lines always have the same gradient
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample size of 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision
Required:
a. For a test with a level of significance of 0.10, compute the critical value; set up the appropriate hypotheses and the calculate the p-value of the test
b. Will the null hypothesis will be rejected with a level of significance of 0.10? Explain why or why not?
Using the z-distribution, we have that:
a)
The hypothesis test is:
[tex]H_0: \mu = 7.4[/tex][tex]H_1: \mu < 7.4[/tex]The p-value is of 0.0668.
The critical value is [tex]z^{\ast} = -1.28[/tex]
b) Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.
Item a:
At the null hypothesis, it is tested if the mean is of 7.4 minutes, that is:
[tex]H_0: \mu = 7.4[/tex]
At the alternative hypothesis, it is tested if the mean is lower than 7.4 minutes, that is:
[tex]H_1: \mu < 7.4[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 7.1, \mu = 7.4, \sigma = 1.2, n = 36[/tex].
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{7.1 - 7.4}{\frac{1.2}{\sqrt{36}}}[/tex]
[tex]z = -1.5[/tex]
Using a z-distribution calculator, the p-value is of 0.0668.
Also using a calculator, considering a left-tailed test, as we are testing if the mean is less than a value, the critical value with a significance level of 0.1 is of [tex]z^{\ast} = -1.28[/tex].
Item b:
Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.
You can learn more about the use of the z-distribution to test an hypothesis at https://brainly.com/question/16313918
There are 6 triangles and 4 circles. What is the
simplest ratio of circles to total shapes?
Answer:
4/10
Step-by-step explanation:
4:10
as there are 4 circles, and 10 total (6 + 4)
simplify by diving by 2.
therefore the answer is,
2:5
(I guess, this could be simplified further, but it wouldn't be a whole number).
A certain factory produces and sells C computers per month. It costs x dollars to produce a single computer, and the factory sells each computer for y dollars. Their monthly net profit is 10,000 dollars.
Write an equation that relates C, x and y.
Answer:
Cy-Cx=10,000 this is the best answer ever
Will mark Brainliest
In questions 6 – 9, state the solutions for the quadratic equation depicted in the graph.
You roll a six sided die. You are given $8 if a 6 comes up, $2 if a 3, 4, 5 comes up, and
nothing otherwise. Find the expected value of the entries.
Expected Value Table for rolling a six-sided die
We want to get the expected value for the given experiment. We will see that the expected value is $2.33
For an experiment with outcomes {x₁, ..., xₙ} each one with probability {p₁, ..., pₙ} the expected value is defined as:
EV = x₁*p₁ + ... + xₙ*pₙ
Here we have 3 outcomes:
x₁ = winning $8x₂ = winning $2x₃ = winning $0.For x₁ we need to roll a 6, this is a probability of 1 out of 6, then:
p₁ = 1/6
For x₂ we need to roll a 3, 4, or 5 (3 out of 6), then:
p₂ = 3/6
For x₃ we need to roll a 1 or a 2 (2 out of 6) so the probability is:
p₃ = 2/6
Then the expected value is:
EV = $8*(1/6) + $2*(3/6) + $0*(2/6) = $2.33
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1. Which of the following is not an undefined term in
Euclidean geometry?
a. plane
b. point
c. bisector
d. line
Answer:
c. bisector
Explanation:
"There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the 'three undefined terms of geometry'"
If point, line, and plane are all undefined terms in Euclidean geometry, then that only leaves one answer left, c. bisector.
56:32=k:28 what is k?
Therefore, k = 49.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
SOMEONE PLS GIVE ME THE ANSWER AND NO FREAKING LINKS.
Calculate the distance between the points M=(-1,-2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answer:
8.9443
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.9443
What is the measure of Zx?
Angles are not necessarily drawn to scale.
Answer:
This question is straightforward if you find different triangles in the figure itself.
Property of a triangle: All internal angles of a triangle must add up to 180°
Take a look at Triangle DBH.
Method A
Angle BHD = 180°-33°-46° (sum of angles in a triangle)
= 101°
Property of angles on a straight line: All angles on a straight line must add up to 180°
Angle x = 180°-101° (supplementary angles)
= 79°
Method B
Take a look at Triangle DBH.
Property of exterior angle (in this case, angle x): An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Angle x = 33°+46°
= 79°
Find x- and y-intercepts of 4x + 2y = 10
Answer:
Below is the graph
Hope This Helps!!!
Answer:
( 5/2 , 0 ) x- intercept , ( 0 , 5 ) y- intercept
Step-by-step explanation:
To find x- intercept , set y = 0
4x + 2(0) = 10
x = 5/2
To find y- intercept , set x = 0
4(0) + 2y = 10
y = 5
Please I really really do need help like now please and thank you
A package weighs P pounds P being a whole number. to ship this package by express costs one dollar and sixty five cents for the first five pounds and twelve cents for each additional pound. the total shipping cost is three dollars and forty five cents. how many pounds of the package weigh?
I give brainliest to first answer
please answer
when a whole number is rounded to the nearest ten the answer is 340
a write down the smallest possible value for the number
b write down the largest possible value for the number
Answer:
a) 335
b) 344
Step-by-step explanation:
The property of 12x2-7=6-2x2+2
if the two coffee shops combine their supplies, how many stirrers will they have for tousday?
Answer:
50?
Step-by-step explanation:
it's 50 20+25i don't even know if this is the correct answee
How many twelfths make one whole
How many twelfths make one whole
Answer:
12
Step-by-step explanation:
1/12x1/x
1x=12x1
x=12
Answer:
12 twelfths make a whole.
Step-by-step explanation:
when the numerator and the denominator of a fraction are the same, they always equal one. 12/12 would simply to one, just like 3/3 or 200/200.
I hope this helps
What is the number of solutions to the system of
equations?
Infinitely Many
Solutions
No Solution
One Solution
Two Solutions
Answer:
infinitely many solutions
Step-by-step explanation:
The lines over lap
Please help! I highly appreciate it! :D
[tex]\huge \bf༆ Answer ༄[/tex]
Total surface Area of the cuboid is ~
[tex] \sf2(lb + bh + lh)[/tex][tex] \sf2[(12 \times 4) + (4 \times 5) + (12 \times 5)][/tex][tex] \sf2[48 + 20 + 60][/tex][tex] \sf2(128)[/tex][tex] \sf256 \: \: ft {}^{2} [/tex]Surface area = 256 ft^2
Surface area (SA) = Total area on the Surface only
SA of cuboid = Area of rectangle (2 sides) + Area of square (2 sides) + Area of other rectangle (2 sides)
SA = 2(12x5) + 2(4x5) + 2(12x4)
SA = 120 + 40 + 96
SA = 256 ft^2
Help meeeeeeeeeeeeeeee
Answer:
D.
Step-by-step explanation:
Complementary angles are two angles whose measures add to 90°.
A.
m<CFD = 150° - 100° = 50°
m<EFD = 180° - 150° = 30°
Sum = 80°
No
B.
m<AFB = 40°
m<DFE = m<EFD = 30°
Sum = 70°
No
C.
m<AFC = 100°
Sum > 100°
No
D.
m<BFC = 100° - 40° = 60°
m<DFE = 30°
Sum = 90°
Yes
Answer: D.
in 3x + 2/3y - 15 < 0, the point (x,9) is a solution for the inequality shown. what is the possible value for x?
a: 2
b: 3
c: 4
d: 5
answer: 2
explanation:
if you plug in all of the numbers available for the equation and using 9 as a substitute for y, you'll see that it will either = 0 or be greater than 0
Logan and his sister, Tessa, are baking oatmeal raisin cookies. Logan uses 1.25-ounce scoops
of dough to form his cookies, and Tessa uses 1 12 -ounce scoops for hers.
Who is making bigger cookies?
Answer:
Logan is making bigger cookies
Step-by-step explanation:
1.25 > 1.12
How many beads would the jeweler need to make 10 bracelets?
Answer:
50 ?
Step-by-step explanation:
You didn't give any detail about how many beads it takes to make one bracelet
x=4y,2x+y=18 solve by substitution show all work
The diagram shows a square pizza box with side lengths of 12 inches. In the box is a circular pizza with a radius of 5 inches. What is the difference between the area of box and the pizza? Use π = 3.14 and round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
Box
Area of the box
Area = s^2
s = 12 inches
Area = 12^2
Area = 144
Pizza
Area = pi r^2
Area = 3.14 * 5^2
Area = 25 * 3.14
Area = 78.5
Difference = 144 - 78.5
Difference = 65.5
What is the hardest metal
if you get it right I'll give you brainliest
Answer:
is tungtset i tink not sure bout
Step-by-step explanation:
mark me brainlest plz
Easy math problem
……………………………………
Answer:
if its easy then answer it .-.
Step-by-step explanation:
Answer:
u =-3
Step-by-step explanation:
What is the simplified form of
3+2−14−24
−4
when x ≠ 4?