Answers
Answer:
(2, -7)
x = 2
y = -7
Step-by-step explanation:
Let's solve this system of equations by elimination.
Start by multiplying the first equation by 2:
[tex]2(4x)+2(3y)=2(-13)\\8x+6y=-26[/tex]
Next, multiply the second equation by 3:
[tex]3(-5x)+3(2y)=3(-24)\\-15x+6y=-72[/tex]
Notice that both equations now have a "6y", meaning we can subtract both equations and thereby eliminating the variable "y" from the equation:
[tex]8x+6y-(-15x+6y)=-26-(-72)\\8x+6y+15x-6y=-26+72\\23x=46[/tex]
Divide both sides by 23
[tex]x=2[/tex]
Substitute 2 for "x" to solve for "y".
[tex]4x+3y=-13\\4(2)+3y=-13\\8+3y=-13[/tex]
Subtract 8 from both sides:
[tex]3y=-21[/tex]
Divide both sides by 3:
[tex]y=-7[/tex]
Therefore the answer is:
[tex](x, y)=(2, -7)[/tex]
Additional Comments:
Note that we can only divide, subtract, multiply, or add both sides of the equation by the same quantity due to the Division, Subtraction, Multiplication, or Addition Property of Equality. These properties state that if you divide/subtract/multiply/add one side of the equation by one quantity, you must do the same to the other side of the equation so that it remains an equation.
Related Questions
Exponential growth/decay problem 2
Answers
Answer:
a) decay
b) 2,950,000
c) 0.025
d) [tex]f(x)=2950000(0.975)^x[/tex]
e) 2,409,123
Step-by-step explanation:
Part (a)
Exponential DECAY, since the population was decreasing annually.
Part (b)
Initial amount = 2,950,000 people (in the year 2000)
Part (c)
Decay factor = 2.5% = 0.025 (in decimal form)
Part (d)
General form of exponential decay function:
[tex]f(x)=a(1-r)^x[/tex]
where:
a = initial amountr = rate of decay (in decimal form)x = time (in years)Given:
a = 2950000r = 0.025[tex]\implies f(x)=2950000(1-0.025)^x[/tex]
[tex]\implies f(x)=2950000(0.975)^x[/tex]
Part (e)
To determine the city's population in 2008:
[tex]x = 2008 - 2000 = 8[/tex]
[tex]\begin{aligned}\implies f(8) & =2950000(0.975)^8\\ & = 2409123\: \sf(nearest\:whole\:number)\end{aligned}[/tex]
Julia made 7 batches of cookies and ate 3 cookies. There were 74 cookies left. Which expression can be used to determine the average number of cookies per batch?
A=74/4
B=(74+7)/3
C=(74+3)/7
D=74/3*7
Answers
Answer:
C
Step-by-step explanation:
She ate 3, so originally 77 cookies. Divide that by 7 batches, which is the equivalent to C
A newly formed life insurance company has underwritten term policies on 120 women between the ages of forty and forty-four. Suppose that each woman has a 1/150 probability of dying during the next calendar year, and that each death requires the company to pay out $50,000 in benefits. Approximate the probability that the company will have to pay at least $150,000 in benefits next year
Answers
The probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
The probability of dying:
P(dying) = 1/150
P(living) = 1 - P(dying) = 1 - 1/150 = 140/150
There are 120 women.
P(x≥3) = 1 - [P(x=0) +P(x=1) + P(x=2)]
[tex]\rm P(x\geq 3)=1-[(120 \ choose \ 0)(1/150)^0)((149/150)^{120})+[/tex]
[tex]\rm (120 \ choose \ 1) ((1/150)^1) ((149/150)^{119}) +[/tex]
[tex]\rm (120 \ choose \ 2)((1/150)^2)((149/150)^{118})][/tex]
P(x≥3) = 0.047
Thus, the probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.
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The group wants to travel from its current location on the map to the South Pole, and then directly back to the base camp. How many miles will they have to travel? Explain your answer.
Answers
Using the Pythagorean Theorem, it is found that the group will have to travel 90 miles.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In this problem:
First, the group travels 5 x 5 = 25 miles to the south pole.Then, the distance to the camp is the hypotenuse of a right triangle with sides of 25 miles and of 12 x 5 = 60 miles, hence:[tex]d^2 = 25^2 + 60^2[/tex]
[tex]d = \sqrt{25^2 + 60^2}[/tex]
d = 65.
The total distance is given by:
Td = 25 + 65 = 90 miles.
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Somebody please help
Answers
Answer:
IM FROM THE FUTURE :3
Step-by-step explanation:
the answer is -6 8-
i think 3:
Solve for x.
3x² -10 = -5
Answers
Answer:
first one is the correct answer
x=15/3 it has to be the 15/3 math isn’t my strong suit but my bf says 15/3
Which relationships describe angles 1 and 2?
Select each correct answer.
vertical angles
adjacent angles
complementary angles
supplementary angles
2
Answers
Answer:
They are adjacent and supplementary
Step-by-step explanation:
Dilation is enlarging or shrinking a figure by using a scale factor.
Using a scale factor bigger than one, creates a
figure.
Using a scale factor between 0 and
creates a
figure.
Create your own
dilation examples or find 2 images of dilation examples. Be
sure the two examples are different by showing one getting larger and one
getting smaller.
Answers
Answer:
Step-by-step explanation:
scale factor bigger than one, in math greater than, the figure is larger than the object being used a figure smaller than 1 creates a figure smaller than the original
Luckily you can just use your web browser to scale a screen up or down in it's scale. try it.. top right ellipse for go ogle chrome lets you scale over 100 per cent or 1 and also under 100 per cent or less than 1 remember 100 per cent = 1.00
Can someone help me please!!?
Answers
Answer:
AB = 21
Step-by-step explanation:
the line EB is parallel to the side of the triangle DC and intersects the other 2 sides proportionally , that is
[tex]\frac{AE}{ED}[/tex] = [tex]\frac{AB}{BC}[/tex] ( substitute values )
[tex]\frac{14}{12}[/tex] = [tex]\frac{AB}{18}[/tex] ( cross- multiply )
12 AB = 14 × 18 = 252 ( divide both sides by 12 )
AB = 21
342.5 divided by 34.25
Answers
342.5/34.25=10
both calculated to 0 decimal places
John, Britteny, Chloe, Kenji, Warner, and Juliette are in a race and are all considered equally fast what is the probability that John and Britteny would be the first two finishers
Detailed explanations are most welcome
Answers
Answer:
1/3
Step-by-step explanation:
There are 6 people partaking in this race.If John and Brittney are to be the first two finishers, then 2 out of the 6 people are the said first two finishers.That gives 2/6.By reducing the fraction, we have:(2÷2)/(6÷2) = 1/3.Hope this helps!
What's the answer to this question? 4*(5t+1)/5
Answers
Answer:
[tex]\boxed{\sf{4t+\dfrac{4}{5} }}[/tex]Step-by-step explanation:
In order to solve this, you must use the distributive property.
[tex]\sf{\dfrac{4\left(5t+1\right)}{5}}[/tex]
Distributive property:
⇒ A(B+C)=AB+AC
⇒ 4(5t+1)
Multiply by expand.
4*5t=20t
4*1=4
Rewrite the problem down.
20t+4
20t+4/5
[tex]\text{FRACTION RULES: }\\\\\\\Longrightarrow: \sf{\dfrac{A\pm \:B}{C}=\dfrac{A}{C}\pm \dfrac{A}{C}}[/tex]
[tex]\Longrightarrow: \sf{\dfrac{20t+4}{5}=\dfrac{20t}{5}+\dfrac{4}{5}}[/tex]
You have to divide the numbers from left to right.
⇒ 20/5=4
[tex]\Longrightarrow: \boxed{\sf{4t+\dfrac{4}{5} }}[/tex]
Therefore, the correct answer is 4t+4/5.Answer:
[tex]4t + \frac{4}{5}[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]\frac{4(5t + 1)}{5}[/tex]
[tex]\frac{(4 * 5t) + (4 * 1)}{5}[/tex]
[tex]\frac{20t + 4}{5}[/tex]
Step 2: Isolate the numerator into two fractions
[tex]\frac{20t +4}{5}[/tex]
[tex]\frac{20t}{5} + \frac{4}{5}[/tex]
[tex]4t + \frac{4}{5}[/tex]
Answer: [tex]4t + \frac{4}{5}[/tex]
HELpppppppppPPPPPPPPPPPPPPPpppppPPPPPPPP
Answers
Answer:
(a) mintutes, seconds
(b) Randomly pick 55 students to run a lap around the track and measure their times
Step-by-step explanation:
(a) When measuring distance like running you measure it in minutes and seconds
(b) When finding the average of a population you have to pick randomly and to get the best results you time them youself
Randomly pick 55 students to run a lap around the track and measure their times.
Sonja is spinning a spinner with 15 equal sectors labeled 1 through 15.
What is P(multiple of 6)?
2/15
4/15
2/5
3/5
Answers
Answer:
2/15
Step-by-step explanation:
there are only 2 numbers which are multiples of 6, which are both 6 and 12. That means it would be a 2/15 probability. You cannot simplify it more, so it will remain the same.
Answer:
2/15
Step-by-step explanation:
:)
Maëlys veut installer une étagère à 60 cm du sol.
Pour vérifier que son installation est bien horizontale,
elle installe une corde à 30 cm au-dessus de l'étagère et
la tend jusqu'au sol afin d'être alignée avec le bord de
l'étagère. Elle arrive à 1,20 m du mur. La distance entre le
point d'attache et l'extrémité de l'étagère est de 50 cm.
l'installation de Maëlys est-elle bien horizontale ?
Answers
How would you solve this?
Answers
Answer:
the answer of the perimeter is B
Professor Mallory determines the distribution of students on five variables in her target population. She then uses nonprobability sampling to select students who fill the pre-established proportions of people in each combination of variables. Which sampling strategy did she use
Answers
The sampling strategy she use was a quota.
Quotas are meant to establish boundaries on the number of specific goods that are allowed to be lawfully imported into the country throughout a distinct period of time. In that, quotas are similar embargoes, except quotas don´t have explicit political purposes as embargoes do.
A Fixed quota would be a maximum amount not to be surpassed, while a tariff rate surcharge allows it, but with a higher duty.
Melissa will paint a jewelry box that is in the shape of a cube. The surface area of the cube can be determined using the formula A = 682 wheres represents the side length the cube Determine the surface area of the box that Melissa will paint to the nearest tenth of a square inch if x = 2.
Answers
The surface area of the box that Melissa will paint is 24 square units
Surface are of a cubeA cube is a solid figure with 6 faces. The formula for calculating the surface area of the cube is expressed as:
A = 6L^2
where
L is the side length of the cube
Given
L = 2units
Substitute
A = 6(2)^2
A = 6 * 4
A = 24 square units
Hence the surface area of the box that Melissa will paint is 24 square units
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In a survey of 800 people, 42% said they shopped online last week. How many people said they shopped online last week?
Answers
336
explanation:
percent. part
_______ = _____
100. whole
42. ?
____ = ____
100. 800
cross multiply
800×42=33,600
then divide by 100
33,600/100=336
Answer:
336
Step-by-step explanation:
If 42% said they shopped online last week, that means the number of people who said they shopped online last week is 42% of 800. "Of" just means we should multiply, and since 42% = 42/100 (since % is just /100), we can use the following to find the answer (I used cross multiplication to simplify):
42 800 42 8
--- * = ---- * = 336
100 1
One limitation of the Chi Square test (and all tests of hypothesis) is that they cannot tell us if relationships between variables are:_________ A. significant B. random C. by chance D. none of the above
Answers
The answer to the limitation of the Chi Square test (and all tests of hypothesis) about relationships between variables is none of the above.
What is the limitation of the chi square test?The Limitation of this type of test is in its sample size requirements, as there is a lot of difficulty of interpretation when samples are large.
Note that Chi Square test and all tests of hypothesis can tell us if relationships between variables are significant, random and also if it occurred by chance and as such they are no limitations here.
Therefore, option d is correct.
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give the answer
the areaaaaaa
Answers
Answer:
16
Step-by-step explanation:
The figure shown is a trapezoid
Area of a trapezoid = 1/2(bottom base length + top base length) × height
Bottom base length = 7 units
Top base length = 1 unit
Height = 4 units
So area = 1/2 ( 7 + 1 ) × 4
==> add 7 and 1
Area = 1/2 (8) × 4
==> multiply 1/2 and 8
Area = 4 × 4
==> multiply 4 and 4
Area = 16
How many times larger is the 5 in 528, 394 as in 352, 107?
A. 5 times as large as
B. 10 times as large as
C. 50 times as large as
D. 100 times as large as
E. 500 times as large as
Answers
Answer: B 10 Times large
Step-by-step explanation:The first 5 is 500,000 And the second 5 is 50,000
500,000÷ 50,000= 10
Four lines meet at a point. The sun of three of the angles at the point is 267. The size of the other angle is
Answers
Answer: 93
Step-by-step explanation:
How many arrangements are there of the letters in the word "greet?"
Answers
Answer: 60
5 / 2
= 5×4×3×2×1/2×1
=120 / 2
= 60.
I hoped this helped! :)
Refer to the article "The Future of Money" in your Money, Money, Money magazine for a complete version of this text.
What is the overall structure of the "Pros and Cons of Cryptocurrency" section of "The Future of Money"?
It contrasts positive aspects of cryptocurrency with negative aspects of cryptocurrency.
It uses comparison to show differences between digital currency and traditional currency.
It explains how advances in computer and phone technologies created a need for cryptocurrency.
It uses reasons and evidence to support opinions about the future of cryptocurrency
Answers
The general structure of this section of the text is to describe both positive and negative aspects of cryptocurrency.
What is "The Future of Money about"?This is a text that describes the recent evolution of money into more modern forms as well as possible ways money might evolve.
What is the section "Pros and Cons of Cryptocurrency" about?This section focuses on the pros (advantages) and cons (disadvantages) of cryptoccurency. Due to this, the section follows a contrasting structure to show negative and positive aspects.
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Answer:
It contrasts positive aspects of cryptocurrency with negative aspects of cryptocurrency.
Step-by-step explanation:
i hope this help anyone that see this :D
Find the volume of the figure. Round answer to nearest hundredths place.
Answers
Answer: 540 nearest hundred is 500
Step-by-step explanation:
I multiplyed them together to get the answer.
Answer:
4834.9
Step-by-step explanation:
1) Split the Figure into a Cone and a Cylinder
2) Cylinder Formula V=πr²h And Cone V=1/3hπr²
3) π[tex]9^{2}[/tex]15 + 1/2(12)π([tex]9^{2}[/tex])
4) 3817.04+1017.88
5) 4834.9
What is the slope of the line?
Answers
Answer:
[tex]-\frac{2}{3} x[/tex]
Step-by-step explanation:
Hey there!
To find slope, you take [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case
y2: 6
y1: 4
x2: -3
x1: 0
Now we plug in this information
[tex]\frac{6-4}{-3-0} \\\\\frac{2}{-3} \\\\-\frac{2}{3}[/tex]
Since this is the slope, you have to add a "x"
So, the slope is [tex]-\frac{2}{3} x[/tex]
The ratio of the measures if the sides of a triangle is 4:6:8, and its perimeter is 126 feet. What are the measures of the sides of the triangles
Answers
Answer:
56 feet.
Step-by-step explanation:
4k+6k+8k=18k=126⟹k=7
Therefore, the lengths are 4⋅7=28, 6⋅7=42 and 8⋅7=56 feet.
Simply the expression.
4 (2m -6) - 3p - 2m + 8
Answers
Let's solve the equation.
4 (2m -6) - 3p - 2m + 8
= 8m - 24 - 3p - 2m + 8 (We simplified 4 (2m -6))
= 6m - 16 - 3p (We added the 8 to the 24)
= 6m - 3p - 16 (We organized the variables together so it matches an answer.)
The answer is A!
Answer: hii
The answer; 6m - 3p -16Step-by-step explanation:
How to solve your problem:
4 (2m -6) - 3p - 2m + 8
Simplify.
Distribute.
4 (2m -6) - 3p - 2m + 8
8m - 24 - 3p - 2m + 8
Add the numbers:
8m - 24 - 3p - 2m + 8
8m - 16 - 3p - 2m
Combine like terms:
8m - 16 - 3p - 2m
6m - 16 - 3p
Rearrange terms:
6m - 16 - 3p
6m - 3p - 16
Solution:
6m - 3p -16
Hopefully this helps you ~
- Matthew
Two trains leave a station going in opposite directions. The northbound train averages 87 miles per hour. The southbound train averages 113 miles per hour. How long will it take for the trains to be 600 miles apart?
Answers
Answer:
It takes 3 hours for the train to be 600 Miles apart