Select the correct answer.
What is the solution to this system of equations?
x-2y = 15
2x+4y=-18
OA. x = 1, y=-6
OB. X= 1, y=-7
ОС. Х 3, y= -6
OD. x= 3, y=-7
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Answers
Answer:
O C. x = 3, y = -6
Step-by-step explanation:
x - 2y = 152x + 4y = -18Take Equation 1 and equate to x.
x - 2y = 15x = 2y + 15Now, substitute in Equation 2.
2x + 4y = -182(2y + 15) + 4y = -184y + 30 + 4y = -188y = -48y = -6x = 15 + 2(-6)x = 3Option CAnswer:
C) x = 3, y = -6
Step-by-step explanation:
[tex]\textsf{Equation 1}:x-2y=15[/tex]
[tex]\textsf{Equation 2}:2x+4y=-18[/tex]
Rewrite Equation 1 to make x the subject:
[tex]\implies x=15+2y[/tex]
Substitute into Equation 2 and solve for y:
[tex]\implies 2(15+2y)+4y=-18[/tex]
[tex]\implies 30+4y+4y=-18[/tex]
[tex]\implies 8y=-48[/tex]
[tex]\implies y=-6[/tex]
Substitute found value of y into Equation 1 and solve for x:
[tex]\implies x-2(-6)=15[/tex]
[tex]\implies x+12=15[/tex]
[tex]\implies x=3[/tex]
Therefore, the solution to the system of equations is:
x = 3, y = -6
Related Questions
Two-hundred people are at a wedding. The dinner tables seat 10 people. How many tables are needed to seat all of the guests?
Answers
Answer:
20 tables
Step-by-step explanation:
200 guests, 10 guests per table. You need to divide 200 people into groups of ten. Therefore, you should form the equation 200/10. The answer would be 20.
Answer:
Required tables = [tex]200 \div 10 = \bf\: 20 \: tables[/tex]
A population of 12,000 fish has a growth rate of 4% each year. Write a model for the situation About how many years will it take for the population to
reach 20,000?
O A 12,000(1.047" = 20,000; 1.6 years
B. 12,000(1.04)" = 20,000: 13.02 years
C. 12,000 0.00 – 20.000; 12.77 years
D. 12,000.00 = 20,000: 5 29 years
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Answer:
B
Step-by-step explanation:
Trial and error into (ABOUT/APPROXIMATELY)
y=12000(1.04)^x
What is the percent of increase from 6 to 9?
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Answer:
50%.
Step-by-step explanation:
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Answer:33,056
Step-by-step explanation:i dont know jut put this answer
The marked price of a car is $49,500. A person can pay deposit of 30%
and interest at 12% per annum is charged on the outstanding balance.
The total amount payable is to be paid in 2 1/2 years. A) the amount of
each monthly installment b) The hire purchase of the car
Answers
The amount of each monthly installment is $1,294 and the hire purchase of the car is: $4,158.
Monthly installementa. Monthly installment
2 1/2 years=30 months
First step
Amount payable=[49,500×(1-.30)] /30 months
Amount payable=(49,500×.70)/30 months
Amount payable=$34,650/30 months
Amount payable=$1,155
Second step
Amount of monthly installment=[$1,155×(1+0.12)
Amount of monthly installment=$1,155×1.12
Amount of monthly installment=$1,293.6
Amount of monthly installment=$1,294 (Approximately)
b. Hire purchase
Hire purchase=$1,155×.12×30 months
Hire purchase=$4,158
Therefore the amount of each monthly installment is $1,294 and the hire purchase of the car is: $4,158.
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The depth of the water at the end of a pier changes periodically along with the movement of tides. on a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? let t = 0 be 12:00 a.m. d = negative 3.75 cosine (startfraction 4 pi over 31 endfraction t) 5 d = negative 3.75 cosine (startfraction 4 pi over 29 endfraction t) 5 d = negative 2.75 cosine (startfraction 4 pi over 31 endfraction t) 6 d = negative 2.75 cosine (startfraction 4 pi over 29 endfraction t) 6
Answers
In this exercise we have to calculate the value of the water depth, so we have: d=5.5Cos(12t)+6
What are periodic waves?
A periodic wave is a wave with a repeating continuous pattern that determines its wavelength and frequency
Putting together some information given in the statement we have:
The minimum depth of 3.25 m occurs at 12:00 am and at 3:30 pm.Therefore the period t=0 will be 12:00 am.The maximum depth of 8.75 m occurs at 7:45 am and at 11:15 pm.Knowing that the formula will be given by an equation similar to:
[tex]d=acos(bt)+k[/tex]
Where:
d = depth, mt = time, hoursa= amplitudeThe amplitude difference is given by:
[tex]8.75-3.25=5.5\ m[/tex]
The mean depth is:
[tex]k=\dfrac{(3.25+8.75)}{2}=6\ m[/tex]
Then writing the equation with;
[tex]d=acos(bt)+k\\\\d=5.5cos(12t)+6[/tex]
Hence the value of water depth will be d=5.5Cos(12t)+6
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Please help with my grade 11 math! Ill give the brainliest!
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Answer:
9.6^2=100^2+100^2-2(100)(100)
theta=cos^-1((9.6^2-100^2-100^2)/(-2(100)(100))
theta=5.5
Step-by-step explanation:
in a certain school of 200 students ,the students can study french,spanish,,both or neither . Just as many study both as study neither .One quarter of those who study spanish also study french.The total number who atudy french is 10 fewer than those who study spanish only .what percent of student study french only
Answers
Answer:
1900
Step-by-step explanation:
i took the est
2x + 5y = 20
6x - 5y = 12
Answers
Answer:
is this a question?
Step-by-step explanation:
First Solve 2x+5y=20 for x
Add -5y to each side
2x=5y-20
Divide both sides by 2
x= -5/2y +10
Next substitute -5/2y +10 for y in the equation 6x-5y=12
6(-5/2y+10) -5y=12
-20y+ 60= 12
Then simplify again by adding -60 to each side
-20y= -48
Then divide by -20 on each side
Y= 12/5 (or 2.4)
Now to find x substitute 12/5 for y in x= -5/2y+10
X= -5/2(12/5) +10
X= 4
So X=4 and Y= 12/5 or 2.4
Hope that helped
Round 3, 295.351 to the nearest tenth.
3, 295.35
3, 295.3
3, 300
0 3,295.4
Answers
Answer:
3,295.4
Step-by-step explanation:
to the nearest tenth is 3,295.4
1. Solve x2+ 3x – 4 = 0
2. Solve 2x2 – 4x – 3 = 0
3. Solve x(x – 2) = 4
4. Solve 9x2+ 12x + 4 = 0
5. Solve x
2+ 2x = 1
WILL GIVE BRAINLIEST
Answers
Answer:
The answer is given in the picture
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
what are the domain and range?
Answers
Answer:
sooo i think it would be
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edit:
it will also be
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i think since y ends at 64 (hightest height above the ground)
Step-by-step explanation:
umm because the graph goes forever? not really sure though since in my college the topics are a little different and they may not teach in yours
I'm stuck on these questions....
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Answer:
call 911
Step-by-step explanation:
they serve anyone
Which expression represents the volume of the composite figure? (2)(4.4)(5) (2)(4.4)(3.9) (2)(4.4)(5) – (2)(4.4)(3.9) one-half(2)(4.4)(5) – one-third (one-half)(2)(4.4)(3.9) one-half(2)(4.4)(5) one-third (one-half)(2)(4.4)(3.9)
Answers
The expression that represents the volume of the composite figure is (1/2)* (4.4)*(2)*(5) + (1/3)* (1/2)*(4.4)*(2)*(3.9)
What will be the volume of the composite figure?The volume of the composite figure will be the sum of the volume of the prism and the volume of the pyramid.
The Volume of the prism = Area of the base * height of the prism
Area of the base = 1/2*4.4 *2
Height of the prism =5
So, the Volume of the prism = (1/2)* (4.4)*(2)*(5)
The volume of the pyramid = 1/3 *(area of the base) * (height of the pyramid)
Area of the base of the pyramid = 1/2*4.4 *2
Height of the pyramid =3.9
So, the volume of the pyramid = (1/3)* (1/2)*(4.4)*(2)*(3.9)
So, total volume = (1/2)* (4.4)*(2)*(5) + (1/3)* (1/2)*(4.4)*(2)*(3.9)
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Answer:
D
It's D for those who want a fast answer!!
Step-by-step explanation:
factor the polynomial
1. w^2+9w+14
2. x^2-14x+45
Answers
Answer:
1. ( w + 7 ) ( w + 2 )
2. ( x - 9 ) ( x - 5 )
Step-by-step explanation:
1.
w² + 9w + 14
= w² + 7w + 2w + 14
= w ( w + 7 ) + 2 ( w + 7 )
= ( w + 7 ) ( w + 2 )
Hence, factorised.
2.
x² - 14x + 45
= x² - 5x - 9x + 45
= x ( x - 5 ) - 9 ( x - 5 )
= ( x - 9 ) ( x - 5 )
Hence, factorised.
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Answer:
I cannot answer this question because it is not complete. Please use complete sentences and questions.
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Note: Angle B = x + 15, Angle C = x + 5
Answers
Answer:
the value of x can be found as 10
Step-by-step explanation:
Pilar did not include the _____.
The mean is _____.
The median is _____.
ILL GIVE BRAINLIEST HELP
Answers
Answer:
Pilar did not include the 14.
The mean is 20.
The median is 15.5.
Step-by-step explanation:
The mean: [tex]\frac{12+15+15+16+18+44}{6} =20[/tex]
The median: 12, 15, 15, 16, 18, 44
The median is [tex]\frac{15+16}{2} =15.5[/tex]
Hope this helps
A bookstore sold the same number of books each day for 17 straight days. The store sold a total of 5,066 books. How many books did the bookstore sell each day? A) 288 books B) 298 books C) 5,049 books D) 5,083 books
Answers
Answer:
B) 298
Step-by-step explanation:
5,066 ÷ 17 = 298 books
A college professor wants to survey a sample of students taking his course. Here are some details about his course:
He teaches 5 sections of the course.
There are 250 total students across those sections.
There are 50 graduate students and 200 undergraduate students taking the course.
Each section has about 50 students (some graduate and some undergraduate).
The professor wants to take a sample of 30 students for a survey. He suspects that opinions on the survey may differ the most based on student type (graduate or undergraduate), so he wants to design his sample to take that into account. Which of these strategies will accomplish his intended design?
a. Randomly select 6 students from each section for the survey.
b. Randomly select 6 graduate students and 24 undergraduate students for the survey
c. For each section, randomly select one of the first 8 students to arrive to class, and every 8th student thereafter to take the survey.
d. Randomly select one of the sections and give the survey to every student in that section
Answers
Answer: B, Randomly select 6 graduate students and 24 undergrad students for the survey.
Step-by-step explanation: This guarantees that each type is proportionately represented in the survey.
Not A because it risks too many or too few graduate students. It is not C because again, it risks too many or too few graduate students. It is not D because each section has about 50 students and the professor only wants 30 in his sample.
Answer:
Step-by-step explanation:
B
Find the measure of the red arc or chord in ⊙C. The measure of arc XYZ is a °
Answers
The points on the red arc are points A and B
The measure of the red arc is 75 degrees
How to determine the measure of arc XYZ?From the complete question, we have:
Angle DCE = 75 degrees
By vertical angles theorem,
Angle ACB = Angle DCE = 75 degrees
So, we have:
Angle ACB = 75 degrees
The measure of the red arc is the same as the measure of the angle ACB.
So, we have:
Red arc = 75 degrees
Hence, the measure of the red arc is 75 degrees
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You rent 3 DVDs and 2 video games for $19. The following week, your friend rents 6 DVDs and 4 video games for $38. Which of the following statements apply?
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Answer:
It is "The video game rentals cost more than the DVD rentals"
Date:
Bell:
Unit 11: Volume & Surface Area
Homework 8: Volume of Pyramids &
** This is a 2-page document. **
Directions: Find the volume of each figure, Round to the nearest hundredth when necessi
1.
2. 3 km
22 cm
14 cm
8 km
14 cm
1/3 (314)
75. 3
3.
4.
-8 ft
5. 7 yd -
3,74
12 ft
23 ya
9 yd
Answers
The volume of any shape is the amount of space in it.
The volume of the cylinder is 1570 square units
How to determine the volume?The question is incomplete. Assume the following parameters
Shape = Cylinder
Radius, r = 10
Height, h = 5.
The volume of a cylinder is:
V = πr^2h
So, we have:
V = 3.14 * 10^2 * 5
Evaluate the product
V = 1570
Using the assumed values, the volume of the cylinder is 1570 square units
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63.6% to a fraction in simplest form
Answers
Answer:
159/250
Step-by-step explanation:
63.6% =
636/1000
divided by 2
318/500
divided by another 2
159/250
Answer:
159/250
Step-by-step explanation:
63.6% = 63.6÷100=.636
636/1000 divide each part by 2 (both are even numbers)
318/500 divide by 2 again (still even)
159/250 no more factors that are the same.
Solve sec (y + pi/2) = - 2 for 0 < y < pi radians.
Help needed!! anyone?
Answers
[tex]~~~~\sec\left(y+\dfrac{\pi}2 \right) = -2\\\\\\\implies \left[\cos \left( y+ \dfrac{\pi}2 \right) \right]^{-1} = -2\\\\\\\implies \left( \cos y \cos \dfrac{\pi}2 -\sin y \sin \dfrac{\pi}2 \right)^{-1} =-2\\\\\\\implies \left(0- \sin y \right)^{-1} =-2\\\\\\\implies \left(-\sin y \right)^{-1} = -2\\\\\\\implies \sin y = \dfrac 12\\\\\\\implies y = n\pi + (-1)^{n} \dfrac{\pi}6\\\\\text{In the interval, }~(0,\pi)\\\\\\y= \dfrac{\pi}6, ~\dfrac{5\pi}6[/tex]
What is the exact decimal equivalent of 7 half’s 12
Answers
The decimal equivalent of 7 half’s is the number in decimal form
The exact decimal equivalent of 7 half’s is 3.5
What is a decimal number?A decimal number is a number represented by an integer and a fractional part
How to determine the decimal equivalant?The number is given as:
7 halves
Express as product
7 * 1/2
Evaluate the product
3.5
Hence, the exact decimal equivalent of 7 half’s is 3.5
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Why is the interest rate one of the biggest factors when calculating the financial charges on credit cards?
Answers
Answer:
Interest rate is one of the biggest factors in calculating finance charges because the interest rate adds a percentage of money not already spent to pay towards the credit cards if not paid in full each month.ANSWER THIS TO GET 23 POINTS AND BRAINLIEST
Answers
Ohhh, interest problems. I haven't done an equation like this in a long time, but I will attempt.
I would say that the answer is the 2nd option. The equation is i = (5200)(0.06)(2.5).
The traditional interest formula is I = (P)(R)(N).
P = the original amount of money given
R = interest rate
N = the amount of time
I hope this answers your question (and that I understood the question correctly!).
-Toremi
Matilda and her family took a trip to Yellowstone National Park to see Old Faithful
erupt. Matilda was standing 125ft from the blast. The blast rose 100ft in the air.
What is the angle from Matilda to the top of the blast?
Answers
Using the slope concept, it is found that the angle from Matilda to the top of the blast was of 38.66º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, the vertical change is of 100 ft, while the horizontal change is of 125 ft, hence:
[tex]\tan{\alpha} = \frac{100}{125}[/tex]
[tex]\alpha = \arctan{\left(\frac{100}{125}\right)}[/tex]
[tex]\alpha = 38.66^\circ[/tex]
The angle from Matilda to the top of the blast was of 38.66º.
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Square A′B′C′D′ is a dilation of square ABCD.
What is the scale factor?
Enter your answer in the box.
Note: Images may not be drawn to scale
Answers
6/2 = 3/1
So 3:1
Meaning the left one is 3 times the size of right one.
OR
2/6 = 1/3
So 1:3
Meaning right one is 1/3 the size of left one