Solve the system of equations.
x + 3y = −1
2x + 2y = 6 (1 point)
(−4, 1)
(2, −1)
(4, −1)
(5, −2)
Answers
the solution to the system of equation is (5, -T
System of equationx + 3y = −1 2x + 2y = 6From equation 1;
x = -1 - 3y
Substitute x = -1-3y into equation 2
x + y = 3
-1-3y + y = 3
-1 -2y = 3
-2y = 4
y = -2
Since x + y = 3
x = 3 + 2
x = 5
Hence the solution to the system of equation is (5, -2)
Related Questions
If the discriminant of a quadratic equation is 4, which statement describes the roots?
-2 complex roots
-2 real roots
-1 real root
-1 complex root
PLEASE HELP
Answers
An equation can have 2 real roots if the discriminant is 4.
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
Answer:
Statement which describes the roots is:
2 real roots
Step-by-step explanation:
If the discriminant D of a quadratic equation follows:
D=0 then there are 2 equal real roots or 1 real root
D>0 then there are 2 unequal real roots
and if D<0 then there are 2 complex roots
Here, we are given the discriminant of a quadratic equation is 4
i.e. D=4 >0
So, it means quadratic equation has 2 real roots
Hence, statement which describes the roots is:
2 real roots
Hence, statement which describes the roots is:
2 real roots
2 cups (into mL of water
Answers
Answer:
about 473 mL
Step-by-step explanation:
For liquid measure, there are 16 cups in a US gallon, which is exactly 231 cubic inches. Each cubic inch is exactly 2.54³ = 16.387064 cubic centimeters--the same number of mL.
So, the exact conversion from cups to mL is ...
1 cup = (231/16)(16.387064) mL = 236.5882365 mL
Multiplying this by 2 gives ...
2 cups = 473.176473 mL
For many purposes, the nearest mL is sufficiently accurate:
2 cups ≈ 473 mL
Please (look at the pionts) I really need help if you help me I will help you if I can. 3. The three salespeople for a local advertising firm are Lola, Ahmed, and Tommy. Lola sold $2030 in ads, Ahmed sold $1540, and Tommy sold $1800. (a) What fraction of the total sales did each salesperson sell? (b) A $100 bonus was awarded to the three salespeople, which they had to share. It was awarded so that each salesperson received the same fraction of $100 as he or she sold of the total sales. How much did each person receive? Round to the nearest whole cent.
Answers
total sales=2030+1540+1800=5370
lola sold 2030/5370 or 37.8026% of the sales
ahmet sold 1540/5370 or 28.6778% of the sales
tommy sold 1800/5370 or 33.5196% of the sales
B.
nice, they are in percent which is parts out fo 100
lola gets $37.8026 or rounded $37.80
ahmet gets $28.6778 or rounded $28.68
tommy gets $33.5196 or rounded $33.52
Marie uses 2.3 oz of nuts for each bag of trail mix she makes. She uses 27.6 oz of nuts in all. How many bags of trail mix does Marie make?
Answers
The total amount is given as 27.6 oz, so you have 27.6=2.3x.
set equation [tex]27.6=2.3x[/tex]
simplify by dividing both sides by 2.3 [tex]\frac{27.6}{2.3}=\frac{2.3x}{2.3}[/tex]
solution: [tex]x=\frac{27.6}{2.3}=12[/tex]
A ship sails due west from a harbor for 28 nautical miles. It then sails S68°W for another 17 nautical miles. How far is the ship from the harbor? (Round your answer to two decimal places.)
Answers
The ship is approximately 26.16 nautical miles from the harbor after following the described path.
To find the distance of the ship from the harbor after sailing due west for 28 nautical miles and then S68°W for another 17 nautical miles, we can use trigonometry to calculate the resultant displacement.
Let's break down the two legs of the journey:
1. Due west for 28 nautical miles is a straight line.
2. Sailing S68°W for 17 nautical miles forms an angle of 68° with the west direction.
Using trigonometry, we can find the horizontal and vertical components of the second leg:
Horizontal component = 17 * cos(68°)
Vertical component = 17 * sin(68°)
The total horizontal displacement from both legs is:
Horizontal displacement = 28 - (17 * cos(68°))
The total vertical displacement from both legs is:
Vertical displacement = 17 * sin(68°)
To find the distance from the harbor, we use the Pythagorean theorem:
Distance = √(Horizontal displacement² + Vertical displacement²)
Calculating:
Horizontal component = 17 * cos(68°) ≈ 6.93 nautical miles
Vertical component = 17 * sin(68°) ≈ 15.52 nautical miles
Horizontal displacement = 28 - (17 * cos(68°)) ≈ 21.07 nautical miles
Vertical displacement = 17 * sin(68°) ≈ 15.52 nautical miles
Distance = √(21.07² + 15.52²) ≈ √(443.9749 + 240.5504) ≈ √684.5253 ≈ 26.16 nautical miles
Therefore, the ship is approximately 26.16 nautical miles from the harbor after following the described path.
Why is it important to start saving for retirement decades before retirement age?
Answers
It is important to start saving for retirement decades before retirement age because of compound interest. When you start saving at a younger age, you have more time for your money to compound. In other words, you can start with a smaller amount of money and after 30 years of compounding, it can grow to a larger amount.
Compounding is the formula 1 + r to the n which means interest compounds into more interest over time.
In a ____ the denominator is one unit
Answers
Simple question! Thank you for the help so far! :D
Answers
Answer:
○ [tex]\displaystyle y ≤ -7[/tex]
Step-by-step explanation:
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
I am joyous to assist you anytime.
Santa has lots of mixed up socks in his sack! If he has 6 green socks, 4 gold socks, 8 black socks and 2 red socks, what is the minimum he needs to pull out of his sack to get a matching pair?
Answers
which fraction is not equivalent to 7/8
a 21/24 b 35/40 c 15/16 d 28/32
Answers
21/24 = 21 divided by 24 = 0.875
35/30 = 35 divided by 40 = 0.875
15/16 = 15 divided by 16 = *0.9375*
28/32 = 28 divided by 32 = 0.875
Answer=15/16 is not equivalent to 7/8.
Final answer:
Option c, 15/16, is the correct answer because it cannot be simplified to 7/8, making it not equivalent to 7/8, while the other options are equivalent after simplification.
Explanation:
The question asks us to identify which fraction is not equivalent to 7/8. To determine this, we need to compare each option with 7/8:
Option a: 21/24 can be simplified by dividing the numerator and the denominator by 3, which gives us 7/8, so this option is equivalent.Option b: 35/40 can be simplified by dividing the numerator and the denominator by 5, which gives us 7/8, so this option is equivalent as well.Option c: 15/16 cannot be simplified to 7/8 because when we divide both by their greatest common divisor, we do not get 7/8. Therefore, this fraction is not equivalent to 7/8.Option d: 28/32 can be simplified by dividing the numerator and the denominator by 4, which gives us 7/8, so this option is equivalent.Hence, the correct answer is option c, which is not equivalent to 7/8.
The math test has 10 multiple choice questions, each with 4 answers. If Betty guesses correctly on the first 2 questions, what is the probability that she will guess correctly on the third question?
Answers
Answer: The probability that she will guess correctly on the third question [tex]=\frac{1}{4}[/tex]
Step-by-step explanation:
Given: The math test has 10 multiple choice questions, each with 4 answers.
To find probability that she will guess correctly on the third question, we need to just look at only one question which has 4 options and one of them is the right answer, thus probability of choosing the right answer from 4 option is the fraction of 1 over 4.
The probability that she will guess correctly on the third question
[tex]=\frac{\text{answer of a question}}{\text{total options of a question}}[/tex]
[tex]=\frac{1}{4}[/tex]
△ABC△ABC is similar to △XYZ△XYZ. Also, side ABside AB measures 6 cm, side BCside BC measures 18 cm, and side XYside XY measures 12 cm.
What is the measure of side YZside YZ ?
Answers
Answer:
36
Step-by-step explanation:
Estimate the fraction equal to 19%
Answers
[tex]\displaystyle\\ 19\% = \boxed{\frac{19}{100} } = \boxed{0.19}[/tex]
find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.
Answers
A regular hexahedron is actually a cube.
Diagonal of a cube D is a hypotenuse of a right triangle which other two legs are face diagonal (f) and length of a side (a):
D² = f² + a²
Face diagonal is a hypotenuse of a right triangle which sides are a and a:
f² = a² + a² =2a²
D² = f² + a²
f² = 2a²
D² = 2a² + a² = 3a²
D = √3a² = √3 * √a² = √3 * a = a√3
Volume of a cube with side a is: V = a³
D = a√3
⇒ a = D/√3
V = a³ = (D/√3)³
We have:
D = 8√2 in
[tex]V= (\frac{D}{ \sqrt{3} } )^{3} =( \frac{8 \sqrt{2} }{ \sqrt{3} } )^{3}=( \frac{8 \sqrt{2} * \sqrt{3} }{ \sqrt{3}* \sqrt{3}} )^{3} =( \frac{8 \sqrt{2*3} }{ \sqrt{3*3}} )^{3} =( \frac{8 \sqrt{6} }{ \sqrt{3^{2} }} )^{3} =( \frac{8 \sqrt{6} }{ 3} )^{3} = \\ \\ = \frac{ 8^{3} *( \sqrt{6} )^{3}}{3^{3}} = \frac{512* \sqrt{6 ^{2} }* \sqrt{6} }{27} = \frac{512*6* \sqrt{6} }{27} = 114sqrt{6} [/tex]
Final answer:
To find the volume of a regular hexahedron with a face diagonal of 8√2 inches, we first calculate the side length of the cube and then use it to determine the volume, resulting in a volume of 512 cubic inches.
Explanation:
The question asks to find the volume of a regular hexahedron (which is a cube), given the diagonal of one of its faces is 8√2 inches. Since we know the face of a hexahedron is a square, we can use the Pythagorean theorem to find the side of the square. The diagonal (d) of a square relates to its side (s) by the formula d = s√2. Therefore, we can solve for s: s = d / √2 = (8√2) / √2 = 8 inches. Now that we have the length of the side of the cube, we can compute the volume (V) using the formula V = s3. Substituting s = 8 inches, we calculate the volume as V = 83 = 512 cubic inches.
What decimal is equivalent to each fraction?
1/6
help plez
Answers
Convert the slope of -0.6 to a fraction in simplest form
Answers
What is "Centroid of a triangle" and why is it important?
Answers
There are 440 students, ratio of male to female students is 6 to 5. Find how many male and female students in a class
Answers
6: 66
5: 55
Males: 6 times 40 = 240 of them
Females: 5 times 40 = 200
What does -2 (3-y) equal to?!!
Answers
*Need Help??!!
The graph shows the number of each kind of CD in Dante's collection. What is the probability that a randomly chosen CD will be country?
A.) 15%
B.) 20%
C.) 25%
D.) 30%
Photo of the graph is attached.
Answers
The probability of getting a country CD out of all the CDs is the number of country CDs divided by the total number of CDs in Dante's Collection.
The total number of CDs in Dante's collection is [tex]6+12+8+4+10=40[/tex].
The total number of country CDs is 12.
So our required probability is [tex]\frac{12}{40}= \frac{3}{10}[/tex].
In percentage this is 3 divided by 10, and then multiply by 100. We get 30%. Answer choice D is correct.
ANSWER: D
Answer: D.) 30%
Step-by-step explanation:
From the given pie chart, we have the number of country CD = 12
The total number of CD's=[tex]12+8+4+6+10=40[/tex]
Now, the probability that a randomly chosen CD will be country is given by :-
[tex]\text{P(country)}=\dfrac{\text{Number of country CD}}{\text{Total CDs}}\\\\=\dfrac{12}{40}=\dfrac{3}{10}=0.3[/tex]
In percent, [tex]0.3\times100=30\%[/tex]
Hence, the probability that a randomly chosen CD will be country is 30%.
Jeffrey is planning to tile his bathroom. He is taking measurements before he goes to the hardware store to buy the tile. What is the best unit of measure for Jeffrey to use?
A.cubic feet
B.yards
C.square feet
D.square yards
Answers
Answer:
(C) Square feet
Step-by-step explanation:
In order to take the measurements, he should use the square feet unit of measure.
As, the cubic feet also known as unit of volume can be defined as the volume of the cube with sides of one foot in length. Since, the bathroom is two dimensional therefore, cubic feet can't be used.
Yards are basically a unit of length use to measure length and perimeter and square yards are used in measuring the long space and the bathroom is bit too small for it.
Therefore, square feet should be used to measure.
A car travels 180 miles north in 3 hours. What is the average velocity? Show your work and include units. Average velocity = distance/time. Know this equation for the test and how to calculate average velocity.
Answers
I hope I helped! :D
The change in position or displacement of an object in the time interval is known as average velocity of the object. The value of the average velocity is 60 miles per hour.
Given-
A car travels 180 miles north in 3 hours.
Average velocity- The change in position or displacement of an object in the time interval is known as average velocity of the object. It can be positive or negative depending upon the sign of the displacement.
[tex]\overline v=\dfrac{\Delta v}{\Delta t}[/tex]
Here [tex]\Delta v[/tex] is the change in displacement and [tex]\Delta t[/tex] is the change in time.
Use this formula to find the average velocity in the given formula we have to put the values velocity and time given in the question. Therefore,
[tex]\overline v=\dfrac{180}{3}[/tex]
[tex]\overline v=60[/tex]
Hence, the value of the average velocity is 60 miles per hour.
For more about the average velocity follow the link below-
https://brainly.com/question/862972
If ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?
A) yes, by AA similarity criterion
B) yes, by SAS similarity criterion
C) yes, by SSA similarity criterion
D) no, not possible to tell.
Answers
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Answer:
Option A is correct.
Yes, by AA similarity criterion
Step-by-step explanation:
AA(Angle-Angle) Similarity Criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In ΔBAC and ΔCED
[tex]\angle BAC = \angle CED = 17^{\circ}[/tex] [Angle] [Given]
[tex]\angle C = \angle C[/tex] [Angle] [Common angle]
Therefore, by AA similarity criterion;
[tex]\triangle BAC \sim \triangle CED[/tex]
Therefore, ΔBAC and ΔCED are similar by AA similarity criterion.
The girls group rented 2 canoes and 3 inner tubes for a total cost of $80. The boys group rented 1 canoe and 7 inner tubes for a total cost of $95. What is the cost to rent 1 canoe?
A. $18
B. $15
C. $25
D. $10
<33 please help
...?
Answers
For the girls,
2c + 3t = 80
For the boys,
c + 7t = 95
Solving the system of equations, multiply the second equation by 2 and subtract them.
2c + 3t = 80
2c + 14t = 190
---------------
11t = 110
t = 10
Substitute t to either equations,
c = 95 - 7t
c = 95 - 7(10)
c = 25
Therefore, one canoe costs $25 (C.)
The cost to rent 1 canoe from the rent made by the group of the girls and boys is $25.
What are word problems?Word problems are a mathematical interpretation by using variables, numbers, and arithmetic operations to solve real-life problems.
From the given information:
The group of girls: 2c + 3t = 80 --- (1)The group of boys: 1c + 7t = 95 ---- (2)Now, we can have a system of equations, and we can solve for the number of canoes and the inner tubes rented.
Using Elimination method:
2c + 3t = 80 --- × (1)
c + 7t = 95 --- × (2)
2c + 3t = 80
-2c + 14t = 190
0 + -11t = -110
-11t = -110
t = -110/-11
t = 10
From equation (1)
2c + 3t = 80
2c + 3(10) = 80
2c + 30 = 80
2c = 80 - 30
2c = 50
c = 50/2
c = 25
Therefore, we can conclude that the cost of the rent of 1 canoe is $25.
Learn more about word problems here:
https://brainly.com/question/21405634
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to which subset of the real numbers does the number 1.68 belong?
a. rational numbers
b. natural numbers, whole numbers, integers, rational numbers
c. rational numbers, irrational numbers
d. none of the above ...?
Answers
The number "1.68" is: natural numbers, whole numbers, integers, rational numbers.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
a.rational number
Step-by-step explanation:
We are given that a real number 1.68
We have to find that given number belongs to which set
We know that
N={1,2,3...}
Whole numbers set ={0,1,2...}
Integers=Z={...-3,-2,-1,0,1,2,,,}
Rational number :That number which can be written in the form of [tex]\frac{p}{q}[/tex] where q is not equal to zero ,p and q are belongs to integers.
Irrational number: That number which is not rational is called irrational number.
Hence, given number 1.68 belongs to rational numbers set.
Answer : a.rational number
For what value of c is the function defined below continuous on (-\infty,\infty)?
f(x) =
{x2−c2,X < 4 ; cx+20,x≥4.
Answers
It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
A function, f, is continuous at x = 4 if
[tex]\lim_{x \rightarrow 4} \ f(x) = f(4)[/tex]
In notation we write respectively
[tex]\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)[/tex]
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just 4c + 20.
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
[tex]\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2[/tex]
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c²
[tex]c^2+4c+4=0 \\(c+2)^2=0 \\c=-2[/tex]
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers [tex](-\infty, +\infty)[/tex]
The area of a rectangle is 70 square inches and the length of the rectangle is 3 inches longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
3w = 70
w(w+3)=70w(w+3)=70
w + 3 = 70
w + 3w = 70
Answers
Use the Law of Detachment to draw a logical conclusion from the two given statements. If not possible, choose not possible. If you drive safely, then you can avoid accidents. Teddy drives safely.
Teddy avoids accidents. If Teddy avoids accidents, he must drive safely. (my ans)
If Teddy does not drive safely, he does not avoid accidents.
not possible
Answers
Premise 2: Teddy drives safely
Conclusion: Teddy avoids accidents
Answer:
Teddy avoids accidents.
Step-by-step explanation:
Change 5000 meters to kilometers.
a.0.5 kmb)5 kmc)50 kmd)500 km
Answers
Convert:
5000 m * (1 km / 1000 m) = 5 km (ANSWER)
option b) 5 km
1 km = 1000 m
Divide the number of meters by 1000:
5000 m / 1000
= 5 km
So, 5000 meters is equal to 5 kilometers.
The correct answer is 5 km.
A company receives $198, of which $13 is for sales tax. The journal entry to record the sale would include a
A : debit to Sales Revenue for $198.
B : credit to Sales Taxes Payable for $13.
C : debit to Cash for $180.
D : debit to Sales Tax Expense for $13.
Answers
Among the choice the answer to
The journal entry to record the sale would include a debit to Sales Revenue for $198.
The answer is A.