The solution of the given system of equations is x =1 and y = -1.
What is a system of equations?In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Given is a system of equations; 4x+2y=2 and y=-3x+2
Solving the equation by substitution, we get,
4x+2(-3x+2) = 2
4x-6x-4 = 2
-2x+4 = 2
-2x = -2
x = 1
Put x = 1 in any of the given equation,
y = -3*1+2
y = -3+2
y = -1
Hence, The solution of the given system of equations is x =1 and y = -1.
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−1,51.27,−1,0,12,57,7677,√2,√8,5
Given the following question:
[tex]-1,5,\frac{1}{2},\frac{5}{7},0,\sqrt[]{2},\sqrt[]{8},-1.27,\frac{76}{77}[/tex]Natural numbers are positive integers.
5 is a natural number
Whole numbers are integers, neither fraction or decimals just integers.
5, and 0 are whole numbers
Integers are a set of numbers that can be expressed without being a fraction/decimal.
-1, 5, and 0 are integers.
Rational numbers are a set of numbers that can be written as fractions.
-1, 5, 1/2, 5/7, 0, 76/77, 1.27 are all rational numbers they can all be expressed as a fraction.
(zero is also rational)
Irrational numbers cannot be expressed as a fraction
√2, √8,
Real numbers are numbers that include rational and irrational numbers.
-1, 5, 1/2, 5/7, 0, 76/77, -1.27, √2, √8
what 82 x 82 x 82 x 82
Answer:45212176
Step-by-step explanation:calculator
Answer:
82x82x82x82, or 82 squared to the 4th power, is 45212176.
Math
T.28 Write an equation for a parallel or perpendicular line 5SH
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Line q has an equation of y = -x+ 2. Line r includes the point (9, -3) and is parallel to
line q. What is the equation of line r?
Skill plans
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = - x + 6===========================
GivenLine q with equation of y = - x + 2,Line r with the point (9, - 3) and parallel to line q.To find Equation of line r.SolutionWe know parallel lines have equal slopes, so line r has the slope of - 1.
Line r is:
y = - x + b, where b- the y-interceptSubstitute the coordinates of the point into this equation and find the value of b:
- 3 = - 9 + bb = - 3 + 9b = 6The equation of line r is:
y = - x + 6Determine whether the given numbers represent the lengths of sides of a right triangle.15,11,4Do the given numbers represent the lengths of the sides of a right triangle?No or Yes
Answer:
No
Explanation:
To determine if the lengths form the side of a right triangle, use the Pythagorean Theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ Where\; c\text{ is the hypotenuse, the longest side} \end{gathered}[/tex]Substitute 15,11 and 4 into the formula:
[tex]\begin{gathered} 15^2=225 \\ 11^2+4^2=121+16=137 \\ \text{Therefore:} \\ 15^2\ne11^2+4^2 \end{gathered}[/tex]Since the Pythagorean Theorem does not hold, the side lengths(15,11,4) do not represent the lengths of the sides of a right triangle.
How far can a family travelin 4 days if they travel 620 milesin two days? (at the same rateof speed)
Let x be the number of miles the family travel in 4 days
620 miles = 2 days
x = 4 days
cross-multiply
2x = 2480
Divide both-side of the equation by 2
x = 1240 miles
• 100%XIsabel is thinking of two numbers. Their greatest common factor is 14. Their least common multiple is 168. One of the numbers is 56.What is the other number?O A. 84Ο Ο ΟOB. 42C. 28O D. 8O E. 7
GCF = 14
LCM = 168
let x and y be the numbers
if X = 56
The other number (y) can be obtained using the formula:
=> (GCF x LCM) / X
=> (14 X 168)/ 56
=> 2352/56
=>42
Option B is correct
5.2=
5.2=
\,\,620(0.5)^{\frac{x}{10}}
620(0.5)
10
x
Answer:
D
Step-by-step explanation:
Need help with homework
we have the expression
[tex]10-4+2(4)^2[/tex]step 1
squared 4 before multiplying
[tex]\begin{gathered} 10-4+2(16) \\ 10-4+32 \end{gathered}[/tex]therefore
step 1 is incorrect
Justine's work is incorrect
the answer is option N 1Which function has the greatest y-intercept?
f(x)
h(x)
g(x)
Answer:
h(x)
Step-by-step explanation:
y-intercept is shorthand for ' y - axis intercept'
the graph which intercepts the y-axis the highest is h(x)
3. Which expressions are equivalent to the given one?
Select each that apply.
20/-4
a. 20 x
b. 20 x-1
c. 5
d. -5
Answer:
b, d
Step-by-step explanation:
20/-4 = -5
20 x (-1/4) = -5
can yall help me with this
In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.There are three main categories of fractions in mathematics. 'Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, the wrong step will be:
(4/7) ÷ (-1/2)Then, the next step should be:
(4/7) × (-2/1)But, the steps it is given as:
(4/7) × (-2/-1)Which makes the error.
Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
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22 more than a number divided by 4
Answer:
X / 4 + 22
Step-by-step explanation:
22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.
helpp me fast thank u pleasee
The value of x from the given equations is 0.6.
The given equations are y=4x and y=-x+3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, 4x=-x+3
⇒ 4x+x=3
⇒ 5x=3
⇒ x=3/5
⇒ x=0.6
Hence, the value of x from the given equations is 0.6.
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A car can travel 100 km on five liters of gas. How many liters will be needed to travel 40 km?
Answer:
2
Step-by-step explanation:
40 x 5 ÷ 100
2 x 5 ÷ 5 = 2
your textbook authors suggest that if your population has fewer than 100 people you should group of answer choices use a stratified sampling method. use simple random selection. find a larger population test everyone in the population.
The proper sampling technique used when the number of samples is less than 100 is saturated sampling where the entire population will be the research sample.
What is saturated sampling ?
According to Arikunto if the population is less than 100 people so the researcher need to take all the samples namely saturated sampling.
What is stratified sampling ?
Stratified sampling is a sampling technique which used when we do a research on a heterogenous population. How to use this technique is to divide the population into several stratum and then take random samples from each stratum an then all the samples that have been taken are collected into one sample.
In conclusion, if the population has fewer than 100 people , the expert suggested to use saturated sampling.
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If four people equally share a 1/2 page to 3/4page.what fraction of the page in the photograph
Step-by-step explanation:
fraction of page of photograph is 3/32
(1/2÷4)*3/4
1/2*1/4*3/4
1/8*3/4
=3/32
Hi please help me in this onei don't know how to solve itfind the value of x
EXPLANATION
If the measure of ∠2= x+78 and the other ∠=40 degrees, by definition we know that sum of interior angles of a triangle is equal to 180 degrees.
Furthermore, we have two congruent legs, so this is an Isosceles triangle with two congruent angles (with the same measure).
Thus,
180 = 40 + 2* m∠2
Substituting m∠2 by the equation as follows:
180 = 40 + 2(x + 78)
Subtracting -40 to both sides:
180 - 40 = 2(x+78)
Simplifying:
140 = 2(x+78)
Dividing both sides by 2:
140/2 = x + 78
Simplifying:
70 = x + 78
Subtracting -78 to both sides:
70 - 78 = x
Simplifying:
-8 = x
Switching:
x = -8
Answer: The value of x is -8.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
Given the definitions of f(x) and g(x) below, find the value of (gof)(3).
f(x) = 2x² - x - 15
g(x) = -5x +9
Answer:
[tex] \huge{ \boxed{gof(3) = 9}}[/tex]
Step-by-step explanation:
In order to find gof(3), we first have to find gof(x). To find gof(x) substitute the f(x) into g(x). That is, for every x found in g(x) substitute it by f(x).
From the question
[tex]f(x) = 2 {x}^{2} - x - 15 \\ g(x) = - 5x + 9 \\ \\ gof(x) = - 5(2 {x}^{2} - x - 15) + 9 \\ gof(x) = - {10x}^{2} + 5x + 75 + 9 \\ \\ gof(x) = - {10x}^{2} + 5x + 84[/tex]
To find gof(3), substitute the value of x that is 3 into gof(x). For every x found in gof(x), replace it by 3 and solve.
[tex]gof(3) = - 10( {3})^{2} + 5(3) + 84 \\ \quad \: \: \: \: \: = - 10(9) + 15 + 84 \\ \: \: \: = - 90 + 15 + 84 \\ = 9[/tex]
We have the final answer as
gof(3) = 9Three friends go grocery shopping together, and each buys the same kind of oranges. LaMar buys 2 pounds (lb) and pays $7.00. Enrico buys 5 pounds and pays $17.50. Anna buys 3 pounds and pays $10.50. Identify the graph and unit price that represent the orange costs.
The unit price of the oranges bought by the three friends is $3.50 per pound.
Lamar bought 2 pounds for $7 , unit price = 7 / 2 = $ 3.5 per pound
Enrico bought 5 pounds for $17.50 , unit price = 17.50 / 5 = $ 3.5 per pound
Anna bought 3 pounds for $10.50 , unit price = 10.5/ 2 = $3.5 per pound
Hence we can see that the unit price rate for the oranges is $3.50 .
The average price of a product is calculated by dividing the total sales income by the number of units sold. Managers must supply "similar" units when a single product is given in many variations, such as different bottle sizes.
By weighting different unit selling prices higher by unit sales mix (%) for each single variant, the determination of average pricing is made practicable. We obtain pricing per statistical unit when we employ a standard rather than a genuine range of sizes and product types.
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Rita started playing a video game at 9:10 A.M. It took her 1 hour and 45 minutes to beat the first level and 1 hour and 25 minutes to beat the second level. Rita played the final level for 1 hour and 10 minutes and finished the game. What time was it when Rita stopped playing the game?
Answer: it would be about 1:30pm
Step-by-step explanation:
17. a = -3: Yes/No?
4a + 3 = -9
can anyone help???????
Answer:
The sum of the angles is 180°.
We already know that one angle is 90°, and the other one is 38.
so: 180-(90+38)=52°
the exterior angle+52°= 180° (beacuse the form a flat angle)
so x=180-52
so: x=128°.
Answer:
128°
Step-by-step explanation:
We know that,
the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.
Accordingly,
38 + 90 = x
128° = x
What is the formula for the sequence
1, 6, 12, 19, 27 ?
Answer: the formula is 5,6,7,8,9,10 every step plus one
Step-by-step explanation:
1+5 =6
6+6=12
12+7=19
19+8=27
27+9=36
It takes 5 workers 12 hours to unload one truck. How long would it take 6 workers to unload the truck?
Which points define the solution set of this linear-quadratic system of equations?
A. point A and point B
B. point D and point F
C. point C and point E
D. point B and point D
Answer:
C. C and E
Step-by-step explanation:
The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.
C and E are the solutions to this system.
Use the table below to answer question 9.
x -3 0 1 3
f(x) 12 0 0 6
g(x) 39 3 7 39
h(x) -14 1 -2 -20
2*f(3)-3*g(1)+h(3)=
answer:
-29
step-by-step explanation:
you need a graphing calculator.
so, let's start by setting up a table (for my sake because that text is confusing)
x f(x) g(x) h(x)
-3 12 39 -14
0 0 3 1
1 0 7 -2
3 6 39 -20
okay, that's out of the way. now, your equation is 2 * f(3) - 3 * g(1) + h(3).
for f(3), we look at the chart to see which f(x) value matches x=3.
f(3) = 6
same with g(1) and h(3)
g(1) = 7
h(3) = -20
now, replacing the functions(x) with their numbers is the next step.
2 * 6 - 3 *7 + (-20)
(2*6) - (3*7) - 20
(12) - (21) - 20 = -29
For which inequality is x= 5 a solutionx < 2x > 9x < 18x > 42
Let's check each inequality if the value x = 5 is part of the solution:
a. x < 2
5 is a value greater than 2, so it isn't part of the solution of this inequation.
b. x > 9
5 is lesser than 9, so it isn't part of the solution of this inequation.
c. x < 18
5 is lesser than
Addison drove 162 miles in 8 hours. What was her speed in miles per hour?
[tex]\fbox{20.25}[/tex]
To find her miles per hour, we need to divide the total miles by the total hours to find how many miles she drives in each hour.
[tex]162\div8[/tex]
[tex]=20.25[/tex]
Mr Kennedy raised beef cattle. The stock tank near the windmill has a diameter of 3 meters. When it is full, the water is 1.5 meters deep. How many cubic meters of water are in the stock tank when it is full use 3.14 for pi.A 7.1 B 10.6 C 42.4 D 14.1
Answer: B 10.6
Explanation:
We would assume that the stock tank is cylindrical. We would calculate the volume by applying the formula,
Volume = πr^h
where
π = 3.14
r is the radius of the cylinder
h is the height of the cylinder
From the information given,
diameter = 3
radius = diameter/2 = 3/2
r = 1.5
h = 1.5
Volume = 3.14 x 1.5^2 x 1.5 = 10.5975 cubic meters
By rounding to the nearest tenth,
Volume = 10.6 cubic meters