This is called system of equations because you are searching a pair of numbers that inserted as x and y verify both equations at the same time.
To solve a system of equation you have to use one equation to express one variable as a function of the other, and substitute the result in the second equation.
In your case you have
y = x - 2
So your y variable will be always equal to x - 2 , even in the second equation. Then we can write
x - 2 = 4x + 1
Here I replaced the "value" of y in the second equation.
Now you have an equation in one variable that you can solve as usual
x - 2 = 4x + 1
4x - x = - 2 - 1
3x = -3
x = -1
With a value for x you can substitute in one of the two equations and obtain y. Because both equations has to be valid at the same time, both equations must give you the same number for y. Let's try:
y = x - 2
y = - 1 - 2
y = -3
and, with the second equation
y = 4x + 1
y = 4 ( - 1 ) + 1
y = - 4 + 1
y = -3
It works! Then our solution is given by x = -1 and y = -3.
To graph this, simply plot these coordinates.
Dalia buys a winter jacket at a used clothing store that costs $30. She lives in Idaho, where the sales tax is 6%. How much does Dalia pay in total?
Serena is taking 4 friends on a trip with her to Louisiana for spring break. They take two cars to the airport where Serena pays $7.00 per car to park. Serena is charged a total of $2114.00 for tickets and parking. She pays the same price for each plane ticket. Using an equation to help you solve, what was the price of each person’s ticket?
Answer:
$420
Step-by-step explanation:
number of people = 5 (4 friends + serena)
number of cars = 2
cost of parking = 7 for each car = 7 * number of cars = 7 * 2 = 14
let t be the cost of each ticket
cost of tickets = t for each person = t * 5
total cost = cost of parking + cost of tickets
= 14 + t * 5
= 2114
2114 = 14 + 5t
subtract 14 from both sides to isolate the variable and its coefficient
2100 = 5t
divide both sides by 5 to isolate t
t = 2100/5 = 420
What is 1 + 1 im dying from sleep deprivation and I lost the grand math challenge bc of this bro help me pls you smart ppl
Answer:
1
Step-by-step explanation:
say you don't have a dog.. your parents get you one dog, and then get you another, you now have 2 :)
Convert 20341 base 5 into decimal system (also verify )
[tex](20341)_5\\\\=(2 \times 5^4 + 0 \times 5^3 + 3 \times 5^2 +4 \times 5^1 +1\times 5^0)_{10}\\\\=(2 \times 625+0+3 \times 25 +20 +1)_{10}\\\\=(1250+75+21)_{10}\\\\=(1346)_{10}[/tex]
Need this asap! What is the denominator of the next term in the geometric sequence?
Answer:
162
Step-by-step explanation:
the pattern in the denominators is ' multiply by 3 '
that is
2 × 3 = 6
6 × 3 = 18
18 × 3 = 54
then the next denominator is
54 × 3 = 162
Answer:
162
Step-by-step explanation:
The multiplication number will be 3.
2x3=6
6x3=18
18x3=54
54x3=162. and so on.
Just make sure to multiply your next answer by 3.
please help i’m struggling
Answer:
5
Step-by-step explanation:
Perimeter is all the sides of a shape added together, and theres 4 sides of a triangle. 20/4=5
Simplify the expression
Answer:
-1
Step-by-step explanation:
Use the Pythagorean Identity:
1 + tan^2(x)= sec^2(x)
Rearrange it. Substitute. Simplify.See image. It's been done two ways on the image. You don't need both. But they both use the process above. See image.
3x8 to the second power
Answer:
the answer is 192 , hope it helps
Which inequality represents all values of x for which the quotient below is defined? Square root 7x2 divide by square root 3x
Inequalities help us to compare two unequal expressions. The correct option is D.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given expression can be solved as,
[tex]\dfrac{\sqrt{7x^2}}{\sqrt{3x}}\\\\= \dfrac{\sqrt{7}x}{\sqrt{3x}}\\\\= \sqrt{\dfrac{7x}{3}}[/tex]
Since the value of (7x/3) is needed to be positive, therefore, the inequality that represents all the values of x for the quotient is defined as x>1.
Hence, the correct option is D.
The complete question is mentioned in the below question.
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Answer: x>0
Step-by-step explanation:
Which of the following is equal to the rational expression when x≠1 or -1 5(x-1)/(x+2)(x-1)
The solution to the given expression will be [tex]\dfrac{-15}{x+2}[/tex]
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The solution will be:-
[tex]= \dfrac{-15(x-1)}{(x+2)(x-1)}[/tex]
[tex]=\dfrac{-15}{x+2}[/tex]
Therefore the solution to the given expression will be [tex]\dfrac{-15}{x+2}[/tex]
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A survey of students in the junior class at Avery's high school provided the following information:
Percentage of students who think there is too much homework
85%
Average number of hours per week spent on homework this year
8 hours
Average number of hours per week spent on homework last year
5 hours
Average number of students with afterschool jobs this year
215 students
Average number of students with afterschool jobs last year
135 students
In three to five complete sentences, write a statement that Avery can present to the school principal explaining why 85 percent of the students in the junior class think there is too much homework.
Avery can explain to her school principal that 85% of juniors think there is a lot of homework because several indicators have increased.
What is an indicator?An indicator is a datum that is taken as a reference to analyze the evolution or change of a fact over time. In this case, the indicators would be:
Weekly hours used to do homeworkNumber of students with work for after school.According to the information, it can be inferred that 85% of Junior students consider that there is an increase in homework because there were the following changes compared to last year:
Increase in hours spent on after school homework, last year the average was 5 hours, this year it is 8 hours.Increase in the number of students with after school jobs, last year it was 135 students, this year it is 215 students.From the foregoing, it can be inferred that the number of homework has increased in Junior students and that is why now 85% of them consider that homework has increased.
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Does anybody know this? ABCD is a parallelogram BDC=110. Find the following values,
Answer:
see explanation
Step-by-step explanation:
in a parallelogram]
• opposite sides are congruent
• opposite angles are congruent
• consecutive angles are supplementary , sum to 180°
• diagonals bisect each other
Then
DC = AB = 15
BC = 2 × WC = 2 × 9 = 18
∠ BAC = ∠ BDC = 110°
∠ DCA = 180° - 110° = 70°
DC = 15 (opposite sides in a parallelogram is parallel and equal to each other)
BC = 18 (the diagonals in a parallogram bisect at their midpoints -> BW = WC = 9 -> BC = 9 + 9 = 18)
angle BAC = 110 (opposite angles are equal to each other)
angle DCA = 70 (consecutive angles add up to 180, angle BAC and angle DCA are consecutive -> 180 - 110 = 70)
The integral in this exercise converges. Evaluate the integral without using a table 0e^0d0
The value of 0e^0d0 is -1 if the integral in this exercise converges after applying limit.
What is convergent of a series?A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We are assuming the:
[tex]=\int\limits^0_{-\infty} {\theta e^{\theta}} \, d\theta[/tex]
Applying limit;
[tex]=\lim_{n \to \infty} \int\limits^0_{-n} {\theta e^{\theta}} \, d\theta[/tex]
After solving the integral:
[tex]=\lim_{n \to \infty} (e^{\theta})|^0_-_p[/tex]
= -(1-0)
= -1
Thus, the value of 0e^0d0 is -1 if the integral in this exercise converges after applying limit.
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96 Eight small bricks have the same mass as three large bricks The mass of one small brick is 1.5kg. What is the mass of one large brick?
Answer:
4 kg
Step-by-step explanation:
Since the mass of one small brick is 1.5 kg, the mass of 8 small bricks is 1.5 × 8, or 12 kg. Since 12 kg is the total mass of 3 large bricks, it follows that each large brick will have a mass of 12 ÷ 3, or 4 kg.
What power of ten do we need to multiply 3.15576 by in order to find an expression equivalent to 31,557,600
Answer:
3.15576 * 10 to the power of 7 will get you 31557600.
Choose the letter of the equation for
the graph.
a. y = sin x + 2
b.y = cos x + 2
c. y = cos(x - 1)
d. y = sin(x - 1)
e. y = sin(x + "/2)
Using translation concepts, it is found that the equation represented on the graph is of:
d. [tex]y = \sin{(x - \pi)}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have a trigonometric function, with amplitude of 1, hence there was no vertical translation, which removes options a and b.
The function is of zero at the origin, 1 at [tex]\frac{\pi}{2}[/tex] and -1 at [tex]\frac{\pi}{2}[/tex]. The sine function is of 0 at [tex]-\pi[/tex], of -1 at [tex]-\frac{\pi}{2}[/tex] and of 1 at [tex]-\frac{3\pi}{2}[/tex], hence option d is correct.
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Using the diagram, determine which statements are true. Select all that apply. m∠1 = 50° m∠3 = (2x + x + 25)° m∠2 = (x + 25)° m∠1 + m∠2 + m∠3 = 180° 50 + 2x+ x + 25 = 180
Answer:
All of them are true except for the second one.
Step-by-step explanation:
Answers A, C, D, E
i need help can someone help meeee
Answer:
1. 6.25 cm 2. 6 cm
3. 6.5 cm 4. 8.8 cm
Step-by-step explanation:
As area = length x width
so, width = area / length ----------(1)
by applying (1) on every part
1. 31.25 / 5
= 6.25 cm
2. 55.5 / 9.25
= 6 cm
3. 48.75 / 7.5
= 6.5 cm
4. 44 / 5
= 8.8 cm
What is the period of the function graphed below?
Answer:
2
Step-by-step explanation:
The period is the distance between two peaks
please help!!(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧will mark brainliest!!!
Step-by-step explanation:
so,
1/12 × $100
5/12 × $20
6/12 × $1
so the expected "payout" is
100/12 + 100/12 + 6/12 = 206/12 = 103/6 ≈ $17.17
minus the $2 entrance fee, the expected value is
17.17 - 2 = $15.17
but of course, there will be 6 losing $1 (while the other 6 will go home with a positive result).
Solve 8 = 2x + 4
Ox=-4
OX= -1
Ox = 0
O x = 7
The equivalent value of x from the equation is x = 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.
Given data ,
Let the equation be represented as A
Now , the value of A is
8 = 2x + 4
On simplifying the equation , we gt
Subtracting 4 on both sides , we get
2x = 8 - 4
2x = 4
Divide by 2 on both sides , we get
x = 2
Therefore , the value of x is 2
Hence , the equation is solved and x = 2
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Harper leans a 24-foot ladder against a wall so that it forms an angle of 69
∘
∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary
The horizontal distance between the base of the ladder and the wall is 67.0 feet.
What is distance?distance is the length between two points.
To calculate the horizontal distance between the ladder and the wall, we use the formula below.
Formula:
cos∅ = adjacent(y)/hypotenous(h)Make y the subject of the equation
h = y/cos∅........ Equation 2Where:
∅ = Angle between the wall and the laddery = horizontal distance between the base of the ladder and the wallh = Lenght of the ladder lean against the wallFrom the question,
Given:
y = 24 foot∅ = 69°Substitute these values into equation 2
y = 24/(cos69°)y = 24/0.358y = 67.0 feet.Hence, The horizontal distance between the base of the ladder and the wall is 67.0 feet.
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Harper leans a 24-foot ladder against a wall so that it forms an angle of 69
∘
∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary
8.6 feet
QPR=7x-9
RPS=4x+22
Find QPR
A 5-pound sack of potatoes is supposed to weigh 5
pounds. However, actual weights of the sacks vary
somewhat. An inspector selects a random sample of 50
sacks of potatoes from the large packaging plant and
weighs them
The inspector will calculate the sample mean and use
that to determine if there is convincing evidence that the
true mean weight of all sacks of potatoes differs from 5
pounds.
Answer:
t test for one mean.
met
met
met
Step-by-step explanation:
Every 30 minutes, a box of crayons is pulled from the assembly line to check the quality. Of 240 checked boxes of crayons, 2 did not pass inspection How many boxes out of 12,000 should the crayon company expect to not pass inspection?
Answer:
100
Step-by-step explanation:
2/240 = ?/12000
12000/240
50
2 x 50
100
2/240 = 100/12000
what is 62.5% as a decimal
Answer:
0.625
Step-by-step explanation:
please give me brainliest :(
Answer:
0.625
Step-by-step explanation:
How to Convert a Percent to a Decimal
Here are two ways to convert a percent to a decimal,
1. Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal.
Example: 62.5% becomes 62.5/100 = 0.625
2. This way is easier and faster. Start by removing the percent sign and moving the decimal point 2 places to the left.
Example: 62.5%
⇒ 62.5
⇒ 6.25
⇒ .625
Hence, the answer is 0.625.
A. y= 1/2x-14
B. y=1/2x-5
C. y=2x-14
D. y=2x-5
Answer:
B. y=1/2x-5
Step-by-step explanation:
From the graph, we read the slope of line JK.
slope = rise/run = -3/-6 = 1/2
The equation we need has the same slope.
y = mx + b
y = (1/2)x + b
It passes through point P(6, -2). Now we find b.
-2 = (1/2)(6) + b
-2 = 3 + b
b = -5
The equation is
y = (1/2)x - 5
Simplify
3x+4.4-2(6.6+x)
What are the solutions of the equation 2x^2=18
Help, been stuck on this problem for 20 minutes!
Answer: 24[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Answer:
24√6
Step-by-step explanation:
(3√8)(4√3) = 3 × 4 × √(4 × 2 × 3) = 12 × √4 × √6 = 12 × 2 × √6 = 24√6