Graph the system of equations on the grid below. Y=4x+7 and 2=x-y
Answers
The two lines intersect at (-3,-5) and thus a common solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here, the system of linear equations as Y=4x+7 and 2=x-y
On solving these two equations we get that the two lines intersect at (-3,-5) and thus a common solution.
The two equations are plotted in the attachment below.
Hence, The two lines intersect at (-3,-5) and thus a common solution.
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Related Questions
(2x + 5) (4x − 3) (5x - 4) can be expanded and fully simplified to give an expression of the form ax³ + bx² + cx + d.
Work out the values of a, b, c and d.
Answers
Answer:
To expand (2x + 5) (4x − 3) (5x - 4), you can use the distributive property and the FOIL method.
The distributive property states that for any two algebraic expressions a and b, and for any two numbers x and y, (a+b)(x+y) = ax + ay + bx + by.
The FOIL method is a way to multiply two binomials. It stands for First, Outside, Inside, Last, and it involves multiplying the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.
Using these methods, you can expand (2x + 5) (4x − 3) (5x - 4) as follows:
(2x + 5) (4x − 3) (5x - 4) = (2x)(4x)(5x) + (2x)(4x)(-4) + (2x)(-3)(5x) + (2x)(-3)(-4) + (5)(4x)(5x) + (5)(4x)(-4) + (5)(-3)(5x) + (5)(-3)(-4)
This can be simplified to:
= 40x³ - 32x² - 60x³ + 48x² - 20x³ + 15x² + 60x - 20x + 100x² - 20x + 12
Combining like terms, we get:
= -12x³ + 143x² + 100x + 12
So, the values of a, b, c, and d are a = -12, b = 143, c = 100, and d = 12.
Step-by-step explanation:
please help me, thank you
Question 7 options:
From the library, one car heads north, and another heads east. Some time later, the northbound car has traveled 17 miles, and the eastbound train has traveled 144 miles. The two cars, measured in a straight line, are ___ miles apart.
Answers
145 miles apart
hope this helps
4(x+7)=38 what does x equal?
Answers
Answer:
2.5
Step-by-step explanation:
Lia need to ell at leat 140 card to make a profit. Monday-thurday he ell 15,7,14,45 card. How many more will he need to ell on friday to make a profit?
Answers
Lisa needs to sell fifty nine (59) cards on Friday to make a profit, based on total 140 cards and the information on number of cards sold per day.
The total number of cards to be sold for profit = number of cards sold till Thursday + Remaining cards
We need to calculate remaining cards, but before that, we will find the sum of sold cards.
Number of cards sold = 15 + 7 + 14 + 45
Performing addition on Right Hand Side of the equation
Number of cards sold = 81
Remaining cards = 140 - 81
Performing subtraction on Right Hand Side of the equation
Remaining cards = 59
Thus, required number of cards is 59.
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The complete question is-
Lisa need to sell at leat 140 card to make a profit. Monday-thursday she sell 15,7,14,45 card. How many more will she need to sell on friday to make a profit?
Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x. (8x 3)(4x 7)
Answers
The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.
THE POLYNOMIALSWhen we multiply two polynomials together, we add the exponents of the x's in each term. In this case, we have 8x³ and 4x⁷. The x in 8x³ has an exponent of 3, and the x in 4x⁷ has an exponent of 7. To find the product of the two polynomials, we add the exponents of the x's in each term, so 3 + 7 = 10. The x in the product will have an exponent of 10. The coefficient, or the number in front of the x, is also multiplied together, so 8 × 4 = 32.So the final answer is 32x¹⁰, where 32 is the coefficient and 10 is the exponent of x.The polynomial 32x¹⁰ is an example of a polynomial, but it's not a characteristic of a polynomial.A polynomial is a mathematical expression involving a sum of powers in one or more variables (such as x, y, z) with non-negative integer exponents and real or complex coefficients. A polynomial can have one or more terms, and each term is separated by a plus or minus sign.Learn more about polynomial here:
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Please help me I am struggling with this
Answers
Step-by-step explanation:
(1). x-intercept: Put y = 0 in the equation y = 2x - 6 and solve for x. The x-intercept is 3.
y-intercept: Put x = 0 in the equation y = 2x - 6 and solve for y. The y-intercept is -6.
(2). x-intercept: Put y = 0 in the equation y = x - 7 and solve for x. The x-intercept is 7.
y-intercept: Put x = 0 in the equation y = x - 7 and solve for y. The y-intercept is -7
(3). x-intercept: Put y = 0 in the equation y = (3/2)x - 9 and solve for x. The x-intercept is -6.
y-intercept: Put x = 0 in the equation y = (3/2)x -9 and solve for y. The y-intercept is -9.
(4). x-intercept: Put y = 0 in the equation y = (-1/4)x + 1 and solve for x. The x-intercept is -4.
y-intercept: Put x = 0 in the equation y = (-1/4)x + 1 and solve for y. The y-intercept is 1.
(5). x-intercept: Put y = 0 in the equation -x + y = -5 and solve for x. The x-intercept is 5.
y-intercept: Put x = 0 in the equation -x + y = -5 and solve for y. The y-intercept is -5.
(6). x-intercept: Put y = 0 in the equation x + 2y = -14 and solve for x. The x-intercept is -14.
y-intercept: Put x = 0 in the equation x + 2y = -14 and solve for y. The y-intercept is -7.
(7). x-intercept: Put y = 0 in the equation 3x - y = -3 and solve for x. The x-intercept is -1.
y-intercept: Put x = 0 in the equation 3x - y = -3 and solve for y. The y-intercept is 3.
(8). x-intercept: Put y = 0 in the equation 5x + 3y = 15 and solve for x. The x-intercept is 3.
y-intercept: Put x = 0 in the equation 5x + 3y = 15 and solve for y. The y-intercept is 5.
help plsss its due by tonight!!
Answers
Answer:
i am pretty sure the answer is d.
Step-by-step explanation:
let me know if this is wrong
john bought 53 cartons of eggs,and each had 24 eggs.250 of the eggs were bad.how many good eggs did she get?
Answers
Answer:
1022
Step-by-step explanation:
total of eggs
= 53 × 24
= 1272
the good eggs
= 1272 - 250
= 1022
Sally has 4 apples for school lunch, her friend asks if she can 2 apples for Sally's 4 apples. How many more apple would Sally have left after giving her friend 2?
Answers
Answer:Sally would have 2 apples left
Step-by-step explanation:Because 4-2=2 so she gave 2 away so she has 2 left.
The robotics club had 80 members. Because of the pandemic that amount decreased by 65%.
How many people are in the robotics club now?
Answers
Answer: 28
Step-by-step explanation:
65% of 80 is 52
80 - 52 = 28
28 people
jeez, 52 people quit? That’s a lot!
sorry if it’s wrong. Have a great day!
Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\bullet$ $P(-3)
Answers
The value of polynomial p(x) when x=0 is 35.
What is a polynomial?
An expression made up of indeterminates and coefficients and utilising solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables is referred to as a polynomial.
The complete question is as follows:
Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).
Given,
p(x) is a polynomial of smallest degree where
p(-3) = p(√7) = p( 1-√6) = 0
p(-1) = 8
So the factors of p are (x+3),(x-√7) and (x - 1+√6)
Given p has rational coeffecients. So we should remove √7 and √6. This can be done by multiplying with conjugates.
(x-√7)*(x+√7) = x²-7
(x-1+√6) * (x-1-√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5
Now the polynomial can be written as
p(x) = c (x+3)(x²-7) (x²-2x-5 )
Here c is a constant and can be determined using p(-1) = 8
p(-1) = c ( -1+3)(-1² - 7 )(-1²-2*(-1) -5)
8 = c(2)(-6)(-2)
c = 1/3
Now the polynomial p(x) = 1/3(x+3)(x²-7) (x²-2x-5 )
Therefore p(0) = 1/3 (3) (-7)(-5) = 35
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**Please help ASAP
A sum of $2000 needs to be split among three people so that the first person receives $120 more than the second person and the third person receives twice as much as the second person. Set up and solve an equation or equations to determine how much each person will receive.
Answers
Answer:
1st person will receive = $590
2nd person will receive = $470
3rd person will receive = $940
Step-by-step explanation:
Total divisible amount = $2000
according to the question:
let 2nd person's received amount = x
1st person's received amount = x + 120
3rd person's received amount = 2x
x + x + 120 + 2x = 2000
4x + 120 = 2000
4x = 2000 - 120
4x = 1880
x = 1880 / 4
thus,
x = 470
1st person will get = x + 120 = 470+120 = $590
2nd person will get = x = $470
3rd person will get = 2x = 2 * 470 = $940
If anyone knows the answer for this question please help!
7th grade math.
Answers
Answer:
47°
Step-by-step explanation:
(180 - 86) / 2 = measure of each congruent angle
94/2 = 47
30 + 10 ⋅ 5 – 45 ÷ 5
Answers
Answer:
71
Step-by-step explanation:
30+10×5-45÷5= 30+50-9=71
What is the y-intercept of the quadratic function f/x )=( x 6 )( x 2?
Answers
The y-intercept of the quadratic function f(x) = (x - 6)(x + 2) is -12.
The y-intercept of a quadratic function is the point at which the graph of the function crosses the y-axis. This means that when x = 0, the value of y is equal to the y-intercept. In the case of the function f(x) = (x - 6)(x + 2), when x = 0, the value of y is equal to -12. This means that the y-intercept of the function is -12. To find the y-intercept, we can also substitute 0 for x in the equation, which would give us 0 = (0 - 6)(0 + 2), which simplifies to 0 = -12, and thus the y-intercept is -12.
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HELP MEWMMEEMEMEMEMEEMMEEM'
Answers
Answer:
Plot A does
Step-by-step explanation:
M
Explain why this is true
PLEASE HELP!!!
Answers
Answer:
The given statement is true because the person they did their steps correctly
a) Locate a point C so that ABC is a right triangle with m ACB ∠ = ° 90 and the measure of one of the acute angles in the triangle is 45° .
b) Locate a point D so that ABD is a right triangle with m ADB ∠ = ° 90 and
the measure of one of the acute angles in the triangle is30° .
c) Locate a point E so that ABE is a right triangle with m AEB ∠ = ° 90 and
the measure of one of the acute angles in the triangle is15° .
d) Find the distance between point C and the midpoint of segment AB .
Repeat with points D and E.
e) Suppose F is a point on the graph so that ABF is a right triangle
withm AFB ∠ =° 90 . Make a conjecture about the point F.
A. 13 X 14
B. 7 X 6
C.20 X 7
D. 103 X 104
Answers
Show the correct relationship between altitude and boiling point.
Altitude
Boiling Point Temp.
Answers
The relationship between altitude and boiling point is given below.
What is altitude?
Altitude is the height above sea level. It is usually measured with a barometer or GPS satellite. Altitude can be used to describe the height of an airplane, a mountain, or even the position of a satellite in space. Altitude can also be used to measure how high a person is standing on Earth. Altitude can also be used to compare the relative heights of two different points on Earth. Altitude is an important factor when flying, as it can determine air pressure, air temperature, and wind speed.
Sea Level 212°F
1,000 ft. 211°F
2,000 ft. 210°F
3,000 ft. 209°F
4,000 ft. 208°F
5,000 ft. 207°F
6,000 ft. 206°F
7,000 ft. 205°F
8,000 ft. 204°F
9,000 ft. 203°F
10,000 ft. 202°F
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A rectangular trunk has a volume of 26,880 cubic inches. The trunk is 48 inches long by 28 inches wide. What is the trunk’s height?
Answers
Exclamation:
26880=4(28)(h)
26880= 112. (h)
_____. ____
112. 112
Answer: 240=h
I hoped this helped!
Answer:
26880=48(28)h 48(28)=1200 26880÷1200=20 h=20
‼️ help me it is due today Find the value of x.
58°
X°
‼️‼️‼️
Answers
What are the properties of a 3 4 5 triangle?
Answers
The right angle with in 3-4-5 triangle is naturally 90 degrees. Always opposite the fourth side, at 53.13 degrees, are the other two angles: 36.87 degrees (just opposite the 3rd side).
Explain the 3 4 5 triangle and its properties?Specialized triangles, such as 3-4-5 triangles, can be solved using the Pythagorean theorem.
Any triangle with a single right (90°) angle is referred to as a right triangle. Typically, a tiny square marker is placed within the right triangle to denote this. In every right triangle, these two sides closest to the right angle are shorter than the hypotenuse, the side directly across from the right angle. A right triangle with integers on each side is known as a Pythagorean triple.Thus, this 3-4-5 right triangle is one of the most well-known Pythagorean triples. The hypotenuse, its longest side opposite its right angle, is measured at 5, while the shorter sides measure at 3 and 4.
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If sin0≈0.3090, what is the approximate vale of csc0?
Answers
Answer:
the approximate of 0•3090 is 0•31
i do not understand how proportionality works
Answers
Answer:
3.5
Step-by-step explanation:
In this problem, the line's constant of proportionality is the same as its slope.
Slope is defined as rise / run (also notated as change in y / change in x).
Using the given point, we can deduce that the line's rise (change in y) is 3.5, and its run (change in x) is 1. Putting these values into the slope formula:
3.5 / 1 = 3.5
So, the constant of proportionality of this line is 3.5.
What number will be multiplied to give -100 and be added to give 8
Answers
Answer:
-12.5
Step-by-step explanation:
Hope it helps u
FOLLOW MY ACCOUNT PLS PLS
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 15 hours, to the nearest whole number?
Answers
The population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours.
Given that,
P_t = P_0 * 2^(t/d) , which refers to the formula for the calculation of the number of bacterial cell in a population.
In the given formula, P_t is the population after t hours, P_0 is the initial population, t is the time in hours and d is the doubling time in hours,
Therefore,
P_0 = 7100
d = 2
t = 15
so,
P_15 = 7100 * 2^(15/2) = 7100 * 181.019= 1285234.9 which is nearly equal to 1285235
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours, the population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235
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How do you find an inverse?
Answers
Answer:
by using 1 to divide the value
Step-by-step explanation:
the inverse of 5/8 is 8/5.
How many combinations of ice cream with a topping can be made if there are 3 kinds or ice cream and 5 toppings?
Answers
Answer: 15 Combinations
Step-by-step explanation: 5x3=15
help i really don’t understand this
Answers
Answer:
45 degree
Step-by-step explanation:
45+45 90 +90 180
All triangles will have 180 degrees angle
If the given figure is rotated 90 degrees counterclockwise around the origin, what are
the new coordinates of point M?
Answers
Answer:
the answer is (-4,2)
hope this helps
Answer:
(-2,4)
Step-by-step explanation: