What is the equation in point slope form of the line that passes through the point (–1,–3) and has a slope of 4?
Answer:
The required equation is y + 3 = 4(x + 1)
Step-by-step explanation:
Since, the point slope form of a line passes through the point [tex](x_1, y_1)[/tex] having slope m is,
[tex]y-y_1 = m(x-x_1)[/tex]
Here,
[tex]x_1 = -1, y_1 = -3\text{ and }m = 4[/tex]
Hence, the equation of the line,
[tex]y+3 = 4(x+1)[/tex]
Or
[tex]y = 4(x+1) - 3[/tex]
Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x – h)2 + k. Which of the following must be true?
h and k cannot both equal zero
k and c have the same value
the value of a remains the same
h is equal to one half –b
Quadratic equations can be expressed in standard form or in vertex form.
The true statement about [tex]\mathbf{y = ax^2 + bx + c}[/tex] and [tex]\mathbf{y = a(x - h)^2 + k}[/tex] is that: the value of a remains the same
The original expression is given as:
[tex]\mathbf{y = ax^2 + bx + c}[/tex]
He wants to rewrite it as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
Expand the above equation
[tex]\mathbf{y = a(x - h)(x - h) + k}[/tex]
Open brackets
[tex]\mathbf{y = a(x^2 - hx - hx + h^2) + k}[/tex]
[tex]\mathbf{y = a(x^2 - 2hx + h^2) + k}[/tex]
Remove bracket
[tex]\mathbf{y = ax^2 - 2ahx + ah^2 + k}[/tex]
Compare the above equation to: [tex]\mathbf{y = ax^2 + bx + c}[/tex]
[tex]\mathbf{ax^2 = ax^2}[/tex]
[tex]\mathbf{-2ahx = bx}[/tex]
[tex]\mathbf{ah^2 + k = c}[/tex]
Analyzing the above equations
[tex]\mathbf{ax^2 = ax^2}[/tex]
Divide both sides by [tex]\mathbf{x^2}[/tex]
[tex]\mathbf{a = a}[/tex]
The above equation means that, the value of a remains unchanged.
Hence, option (c) is true
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A consistent system of equations is a system with __________.
the same line
parallel lines
intersecting lines and lines that have the same slope
intersecting lines and lines that have the same equation
Kate ate 1 out of 4 of her orange. ben eat 2 out of 4 of his banana. did kate and ben eat 1 out of 4 add 2 out of 4 equal 3 out of 4 of their fruit? explain
The leg of a right triangle is 2 units and the hypotenuse is 4 units. what is the length, in units, of the other leg of the triangle
Use you graph to estimate the value of x when y = 2. How would you work that out?
What is the slope of this graph?
−1/3
3
1/3
−3
Find the 9th term of the following geometric sequence: 1, –3, 9, –27. PLEASEEEEE HELP!!!!!!
A. –5,661
B. 7,241
C. –2,456
D. 6,561
What is the end behavior of f(x) = (x − 3)2(x + 5)(x − 2)3?
T he end behavior of f(x) can be described as:
As x → -∞, f(x) → +∞
As x → +∞, f(x) → +∞
To determine the end behavior of f(x) = (x − 3)²(x + 5)(x − 2)³, we need to consider the degree and leading coefficient of the polynomial.
1. Degree of the Polynomial:
The degree is the highest sum of exponents of the variable x in any term. In this case:
(x - 3)² contributes a degree of 2 (x² term)
(x + 5) contributes a degree of 1 (x term)
(x - 2)³ contributes a degree of 3 (x³ term)
Adding these degrees, we get a total degree of 2 + 1 + 3 = 6.
2. Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest degree. Since all factors have a leading coefficient of 1, the leading coefficient of the entire polynomial will also be 1 (positive).
3. End Behavior Based on Degree and Leading Coefficient:
Even Degree & Positive Leading Coefficient: When the degree is even and the leading coefficient is positive, both ends of the polynomial will approach positive infinity. In other words, as x approaches both positive and negative infinity, f(x) will also approach positive infinity.
Therefore, the end behavior of f(x) can be described as:
As x → -∞, f(x) → +∞
As x → +∞, f(x) → +∞
Complete question:
What is the end behavior of [tex]f(x) = (x - 3)^{2} (x + 5)(x - 2)^{3}[/tex]?
Which equation could be used to solve the following system?
x+y=11
4x^2-3y^2=8
A. 4(y + 11)2 – 3y2 = 8
B. 4(11 – y)2 – 3y2 = 8
C. 4(y – 11)2 – 3y2 = 8
D. 4(–11y)2 – 3y2 = 8
we have
[tex]x+y=11[/tex]
[tex]x=11-y[/tex] --------> equation A
[tex]4x^{2} -3y^{2}=8[/tex] ----> equation B
Substitute equation A in equation B
[tex]4(11-y)^{2} -3y^{2}=8[/tex]
therefore
the answer is the option B
[tex]4(11-y)^{2} -3y^{2}=8[/tex]
what times what equals 429
Which one is the greater quantity 1/3 of a box of corn crinkles or 50% of a box of corn krinkles
Jasmine wants to use her savings of $1,128 to buy video games and music CDs. The total price of the music CDs she bought was $72. The video games cost $43 each. What is the maximum number of video games that Jasmine can buy with her savings?
24
25
26
27
Answer: 24 video games
Step-by-step explanation: jasmine has 1,128 bucks originally. she gets some megadeth and metallica cd's (cause if she's got taste, that's probably what she got) and that adds up to 72 bucks. now she wants to buy a whole bunch of video games, which cost 43 each (imagine she got fortnite mod's. ew) so we put that in an equation-
$1,128 - $72 = $1,056
$1,056 divided by 43 equals 24.55813953488372.
when dealing with money, you always round down, so the total number of games she bought was 24
please mark brainliest
Solve the following equation: 2x - 3 = 17.
a. 5
b. 7
c. 10
d. 12
The number 0.1111... repeats forever; therefore, it is irrational. True or False.
I need help on this asap i'll give you so many points!!
Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?
Answer:
Quadratic formula for given equation is [tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]
Step-by-step explanation:
Given Quadratic Equation is 7x² = 9 + x
We need to find correct Quadratic formula for the given quadratic equation.
If the quadratic equation is in standard for,
ax² + bx + c = 0
then quadratic formula is given by,
[tex]x=\frac{-b\pm\sqrt{b-4ac}}{2a}[/tex]
First we rewrite the quadratic equation,
7x² - x - 9 = 0
by comparing with standard form of equation we get,
a = 7 , b = -1 and c = -9
oNw putting these value in quadratic formula we get,
[tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]
Therefore, Quadratic formula for given equation is [tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]
A girl is 18 years old and her brother is a third of her age. When the girl is 36 what would be the age of the brother?
Cylinder has a height of 14 centimeters and its circle bases have a radius of 10 centimeters. find the surface area of the cylinder.
2(100 ) + 140 square centimeters
1,400 + 140 square centimeters
2(100 ) + 280 square centimeters
2(1,400 ) + 2(140 ) square centimeters
y = 3x
x + 2y = -21
Solve the system. Write your answer as an ordered pair (x, y)
V-15=-27 what's they equation
The given expression V-15=-27 gives the value of v = -12.
Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
And we know that a mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given expression is:
V-15=-27
To solve this equation:
Add 15 on both sides
v - 15 + 15 = - 27 + 15
v = -12
Hence,
The given expression gives the value of v = -12
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Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?
−5x − 7 < −22 and −5x − 7 ≥ −3
−5x − 7 > −22 and −5x − 7 ≥ −3
−5x > −22 and −7 ≥ −3
−5x − 7 < −22 and −5x − 7 ≤ −3
Estimate 24% of 33.
a) 17
b) 12
c) 2
d) 8
Which of the following recursive formulas represents the same geometric sequence as the formula an = 3 * 3n - 1?
A.an = 9 * an - 1
B.an = 3 * an - 1
C.an = 9 + an - 1
D.an = 3 + an - 1
The recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] is option B: [tex]\( a_n = 3 \times a_{n-1} \).[/tex]
To find the recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex], we need to find a recursive formula that generates the same sequence.
The formula [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] can be rewritten as:
[tex]\[ a_n = 3 \times 3^{n-1} = 3 \times 3^n \times 3^{-1} = 3 \times \left(3 \times 3^{n-1}\right) \][/tex]
This indicates that each term is 3 times the previous term. So, the recursive formula should involve multiplying the previous term by 3.
Let's examine the options:
A. [tex]\( a_n = 9 \times a_{n-1} \)[/tex] - This represents multiplying the previous term by 9, not 3.
B. [tex]\( a_n = 3 \times a_{n-1} \)[/tex] - This represents multiplying the previous term by 3, which matches the original sequence.
C. [tex]\( a_n = 9 + a_{n-1} \)[/tex] - This represents adding 9 to the previous term, not multiplying it.
D. [tex]\( a_n = 3 + a_{n-1} \)[/tex] - This represents adding 3 to the previous term, not multiplying it.
Therefore, the recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] is option B: [tex]\( a_n = 3 \times a_{n-1} \).[/tex]
Please solve:
x+y=8.
xy=15. ...?
During which two time intervals does the particle undergo equal displacement?
Choices:
a) AB & BC
b) AB & DE
c) BC & DE
d) CD & DF
It’s AB and DE so it would be b
Which of the pairs of angles are complementary
Which of the following is something that will not affect your homeowners insurance premium? a. the distance of the home from a school b. the distance of the home from a flood plain c. the distance of the home from a fire station d. the distance of the home from a fire hydrant
Answer:
a. the distance of the home from a school
Step-by-step explanation:
The distance your home is from a flood plain can potentially increase your homeowner's insurance. If your house is close to a flood plain, your insurance will increase.
The distance your home is from a fire station or a fire hydrant either one can lower your insurance. If your home is within so many feet of a hydrant, you get a discount on your insurance; if it is close enough to a fire station, you get a discount as well.
Since the distance a home is from a school has no bearing on the cost of repairing or replacing the home, this will not affect your homeowner's insurance.
Which of the following conditions must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population?
Which ordered pair is a solution to this equation?
(x + 3) y = 14
A. (3, 2)
B. (5, 2)
C. (11, 1)
D. (7, 2)