The equation of parabola will be;
⇒ y = 4 ( x + 4)² - 8
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The vertex = (- 4, - 8)
And, The focal diameter = 16
Now,
Since, The vertex (h, k) = (- 4, - 8)
And, The focal diameter (4a) = 16
⇒ 4a = 16
⇒ a = 4
Hence, The equation of parabola with vertex (h, k) will be;
⇒ y = a (x - h)² + k
Substitute all the values, we get;
⇒ y = 4 (x - (-4))² + (-8)
⇒ y = 4 ( x + 4)² - 8
Thus, The equation of parabola will be;
⇒ y = 4 ( x + 4)² - 8
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Answer:
Step-by-step explanation:
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Rewrite the following equation in slope-intercept form (y = mx + b), then identify the slope (m =) and y-intercept (b =) of the equation.
-3y – 5 = -2(x + 11) + 2
Answer: y = [tex]-\frac{2}{3} x[/tex] -5
Step-by-step explanation:
Distribute:
-3y-5=-2x(x+11)+2
Rewrite:
-3y-5=-2x-22+2
Combind alike terms:
-2x-20
Rewrite again:
-3y-5=-2x-20
Add 5 to both sides and rewrite:
-3y=-2x-15
Divide by -3:
y=[tex]-\frac{2}{3} x[/tex] - 5
(Sorry if it's incorrect im barely paying attention lol)
What would you use to graph the inequality y ≥ 4 ?
The coordinate plane
A number line
The origin
This inequality cannot be graphed.
A number line use to graph the inequality y ≥ 4.
How do you graph an inequality?Treat the,, >, or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.Pick a point that is not on the line next. Verify if the inequality is satisfied by this point. The area containing that point should be shaded if it satisfies the inequality. Shade the area that does not contain that point if it does not satisfy the inequality. Every point in the shady area satisfies the inequality.Explanation :
y = − 4 is a horizontal line at -4, since
y ≥ − 4, the area above -4 will be shaded and the line will be solid since it is greater than AND equal to:
graph{y>=-4 [-10, 10, -5, 5]}
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In the continuous Efm=300+20m. series, if mean (x)=15+m and Find the number of terms N.
Answer:
the number of terms N in the series is approximately 8.57, which is approximately equal to 9.
Step-by-step explanation:
The mean of a series is calculated by taking the sum of all the terms in the series and dividing it by the number of terms. In this case, the mean of the continuous series Efm=300+20m is given as x=15+m.
To find the number of terms N in the series, we can use the formula for the mean to solve for N. The formula for the mean is:
mean = sum of terms / number of terms
Substituting the given values, we get:
15+m = (300+20m) / N
We can then multiply both sides of the equation by N to isolate the sum of terms:
(15+m) * N = 300+20m
This simplifies to:
15N + mN = 300 + 20m
We can then combine like terms to get:
(15+20)N = 300
35N = 300
Dividing both sides by 35, we get:
N = 300/35
N = 8.57
Since the number of terms must be a whole number, the number of terms N in the series is approximately 8.57, which is approximately equal to 9.
Identify the vertex, axis of symmetry, and the direction of opening of the graph of g(x) = |x| - 8.
A. (0, -8); y = -8; opens up
B. (0, -8); x = 0; opens up
C. (8, 0); x = 0; opens down
D. (-8, 0); x = -8; opens down
A. (0, -8); y = -8; opens up will be the correct solution for the graph of given modulus function g(x) = |x| - 8.
What is modulus function?
Regardless of whether a number is positive or negative, the modulus function, also known as the absolute value function, determines its magnitude. No matter what the number or variable, it always returns a non-negative value. The expression y = |x| or f(x) = |x|, where f: R (0,) and x R, denotes a modulus function.
When x is a real number, then |x| is its modulus. f(x) will have the same value as x if x is not negative. If x is negative, then f(x) will have the magnitude of x; if x is negative, then f(x) = -x. Here is a summary of the modulus function formula.
As we can see in the graph attached that the f(x) is zero at y=-8 and it is a modulus function so the graph will open upwards
but the graph is little shifted to y=-8 because the equation given to us is |x|-8 =g(x) so it will shift down according to the rule
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Need help on this question ASAP PLEASE AND THANK YOU
Answer:
which class question is this
In the coordinate plane, line q has slope 6 and y-intercept (0, 8). Line p is the result of dilating line q by a factor of 4 with center (0, 4). What is the y-intercept and slope of line p?.
The line r has slope 6 and coordinates in the specified coordinate plane, based on the given dilation (0, 12)
Dilation:
Dilation is the scaling factor multiplied by the supplied line to line ratio.
Given
Line p in the coordinate plane has a y-intercept and a slope of 6. (0, 8). Line p is dilated by a factor of 4 with center to produce line r. (0, 4).
Here, we need to determine line r's slope and y-intercept.
Here, the scaling factor is known to be 4.
Consider the line r's slope, which won't change, and its intercept, which will be their ordinate added.
So, it can be written as,
=> Intercept = 8 + 4
=> Intercept = 12
Therefore, the line r has slope 6 and coordinate (0, 12).
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HELP ASAP!! graph the system of equations below by graphing both equations below on a piece of paper. what is the solution?
y=x-1
y=3x+1
A. 1, -2
B. -1, -2
C. 2, 1
D. -1, -1
Answer: Our answer set is( -1,-2 )
Step-by-step explanation:
y = x - 1
y = 3x + 1
We can use the combine method here.
==> - 1y + 1x = 1 (y = x - 1)
==> -1y +3x = -1 (y = 3x + 1)
- 1y + 1x = 1
-1y +3x = -1
To single out any of the two variables, we need them to cancel out. Let us choose to cancel out y. We therefore multiply by negative 1 in the first re-arranged equation.
==> -1* (- 1y + 1x )= (1 ) * -1
Now we add the equations
==> 1y -1x = -1
==>-1y +3x = -1
______________
2x = -2
Divide.
==> x = -1
Now we insert x into any of the two original equations;
y = (-1) - 1
==> y = -2
Our answer set is( -1,-2 )
how can I solve this
Answer: S=$2 and L=$8
Step-by-step explanation:
This question is a simultaneous equation.
(1) 4L+3S=$34
(2) 2L+S=$16 (*2)
(3) 4L+2S=$32
(1)-(3)
4L+3S=$34
-4L+2S=$32
S=$2
Substitute s=2 into (2)
2L+S(2)=$16
2L+2=$16 (-2)
2L=$16 (/2)
L=$8
.
In Alaska, the temperature is currently -14°F, and in Mt. Olive it is currently 67°F.
What is the difference in temperature between Alaska and Mt. Olive?
And please explain
Answer:
81
Step-by-step explanation:
it is asking only for the difference nothing else so do
14+67 because the value is in the - we use addition for this scenario if it's for example
difference between 10f and 50f you minus it
10-50 = 40
If you spin a 3 circle spinner 120 times, about how many times would you expect it to land on B?
Around 80 times we should expect it to land on B.
What is time?Time is basically a measure of non-stop, consistent change in our own surroundings. Usually we can see through a specific point of view. Concept of time is self-evident and intuitive. Describing the fundamental nature of time is quite difficult.
As per the given condition-
Spin circle=3
Time = 120 sec
the total is 3
the red and orange equals to 2
2/3 times 120
240/3
=80 times
Thus, the correct answer is 80 times.
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Given the matrices A and B shown below, find A + B.
A = 1 -1 1] B = [-4 -4 0]
What is the equation of a line with a y-intercept of −5 and a slope of 8? A.y=−5x+8 B.y=8x−5 C.y=−5x−8 D.y=8x+5
On solving the provide question, we got that - he equation of a line with a y-intercept of −5 and a slope of 8 is8x - y +5 = 0
What is slope?The change in the y coordinate of a line with respect to the change in x coordinate is called the slope of the line. There was no net change in the x coordinate, but no net change in the y coordinate.
By using the Slope formula
(y - y1) = m (x - x1)
where m is slope
so,
(y - 5) = 8 X (x-0)
8x - y +5 = 0
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Please help
What inequality does the number line show?
Write your answer starting with
x (example: x < 3)
Answer:
x ≥ -7
Hope this helps : )
Step-by-step explanation:
The number line is showing a closed dot which means that the number the dot is on is a solution to the equation too. Since the arrow is pointing to the right (positive/greater numbers), then the sign is greater than and equal to.
Alice's savings account earns 3.75% interest per year. If she put $9,500 into the savings account, how much interest would be earned in a year?
Hello,
I hope you and your family are doing well!
To calculate the amount of interest earned on a savings account, you can use the following formula:
interest = principal * rate * time
In this case, the principal is $9,500, the rate is 3.75%, and the time is 1 year. Plugging these values into the formula, we get:
interest = $9,500 * 3.75% * 1 year = $356.25
So, in a year, Alice would earn $356.25 in interest on her savings account.
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Happy Holidays!
Examine the table, which represents a linear function.
Input (x) Output (y)
−3 14
0 7
3 0
6 −7
What is the initial value of the function?
A: 3
B: -3
C: 0
D: 7
Answer: 7
Step-by-step explanation:
The initial value of the function is the value of [tex]y[/tex] when [tex]x=0[/tex].
3 The Chemistry teacher requests a report on the topic: Sustainable energy. Chapter 5 of the textbook must be used and the delivery date is in three days. What kind of resources were provided for this investigation?
material and administrative
economic and didactic
institutional and methodological
time and source
Knowing that the teacher indicates the chapter of the book to use and the delivery date, the resources that were provided for the research on sustainable energy are:
WeatherFont¿What are the resources for conducting research?They are elements that must be taken into account and that are usable to develop the investigation.
Some examples of these resources are:
Time: it indicates the time that the investigation will take.Source: represents these bibliographic elements from which information is extracted to develop the investigation.¡Hope this helped!
Simplify the following monomials. Express final answers using only positive exponents.
[tex]\frac{8}{8^{3} }[/tex]
[tex]\frac{(-3)^{4} }{(-3)^{3} }[/tex]
The simplified monomial for the first scenario will be 1/8². The simplified monomial for the second situation will be (-3)¹.
What is exponent?Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6*6*6*6. You can write this as 6^4. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6. A number or letter written above and to the right of a mathematical expression known as the base is termed an exponent. It denotes that the base is to be increased in strength. The base is x, while the exponent or power is n.
Here,
The law of exponents say that,
aⁿ/aˣ=aⁿ⁻ˣ
1. 8/8³
=8¹-³
=8⁻²
=1/8²
2. (-3)⁴/(-3)³
=(-3)⁴⁻³
=-3¹
For first case, the monomial resulted after simplifying will be 1/8². For second case, the monomial resulted after simplifying will be (-3)¹.
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If 30200 dollars is invested at an interest rate of 6 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$30200\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=30200\left(1+\frac{0.06}{1}\right)^{1\cdot 5} \implies A=30200(1.06)^5\implies A \approx 40414.41[/tex]
3. Find the volume of a sphere with a radius of 4 ft. (1 point)
Answer: =268.19047cm^3 or 268.08 rounded
Step-by-step explanation: using [tex]\frac{4}{3} *\pi *r^{3}[/tex] to get my answer.
Hope this helps :)
Determine the equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x.
Option:
The equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x is [tex]$\frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1$[/tex]
The answer provided below has been developed in a clear step by step manner.
Given asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex] and
vertices (1,6) and (1,-12)
What is hyperbola ?
Standard hyperbola through origin when values of x for the vertices are equal. [tex]$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$[/tex]
Now solve the asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex]
After solving we get [tex]$\mathrm{x}=1 \quad$[/tex]and [tex]$\quad \mathrm{y}=-3$[/tex]centre =(1,-3)
translation in form of [tex]$\mathrm{x}_1$[/tex] and [tex]$\mathrm{y}_1$[/tex]
[tex]$\mathrm{x}_1=\mathrm{x}-1 \quad$[/tex] and [tex]$\quad \mathrm{y}_1=\mathrm{y}+3$[/tex]
Distance from vertices (1,6) and (1,-12) to centre (1,-3) is [tex]$9=\mathrm{a}$[/tex]vertical symmetry the asymptotes have a slope [tex]$=\pm 3=a / b$[/tex] so [tex]$\mathrm{b}=\frac{9}{3} \Rightarrow \mathrm{b}^2=9$[/tex]
Put all the values of a and b into original equation
[tex]$$\begin{aligned}& x_1=x-1 \quad \text { and } \quad y_1=y+3 \\& \Rightarrow \frac{(y+3)^2}{3^2}-\frac{(x-1)^2}{9^2}=1 \\& \Rightarrow \frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1\end{aligned}$$[/tex]
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What is the slope of line m?
Answer:-1/2
Step-by-step explanation:
Find BR if D is the circumcenter of △ABC, CD=11.1 and RD=5.2. Round to the nearest tenth
Answer:
BR=9.8
Step-by-step explanation:
a²+b²=c²
5.2²+b²=11.1²
27.04+b²=123.21
b²=96.17
b=[tex]\sqrt{ 96.17}[/tex]
b=9.8
Question 2-4
Dad mowed 60% of the yard in 30 minutes. At this rate, how many minutes will it take him to mow the
entire yard?
minutes
The number of minutes will it take him to mow the entire yard will be 50 minutes.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Dad mowed 60% of the yard in 30 minutes.
Let 'A' be the entire area of the lawn and 'x' be the total time to mow the entire lawn. Then 60% of the lawn is given as,
⇒ 60% of A
⇒ 0.60A
The ratio of the area of the lawn to time remains constant. Then the equation is given as,
0.60A / 30 = A / x
x = 30 / 0.60
x = 50 minutes
The number of minutes will it take him to mow the entire yard will be 50 minutes.
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The arenas pay for two cars every month they pay $250 for Miss Herrera's car and 375 for Mr. editor struck what kind of expense is a car payment made each month
Please Help
The product of two consecutive, negative integers is 182.
What equation represents the situation?
Thanks to whoever can solve it
The equation that represent the product of to consecutive numbers being 182 is x^2 + x -182 = 0
What is a quadratic equation?Quadratic equations are second-degree algebraic expressions and are of the form ax^2+ bx + c = 0. The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2.”
let the two consecutive negative numbers be -x and -x-1
their product - x( -x-1) = 182
multiply out you have
x^2 + x = 182
which is finally reduced to
x^2 + x - 182 = 0
In conclusion the equation that represent the above question is x^2 + x - 182 = 0
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A person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000. Give full explanation 
If person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000 then he spends 8750 of his monthly income.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a person saves 12.5% of his income.
The monthly income of the person is 10000.
We need to find how much he spend in a month.
Convert 12.5 % to the decimal value by dividing 12.5 by 100.
12.5/100=0.125
Now multiply 0.125 with 10000
0.125×10000
1250
Subtract 1250 from 10000
10000-1250
8750
Hence, person spends 8750 of his monthly income.
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What is the solution to this system of equations? 3x+y+2z=6 6x−2y=2 3x+y−2z=0
The value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3x+y+2z=6 6x−2y=2 3x+y−2z=0
What is a linear equation?It is defined as the relation between three variables, if we plot the graph of the linear equation we will get a plane.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The linear equations are:
3x+y+2z=6
6x−2y=2
3x+y−2z=0
From equation (I) and (III)
6x + 2y = 6
From the above equation and equation (II)
12x = 8
x = 8/12 = 2/3
y = 1
z = 3/2
Thus, the value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3x+y+2z=6 6x−2y=2 3x+y−2z=0
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There are 152 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 31 fans?
Answer:
182
Step-by-step explanation:
152
+31
---------
182
Which uses the GCF to generate an expression equivalent to 24v-84?
O3(8V-28)
O 6(4v-14)
O 12(2v-7)
O 24(V-60)
Answer:
(c) 12(2v-7)
Step-by-step explanation:
You want the expression resulting from factoring out the greatest common factor from the sum 24v -84.
GCFThe greatest common factor here is the GCF of 24 and 84. We note that ...
24 = 12·2
84 = 12·7
and 2 and 7 have no common factors. Then the GCF of 24 and 84 is 12.
The factored expression is ...
24v -84 = 12(2v -7)
__
Additional comment
The GCF can also be found by considering the remainder from dividing 84 by 24. That remainder is 12, which divides both numbers with a remainder of 0. Hence 12 is the GCF.
If the remainder did not divide both numbers with a remainder of 0, then the process is repeated to find the GCF of the smaller number (24) and the remainder. (This is a description of Euclid's algorithm for finding the GCF.)