The quadratic equation with a vertex at (-1, -5) that passes through (2, 13) is:
y = 2*(x + 1)^2 - 5
How to find the quadratic equation?A quadratic equation with a leading coefficient a and a vertex (h, k) is written as:
y = a*(x - h)^2 + k
Here we know that the vertex is (-1, -5), then our parabola is something like:
y = a*(x + 1)^2 - 5
Now we also know that the quadratic equation contains the point (2, 13), then we can replace the values to get:
13 = a*(2 + 1)^2 - 5
13 = a*3^2 - 5
13 = a*9 - 5
13 + 5 = a*9
18/9 = a
2 = a
Then the quadratic equation is:
y = 2*(x + 1)^2 - 5
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party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $25. The total cost to rent 6 chairs and 5 tables is $49. What is the cost to rent each chair and each table?
The cost to rent each chair and each table is $2.75 and $6.50 respectively.
How to calculate the cost?The total cost to rent 2 chairs and 3 tables is $25. This will be:
2c + 3t = 25
The total cost to rent 6 chairs and 5 tables is $49. This will be:
6c + 5t = 49
2c + 3t = 25
6c + 5t = 49
6 × (2c + 3t = 25)
2 × (6c + 5t = 49)
12c + 18t = 150
12c + 10t = 98
Subtract
8t = 52
Divide
t = 52/8
t = 6.5
Cost to rent table = $6.50
Since 2c + 3t = 25
2c + 3(6.5) = 25
2c + 19.5 = 25
Collect like terms
2c = 25 - 19.5
2c = 5.5
c = 5.5/2
c = 2.75
Cost to rent chair = $2.75.
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what do they mean, (Grade 10 real numbers)
X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.
So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.
So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.
Determine the vertex of the graph of the following parabola. f(x)=−(x+1)2−6
The vertex of the graph of the parabola is at the point (-1, -6)
How to find the vertex of the parabola?We know that for any parabola with a vertex at the point (h, k) and a leading coefficient a, can be written in vertex form as:
y = a*(x - h)^2 + k
In this case the parabola is:
f(x) = (-1)*(x + 1)^2 - 6
Comparing this with the general form, we can see that:
h = -1
k = -6
Then the vertex of the parabola is (-1, -6)
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What is the true solution to 2 In en 5x = 2 In 15?
x= 0
x= 3
x= 9
x= 15
The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.
Given,
2 ln e^ ln (5x) = 2 ln (15)
Apply log rule;
logₐ (aᵇ) = b
ln (e^ln (5x)) = ln (5x)
2 ln (5x) = 2 ln (15)
Divide both sides by 2;
2 ln (5x) / 2 = 2 ln (15)/ 2
ln (5x) = ln (15)
For ln (5x) = ln (15), solve for 5x = 15;
That is,
5x = 15
Then,
x = 15/5
So,
x = 3
Check this by substituting it to 2 ln (5x) = 2 ln (15);
x = 3
2 ln (5 × 3) = 2 ln (15)
x = 3 makes this true.
Therefore,
The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.
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Which number is divisible by 5 and 10? I NEED HELP FAST
Answer: Many even numbers are divisible by ten. A simple answer to that is 20. 30 is also, and so is 40. Any number going up by 10 will be divisible by 10 and 5. 10 is also divisible by 10 and 5.
Angles X and Y are supplementary. Angle X measures 127.42°, and angle Y measures (m − 12)°. Find m∠Y. anwsers 115.42° 74.84° 64.58° 52.58°
The measure of angle Y, m ∠Y, is 52.58°. The correct option is the last option 52.58°
Calculating the measure of an angleFrom the question, we are to determine the measure of angle Y.
From the given information,
Angles X and Y are supplementary angles.
NOTE: Supplementary angles are angles that sum up to 180°
Thus,
m ∠X + m ∠Y = 180°
Also,
From the given information,
Angle X measures 127.42°
That is,
m ∠X = 127.42°
Therefore,
127.42° + m ∠Y = 180°
m ∠Y = 180° - 127.42°
m ∠Y = 52.58°
Hence, the measure of the angle is 52.58°
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pls help I don't get the problem
Simplified form is the -(1+sinα).
Given in question,
[tex]cos^{2}[/tex]α/sinα-1
[tex]sin^{2}[/tex]α + [tex]cos^{2}[/tex]α = 1
[tex]cos^{2}[/tex]α = 1 - [tex]sin^{2}[/tex]α
[tex]cos^{2}[/tex]α/sinα-1 = (1 - [tex]sin^{2}[/tex]α ) / (sinα-1)
= (1-sinα)(1+sinα)/(sinα-1)
= (1-sinα)(1+sinα)/-(1-sinα)
= (1+sinα)/-1
= -(1+sinα)
Hence, in simplified form [tex]cos^{2}[/tex]α/sinα-1 = -(1+sinα)
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The point N lies on the segment MP
Find the coordinates of N so that MN is 3/7
of MP.
M(-4,6)
N (?,?
P (17,-22)
The coordinates of N are (5,-6) so that segment MN is 3/7 of MP.
Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).
now we have to find the coordinates of N such that the MN : NP is 3:4 .
We will use the section formula:
The section formula states that:
[tex]{\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}[/tex]
Where the coordinates of the points are given and the ratio in which the points are divided is given.
Now we will substitute the values:
[tex]{\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}[/tex]
Solving we get:
N=(5,-6)
The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.
Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.
Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.
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Help. I'll mark as brainlist. I am always giving brainlist points.
Answer: 18 square unit
Step-by-step explanation:
We can divide the shape into two pieces.
a triangle and a square.
The square is 2*6=12 square unit
and the triangle is 1/2*6*2=6 square unit
So if we sum this up we get the answer
answer = 6+12 = 18 square unit
NO LINKS!! State the Domain and Range for each graph
Both end points are represented by closed circles, it means both points are included.
The graph is restricted between the end points from left to right and between the end point and the highest point from bottom to top.
Domain, the set of possible x- coordinates:
x ∈ [- 2, 6]Range, the set of possible y- coordinates:
y ∈ [- 3, 7]The graph on the rightBoth end points are represented by arrows directed to left and right, it means both ends are indefinite but lines are parallel to the x-axis.
It makes x-values infinite but y-values restricted between the two lines.
Domain, the set of possible x- coordinates:
x ∈ (- ∞, + ∞)Range, the set of possible y- coordinates:
y ∈ [1, 5]Answer:
1. Domain: [-2, 6]
Range: [-3, 7]
2. Domain: (-∞, ∞)
Range: [1, 5]
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1The domain of the function is restricted since the curve has two distince endpoints. As each endpoint is marked by a closed circle, the x-value of the endpoints is included in the domain.
Domain: [-2, 6]The function has a maximum point at (-1, 7) and a minimum point at (6, -3).
Therefore, the range of the function is restricted.
Range: [-3, 7]Question 2As there are arrows at both endpoints of the function, and the function is continuous between the arrowheads, the domain is unrestricted.
Domain: (-∞, ∞)The maximum y-value is y = 5. When x < 1, the line continues indefinitely at y = 5.
The minimum value is y = 1. When x > 1, the line continues indefinitely at y = 1.
Therefore, the range of the function is restricted.
Range: [1, 5]Martina is taxed at a rate of 25% for her federal taxes. Last year, she reduced her taxable income by contributing to a flexible savings plan in the amount of $2,700. If her
wages before the deduction were $68,000, how much did she save in federal taxes by using the FSA?
▸
Answer:
14300
Step-by-step explanation:
this is the answer that I got I hope it works
Saving of Martina in taxes = $675
What is FSA?A flexible spending account (FSA) is a type of savings account, usually for healthcare expenses, that sets aside funds for later use. It is also known as a flexible spending arrangement, is one of a number of tax-advantaged financial accounts, resulting in payroll tax savings.
Given,
Wages of Martina = $68000
Tax rate = 25%
Amount to flexible savings = $2700
Then saving in taxes = $2700 × 25/100
= $675
Hence, Martina saved $675 in taxes using FSA.
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Find an explicit formula for the arithmetic sequence 10,-10,-30,-50,...10,−10,−30,−50,...10, comma, minus, 10, comma, minus, 30, comma, minus, 50, comma, point, point, point. Note: the first term should be \textit{c(1)}c(1)start text, c, left parenthesis, 1, right parenthesis, end text. c(n)=c(n)=c, left parenthesis, n, right parenthesis, equals
An explicit formula for the arithmetic sequence is aₙ = 10 - 20(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 10
Second term, a₂ = -10
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = -10 - 10
Common difference, d = -20
Substituting the parameters into the mathematical expression, we have;
aₙ = 10 + (n - 1)(-20)
aₙ = 10 - 20(n - 1).
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Jillian sells handmade t- Shirts and large purses; each tea shirt costs $15. Each Large purse goes for $59 and the cost of small purses is $32 each. In the first week she sold 4 t-shirts and 3 large purses and 9 small. In the second week she sold another 5 t-shirts, 7 large bags and 4 small ones. Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses. What was the exact amount she made in 3 weeks?
Jillian made the exact amount was $1598 in 3 weeks.
Each t-shirt costs $15.
Each Large purse goes for $59
And the cost of small purses is $32 each.
In the first week, she sold 4 t-shirts and 3 large purses, and 9 small ones.
Her earning in the first week = 4 × $15 + 3 × $59 + 9 × $32 = $525
In the second week, she sold another 5 t-shirts, 7 large bags, and 4 small ones.
Her earning in the second week = 5 × $15 + 7 × $59 + 4 × $32 = $616
Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses.
Her earning in the Last week = 8 × $15 + 3 × $59 + 5 × $32 = $457
The exact amount she made in 3 weeks = $525 + $616 + $457 = $1598
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You have a 64-ounce pitcher of tea.
After you pour as many 7-ounce cups of tea as possible, how much tea will be left
over?
Answer:
You can pour nine 7-ounce cups of tea (63 ounces) and be left with one ounce of tea.
Step-by-step explanation:
Dividing 64 by 7 and finding the remainder.
+83--95 x + 7+72÷-9 what is the answer
Answer:
7.4
Step-by-step explanation:
Not completely sure because that equation is really hard to read. You might have put it in wrong.
Answer:
-95x + 91
Step-by-step explanation:
72/9 = 8
83 - 95x + 8
91 - 95x or -95x + 91
Which is bigger 21.17 or 2.117
Answer:
21.17
Step-by-step explanation:
If you were to round each number to the nearest whole number you would get :
21.17 ⇒ 21
2.117 ⇒ 2
Now the question is , which is bigger 21 or 2?
Now that is a very straightforward answer (21 in case your still lost)
Hope this helped and have a good day
**BRAINLIEST** TO WHOEVER ANSWERS CORRECTLY! PLEASE HELP ME!
- During a certain time of year, the daily temperature in a certain city, in degrees Celsius follows a periodic pattern. The graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day.
- Write an equation for the graph below in terms of Y (temperature in degrees Celsius) and T (time in hours) to represent the given context.
ANSWER SHOULD BE IN THIS FORM
y = ( a ) sin ( b ) (t - h) + k
GRAPH IS GIVEN BELOW PLEASE HELP ME OUT!
Answer:
y = A cos B(x - C) + D
Step-by-step explanation:
The equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -
y = √180 sin (π/12.5)(t - 25) + 12
What is the general equation of a sinusoidal wave?The sinusoidal wave is of the form -
y{x} = A sin (ωt - kx + Ф)
Given is that during a certain time of year, the daily temperature in a certain city (in degrees Celsius) follows a periodic pattern.
We can write the amplitude as -
A = √(18 - 12)² + (13 - 1)²
A = √(36 + 144)
A = √180 ... { 1 }
{K} = 12 ... { 2 }
The time taken to complete one complete wave is 25 hours. So, we can write -
{T} = 25 ... { 3 }
ω = 2π/T = 2π/25 = π/12.5
{ω} = π/12.5 ... { 4 }
So, we can write the equation as -
y = √180 sin (π/12.5)(t - 25) + 12
Therefore, the equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -
y = √180 sin (π/12.5)(t - 25) + 12
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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Tough question help asap
The function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Given,
The function; f(x) = 9 × 4ˣ
The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. coordinate's
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
We have to find the following function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Learn more about functions here;
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Find the slope of this line.make it a fraction.
Answer:
[tex]\frac{-2}{3}[/tex]
Step-by-step explanation:
to find the slope of linear line, you need two points. It does not matter which pints you use. I am going to use (0,5) and (3,3) The slope is the change in y over the change is x. Our y values are 3 and 5. Our x values are 3 and 0
[tex]\frac{3-5}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex]
Consider the polynomial function []
p
given by p(x)=5x3+8x2−3x+1
A(x)
. Evaluate the function at x=−2
x
.
See question in screenshot below:
Answer:
1440/17 degrees (approximately 84.7059 degrees)
19π/9 radians ---> or π * 19/9 radians
Step-by-step explanation:
The conversion factor for radians to degrees is 180/π
8π/17 * 180/π = 1440/17 degrees (approximately 84.7059 degrees)
The conversion factor for degrees to radians is π/180
380 * π/180 = 380π/180 = 19π/9 radians
Bob invested his savings in two investment funds. The amount he invested in Fund A was 3 times as much as the amount he invested in Fund B. Fund A returned a 5% profit and Fund B returned a 7% profit. How much did he invest in Fund B, if the total profit from the two funds together was $2200?
The amount that he invested in Fund B if the total profit from the two funds together was $2200 is $8,800.
How to find the amount invested?Let x represent the amount invested in Fund B
Let 3x represent the amount invested in Fund A
Hence,
.07x + .05(3x) = 2200
.07x + .15x = 2200
.25x = 2200
Divide both side by .25x
x = 2200/.25
x = $8,800 (invested in Fund B)
Fund A:
3x = 3(8,800)
3x = $26,400 (Invested in Fund A)
Therefore $8800 was invested in Fund B.
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find the difference in centimetres between 5m and 465cm
Answer:
35 cm
Step-by-step explanation:
A taxi ride cost a customer a total of \$13.73$13.73dollar sign, 13, point, 73, which included 4\%4%4, percent sales tax and then a \$1$1dollar sign, 1 surcharge. What was the subtotal before the surcharge and sales tax?
The subtotal before the surcharge and sales tax is $12.2
How to determine the subtotal amount?In this question, we have the following parameters
Total = $13.73
Sales tax = 4%
Surcharge = $1
The above parameters imply that:
Total = Subtotal * (1 + sales tax) + Surcharge
Substitute the known values in the above equation, so, we have the following representation
13.73 = Subtotal * (1 + 4%) + 1
This gives
Subtotal * (1 + 4%) = 12.73
Divide both sides by 1.04
Subtotal = 12.2
Hence, the subtotal is $12.2
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Apply the properties of operations to multiply the expression
The properties of operations to multiply the expression are commutative property, associative property, and distributive property.
Let us understand the properties of operations to multiplication:
The foundation of arithmetic is the Properties of Operations; we use them when performing computations and recalling basic facts.
There are basically three properties of operations to multiplication which are:
Commutative Property: The commutative property of multiplication states that the order in which values are multiplied does not matter and will result in the same answer. That is to say: a * b = b * aAssociative Property: The associative property of multiplication states that when three or more numbers are multiplied, the order in which the multiplication occurs has no effect on the answer. That is to say: (a * b) * c = a * (b * c)Distributive Property: Students are asked to create two groups of six (2 x 6) using connecting cubes and to locate two hidden facts inside the 2 x 6 such as 2 x 3 and 2 x 3. That is: 2 x 6 = 2 x 3 + 2 x 3.Thus, the properties of operations to multiply the expression are commutative property, associative property, and distributive property.
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I'm taking the math pert tomorrow I've failed it 2 times already I've been studying nonstop for the past two weeks and still feel like I'm going to fail any tips on how to pass ?
help pleaseeeeee !!!
Answer:
[tex]\sqrt{6}, -\sqrt{6}[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+3x^2-6x-18 \\ \\ =x^2(x+3)-6(x+3) \\ \\ =(x^2-6)(x+3) \\ \\ \implies (x^2-6)(x+3)=0 \\ \\ x=\pm \sqrt{6}, -3[/tex]
Evaluate for A(12). Round your answer to the nearest hundredth.
The value the function A(12) is 2960.94
How to evaluate the function?From the question, we have the following function definition that can be used in our computation:
A(t) = 710e⁰°¹¹⁹⁺
To calculate the function A(12), we set t to 12
i.e. calculate A(t) when t = 12
This equation becomes
A(12) = 710e⁰°¹¹⁹ˣ¹²
Evaluate the products
A(12) = 710e¹°⁴²⁸
Evaluate the exponents
A(12) = 2960.94
Hence, the solution is 2960.94
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Solve the inequality.
Question 1
3y≤−9
The solution is
The solution of the given inequality is y ≤ -3.
The given inequality is -
3y ≤ −9
We have to solve this given inequality.
Now, we have the inequality as -
3y ≤ −9
=> y ≤ -3
Thus, the solution of the given inequality is y ≤ -3.
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