Solution:
Given:
[tex]\text{Parabola with vertex (2,-3) that open downwards}[/tex]The equation of a parabola in vertex form is given by;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ \text{where;} \\ (h,k)\text{ is the vertex} \\ \\ \text{Hence,} \\ h=2 \\ k=-3 \end{gathered}[/tex]Hence, the equation of the parabola is;
[tex]\begin{gathered} y=a(x-2)^2-3 \\ \\ \text{For the parabola to open downwards, then;} \\ a<0 \\ a\text{ must be negative} \end{gathered}[/tex]Hence, from the options, the equations that have a as negative and in the form gotten above will be selected.
Therefore, the equations of a parabola with vertex (2,-3) that open downwards are;
[tex]\begin{gathered} y=-2(x-2)^2-3 \\ \\ y=-(x-2)^2-3 \end{gathered}[/tex]The monthly mortgage payment on the Flynn's home is $634.8. Additionally, they pay $1,785.13 in annual real estate taxes and $726 per year in homeowner's insurance.
What is the total amount of their entire monthly payment?
State your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
Answer: 695.30
Step-by-step explanation: We know that 634.8 is what the monthly mortgage is, then we use the value of $726 and divide it by 12 which represents the 12 months in a year. So 726 ÷ 12 = 60.5 therefore monthly he will additionally need to pay that amount. I don't think the annual real estate taxes are going to be used for this problem. So after this, we do the following equation. 634.8 + 60.5 = 695.3. We round this value to the nearest cent and we get 695.30. When the digit to the right is less than 5 we round toward 0... 695.3 was rounded down toward zero to 695.30
Analyze the diagram. Which quadrilateral is a kite?
Quadrilateral N M O P is shown. Sides P N and N M are congruent.
Quadrilateral A B C D is shown. Sides A D and D C are congruent. Sides A B and B C are congruent.
Quadrilateral N M O P is shown. All sides are different lengths.
Answer: in the picture
Answer:
Quadrilateral ABCD
Step-by-step explanation:
Geometry ?Use the photo to help me solveTriangle DEF is shown. What is the coordinate of D if triangle D E F is created by dilating DEF with a scale of 0.5 about the origin
Since the scaling factor of the dilation (0.5) is fewer than 1, it shrinks (make smaller) the triangle around the origin (zero). Intuitively, the dilation is getting the points of the triangle closer to zero (in a way that preserves the shape of the triangle).
Formally, to know the coordinates of a point of the triangle after the dilation, we just need to multiply the original coordinates of the point by the scaling factor (this works for the dilation is around zero).
The original coordinates of D are
[tex](3,0)\text{.}[/tex]Multiplying them by the scale factor, we get
[tex]0.5\cdot(3,0)=(0.5\cdot3,0.5\cdot0)=(1.5,0)\text{.}[/tex]AnswerThe coordinates of D after the given dilation is
[tex](1.5,0)\text{.}[/tex]find they distance between poind A nada point B
We get that the distance is
[tex]d=\sqrt[]{(5-2)^2+(5-1)^2}=\sqrt[]{9+16}=\sqrt[]{25}=5[/tex]so the answer is 5
I’m confused on this drag and drop assignment can someone please help me out? I’ll give brainliest
The most appropriate choice for the similarity of figures will be given by:
(A) ZY = 20(B) x = 12(C) 22.5 cm on the drawing represented 9 miles on the ground.What is the similarity of the figures?Two figures are said to be similar if the corresponding angles are equal and the corresponding sides are in the same ratio.So,
(A) HIJK∼WXYZ [Given].
HJ/WX = KJ/ZY6/5 = 24/ZY6 × ZY = 24 × 5ZY = 24×5/6ZY = 20(B) The two triangles are similar [Given].
2/2+4.5 = x/396.5x = 39×2x = 39×2/6.5x = 12(C) 5cm on the drawing represented 2 miles on the ground.
Let 22.5 cm on the drawing represent x miles on the ground.
The problem:
5/22.5 = 2/x5x = 22.5 × 25x = 45x = 45/5x = 9 miles22.5 cm on the drawing represented 9 miles on the ground.
Therefore, the most appropriate choice for the similarity of figures will be given by:
(A) ZY = 20(B) x = 12(C) 22.5 cm on the drawing represented 9 miles on the ground.To learn more about the similarity of figures, refer to the link:
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Calculate the final price. Round all answers to the hundredths place and make sure to write your answer in the form of $12.34. Book: $14.99. Discount: 15%
We will determine the final price as follows:
[tex]p=14.99-(14.99)(0.15)\Rightarrow p\approx12.74[/tex]So, the final price is approximately $12.74.
Yep I am watching the last one on my birthday
Given the functions
[tex]\begin{gathered} f(x)=2x-10 \\ g(x)=2x^2+12x+18 \\ h(x)=2x^3-8x^2-10x \end{gathered}[/tex]The graph of the given functions
From the graph of the functions above, it can be seen that each of the functions have the same domain
[tex]-\inftyThus, the domain is the same for each function.The answer is the first option.
You flip a coin twice what is the probability of getting tails and then getting tails
The probability a single event A occurs is:
[tex]P(A)=\frac{\text{ number of favorable outcomes to A}}{\text{ number of total outcomes}}[/tex]The probability P two consecutive events A and B occurs is:
[tex]P=P(A)*P(B)[/tex]So, let's consider the probability of the first event: getting tails.
Favorable outcomes: Tail
Number of favorable outcomes: 1
Total outcomes: Tail, Head
Number of total outcomes: 2
So, the probability of getting a tail is:
[tex]P(A)=\frac{1}{2}[/tex]So, let's consider the probability of the second event: getting tails in the second time.
Favorable outcomes: Tail
Number of favorable outcomes: 1
Total outcomes: Tail, Head
Number of total outcomes: 2
So, the probability of getting a tail is:
[tex]P(B)=\frac{1}{2}[/tex]Finally, let's calculate the probability of getting a tail twice.
[tex]\begin{gathered} P=P(A)*P(B) \\ P=\frac{1}{2}*\frac{1}{2} \\ P=\frac{1}{4} \end{gathered}[/tex]Answer: The probability is 1/4.
Decide which of the two given prices is the better deal and explain why.
You can buy shampoo in a 6-ounce bottle for $3.19 or in a 15-ounce bottle for $11.99
A line has a slope of 2 and passes through the point ( - 8 , 1 ). Which of the following represents the equation for this line?
A) y = 2x - 7
B) y = 2x + 8
C) y = 2x + 9
D) y = 2x + 17
Answer:
D
Step-by-step explanation:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since line has slope of 2, equation is y = 2x + c.
Substitute (-8, 1) into the equation to find c
1 = 2(-8) + c
c = 17
Hence, equation of line is y = 2x + 17.
The correct answer is [D]
Hence, the equation of line is y = 2x + 17.
What is slope?Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical.
If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.The slope of a line is 0 if it is horizontal. This function is constant.The slope is unknown if a line is vertical.Y = mx + c, where m is the slope and c is the y-intercept, is the equation for a line.
Since the line has slope of 2, equation is y = 2x + c.
Substitute (-8, 1) into equation to find c
1 = 2(-8) + c
c = 17
Hence, the equation of line is y = 2x + 17.
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Select the correct operator for the following exponential expression.(-2)^4 ? 2^4 A. C. =
solve each of the expressions
[tex](2)^4=2\cdot2\cdot2\cdot2=16[/tex][tex](-2)^4=(-2)\cdot(-2)\cdot(-2)\cdot(-2)=16[/tex]the correct operator is =.
The diameter of Jupiter is about 1.43•10^5km. The diameter of the Earth is about 12,700km. About how many times greater is the diameter of Jupiter that the diameter of Earth
The diameter of the Earth is 11.3 times less than the diameter of the Jupiter
Ratio and proportionsFractions are written as a ratio of two integers. Given the following parameters;
Diameter of Jupiter = 1.43•10^5km
Diameter of Earth = 1.27 * 10^4km
Find the ratio
Ratio = Jupiter/Earth
Ratio = 1.43•10^5/1.27*10^4
Ratio = 1.13 * 10^1
Ratio = 11.3
Jupiter = 11.3 of Earth
This shows that the diameter of Jupiter if 11.3 times greater than Earth.
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Which expression evaluates to 2048?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
The expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.
What is meant by exponent rule?Exponent rules include: Rule of the product of powers: When multiplying like bases, add the powers together. Rule of the quotient of powers: When splitting like bases, take the powers out. Power of powers rule: When increasing a power by another exponent, multiply all the powers together.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let the value be 2048
[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex]
simplifying the above expression we get
[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3=512 \\[/tex]
[tex]$&=512\left(\frac{1}{2^{-1}}\right)^2[/tex]
By using exponent rule, we get
[tex]$&\left(\frac{1}{2^{-1}}\right)^2=\frac{1^2}{\left(2^{-1}\right)^2} \\[/tex]
[tex]$&=512 \cdot \frac{1^2}{\left(2^{-1}\right)^2}[/tex]
1² = 1
[tex]$&=512 \cdot \frac{1}{\left(2^{-1}\right)^2}[/tex]
[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]
[tex]$=512 \cdot \frac{1}{\frac{1}{4}}$$[/tex]
[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]
[tex]$=512 \cdot \frac{1}{\frac{1}{4}}[/tex]
[tex]$&\frac{1}{\frac{1}{4}}=4 \\\pi[/tex]
= 512 × 4
= 2048
By simplifying the expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.
Therefore, the correct answer is option (b).
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What is the area of triangle ADC is ? Square units?
Given:
The triangle ADC is formed by reflecting the triangle ABC across the line segment AC
So, the triangles ABC and ADC are congruent
The area of the triangle ADC = Area of the triangle ABC
The area of the triangle = 1/2 * base * height
Base = AC = 4 units
Height = BE = 3 units
So, the area will be as follows:
[tex]Area=\frac{1}{2}*AC*BE=\frac{1}{2}*4*3=6[/tex]So, the answer will be:
Area of the triangle ADC is 6 square units
the formula for the volume of a cylinder is V=πr²h A cylinder has a volume of 300p feet³ and a radius of 5 feet (A) Solve the formula V= πr²h for h (B) Find the height of the cylinder
A) To solve the formula for h:
1. Divide both sides of the equation into π*r²:
[tex]\begin{gathered} \frac{V}{\pi\cdot r^2}=\frac{\pi\cdot r^2\cdot h}{\pi\cdot r^2} \\ \\ \frac{V}{\pi\cdot r^2}=h \end{gathered}[/tex]B) You have the next data:
V=300πfeet³
r=5feet
Substitute those values in the formula you get in A) and calculate the h:
[tex]\begin{gathered} h=\frac{300\pi\cdot ft^3}{\pi\cdot(5ft)^2} \\ \\ h=\frac{300ft^3}{25ft^2}=12ft \end{gathered}[/tex]Then, the height of the cylinder is 12 feetWhat is the value of the following sum: 1+2+3+…+397+398+399+400?
Answer:
80,200
Step-by-step explanation:
There is a formula for the sum of a series of numbers from a_1 to a_n.
S = (a_n * a_n+1)/2
This formula means: multiply the last number of the series by what would be the next number, and divide by 2.
The last number you have is 400. The next number would be 401.
Multiply 400 by 401 and divide by 2. That is the sum of the 400 numbers.
S = (401 * 402)/2
S = 160400/2
S = 80200
Answer: The sum is 80,200
Here's a way to understand the formula.
You are adding 400 numbers, from 1 to 400.
Write the first 200 numbers on a line:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... 198 199 200
Now write the next 200 numbers, from 201 to 400 under these numbers, but start from 400 and go down 1 each number to the right.
You end up with these two lines:
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
Now add every two numbers in the same column.
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
------------------------------------------------------------------------------------------------------
401 401 401 401 401 401 401 401 401 ... 401 401 401
Now you have 200 times the number 401.
200 * 401 = 80,200
A person has a rectangular board 14 inches by 18 inches around which she wants to put a uniform border of shells. If she has enough shells for a border whose area is 320 square inches, determine the width of the border.
The width of the border will be 8 inches.
In the given question, it is stated that a rectangular board has dimensions of 18*14 around which a person has to put a border of shells. If there are enough shells for the border of an area of 320 square inches, we need to find out the Width of the border.
Firstly, we know the Area of Rectangle is l*b => Length*Breadth
So, now we calculate the area of the board with dimensions l = 18 and b = 14
=> A₁ = l*b
=> A₁ = 18*14
=> A₁ = 252 square inches
We get the Area of the Board as 252 Square inches.
Now, there are shells enough to cover a border area of 320 square inches.
So, the Board and Border area will be A₁ + A, where A₁ and A are the areas of the Board and border respectively.
So, Total Area = 252 + 320
Total = 572 Square inches.
Now, let 'w' be the width of the border. Then the dimensions for the board will be
l = (18 + w)
b = (14 + w)
Using the formula for the Area of the rectangle, we get
=> Total = l * b
=> Total = (18 + w)*(14 + w)
=> 572 = w² + 32m + 252
=> w² + 32m - 320 = 0
=> w² + 40w -8w -320
=> w(w + 40) -8(w + 40)
=> (w+40) (w-8)
We get factors as w = -40 and 8
Since Width can not be negative quantity, width w will be 8 inches.
Hence, the width will be 8 inches for the border.
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Find the coordinates of the vertex of the following parabola algebraically. Writer answer as an (x,y) point y=-x² - 7
The expression we have is:
[tex]y=-x^2-7[/tex]We need to compare this equation of our parabola, with the general equation of a parabola in vertex form:
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex of the parabola, and a indicates if the parabola opens up or opens down (if a is positive the parabola opens up, and if a is negative the parabola opens down).
We take our equation:
[tex]y=-x^2-7[/tex]And we arrange the terms so that it looks like the vertex form:
[tex]y=(-1)(x-0)^2+(-7)[/tex]And we can find the values of a, h, and k:
[tex]\begin{gathered} a=-1 \\ h=0 \\ k=-7 \end{gathered}[/tex]We only need h and k for the vertex:
[tex](h,k)=(0,-7)[/tex]Answer: the vertex is at (0,-7)
There are 8 1/2 cups of fruit punch shared equally among 4 friends. How many does each friend get?
Answer:
17/8 or 2 and 1/8 cups
Step-by-step explanation:
turn the 8 and 1/2 into one fraction :
17/2
then divide that by 4:
17/8
2. A ladder rises 20 feet for every horizontal change of 4 feet. What is the slope of the ladder?A. O 5C. O 20D.OChoose
The slope is defined as rise/run - in other words, for every step you take horizontally, how many steps you should take vertically to get to a point on the same line.
In our case, the ladder rises 20 feet for every horizontal change of 4 feet; therefore, the slope is
[tex]\frac{\text{rise}}{\text{run}}=\frac{20ft}{4ft}[/tex]dividing 30 ft by 4 ft gives 5; therefore,
[tex]\frac{\text{rise}}{\text{run}}=5.[/tex]Hence, the correct answer to choose is A. 5.
I need help with unit rate fractions pls try to explain very very easily and well and answer quickly i gave an example
To find out the unit rate
Divide cups of sugar by the teaspoon of vanilla
so
[tex]\frac{2}{3}\colon2=\frac{2}{3*2}=\frac{1}{3}[/tex]The answer is 1/3
Option A
7 1/5 - 6 2/5= ?
A. 1 4/5
B. 4/5
C. 1 1/5
D. 13 3/5
Hello!
So, we are given the following to solve:
[tex]7\frac{1}{5} -6\frac{2}{5}[/tex]
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form of Solution:
[tex]\frac{4}{5}[/tex]
Hence, the correct choice is B. Hope this helps!
Answer:
B. 4/5
Step-by-step explanation:
7 1/5= to 36/5
6 2/5= to 32/5
subtract both numbers on top and keep the bottom, which equals to 4/5
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The solution of the given equation w.r.t m is m = 3 ,i.e., option A
What are Algebraic equations?With one exception, algebraic equations are essentially algebraic expressions.
An = sign is required in all algebraic equations.
No matter what kind of equation it is, all equations use the = sign.
The next topic is algebraic expression, which lacks the operators =,,, >, and.
To put it simply, there is no comparison between two terms in an algebraic statement.
Algebraic expressions frequently use terms like polynomial and square root.
So you now recognize the distinction between the two?
1) An algebraic equation has the symbol =, and 2) an algebraic expression lacks any comparison symbols (such as > and =).
As per the question:
[tex]6\frac{1}{9} + 3\frac{1}{3} =28\frac{1}{3}[/tex]
55/9 + 10/3 = 85/3
(55m+30m)/9 = 85/3
85m/9 = 85/3
85m = (85*9)/3
85m = 85*3
m = (85*3)/85
∴ m = 3
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Equation 1: A [-4x+7y=4]
Equation 2: B [3x-3y=6]
Think about using the elimination method to solve this system.
Question 1: If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be ______ and the value of B must be ______.
Question 2: If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be ______ and the value of B must be _____.
Using the elimination method, the value of A and B must 3 and 4 respectively to eliminate x in the equation. The value of A and B must be 3 and 7 respectively to eliminate y.
How to solve system of equation?System of equation can be solved using elimination method, substitution method of graphical method.
But we are asked to use elimination method.
Therefore, the system of equation are as follows:
Equation 1: A [-4x + 7y = 4]
Equation 2: B [3x - 3y = 6]
Therefore,
If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 4.
If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 7.
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What is the x-intercept?
Answer:2.5
Step-by-step explanation:
l
I
------------------ x intersept
I
I
y intersept
Money set aside to pay for small, unforeseen expenses is called a(n) _____.
A.
down payment
B.
emergency fund
C.
mutual fund
D.
equity fund
Answer:
B. Emergency fund.
Step-by-step explanation:
What is the arc length of CD in the circle below?
Solution
[tex]\begin{gathered} \theta=35^0 \\ r=8ft \end{gathered}[/tex]The formula for arc length is;
[tex]\begin{gathered} A=\frac{\theta}{360}\times2\pi r \\ \\ \Rightarrow A=\frac{35}{360}\times2\pi\times8=4.88\text{ feet} \end{gathered}[/tex]choose the equation that could be used to find two consecutive integers whose sum is 67.
d) n + (n +1) = 67
1) Let's call the first number as n, and its consecutive as n +1
Then we can write:
n + (n +1) = 67
n +n +1 = 67
2n +1 = 67
2n = 66
n= 33
and n+1 = 34
2) Hence, the answer is n + (n +1) = 67
If f(x) = 1 x - 2 v
x-2, what is f¹(x)?
Answer:
f¯¹(x) =9x+18, for the pictorial(image) question
what is the send question is it asking derivative or inverse
If it is inverse f¯¹(x)=-x-2 as it is
Or if it is derivative f'(x)=-1
Step-by-step explanation:
For the image question f(x)=1/9x-2,f¯¹(x)=?
f(x)=1/9x-2............given
y=1/9x-2................swapping f(x) by y to Easily write
x=1/9y-2................interchanging x and y
1/9y-2=x................changeling side of equation
9(1/9y-2)=(x)9.......multiplying both sides by 9 to override the fraction on the right side
y-18=9x
y=9x-18.................Return to where it were
f¯¹(x)=9x+18..........swap back f¯¹(x) in the y
For the question f(x)=-x-2,f¯¹(x)=?
following the ☝️ arrangement
y=-x-2
x=-y-2
-y-2=x
-y=x+2
y=-x-2
f¯¹(x)=-x-2
Solve |3x + 7 = 4x for x.A) Infinitely many solutionsB) 7 and -7C) No solutionOD) -7 or 1
The given equation is
[tex]\lvert{3x+7}\rvert=4x[/tex]We will solve it in this way
[tex]3x+7=4x,3x+7=-4x[/tex]For the 1st equation
[tex]3x+7=4x[/tex]Subtract 7 from each side
[tex]\begin{gathered} 3x+7-7=4x-7 \\ 3x=4x-7 \end{gathered}[/tex]Subtract 4x from both sides
[tex]\begin{gathered} 3x-4x=4x-4x-7 \\ -x=-7 \\ x=7 \end{gathered}[/tex]For the 2nd equation
[tex]3x+7=-4x[/tex]Subtract 3x from both sides
[tex]\begin{gathered} 3x-3x+7=-4x-3x \\ 7=-7x \end{gathered}[/tex]Divide both sides by -7
[tex]\begin{gathered} \frac{7}{-7}=\frac{-7x}{-7} \\ -1=x \end{gathered}[/tex]The solutions are
7, -1
The answer should be B