Answer:
[tex]A=3[/tex]
Explanation: We are given two points, P1 is vertex and P2 is another point on the parabola:
[tex]\begin{gathered} P_1(2,-4) \\ P_2(3,-1) \end{gathered}[/tex]The general form of the equation of a parabola is:
[tex]y(x)=A(x\pm B)^2+C[/tex]Where A is the Coefficient of the parabola function which is responsible for compression and stretch, likewise B is responsible for the translation along the x-axis and C is responsible for translation along the y-axis.
We know that our function is translated 2 units towards the right and 4 units downwards:
Therefore:
[tex]\begin{gathered} B=-2 \\ C=-4 \end{gathered}[/tex]And this turns the parabola equation into:
[tex]y(x)=A(x-2)^2-4[/tex]Using P2 we can find the constant-coefficient as:
[tex]\begin{gathered} y(x)=A(x-2)^2-4_{} \\ P_2(3,-1) \\ \\ \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(3)=A(3-2)^2-4=-1\rightarrow A-4=-1 \\ \because\rightarrow \\ A=3 \end{gathered}[/tex]Which graph best represent a line perpendicular to the line of the equation y= -1/3x - 7 ?
The equation of the given line is
[tex]y=-\frac{1}{3}x-7[/tex]Where: The slope is -1/3
Perpendicular lines have additive reciprocal slopes which means if the slope of one of them is m, then the slope of the other is -1/m
Then the slope of the perpendicular line to the given line is 3
So, we have to look for the graph of positive slope
The graphs of A and D have positive slopes because the directions of the lines are increasing from left to right
Then we have to find the slope of each line to find the correct choice
Since the slope of the line is 3, then the y part increases 3 units for 1 part increases of x
We can see that in graph A
The answer is A
which expressions are equivalent to 5(–2k – 3) + 2k?a) (-5•3)-8kb) -15c) none of em
$72 for 7/1/2 hours Part A Find the unit rate. How much would it be for 40 hours?
We have that for seven and a half hours, you get 72$, then we have the following rule of three:
[tex]\begin{gathered} 72\rightarrow7\frac{1}{2}hours \\ x\rightarrow1hour \end{gathered}[/tex]then we have that:
[tex]\begin{gathered} x=\frac{72\cdot1}{7\frac{1}{2}}=\frac{72}{\frac{15}{2}}=\frac{144}{15}=9.6 \\ x=9.6 \end{gathered}[/tex]therefore, for each hour, you get $9.6
So, for 40 hours we have:
[tex]40\cdot9.6=384[/tex]finally, we have that for 40 hours you get $384
Please see the photo below. Please draw the photo on a piece of paper or computer/laptop. Thank you.
The Solution:
Given:
Required:
To construct a bisector of each of the given lines.
Steps:
1. Take your compass and put the pin on one end of the line, and then expand the compass to at least more than half the length of the line ( but not greater than the length of the line).
2. Make an arc on the upper side and the lower side of the middle of the line, and then repeat the process when you take the pin mouth of the compass to the other end of the given line.
3. Connect the pairs of intersections of the arcs to make a straight line.
The straight is the required bisector.
Below is an example with the first line:
The midpoint of AB is M(6,1). If the coordinates of A are (4,8), what are the coordinates of B?
Midpoint : (6,1)
Point A : (4,8)
Point B (xb,by)
Midpoint (xm, my)=( x1+x2) /2 , ( y1+y2)/2
So:
xm= 6 = (4+xb) /2
6 = (4+xb) /2
Solve for xb
6 x 2 = 4+ xb
12 = 4+xb
12-4 = xb
8 = xb
For Yb:
my= 1 = (8+yb) /2
1 = (8+yb) /2
Solve for yb
1(2) = 8+yb
2 = 8+ yb
2-8 = yb
-6 = yb
Coordinate of B = (xb,yb) = (8,-6)
The graph is shifted 1 unit down and 4 units left
To answer this question, we need to remember the rules of transformation of functions, these rules are shown below:
Using these rules, we have that the equation that represents the new graph is:
[tex]y=\sqrt[3]{x+4}-1[/tex]While playing golf, Maurice hits the golf ball and it travels 361.87 feet. Assume the golf ball travels the same distance everyTime they hit it. Estimate the total amount of distance the ball will travel after 15 hits.Round the distance traveled each time the golf ball was hit to the nearest ten feet before calculating
Answer:
5400 feet
Explanation:
The distance the ball travels each time it was hit = 361.87 feet
First, this distance is rounded to the nearest ten feet.
[tex]361.87\approx360\:feet[/tex]Multiply 360 by 15 hits:
[tex]360\times15=5400\:feet[/tex]The total amount of distance the ball will travel after 15 hits is 5400 feet.
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated usi Xthe origin as the center of dilation.Which rule could represent this dilation?
The rule for a dilation by a factor of k using the origin as the center of dilation, is:
[tex](x,y)\rightarrow(kx,ky)[/tex]In the options A and B, additions and substractions are involved. Then, they cannot be the rule of a dilation about the origin.
In the options C and D, we can see that both are dilations about the origin. The factor used in the option C is 5/4, while the factor used in the option D is 0.9.
Nevertheless, notice that 5/4 is greater than 1 and 0.9 is smaller than 1.
Then, the dilation from option C would produce a bigger polygon, while the dilation from option D will produce a smaller polygon.
Since the polygon must be a smaller one, then the rule that could represent this dilation is:
[tex](x,y)\rightarrow(0.9x,0.9y)[/tex]Which corresponds to option D.
What is the difference between the decimal forms of rational numbers and the decimal forms of irrational numbers?
The decimal forms of rational numbers can be finite, i.e. have a non infinite number of digits. In case they have infinite digits then these are periodic. This means that there's a patron of digits that is repeated infinitely.
Irrational numbers on the other hand can only have infinite digits on their decimal form and they are not periodic.
Multiply. -8. -9/3 . 2/-5Write your answer in simplest form.
To multiply these numbers, the first step is to writhe "-8" as an improper fraction, to do so, divide it by 1
[tex](-\frac{8}{1})\cdot(-\frac{9}{3})\cdot(-\frac{2}{5})[/tex]Next is to solve the multiplication, to do so, first multiply the first two terms of the multiplication:
[tex](-\frac{8}{1})\cdot(-\frac{9}{3})[/tex]The multiplication is between two negative numbers, when you multiply two negative numbers, the minus signs cancel each other and turn into a positive value, this is called "double-negative"
[tex](-\frac{8}{1})\cdot(-\frac{9}{3})=\frac{8\cdot9}{1\cdot3}=\frac{72}{3}[/tex]Next multiply the result by the third fraction -2/5
This time you are multiplying a positive and a negative number, so the result of the calculation will be negative
[tex]\frac{72}{3}\cdot(-\frac{2}{5})=-\frac{72\cdot2}{3\cdot5}=-\frac{144}{15}[/tex]Final step is to simplify the result, both 144 and 15 are divisible by 3, so divide the numerator and denominator by 3 to simplify the result to the simplest form:
[tex]-\frac{144\div3}{15\div3}=-\frac{48}{5}[/tex]The worktop is to be covered with square tiles each measuring 4cm by 4cm. How many tiles are needed to cover the worktop.
PLease help and show clear explaination and answer now
ITS FOR LEVEL 2 GET DIFFERENT ANSWERS
1900 tiles are needed to cover the worktop.
From the question, we have
The surface area of the worktop is 3.04m squared.
The worktop is to be covered with square tiles each measuring 4cm by 4cm.
Number of tiles = (3.04*10000)/(4*4)
=1900
Multiplication:
To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
Complete question:
The worktop is to be covered with square tiles, each measuring 4 cm by 4 cm. How many tiles are needed to cover the worktop?The surface area of the worktop is 3.04m squared.
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Which of the following best represents the graph of a line with an undefined slope?
we know that
The slope is undefined, when we have a vertical line
therefore
the answer is the option 4 (vertical line)A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach?A. 14,2 feetB. 7 feetc. 28/2 feetD. 7,2 feet
Answer: The problem can be visualized with the help of the following diagram:
Therefore the building height can be determined by using the pythagorean theorem, the steps are as follows:
[tex]\begin{gathered} x^2+x^2=14^2 \\ \\ 2x^2=14^2 \\ \\ x=\sqrt{\frac{14^2}{2}}=\sqrt{98} \\ \\ h=x=9.899ft \\ \\ \end{gathered}[/tex]Therefore the ladder reaches 9.9ft up the wall.
A glider files 8 miles south from the airport and then 15 miles east. Then it files in a straight line back to the airport. What was the distance of the glider's last leg back to the airport ?
The schematic diagram below represents the path followed by the glider,
The point A represents the location of the airport.
Observe that the path of the glider forms a right angled triangle ABC.
So the hypotenuse AC can be calculated by using Pythagoras Theorem as,
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2=(8)^2+(15)^2 \\ AC^2=64+225 \\ AC^2=289 \\ AC^2=17^2 \\ AC=17 \end{gathered}[/tex]Thus, the distance of the glider's last leg back to the airport is 17 miles.
So the second option is the correct choice.
complete the input output table for the linear equation y=5x+1
We have the next linear equation y=5x+1
For the first row,
y=11
we substitute the value in the equation
11=5x+1
we clear x in order to know the value of x
5x=11-1
x=10/5
x=2
For the second row
x=4
we substitute the value in the equation
y=5(4)+1
y=20+1
y=21
For the third row
y=31
we substitute the value in the equation
31=5x+1
5x=31-1
5x=30
x=6
For the fourth row
x=8
we substitute the value in the equation
y=5(8)+1
y=40+1
y=41
The table of the equation
x y
2 11
4 21
6 31
8 41
x+2x+5=x+19please help
To solve this equation
Step 1:
x + 2x + 5 = + 19
Write an equation for a line going through the point (-5, -10) that is parallel to theline 1/5x-1/6y = 7.
Two lines are parallel if they have the same slope. In order to better visualize the slope of the line we will express it in the slope-intercept form, which is done below:
[tex]\begin{gathered} \frac{1}{5}x-\frac{1}{6}y\text{ = 7} \\ \frac{1}{5}x-7=\frac{1}{6}y \\ \frac{1}{6}y\text{ = }\frac{1}{5}x-7 \\ y\text{ = }\frac{6}{5}x\text{ - 42} \end{gathered}[/tex]We now know that the slope of the line is 6/5, because in this form the slope is always the number that is multiplying the "x" variable. So we need to find a line of the type:
[tex]h(x)\text{ = }\frac{6}{5}x+b[/tex]Therefore the only needed variable is "b", which we can find by applying the known point (-5, -10).
[tex]\begin{gathered} -10\text{ = }\frac{6}{5}\cdot(-5)\text{ + b} \\ -10=-6+b \\ b=-10+6 \\ b=-4 \end{gathered}[/tex]The expression of the line is then:
[tex]h(x)\text{ = }\frac{6}{5}x-4[/tex]Convert each equation to slope-intercept form. Then label the slope & y-intercept.
C. The equation is
[tex]4x-6y=18[/tex]An equation is in slope-intercept form if it is in the form
[tex]y=mx+c[/tex]Expressing the given equation in slope-intercept
This gives
[tex]\begin{gathered} 4x-6y=18 \\ -6y=-4x+18 \end{gathered}[/tex]Divide through by -6
This gives
[tex]\begin{gathered} -\frac{6y}{-6}=-\frac{4x}{-6}+\frac{18}{-6} \\ y=\frac{2}{3}x-3 \end{gathered}[/tex]Therefore, the slope-intercept form of the given equation is
[tex]y=\frac{2}{3}x-3[/tex]
Where
slope = 2/3
y-intercept = -3
order the numbers -7,7,1 and -1 from least to greatest.
as we move towards the right,the value of the numbers on a number line increases. The numbers to the left of zero are negative while the numbers to the right of zero are positive.
Therefore, by ordering the numbers from least to greatest, it would be
- 7, - 1, 1, 7
How to actually do this because it’s say I’m wrong
we have that
the algebraic expression that represents this situation is
15-(9+2.65+1.35+2(1.74))
therefore
George needs to put a parenthesis before the 9
15. Graph the system of linear equations on your calculator and select the solution.fy=5x - 10y=x+6O(-4,-10)O (10,4)O (4,10)O (4,-10)O (-4, 10)
Given:
y = 5x - 10
y = x + 6
To find:
We need to find the value of x and y from the above equations.
The average price of a new home in a neighborhood in thousands of dollars (f(x)) is related to the number of years since the neighborhood was built (x) in the function: Use the graph of the function to describe its domain.A. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to 100B. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to infinity C. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from zero to infinityD. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from 0 to 100l
As given by the question
There are given that the graph of the function.
Now,
According to the domain concept, the domain is defined for the input valuewhich is given in the x-axis.
That means, all x-axis input value range is called domain.
Then,
From the given graph:
The domain is the number of years since the neighborhood was built, that represent the range of x-axis 0 ti infinity.
Hence, the correct option is C.
Acompanyhas14employeeswithasalaryof$21,000,11employeeswithasalaryof$23,800,18employeeswithasalaryof$26,300,four withasalaryof$32,000,fivewithasalaryof$39,500,andonewithasalaryof$145,700.Findthefollowingforsalarymadebyemployeesofthecompany:a)Mean b)Median c)Moded) Inafullsentence,explainwhatthisinformationtellsyouaboutwhatmoneymadebyemployeesofthecompany actuallymeansabouteachindividualemployee.
The company has different staff with different salaries scale
No of employees Salary
14 $21,000
11 $23,800
18 $26,300
4 $32,000
5 $39,500
1 $145,700
To find mean
Mean = summation of salary x no of employees / Total number of employees
[tex]\operatorname{mean}\text{ = }\frac{14\text{ x 21,000 + 11 x 23,800 + 18 x 26,300 + 4 x 32,000 + 5 x 39,500 + 1 x 145,700}}{14\text{ + 11 + 18 + 4 + 5 + 1}}[/tex]14 x 21000 = 294, 000
11 x 23,800 = 261,800
18 x 26,300 = 473,400
4 x 32,000 = 128,000
5 x 39,500 = 197,500
1 x 145,700= 145,700
Frequency = 14 + 11 + 18 + 4 + 5 + 1
Frequency = 53
[tex]\begin{gathered} \operatorname{mean}\text{ =}\frac{294,000\text{ + 261,800 + 473, 400 + 128,000 + 197,500 + 145700}}{53} \\ \operatorname{mean}\text{ = }\frac{1,\text{ 500, 400}}{53} \\ \text{Mean = 28,309.43} \end{gathered}[/tex]Mean = 28, 309.43
Mode is the highest number of employees salaries that appear most
From the table, The highest number is 18
18 number of the employees received 26, 300
The mode is $26,300
To calculate the median
Firstly, get the total number of employees in the company
The total number = 14 + 18 + 11 + 4 + 5 + 1
Total number of employees = 53
Median = total number + 1 / 2
Median = 53 + 1 /2
Median = 54/2
Median = 27th position
This implies fall between the 27th position of the employee
The median is $26, 300
which expression is equivalent to the following 6(y+4)
Given:
6(y + 4)
Let's find the equivalent expression.
To find the equivalent expression, apply distributive property.
Distribute 6 to the numbers in the parentheses.
We have:
6(y + 4)
= 6(y) + 6(4)
= 6y + 24
Therefore, the equivalent expression is: ^
4 i Rotate the figure 90° counterclockwise about the origin, and then reflect in the x-axis. Polygon 1. Move PREV 1 2 3
to rotate 90 degrees counterclockwise we must transform the points like this
[tex](x,y)\longrightarrow(y,-x)[/tex]and then invert the sign of the y-coordinate or the second coordinate of each point, so the total transformation is
[tex](x,y)\longrightarrow(y,x)[/tex]now, transform each point
[tex](0,4)\longrightarrow(4,0)[/tex][tex](0,1)\longrightarrow(1,0)[/tex][tex](2,1)\longrightarrow(1,2)[/tex][tex](2,4)\longrightarrow(4,2)[/tex]A pendant has a 5/8 inch by 1/2 inch rectangular shape with a 1/3 inch silver border. What are the dimensions of the pendant, including the silver border? (Use the larger value for length and the smaller value for width.)
Length of pendant including silver border is = 23/24 inch
The width of the pendant including the silver border is = 5/6 inch
What is the sum of fractions?When adding two fractions with the same denominator (lower number), just add the numerator (upper number) and leave the denominator unchanged if the fractions are like. To add fractions with different denominators, you must rewrite the fractions so that they have a common denominator before computing the sum.
The first step is to find the least common multiple (LCM) of the denominators.This LCM will become the lowest common denominator (LCD) for the fractions.Then, rewrite each fraction by multiplying both the numerator and denominator to a number so you can get LCM as the denominator.Now add the numerators leaving denominators unchanged.For the given case,
The length of the pendant including the silver border is
(5/8)+ (1/3) = (15+8)/24
= 23/24 inch
The width of the pendant including the silver border is
(1/2) + (1/3) = (3 + 2)/6
= 5/6 inch
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Question 3: 12 ptsA circular pool is surrounded by a circular walkway. The radius of the pool is y - 4 and the radius of the full circleformed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, notincluding the space covered by the pool.The area of a circle is given by A = r7?, where r represents the radius of the circle.)O 16ny + 32O 16TyO-16nyO 32
Explanation
Step 1
the area of a circle is given by:
[tex]\begin{gathered} \text{Area}_c=\pi r^2 \\ \text{where r is the radius} \end{gathered}[/tex]so, the area of teh walkway will be the difference of areas
[tex]\begin{gathered} A_{walkway}=A_{entire\text{ circle}}-Area_{pool} \\ \text{replace} \\ A_{walkway}=\pi(y+4)^2-\pi(y-4)^2 \end{gathered}[/tex]Step 2
expand the polynomius:
[tex]\begin{gathered} A_{walkway}=\pi(y+4)^2-\pi(y-4)^2 \\ A_{walkway}=\pi(y^2+8y+16)^{}-\pi(y^2-8y+16) \\ A_{walkway}=\pi(y^2+8y+16)^{}-\pi(y^2-8y+16) \\ A_{walkway}=\pi(y^2+8y+16-(y^2-8y+16)) \\ A_{walkway}=\pi(y^2+8y+16-y^2+8y-16)) \\ A_{walkway}=\pi(16y) \\ \end{gathered}[/tex]therefore, the answer is
[tex]16\text{ }\pi\text{ y}[/tex]I hope this helps you
Find the distance between the two points in simplest radical form.(8,6) and (3,−6)
Given
Two points (8,6) and (3,−6)
Find
distance between the two points
Explanation
Distance between the two points is given by
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]so , distance between (8,6) and (3,−6) is
[tex]\begin{gathered} d=\sqrt{(3-8)^2+(-6-6)^2} \\ d=\sqrt{25+144} \\ d=\sqrt{169} \\ d=13 \end{gathered}[/tex]Final Answer
Therefore , the distance between these two points is 13
Find the answer to this question.
Check the picture below.
so let's get "h" and thus we can get the area of the trapezoid.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{17^2 - 8^2}=h\implies \sqrt{225}=h\implies 15=h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=12\\ b=20 \end{cases}\implies A=\cfrac{15(12+20)}{2}\implies A=240~m^2[/tex]
well, for that, that'd be 2 can plus some more for the remaining 40 m², so I'd think 3 cans will do it,
[tex]\pounds 19.75\cdot \stackrel{cans}{3}\implies \text{\LARGE \pounds 59.25}[/tex]
D (x - 4) B . In the figure shown, what is the value of x? C •E 19 A F
x = 23
Explanation:Given: triangle ABC and triangle DEF
we need to find the triangle congruency theorem in order to determine the value of x.
AB = DE
AC = DF
∠A = ∠D
the sides BC and EF respectively were not marked.
Since, we were not given the value of the angles but we know they are equal. And two sides of triangle ABC and the corresponding two sides of triangle DEF were given. It means BC is equal to EF.
The sides opposite ∠A = BC
The sides opposite ∠D = EF
BC = EF
x - 4 = 19
collect like terms:
x = 19 + 4
x = 23