After solving all the equations, we can conclude that equation (D) [y = (x + 1)² - 1] had a graph that is a parabola with vertex (-1, -1).
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the form of the equation of the vertical parabola:
y = a(x - h)² + kWhere h and k are the vertexes.Now, calculate each equation as follows:
(A) y = (x - 1)² + 1
Vertex: (1, 1)Then, the wrong answer.(B) y = (x - 1)² - 1
Vertex: (1, -1)Then, the wrong answer.(C) y = (x + 1)² + 1
Vertex: (1, 1)Then, the wrong answer.(D) y = (x + 1)² - 1
Vertex: (-1, -1)Then, this is the correct option.Therefore, after solving all the equations, we can conclude that equation (D) [y = (x + 1)² - 1] had a graph that is a parabola with vertex (-1, -1).
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Complete question:
Which equation has a graph that is a parabola with a vertex at (–1, –1)?
A.y = (x – 1)2 + 1
B.y = (x – 1)2 – 1
C.y = (x + 1)2 + 1
D.y = (x + 1)2 – 1
hello I am stuck on this problem in need of help please thank you
First let's do a quick table to help us, when we have S = 0 we cannot make any cookies, then N = 0. When we have one cup of sugar S = 1 we can make 30 cookies, then N = 30. For S = 2, which means, 2 cups of sugar we can make 60 cookies, and so on, then we can do a table like
Then we can see that the relation between N and S is 30, because N = 30.S, for each unit of S that we put we get 30 more cookies, then the equation is
[tex]N=30S[/tex]And if we want to solve it for S
[tex]S=\frac{N}{30}[/tex]Looking at the graph we can see that S is in the y-axis, therefore we are going to use the equation where we have S on the left side, which means, solved for S. Then we are going to plot the equation:
[tex]S=\frac{N}{30}[/tex]This equation is a line, a very simple graph! you can plot two points and then draw a line, for example, use the point (30,1) and (60,2), if we plot these points we get
Now we draw a line that connects these two points, and we have the graph!
In New York State, the minimum wage has grownexponentially. In 1966, the minimum wage was$1.25 an hour and in 2015, it was $8.75.Algebraically determine the rate of growth to thenearest percent.
The Solution.
In 1966, which is the initial year(t); t = 0, and minimum wage(y), y = $1.25
Similarly.
In 2015, t = 49 years , (that is, 1966 to 2015), and y = $8.75
The rate of growth to the nearest percent is
[tex]\text{Rate of growth =}\frac{y_2-y_1}{t_2-t_1}\times100[/tex][tex]\begin{gathered} \text{Where y}_2=8.75,t_2=49\text{ years} \\ y_1=\text{ \$1.25},t_1=0 \end{gathered}[/tex]Substituting into the formula above, we get
[tex]\text{Rate of growth =}\frac{8.75-1.25}{49-0}\times100[/tex][tex]\text{Rate of growth = }\frac{7.5}{49}\times100=15.31\approx15\text{ \%}[/tex]Hence, the correct answer is 15%
How is a dilation different from all other transformations in this unit?O A dilation changes both angle size and side lengths of the pre-image.O A dilation changes side lengths.O A dilation does not have a pre-image.A dilation is not a transformation.< Previous
A dilation is a non-rigid transformation, which means it changes the size of the shape. Specifically, it changes the sides, not the angles.
Therefore, the answer is A dilation change side lengths.
I need help on this I can’t remember how to do it
Answer:
[tex]g(x)=7^{\frac{x}{3}}+1[/tex]Explanation:
The function f(x) is given as:
[tex]f(x)=7^x+1[/tex]If a function, f(x) is horizontally compressed by a factor of k units, the transformation rule is:
[tex]f(x)\to f(kx)[/tex]Therefore, if f(x) is transformed to g(x) through a horizontal compression by a factor of 1/3, the function g(x) is:
[tex]g(x)=7^{\frac{x}{3}}+1[/tex]Find the absolute value of -1818-181/18-1/18Find the opposite of -2525-251/25-1/25
the absolute value of a number does not contain negative sign
so the absolute value of the given expression (-18) is,
= 18
thus, the answer is option A.
3
the opposite of -25 will be,
= -(-25)
= 25
thus the answer is for the second question is option A
this one is super hard
Answer:
16, 767
Explanation:
The second term of the sequence is
23 * 3 = 69
the third term is
23* 3 *3 = 207
the fourth term is
23 * 3* *3 *3
the fifth term is
23 *3* *3 *3 *3
the sixth term is
23 *3* *3 *3 *3 * 3
the seventh term is
23 *3* *3 *3 *3 * 3* 3 = 16767
which is our answer!
4. A cylinder has a volume of 198 cm^3,and itsbase has an area of 22 cm^2.What is theheight of the cylinder?Please hurry
1) Let's find out the height of that cylinder, by plugging it into the formula:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ 198\text{ =}\pi\cdot rh \\ \end{gathered}[/tex]2) The Base area is given by:
[tex]\begin{gathered} A_B=\pi\cdot r^2 \\ 22=\pi\cdot r^2 \\ \frac{22}{\pi}=\frac{\pi}{\pi}r^2 \\ r=\sqrt[]{\frac{22}{\pi}} \end{gathered}[/tex]So now let's plug that radius
[tex]undefined[/tex]5. Logan is cooking carrots as part of his dinner. He is in a rush so he wants them to cook as fast as possible. He decides to cut them into small pieces so they cook faster. Will this work? Use the dimensions of two pieces of carrot to justify your answer.
Let's imagine a piece of carrot that has a shape of a cylinder, and the total surface area of the carrot is S.
If we cut the carrot in half, with a cut parallel to the cylinder base, we will have two smaller cylinders, but the total surface area will increase, since the "internal" part of the bigger cylinder will now be an external area for the new 2 pieces:
In the drawing, the green circles in the right image will add to the total surface area.
If only the base of the cylinder is touching the pan, the surface area will double (from pi*r² to 2*pi*r²), since we will have two pieces of carrot instead of one, with the same base area.
If a bigger surface area is in contact with the pan, the carrots will cook faster. Therefore the answer is YES.
select all the sets of the value that could be the side length of Triangle z.sides are 7,4,10
We will determine if the sets are proportional, if they are, then those will be the sets of lengths that would belong to triangle z, that is:
a.
[tex]\frac{4}{8}=\frac{7}{11}=\frac{14}{10}\Rightarrow\frac{1}{2}\ne\frac{7}{11}\ne\frac{7}{5}[/tex]So, set a is not one.
b.
[tex]\frac{4}{10}=\frac{7}{17.5}=\frac{10}{25}\Rightarrow\frac{2}{5}=\frac{2}{5}=\frac{2}{5}[/tex]So, set b could be a set of lengths that belong to triangle z.
c.
[tex]\frac{4}{6}=\frac{7}{9}=\frac{10}{11}\Rightarrow\frac{2}{3}\ne\frac{7}{9}\ne\frac{10}{11}[/tex]So, set c is not one.
d.
[tex]\frac{4}{6}=\frac{7}{10.5}=\frac{10}{15}\Rightarrow\frac{2}{3}=\frac{2}{3}=\frac{2}{3}[/tex]So, set d could be a set of lengths that belong to triangle z.
e.
[tex]\frac{4}{8}=\frac{7}{14}=\frac{10}{20}\Rightarrow\frac{1}{2}=\frac{1}{2}=\frac{1}{2}[/tex]So, set e could be a set of lengths that beling to triangle z.
So, the options that could be candidate are: b, d & e.
Write and solve addition equations3/8 + n = 7/8
So,
We're going to solve:
[tex]\frac{3}{8}+n=\frac{7}{8}[/tex]For n:
[tex]\begin{gathered} n=\frac{7}{8}-\frac{3}{8} \\ \\ n=\frac{4}{8} \end{gathered}[/tex]Therefore, n=4/8
Examine the figure below.If AABC is similar to ADEF, determine the measure of
We have two similar triangles.
They will have proportional sides and equal measures.
Then, if we have to evaluate Then, we can write:
[tex]\begin{gathered} m\angle A=m\angle D \\ 3x+18=4x+2 \\ 3x-4x=2-18 \\ -x=-16 \\ x=16 \end{gathered}[/tex]Knowing x, we can calculate m[tex]\begin{gathered} m\angle A=3x+18 \\ m\angle A=3\cdot16+18=48+18=66\degree \end{gathered}[/tex]Answer: the measure of A is 66º
Spread of Data Worksheet
1. Construct the box-and-whisker plot for the number of episodes in each season of the TV show "The
Office.
Season
1
2
3
4
5
6
7
8
9
Number of
Episodes
6
22
25
19
28
26
26
24
25
The Box and Whisker Plot is shown in the graph below .
Box and Whisker Plot :
It is plotted to display variation in a set of data . In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph.
How to construct a box and whisker plot ?
The left and right sides show the lower and upper quartiles of the data resp. . The box covers the interquartile interval where half the data is found .The vertical line that split the data in two is the median of data .
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Given the following angles of a regular polygon, 120°, (4*x+-3)°, (x+14)°, 45°, 135°, (x-31)°, and (x*6+20)°, what is the value of x?
Since the polygon has seven angles we deduce it is a heptagon. In that case the sum of the interior angles must be equal to 900°. We can formulate the following equation accordingly.
120°+(4*x-3)°+ (x+14)°+ 45°+ 135°+ (x-31)°+ (x*6+20)° = 900°
120°- 3° +14° + 45° + 135° - 31° + 20 + 4x + x + x + 6x = 900° (Organizing)
300 ° + 12x = 900° (Operating like terms)
12x= 900° - 300° (Transposing 300° to the other side of the equation)
12x= 600° (Subtracting 300° from 900°)
12/12x= 600° / 12 (Dividing by 12 on both sides of the equation)
x= 50°
Answer is: x= 50°
Find the unknown angle measure. 33 mZFGH: mZGFH: mzGHF: 33° х F 28 H
m∠FGH =33º, m∠GFH =119º and m∠GHF= 28º
1) Since the sum of all interior angles of any triangle is always equal to 180º, we can write:
m∠f + m∠H + m∠G = 180º Plug it into that the following measures
x +33º +28º= 180º
x + 61º = 180º
x = 180 -66
x =119º
2) Then we can write:
m∠FGH =33º, m∠GFH =119º and m∠GHF= 28º
Jaden and Lola are hosting events that are catered by the same company. Jaden plans to have 82 adults and 96 children attend, so the total projected cost of his meals is $5,664. Lola has 65 adults and 49 children on his guest list, so she will pay the caterer $4,002. How much does the caterer charge for each meal?
Let's use the variable x to represent the cost of one adult meal, and y to represent the cost of one child meal.
If the cost of 82 adult meals and 96 children meals is $5,664, we can write the following equation:
[tex]82x+96y=5664[/tex]If the cost of 65 adult meals and 49 children meals is $4,002, we can write the equation:
[tex]65x+49y=4002[/tex]To solve this system, let's solve the second equation for y and then use its value in the first equation:
[tex]\begin{gathered} 65x+49y=4002 \\ 49y=4002-65x \\ y=\frac{4002-65x}{49} \\ \\ 82x+96y=5664 \\ 82x+96(\frac{4002-65x}{49})=5664 \\ 82x+7840.653-127.347x=5664 \\ -45.347x=-2176.653 \\ x=48 \\ \\ y=\frac{4002-65\cdot48}{49} \\ y=18 \end{gathered}[/tex]Therefore every adult meal costs $48 and every child's meal costs $18.
A group of biologists is surveying the mice population in a forest. The equatio n=75 times 3t gives the total number of mice, n, t years after the survey began. What does the number 3 mean in the situationA: the common difference B: The original population of miceC: the common ratioD: the slop
I think the equation should be
[tex]n=75\cdot3^t[/tex]where 3 is the common ratio of the exponential function
so the answer is C.
The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of h (in red).Write down the expression for h *(x)The function f is defined * x/-=(x)/^ q
An accountant charges a fee of $100 to complete a company's taxes. The accountant also charges an additional $35 per hour to complete the taxes. Which of the following equations can be used to describe this problem? y = 35 − 100x y = 35 + 100x y = 100 − 35x y = 100 + 35x
We have that 100 is a fix amount and if x describes the additional charges per hour we have that the equations is 100 + 35x. The answer is y = 100 + 35x
Solve for 2. Enter the solutions from least to greatest.x^2 - 3x - 40 = 0lesser x = [ ]greater x = [ ]
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
x^2 - 3x - 40 = 0
x1 = ?
x2 = ?
Step 02:
Quadratic equation:
roots:
x² - 3x - 40 = 0
(x - 8)(x + 5) = 0
x1 = 8
x2 = -5
The answer is:
lesser x = -5
greater x = 8
Question 18 of 30Use the formula below to solve the given problem. In the formula, drepresents the distance an object falls, in meters, and trepresents the timethat an object falls, in seconds. Round to the nearest tenth and do not includeunits in your answer.A screw from the space shuttle in outer space falls from the space shuttle.How far would the screw fall in 11 seconds?ſa=t•2.8Answer here
SOLUTION
We were asked to find how far the screw will fall in 11 seconds.
How far simply means the distance. So we will find the distance using the formula they gave to us.
[tex]\begin{gathered} So\text{ from the formula }\sqrt[]{d}\text{ = t . 2.8, } \\ \sqrt[]{d}\text{ = t }\times\text{2.8, d = distance that we want to find, t = time = 11seconds} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{d\text{ }}\text{ = 2.8t, when we multiply t by 2.8 } \\ \text{Now, we will take the square of both sides to remove the }\sqrt[]{\text{ }}\text{ } \\ (\sqrt[]{d})^2=(2.8t)^2 \\ d=(2.8\times11)^2 \\ d=30.8^2 \\ d\text{ = 948.64} \\ d\text{ = 948.6 to the nearest tenth} \end{gathered}[/tex]Therefore, the answer is 948.6 to the nearest tenth
What is the answer for x?
By the concept of parallels lines the value of x is 4 .
What are parallels lines?Coplanar, straight lines that don't intersect anywhere are considered parallel lines in geometry. Lines in the same three-dimensional space that never cross one another and are said to be parallel. Curves that are parallel to each other and maintain a setting a minimum distance do not touch or intersect. Lines in a plane that consistently have the same separation are said to be parallel. Nothing can cross a parallel line. Lines that cross at a straight angle of 90 degrees are called perpendicular lines. Two lines in the same plane that are equally spaced apart and never cross each other are referred to in geometry as parallel lines. Both vertical and horizontal can be used. Parallel line examples abound in daily life, such as the rows of notebooks and zebra crossings.
9x - 6 = 6x + 6
3x = 12
x = 4
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13. A table costs $439. It is on sale for 40%off. a How much do you save? b. What isthe sales price? Solve question#3 parts a &b.a. I saveb. The sales price isу
A table costs 439, and it is on sale for 40%. That means we shall deduct 40% of 439 from the actual cost as follows;
[tex]\begin{gathered} \text{Sales}=\text{Cost}-\text{Discount} \\ \text{Sales}=439-(439\times\frac{40}{100}) \\ \text{Sales}=439-(439\times0.40) \\ \text{Sales}=439-175.60 \\ \text{Sales}=263.40 \end{gathered}[/tex]Therefore,
The savings is $175.60
The sales price is $263.40
write your own multiple event probability problem and solve it as if you are explaining your reasoning to a friend.
Problem:
You and your sister have six-sided dice each one. What is the probability that if both roll your dice, you get an even number and your sister get an odd number.
Now, each dice has 6 numbers: 1,2,3,4,5,6
The even numbers are: 2,4,6 (3 options)
The odd numbers are: 1,3,5 (3 options)
Now, the probability of rolling an even number is:
[tex]P(e)=\frac{3}{6}[/tex]And the probability of rolling an odd number is:
[tex]P(o)=\frac{3}{6}[/tex]Then, the probability that you get an even number and your sister an odd number is the product of the probabilities of each event:
[tex]\begin{gathered} P(e\cap o)=P(e)*P(o) \\ \\ P(e\cap o)=\frac{3}{6}*\frac{3}{6} \\ \\ P(e\cap o)=\frac{9}{36}=\frac{1}{4} \end{gathered}[/tex]The probability is 1/4
Hi I want to double check if I’m right, thank you
Solution
The whole shape is a trapezoid
a= 10 , b = 10 +7+7 = 24 , h = 9
Formula
[tex]A=\frac{1}{2}(a+b)h[/tex][tex]\begin{gathered} A=\frac{1}{2}(10+24)9 \\ A=\frac{1}{2}(34)9 \\ A=153units^2 \end{gathered}[/tex]The correct answer is 153
Find the lateral surface area of the following cylinder:r = 3 cmh = 3 cmLSA = [?]π cm?Leave your answer in terms of pi
In order to calculate the lateral surface area of the cylinder, we can use the following formula:
[tex]\text{LSA}=2\pi rh[/tex]Where r is the radius and h is the height of the cylinder.
Using r = 3 and h = 3, we have:
[tex]\begin{gathered} \text{LSA}=2\pi\cdot3\cdot3 \\ \text{LSA}=18\pi \end{gathered}[/tex]So the LSA is equal 18π cm², therefore the answer is 18.
Describe the rotation:A) 180 degreesB) 90 degrees counterclockwise C) 90 degrees clockwise
The image 1 is rotated 90 degree clockwise to get image 2.
Place the following from least to greatest 9square root of 6square root of 101.53.14159
[tex]\begin{gathered} \sqrt[]{6}=2.44\cdots \\ \sqrt[]{10}=3.16\cdots \end{gathered}[/tex]
Therefore, the given number ordered from least to greatest is:
[tex]1.5,\sqrt[]{6},3.14159,\sqrt[]{10},9[/tex]Need help with this homework Part 2) construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the para bola what are the coordinates of the point of intersection,A, of the access of symmetry and directrix of the parabola
After following the instructions in part A, the result is
In general, the equation of a horizontal line is y=a, with 'a' a constant. In our case, the line has to be 6 units below F; then y=4-6=-2. The equation of the directrix is y=-2
Part 2)
In Geogebra, go to Tools->Construct->Perpendicular Line; then, click on point F and line y=-2. A new line should appear on your screen, then go to Tools->Points->Intersect and select both lines. After naming the intersection point as 'A', the result is
The answer to part 2) is A=(6,-2)
The engines of a plane are pushing itdue north at a rate of 300 mph, andthe wind is pushing the plane 20°west of north at a rate of 40 mph. Inwhat direction is the plane going?O[?]Round to the nearest tenth.
STEP - BY - STEP EXPLANATION
What to find?
The direction in which the plane is going.
Given:
From the question given; the engines of a plane are pushing it due north at a rate of 300 mph, and the wind is pushing the plane 20° west of north at a rate of 40 mph.
We know that;
The steps below show the incomplete solution to find the value of n for the equation 4n − 2n + 4 = −1 + 17:Step 1: 4n − 2n + 4 = −1 + 17 Step 2: 4n − 2n + 4 = 16 Step 3: 2n + 4 = 16Which of these is most likely the next step? (5 points)2n = 122n = 42n = 82n = 20
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
4n − 2n + 4 = −1 + 17
Step 02:
We must apply the algebraic rules to find the solution.
Step 1: 4n − 2n + 4 = −1 + 17
Step 2: 4n − 2n + 4 = 16
Step 3: 2n + 4 = 16
2n + 4 = 16
2n = 16 - 4
2n = 12
The answer is:
2n = 12