Answers
In order to complete the square remember that
[tex](x\pm a)^2=x^2\pm2\cdot x\cdot a+a^2[/tex]first, equal the expression divide all the expressions by 2,
[tex]\begin{gathered} f(x)=2x^2+4x+7 \\ 2x^2+4x+7=0 \\ 2x^2+4x=-7 \\ x^2+2x=-\frac{7}{2} \end{gathered}[/tex]then, we can find "a" using the second portion of the definition
[tex]\begin{gathered} 2\cdot x\cdot a=2x \\ a=\frac{2x}{2x} \\ a=1 \end{gathered}[/tex]then,
[tex]a^2=1^2=1[/tex]add 1 on both sides
[tex]\begin{gathered} x^2+2x+1=-\frac{7}{2}+1 \\ x^2+2x+1=-\frac{5}{2} \end{gathered}[/tex]rewrite as a square expression on the left,
[tex](x+1)^2=-\frac{5}{2}[/tex]multiply both sides by 2
[tex]2(x+1)^2=-5[/tex]bring all to the left side and equal to f(x)
[tex]\begin{gathered} f(x)=2(x+1)^2+5 \\ \text{The vertex is at (-1,5)} \\ \text{the axis of symmetry is x=-1} \end{gathered}[/tex]Related Questions
I need help solving an answering this practice problems from my pre-calculus prep guide
Answers
The general formula of a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]where,
n = 6
a₁ = -8100
r = -0.1
Replacing on the formula:
[tex]\begin{gathered} a_6\text{ = -8100}\times(-0.1)^{6-1} \\ a_6\text{ = 0.081} \end{gathered}[/tex]Pls answer very desperate ty
The science club members are using transformations on coordinate grids to track the movement of constellations in the sky. Choose the left side of the constellation depicted by the line passing through (1,7) and (2.5,1), and find the linear functions that correspond to the series of motions of the side given below.
1) Shift the side down 5 units.
2) Vertically stretch the result of the shift by 3.
3) Shift the result of the stretch 2 units to the left.
Answers
The linear function passing through points (1,7) and (2.5, 1) is given by:
y = -4x + 11.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function.The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).For this problem, the two points that form the function are given as follows:
(1,7) and (2.5, 1).
The slope is given by change in y divided by change in x, hence it is given by:
m = (1 - 7)/(2.5 - 1) = -4.
Then:
y = -4x + b.
When x = 1, y = 7, hence we can find the intercept b of the function as follows:
7 = -4(1) + b
b = 7 + 4
b = 11.
Hence the equation is:
y = -4x + 11.
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For each graph below, state whether it represents a function.
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Graph 1: No, because it fails the vertical line test.
Graph 2: No, because it fails the vertical line test.
Graph 3: Yes, because it passes the vertical line test.
Graph 4: Yes, because it passes the vertical line test.
Graph 5: No, because it fails the vertical line test.
Graph 6: Yes, because it passes the vertical line test.
L C R
U (4, 14) (9, 6) (5, 3)
M (8, 2) (6, 12) (1, 7)
D (11, 5) (16, 3) (9, 8)
Answers
Explanation: huh
Becky a sales women is offered two salary plans. Plan 1 is 400 per week salary plus 2% commission sales. Plan 2 is a 300 per week salary plus a 18% commission of sales. How much would Becky need to make in sales for the salary to be the same from both plans?
Answers
Let the commission sales = X
Salary Plan 1
salary per week = $400
commission sales = 2%
[tex]\text{Commision sales = 2\%}\times X=\text{ \$0.02X}[/tex]Salary Plan 2
salary per week = $300
commission sales = 18%
[tex]\text{ Commission sales = 18\%}\times X=\text{ \$0.18X}[/tex]Becky's salary for both plans (inclusive of commission sales) would be:
Plan 1:
[tex]\text{ \$400+0.02X}[/tex]Plan 2:
[tex]\text{ \$300+0.18X}[/tex]In order to find how much Becky needs to make in sales for salary to be the same from both plans would be:
[tex]\begin{gathered} \text{ \$400+0.02X= \$300+0.18X} \\ \text{collect like terms} \\ 0.18X-0.02X=400-300 \\ 0.16X=100 \\ X=\frac{100}{0.16}=625 \end{gathered}[/tex]Therefore, the commission sales should be $625
What is the volume of a prism that is 10 mi tall with a right triangle for a base with side lengths 6 mi, 8 mi, and 10 mi ?
Answers
The expression for the volume of the Prism is 1/3(Base area x Height)
In the given prism
Height = 10 mi
Base is in the shape of right angle triangle
Area of right angle triangle = 1/2 x Base x Height
Area of right angle triangle = 1/2 x 8 x 6
ARea of right angle triangle = 24
Area of base of the prism = 24mi².
Volume of the prism = 1/3 (Base area x Height)
Volume of the prism = 1/3 (24 x 10)
Volume of the prism = 1/3(240)
Volume of the prism = 80mi³.
The volume of prism is 80 mi³.
A rectangular driveway is 9 feet wide, and it has an area of 135 square feet. How lo g is the driveway
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Area of a Rectangle
Given a rectangle of length L and width W, the area is calculated as follows:
A = L.W
We are given the area of A=135 square feet and the width is W= 9 ft. Solving for L:
[tex]L=\frac{A}{W}=\frac{135ft^2}{9ft}=15ft[/tex]The driveway is 15 feet long
8.20y + 4) = 6.7s +5.2
Answers
distribute the parentheses
[tex]\begin{gathered} 8.2y+32.8=6.7s+5.2 \\ \end{gathered}[/tex]substract 32.8 on both sides
[tex]undefined[/tex]Describe a series of transformations Matt can perform to device if the two windows are congruent
Answers
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
Define transformations.There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
Given Data
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. The direction of a rotation, whether it be in a clockwise or counterclockwise counterclockwise. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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What subset of real numbers does 1/2 belongs to?
Answers
Answer:
It belongs to the sets of natural numbers, {1, 2, 3, 4, 5, …}.
It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and whole number.
Answer: rational numbers if thats an answer
Step-by-step explanation:
I need help with homework I got the picture with the questions
Answers
We have the following:
[tex]\begin{gathered} \text{CAE}=135-45=90\degree \\ \text{EAF}=45-15=30\degree \\ \text{CAF}=\text{CAE}+\text{EAF}=90+30=120\degree \end{gathered}[/tex]I’m trying to do my homework help
Answers
The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5
What is the Average Rate of Change of the function?
Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Now, the formula for the average rate of change over the interval (a, b) is;
f'(x) = [f(b) - f(a)]/(b - a)
Now, we are given the interval as -6 ≤ x ≥ 2.
From the given polynomial graph, we see that;
f(2) = 0 and f(-6) = 40
Thus;
f'(x) = [f(-6) - f(0)]/(2 - (-6))
f'(x) = (40 - 0)/8
f'(x) = 5
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Noah operates an orange juice stand. On Monday he used 3 3/10 bags of oranges. On Tuesday he used 1/6 as many oranges as on Monday. How many bags of oranges did Noah use on Tuesday?
Write your answer as a fraction or as a whole or mixed number.
Answers
The number of bags of oranges Noah used on Tuesday as required to be determined in the task content is; 11/20 bags of oranges.
What is the number of bags of oranges used by Noah on Tuesday?It follows from the task content that Noah used 3 3/10 bags of oranges on Monday.
Hence, by expressing the mixed number, 3 3/10 as a fraction; we have; 33/10.
Therefore, since he uses 1/6 as many oranges as on Monday on Tuesday;
The number of bags of oranges used on Tuesday is; (1/6) × 33/10
= 33/60
= 11/20.
Therefore, the number of bags of oranges Noah uses on Tuesday is; 11/20.
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I am thinking the answer is 8, because it's bisecting, and I was told when a bisection is taking place in an angle, the sides are congruent, and by just the look of the eye, they look the same length. If I'm wrong, could I get a explanation on how to find the length?
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BISECTRIZ: Divide the interior or exterior angle of each vertex into two congruent angles. Then we have that the angle that ES starts and that shares the 2 right triangles is the same:
As we can see, both triangles share the angle and the hypotenuse, that is, their height is also the same, so the height of PC is equal to 8
Which expression can be used to determine the number of downloads on the meh day after the game was available
Answers
we have the sequence
1,790 2,555 3,320 4,085 4,850
so
a1=1,790 ----> first term
a2=2,555
a3=3,320
a4=4,085
a5=4,850
Find out the difference between consecutive terms
a2-a1=2,555-1,790=765
a3-a2=3,320-2,555=765
a4-a3=4,085-3,320=765
a5-a4=4,850-4,085=765
This is an arithmetic sequence
The common difference is d=765
so
[tex]a_n=a_1+d\left(n-1\right)[/tex]we have
d=765
a1=1,790
substitute
[tex]\begin{gathered} a_n=1,790+765(n-1) \\ a_n=1,790+765n-765 \\ a_n=1,025+765n \end{gathered}[/tex]The answer is option Bin the equation 8x - 1 = 3x + 4 the variable x represents the same value. Which value of x is the solution of the equation; x = 0, 1, 2, or 3? Explain.
Answers
Given the following expression:
a.) 8x - 1 = 3x + 4
Let's determine the value of x,
8x - 1 = 3x + 4
8x - 1 + 1 - 3x = 3x + 4 + 1 - 3x
8x - 3x = 4 + 1
5x = 5
5x/5 = 5/5
x = 1
Therefore, x = 1.
And then move the consistent to the right side and change the sign and you should get 8x-3=4+1
now you should have 8x-3x=4+1 now collect like terms and you should get 5x=4+1
Add the numbers And you should get 5x=5 divide both sides by 5 and you should get x1
Use the above data to calculate the correlation coefficient Answer Choices.0.890.94-0.89-0.94
Answers
Using the table, we have the following points:
(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)
Let's find the correlation coefficient.
To find the correlation coefficient, apply the formula:
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-\Sigma(x)^2)(n}\Sigma y^2-\Sigma(y)^2)}[/tex]Where:
n = 5
Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5
Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23
Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85
Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75
Σy² = 109.6
Plug in values in the formula and solve for r.
We have:
[tex]\begin{gathered} r=\frac{5(108.85)-(22.5)(23)}{\sqrt{(5(109.75)-22.5^2)(5(109.6)-(23)^2}} \\ \\ r=0.94 \end{gathered}[/tex]Therefore, the coefficient is 0.94
ANSWER:
0.94
The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.Which function defines the area of the rectangle?Hint: A=l⋅w
Answers
The area of a rectangle is calculated using the formula:
[tex]A=l\times w[/tex]where l is the length and w is the width.
The functions for the length and width are given to be:
[tex]\begin{gathered} l(x)=2x+1 \\ w(x)=x+4 \end{gathered}[/tex]Therefore, the area of the rectangle will be:
[tex]A=(2x+1)(x+4)[/tex]We can apply the FOIL Method:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Therefore, we have:
[tex]\begin{gathered} \left(2x+1\right)\left(x+4\right)=2x\cdot x+2x\cdot\:4+1\cdot\:x+1\cdot\:4 \\ =2x^2+8x+x+4 \end{gathered}[/tex]Simplifying, the area is:
[tex]a(x)=2x^2+9x+4[/tex]The SECOND OPTION is correct.
8. Jen receives 8 dollars each week for allowance. She also had 35 dollars saved from birthday gifts. If she currently has 195 dollars, write an equation to represent how many weeks Jen has been saving money. a. 8w + 195 +35 b. 8 + 35 = 195w c. 8w + 35 = 195 d. 8w-35 = 195
Answers
the equation for the saved money is
195 = 8w + 35
here w = no. of weeks.
so the answer is 8w + 35 = 195
Four year after a maple tree was planted its height was 9 feet. By 8 years is grew to 12 feet. What is the growth rate and how tall was it when it was planted!
Answers
The Growth rate is 3/4 ft/year
What is Growth rate ?
Growth rates are computed by dividing the difference between the ending and starting values for the period being analyzed and dividing that by the starting value. Formula is, Growth rate = Absolute change / Previous value.
growth rate = (12-9)/(8-4)
= 3/4 ft/year
Therefore, The Growth rate is 3/4 ft/year
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Find the length, width, area, and aspect ratio of a SAMSUNG Flat 75-Inch 4K 8 Series UHD Smart TV with HDR and Alexa Compatibility.
Answers
The dimensions that we must use in this problem, are the dimensions of the screen of a TV of 75 inches:
• W = width = 65.4" ,
,• H = heigh = 36.8".
• The form of the TV is a rectangle, we compute the area A of the rectangle by the following formula:
[tex]A=W\cdot H=65.4in\cdot36.8in=2406.72in^2.[/tex]• The aspect ratio r is given by the quotient of the width (W) by the height (H):
[tex]r=\frac{W}{H}=\frac{65.4in}{36.8in}=1.777.[/tex]• The length of the TV diagonal L can be computed using Pitagoras Theorem:
[tex]L=\sqrt[]{W^2+H^2}=\sqrt[]{(65.4in)^2+(36.8in)^2}\cong75.04in.[/tex]Answer
• width = 65.4",
,• heigh = 36.8",
,• area = 2406.72in²,
,• aspect ratio = 1.777
,• length of the diagonal = 75.04in.
fastest answer gets brainlyest
Answers
Answer:
see my photo bro. hope it can help.
Answer:
[tex]\textsf{(a)} \quad \overline{v}=-8t-4h-2[/tex]
[tex]\textsf{(b)} \quad v(t)=-8t-2[/tex]
[tex]\textsf{(c)} \quad L(t)=-26t+41[/tex]
(d) See attachment.
Step-by-step explanation:
Given equation for displacement:
[tex]s(t)=-4t^2-2t+5[/tex]
Part (a)Average velocity formula:
[tex]\boxed{\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}[/tex]
where:
[tex]\overline{v}[/tex] = average velocitys(t₁) = position function at t₁s(t₂) = position function at t₂t₁ = initial timet₂ = final timeTo find the average velocity of s(t) between the inputs t and t+h:
[tex]\textsf{Let}\;t_1 = t[/tex][tex]\textsf{Let}\; t_2 = t+h[/tex]Find expressions for s(t) at t₁ and t₂:
[tex]\implies s(t_1)=s(t)=-4t^2-2t+5[/tex]
[tex]\begin{aligned}\implies s(t_2)=s(t+h)&=-4(t+h)^2-2(t+h)+5\\&=-4(t^2+2th+h^2)-2t-2h+5\\&=-4t^2-8th-4h^2-2t-2h+5\end{aligned}[/tex]
Substitute the found values into the average velocity formula:
[tex]\begin{aligned}\implies \overline{v} =\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}&=\dfrac{(-4t^2-8th-4h^2-2t-2h+5)-(-4t^2-2t+5)}{(t+h)-t}}\\\\&=\dfrac{-4t^2-8th-4h^2-2t-2h+5+4t^2+2t-5}{t+h-t}\\\\&=\dfrac{-8th-4h^2-2h}{h}\\\\ &=-8t-4h-2\\\\ \end{aligned}[/tex]
Therefore, the average velocity between the inputs t and t+h is:
[tex]\boxed{\overline{v}=-8t-4h-2}[/tex]
Part (b)To find the equation for instantaneous velocity v(t), differentiate the equation for displacement:
[tex]\begin{aligned}\implies v(t)&=s'(t)\\&=2 \cdot -4t^{(2-1)}-1 \cdot 2t^{(1-1)}+0\\&=-8t-2\end{aligned}[/tex]
Part (c)Find the value of s when t = 3:
[tex]\begin{aligned}\implies s(3)&=-4(3)^2-2(3)+5\\&=-4(9)-6+5\\&=-36-6+5\\&=-42+5\\&=-37\end{aligned}[/tex]
To find the gradient of s(t) at t = 3, substitute t = 3 into the differentiated function:
[tex]\begin{aligned}\implies s'(3)=v(3)&=-8(3)-2\\&=-24-2\\&=-26\end{aligned}[/tex]
Substitute the found gradient and found point (3, -37) into the point-slope form of a linear equation to find the equation of the tangent line L(t):
[tex]\begin{aligned}\implies s-s_1&=m(t-t_1)\\s-(-37)&=-26(t-3)\\s+37&=-26t+78\\s&=-26t+41\\\implies L(t)&=-26t+41\end{aligned}[/tex]
Part (d)See attachment.
Evaluate the following expressionsYour answer must be an exact angle in radians and in the interval Example: Enter pi/6 for lceil- pi 2 , pi 2 ] pi R
Answers
Help step by step pleaseeee
Answers
The graphic below includes the graph of the provided question.
The horizontal axis is x-axis
The vertical axis is y-axis.
How do collinear points work?Points that are situated along the same straight line but within a single line are known as collinear points. Two or more points in Euclidean geometry are said to be collinear if they are situated on a line that is either close to or far from one another.
In light of the information provided:All the points necessary to solve the equation will be positive and negative in turn, and that point will form a straight line through the origin, indicating that all the points are collinear.
You can change the value to fit your graph in the diagram that corresponds to the graph for the question that is attached below.
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While studying abroad, Alan wants to make 6 batches of his mothers enchilada recipe to feed his classmates. The recipe calls for 20oz of cheese for each batch. The local market sells cheese by the gram. How many grams of cheese alan should by. USE 1 oz = 28 g AND DON'T ROUND ANY COMPUTATIONS.
Answers
The total cheese used by Alan to make 6 batches of recipe is 3360 g
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
1 oz = 28 g
The recipe calls for 20 oz. of cheese for each batch. Hence:
Total cheese in gram for each recipe = 20 oz. * 28 g per oz. = 560 g
There are 8 batches, hence:
Total cheese = 560 g * 6 batches = 3360 g
The total cheese is 3360 g
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Using synthetic division what is the first row for the dividend (divided) and the divisor value using synthetic division process:
2x3−10x+2/x−4
Answers
Using synthetic division, the solution to the polynomial fraction expression is; 2x² - 10 + 12/(x - 4)
How to use Synthetic Division?We are given the polynomial fraction as;
(2x³ - 10x + 2)/(x- 4)
This means that we want to divide the polynomial (2x³ - 10x + 2) by (x - 4) using synthetic division.
For the divisor, we have x - 4, and that means x - 4 = 0, x = 4
So, we'll be using 4 for the synthetic division and we have;
-1 | 2 0 -10 2
× 0 0 10
-------------------------
2 0 -10 12
Now we will form the expression in the form of fraction again;
2x² - 10 + (12/(x - 4))
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Select all the figures that have sides that to be perpendicular
A
B
C
D
E
HELP
Answers
The figures that have sides that to be perpendicular are figures A and E.
What is defined as the perpendicular?Perpendicular lines are two distinct lines that intersect at 90°, or a right angle.The symbol " represents perpendicular lines. If m and n are two lines that intersect at 90°, they are perpendicular to one another and are symbolized as m ⊥ n. The intersection of two perpendicular lines is known as the foot of a perpendicular.Perpendicular Line PropertiesThese lines are always at right angles when they intersect.If two lines have become perpendicular to each other, they are parallel and will not intersect.Adjacent square and rectangle sides always are perpendicular to the other.For the given question;
As we can see that the only in figures A and E, there are two lines making an angle of 90 degrees.
Thus, only figures A and E have the sides perpendicular to each other.
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2. The polygon on the grid represents the floor plan of a factory. The manager labeled each side to describe it. For example, N1 means North 1. у 84 5 N1 W1 E1 S2 --10-8-8-7-6-5-4-3-2-11 B 1 2 3 W2 2 -3 si -6 (a) The polygon has six sides. Find the length of each side of the polygon. (b) Each unit on the grid represents 25 feet. Find the perimeter of the factory. Show your work. Denne
Answers
Solution:
Given:
A polygon on a grid.
Question 2a:
The length of each side of the polygon on the grid is given by;
[tex]\begin{gathered} N1=13\text{units} \\ E1=7\text{units} \\ S1=5\text{units} \\ W2=4\text{units} \\ S2=8\text{units} \\ W1=3\text{units} \end{gathered}[/tex]Question 2b:
Perimeter is the sum of the outer sides enclosing a shape.
Hence, the perimeter of the factory is;
[tex]P=N1+E1+S1+W2+S2+W1[/tex]Thus,
[tex]\begin{gathered} P=N1+E1+S1+W2+S2+W1 \\ P=13+7+5+4+8+3 \\ P=40\text{units on the grid} \\ \\ \text{But each unit on the grid represents 25 f}eet. \\ \text{Hence, } \\ P=40\times25 \\ P=1000\text{feet} \end{gathered}[/tex]Therefore, the perimeter of the factory is 1000 feet.
The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
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0.80 x 100= 80
Answers is 80%
name a number that is not a whole number
Answers
Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
For example.
- 2, - 10