Quadratic Functions in Standard FormCaroline wrote these steps to graph f(x) = 2x2 + 4x + 5 on note cards, but they gotmixed up. Help Caroline by re-writing the steps in the correct order. Use the notecards to complete the steps below.
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1.- Determine the vertex...
2.- The axis of symmetry...
3.- The y-intercept...
4.- Plot a point...
5.- Plot another point...
The above is the correct order of the cards, now the reason for that first you have to find the vertex. Now, the axis of symmetry is a straight line that passes through the vertex. Later you have to find another 2 points reflected by the symmetry axis and finally construct the graph.
Related Questions
Which of the following completes the statement below?MZBAC = {(MBC + mED00חוBERXRmZEADA0DBDC
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Answer:
m(arc)ED
Explanation:
In the diagram:
[tex]m\angle\text{BAC}=\frac{1}{2}(m\widehat{BC}+m\widehat{ED})[/tex]The first option is correct.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
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add and subtract scientific notation 1) 5.1 x 106 + 2.3 x 106 =
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Solucionamos de la siguiente manera:
[tex]5.1\cdot10^3+2.3\cdot10^6=(5100)+(2300000)=2305100[/tex]Como ya se sabe, la notación 10^3 representa miles y la notación 10^6 representa millones, por lo que al sumarles obtendremos notación de 10^6 (generalmente); aunque en nuestro caso al llevarle nuevamente a notación científica obtendremos lo siguiente:
[tex]2.3051\cdot10^2[/tex][Otra parte de la notación científica es que esta indica cuantos valores a derecha o izquierda se "mueve" el punto.]
I need help with this please and thank you im just really confused
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To find the values of x and z, apply the opposite angles theorem.
Opposite angles are angles that can be said to be non-adjacent angles formed by two intersecting lines.
Opposite angles are congruent.
• Measure of angle Z:
∠z and 110 are opposite angles.
Thus, we have:
m∠z = 110°
• Value of x:
Given that total measure of angles = 360
We have:
[tex](5x-20)=\frac{360-110-110}{2}[/tex]Let's solve for x:
[tex]\begin{gathered} 5x-20=\frac{140}{2} \\ \\ 5x-20=70 \\ \\ \text{Add 20 to both sides:} \\ 5x-20+20=70+20 \\ \\ 5x=90 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{90}{5} \\ \\ x=18 \end{gathered}[/tex]ANSWER:
x = 18
z = 110°
I need to know the answer and how to solve
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We have by theorem that supplementary angles add up to 180° [The sum of both angles gives as result a straight line; then, the following is true:
[tex]151+x=180\Rightarrow x=29[/tex]So, the value of x is 29°.
Find the general equation of the circle having a diameter with endpoints at A(-2,3) and B(4,5).
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The equation of a circle whose center is (a, b) and which has a radius r is given as:
(x - a)² + (y - b)² = r²
For the circle with endpoints at A(-2,3) and B(4,5).
The center (a, b) of the circle is calculated as:
[tex]\begin{gathered} a=\frac{-2+4}{2} \\ a=\frac{2}{2} \\ a=1 \\ b=\frac{3+5}{2} \\ b=\frac{8}{2} \\ b=4 \end{gathered}[/tex]The center, (a, b) = (1, 4)
The diameter(D) of the circle is the distance between the endpoints A(-2,3) and B(4,5).
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(4-(-2))^2+(5-3)^2} \\ D=\sqrt[]{(4+2)^2+2^2} \\ D=\sqrt[]{6^2+2^2} \\ D=\sqrt[]{36+4} \\ D=\sqrt[]{40} \end{gathered}[/tex]The diameter of the circle = √40
Radius = Diameter / 2
r = d/2
r = √40 / 2
Substituting a = 1, b = 4, and r = √40 / 2 into the general equation of a circle:
[tex]\begin{gathered} (x-1)^2+(y-4)^2=(\frac{\sqrt[]{40}}{2})^2 \\ (x-1)^2+(y-4)^2=\frac{40}{4} \\ (x-1)^2+(y-4)^2=\text{ 10} \end{gathered}[/tex]The general equation of the circle is:
[tex](x-1)^2+(y-4)^2=\text{ 10}[/tex]Please answer all. How do you determine the dose-specific response of a drug given f(x)?
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__________________
Just replace in value of x in the function
f(0.1) = 100* (0.1)^2 / ((0.1)^2 + 0.17) = (1)/(0.18) = 5.56
f(0.1) = 5.56
f(0.8) = 100* (0.8)^2 / ((0.8)^2 + 0.17) = (64)/(0.81)= 79.01
f(0.8) = 79.01
_______________________
derivative of a quotient
Q(x)= f(x)/g(x)
Q'(x)= (f'(x)*g(x) - f(x)*g'(x)) / (g(x) ^2)
[tex]Q^{\prime}\mleft(x\mright)=\frac{f^{\prime}\mleft(x\mright)\cdot g\mleft(x\mright)-f\mleft(x\mright)\cdot g^{\prime}\mleft(x\mright)}{g\mleft(x\mright)^2}[/tex]_____________________________
If f(x) = 100* (x^2) / (x^2 + 0.17),
f'(x)= 100 * ( 2x* (x^2 + 0.17) - 2x*x^2 ) / (x^2 + 0.17)^2
f'(x)= 100 * ( 2x^3 + 2x* 0.17 - 2x^3 ) / (x^2 + 0.17)^2
f'(x)= 100 * ( 2x* 0.17 ) / (x^2 + 0.17)^2
f'(x)= 34*x/ (x^2 + 0.17)^2
_________________________
Just replace in value of x in the function
f'(0.1)= 34*(0.1)/ (0.1^2 + 0.17)^2
f'(0.1)= 3.4/ (0.18)^2
f'(0.1)= 104.9
f'(0.8)= 34*(0.8)/ (0.8^2 + 0.17)^2
f'(0.8)= 27.2/ (0.81)^2
f'(0.8)= 41.46
Good morning I could really use some help solving this problem!
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If the new line passes through the point (-6, 2), let's use x = -6 and y = 2 in the equation and then solve it for 'a':
[tex]\begin{gathered} y=\frac{1}{2}x+a\\ \\ 2=\frac{1}{2}(-6)+a\\ \\ 2=-3+a\\ \\ a=2+3\\ \\ a=5 \end{gathered}[/tex]Therefore the value of 'a' is 5.
The circle has center O. Its radius is 3 m, and the central angle a measures 60°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer
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Explanation
The area of a portion of a circle with radius 'r' and angle 'a' (in radians) is:
[tex]A_{\text{portion}}=\frac{1}{2}\cdot r^2\cdot a[/tex]In this problem r = 3m, a = 60º.
First we have to express the angle in radians:
[tex]a=60º\cdot\frac{\pi}{180º}=\frac{1}{3}\pi[/tex]The area of the shaded region is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot(3m)^2\cdot\frac{1}{3}\pi \\ A=\frac{1}{2}\cdot9m^2\cdot\frac{1}{3}\pi=\frac{3}{2}\pi \end{gathered}[/tex]Answer
The area is:
[tex]A=\frac{3}{2}\pi[/tex]Distance travelled = rate (or speed) * time.If Alan drives 44 miles at a constant speed of 44 mph. How long will it take? (Be sure to includeunits.)
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We are given that Alan at a constant speed of 44 miles per hour. We are asked to determine the time to travel a distance of 44 miles. To do that we will use the following formula:
[tex]d=vt[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ v=\text{ velocity} \\ t=\text{ time} \end{gathered}[/tex]Now, since we are asked to determine the time we will divide both sides by the velocity:
[tex]\frac{d}{v}=t[/tex]Now we substitute the values:
[tex]\frac{44miles}{44\frac{miles}{hour}}=t[/tex]Now we solve the operations:
[tex]1\text{hour}=t[/tex]Therefore, the time to travel 44 miles is 1 hour.
At the grocery store, halibut costs $20 per pound and salmon costs $17 per pound. Which of the following situations can be modeled by the equation below? 20(x-5) = 17xA) The cost of x pounds of salmon is $5 less than the cost of x pounds of halibutt B) The cost of x pounds of halibut is $5 less than the cost of x pounds of salmon C) The cost of pounds of salmon is the same as the cost of x-5 pounds of halibutD) The cost of x pounds of halibut is the same as the cost of x-5 pounds of salmon.
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Answer: C.
The cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut
[tex]\begin{gathered} \text{halibut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]Explanation:
Given the model;
[tex]20(x-5)=17x[/tex]where x is the number of pounds.
The cost per pound of Halibut is;
[tex]\text{ \$20}[/tex]So, the corresponding number of pounds of Halibut on the model is;
[tex]x-5[/tex]Also, the cost per pound of Salman is;
[tex]\text{ \$17}[/tex]the corresponding number of pounds of Salmon on the model is;
[tex]x[/tex]Since they are equal to each other, then the cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut
[tex]\begin{gathered} \text{hailbut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]After a 30% discount, the price of a t-shirt was $14. What was the price BEFORE the discount?
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Price after discount = $14
discount = 30%
x (1-30/100) = 14
x (1-0.3) = 14
x 0.7 = 14
Solve for x (original price )
x = 14/0.7
x = 20
Grayson needs to order some new supplies for the restaurant where he works. The restaurant needs at least 261 forks. There are currently 205 forks. If each set on sale contains 10 forks, which inequality can be used to determine the minimum number of sets of forks Grayson should buy?
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ANSWER
[tex]10x\ge56[/tex]EXPLANATION
We have that the restaurant needs at least 261 forks.
There are currently 205 forks.
First, we have to find the number of forks that the restaurant currently needs.
We do that by finding the difference between the number of forks they have from the number of forks they need:
261 - 205 = 56 forks
They need at least 56 forks.
We have that each set of forks on sale has 10 forks each.
Let the number of sets they need be x.
This means that the amount of forks they should buy must be greater than or equal to 56. That is:
[tex]\begin{gathered} x\cdot10\ge56 \\ \Rightarrow10x\ge56 \end{gathered}[/tex]That is the inequality that can be used to determine the minimum number of sets of forks Grayson should buy.
22% 38% 1/4 21/10 three 5/10 and 3/8 from least to greatest value
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The ascending order for the given values will be 22%<1/4<3/8<38%<21/10<3 5/10 as the definition of ascending order will be "When numbers are arranged in ascending order, they are done so from smallest to largest."
What is ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. Ascending order, also known as increasing order of importance, is the exact opposite of descending order. The order of the items is lowest to highest value. The smallest value is placed first in the order, and the biggest value is placed last. As a result, if you were to put the numbers from the previous section in ascending order, they would be as follows: 11, 20, 49, 80, 56, and so on. The first number is always the smallest, in this case 11. The last number is always the largest, in this case 80.
Here,
22%=0.22
38%=0.38
1/4=0.25
21/10=2.1
3 5/10=3.5
3/8=0.375
22%<1/4<3/8<38%<21/10<3 5/10
According to the definition of ascending order, the given values will be in ascending order as follows: 22%<1/4<3/8<38%<21/10<3 5/10 "Numbers are arranged from smallest to largest when they are arranged in ascending order."
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Find the inverse function of f.f(x) = 7 - 9x3f^-1(x) =
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ANSWER
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]EXPLANATION
We want to find the inverse function of the given function:
[tex]f(x)=7-9x^3[/tex]To do this, we have to make x the subject of the formula.
Let f(x) be y:
[tex]\begin{gathered} y=7-9x^3 \\ 9x^3=7-y \\ x^3=\frac{7-y}{9} \\ \Rightarrow x=\sqrt[3]{\frac{7-y}{9}} \end{gathered}[/tex]Now, replace x with f^(-1)(x) and y with x:
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]That is the inverse function of f.
erica has 32 pairs of shoes. 5/8 of erica's shoes are high heels how many of her shoes are high heels?
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Given Data:
Total number of shoes Erica has is: t=32
The portion of high heel shoes is: r=5/8
The expression to calculate the total number of high heel shoes is,
[tex]\begin{gathered} \text{Total Number of high h}eel\text{ shoes=r}\times t \\ =\frac{5}{8}\times32 \\ =5\times4 \\ =20 \end{gathered}[/tex]Thus, Erica has 20 high heel shoes.
Is 8.012 greater or less than 8.03
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In order to compare the numbers, we need to check each pair of digits that are in the same position before and after the decimal point.
We start from the left to the right. If the result of one number is greater, than this number is greater than the other number. If the digits of both numbers are the same, we move to the next digit and compare them.
So we have:
Unit position: 8 and 8
Equal results, so let's check the next digit.
Tenth position: 0 and 0.
Equal results, so let's check the next digit.
Hundredth position: 1 and 3.
3 is greater than 1, so the second number is greater than the first one.
Therefore 8.012 is less than 8.03.
Because if you add extra 0s on the end of 8.03 then you see that it’s bigger
Name:Date:6. The table shows the postage charges for sending letters to Country A.How much does it cost to send a letter weighing 80 ounces to Country A?First 30 Ounces60For Every Additional 10 Ounces35
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The first 30 ounces costs 60¢.
For every additional 10 ounces the cost increases in 35¢.
From the given 80 ounces, the first 30 costs 60¢ and the other 50 ounces, by considering it is 5 times 10 ounces, cost 5*(35¢) = 175¢.
Then, the total cost is:
total = 60¢ + 175¢ = 235¢
What number makes the equation true? Enter the answer in the box.+5= 9
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The complete information for the question was not provided by the student, however we can assume that the box is either to the left or to the right of the equal sign:
If it's to the left, we have:
Box + 5 = 9
Box = 9 - 5
Box = 4
If it's to the right, we have:
5 = 9 - Box
5 - 9 = - Box
-4 = - Box
4 = Box
Answer: No matter if the box is to the left or to the right of the equal sign, the number in the box that makes the equation true is 4
16. The area of the rectangle is x^2+14x+24.Find the length and width (the factors),then determine the perimeter of the rectangle.Length:Width:Perimeter:
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Given a rectangle of width W and length L, the area is calculated by:
A = W.L
The perimeter of the rectangle is:
P = 2(W + L)
We are given the area of a rectangle with the equation:
[tex]A=x^2+14x+24[/tex]To find the dimensions of the rectangle, we must factor the polynomial.
It's easily done by inspection: find two numbers that added result in 14 and multiplied result in 24. Those numbers are 12 and 2, thus:
[tex]x^2+14x+24=(x+2)(x+12)[/tex]The factors are the width and the length of the rectangle (the width smaller than the length), thus:
Width = x+2
Length = x + 12
Now calculate the perimeter:
P = 2( x + 2 + x + 12)
P = 2( 2x + 14)
Perimeter = 4x + 28
If 14 people want to share 24 oranges equally, how many oranges will each person get?
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Given data:
The total number of oranges is: 24
The total number of people is: 14
The expression to calculate the number of oranges a person has is,
[tex]\begin{gathered} \frac{Total\text{ number of oranges}}{\text{Total number of people}}=\frac{24}{14} \\ =1+\frac{5}{7} \\ =1.714\text{ oranges.} \end{gathered}[/tex]Thus, each person gets 1 orange and 5/7 of an orange.
Your lacrosse team wins 4 of the games that it plays. Describe huikelihood of winning.
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the statement say us the rate of winning is 3/4 then the probability is the same
but performance it on decimals
[tex]\frac{3}{4}=0.75[/tex]probability is 0.75
Find the reference angle for a rotation of 334º.
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We are asked to find the reference angle for a standard angle of 334°
Recall that the reference angle is the angle that is measured with respect to the x-axis.
First, we need to find out in which quadrant the given standard angle lies.
334° lie in the 4th quadrant (180° to 360°)
So, the reference angle can be found as
[tex]\begin{gathered} \theta^{\prime}=360\degree-\theta \\ \theta^{\prime}=360\degree-334\degree \\ \theta^{\prime}=26\degree \end{gathered}[/tex]Therefore, the reference angle is 26°
The ratio of 8th graders in a chess club to the total number of members is 0.45.What is the decimal in fraction form?Enter the correct answers in the boxes.
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The ratio of 8th graders in a chess club to the total number of members is 0.454545...
This is called a repeating decimal.
Let us convert this decimal into a fraction.
[tex]x=0.4545\ldots[/tex]Step 1:
Multiply by 100
[tex]\begin{gathered} 100\times x=100\times0.4545\ldots \\ 100x=45.45\ldots \end{gathered}[/tex]Step 2:
Subtract x
[tex]\begin{gathered} 100x-x=45.45\ldots-0.4545 \\ 99x=45 \end{gathered}[/tex]Step 3:
Finally, divide by 99
[tex]\begin{gathered} \frac{99x}{99}=\frac{45}{99} \\ x=\frac{45}{99} \end{gathered}[/tex]Therefore, the fraction form is
[tex]x=\frac{45}{99}[/tex]A recipe calls for 1/2 cup sugar, a cup of flour and 1/3 cup of milk. I need to make 3 batches. How much of each ingredient will I need?
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The recipe calls for
1/2 cup of sugar : 1 cup of flour : 1/3 cup of milk for 1 batche
We need to make 3 batches, so
Multiply each ingredient bu 3
Sugar = 1/2 * 3 = 3/2 cups
Flour = 1 * 3 = 3 cups
Milk = 1/3 * 3 = 1 cup
3/2 cups of sugar : 3 cups of flour : 1 cup of milk
Someone please help me with this problem in the most simple easy way possible no long explanation needed.
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ANSWER:
2797.74 cubic inches
EXPLANATION:
Given:
Height of the cylinder(h) = 11 inches
Radius of the cylinder(r) = 9 inches
Pi = 3.14
To find:
The volume(V) of the cylinder
We'll go ahead and determine the volume(V) of the cylinder using the below formula;
[tex]\begin{gathered} V=\pi r^2h \\ =3.14*9^2*11 \\ =31.4*81*11 \\ =2797.74\text{ cubic inches} \end{gathered}[/tex]So the volume of the cylinder is 2797.74 cubic inches
The highest recorded temperature in Massachusetts was one hundred seven degrees Fahrenheit on August 27, 1975. The average monthly high temperature is 81.7 degrees Fahrenheit. How many degrees hotter than average was the temperature on August 27, 1975?
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Answer:
25.3°F
Explanation:
We need to find the difference between the temperature on August 27, 1975, and the average temperature. So, the difference is equal to:
107 °F - 81.7°F = 25.3°F
It means that on August 27, 1975, the temperature was 25.3°F hotter than average.
7 - 6u = 5u + 29 solve for u
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Answer:
u = -2
Explanation:
Given the expression;
7 - 6u = 5u + 29
We are to find the value of u;
Collect like terms;
-6u - 5u = 29 - 7
-11u = 22
Divide both sides by -11;
-11u/-11 = 22/-11
u = -2
Hence the value of u is -2
The solution of u in the equation is,
⇒ u = -2
Given that;
the expression is,
⇒ 7 - 6u = 5u + 29
Now, We have to find the value of u;
⇒ 7 - 6u = 5u + 29
Combine like terms;
⇒ -6u - 5u = 29 - 7
⇒ -11u = 22
Divide both sides by -11;
⇒ -11u/-11 = 22/-11
⇒ u = -2
Therefore, the value of u is -2.
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someone help me please this is the last question and can't get it wrong
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We can use the fact that the sum of angles in a triangle is 180degrees and the sine rule to find the missing angle and sides. This will give us a single unique triangle.
So the right answer is 1 triangle
The plastic lid of a cylindrical container is a circle. The lid has a radius of 9centimeters. What is the circumference of the lid?
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We are asked to determine the circumference of a 9 cm radius circle. To do that we will use the following formula:
[tex]S=2\pi r[/tex]Where:
[tex]\begin{gathered} S=\text{ circumference} \\ r=\text{ radius} \end{gathered}[/tex]Now, we substitute the value of the radius:
[tex]S=2\pi(9cm)[/tex]Solving the operations:
[tex]S=18\pi=56.55cm[/tex]Therefore, the circumference is 56.55 cm.