The function’s equation written in factored form and in vertex form are respectively;
f(x) = 2x(x - 4)
f(x) = 2(x - 2)² - 8
How to Interpret Quadratic Graphs?The factored form of a quadratic function is;
f(x) = a(x - p)(x - q)
where:
p and q are the x-intercepts
a is a constant
Now, we are given x-intercepts as; (0, 0) and (4, 0)
Thus;
f(x) = a(x - 0)(x - 4)
f(x) = ax(x - 4)
To find a, substitute the given vertex (2, -8) into the equation and solve for a:
2a(2 - 4) = -8
-4a = -8
a = 2
Thus;
f(x) = 2x(x - 4)
The vertex form of a quadratic equation is;
f(x) = a(x - h)² + k
where:
(h, k) is the vertex
a is constant
Since vertex is (2, -8), then we have;
f(x) = a(x - 2)² - 8
Put the coordinate (0, 0) to find a;
0 = a(0 - 2)² - 8
4a = 8
a = 2
Thus;
f(x) = 2(x - 2)² - 8
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. You want to buy some underwear. Apackage of 8 costs $3.12. A package of 15costs $6.15. A package of 20 costs $7.60.Which package is the best buy?
We shall consider the options one after the other before choosing the best option;
Option 1;
[tex]\begin{gathered} \text{Pack of 8 costs 3.12} \\ 1\text{ unit = }\frac{3.12}{8} \\ 1\text{ unit=0.39} \end{gathered}[/tex]Option 2;
[tex]\begin{gathered} \text{Pack of 15 costs 6.15} \\ 1\text{ unit=}\frac{6.15}{15} \\ 1\text{ unit=0.41} \end{gathered}[/tex]Option 3;
[tex]\begin{gathered} \text{Pack of 20 costs 7.60} \\ 1\text{ unit=}\frac{7.60}{20} \\ 1\text{ unit=0.38} \end{gathered}[/tex]Based on the calculations above, the third option is the best deal because that would make you pay the least amount per underwear. By choosing option 3, you will end up paying $0.38 for each underwear.
Therefore, "a package of 20 costs $7.60" is the best buy.
Famous piece of artwork was up for bid at a museum auction. The minimum bid was more than $20,000. Determine which inequality represents the bid for the artwork.
The inequality to illustrate the information that the minimum bid was more than $20,000 is b > 20000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the minimum bid be represented by b.
Since it's more than 20000, it implies that it's greater than. This will be illustrated as b > 20000.
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Given Δ ABC with points A (-1,2) B(4,-3) and C (0,0) dilated about a center at the origin by a scale factor of 0.5, what are the coordinates of A'? Show all work.
The coordinates of A' is (-0.5, 1)
What is Scale Factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.
A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size.
Given:
A (-1,2) B(4,-3) and C (0,0)
First ABC is dilated by 0.5.
The transformation rule of this dilation is:
(x, y)--> 0.5 (x, y)--> (0.5x, 0.5y)
So, the coordinate of A' after dilation is
(-1, 2 ) --> 0.5(-1, 2)--> (-0.5 , 1)
Hence, the coordinates of A' is (-0.5, 1)
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A certain insecticide kill 70% of all insects in a laboratory experiments A sample of 10 insects is exposed to the insecticide in a particular experiment what is the probability that exactly 3 insectswill die round your answer to four decimal places
The probability that exactly three insects will die is 0.343
Given 70% chance that an insect will die.
let A be the event that 1 insect dies.
P(A) = 0.7
The probability that the insect will not stay alive
= 1 - P(A)
= 1 - 0.7
= 0.3
Now there is a sample of 10 insects that are affected by the insecticide.
Therefore number of ways exactly 3 insects will die using binomial distribution is
= 10C3 × (0.7)³ × (0.3)⁷
= 120 × (0.7)³ × (0.3)⁷
=0.00901
≈ 0.009
Hence the required probability is 0.009 .
A probability distribution is an idealised frequency distribution. The frequency distribution of a certain sample or dataset serves as a description of it.
It is the frequency with which each conceivable value of the variable appears in the dataset. How frequently a value emerges in a sample is determined by its probability of occurrence.
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which of the following expression is equivalent to 7 y + 21 y(7+21) 7(y+21). 7(y+3. 21y+7
The expression given is;
[tex]\begin{gathered} 7y+21 \\ \text{The equivalent is;} \\ =7(y+3) \\ We\text{ use 7 to factor both sides of the expression, hence} \\ \frac{7y}{7}=y \\ \text{And} \\ \frac{21}{7}=3 \\ \text{Therefore, the answer is } \\ 7(y+3) \end{gathered}[/tex]The correct answer is option C
When two dice are rolled, find the probability of getting a 4 on each one.
step 1
the probability of get 4 in one dice is
P=1/6
so
the probability of get 4 in two dices is
(1/6)*(1/6)=1/36
answer is the third optionSOMEONE PLEASE HELP ME ON THIS!! ITS DUE REALLY SOON AND I DON’T GET IT LIKE AT ALL!
a) The proportional relationship is: M = 2.4R.
b) The graph of the proportional relationship is given by the first image at the end of the answer, and they would raise $2,400 selling 1000 tickets.
3. The slope of the function, and the relation with the graph, is as follows:
Greater than 1: Significant vertical increase.Equal to 1: Inclination of 1.Less than 1: Significant horizontal increase.4. The graph is given by the second image at the end of the answer.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one, and the higher it's value, the higher the vertical increase of the function.b is the y-intercept of the function, which is the initial value of the function, that is, it's value when the function crosses the y-axis.A proportional relationship is a linear function with intercept zero, hence it is given as follows:
y = mx.
Item a states that the students collect $24 for selling 10 raffles, hence the slope is:
m = 24/10 = 2.4.
Hence the equation is:
M = 2.4R.
If they sold 1000 tickets, the amount they would raise is of:
y = 2.4 x 1000 = $2,400.
The domain of this graph excludes negative values, as the number of raffles sold cannot be negative.
The function for item 4 is:
y = 3/11(x - 2).
Hence the intercepts are:
x-intercept (2,0).y-intercept (0, -6/11).The graph connecting these poins is the second one at the end of the answer.
Missing InformationThe text before item a is:
The students collect $24 for selling 10 raffles.
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Can you help me with this one please? Only part b
Simplifying,
[tex]\begin{gathered} ((5+2i)^2-2)i\rightarrow(25+20i+4i^2-2)i\rightarrow(23+20i-4)i \\ \\ \rightarrow(19+20i)i\rightarrow19i+20i^2\rightarrow-20+19i \end{gathered}[/tex]Understand the if a quadratic equation is factorable.
Given the following quadratic expression:
[tex]\text{ }\frac{169}{9}=(x-6)^2[/tex]Let's check if the given equation can be solved by factoring.
a.) Let's determine the original equation.
[tex]\text{ }\frac{169}{9}=(x-6)^2[/tex][tex]\text{ }\frac{169}{9}=x^2\text{ - 12x + 36}[/tex][tex]x^2\text{ - 12x + 36 - }\frac{169}{9}\text{ = 0}[/tex][tex]\text{ }x^2\text{ - 12x + }\frac{324}{9}\text{ - }\frac{169}{9}\text{ = 0 }\rightarrow\text{ }x^2\text{ - 12x + }\frac{324-169}{9}\text{ = 0 }[/tex][tex]x^2\text{ - 12x + }\frac{155}{9}\text{ = 0 }[/tex]From the original equation, we observed that the constant 155/9 is not a perfect square. For the original quadratic equation to be factorable, we must apply the method of completing the square.
Therefore, we can say that the original quadratic equation can't be solved by factoring.
Select the correct answer.
What is the result of this operation?
13 10
6
2 5
3 -26
- 14 -6 11
8 -12 9
6 10 151
+ 10 0 9
1 0
ОА.
O
OB.
16 22 16
2 14 -
-5 17
1-16 -22
-2 -14
5 -17 2
(10 -2 -2
10 2 3
19 -7 2 )
1-10 221
-10 -2 -3
-9 7-2
ОС,
OD
We need to operate the next matrixes.
First, subtract the next matrixes:
13 10 7
6 8 1
2 5 0
-
3 -2 6
14 -6 11
8 -12 9
=
13-3 10-(-2) 7-6
6-14 8-(-6) 1-11
2-8 5-(-12) 0-9
=
10 12 1
-8 14 -10
-6 17 -9
Now, the result adds to the next matrix:
10 12 1
-8 14 -10
-6 17 -9
+
6 10 15
10 0 9
1 0 7
=
10+6 12+10 1+15
-8+10 14+0 -10+9
-6+1 17+0 -9+7
=
16 22 16
2 14 -1
-5 17 -2
Therefore, the correct answer is the first one.
Find the measure of 44.
72° 118°
118°
44
44 =
[?]°
Enter
The measure of angle 4 is 72°
We can observe that we have been given two parallel lines intersected by a transversal.
We need to find the measure of angle 4.
We can observe that angle which measures 72 degrees angle 4 are corresponding Angles.
We know that the Corresponding Angles are congruent.
Therefore, the measure of angle 4 is 72°
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Carl bought an airline ticket. Two weeks ago, the cost of the flight was $300. Noe the cost is $375. what is the percent increase?
We have the following equation
[tex]\frac{375-300}{300}\cdot100=\frac{75}{3}=25\text{ \%}[/tex]so the percent increase is 25%
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]
If Brady & Mathew knows that it will sell many of these cameras, should it expect to make or lose money from sell them? How much?
Given:
• Profit per camera = $186
,• Cost of replacing the camera = $3100
,• Probability it will be replaced once = 4% = 0.04
,• Probability it will be replaced twice = 1% = 0.01
,• Probability it will not be replaced = 95% = 0.95
Now, let's determine if the company should expect to make money or lose money from selling the camera.
Let's find the expected cost of repair.
We have:
E = (0.04 x 3100) + (0.01 x 2 x 3100) + (0.95 x 0)
E = 124 + 62 + 0
E = 186
Therefore, the expected cost of repair is $186.
We can see the profit per camera and the expected cost of repair are the same.
Profit per camera = Expected cost of repair
Since they are equal, the company should expect to neither make nor lose money from selling these cameras.
ANSWER:
Brady & Matthew should expect to neither make nor lose money from selling these cameras.
8) -14x-7y - 18
-6x-3y-6
I need help badly
IS THIS A RELATION A FUNCTION? Justify your answer
Answer:
A is the correct answer.
Please help!!Here is a scale drawing of a playground. The scale is 1 centimeter to 30 meters. Make another scale drawing of the same playground at a scale of 1 centimeter to 20 meters. Take a picture of your drawing and upload it. Then, answer the following question: How do the two scale drawings compare?
Answer:
The second scale gives us a bigger drawing than the first scale.
Explanation:
Let's draw the initial scale figure with its measures in centimeters:
So, if the scale is 1 cm to 30 meters, the true length of side A will be:
[tex]A=2\operatorname{cm}\times\frac{30\text{ meters}}{1\text{ cm}}=60\text{ meters}[/tex]In the same way, the true length of sides B and D of a playground is:
[tex]\begin{gathered} B=2\operatorname{cm}\times\frac{30\text{ meters}}{1\text{ cm}}=60\text{ meters} \\ D=4\operatorname{cm}\times\frac{30\text{ meters}}{1\text{ cm}}=120\text{ meters} \end{gathered}[/tex]Now, if we scale the length in meters to centimeter but using the new scale 1 cm to 20 meters, we get that the new scale lengths will be:
[tex]\begin{gathered} A=60\text{ meters}\times\frac{1\text{ cm}}{20\text{ meters}}=3\text{ cm} \\ B=60\text{ meters}\times\frac{1\text{ cm}}{20\text{ meters}}=3\text{ cm} \\ D=120\text{ meters}\times\frac{1\text{ cm}}{20\text{ meters}}=6\text{ cm} \end{gathered}[/tex]So, the new scale drawing is:
Then, we can compare both scale drawing and observe that the second scale gives us a bigger drawing than the first scale.
solve the following equations by the trial and error method 2(p-3) =6
For the following equations, by the trial and error method in 2(p-3) =6 the value of p is 9
Trial and error is assuming a value for a unkown variable, observing if it works, and if it doesn't trying a new value for the variable.
2p-3 = 15
p=6
2(6) -3 = 9
p=7
2(7)-3 = 11
p=8
2(8)-3 = 13
p=9
2(9)-3 = 15
so, p is 9
For the following equations, by the trial and error method in 2(p-3) =6 the value of p is 9
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Maddie borrowed $1500 at a 4% interest rate. If she pays off the loan in 3 years.
how much will she pay in total with interest?
$1,680
$50
$500
$180
Answer:
1680
Step-by-step explanation:
Answer:
I guess if she is Pays the money in three years, she will pay a capital of 1500/3 per year, which is 500$ per year. The Interest she pays the first year is: I=Debt*interest rate, so I=1500$*0.04, which is: I=60$. So without other information, i assume she pays 60$ each year, so in three years: I=60*3 --> 180$.
Find the derivative of the function. Remember to use logarithmic properties before differentiating.y = x(3^2x)
Find the derivative of the function. Remember to use logarithmic properties before differentiating.
y = x(3^2x)
______________________________
y= u(x) v(x)
u(x) = x
v(x) = 3^2x
_____________
u'(x) = 1
____________
y = a ^f (x)
y'= f '(x) a ^f (x) (ln a)
v(x) = 3^2x
v'(x) = 2 * 3^2x* ln (3)
_______________
dy/ dx = u'(x)v(x) + u(x) v'(x)
dy/ dx = 1* 3^2x + x *2 * 3^2x* ln (3)
dy/ dx = 3^2x (1+2x* ln (3))
________________
Answer
dy/ dx = 3^2x (1+2x* ln (3))
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25 over 23 as a decimal rounded to the nearest hundredth
Answer:
1.09
Step-by-step explanation:
25/23 is the same thing as 25 divided by 23
Once you get answer round to nearest hundreth
Anthony had 2 grams of pepper. Then he used 0.99 grams of the pepper to make some scrambled eggs. How much pepper does Anthony have left?
Answer:2- 0.99 = 1.01
Step-by-step explanation:
2=2.00
2.00-0.99=1.01
easy
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Solve the inequality
6(x/2+4)≥9
3x+24=9
3x=9-24
3x=-15
x=-5
Use the model of the rectangular prism to answer the question. The width of the
prism is (2x - 2) ft, and its height is (x + 7) ft. The area of the base of the prism is
(3x2 + 3x - 4) ft².
Could the length of b be (3x - 1) ft? Complete the explanation.
Answer:
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
Step-by-step explanation:
Given dimensions of a rectangular prism:
Width = (2x - 2) ftHeight = (x + 7) ftArea of the base = (3x² + 3x - 4) ft²The area of the base of a rectangular prism is the product of the width of the base and the length of the base.
To determine if length b could be (3x - 1) ft, multiply b by the width of the base of the prism.
[tex]\begin{aligned}\implies \sf Area\;of\;base&=\sf length \times width\\&=b \times (2x-2)\\&=(3x-1)(2x-2)\\&=3x(2x-2)-1(2x-2)\\&=6x^2-6x-2x+2\\&=6x^2-8x+2\end{aligned}[/tex]
Therefore, the length of b cannot be (3x - 1) as the area of the base when b is (3x - 1) is not equal to the given area of the base.
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
The diagram shows the molecular structure of water. A diagram representing a molecule of water is shown. There is an O at the top with an H branching to its left and another H branching to its right. The ratio of hydrogen atoms to oxygen atoms in water is always the same. How many oxygen atoms (O) are there when there are 8 hydrogen atoms (H)? Enter the correct answer in the box. oxygen atoms
By using ratio, it is obtained that if there are 8 atoms of hydrogen, there are 4 atoms of oxygen.
What is ratio?
Ratio is used to find a comparision between two quantities with the same unit
The first part of the ratio is called antecedant and the second part of the ratio is called consequent.
Here,
In a molecule of water, there are 2 atoms of hydrogen and 1 atom of oxygen
Ratio of hydrogen and oxygen = 2 : 1
Number of atoms of hydrogen = 8
Let the number of hydrogen atom be 2x and number of oxygen atom be x
By the problem,
[tex]2x = 8\\x = \frac{8}{2}\\x = 4[/tex]
Number of oxygen atom = 4
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Which equation represents the line that is perpendicular to y = 1/6 and passes through (-8,-2)?
Answer:
If it is perpendicular: mperp..=-1/m, so:
mperpendicular= -6.
formula of the line passing through one point:
y-y0=m(x-x0)
so: y+2=-6(x+8)
y=-6x+48-2
y=-6x+46 is the answer
In the first week of July, a record 1,020 people went to the local swimming pool. In the second week, 105 fewer people went to the pool than in the first week. In the third week, 140 more people went to the pool than in the second week. In the fourth week,239 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
Step-by-step explanation:
huhhhhh
how do I do this on a line?[tex]3 \ \textless \ 2x - 3 \leqslant 13[/tex]
Let the inequality:
[tex]3\text{ }<\text{ 2x - 3}\leq\text{ 13}[/tex]1. we add + 3 :
[tex]3\text{ +3}<\text{ 2x }\leq\text{ 13}+3[/tex]this is equivalent to :
[tex]6<\text{ 2x }\leq\text{ 1}6[/tex]we resolve for x ( we divide by 2) :
[tex]3<\text{ x }\leq8[/tex]that is the interval:
[tex](3,\text{ 8}\rbrack[/tex]on the real line, the interval is:
On the other hand, the inequality:
[tex]-2\text{ }<\frac{3+x}{4}\leq\text{ 3}[/tex]
1. Multiply by 4:
[tex]-8\text{ }<3+x\leq12[/tex]2. Add -3:
[tex]-11\text{ }that is the interval:[tex](-11,\text{ 9}\rbrack[/tex]
on the real line, the interval is:
Out of 20 attempts a basket ball player only scored 8 times what percent of his chances did he score?
Answer:
40%
Step-by-step explanation:
20 x 5 = 100
8 x 5 = 40
Which means 8 out of 20 is 40% of 20.