We are given the function;
[tex]f(x)=-4x^2+12x-9[/tex]The input of this function as it is, is x. To evaluate the function at any given output we would simply replace/substitute the value of x with the value provided.
If for example, we are given the function and we have to evaluate its value at f(3), what we will simply do is replace x with two in the function. This is shown below;
[tex]\begin{gathered} f(x)=-4x^2+12x-9 \\ f(3)=-4(3)^2+12(3)-9 \\ f(3)=-4(9)+36-9 \\ f(3)=-36+36-9 \\ f(3)=-9 \end{gathered}[/tex]Therefore, the value of the function at f(3) is -9.
This is basically the procedure we shall use when evaluating a function at any given output value.
PLEASE HELP!!! thank you
The congruent statement for the triangle is ΔVXW ≅ ΔRPQ
What are congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .
In other words, two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.
Therefore, for the two triangles the to be congruent the corresponding sides are and the angles are equals also.
Hence,
∠V ≅ ∠R
∠W ≅ ∠Q
∠X ≅ ∠P
Therefore, ΔVXW ≅ ΔRPQ
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In a bakery, the ratio of fruit scones to cheese scones is 3:4.
a) Given that there are 24 cheese scones, how many fruit scones are there?
b)
If 6 fruit scones were sold, what would be the new ratio of fruit scones to cheese scones?
Answer:
a) 18 and b)1:2
Step-by-step explanation:
for a i divided 24 by 4 (24:4) and got 6 the i multiplied 3 by 6 and got 18. also you could do a proportion and fruit scones would be x so you have to calculate x. if you don't know how to do proportions you can ask me i can explain.
for b since i got the count was 18:24. i took away those six from 18 and got with the ratio 12:24. i divided both sides by twelve and got 1:2
Answer:
a) 18 fruit scones
b) 6:8
Step-by-step explanation:
a) The ratio is 3:4 given that there 3 fruit scones to 4 cheese scones so if there are 24 cheese scones, 24/4=6, 3*6=18 so there 18 fruit scones.
b) The ratio is 3:4 given that there 3 fruit scones to 4 cheese scones so if there are 6 fruit scones, 6/3=2, 2*4=8 so there are 8 cheese scones. The new ratio would be 6:8
The average 12 ounce cola contains 33 grams of sugar. How many grams of sugar are contained in a 68 ounce bottle of soda?
Answer:
There are 55 grams of sugar in a 20-ounce bottle of soda.
Step-by-step explanation:
So if your looking for a 68 ounce bottle of soda we know there would be about 165 grams of sugar just in 60 ounces. as then you would find the amount of 8 grams of sugar.
Donna makes $10.50 each hour she works at her job how much money does she make for 15.75 hours of work round your answer to the nearest cent
To solve this problem, multiply Donna's earnings per hour by the number of hours of work. This is $10.50 times 15.75.
[tex]10.50\cdot15.75=165.375\approx165.38[/tex]She makes $165.38 for 15.75 hours of work.
2. Booker's father sells computer software and earns a 4.25% commission on every software package he sells. How much commission would he earn on a software package that sold for $15,725? Round to the nearest cent. (Example 1)
To solve the exercise you can use a rule of three, like this:
[tex]\begin{gathered} \text{\$}15,725\rightarrow100\text{\%} \\ \text{\$}x\rightarrow4.25\text{\%} \\ x=\frac{4.25\text{\%}\cdot\text{ \$15,725}}{100\text{\%}} \\ x=\text{ \$}\frac{4.25\cdot\text{15,725}}{100} \\ x=\text{ \$}\frac{68831.25}{100} \\ x=\text{ \$668.31} \end{gathered}[/tex]Therefore, the commission earned will be $668.31.
what is the area of a circle with the diameter of 16 cm
Answer:
201.06 square centimeters.
Explanation:
The formula for finding the area of a circle is:
[tex]\text{Area}=\pi r^2[/tex]Given that the diameter = 16 cm
[tex]\begin{gathered} \text{Radius,r}=\text{Diameter}\div2 \\ =16\div2 \\ r=8\operatorname{cm} \end{gathered}[/tex]Next, substitute r=8cm into the formula for area.
[tex]\begin{gathered} A=\pi\times8^2 \\ =64\pi \\ =201.06\operatorname{cm}^2 \end{gathered}[/tex]The area of the circle is 201.06 square centimeters.
What are the roots of 2x^2+4x+7 ? Show your work.
The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.
Define quadratic function.A quadratic function has the generic form f(x)=ax²+bx+c. A parabola, a kind of two-dimensional curve, is the graph of a quadratic function. A polynomial function of degree two in one or more variables is known in algebra as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.
Function:
2x² + 4x + 7 = 0
ax² + bx + c = 0
x = [tex]\frac{-b +-\sqrt{}b^{2}- 4ac }{2a}[/tex]
a = 2
b = 4
c = 7
Using quadratic function,
x = [tex]\frac{-4\sqrt{} 4^{2} -4(2)(7)}{2(2)}[/tex]
x = [tex]\frac{-4+-\sqrt{-40} }{4}[/tex]
So,
i = √-1
x = [tex]\frac{-4+-2i\sqrt{10} }{4}[/tex]
Simplifying,
x = -1 +-√10/2
Roots are:
x = -1 + i√10/2
x = -1 - i√10/2
The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.
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If a spring is stretched 10cm by a weight of 8kg how much will it be stretched by 3kg
The amount of string that can be stretched by 3 kg weight is 5/ 4× 3
= 15 / 4 = 3.75 cm
Given ; The string is attached to a weigh whose weight is 8 kg
the length of the string which is being stretched is 10 cm
The amount of string that can be stretched by 3 kg weight can be calculated by unitary method
According to the unitary method ;
the string when attached to a 1 kg weight the length will be = 10 / 8 = 5 /4
Thus the amount of string that can be stretched by 3 kg weight is 5/ 4× 3
= 15 / 4 = 3.75 cm
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I need the correct answer i have 1 more chance at the question and i must complete 100% mastery to get credit for my homework
Given:
The equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]Required:
Find the non-zero solution to the equation.
Explanation:
The given equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]Rewrite the equation as:
[tex]2x^{\frac{5}{3}}=18x[/tex]Divide both sides by 2.
[tex]x^{\frac{5}{3}}=9x[/tex]Take cube on both sides.
[tex]\begin{gathered} (x^{\frac{5}{3}})^3=(9x)^3 \\ x^5=729x^3 \\ x^5-729x^3=0 \end{gathered}[/tex]Take out common x
[tex]x^3[/tex][tex]x^3(x^2-729)=0[/tex]Find the factor by using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex][tex]\begin{gathered} x^3(x-27)(x+27)=0 \\ x=0,27,-27 \end{gathered}[/tex]Final Answer:
Thus the non-zero solutions to the given equation are x =27, -27.
3) Sketch a graph, labelling and scaling the axes, of the line y = 2x – 3.
y = 2x - 3
Put x = 0 and solve
y = 2(0) - 3
y = 3
We have a point (0, 3)
Put y = 0 and solve for x
0 = 2x - 3
2x = 3
x = 3/2
x = 1.5
The second point is (1.5, 0)
Below is the graph
The inequality 2c−3<9 represents the amount of money a student can spend on c candy bars. Select the values that best complete the sentence. The solution to the inequality is , and it represents that the student can buy a maximum of whole candy bars.
He can buy 5 candy at most with this inequality 2c-3<9 as the inequality will result in c<6 as the definition of inequality says, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another".
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. The greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols. Take the same amount away from both sides. Add the same positive number to both sides. Subtract the same positive number from both sides. Reverse the sign and multiply both sides by the same negative number.
Here,
2c-3<9
add 3 both side,
2c-3+3<9+3
2c<12
divide both side by 2,
c<6
According to the definition of inequality, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another," he can only purchase a maximum of 5 candies with the inequality 2c-3<9.
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Simplify the expression 2n/6n+4 times 3n+2/3n-2
Answer:11n^3/9-2n^2/3+44n/3-8Step-by-step explanation:
Step-by-step explanation:
9=4/t Math Answer 6th grade problem
9=4/t
To solve for t
multiply both-side of the equation by t
That is;
[tex]9\times t=\frac{4}{t}\times t[/tex]9t = 4
divide both-side of the equation by 9
That is;
[tex]\frac{9t}{9}\text{ =}\frac{4}{9}[/tex][tex]t=\frac{4}{9}[/tex]Arsenia has 80 movie posters and 40 band posters. She plans to sell 24 movie posters. She says that if she
also sells 24 band posters, the ratio of movie posters to band posters stays the same. Is that true? Why or
why not? Complete the explanation.
No. Arsenia's statement is not true because if it was true then before and after selling the posters, the ratio have to be same which is 2:1.
Given,
Arsenia has 80 movie posters and 40 band posters
She plans to sell 24 movie posters and 24 band posters.
Number of remaining movie posters =80-24=56
Number of remaining band posters=40-24=16
Ratio of movie posters and band posters before selling,
[tex]80:40=2:1[/tex]
Ratio of movie posters and band posters after selling,
[tex]56:16=7:2[/tex]
Thus, Arsenia's statement is not true because if it was true then before and after selling the posters, the ratio have to be same which is 2:1
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13+v+2v=v+3+4combine like termsmove letters to the leftwhat's left?add or subtract constantwhat's left?divide coefficientanswer
13+v+2v=v+3+4
Combine like terms
13+3v=v+7
Move letters to the left
13+3v-v =7
13+2v=7
Subtract constant
2v=7-13
2v=-6
divide both side by 2
2v/2 = -6/2
v = -3
1. {(1, -2), (-2, 0), (-1, 2), (1, 3)}2. {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15}}Is the relation a function
To find if a relation is a function, identify if there is more that one value of y for the same value of x (if there are more than one value for one value of x is not a function)
Ordered pairs (x,y)
1.
x y
1 -2
-2 0
-1 2
1 3
As there are two values of y when x=1. (1 , -2) and (1 ,3). The relation is not a function2.
x y
1 1
2 2
3 5
4 10
5 15
As there are no more than one value of y for the same value of x. The relation is a function.A cheeseburger it’s twice the price of a slice of pizza and order of three cheeseburgers and four slices of pizza is $15 right in the Quetion for for the green information
Answer: 45+x = 45x
Step-by-step explanation:
15)The demand equation for a certain product is given by the formulap = 32-10.0001x+1where x is the number of units sold in a month and p is the price perunit. If the price is set at $14.75 for the month, how many units will be sold?
The demand equation is given to be:
[tex]p=32-\sqrt{0.0001x+1}[/tex]where p is the price and x is the number of units sold.
If the price per unit is $14.75, the number of units will be calculated as follows:
[tex]\begin{gathered} p=14.75 \\ \therefore \\ 14.75=32-\sqrt{0.0001x+1} \end{gathered}[/tex]Subtracting 32 from both sides, we have:
[tex]\begin{gathered} -\sqrt{0.0001x+1}=14.75-32 \\ -\sqrt{0.0001x+1}=-17.25 \end{gathered}[/tex]Multiply both sides by -1:
[tex]\sqrt{0.0001x+1}=17.25[/tex]Square both sides:
[tex]\begin{gathered} 0.0001x+1=17.25^2 \\ 0.0001x+1=297.5625 \end{gathered}[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 0.0001x=297.5625-1 \\ 0.0001x=296.5626 \end{gathered}[/tex]Divide both sides by 0.0001:
[tex]\begin{gathered} x=\frac{296.5625}{0.0001} \\ x=2965625 \end{gathered}[/tex]The number of units sold will be 2,965,625 units.
multiply: 1/6 (-3/7) answer in simplest form
1/6 (-3/7)
[tex]\frac{1}{6}\cdot\frac{-3}{7}=\frac{-3}{6\cdot7}=\frac{-3}{2\cdot\text{ 3 }\cdot\text{ 7}}=\frac{-1}{2\cdot7}=\frac{-1}{14}[/tex]Answer:
-1 /14
[tex]\frac{-1}{14}[/tex]Let Ln denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the given function on the indicated interval. (Round your answer to four decimal places.) L4 for f(x) = 1/x-1on [3, 4] L4 =
The indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.
Let Ln denote the left-endpoint sum using n sub intervals.
We are given that
[tex]f(x) = \frac{1}{x-1}[/tex] [3,4]
We have to find L4
It means n = 4
x = [tex]\frac{b-a}{n} = \frac{4-3}{4} = \frac{1}{4}[/tex] = 0.25
Now, intervals are
[3, 3.25], [3.25, 3.50], [3.5, 3.75], [3.75, 4]
Now,
[tex]L_{4} = f(x_{0}) \triangle x+f(x_{1})\triangle x +f(x_{2})\triangle x+f(x_{3})\triangle x\\ \\ L_{4} = \frac{1}{3-1} (0.25)+\frac{1}{3.25-1}(0.25)+\frac{1}{3.5-1}(0.25)+\frac{1}{3.75-1}(0.25)\\ \\ L_{4} = 0.7595[/tex]
Hence the answer is the indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.
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Solve by using Substitution: 3x-y=13 2x +2y = -10
Use the diagram below in the following given information to prove the opposite size of a parallelogram are congruent
Given:
ABCD is a parallelogram.
To prove:
[tex]AD\cong BC\text{ and AB}\cong CD[/tex]Proof:
[tex]\begin{gathered} \text{ABCD is a parallelogram}\ldots\ldots\text{ given.} \\ DC\parallel AB\text{ and AD}\parallel BC\ldots\ldots..by\text{ definition of parallelogram} \\ \angle\text{DCA congruent to }\angle\text{BAC; }\angle BCA\text{ congruent to }\angle DAC\ldots\ldots\text{.}AI\text{ angles theorem} \\ AC\cong AC\ldots.\text{ reflexive property} \\ \Delta ADC\cong\Delta CBA\ldots.by\text{ ASA} \\ AD\cong BC\text{ and AB}\cong CD\ldots\ldots by\text{ CPCTC} \end{gathered}[/tex]
Hence proved.
a movie theater is having a special. if a group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75. use the expression 4(5.75 + 7.25) to find the total cost for 4 friends.
The total cost for the 4 friends will be $52.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75.
Now,
Since, a group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75.
Hence, We can formulate;
The total cost = 4 (5.75 + 7.25)
= 23 + 29
= 52
Thus, The total cost for the 4 friends will be $52.
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Question 13A neighborhood association surveyed its residents regarding marital status and living situation. The results are in the table. What is the probabilitythat a resident is married given that the person owns their home?TotalOwns a Home150Rents a Home17032080250330173SingleMarriedDivorcedWidowedTotal53373201205059087910O050을拉茲结印0
This question is a conditional probability question
P(B|A) means Event B given Event A
In other words, event A has already happened, now what is the chance of event B?
From the given question
let
B = the event that a resident is married.
A = the event that the person owns their home.
So
Thus
[tex]P(B\text{/A)=}\frac{80}{320}=\frac{1}{4}[/tex]What is 100 times 95 times 38
Answer: 361000
Step-by-step explanation:
6x2−2x=0
The 1st x is to the 2nd power
Answer:
x = 0 x = 1/3
Some of the children at a nursery arrive by car.
. 40% of the children at the nursery are boys.
70% of the boys at the nursery arrive by car.
• 60% of the girls at the nursery arrive by car.
What is the probability that a child chosen at random from the nursery arrives by car?
Answer:
Will assume that there are 100 kids.
100 x 40% =40 of them are boys
40 x 70% = 28 boys arrive by car.
100 - 40 = 60 - Number of girls in Nursery.
60 x 60% = 36 of them arrive by car.
28 boys + 36 girls = 64 - kids that arrive by car.
64 / 100 = 64% - probability of a randomly picked kid that he/she arrived by car.
Which quadrant includes every points with a positive x-coordinate and a negative y-coordinateA) Quadrant IB) Quadrant IIC) Quadrant IIID) Quadrant IV
Hello!
Let's write some information about each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
Answer:Alternative D) Quadrant IV
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD.A. 18B. 32C. 16D. 6
For the given parallelogram, the diagonals AC and BD intersect at point E. That means;
[tex]\begin{gathered} BE=DE \\ \text{Also,} \\ AE=CE \end{gathered}[/tex]Substitute for the given values and we'll have;
[tex]\begin{gathered} BE=DE \\ y+10=4y-8 \\ \text{Collect all like terms and you'll have;} \\ y-4y=-8-10 \\ -3y=-18 \end{gathered}[/tex]Divide both sides by -3 and you'll have;
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-18}{-3} \\ y=6 \end{gathered}[/tex]Note that line segment BD is made up of;
[tex]\begin{gathered} BD=BE+DE \\ BD=(y+10)+(4y-8)_{} \\ BD=y+10+4y-8 \\ BD=4y+y+10-8 \\ BD=5y+2 \\ \text{When y=6, we now have} \\ BD=5(6)+2 \\ BD=30+2 \\ \text{BD}=32 \end{gathered}[/tex]Therefore, the answer is option B
If a number is tripled and then subtracted from 15 the result is 5 more than twice the number?
The number in the word problem is 2
How to find the number
let the number be x
from the question it is deduced that
If a number is tripled and then subtracted from 15 = 15 - 3x
5 more than twice the number = 2x + 5
equating both sides
15 - 3x = 2x + 5
collecting like terms
15 - 5 = 2x + 3x
10 = 5x
x = 2
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