The values of the expression [tex]6x - x^2[/tex] are evaluated for x values from 0 to 6 and a symmetrical pattern around x = 3 is observed, with the expression value increasing up to x = 3 and then decreasing symmetrically.
The expression to evaluate is [tex]6x - x^2[/tex]. Let's plug in each value of x into the expression and see the result.
For x = 0: the expression becomes [tex]6(0) - (0)^2[/tex] = 0.For x = 1: the expression becomes [tex]6(1) - (1)^2[/tex]= 5.For x = 2: the expression becomes [tex]6(2) - (2)^2[/tex] = 8.For x = 3: the expression becomes [tex]6(3) - (3)^2[/tex] = 9.For x = 4: the expression becomes [tex]6(4) - (4)^2[/tex] = 8.For x = 5: the expression becomes [tex]6(5) - (5)^2[/tex] = 5.For x = 6: the expression becomes [tex]6(6) - (6)^2[/tex] = 0.The pattern we can observe from filling the table is that the value of the expression increases until x = 3 and then decreases symmetrically.
At x = 0 and x = 6, the expression has a value of 0, creating a symmetry about the axis x = 3, which is the vertex of the parabola represented by the given quadratic expression.
Carly has 2 more nickles than dimes in her pocket She has 40 cents How many nickels does carly have ? how many dimes does carly have?
Carly has 2 dimes and 4 nickels in her pocket.
Explanation:Let's assume Carly has x dimes in her pocket. Since Carly has 2 more nickels than dimes, she would have x + 2 nickels. The value of x dimes is 10x cents and the value of (x + 2) nickels is 5(x + 2) cents. Since Carly has 40 cents in total, we can set up the equation: 10x + 5(x + 2) = 40.
Simplifying the equation gives us: 10x + 5x + 10 = 40. Combining like terms gives us: 15x + 10 = 40. Subtracting 10 from both sides gives us: 15x = 30. Dividing both sides by 15 gives us:
x = 2.
Therefore, Carly has 2 dimes and 4 nickels.
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you are biking at a speed of 18mph. you are 3 miles behind your friend, who is biking at a speed of 12mph. write and solve an equation to find the amount of time it takes for you to catch up to your friend
What property is 0+91=91
Do b. I will say thanks
What is the solution to the system of equations? { 4x−3y=26 3x+2y=11
round the factors to estimate the products. 697 x 82=
what is the reciprocal of 60
In order to find the reciprocal of a number, we should just flop it over, like so:-
[tex]\sf{The~reciprocal~of~a~is~\frac{1}{a}}[/tex]
According to the formula, the reciprocal of 60 is:-
[tex]\bigstar{\boxed{\pmb{\frac{1}{60}} \longleftarrow\sf{reciprocal~of~60}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? 4 32 128 512
Answer:- 512
Explanation:-
We know that [tex](m+1)^{th},\ (T_{m+1})[/tex] in the binomial expansion [tex](p+q)^n[/tex] is given by
[tex]T_{m+1}=^nC_m\ p^{n-m}q^m[/tex]
Assume that [tex]x^9y[/tex] occurs in the [tex](m+1)^{th}[/tex] term of the expansion of [tex](2y+4x^3)^4=(4x^3+2y)^4[/tex]
[tex]T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m[/tex]
Comparing power of x and y in [tex]x^9y[/tex] we get m=1
Thus term for m=1 [tex]=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y[/tex]
Thus the coefficient of [tex]x^9y[/tex] is 512.
Peyton is altering her new jacket to enter it into the Bodacious Bedazzling Contest. In order for a garment to be considered "bedazzled," it must contain an amount of gems that fall within the range of the following inequality 132 ≤ ½x + 8 ≤ 193. Find the range of gems Peyton must use to enter he jacket in the contest.
Answer:
the range will be 248 ≤ x ≤ 370
Step-by-step explanation:
The given inequality models the range of amount of gems.
132 ≤ 1/2x + 8 ≤ 193
So we have to solve the inequality for the value of x.
132 ≤ [tex]\frac{1}{2}x[/tex] + 8 ≤ 193
Now we subtract 8 from the inequality.
132 - 8 ≤ ([tex]\frac{1}{2}x[/tex] + 8) - 8 ≤ 193 - 8
124 ≤ [tex]\frac{x}{2}[/tex] ≤ 185
Now we multiply the inequality by 2
124 × 2 ≤ [tex](\frac{x}{2})[/tex] × 2 ≤ 185 × 2
248 ≤ x ≤ 370
So the range will be 248 ≤ x ≤ 370
Find an equation for the line with slope m through the point (a,c).
The equation of a line with a given slope and passing through a point can be found using the point-slope formula.
To find the equation of a line with a given slope (m) passing through a point (a, c), we can use the point-slope formula. The point-slope formula is given by:
y - c = m(x - a)
where (x, y) represents any point on the line. This equation represents a line with slope m passing through the point (a, c).
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what is square root of -36?
the square root of a negative number needs to end in I
so find the square root of 36 and add an I
sqrt(36) = 6
so sqrt(-36) = 6i
It takes Henry 3 hours to paint someone’s portrait how many hours would it take for him to paint all 8 of his friends’ portraits
HELP ME ASAP!!!
Ralph ate 1/2 of a pie before dinner. After dinner he ate 1/3 of what was left. What fraction of the pie did he eat after dinner?
Answer:
1/6
Step-by-step explanation:
1/2 * 1/3 = 1/6.
What is the change in temperature from -8°F to 14°F?
What is the ratio of 48 cans for $9.00
Charles will babysit for up to 4 hours and charges $7 per hour. Write a function in function notation for this situation.
Answer:
The function is [tex]C(x)=7x[/tex]
Step-by-step explanation:
Given : Charles will babysit for up to 4 hours and charges $7 per hour.
To find : Write a function in function notation for this situation ?
Solution :
Let the work done by Charles in 'x' hour.
The charges is $7 per hour.
To create a function of x,
The cost function of 'x' hour is [tex]C(x)=7x[/tex]
Charles will babysit for up to 4 hours.
So, The cost for 4 hour is [tex]C(x)=7\times 4[/tex]
[tex]C(x)=\$28[/tex]
For what values of y:is the value of the fraction 7−2y /6 greater than the value of the fraction 3y−7 /12 ?
Answer:
y<3
Step-by-step explanation:
Do you do rsm lol
y<3 is the value.
What is inequality?In mathematics, an inequality is a relation that makes a non-equal assessment between two numbers or different mathematical expressions. Its miles are used most often to evaluate numbers at the quantity line by means of their size. There are several unique notations used to represent exceptional types of inequalities:
The notation a < b means that a is less than b.
The notation a > b approach that a is greater than b.
The range of y which will satisfy this inequality will result in the first fraction of a larger value as compared to the second fraction.
Multiplying both sides of an inequality by 12, we get:
12×10>12×3y-7/12
2(7-2y)>3y-7
14-4y3y-7
14+7>3y+4y
21> 7y
3>9
y<3
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Affonso has 14 fewer dimes than nickels. He has 21 dimes.
Use the five-step problem-solving plan.
How many nickels does Affonso have?
Enter you answer in the box.
add the fractions and write your answer in lowest terms
2/5 + 1/9
A. 1/15
B. 23/45
C. 3/14
D. 19/45
3F equals -8.5 what does F equals
3F=-8.5
F = -8.5 / 3 =-2.8333333
round answer as needed
Help me ASAP!!
A map has a scale of 1 inch = 8 miles. What is the actual distance if the distance on the map is 7.5 inches?
11a+9=4a+30 what is the answer
2.5 repeating as a mixed number
which of the following numbers that when divided by 1/2, give a result less than 1/2 ? select all that apply 3/8, 3/16,6/25,1/3
Answer:
theheckisthis thing
Step-by-step explanation:
How many fourths are in two wholes? Use a fraction model to help you. Show two whole divided into four equal pieces. 2 dived by 1/4
If 20% of the science students at Central High study on physics, 25% study chemistry and the rest study only biology, what is the smallest number of science students who could be studying biology?
Given that 20% of students are studying Physics and 25% Chemistry, the rest, which is 55% are studying Biology. In the simplest case, where the total of students is 100, the smallest number of Biology students would be 55.
Explanation:The question asks us to identify the smallest possible number of students studying biology. Given that 20% of students study Physics and 25% study Chemistry, we can emphasize that the rest are studying Biology. In the simplest situation, the total number of science students could be 100 because percentages are based on 100. Therefore, for this case, 20 students are studying Physics, 25 are studying Chemistry, and the rest which is 55, are studying Biology. Thus, the smallest possible number of Biology students can be 55.
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What is the Value Of X in this diagram
Your digital camera has a 512 megabyte memory card. You take low resolution pictures requiring 4 megabytes of memory each and high resolution pictures requiring 8 megabytes of memory each. Write an equation for the number of low and high resolution pictures you can take.
The number of low and high resolution pictures that can be taken with a 512 megabyte memory card is determined by the equation 4L + 8H = 512, where L represents low resolution pictures and H represents high resolution pictures.
To determine the number of low and high resolution pictures that can be taken with a 512 megabyte memory card, we can set up an equation based on the storage requirements of each type of picture. Let's use L to represent the number of low resolution pictures and H to represent the number of high resolution pictures.
Because each low resolution picture requires 4 megabytes and each high resolution picture requires 8 megabytes, we can write the equation as:
4L + 8H = 512
This equation shows that the total memory used by L low resolution pictures and H high resolution pictures cannot exceed 512 megabytes, the capacity of the memory card.
What percent of 86 is 50 to the nearest whole percent
Answer:
58%
Step-by-step explanation:
Let us suppose x percent of 86 is 50.
Therefore, we have the below equation
x% of 86 = 50
Eliminating percentage, we get
0.0x × 86 = 50
Solve for x
[tex]0.0x\times86=50\\\\0.0x=\frac{50}{86}\\\\x=\frac{50}{86}\times100\\\\x=58.1[/tex]
Hence, in nearest whole percent, we have
x = 58%
Therefore, 58% of 86 is 50
The perimeter of a rectangle is 24cm. If the length in y cm, what is the width?