[tex]f(x) = 3 {x}^{2} + 5x + 1 \\ \\ \frac{f(x + h) - f(x)}{h} \\ \\ \frac{(3(x + h)^{2} + 5(x + h) + 1) - (3 {x}^{2} + 5x + 1 }{h} \\ \\ \frac{(3( {x}^{2} + 2xh + {h}^{2}) + 5x + 5h + 1) - 3 {x}^{2} - 5x - 1}{h} \\ \\ \frac{3 {x}^{2} + 6xh + 3 {h}^{2} + 5x + 5h + 1 - 3 {x}^{2} - 5x - 1 }{h} \\ \\ \frac{6xh + 3 {h}^{2} + 5h}{h} \\ \\ \frac{h(6x + 3h + 5)}{h} \\ \\ = 6x + 3h + 5[/tex]
Which is the equation of a parabola with vertex (0, 0), that opens to the right and has a focal width of 8? a.y^2=8x b.y^2=-8x c. x^2=8y d. x^2=-8y
Answer:
b
Step-by-step explanation:
simplify 4 n^5 + 3.5 n^5 + (-2.1 n^5)
Answer:
[tex]\large\boxed{4n^5+3.5n^5+(-2.1n^5)=5.4n^5}[/tex]
Step-by-step explanation:
[tex]4n^5+3.5n^5+(-2.1n^5)=4n^5+3.5n^5-2.1n^5\qquad\text{combine like terms}\\\\=(4+3.5-2.1)n^5=5.4n^5[/tex]
The losing candidate in a mayoral election received 10,200 votes, which represented 30% of all votes cast in the election.
A. Dorian claims that the total number of votes cast in the mayoral election was 3,060. Dorian made a mistake in his calculations. Why is his claim not reasonable? Explain your answer.
B. Find the total number of votes cast in the mayoral election. Explain how you found your answer.
well, in the election, the losing candidate received 10200 votes, and we know that's 30% of the whole votes cast, le's say the whole amount is "x" or namely 100%.
B)
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 10200&30\\ x&100 \end{array}\implies \cfrac{10200}{x}=\cfrac{30}{100}\implies \cfrac{10200}{x}=\cfrac{3}{10} \\\\\\ 102000=3x\implies \cfrac{102000}{3}=x\implies 34000=x[/tex]
A)
Dorian's 3060 is really 30% of 10200, however, the losing candidate received 30% of the total votes cast, and that is 10200, so Dorian mistakenly is using 30% of the 30% received by the losing candidate as point of reference for her total.
Final answer:
Dorian's claim is incorrect because dividing 10,200 votes by 30% (or 0.30) gives 34,000 votes, which is the correct total number of votes cast in the mayoral election. Therefore, the calculation shows that the total votes are much higher than Dorian's claim of 3,060 votes.
Explanation:
A. Dorian's claim that the total number of votes cast in the mayoral election was 3,060 is not reasonable because if the losing candidate received 10,200 votes which represented 30%, then the total votes should be much higher than 3,060. To find the total, you would divide the number of votes the candidate received by the percentage they represent.
B. To find the total number of votes cast in the mayoral election, you would set up the equation 10,200 = 0.30 * Total Votes. Dividing 10,200 by 0.30 gives the total number of votes cast, which is 34,000.
Equation: Total Votes = 10,200 votes / 0.30 = 34,000 votes
On a number line, show all values of x that have the absolute value less than 3
Unfilled circle on 3, filled circle on 0, line connecting the circles.
•—————o
0 3
The values of x that have the absolute value less than 3 are plotted in the figure attached.
What is the number line?The number line should be represented in the straight line that have the zero point in the middle, having the positive and negative numbers that should be listed on the other side.
Given that to plot all values of x that have the absolute value less than 3,
It can be written as |x| ≤ 3
We can say that,
The values of x that have the absolute value greater than 3 are -3 and 3. It should be located into the equal intervals.
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This is the mathematical relation relating the three sides, a, b, c, of a right triangle.
Answer:
It is the famous Pythagorean theorem which is this equation:
a^2 + b^2 = c^2,
where a and b are the legs and c is the hypotenuse.
Answer:
Pythagorean theorem
Step-by-step explanation:
What is the degree of the function f(x)= x(x+1)2 (2x-3)(x+2)2
Answer:
6
Step-by-step explanation:
Given equation is [tex]f(x)= x(x+1)^2 (2x-3)(x+2)^2[/tex].
Now we need to find about what is the degree of the give function.
We know that degree of polynomial function is the highest exponent of the variable (x).
So we can either expand the whole equation or count the degree of each factor then add those to get the degree of the given function.
Second choice will be easier.
Degree of [tex]x[/tex] = 1
Degree of [tex](x+1)^2[/tex] = 2
Degree of [tex](2x-3)[/tex] = 1
Degree of [tex](x+2)^2[/tex] = 2
Hence degree of the given polynomial function = 1+2+1+2=6
The price of a gallon of milk went from $2.70 to $3.50 in four years. Find the rate of change of the price of the milk
milk went up to a $1.20
Answer:
The rate of change in price is
$0.2 per year
Step-by-step explanation:
This problem bothers on rates
Given data
Initial price of milk = $2.7
Final price of milk = $3. 5
Time duration = 4 years
Hence the rate of the change of price can be estimated as follows
= Δ in price/Δin time
= (Final price - initial price)/4
=3.5-2.7/4
=0.8/4
=$0.2 per year
help with 11a please?? (25 points)
Answer:
so A = 45degrees because tan^-1(1) = 45 and c = 30 because the half triangle is a 30-60-90 triangle so d = 105
Since its a 30-60-90 triangle and you know that one of the sides is 6, you can now infer that the rest of the sides are 8, and 10.
Also using the 6 side you can use a 3-4-5 triangle by dividing 6 by 4 wich equals 1.5 then multiply that by 3 to get the other sides by using Pythagorean therom. so the sides are 10, 7.5 and 12.5 witch gives you the bas and since area = 1/2bh area= 1/2(12.5 times 6)= 37.5
A = 37.5
A car left Sacramento, California, and traveled at an average speed of 95 km/h to Redding California. The distance between the two cities is 260 km. How many hours was the car traveling?
About 2 hours
(About 2 hours and 25 minutes exactly)
I added minutes anyways
260 divided by 95 = 2 Remainder 25
Hrs Mins
Tim needs 3 pounds of vegetables for a vegetable soup recipe.
He already has 2/3 pound of carrots and 1/4 pound of celery.
Drag the vegetables Tim can add to what he already has to make exactly 3 pounds of vegetables.
Answer:
25/12 - pounds more vegetables
Step-by-step explanation:
first we need to put these variables into like terms
36/12 - 3
8/12 - 2/3
3/12 - 1/4
add the last two up and subtract from the first and you get how much you need left over
Tim already has 11/12 pounds of vegetables. He requires Problem Solving for an additional 2 1/12 pounds of vegetables to reach the desired 3 pounds for his soup recipe. Therefore, option B is the correct answer.
The problem is asking about the amount of vegetables Tim needs to add to reach a total of 3 pounds for his soup. Given, he already has 2/3 pound of carrots and 1/4 pound of celery, he already has a combined total of 2/3 + 1/4 = 11/12 pounds of vegetables.
Now, we need to find out how many more pounds of vegetables he needs to reach 3 pounds. To do this, subtract the weight of the vegetables he has from the total weight required: 3 pounds - 11/12 pounds = 25/12 or 2 1/12 pounds.
So, Tim needs to add an additional 2 1/12 pounds of vegetables for his soup. Looking at the options given, Tim should choose option B) 1 1/12 pounds of zucchini.
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The probable question may be:
Tim is preparing a vegetable soup recipe that requires a total of 3 pounds of vegetables. Currently, he has 2/3 pound of carrots and 1/4 pound of celery. To make exactly 3 pounds of vegetables, what additional amount of vegetables should Tim add to his existing ingredients?
Additional Information:
Tim needs 3 pounds of vegetables in total.
He already has 2/3 pound of carrots.
He also has 1/4 pound of celery.
Options for Tim to add to his existing ingredients to make a total of 3 pounds:
A) 5/12 pound of broccoli
B) 1 1/12 pounds of zucchini
C) 2/3 pound of spinach
D) 3/4 pound of tomatoes
(please for the sake of me passing highschool please god in heaven help me i dont want to fail highschool)
How long does it take Heather to do a single push-up?
A.
4 seconds
B.
14 seconds
C.
3 seconds
D.
2 seconds
Your answer is D. 2 seconds because her distance from the floor is consistent. Every push-up is 2 seconds apart, therefore it’s D.
QUICKK
Solve for x. You must write your answer in fully simplified form.
To solve divide both sides by 4 to cancel out the 4 on the x side to get x alone. Then just do -10/4. That gives you 2.5 so (X=2.5). Hope I helped and have a great day and night
Answer:
-5/2
Step-by-step explanation:
We start with 4x = -10 and want to solve this for x.
We divide both sides by 4 (which isolates x), obtaining:
x = -10/4
and then we reduce this to x = -5/2.
In a cafeteria,
3
-
8
of the students are eating salads , and
1
-
4
are eating sandwiches. There are 24 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
The number of students not eating salads and sandwiches are 9
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here: 3/8 of the students in the cafeteria eat salads and 1/4 of the students eat sandwiches.
∴3/8×24+1/4×24=9+6
=15
Thus the number of students eating lunches other than salads or sandwiches are 24-15=9
Hence, The number of students not eating salads and sandwiches are 9
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The first morning Courtney walked on a beach for 20 minutes . She finished 30 minutes before high tide at what time did Courtney start her walk
Martha walked for 0.67 hours.
Here's how we can calculate it:
Total time spent hiking:
12:30 AM - 11:30 PM = 1 hour (since 12:30 AM is midnight and the same as 00:30 AM)
Convert hours to minutes: 1 hour * 60 minutes/hour = 60 minutes
Time spent running:
Subtract the walking time from the total time: 60 minutes - 20 minutes = 40 minutes
Convert running time to hours:
Divide minutes by minutes per hour: 40 minutes / 60 minutes/hour = 0.67 hours
Therefore, Martha walked for 0.67 hours.
Question
If Martha went on a hiking trip at 11:30 PM, and walked for 20 minutes, and ran the rest, and came back at 12:30 AM, how many hours did Martha WALK?
Please show me how to do this problem
Answer:
Hi there, you can use Pitagoras relationship to solve this up (Without using any other "tool".
Point A is located wheter in (-6,8) or could be located in (-6,8)
Step-by-step explanation:
Point A is 10 units away from the origin, and its x coordinate is -6, using this information, you can draw a triangle from 0 to -6 (the basis) and using 10 as the hypotenuse, so, you have this equation:
[tex]H^{2} = x^{2} +y^{2}[/tex]
solving for Y variable, you have this
y=±[tex]\sqrt{10^{2}-(-6)^{2} }[/tex]
Note the combined sing ±, meaning that y=8 is a valid answer and that y= -8 is also a valid answer.
Hope It helps
What is an algebraic expression for “23 more than y”
➷ It would be y + 23
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
The algebraic expression for 23 more than y is y + 23
An algebraic expression usually shows the relationship between a variable and a whole number with its arithmetic operations.
In the given question,
Let say the unknown number is yNow when y is more than 23, we have the algebraic expression for 23 more than y as:
y + 23Learn more about algebraic expression here:
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Please help! I am leaving for beach today and want to get homework done first
Answer:
t = 1
Step-by-step explanation:
Formula
i = prt
Givens
P = 500
i = 25
r = 5% = 5/100
t = ?
Solution
25 = 500 * 5/100 * t Cancel out 100 on the right
25 = 5*5*t Combine the right
25 = 25 * t Divide by 25
25/25 = 25*t/25
t = 1
Answer: " 1 year . "
_________________________________________________
Step-by-step explanation:
_________________________________________________
Use the formula/equation:
I = Prt ; that is; " I = P × r × t " ;
in which:
" Interest (in dollars) =
Principal amount ("P" ; in dollars) * r ["rate"] * time ("t", in years) ] ;
Note: the rate, "r" ; refers to the interest rate.
We wish to solve for the "time, "t" .
_________________________________________________
I = Prt ;
_________________________________________________
Let us isolate "t" one one side of the equation;
by rearranging the formula;
We know: I = Prt ;
Divide each side of the equation by "Pr" :
I/ (Pr) = [ (Prt) / (Pr) ] ;
to get:
I / (Pr) = t ;
↔ t = I (P * r ) ;
Now, plug in our given values, and solve for "t" ; time, in years.
Given: P = 500 (dollars) ;
I = 25 (dollars) ;
r = 5% ; Note, for the purposes of this formula; we write this as a "decimal" ;
r = 5% = 5/100 = 0.05 ;
_________________________________________________
t = I / (P * r) ;
t = 25 / (500 * 0.05) ;
t = 25 / (25) ;
t = 1 yrs.
_________________________________________________
Hope this helps!
Best wishes in your academic pursuits
— and within the "Brainly" community, as well!
_________________________________________________
Which graph represents this system? y = 1/2 x +3 y = 3/2x -1
Answer:
The attached picture is the requested graph
Step-by-step explanation:
The system
[tex]y=\frac{3}{2}x-1\\ y= \frac{1}{2}x+3[/tex]
Has the following solution
x = 4 and y = 5 , which serves us to plot the desire graph, both function are lines and they intercept in (4,5)
Answer: A
Step-by-step explanation:
The measures of the three angles of a triangle are given by 3x + 1, 2x − 3, and 9x. What is the measure of the smallest angle?
Answer:
23°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
3x + 1 +2x - 3 + 9x = 180 ( simplify left side )
14x - 2 = 180 ( add 2 to both sides )
14x = 182 ( divide both sides by 14 )
x = 13
The 3 angles are
3x + 1 = (3 × 13) + 1 = 39 + 1 = 40°
2x - 3 = (2 × 13) - 3 = 26 - 3 = 23° ← smallest angle
9x = 9 × 13 = 117°
Find the surface area of the rectangular prism. A. 69.26 ft^2 B. 70.78 ft^2 C. 71.88 ft^2 D. 72.88 ft^2
Answer:
D
Step-by-step explanation:
The surface area of the rectangular prism is the sum of all the 6 faces.
There are 2 faces with length 3 ft and width 3.4 feet. Hence,Area = 2 (3*3.4) = 20.4
There are 2 faces with length 3 ft and width 4.1 ft. Hence,Area = 2 (3*4.1) = 24.6
There are 2 faces with length 3.4 ft and width 4.1 ft. Hence,Area = 2 (3.4*4.1) = 27.88
Thus, Surface Area = 20.4 + 24.6 + 27.88 = 72.88 ft ^2
Answer:
The correct answer option is D. 72.88 ft^2.
Step-by-step explanation:
We are given a diagram of a rectangular prism with width 3 ft, length 3.4 ft and height 4.1 ft and we are to find its surface area.
We know that the surface area of a rectangular prism is given by:
[tex]2(wl \times hl \times hw)[/tex]
So substituting the given values in the above formula to get:
Surface area of rectangular prism = [tex]2[(3 \times 3.4) + (4.1 \times 3.4) + (4.1 \times 3)][/tex] = 72.88 ft^2
from least to greatest
4.769,4.904,4.422
Answer:
4.422, 4.769, 4.904
Step-by-step explanation:
Answer:
LEAST: 4.422
AVERAGE: 4.769
GREATEST: 4.904
I HOPE THIS HELPED !!
what is the answer to -42-34+15= 61
Answer:
-61
Step-by-step explanation:
-42-34=-76= -61
A basketball team plays 3 games in a holiday tournament. According to the tree diagram, how many outcomes are possible?
A) 5
B) 6
C) 7
D) 8
Answer: the answer is D
Step-by-step explanation: there is 8 different strands of outcomes
Answer: D, or 8.
Step-by-step explanation: The first part is a pretty simple win or lose diagram.
That's two possibilities.
The next choice has both Win, both Lose, Lose-Win, or Win-Lose.
That's four possibilities.
The next and last choice is the following: All Win, All Lose, Win-Win-Lose, Lose-Lose-Win, Lose-Win-Win, Win-Lose-Lose, Win-Lose-Win, and Lose-Win-Lose. That leaves a total of 8 combinations.
Find the difference 5x/x^2-x-6 (-) 4/x^2+4x+4
The difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].
To subtract the two rational expressions [tex]\( \frac{5x}{x^2-x-6} \) and \( \frac{4}{x^2+4x+4} \)[/tex], we need to find a common denominator.
First, factor the denominators:
1. x²-x-6 = (x-3)(x+2)
2. x²+4x+4 = (x+2)²
The common denominator will be (x-3)(x+2)(x+2).
Now, rewrite the expressions with the common denominator:
1. [tex]\( \frac{5x}{(x-3)(x+2)} \)[/tex]
2. [tex]\( \frac{4}{(x+2)^2} \)[/tex]
To subtract, the numerators remain the same, so the expression becomes:
[tex]\[ \frac{5x}{(x-3)(x+2)} - \frac{4}{(x+2)^2} \][/tex]
To combine the fractions, we need to rewrite the first fraction with the common denominator:
[tex]\[ \frac{5x(x+2)}{(x-3)(x+2)(x+2)} - \frac{4(x-3)}{(x-3)(x+2)(x+2)} \][/tex]
Now, we can subtract the fractions:
[tex]\[ \frac{5x(x+2) - 4(x-3)}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 10x - 4x + 12}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \][/tex]
So, the difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].
To find the difference between the two rational expressions, we first need to factorize the denominators and simplify where possible. Let's break it down step by step:
1. Factorize the denominators:
[tex]\(x^2 - x - 6 = (x - 3)(x + 2)\) \(x^2 + 4x + 4 = (x + 2)^2\)[/tex]
2. We rewrite the expressions with common denominators:
[tex]\(\frac{5x}{(x - 3)(x + 2)} - \frac{4}{(x + 2)^2}\)[/tex]
3. To simplify these, we need a common denominator, The least common denominator is [tex]\((x - 3)(x + 2)^2\).[/tex], so to get it, we multiply (x + 2) with Expression 1 and (x - 3) with Expression 2 on both numerator and denominator. We get:
[tex]\(\frac{5x(x + 2)}{(x - 3)(x + 2)^2} - \frac{4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]
4. We combine the fractions:
[tex]\(\frac{5x(x + 2) - 4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]
[tex]\(= \frac{5x^2 + 10x - 4x + 12}{(x - 3)(x + 2)^2}\) \(= \frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\)[/tex]
So, the difference between the two rational expressions is [tex]\(\frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\).[/tex]
Complete the square and write the equation in standard form. Then give the center and radius of the circle. 10x2 + 10y2 = 100
2 + y2 = 10 (0, 0), r = 10
x2 + y2 = 100 (0, 0), r = 10
x2 + y2 = 10 (0, 0),
r = 10‾‾‾√
(x - 10)2 +(y - 10)2 = 10 (10, 10),
r = 10‾‾‾√
Answer:
Center: (0,0)
Radius: [tex]r=\sqrt{10}[/tex]
Step-by-step explanation:
The given circle has equation
[tex]10x^2+10y^2=100[/tex]
In order to complete the square, we must make sure the coefficient of the quadratic terms are unity.
We divide through by 10 to obtain;
[tex]x^2+y^2=10[/tex]
The coefficient of the linear terms of both variables are zero.
Therefore the equation can be rewritten as;
[tex](x-0)^2+(y-0)^2=10[/tex]
Comparing to [tex](x-h)^2+(y-k)^2=r^2[/tex]
We have (h,k)=(0,0) to the center of the circle and [tex]r=\sqrt{10}[/tex] to be the radius of the circle.
Answer:
Equation: x² + y² = 10
center = (0, 0)
radius = √10
Step-by-step explanation:
The general equation of a circle is ;
(x - a)² + (y - b)² = r²
Where (a, b) is the coordinate of the center of the circle, and r is its radius.
Where the center is (0,0), the equation becomes,
x² + y² = r²
In our case we have;
10x² + 10y² = 100
dividing both side by ten,
x² + y² = 10
∴ center = (0, 0)
radius = √10
you can afford to pay a maximum of 1/2 of your monthly income for rent? True or false
Answer with explanation:
We will use [tex]\frac{28}{36}[/tex] rule here, to prove that, the statement given is Incorrect,which is you can afford to pay a maximum of 1/2 of your monthly income for rent.
[tex]\frac{28}{36}[/tex] rule, states that,you can use , 28% of gross monthly Income for Housing expenses, and 36 % of your gross monthly income is used for Debt purposes.
→→[tex]\frac{1}{2}[/tex] of monthly income =50 % of Monthly Income
we can use ,only 28% of Monthly income for rent Purpose.
False Statement
EASY! WILL MARK BRAINEST!! What is f(3) for the function f(x)=7x+5
Answer:
26 is the answer
Step-by-step explanation:
Plz help !!!
The graph shows the system y=-x+2 and y=-x^2+x+1
Answer:
=x=1
y=1
2nd choice is the correct answer, (1, 1).
Answer to number three?
Answer:
Step-by-step explanation:
Supplementary angles mean the angles add up 90 degrees.
So, 4x + 18 + 2x + 12 = 90.
Combine like terms...
6x + 30 = 90
Subtract 30 from both sides.
6x = 60
Divide by 6
x = 10
Then to find the measure of angles RST, we plug in 10 for x.
4(10) + 18 = RST
RST = 40 + 18
RST = 58
Find the surface area of the regular hexagonal pyramid. Round your answer to the nearest hundredth. A. 69.18 m^2 B. 79.18 m^2 C. 89.18 m^2 D. 99.18 m^2
Answer: OPTION B
Step-by-step explanation:
Use the following formula:
[tex]SA=\frac{pl}{2}+B[/tex]
Where p is the perimeter of the base, l is the slant height and B is the area of the base.
The perimeter is:
[tex]p=6*s=6*3m=18m[/tex]
Where s is the lenght of a side.
The slant height is given:
[tex]l=6,2m[/tex]
The area of the base is:
[tex]B=\frac{3\sqrt{3}s^2}{2}=\frac{3\sqrt{3}(3m)^2}{2}=23.382m^2[/tex]
Where s is the length of a side.
Substitute values. Then, the result is:
[tex]SA=\frac{(18m)(6.2m)}{2}+23.382m^2=79.18m^2[/tex]
Answer:
The correct answer option is B. 79.18 m^2.
Step-by-step explanation:
We are given a diagram of a regular hexagonal pyramid with height 5.6 m, slant height 6.2 m and base edge length 3m.
We know that the surface area of a regular hexagonal pyramid is given by:
[tex]\frac{PI}{2} +B[/tex]
where P = perimeter of the base, I = slant height and B = base area.
Perimeter of base = [tex]3 \times 6[/tex] = 18 m^2
Base area (area of hexagon) = [tex]\frac{3\sqrt{3} }{2} a^2[/tex] = [tex]\frac{3\sqrt{3} }{2} 3^2[/tex] = 23.38 m^2
Surface area of hexagonal pyramid = [tex]\frac{18 \times 6.2}{2} +23.38[/tex] = 79.18 m^2