Answer:
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
(a-b)(a+b) = a^2 - b^2
Step-by-step explanation:
WILL MARK BRAINLIEST!!! 40 POINTS!! ACTUAL ANSWERS, PLZZZ
Answer:
Part A:
[tex]\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807[/tex]
Part B:
The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.
It means:
[tex]\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]
[tex]\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]
[tex]\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]
But when it is about division:
[tex]\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}[/tex]
Example of subtraction of polynomials:
[tex](2x^2+2x+3) - (x^2+5x+2)[/tex]
[tex]x^2-3x+1[/tex]
Step-by-step explanation:
First, it is very important to define what is a polynomial in standard form:
It is when the terms are ordered from the highest degree to the lowest degree.
Therefore I can give:
[tex]x^5-5x^4+3x^3-3x^2+7x+20[/tex]
but,
[tex]x^5+3x^3-3x^2+7x+20-5x^4[/tex] is not in standard form.
For this question, I can simply give the answer: [tex]x^5-5x^4+3x^3-3x^2+7x+20[/tex] and it is correct.
But I will create a fifth-degree polynomial using this formula
[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex]
Also, note that
[tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]
For [tex]a=x \text{ and } b=7[/tex]
[tex]$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$[/tex]
[tex]\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5[/tex]
Sorry but I will not type every step for each value of [tex]k[/tex]
The first one is enough.
For [tex]k=0[/tex]
[tex]$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$[/tex]
Doing that for [tex]k[/tex] values:
[tex]\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807[/tex]
Answer:
Ty for the free pointsd!
Step-by-step explanation:
What is the vertex of the graph of the function f(x) = x2 + 3x - 2?
Answer:
see below
Step-by-step explanation:
We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.
f(x) = x² + 3x - 2
= (x² + 3x + 9/4) - 9/4 - 2
= (x + 1.5)² - 4.25
The vertex is (-1.5, -4.25).
Please help I am not sure how to solve this problem.
Answer:
Measure of arc TSU = 201°
Step-by-step explanation:
For the inscribed circle of triangle XYZ, we have;
∠XZY = 21°
Segment TZ and segment UZ are tangent to circle R
Therefore, ∠ZUR = ∠ZTR = 90° (angle formed by a tangent)
Length UR = Length TR = Radius of circle R
∴ ΔZTR ≅ ΔZUR Side Angle Side (SAS) rule of Congruency
∴ ∠RZT ≅ ∠RZU, (Congruent Parts of Congruent Triangles are Congruent, CPCTC)
∠XZY = ∠RZT + ∠RZU (Angle summation)
21° = ∠RZT + ∠RZU = 2×∠RZU (Transitive property)
∠RZU = 21°/2 = 10.5° = ∠RZT
∴ ∠URZ = 180- 90 - 10.5 = 79.5° = ∠TRZ (CPCTC)
arc TU = ∠URT = ∠URZ + ∠TRZ = 79.5 + 79.5 = 159° (angle addition)
∴ Measure of arc TSU = 360° - 159° = 201° (Sum of angles at the center of the circle R)
Measure of arc TSU = 201°.
the question is in the attachment...
Answer:
11 minutes. 1/4 of 44 is 11
The equation of line l is -3y+4x=9 Write the equation of a line that is parallel to line l and passes through the point (-12,6). a) -3y+4x-69=0 b)-3y+4x-69=0 c)-3y+4x-39=0 d) 3x-3y+66=0
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
- 3y + 4x = 9
3y = 4x - 9
Divide both sides by 3
y = 4/3x - 3
Comparing with the above formula
Slope / m = 4/3
Since the lines are parallel their slope are also the same
So slope of the parallel line l is also 4/3
Equation of the line using point (-12 , 6) is
y - 6 = 4/3(x + 12)
Multiply through by 3
That's
3y - 18 = 4(x + 12)
3y - 18 = 4x + 48
We have the final answer as
4x - 3y + 66 = 0Hope this helps you
Question 30 The Royal Fruit Company produces two types of fruit drinks. The first type is pure fruit juice, and the second type is pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Answer:
The answer is below
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?
Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).
Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:
x + y = 80 . . . 1)
Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:
0.65x + 0.9y = 68 . . . 2)
We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:
0.65x + 0.65y = 52 . . . 3)
Subtract equation 3 from 2 and solve for y:
0.25y = 16
y = 16/0.25 = 64
y = 64 pints
Put y = 64 in equation 1:
x + 64 = 80
x = 80 - 64 = 16
x = 16 pints
Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.
Tina had d dollars. She bought three cupcakes for her and her friends, which cost c dollars each. How much money does she have left after being so nice?
Answer: $(d-3c)
Step-by-step explanation:
Total amount Tina had = $d
Cost of cupcakes = $c
Number of cupcakes purchased = 3
Therefore,
Total cost of cupcakes = cost per cupcake × number of cupcakes
Total cost of cupcakes = $c × 3 = $3c
Amount left after cupcake purchase:
Total amount Tina had - total cost of cupcakes :
$d - $3c
HELP ME PLEASSSSEE On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?
Answer:
3 degrees F
Step-by-step explanation:
if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.
i hope this helped?
Plz Help. Will give braniest if answered correctly with an explanation!!!
angle HDG = angle HFE
==========================================================
Explanation:
We have the statement [tex]\triangle DHG \cong \triangle FHE[/tex] given to us. Note that "H" is in the middle for both sequences of three letters. For DHG, start at H and move back one space to get to D. Move back another unit to wrap around to G. So the new sequence is HDG which forms the first angle.
Follow the same pattern but for FHE now. Start at H, move backward one spot to F, then move back again to wrap around to E. We have HFE
This shows angle HDG pairs up with angle HFE. The corresponding angles are congruent due to CPCTC
CPCTC = corresponding parts of congruent triangles are congruent
Notice how angles HDG and HFE are alternate interior angles, which lead to showing DG is parallel to EF.
3. Daniel is a very good television salesperson. His annual sales average at $187,400. His
commission on sales is 30% and his annual base salary is $40,000. On average what is his
annual gross income?
Answer:
$96,220
Step-by-step explanation:
Daniel is a very good sales person
His annual sales average is $187,400
His commission on sales is 30%
= 30/100
= 0.3
His annual base salary is $40,000
Therefore, Daniel's annual gross income can be calculated as follows
Annual gross income= Annual base salary + Commission on sales
= $40,000 + (30/100 × $187,400)
= $40,000 + 0.3×$187,400
= $40,000+$56,220
= $96,220
Hence Daniel's annual gross income is $96,220
Jake is going to call one person from his contacts at random. He has 30 total contacts. 16 of those contacts are people he met at school.
What is P(Call a person from school)
Answer:16/30
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Find the value of M angle 2 + M angle 4
Answer:
200°
Step-by-step explanation:
<2 = 90° (right angle)
<3 = 70° (vertically opposite angles)
<4 + <3 = 180° ( angles on a straight line)
<4 + 70 = 180°
<4 = 180° - 70°
<4 = 110°
<2 + < 4
= 90 ° + 110° = 200°
Which describes how to graph g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function?
Answer:
[tex]f(x) =\sqrt[3]{x}[/tex]
Step-by-step explanation:
Hello!
Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:
[tex]g(x) = \sqrt[3]{x-5}+7[/tex]
To have the the parent function, we must find the parent one, let's call it by f(x).
[tex]f(x) =\sqrt[3]{x}[/tex]
This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.
Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.
Answer:
5 units to the right and 7 units up (B on edge)
Step-by-step explanation:
The table shows the height increases in inches, of some of the girls in Gina’s class from last month to this month. What girl had a height increase that was greater than 1/2 inch?
The correct answer is Maxine
Explanation:
One of the easiest ways for knowing if a fraction is greater than another is by converting fractions to decimal numbers. This implies dividing the numerator (top number) by the denominator (bottom number). In the case of fraction, [tex]\frac{1}{2}[/tex] the decimal number is 0.5 considering 1 divided into 2 is equal to 0.5. Now to know if other fractions are greater or smaller, this process needs to be repeated.
Gina: [tex]\frac{3}{8} = 0.375[/tex]
Maxine: [tex]\frac{2}{3} = 0.666[/tex]
Shari: [tex]\frac{2}{4} = 0.5[/tex]
Vanessa: [tex]\frac{3}{12} = 0.25[/tex]
According to this, the girl with a heigh increased greater than 1/2 inch is Maxine because 0.666 (Maxine heigh increase) is greater than 0.5 (1/2 inch).
if a student is selected at random find the probability the student is a male given that it's a senior. Round to the nearest whole percent.
Answer: 40%.
Step-by-step explanation:
From the table : Total Seniors = 2+3= 5
Number of male seniors = 2
If a student is selected at random find the probability the student is a male given that it's a senior:
P(Male | senior)[tex]=\dfrac{\text{Number of male seniors}}{\text{Total seniors}}[/tex]
[tex]=\dfrac{2}{5}[/tex]
In percent, [tex]\dfrac{2}{5}\times100=40\%[/tex]
Hence, the probability the student is a male given that it's a senior. =40%.
The probability of the student is a male senior is 7%.
Given, here from the 2- way table the total no. students will be 30.
We have to find out the probability of the student select at random, student is a senior male .
We know that, the probability of an event E, will be
[tex]P(E)=\dfrac{No.\ of \ favaurable\ outcomes}{Total\ outcomes}[/tex]
Now,
[tex]P( Senior\ male)= \dfrac{2}{30} \\\\P( Senior\ male)=0.06\\[/tex]
Representing it in percentage as,
[tex]P( Senior\ male)=0.06666\times100\%\\P( Senior\ male=6.66\%[/tex]
Hence the nearest whole percent will be 7%.
Thus probability of the student is a male senior is 7%.
For more details on probability follow the link:
https://brainly.com/question/795909
An ancient Greek was born on April 1st, 35 B.C. and died on April 1st, 35 A.D. How many years did he live?
Answer:
69 years
Step-by-step explanation:
Data provided in the question
Born date of an Ancient Greek = April 1st 35 BC
Diet date of an Ancient Greek = Aril 1st 35 AD
Based on the above information
We can say that
35 + 35 = 70
We deduct 1 as there is no zero
So, it would be
= 70 - 1 year
= 69 years
Hence, An ancient greek lives 69 years and the same is to be considered
What is the area of this polygon?
Enter your answer in the box.
units2
Answer:
39 units²
Step-by-step explanation:
The figure is composed of a rectangle VEDR and Δ RMV
Area of rectangle = VE × ED = 5 × 6 = 30 units²
Area of Δ = 0.5 × RV × perpendicular from M to RV
= 0.5 × 6 × 3 = 9 units²
Thus
Area of polygon = 30 + 9 = 39 units²
Is 3/4 = 9/12 greater or less than 1/2
Answer:
greater than
Step-by-step explanation:
To compare 3/4 to 1/2, let's convert 1/2 so that it has a denominator of 4. This would then be 2/4. Because 3 > 2, 3/4 > 2/4 which means 3/4 > 1/2.
Answer:
Greater
Step-by-step explanation:
It is greater than 1/2 because when you divide the fractions you get- 1/2 = 0.5, 3/4 = 0.75 And this makes it greater.
What the answer now answer only if now answer corry
Answer:
Approximately 11.5 units.
Step-by-step explanation:
We need to find the side opposite to ∠W. We are given the two angles ∠W and ∠X. We are also given that Side X is equal to 7. Therefore, we can use the Law of Sines.
Now, like last time, use the Law of Sines:
[tex]\frac{\sin(V)}{v}=\frac{\sin(W)}{w}=\frac{\sin(X)}{x}[/tex]
We can ignore the first term. Plug in 144 for ∠W, 21 for ∠X, and 7 for x.
[tex]\frac{\sin(144)}{w}=\frac{\sin(21)}{7}[/tex]
Cross multiply:
[tex]7\sin(144)=w\sin(21)\\w=\frac{7\sin(144)}{\sin(21)} \\v\approx11.4812\approx11.5[/tex]
The table shows the probabilities of certain prizes in a restaurant's contest where the first 100 customers are winners. How does the $100 gift card affect the measure of center of the data? A) it increases the mean value of the prizes B) it decreases the mean value of the prizes C) it increases the median value of the prizes D) it decreases the median value of the prizes
Answer:
A) it increases the mean value of the prizes.
Step-by-step explanation:
The median is resistant to large outliers, so it does not change if there is an especially large or small value. So, we can eliminate choices C and D.
I am actually not sure whether the data in the table count $100 as a large prize or a small one, but I am assuming it is a large prize. So, an extremely large prize would increase the mean value of the prizes.
Hope this helps!
The $100 gift card affect the measure of center of the data by increases the mean value of the prizes.
Option A is the correct answer.
What is median?It is the middles value of the given set of numbers after arranging the given set of numbers in an order.
We have,
The $100 gift card has a much larger value compared to the other prizes, and it is only given to one person.
Therefore, adding the $100 gift card to the prizes will significantly increase the total value of the prizes, which will affect the measures of center of the data.
The mean and median are two common measures of center in statistics. The mean is the sum of all the values divided by the number of values, while the median is the middle value when the data is arranged in order.
Adding the $100 gift card will increase the mean value of the prizes, but it will not affect the median value, since the median only depends on the order of the data, not the values themselves.
Therefore,
It increases the mean value of the prizes.
Learn more about median here:
https://brainly.com/question/28060453
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Exercise topic: Permutations and Combinations. A company wants to hire 3 new employees, but there are 8 candidates, 6 of them which are men and 2 are women. If the selection is random: a) In how many different ways can choose new employees? b) In how many different ways can choose a single male candidate? c) In how many different ways can choose at least one male candidate? with procedures. Help me please..
Answer:
(a) 56 ways
(b) 6 ways
(c) 56 ways
Step-by-step explanation:
Given:
candidates: 6 mail, 1 female
number to hire : 3
a) In how many different ways can choose new employees?
use the combination formula to choose r to hire out of n candidates
C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways
b) In how many different ways can choose a single male candidate?
6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways
c) In how many different ways can choose at least one male candidate?
To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.
Since there are only two females, there is no way to choose 3 female candidates.
In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.
Help!! I WILL GIVE BRAINLIEST I NEED HELPPPPPPPPPPPPPPPPPPP PLEASE PLEASE PLEASE PLEASEEEEEEEEEEEEE IM DEADD I REALLY NEED HELP ASAP ITS URGENT
Answer:
arc axb=4.938
Step-by-step explanation:
to find the measure of arc AXB find angle P first
length of the arc=rФ
in triangle APQ sin angle APQ= opp/hyp=AQ(radius)/PQ=5/√5+√21
in traingle PQB sin angle BPQ= opp/hyp.=5/√5+√21
angle P"
2arcsin 5/√5+√21= 94.324 degrees=(π*94.324)/180=1.64626 rad.
arc AXB=Фr (Ф=94.324 , r=3)
arc axb=4.938
y=tan(x-30) period and amplitude
Answer:
No amplitude
Period is pi
Step-by-step explanation:
Caisha has a circular garden with a radius of 4 ft. She needs to put a layer of soil on top. Each bag of soil covers 9.42 square feet. How many bags of soil will she need to buy? 5 bag 6 bags 7 bags 8 bags
Answer:
6 bags
Step-by-step explanation:
Hey there!
Well first we need to find the area of the circle using,
π r^2
4*4 = 16
16 * pi ≅ 50.27
So now to find how much bags needed we do,
50.27 ÷ 9.42 = 5.34
Meaning 6 bags of soil is needed.
Hope this helps :)
Answer:
Caisha will need 6 bags of soil.
(B.) 6 bags :)
Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.
Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g
Determine the equation of a line that passes through A(2,5) and is parallel to the line defined by 3x−y+12=0. State the equation in slope y-intercept form.
Answer:
Step-by-step explanation:
-y = -3x - 12
y = 3x + 12
y - 5 = 3(x - 2)
y - 5 = 3x - 6
y = 3x - 1
can someone please help me
Answer:
B
Step-by-step explanation:
Because this equation is just a normal greater than symbol, it has to be a dotted line.
This graph starts at -2 and goes up 1 and right 3(this cancels out C as an option)
Than you shade the region with the larger number vaules, since it is greater than.
Find the length of, x, of the third side of the triangle.
Answer:
i do not know either so please help me because this is not my level
Answer:
8=x
Step-by-step explanation:
can u give me a 5 star plz ty :)
Taylor had \$147$147dollar sign, 147. Then she spent \$42$42dollar sign, 42 on sneakers. Then, Taylor earned \$53$53dollar sign, 53 by winning a race in her new sneakers! Estimate how much money Taylor has left
Answer:
She has 158 dollars.
Step-by-step explanation:
This problem tells us that originally Taylor had 147 dollars, but she spent 42 dollars on sneakers, thus she now has [tex]147-42 = 105[/tex] dollars. However, she later won a race wearing those sneakers and earned 53 dollars, therefore she now has [tex]105 + 53 = 158[/tex] dollars.
Thus, Taylor has 158 dollars left now.
A carpenter makes wooden chairs. He has enough wood to make 30 chairs. He makes $60 profit on a dining chair and $90 profit on a rocking chair. It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair. He only has 40 hours available to work on the chairs. The carpenter wants to maximize his profit given the constraints. He draws the graph below to represent this situation. Drag and drop the correct numbers to complete the statements below. Given the restraints, the carpenter can maximize profits by making Response area dining chairs and Response area rocking chairs. His total profit for all the chairs will be $Response area.
Answer:
The carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
Step-by-step explanation:
Let x be the no. of dining chairs and y be the no. of rocking chair
Time taken by carpenter to make 1 dining chair = 1 hour
Time taken by carpenter to make x dining chairs = x hours
Time taken by carpenter to make 1 rocking chair = 2 hour
Time taken by carpenter to make y rocking chairs = 2y hours
He only has 40 hours available to work on the chairs.
[tex]\Rightarrow x+2y \leq 40[/tex]
He has enough wood to make 30 chairs.
[tex]\Rightarrow x+y\leq30[/tex]
He makes $60 profit on a dining chair and $90 profit on a rocking chair.
So, profit =60x+90y
Plot the equations on graph
Refer the attached figure
Coordinates of feasible region
(0,20),(20,10) and (30,0)
Profit =60x+90y
At(0,20)
Profit = 1800
At(20,10)
Profit = 1200+900=2100
At(30,0)
Profit=900
So,the carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100