[tex](x^{2} +8x+16)(x^{2} -8x+16)\\(x+4)^{2} (x-4)^{2} \\(x^{2}-16)^{2} \\[/tex]
it is true; just work them out, you should get what they got :))
Answer:
True.
Step-by-step explanation:
We have been given an equation [tex][x^2 + 8x + 16]\cdot [x^2- 8x+16] = (x^2-16)^2[/tex]. We are asked to determine whether our given equation is true or false.
To answer our given problem, we will simplify left side of our given equation using distributive property as:
[tex]x^2(x^2- 8x+16)+ 8x(x^2- 8x+16)+16(x^2- 8x+16)[/tex]
[tex]x^4- 8x^3+16x^2+ 8x^3-64x^2+128x+16x^2-128x+256[/tex]
Combine like terms:
[tex]x^4- 8x^3+ 8x^3+16x^2+16x^2-64x^2+128x-128x+256[/tex]
[tex]x^4-32x^2+1256[/tex]
Now, we will expand right side of our given equation using perfect square formula as:
[tex](x^2-16)^2=(x^2)^2-2(x)(16)+16^2[/tex]
[tex](x^2-16)^2=x^4-32x+256[/tex]
Since both sides of our given equation are equal, therefore, our given statement is true.
When navigating the maze, the robot will only need to go north, south, east, and west. It can be useful to use the complex plane to represent these directions. When using the complex plane this way, we use numbers such that their magnitude is equal to 1. If we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?
Answer:
N=i
S = -i
E =1
W = -1
Step-by-step explanation:
If facing north is represented by i, then facing south would be the opposite or -i.
We can let facing east be 1 because the magnitude has to be 1, so facing west would be the opposite or -1
Figure ABCD is a parallelogram with point C (−4, 1). Figure ABCD is rotated 90° clockwise to form figure A′B′C′D′. What coordinate would be the output for point C'?
C' (1, 4)
C' (1, −4)
C' (−1, −4)
C' (−1, 4)
Use the distributive property to remove the parentheses.
-5(-6w+3v-5)
Answer:
[tex] 30w - 15v + 25 [/tex]
Step-by-step explanation:
Multiply -5 by each term inside the parentheses.
[tex] -5(-6w+3v-5) = [/tex]
[tex] = -5 \times (-6w) + (-5) \times 3v + (-5) \times (-5) [/tex]
[tex] = 30w - 15v + 25 [/tex]
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
Multiply.
Answer:
Alternative A
Step-by-step explanation:
2x(x² + 2x - 6)
2x³ + 4x² - 12x
I hope I helped you
Answer: A
Step-by-step explanation:
2x(x² + 2x - 6)
= 2x(x²) + 2x(2x) + 2x(-6)
= 2x³ + 4x² - 12x
In a right triangle one acute angle measures 48 more than 2 times the other. If the sum of the measure of the two acute angles must equal 90 find the measure is the acute angles
A)14,76 B)16,74 C)15,78. D)13,77
Answer:
A
Step-by-step explanation:
let one acute angle be x then the other is 2x + 48
Their sum is 90 , hence
x + 2x + 48 = 90
3x + 48 = 90 ( subtract 48 from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
the 2 acute angles are x = 14° and (2 × 14 ) + 48 = 28 + 48 = 76°
if k=[-4/2 6/-3] and m=[2/8 -2/5] what is x when 2x -k = m
[tex]k=\left[\dfrac{-4}{2},\ \dfrac{6}{-3}\right]=[-2,\ -2]\\\\m=\left[\dfrac{2}{8},\ \dfrac{-2}{5}\right]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\x=[a,\ b]\\\\2x-k=m.\ \text{Substitute:}\\\\2[a,\ b]-[-2,\ -2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a,\ 2b]-[-2,\ -2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a-(-2),\ 2b-(-2)]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a+2,\ 2b+2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\iff2a+2=\dfrac{1}{4}\ \wedge\ 2b+2=-\dfrac{2}{5}[/tex]
[tex]2a+2=\dfrac{1}{4}\qquad\text{subtract 2 from both sides}\\\\2a=\dfrac{1}{4}-2\\\\2a=\dfrac{1}{4}-\dfrac{8}{4}\\\\2a=-\dfrac{7}{4}\qquad\text{divide both sides by 2}\\\\\boxed{a=-\dfrac{7}{8}}\\\\2b+2=-\dfrac{2}{5}\qquad\text{subtract 2 from both sides}\\\\2b=-\dfrac{2}{5}-2\\\\2b=-\dfrac{2}{5}-\dfrac{10}{5}\\\\2b=-\dfrac{12}{5}\qquad\text{divide both sides by 2}\\\\\boxed{b=-\dfrac{6}{5}}\\\\Answer:\ \boxed{x=\left[-\dfrac{7}{8},\ -\dfrac{6}{5}\right]}[/tex]
Answer:
It's B on edge 2021
Step-by-step explanation:
...
Tim can eat 7 apples at a time and barry can eat 2 apples at a time . How many more apples can tim eat
Answer: 5
Step-by-step explanation: Take 2 from 7 to get 5
can someone help me with this question?
Answer:
Go to graphing website desmos.com and plug the equation in to see graph
Step-by-step explanation:
1) Starting graph: Linear Graph (x)
Translations:
|x| erase left and copy right, in this case it makes an absolute value graph or a "V graph" informal term
-3(move right)
-2(down 2)
2) Order goes as follows: "||", -3, -2
Graph: see attached
Translations:
The parent graph is y = |x|
a horizontal shift 3 units to the right makes a new graph of: y = |x - 3|
a vertical shift 2 units down makes a newer graph of: y = |x - 3| - 2
Translations are as follows:
horizontal shift 3 units to the rightvertical shift 2 units downThere are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.
Answer:
[tex]P(t)=170\cdot (1.30)^t[/tex]
Step-by-step explanation:
We have been given that there are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year.
We can see that deer population is increasing exponentially as each next year the population will be 30% more than last year.
Since we know that an exponential growth function is in form: [tex]f(x)=a*(1+r)^x[/tex], where a= initial value, r=growth rate in decimal form.
It is given that a=170 and r=30%.
Let us convert our given growth rate in decimal form.
[tex]30\text{ percent}=\frac{30}{100}=0.30[/tex]
Upon substituting our given values in exponential function form we will get,
[tex]P(t)=170\cdot (1+0.30)^t[/tex]
[tex]P(t)=170\cdot (1.30)^t[/tex]
Therefore, the function [tex]P(t)=170\cdot (1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.
During the basketball season, Cory made 21 of the 60 baskets she attempted. Krista made 16 of the 40 baskets she attempted. Paula made 17 of the 50 baskets she attempted. Write the names of the players in order from the least percentage of baskets made to the greatest percentage of baskets made
Answer: Paula, Cory, Krista
Step-by-step explanation: You would divide the attempted baskets with the ones that they already did make: Cory got 35% of her attempted baskets (21 divided by 60), Krista got 40% of her attempted baskets (16 divided by 40), and Paula got 34% of her attempted baskets (17 divided by 50). Hope this helped!
Answer:
Krista cory paul
Step-by-step explanation:
saw it after searching on google
How many different ways can the first 12 letters of the alphabet be arranged?
There are 479001600 different ways the first 12 letters of the alphabet can be arranged.
The first 12 letters of the alphabet can be arranged in 479,001,600 different ways.
The question asks how many different ways the first 12 letters of the alphabet can be arranged. This type of problem is addressed by using permutations, which is a concept in combinatorics, a branch of mathematics. When we talk about arranging a set of items, we are often dealing with permutations.
The formula to determine the number of permutations of a set of n distinct objects is given by n!, which is read as 'n factorial'. The factorial of a number n is the product of all positive integers less than or equal to n.
So, for the first 12 letters of the alphabet, which are 'A, B, C, D, E, F, G, H, I, J, K, L', the number of different ways to arrange these letters would be:
12! (12 factorial)
To calculate 12!, you multiply all the whole numbers from 1 to 12 together:
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 479,001,600
Sweets are sold loose, or pre-packed in 120g bags. The 120g bags are ?1.49 each. The loose sweets are ?0.89 for 100g. By calculating the price per gram, determine which is better value.
Answer:
The loose sweets at ?0.89 for 100 g.
Step-by-step explanation:
First, calculate the price per gram. You do this by dividing the price by the grams.
?1.49 / 120 g = 1.49 / 120 = 0.0124 (4 dp)
Because the answer was very long, I have rounded it to 4 decimal places (4 dp).
?0.89 / 100 g = 0.89 / 100 = 0.0089
Next, you must calculate both pre-packed and loose sweets to the same weight. I am calculating them both to 100 g.
0.0124 x 100 = 1.24
0.0089 x 100 = 0.89
Finally, the cheapest product for 100 g will be the better value. In this case, it is the loose sweets.
A store has a sale on paper cups, 2 packs for $15.00. There are 100 cups in each pack. During the sale, what is the unit price per cup?
15/2=7.5
7.5/100=0.075
0.075$ per cup.
-TheOneandOnly003
The unit price per cup during the sale is calculated by dividing the total cost of $15.00 by the total number of cups (200). The result is $0.075 per cup.
Explanation:To find the unit price per cup during the sale, we must first determine the total amount of cups you are getting for the price. Given that you purchase 2 packs for $15.00, and each pack contains 100 cups, you're buying a total of 200 cups for $15.00. To get the price per cup, you then divide the total price by the total number of cups.
Step 1: Calculate the total number of cups: 2 packs * 100 cups/pack = 200 cups
Step 2: Calculate the price per cup: $15.00 / 200 cups = $0.075 per cup
So, the unit price per cup during the sale is $0.075.
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solve using quadratic equation: 6x^2 + 7x +2=0
In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
To find the measures of the angles in ΔADE, we can apply the angle bisector theorem and the fact that DE is parallel to AB. The measures of ∠ADE, ∠AED, and ∠DAE are denoted as x, y, and z, respectively.
Explanation:In ΔADE, we know that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B. We also know that DE is parallel to AB. Given that m∠ADE is 34° smaller than m∠CAB, we need to find the measures of the angles in ΔADE.
Let's denote the measures of ∠ADE, ∠AED, and ∠DAE as x, y, and z, respectively.
From the angle bisector theorem, we know that ∠CAD = ∠DAB = y+z.
Since DE is parallel to AB, we have ∠ADE = ∠CAB = x+y+z.
Therefore, the measures of the angles in ΔADE are ∠ADE = x, ∠AED = y, and ∠DAE = z.
One side of a kite is 5 cm less than 2 times the length of another. If the perimeter is 14 cm, find the length of each side of the kite.
A) 5 cm, 5 cm
B) 4.2 cm, 3.4 cm
C) 6.3 cm, 7.7 cm
D) 4 cm, 3 cm
D) 4 cm, 3 cm
Step-by-step explanation:Let x represent the length of "another" side. Then "one side" can be represented by (2x -5 cm).
The perimeter of the kite is the sum of two sides of each length:
... P = 14 cm = 2(x) + 2(2x -5 cm)
Dividing by 2 and collecting terms, we have ...
... 7 cm = 3x -5 cm
... 12 cm = 3x
... 4 cm = x . . . . the length of "another" side
... 2(4 cm) -5 cm = 3 cm . . . . the length of "one side"
The two different side lengths are 4 cm and 3 cm.
What is 2x^3-x^2+3 divided by x-3?
Answer: (A) 2x² + 5x + 15 + [tex]\bold{\dfrac{48}{x-3}}[/tex]
Step-by-step explanation:
x - 3 = 0 ⇒ x = 3
Using synthetic division:
3 | 2 -1 0 3
| ↓ 6 15 45
2 5 15 48 ← remainder
Factored polynomial is: 2x² + 5x + 15 + [tex]\dfrac{48}{x-3}[/tex]
Your parents have $2745.69 on credit card with a 12.75% apr. They miss their minimum payment and there is a late fee of $29.00. How much is their balance at the beginning of they second month
Answer: Their balance at the beginning of their second month is $2803.86.
Step-by-step explanation:
Since we have given that
Amount on credit card = $2745.69
APR on credit card = 12.75%
Late fee = $29
According to question, they miss their minimum payment .
So, their balance at the beginning of their second month is given by
[tex]2745.69\times \frac{12.75}{12\times 100}\\\\=29.17\\\\\text{After late fees }=29.17+29\\\\=58.17\\\\\text{ Amount in the beginning of their second month }\\\\=\$2745.69+58.17\\\\=2803.86[/tex]
Hence, their balance at the beginning of their second month is $2803.86
Answer:
2,803.86
Step-by-step explanation:
1 _____ 2
Choose the relationship symbol to make a true statement.
<
=
>
Answer:
The answer =
Step-by-step explanation:
If triangle ABC is congruent to triangle XYZ, then which of the following is congruent to ∠Z?
option 1. ∠A
option 2. ∠B
option3. ∠C
option 4. ∠X
Answer:
The answer is ∠CStep-by-step explanation:
If the reclusive rule for a geometric sequence is a1 = 6 an = 2an-1.
What would be the explicit rule?
[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=6,\ a_n=2\cdot a_{n-1}.\\\\\text{Therefore}\ r=2.\ \text{Substitute:}\\\\a_n=6\cdot2^{n-1}=6\cdot2^n\cdot2^{-1}=6\cdot2^n\cdot\dfrac{1}{2}=\boxed{3\cdot2^n}[/tex]
Sam is going to the store to buy pumpkins. Small pumpkins cost $2.50 and large pumpkins cost $6.00. He needs to buy at least 20 pumpkins, and he can spend no more than $90.
Which transformations map the strip onto itself?
PLEASE help!!!! Will give BRAINLIEST.
Thank you very much!
Answer: D.
A horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180° rotation.
The transformations that can map a strip onto itself in geometry are reflection, rotation, and translation. Reflection flips the shape over an axis, rotation turns it around a central point, and translation moves it along a vector without changing its orientation.
Explanation:In mathematics, particularly geometry, there are several types of transformations that can map a figure onto itself. Probably you are referring to a strip as in a planar shape, such as a rectangle or square. The main transformations that can map this strip onto itself are: reflection, rotation, and translation.
Reflection is like flipping the strip over an axis. If the strip is symmetrical, it will map onto itself. Rotation means turning the strip around a central point. For instance, rotating a square shape 90, 180, 270, or 360 degrees about its center will map it onto itself. Lastly, translation keeps the strip in the same orientation and moves it along a vector direction. As long as it doesn't interfere with its setting, it would still map onto itself.
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On a piece of paper graph f(x)=-1
Answer:
on the y axis ( the vertical line ) circle -1
:)
Unfortunately, I'm having file upload issues so I'll just say what it is. f(x) means value of the function, which is the y-value. So you're basically plotting y=-1. No matter what your x-value is, the y-value is always -1. So, it is a horizontal line crossing -1 on the y-axis, extending to infinity on either side.
Find the value of X in the diagram. HELP ASAP!!
Answer:
10 =x
Step-by-step explanation:
The figure in the diagram is an equilateral triangle, which means all sides are equal and all angles are equal. If all angles are equal, each angle is equal to 60 degrees (180/3=60). Therefore <B =60.
60 = 5x+10
Subtract 10 from each side
60-10 = 5x+10 -10
50 = 5x
Divide each side by 5
50/5 = 5x/x
10 =x
Using the attached link below.
A. Find sin x and csc y
B. Find tan x and cot y
C. Find cos x and sec y
D. And if sin theta = 2/3, find the values of cos theta and tan theta
[tex]\text{Use the Pythagorean theorem:}\\\\r-hypotenuse\\\\r^2=7^2+5^2\\\\r^2=49+25\\\\r^2=74\to r=\sqrt{74}[/tex]
[tex]\sin=\dfrac{opposite}{hypotenuse}\\\\\cos=\dfrac{adjacent}{hypotenuse}\\\\\tan=\dfrac{opposite}{adjacent}\\\\\cot=\dfrac{adjacent}{opposite}\\\\\text{We have}\\\\for\ the\ angle\ y:\\\text{opposite = 7}\\\text{adjacent = 5}\\\text{hypotenuse = }\ \sqrt{74}\\\\for\ the\ angle\ x:\\\text{opposite = 5}\\\text{adjacent = 7}\\\text{hypotenuse = }\ \sqrt{74}[/tex]
[tex]\csc x=\dfrac{1}{\sin x}\\\\\sec x=\dfrac{1}{\cos x}[/tex]
[tex]A.\\\\\sin x=\dfrac{5}{\sqrt{74}}=\dfrac{5\sqrt{74}}{74}\\\\\csc y=\dfrac{1}{\frac{7}{\sqrt{74}}}=\dfrac{\sqrt{74}}{7}\\\\B.\\\\\tan x=\dfrac{5}{7}\\\\\cot y=\dfrc{5}{7}\\\\C.\\\\\cos x=\dfrac{7}{\sqrt{74}}=\dfrac{7\sqrt{74}}{7}\\\\\sec y=\dfrac{1}{\frac{5}{\sqrt{74}}}=\dfrac{\sqrt{74}}{5}[/tex]
[tex]D.\\\sin\theta=\dfrac{2}{3}\\\\\sin^2\theta+\cos^2\theta=1\to\left(\dfrac{2}{3}\right)^2+\cos^2\theta=1\\\\\dfrac{4}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{4}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{5}{9}\to\cos\theta=\sqrt{\dfrac{5}{9}}\to\cos\theta=\dfrac{\sqrt5}{3}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\to\tan\theta=\dfrac{\frac{2}{3}}{\frac{\sqrt5}{3}}=\dfrac{2}{3}\cdot\dfrac{3}{\sqrt5}=\dfrac{2}{\sqrt5}=\dfrac{3\sqrt5}{5}[/tex]
Write an equation. Is the given value a solution? A farmer sees 23 of his cows out of the barn. He knows that he has 42 cows altogether. Let c represent the number of cows still in the barn. Could c = 19?
By establishing and solving the equation c + 23 = 42, where c represents the number of cows in the barn, it is demonstrated that c = 19 is indeed a correct solution to the problem.
The student needs to determine if c=19 is a solution for the equation representing the number of cows still in the barn. To represent the total number of cows with those seen outside and those inside, we can write the equation c + 23 = 42. This equation sums the number of cows outside (23) with those still in the barn (c) to get the total number of cows (42).
Calculating the Unknown
Firstly, define the symbol c as the number of cows still in the barn. Then, using our equation c + 23 = 42, we can solve for c by subtracting 23 from both sides of the equation, getting c = 42 - 23, which simplifies to c = 19.
Evaluating the Solution
Substituting c = 19 back into the original equation to check if it makes sense, we get 19 + 23 = 42, which is a true statement, confirming that the value of c is indeed 19 and it is the correct solution.
What is the sum of the first 75 even numbers starting with 2? Enter your answer in the box.
Answer:
5700
Step-by-step explanation:
step 1 Address the formula, input parameters & values.
Input parameters & values:
The number series 2, 4, 6, 8, 10, 12, . . . . , 150.
The first term a = 2
The common difference d = 2
Total number of terms n = 75
step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + Tn)
= 75/2 x (2 + 150)
= (75 x 152)/ 2
= 11400/2
2 + 4 + 6 + 8 + 10 + 12 + . . . . + 150 = 5700
Therefore, 5700 is the sum of first 75 even numbers.
Final answer:
To find the sum of the first 75 even numbers starting with 2, use the sum of arithmetic sequence formula: (75/2) * (2 + 150) = 5,700.
Explanation:
The sum of the first 75 even numbers starting with 2 can be calculated using the formula for the sum of an arithmetic sequence. An arithmetic sequence is a sequence of numbers with a constant difference between consecutive terms. In this case, the common difference is 2, since we are dealing with even numbers.
To find the sum of the first 75 even numbers, we use the formula: Sum = (n/2) * (first term + last term), where 'n' is the number of terms. The first term is 2 and the 75th even number can be found by the formula: last term = first term + (n-1)*difference. Thus, the last term = 2 + (75-1)*2 = 2 + 148 = 150.
Using the sum formula: Sum = (75/2) * (2 + 150) = 37.5 * 152 = 5,700. Therefore, the sum of the first 75 even numbers starting with 2 is 5,700.
There are 8 blue marbles, 9 green marbles, 5 yellow marbles, and 6 orange marbles in a bag. What is the probability of drawing an orange marble?
Answer:
3/14
Step-by-step explanation:
Probability( Drawing an orange marble) = number of orange marbles/ total number of marbles in the bag.
= 6 / (8+9+5+6)
= 6/28
= 3/14
he law of cosines for RST can be set up as 52 = 72 + 32 – 2(7)(3)cos(S). What could be true about RST? Law of cosines: a2 = b2 + c2 – 2bccos(A)
Answer:
The length of RT is 5. The length of RS and ST is either 7 or 3.
Step-by-step explanation:
The Law of Cosine is defined as
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]
It is given that, the law of cosine for triangle RST can be set up as
[tex]5^2=7^2+3^2-2(7)(3)\cos(S)[/tex]
Therefore the length of opposite side of angle S is 5. The opposite side of angle S is RT, therefore the length of RT is 5.
The length of two other sides are either 7 or 3.
Therefore length of RT is 5. The length of RS and ST is either 7 or 3.
Answer:
answer is d on edge
Step-by-step explanation: