[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (a-5)^2(5+a)^2\implies (a-5)^2(a+5)^2\implies [(a-5)(a+5)]^2\implies \stackrel{\stackrel{\textit{difference}}{\textit{of squares}}}{[a^2-5^2]^2} \\[2em] [a^2-25]^2\implies (a^2-25)(a^2-25)\implies \stackrel{\mathbb{F~O~I~L}}{a^4-50a^2+25^2}\implies a^4-50a^2+625[/tex]
Can someone please help me with these?
Answer:
Step-by-step explanation:
Solve for z
1. x. 45
_ = _
16. 40
2. x. 1
_ = _
5. 4
3. 2.5. x
_ = _
10. 50
4. x. 2
_ = _
6. 9
Step-by-step explanation:
[tex]1.\ \dfrac{x}{16}=\dfrac{45}{40}\qquad\text{cross multiply}\\\\40x=(16)(45)\\\\40x=720\qquad\text{divide both sides by 40}\\\\\boxed{x=18}\\\\======================[/tex]
[tex]2.\ \dfrac{x}{5}=\dfrac{1}{4}\qquad\text{cross multiply}\\\\4x=(1)(5)\\\\4x=5\qquad\text{divide both sides by 5}\\\\\boxed{x=\dfrac{4}{5}}\\\\======================[/tex]
[tex]3.\ \dfrac{2.5}{10}=\dfrac{x}{50}\qquad\text{cross multiply}\\\\10x=(2.5)(50)\\\\10x=75\qquad\text{divide both sides by 10}\\\\\boxed{x=7.5}\\\\======================[/tex]
[tex]4.\ \dfrac{x}{6}=\dfrac{2}{9}\qquad\text{cross multiply}\\\\9x=(6)(2)\\\\9x=12\qquad\text{divide both sides by 9}\\\\x=\dfrac{12}{9}\\\\x=\dfrac{12:3}{9:3}\\\\\boxed{x=\dfrac{4}{3}}[/tex]
a population of 40,000 decreases by 3.1% each year. what is the approximate population in 4 years
[tex]\bf \textit{Amount of Population Decay} \\\\ A=Pe^{-rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &40000\\ r=rate\to 3.1\%\to \frac{3.1}{100}\dotfill &0.031\\ t=\textit{elapsed time}\dotfill &4\\ \end{cases} \\\\\\ A=4000e^{-0.031(4)}\implies A=40000e^{-0.124}\implies A=\cfrac{4000}{e^{0.124}} \\\\\\ A\approx 35335.194\implies \stackrel{\textit{rounded up}}{A\approx 35335}[/tex]
Amount of population Decay A= Pe^-re
A= accumulated amount
P= initial amount =40000
r=rate ⇒3.1% ⇒ 3.1/100. ⇒0.031
t = elapsed time ⇒ 4
A=40000e ^0.031(4) ⇒A=40000 ^0.124⇒A=40000/e^0.124
A ≈35335.194 ⇒ A ≈ 35335.(rounded up
What is called population?The population means is nothing but the average of this group of items. It is basically arithmetic mean of the group and can be calculated by taking a sum of all the data points and then dividing it by the number of items we have in the group.
What is called population?A population is defined as a group of individuals of the same species living and interbreeding within a given area. Members of a population often rely on the same resources, are subject to similar environmental constraints, and depend on the availability of other members to persist over time.
What is population and its example?Population is the number of people or animals in a particular place. An example of population is over eight million people living in New York City.
learn more about population, refer
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Which expression represents the product of 6 and y?
A. 6y
B.6 + y
C.6 − y
D. 6 over y
I think it is A for this question
I think the answer is B) 6 + y because and usually means add
Assume that the following events are independent:
• probability that a student is a high school junior is 0.47
• probability that a student is a high school junior and owns a car is 0.14
What is the probability that a student owns a car, given that the student is a high school junior? (round to hundredths)
A)0.07
B)0.30
C)0.33
D)0.61
Answer:
option B
0.30
Step-by-step explanation:
Given in the question,
probability that a student is a high school junior = P(A) = 0.47
probability that a student is high school junior and owns car = P(A∩B) = 0.14
It is question of conditional probability
Formula to use
Probability = P (A∩B) / P (A)
= 0.14 / 0.47
= 0.297
≈ 0.30
Answer:
0.30
P(A|B) =
P(A and B)
P(B)
=
0.14
0.47
= 0.29787
Step-by-step explanation:
Find the equation of the line
Use exact numbers
Y=___x+___
the equation for your answer is y=mx+b
Answer:
[tex]y=-\frac{1}{4} x-6[/tex]
Step-by-step explanation:
Slope-Intercept Form
[tex]y=mx+b[/tex]
y: range
m: slope
x: domain
b: y-intercept
We can see that the line intersects at [tex](0,-6)[/tex], which is the y-intercept. We now have:
[tex]y=mx-6[/tex]
To find the slope, we need to start at the y-intercept. We need to find another nice point we can use. There is a nice point at [tex](4,-7)[/tex]. Start at the y-intercept, go down one unit, and go right four units. By doing that, you just found your slope.
[tex]y=-\frac{1}{4} x-6[/tex]
We know it is negative because as the x values become greater, the y values become less.
x2 + 3x - 4 = 0 Find the value of the discriminant. A) 5 B) 6 C) 10 D) 25
Answer:
D
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0, then the discriminant is
Δ = b² - 4ac
x² + 3x - 4 = 0 ← is in standard form
with a = 1, b = 3, c = - 4
b² - 4ac = 3² - (4 × 1 × - 4) = 9 - (- 16) = 9 + 16 = 25 → D
Easy quick Algebra 2 question. Will give brainliest!
Answer:
Option D
Step-by-step explanation:
The domain of h(x) cannot include 0
h(0) = sqrt (-3) = i sqrt(3)
Which is an imaginary number, and doesn't make sense for the equation to represent imaginary numbers if we are talking about the production of hammers.
The same reasoning can be applied for the second statement.
The domain of the graph should not include zero, beacuse zero people cannot produce any wrenches.
Option D.
If this figure were cut exactly in half along the red line, what would be the area of each part? Please hurry still in math class
A) 18 cm2
B) 24 cm2
C) 38 cm2
the answer is C because it is the right answer
Answer:
The answer is D/trust me
Step-by-step explanation:
the other answer is wrong
Accidentally checked in help me plz!!!!!!
Answer:
It is 1/4!
Step-by-step explanation:
Because if you 4 1/4 will equal 1 now do that until you reach 16 then add two 1/4 then you will get you answer.
Please mark me as Brainiest.
And please let me know if you got it correct im curious.
Thank You!:)
Glad to Help!
BTW sorry if you did not understant my explanation.
Answer: 4
Step-by-step explanation:
[tex]16^{\frac{1}{2}}=\sqrt{16}=\sqrt{4\cdot 4}=\boxed{4}[/tex]
Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.
ok did you get what I solved I hope it's fine by you, if you have a problem with the way I solved it still ask questions ok
Is this correct on using the mean , median, mode, and range ?
Answer:
Yes it is the correct "mean" for that
Need help with this please!
Answer:
[tex]y=x^2[/tex]
Step-by-step explanation:
The given relation is
D={(x,y):(3,9),(5,25),(-2,4)}
We can see that;
[tex]3\to 3^2=9[/tex]
[tex]5\to 5^2=25[/tex]
[tex]-2\to (-2)^2=4[/tex]
Hence in general,
[tex]x\to x^2[/tex]
Therefore the equation for the relation is;
[tex]y=x^2[/tex]
what can you tell about the average number of dogs treated by each veterinarian in the past year
Answer: HOPE THIS HELPS! :D ;D
On average, A New Leash on Life Animal Clinic treats MORE DOGS PER DAY than No Ruff Stuff Animal Hospital.
Step-by-step explanation:
So the first option would be correct.
The average number of dogs that should be treated should refer to the first option.
Information regarding the average number of dogs:
Since the average number of dogs should be treated so here the new leash on life animal clinic should be treated more dogs per day as compared to no ruff stuff animal hospital. Therefore, the other options are incorrect.
Learn more about the dogs here: https://brainly.com/question/13305782
if y varies inversely with x and y =5 when x=20 find x when y = -4
Answer:
x=-25
Step-by-step explanation:
Inverse variation
xy =k
We know x and y
20*5 =k
100 =k
So the formula is
x y = 100
We know y = -4
x (-4) = 100
Divide each side by -4
-4x/-4 = 100/-4
x = -25
Is 5 feet greater than 60 inches
Answer:
equal
Step-by-step explanation:
you can convert 60 into 5 feet
Answer:
No. They are equal to each other.
Step-by-step explanation:
12 inches = 1 foot
5 feet = 12 * 5 = 60 inches
5 feet = 60 inches
Evaluate the expression (65+(1/5•5)+6) divided by 9
(65+(1/5•5)+6)÷9
=(71+1)÷9
=72÷9
=8
The expression (65+(1/5\u00b75)+6) divided by 9 simplifies to 72 divided by 9, which equals 8.
To evaluate the expression (65+(1/5\u00b75)+6) divided by 9, we need to follow the order of operations, sometimes known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, we solve the operation inside the parentheses:
1/5\u00b75 = 165 + 1 + 6 = 72Now, we divide the result by 9:
72 div 9 = 8The final answer is 8.
Carlo's wants to use 3 triangles to make a square. can he
Carlo can use 3 triangles to make a square if the triangles are the correct size and type, such as right-angled triangles, whose hypotenuses can form one side of the square.
Alternatively, he could arrange the triangles to cover half the square's area; however, this would require six triangles, not three.
Explanation:It is theoretically possible for Carlo to use 3 triangles to make a square, but it requires the right types and sizes of triangles.
A square is a geometrical shape with four equal sides and four right angles.
Triangles, on the other hand, have three sides and can have various angles.
If Carlo is using right-angled triangles, he might arrange them in such a way that the hypotenuses form one side of the square and the other sides of the triangles complete the remaining sides of the square.
However, this would need a bit of creative thinking and specific side lengths for the triangles to ensure the sides of the resulting square are equal.
Another way to approach this is by considering the area of the shapes.
By dissecting the square into smaller squares, and further into triangles, if three triangles can be arranged to form a larger triangle that covers exactly half the area of the square, then two sets of such triangles would be required to form the entire square.
For this right triangle, what is the cosine of angle C?
A) 12/13
B) 13/12
C) 5/12
D) 5/13
50 points, again by 5 pm.
after I completed the activity, I will go through any questions I may have needed help with and Mark those who were correct.
Answer:
A cos C = 12/13
Step-by-step explanation:
cos theta = adjacent side/ hypotenuse
cos C = BC/AC
But we don't know BC, but we can find it using the Pythagorean theorem
a^2 +b^2 = c^2
5^2 +BC^2 = 13^2
25 + BC ^2 =169
Subtract 25 from each side
BC^2 = 169-25
BC ^2 = 144
Taking the square root of each side
BC =12
cos C = 12/13
a square field has an area of 2000 square feet. to the beat fest foot, how much fencing would be needed to enclose the field
Answer:
180 feet
Step-by-step explanation:
√2000 = 44.8
44.8 x 4 = 179.2 = 180 feet
The amount of fencing that would be needed to enclose this square field is 178.88 feet.
A square field would have both the length and the width being equal both of them could be represented as x.
Area of a square = Length x Width
2,000 = x × x
x² = 2,000
x = √2,000
x = 44.72 feet
The fencing needs to go around the field which means it needs to go around the field's perimeter.
Perimeter of Square = Length x 4
= 44.72 x 4
= 178.88 feet
In conclusion, 178.88 feet of fencing would be needed.
Find out more at https://brainly.com/question/19176786.
If a triangle has side lengths of 14, 48, and 50 units respectively, what type of triangle is it?
By applying the Pythagorean theorem, it's determined that a triangle with side lengths of 14, 48, and 50 units is a right-angled triangle, as the sum of the squares of the two shorter sides equals the square of the longest side.
Explanation:To determine the type of triangle with side lengths of 14, 48, and 50 units, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
This can be represented by the equation c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
In this case, if we consider 50 as the potential hypotenuse (c), and 14 and 48 as the other two sides (a and b), we plug these values into the equation to check: 50² = 14² + 48².
Calculating each side of the equation gives us 2500 = 196 + 2304, which simplifies to 2500 = 2500.
Since both sides of the equation are equal, this confirms that the triangle is indeed a right-angled triangle.
algebra nation test your self
Answer:
did you know when u create a number or an equation or anything dealt with math it never stops. A number can go on and on like how a decimal number can go on and on. So why was math ever created?
So you know what to do in your grown-up life
What is the value of a in the equation 5a - 10a = 45 when b = 3
Answer:
x=-9
Step-by-step explanation:
B is unnecessary here, so we can ignore it. The first thing we do in this equation is simplify by adding like terms. 5a-10a=-5a. So, the equation is now -5a=45. To solve a, we need it by itself. To do that, we undo the multiplication by diving both sides of the equation by -5. 45 divided by -5 is -9, and then we have x=-9.
The equation of the line of best fit of a scatter plot is y= -7 - 2. What is the y intercept
Answer:
(0,-9)
Step-by-step explanation:
You simply solve the equation and you get the y value. And since the x value is zero...
TA DA!!!!
Answer:
Its -2, I took the test and got it right i dont think this person ^ knows what you meant i might even be wrong with what you want but if its mulitiple choices its -2
The teacher passed out math books.The length is 10 inches and the width is 8 inches.What is the perimeter of each book?
Answer:
36 inches
Step-by-step explanation:
P= 2l + 2w
P= 2(10) + 2(8)
P= 20 + 16
P= 36
Answer:
The answer is 36inches
Step-by-step explanation:
to find out a perimeter of something you need to add the the with and length so basically all you had to do was
10+10+8+8 = 36 inches
hope this helps bye
Randys bicycle tires have a diameter of 42 centimeters. which is the circumference of one of the tires?use 3.14 for pi
Answer:
C =131.88 cm
Step-by-step explanation:
We can find the circumference of a circle by using
C = pi * diameter
C = 3.14 * 42
C =131.88 cm
Answer:
131.88 cm²Step-by-step explanation:
Well,
Here we go:
Circumference of circle or the tire = 2πr = 2 × 3.14 × [tex]\frac{42}{2}[/tex]
= 131.88 cm²
which one isn't? anyone know the answer to it
Answer:
Greater than 5 and less than 6
Step-by-step explanation:
To find the square root of 34, find the closest perfect squares to it.
The closest perfect squares are 25 and 36
The square root of 25 is 5
The square root of 36 is 6
Therefore, the square root of 34 is greater than 5, and ess than 6.
(It's in between 5 & 6).
Brainliest! And 89 points hurry dont have much time! There are 10 fish tanks at a pet store. The data shows the number of fish in each tank.
30, 32, 41, 38, 42, 30, 35, 38, 40, 45
Create a histogram of this data.
To create a histogram, hover over each number of fish range on the x-axis. Then click and drag up to plot the data.
There are no tanks with less than 30 fish, so the first two groups ( 20-24) and (25-29) aren't used.
There are 3 tanks with 30-34 fish.
There are 3 tanks with 35-39 fish.
There are 3 tanks with 40-44 fish.
There are 1 tanks with 45-49 fish.
Now drag the bars for each group to the number of tanks.
See attached picture:
Answer:
There are no tanks with less than 30 fish, so the first two groups ( 20-24) and (25-29) aren't used.
There are 3 tanks with 30-34 fish.
There are 3 tanks with 35-39 fish.
There are 3 tanks with 40-44 fish.
There are 1 tanks with 45-49 fish.
Now drag the bars for each group to the number of tanks.
Step-by-step explanation:
Solve: –7(3x – 7) + 21x ≥ 50
Answer:
no solution
Step-by-step explanation:
if you simplify it all then you have to flip creating 50 = 49
The variable got eliminated. Then inequality –7(3x – 7) + 21x ≥ 50 has no solution.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
–7(3x – 7) + 21x ≥ 50
Simplify the inequality, then we have
–7(3x – 7) + 21x ≥ 50
–21x + 49 + 21x ≥ 50
–21x + 49 + 21x ≥ 50
–21x + 21 ≥ 1
The variable got eliminated. Then inequality –7(3x – 7) + 21x ≥ 50 has no solution.
More about the inequality link is given below.
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Write the absolute value equation if it has the following solutions. Hint: Your equation should be written as |x−b| =c. (Here b and c are some numbers.) Chapter Reference b Two solutions: x=2, x=12.
[tex]|x-7|=5[/tex]
ExplanationWe know that we need to write our absolute value equation as [tex]|x-b|=c[/tex]. We also know that the solutions must be [tex]x=2[/tex] and [tex]x=12[/tex]. We need to replace those values for [tex]x[/tex] in our absolute value equation, so we can create a system of equations and find the values of [tex]b[/tex] and [tex]c[/tex].
- For [tex]x=2[/tex]
[tex]|x-b|=c[/tex]
[tex]|2-b|=c[/tex] equation (1)
- For [tex]x=12[/tex]
[tex]|x-b|=c[/tex]
[tex]|12-b|=c[/tex] equation (2)
Now we can solve our system of equations step-by-step:
Step 1. Replace equation (1) in equation (2)
[tex]|12-b|=|2-b|[/tex]
Step 2. Square both sides of the equation to get rid of the absolute values
[tex]|12-b|=|2-b|[/tex]
[tex](12-b)^2=(2-b)^2[/tex]
Step 3. Use the square of a binomial formula: [tex](a-b)^2=a^2-2ab+b^2[/tex] and solve the equation.
For our first binomial, [tex](12-b)^2[/tex], [tex]a=12[/tex] and [tex]b=b[/tex]; for our second binomial, [tex](2-b)^2[/tex], [tex]a=2[/tex] and [tex]b=b[/tex]
[tex](12-b)^2=(2-b)^2[/tex]
[tex]12^2-(2)(12)(b)+b^2=2^2-(2)(2)(b)+b^2[/tex]
[tex]144-24b+b^2=4-4b+b^2[/tex]
[tex]144-24b=4-4b[/tex]
[tex]140=20b[/tex]
[tex]b=\frac{140}{20}[/tex]
[tex]b=7[/tex] equation (3)
Step 4. Replace equation (3) in equation (2) to find the value of [tex]c[/tex]
[tex]|12-b|=c[/tex]
[tex]|12-5|=c[/tex]
[tex]|7|=c[/tex]
[tex]c=7[/tex]
Putting it all together we can conclude that our absolute value equation is [tex]|x-7|=5[/tex]
Answer:Ix-7I=5
Hope this helps lol