room=400
Ppl=25p
Total cost=775
775=25p+400 ⟨—— equation
775-400=25p
375/25=p
15=p
15 people attended his party
Write the equation of the line in slope-intercept form using the two points: E(-1, 3) and F(-2, -3).
Answer:
[tex]\large\boxed{y=6x+9}[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points E(-1, 3) and F(-2, -3). Substitute:
[tex]m=\dfrac{-3-3}{-2-(-1)}=\dfrac{-6}{-2+1}=\dfrac{-6}{-1}=6[/tex]
Therefore the equation of a line is:
[tex]y=6x+b[/tex]
Put the coordinates of the point E(-1, 3) to the equation and solve it for b:
[tex]3=6(-1)+b[/tex]
[tex]3=-6+b[/tex] add 6 to both sides
[tex]9=b\to b=9[/tex]
Finally we have:
[tex]y=6x+9[/tex]
The difference between the two roots of the equation 3x2+10x+c=0 is 4 2/3 . Find the solutions for the equation.
Answer:
x1 = - 4
x2 = 2/3
Step-by-step explanation:
Divide the equation by 3 to give
x^2 + 10x/3 + c/3 = 0
The sum of the two roots = - 10/3
So
x1 + x2 = -10/3
x1 - x2 = 4 2/3 Add these two equations.
2x1 = -10/3 + 4 2/3 Change 4 2/3 to an improper fraction
2x1 = -10/3 + 14/3 Combine the right
2x1 = 4/3 Divide by 2
2x1/2 =4/3//2
x1 = 2/3
=====================
x1 + x2 = - 10/3
2/3 + x2 = - 10/3
x2 = - 10/3 - 2/3
x2= -12/3
x2 = - 4
=================
(x - 2/3)(x +4) = 0 Multiply through by 3
(3x - 2)(x + 4) =0
==============
Check
(3x - 2)(x + 4) = 0
3x^2 + 12x - 2x - 8 =0
3x^2 + 10x - 8 = 0
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]
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.
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
A store owner paid 15$ for a book. She marked up the price of the book by 40% to determine its sellings price what is the selling price of the book
Answer:
$21
Step-by-step explanation:
She bought the book for $15.
15 x 40% = 6
Since she rised the price just add 6 to 15
Hope it was helpful ^^ <3
Good Luck
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
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
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.
What is the perimeter of triangle ABC ?
Answer:
The perimeter is equal to [tex](y+39)\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of the triangle is equal to the sum of the length of its sides.
so
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=(y+7)+18+14[/tex]
[tex]P=(y+39)\ units[/tex]
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
HURRY ANSWER THIS AND I WIL GIVE YOU BRAINLEST!!!!
Malia solved an equation, as shown below:
Step 1: 6x = 48
Step 2: x = 48 – 6
Step 3: x = 42
Part A: Is Malia's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Part B: How many solutions will this equation have?
her resolution is incorrect because it's 6 times x=48. so to get rid of of the six you have to divide it on both sides, so x can be alone. and that's will only have one solution which is x=8
Is this correct on using the mean , median, mode, and range ?
Answer:
Yes it is the correct "mean" for that
how many different permutations can you make with the letters in the word seventeen A.7560 B.15120 C 17! D.3780
Answer:
A. 7560
Step-by-step explanation:
There are nine letters in the word SEVENTEEN:
1 S
4 Es
1 V
2 Ns
1 T
Possible positions:
For the S, any one of the nine positions. That's ⁹C₁ positions.
For the Es, any four of the remaining eight positions. That's ⁸C₄ positions.
For the V, any one of the remaining four positions. That's ⁴C₁ positions.
For the N, any two of the remaining three positions. That's ³C₂ positions.
For the T, only one way to fill the last position. That's ¹C₁ position.
Total number of positions
= ⁹C₁ × ⁸C₄ × ⁴C₁ × ³C₂ × ¹C₁ = 9 × 70 × 4 × 3 × 1
= 7560
There are 7560 permutations of the letters in the word SEVENTEEN.
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.
An employee’s new salary is $16,275 after getting a 5% raise. What was the salary before the increase in pay?
Answer:
$15,500
Step-by-step explanation:
Let s represent the initial salary. That salary, plus a 5% raise, comes out to 1.05s = $16,275.
Solve for s by dividing both sides by 1.05:
s = $16,275 / 1.05 = $15,500.
The original salary was $15,500.
Final answer:
The original salary before a 5% raise resulting in a new salary of $16,275 was $15,500. We found this by dividing the new salary by 1.05.
Explanation:
The question asks us to determine an employee's original salary before a 5% raise. To solve this, we assume that the new salary ($16,275) is 105% of the original salary (100% + 5% raise). Therefore, we can set up the following equation: Original Salary × 1.05 = $16,275. Now, we want to find the Original Salary, so we divide $16,275 by 1.05.
Original Salary = $16,275 ÷ 1.05
When we divide $16,275 by 1.05, we get the Original Salary = $15,500.
Therefore, before the increase in pay, the employee's salary was $15,500.
Pete played 18 tennis matches in a week. Jack played 6 fewer matches than Pete.
How many times the number of matches pete played is the number of matches jack played?
Answer:
Pete played 1.5 times the number of matches that Jack played.Step-by-step explanation:
Pete played 18 tennis matches in a week.
P = 18
Jack played 6 fewer matches than Pete.
J = P - 6
J = 18 - 6
J = 12
How many times the number of matches pete played is the number of matches jack played?
18 / 12 = 1.5
Pete played 1.5 times the number of matches that Jack played.
Answer:
Pete played 1.5 times the amount of matches Jack did.
Step-by-step explanation:
In order to find this, first find the number that Jack played. Since he played 6 fewer than Pete we can solve by subtracting 6 from Pete's number.
18 - 6 = 12
Now to find how many more times higher it is, divide the number Pete does by Jack's number. 18/12 = 1.5
A line passes through the point (-4,-1) and has a slope of -3/2
Answer:
y=-3/2x-1
explanation:
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:
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
find the radius of a circle with an area of 89 sqaure feet.
Answer:
5.32255
Step-by-step explanation:
if the circle's surface area is 89 square feet. The circle's radius will then be 5.32 feet.
What is the area of a circle?It is the closely curving line drawn from the center to an equally distant point. The distance separating a circle's center and perimeter is its radius.
Let r be the radius of the circle. Then the area of the circle is written as,
A = πr² square units
The area of the circle is 89 square feet. Then the radius of the circle will be given as,
89 = πr²
Simplify the equation, then the radius is written as,
πr² = 89
r² = 28.34
r = 5.32 feet
if the circle's surface area is 89 square feet. The circle's radius will then be 5.32 feet.
More about the area of a circle link is given below.
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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 statement is true about the end behavior of the function?
As the x-values go to positive infinity, the function's values go to positive infinity.
Answer: D, As the x values go to positive infinity, the functions values go to positive infinity.
Step-by-step explanation:
This is true for just about any [tex]y=x^{3}[/tex] graph. As the value of the input (x) get larger, the value of the output (y) will get exponentially larger.
If a leg of a 45-45-90 triangle is 11 then the hypotenuse is...
a)11
b)11√3
c)11√2
d)5.5
Include work if possible :)
Answer:
c)11√2
Step-by-step explanation:
Given that two of the angles are equal ,each measuring 45 degrees then two legs will be equal as well each measuring 11 units. We have a right angled triangle with two sides given and we are required to determine the hypotenuse. We use Pythagoras theorem;
hypotenuse^2 = 11^2 + 11^2
hypotenuse ^2 = 242
hypotenuse = [tex]\sqrt{242}[/tex]
hypotenuse = [tex]11\sqrt{2}[/tex]
Answer:
a) 11
Step-by-step explanation:
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.
Which statement is the correct interpretation of the inequality –5 > –6? (1 point)
Select one:
a. On a number line, −5 is located to the left of 0 and –6 is located to the right of 0.
b. On a number line, −5 is located to the right of 0 and –6 is located to the left of 0.
c. On a number line, −5 is located to the left of –6.
d. On a number line, −5 is located to the right of –6.
Answer: OPTION D.
Step-by-step explanation:
The symbol of the inequality ">" means "greater than". Then, -5 is greater than -6.
If a negative number -a is greater than other negative number -b , then the distance between -a and zero is shorter than the distance between -b and zero.
You can see in the number line attached that -5 is closer to 0 than -6. Therefore, -5 is located to the right of -6.
Answer:
D
Step-by-step explanation:
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
Please help me I don’t understand
Quick Anwser:
Numbers 3-4, you already have the name, BUT you have to classify if the sides are equal. So, for 3-4 ALSO put, “ top and bottom are equal “ or “sides are the same” so for the rhombus, as an example, say, “all sides are the same”..understand?
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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consider the equation x^2=36. Which of the statements below are true? select all that apply
Answer:
See possible solutions below.
Step-by-step explanation:
The equation x^2 = 36 is a polynomial equation.
It can be solved by using a radical on both sides. The solution is x = +/- 6.
The equation has two solutions. x = -6, 6.
While this is a polynomial equation, it is specifically called a quadratic since the exponent is 2.
The equation x^2 = 36 has two real number solutions: x = 6 and x = -6. Statements that acknowledge both of these solutions as possible would be true.
Explanation:The equation in question is x^2 = 36. To solve this equation, one must realize that there are two real number solutions since squaring either a positive or negative number will result in a positive number. Taking the square root of both sides of the equation gives us two solutions: x = 6 and x = -6.
Therefore, any statement claiming that there is only one solution is incorrect. The true statements would acknowledge the existence of two solutions, one positive and one negative.