[tex]-4x-4y = 24~~...(i)\\\\3x +10 = y~~....(ii)\\\\\text{Substitute}~ y = 3x +10~ \text{in eq (i):}\\\\-4x -4(3x+10) = 24\\\\\implies -4x -12x -40=24\\\\\implies -16x =24+40\\\\\implies -16x = 64\\\\\implies x =- \dfrac{64}{16}\\\\\implies x = -4\\\\\text{Substitute}~ x = -4 ~ \text{in equation (ii) to find y:} \\\\y=3(-4) +10 = -12 +10 = -2\\\\\text{Hence,}~(x,y) = (-4,-2)[/tex]
please helppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!
So here, ABCD is being inscribed in a circle, so ABCD is a cyclic quadrilateral (as inscribed in a circle) also, there exists a property of cyclic quadrilateral, i.e, the sum of opposite angles of a cyclic quadrilateral is 180°, so we can just write the following equation using this :
[tex]{:\implies \quad \sf y^{\circ}+83^{\circ}=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf y^{\circ}=180^{\circ}-83^{\circ}}[/tex]
[tex]{:\implies \quad \sf y^{\circ}=97^{\circ}}[/tex]
[tex]{:\implies \quad \boxed{\bf{y=97}}}[/tex]
Use the Distributive Property to solve the equation.
3(x-6)+6=5x-4
what is x?
Answer:
x = -4
Step-by-step explanation:
1) Distribute
3(x - 6) + 6 = 5x - 4
3x - 18 + 6 = 5x - 4
2) Add the numbers
3x - 18 + 6 = 5x - 4
3x - 12 = 5x - 4
3) Add 12 to both sides
3x - 12 = 5x - 4
3x - 12 + 12 = 5x - 4 + 12
4) Simplify
Add The Numbers:
3x - 12 + 12 = 5x - 4 + 12
3x = 5x - 4 + 12
Add the numbers:
3x = 5x - 4 + 12
3x = 5x + 8
5) Subtract 5x from both sides
3x = 5x + 8
3x - 5x = 5x + 8 - 5x
6) Simplify
Combine like terms:
3x - 5x = 5x + 8 - 5x
-2x = 5x + 8 - 5x
Combine like terms:
-2x = 5x + 8 - 8
-2x = 8
7) Divide both sides by each factor
-2x = 8
-2x/-2 = 8/-2
8) Simplify
Cancel terms that are in both the numerator and denominator:
-2x/2 = 8/-2
Divide the numbers:
x = 8/-2
x = -4
Solution:
x = -4
Three friends decide to rent an apartment and split the cost evenly. they each paid $640 towards the total move in cost of first and last month's rent and a security deposit. if rent is $650 per month, how much was the security deposit? a. $10 b. $207 c. $620 d. $1,270
The total amount of security deposit, deposited by three friends after paying the rent is $620.01. Option C is the correct option.
What is a monthly payment?The monthly payment is the amount which is required to pay each month to pay off the borrowed principal amount or the rent of a service charged monthly.
The rent of the apartment is $650 per month. The rent for the two months (first and last) is,
[tex]\rm M = 2\times 650\\\\M =1300[/tex]
This rent is paid by three friends. Thus, the amount which is paid by an individual friend is,
[tex]\rm P=\dfrac{1300}{3}\\\\P=433.33[/tex]
They each paid $640 towards the total move-in cost of first and last month's rent and a security deposit. Therefore,
[tex]\rm P=640-433P=206.67\\\\[/tex]
Thus, $206.67 is paid by each of them towards security deposits. The total amount of security deposit, deposited by 3 of them, is,
[tex]\rm SD=206.67\times 3\\\\SD=620.01[/tex]
Hence, the total amount of security deposit, deposited by three friends after paying the rent is $620.01. Option C is the correct option.
Learn more about the monthly payment here;
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Answer:
Option C
Step-by-step explanation:
I got it right on the test
Classify the number as natural, whole, integer, rational, and/or irrational. select all terms that are correct. natural whole integer rational irrational 4,563 natural – 4,563 whole – 4,563 integer – 4,563 rational – 4,563 irrational – 4,563
The given number 4,563 is a natural, whole, integer, and rational number.
What are the different types of numbers?A number is a fundamental component of mathematics. there are different types of numbers such as whole numbers, integers, natural numbers, rational and irrational numbers, etc.
Whole numbers are numbers such as 0, 1, 2, ... This is a whole number.
Natural numbers can also be counting numbers. They are the whole numbers but starting at 1, not 0.
Integers are whole numbers with negatives. This is an integer.
Rational numbers are any numbers that can be written as a fraction.
We can write this as 4563/1, so it is rational.
Learn more about numbers;
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Which term describes the red curve in the figure below?
A. Hyperbola
B. Parabola
C. Ellipse
D. Circle
Answer:
Hyperbola
Step-by-step explanation:
Sorry if incorect
Hope this helps
Last week, Harry ran 5 laps around the lake. Sophia ran 1 5/6 times as many laps around the lake as Harry did. How many laps around the lake did Sophia run?
Answer:
9 1/6 laps
Step-by-step explanation:
1 5/6 * 5 = 11/6 *5 = 55/6 = 9 1/6
Bob drew a line he thought was close to many of the points and found the equation of the line. He used the points (165, 168) and (174, 178) on his line to find the equation. What is the equation of Bob’s line? If entering decimal values, round to the tenths place.
What does Bob’s equation predict for the height of a person with an arm span of 162 cm? If entering a decimal value, round to the tenths place
We will see that the linear equation is:
y = 1.1*x -13.5
b) The predicted height is 164.7cm
How to get the linear equation?
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
In this case, the line passes through (165, 168) and (174, 178), then the slope is:
a = (178 - 168)/(174 - 165) = 10/9 = 1.1
Then the line is:
y = 1.1*x + b
To get the value of b, we use one of the given points, for example if we use the first one (165, 168) we must have x = 165 and y = 168, replacing that we get:
168 = 1.1*165 + b
168 - 1.1*165 = b = -13.5
The equation is:
y = 1.1*x -13.5
Now we want to find the height of a person with an arm span of 162cm, then we replace x by 162 to get:
y = 1.1*162 -13.5 = 164.7
The predicted height is 164.7cm
If you want to learn more about linear equations, you can read:
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The polynomial equation x cubed minus 4 x squared 2 x 10 = x squared minus 5 x minus 3 has complex roots 3 plus-or-minus 2 i. what is the other root? use a graphing calculator and a system of equations. –3 –1 3 10
The negative one is the third root of the equation x³ - 4x² + 2x + 10. Then the correct option is B.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
The polynomial equation is given below.
[tex]\rm x ^3-4 x ^2+2 x+ 10 = x ^2 -5 x-3[/tex]
The equation can be written as
[tex]\rm x ^3-5 x ^2+7 x+ 13 = 0[/tex]
The equation has a complex root [tex]- 3 \pm 2 \iota[/tex]
Put x = -1, then we have
[tex]\begin{aligned} (-1) ^3-5 (-1) ^2+7 (-1)+ 13 = 0\\\\-1 - 5 - 7 + 13 = 0\\\\0=0 \end{aligned}[/tex]
The equation is satisfied by the negative one. Then the negative one is the third root of the equation.
More about the polynomial link is given below.
https://brainly.com/question/17822016
Answer:
B on edge
Step-by-step explanation:
because B is -1
plewse help me i need help!!?
Answer:
A
Step-by-step explanation:
[tex] - \frac{4}{3} \times \frac{4}{1} = - \frac{1}{3} [/tex]
Hope this helps
HELP PLS!!!! I would appreciate it <333
A circle has a circumference of 26 millimeters. What is the circle's
radius? Use 3.14 for pi and round your answer to the nearest tenth
Answer:
4.1
Step-by-step explanation:
it was right sooo
Simplify the given polynomial expressions as much as possible.
(3x - 6)(8x + 2)
Answer:
Step-by-step explanation:
Remark
All you can really do is remove the brackets. Use FOIL
Solution
First: 3x*8x = 24^2
Outside: 2* 3x = 6x
Inside: -6*8x = - 48x
Last: -6*2 = - 12
Answer
24x^2 + 6x - 48x - 12
24x^2 - 42x - 12
Gina rolls a six-sided die, numbered 1 to 6. She wants to find the probability of
rolling a number less than 6. The size of the sample space is 6, because Gina can
roll any of the six numbers on the die. What is the size of the event space?
The size of the event space is
The solution is
Answer:
5/6
Step-by-step explanation:
thats what it is
The State Board of Education has $1,742 to buy new calculators. If each calculator costs $2, how many calculators can the board buy?
Answer:
871
Step-by-step explanation:
The State Board of Education can buy 871 calculators with the available budget.
Here, we have to find out how many calculators the State Board of Education can buy,
We have to divide the total amount they have ($1,742) by the cost of each calculator ($2):
So, we get,
Number of calculators = Total amount / Cost per calculator
Number of calculators = $1,742 / $2
Number of calculators = 871
So, the State Board of Education can buy 871 calculators with the available budget.
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#SPJ3
Patrick added 1/4 teaspoons of cayenne pepper and 1/3 teaspoons of black
pepper to his enchilada sauce. What is the total amount of the two spices that
Patrick added to his sauce?
how do you find the area of a polygon in a coordinate plane?
Answer: Use this formula
Area = (number of sides × length of one side × apothem)
Step-by-step explanation: The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].
7. Square numbers, such as 1, 4, 9, etc., can be formed by adding consecutive add made beginning with 1. Which is NOT an example of this fact? 1 + 3 + 5 1 +3 + 5 + 7 1+3 + 5 + 7 +9
Assume there are 365 days in a year. (40 points!!!) NEED HELP ASAP will mark brainlist
-What is the probability that ten students in a class have different birthdays?
-What is the probability that at least ten students in a class share their birthday?
check out brainly.com/question/7567074, same question, verified answer
The function, f(n) = 70n – 400, models the profit of the instructor of a guitar class per month, where n is
e number of students enrolled in the class.
How many students must be enrolled in the class for the instructor to make a profit?
ow many students must be enrolled in the class if the instructor needs to make $1,000.00 profit per
onth?
Using the given function, it is found that:
6 students need to be enrolled for the instructor to make a profit.20 students must be enrolled for the instructor to make a profit of $1,000 a month.What is the profit function?The profit when n students are enrolled in the class is given by:
f(n) = 70n - 400.
A profit is made when f(n) > 0, hence:
70n - 400 > 0
70n > 400
n > 5.71.
6 students need to be enrolled for the instructor to make a profit.
A profit of $1,000 is made when f(n) = 1000, hence:
70n - 400 = 1000
70n = 1400.
n = 20.
20 students must be enrolled for the instructor to make a profit of $1,000 a month.
More can be learned about functions at https://brainly.com/question/25537936
Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function:
f(n) = 70n - 400
To make a profit, f(n) > 0, hence:
70n - 400 > 0
n > 6
For a profit of $1000:
70n - 400 = 1000
n= 20
Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.
Find out more on equation at: https://brainly.com/question/2972832
Frank is 6 years older than his brother Joe. The sum of their ages is 38. How old is Joe AND Frank?
Answer:
Joe is 16, Frank is 22
Step-by-step explanation:
To find the solution to this problem, we first divide 38 by two.
38 / 2 = 19.
Then, we subtract 6 from 19 and have 19 and 13. Obviously, 19 is 6 more than 13 (19 - 13 = 6). Now, we need to make sure our number on the left is always 6 more than the number on the right. 19 + 3 = 22, 13 + 3 = 16. Since Frank is older than Joe by 6 years, we get 22 and 16 as their ages.
help me with this
forgot how to do it
Answer:
C =113.04 ft
Step-by-step explanation:
[tex]C = 2\pi \: r \\ \\ \implies C =2(3.14)(18) \\ \\ \implies C =113.04 \: ft[/tex]
(f-g)(x) f(x)=6x-7 g(x)=9x-4
mcgraw hill algebra 1 chapter 8 lesson 1 question 20
Step-by-step explanation with the answer:
Use the given functions to set up and simplify (f−g) & (x) . -3 x -3
For what values of a make each expression true. |a|=-a
Answer:
a=0
Step-by-step explanation:
help me please need help
missing lengths
Step-by-step explanation:
For example ............
Answer:
4. y=3√2 and x=36
Step-by-step explanation:
Here,
interior angle of triangle = 180°
So, 90°+45°+45°=180°
Therefore, the triangle is isosceles triangle
So,
y=3√2 (the corresponding sides of corresponding angle of isosceles triangle are equal)
Again, x^2=(3√2)^2 + (3√2)^2
or, x= √(18 + 18)
or, x=√36
or, x=6
What is the solution to 2x2 8x=x2-16? x=-4 x=-2 x=2 x=4
The solution of the quadratic equation 2x² + 8x = x² - 16 is given as a negative of 4.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The equation is given below.
2x² + 8x = x² - 16
Then on simplifying, we have
x² + 8x + 16 = 0
x² + 4x + 4x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)² = 0
x = -4
More about the factorization link is given below.
https://brainly.com/question/6810544
Answer:
The solution of the quadratic equation 2x² + 8x = x² - 16 is given as a negative of 4.
Step-by-step explanation:
You roll a number cube one time. What is the probability that you roll a 6 or 4? Enter your answer as a fraction in simplest form.
Answer:
1/3 because there are 6 numbers on a number cube and the probability of rolling a 6 or 4 is 2/6 and simplified it would be 1/3
Step-by-step explanation:
if it is right, please mark as brainliest
9. A car is being tested for reliability on a
track by driving at a constant speed. The
car has traveled 150 miles in 3 hours.
a. Complete the table below.
b. If the car breaks down 4.5 hours into
the test and has to stop for a repair
before continuing, what ratio(s) of
distance to time would be affected?
c. How would you expect the ratio to
change? Explain your reasoning.
Help anyone???
Answer:
Step-by-step explanation:
See attached image.
Q4
Find the diameter of a circle if the length of the arc with subtended angle 175° is 12 cm.
(Use it in your calculator.)
1750
B
Answer:
: L = r * θ = 15 * π/4 =
Step-by-step explanation:
Find the zeros of the function f(x) = x² + 49.
Answer:
does not have
Step-by-step explanation:
the function will never equals zero. because x² is always a positive number. The minimum is 49.
Answer:
no step-by-step answer
x= 7 and x= -7
i need help question below :)
Answer:
8 mins - 5hrs - 8 mins (all of the answers are in order btw).
3. Triangle ABC with AB = 3 cm, LABC = 40°,
=
and Z BAC = 70°.
Construct a triangle with the given conditions
Answer: Right angled triangle
Step-by-step explanation: Find attached in the picture