Answer:
y = x -1
Step-by-step explanation:
x - y = 7
We need to put this in slope intercept form to find the slope.
Add y to each side
x-y+y =7+y
x = y+7
Subtract 7 from each side
x-7 = y+7-7
x-7 = y
The slope is 1 since it is in the form y = mx+b
We have a slope 1 and an point (1,0)
We can use point slope form to make an equation
y-y1 = m(x-x1)
y-0 = 1(x-1)
y = x -1
This is in slope intercept form
Determine if the two figures are congruent and explain your answer.
Answer:
They can be congurent depending on which two figures you are using
Step-by-step explanation:
The areas of two circles are in the ratio 49:64. Find the ratio of their circumferences.
Answer:
7 : 8
Step-by-step explanation:
Given 2 similar figures with circumference ratio a : b
Then the ratio of the corresponding areas = a² : b²
Here the ratio of areas = 49 : 64
Taking the square root of both gives ratio of circumference
ratio of circumference = [tex]\sqrt{49}[/tex] : [tex]\sqrt{64}[/tex] = 7 : 8
The product of the polynomials (2ab + b) and (a2 – b2)
Answer:
= 2a³b - 2ab² + a²b - b³
Step-by-step explanation:
We multiply the each term in the first polynomial by each in the other as follows.
2ab(a² - b²) + b(a² - b²)
We then open the brackets and get the following.
2a³b - 2ab² + a²b - b³
We can not simplify the product further than this since it has no like terms.
Answer:
First is C
Second is 2
Step-by-step explanation:EDGE 2021
Which point is an x-intercept of the quadratic function f(x)=(x-4)(x+2)
Answer:
x = - 2 or x = 4
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
(x - 4)(x + 2) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
The x- intercepts are at x = - 2, x = 4
Find each product or quotient. Use significant digits.
0.0505 m X 665 m
Triangle ABC is a right triangle. Find the measure of side b. Round to the nearest hundredth.
A) 6.13 cm
B) 6.71 cm
C) 9.53 cm
D) 10.54 cm
E) 12.45 cm
Answer:
Applying the trigonometric functions, 8/b=Tan40
b=8/Tan40
Answer:
C) 9.53 cm
Step-by-step explanation:
We know this is a right triangle, so we can use trig relations
tan A = opposite side/ adjacent side
tan 40 = 8/b
Multiply each side by b
b tan 40 = 8
Divide each side by tan 40
b tan 40 / tan 40 = 8 / tan 40
b = 8/ tan 40
b = 9.534028741
Which expression represents the amount of punch Milena will need for her party?
g + 20
3g
3g + 20
3(20)
Answer:3g+20 on edg
Step-by-step explanation:
Since the guests equals g and 3 cups per guest it would be 3g+ extra 20 so the answer would be 3g+20
The vertex of this parabola is at (-3, -2). Which of the following could be its equation?
Answer:
y = a(x + 3)² - 2 where a is any real number except 0.Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (-3, -2) → h = -3 and k = -2.
Substitute:
[tex]y=a(x-(-3))^2+(-2)=a(x+3)^2-2[/tex]
The equation of parabola is , [tex]y= -2(x+3)^{2} - 2[/tex]
What is a parabola?Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.What are the 4 types of parabola?There are three types of parabolas. The three forms are: vertex form, standard form and intercept form. Each form provides you a different key feature for the graph.What is parabola and examples?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.What is equation of parabola?[tex]y = a(x- h)^{2} + K[/tex].
According to the question:
Applying value in equation gives.
[tex]y= -2(x-(-3))^{2} -2\\[/tex]
[tex]y= -2(x+3)^{2} - 2[/tex]
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Rewrite the function by completing the square.
f(x) = x2 – 10x + 44
+
f(x) = (x+
Answer:
[tex]f(x)=(x-5)^{2}+19[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-10x+44[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-44=x^{2}-10x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)-44+25=x^{2}-10x+25[/tex]
[tex]f(x)-19=x^{2}-10x+25[/tex]
Rewrite as perfect squares
[tex]f(x)-19=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}+19[/tex]
5 - 7 second power + 6 - 7 second power + 5 - 7 second power + 6 - 7 second power + 10 - 7 second power + 10 - 7 second power
ANSWER: -252
HOW TO GET IT:
Simply follow PEMDAS. Solve each exponent first, then do the rest.
Answer:
144
Step-by-step explanation:
5-7 = 2 2^2 + 6 = 10 - 7 = 3^2 = 9 + 10 = 19 - 7 = 12^2 = 144
I hope this helps even if I am too late! :)
Solve the equation log4(x + 20) = 3
Answer:
x = 44
Step-by-step explanation:
log4(x + 20) = 3
Raise each side to the power of 4
4^ log4(x + 20) = 4^3
x+20 = 4^3
x+20 = 64
Subtract 20 from each side
x+20-20 = 64-20
x = 44
What is the inverse of y=^x3
Answer:
Inverse of y=x^3 is f^-1(x) = ∛x
Step-by-step explanation:
We need to find the inverse of y=x^3
Step 1:
Interchange the variables:
x= y^3
Step 2: Now solve to find the value of y
=> y^3 = x
taking cube root on both sides of the equation
∛y^3 = ∛x
y=∛x
Step 3: Replace y with f^-1(x)
f^-1(x) = ∛x
So inverse of y=x^3 is f^-1(x) = ∛x
Find the quotient. Simplify your answer.
y-4/y ÷ 6/y
Answer: [tex]\frac{y-4}{6}[/tex]
Step-by-step explanation:
To find the quotient asked, you need to make the division indicated.
You can follow these steps:
1. Find the reciprocal of [tex]\frac{6}{y}[/tex]. You need to turn it upside down. Then you get that the recriprocal is:
[tex]\frac{y}{6}[/tex]
2. Now you must multiply [tex]\frac{y-4}{y}[/tex] by [tex]\frac{y}{6}[/tex]:
[tex](\frac{y-4}{y})(\frac{y}{6})=\frac{(y-4)(y)}{(y)(6)}[/tex]
3. Simplifying, you get that the quotient is:
[tex]=\frac{y-4}{6}[/tex]
A die is rolled. What is the probability of rolling the following?
a multiple of 2 or a multiple of 5
Answer:
2/3 chance (67%)
Step-by-step explanation:
Multiples of 5:
(5)
Multiples of 2:
(2)
(4)
(6)
This is a 4/6 chance or 2/3
[tex]|\Omega|=6\\|A|=3+1=4\\\\P(A)=\dfrac{4}{6}=\dfrac{2}{3}\approx67\%[/tex]
Which is equivalent
Answer:
[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]
Step-by-step explanation:
This question is on rules of rational exponential
where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;
General expression
[tex]a^\frac{1}{n} =\sqrt[n]{a}[/tex]
Thus [tex]\sqrt[3]{x} =x^\frac{1}{3}[/tex]
Applying the same in the question
[tex]\sqrt[3]{x^5y} =x^\frac{5}{3} y^\frac{1}{3}[/tex]
=[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]
Answer: Second option
[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
Step-by-step explanation:
By definition we know that:
[tex]a ^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]
In this case we have the following expression
[tex]\sqrt[3]{x^5y}[/tex]
Using the property mentioned above we can write an equivalent expression for [tex]\sqrt[3]{x^5y}[/tex]
[tex]\sqrt[3]{x^5y} = (x^5y)^{\frac{1}{3}}[/tex]
[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
Therefore the correct option is the second option
Compute the permutation. 8 P 4 32 1,680 6,720
ANSWER
[tex]^8P_4=1680[/tex]
EXPLANATION
The given permutation is
[tex]^8P_4.[/tex]
Recall the formula for permutation
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
We substitute n=8, and r=4 to obtain:
[tex]^8P_4=\frac{8!}{(8-4)!}[/tex]
[tex]^8P_4=\frac{8!}{4!}[/tex]
Recall the factorial expansion
[tex]n! = n \times (n - 1) \times (n - 2)...3 \times 2 \times 1[/tex]
We apply this expansion to get:
[tex]^8P_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!}[/tex]
[tex]^8P_4=8 \times 7 \times 6 \times 5[/tex]
[tex]^8P_4=1680[/tex]
6th grade-Write an inequality to represent the situation: The temperature stayed above -15 degrees. Thanks guys!
Let temperature = T
"The temperature stayed above -15 degrees. " means that the temperature is always greater than -15 degrees.
Therefore,
-15 degrees < T
g(x) = x3 + 6x2 + 12x + 8
Determine the function's value when x = -1
g(x)
g(-1) = -3
9(-1) = 0
9(-1) = 1
g(-1) = 27
64
125
Answer:
g(-1) = 5 - 4 = 1
Step-by-step explanation:
Please use " ^ " to denote exponentiation: g(x) = x^3 + 6x^2 + 12x + 8.
Substitute -1 for x in this equation: g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8
Then: g(-1) = -1 + 6 - 12 + 8, or
g(-1) = 5 - 4 = 1
Answer:
The answer is C
Step-by-step explanation:
I just took the test and got it right.
Hopefully this helps you :)
pls mark brainlest ;)
Write the real number 12 as a complex number in form of a+bi
[tex]12+0i[/tex]
.....................
Answer:
12+0i
Step-by-step explanation:
Consider a graph of the equation y = 2x - 1. What is the y-intercept?
Answer:
[0, -1]
Step-by-step explanation:
According to the Slope-Intercept Formula y = mx + b, b is your y-intercept, and in the above raisin, you have your answer in place of that b.
Answer:
[0, -1], or just -1
Which of the symbols correctly relates the two numbers ?
Answer:
C. >
Step-by-step explanation:
The answer is C. because 65 is greater than 56!
Beth rented a bike from Julia’s Bike. It cost $19.60 plus $6 per hour. If Beth rented the bike for two and half hours, how much did she pay ?
Answer:
She payed $34.60.
Step-by-step explanation:
It cost $19.60, just to rent the bike.
Then multiply $6 × 2 (hours) = 12
Now 6 ÷ 2 = 3 (half hour)
Add 12 + 3 = 15
Add everything together
19.60 + 15
You then get $34.60.
She paid $34.60.
What is the unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given
It cost $19.60, just to rent the bike.
Then multiply $6 × 2 (hours) = 12
Now 6 ÷ 2 = 3 (half hour)
Add 12 + 3 = 15
Add everything together
19.60 + 15
You then get $34.60.
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Shirts cost $20 each and ties cost $12 each. Write an expression for the cost of s shirts and t
ties.
20 + 12
The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
Answer:
2+3
Step-by-step explanation:
Evaluate b^2 for b=9
Answer: It's 81
Step-by-step explanation:
So, if B= 9 then it's 9^2 which is 9 x 9 = 81
Hope my answer has helped you and if not i'm sorry.
What is the measure of arc AC? Enter your answer in the box. AC is (7x-2) degrees. ABC is inscribed with (2.5x + 4) degrees
Answer:
The measure of arc AC is equal to 33°
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
∠ABC=(1/2) arc AC
substitute the values
(2.5x+4)=(1/2)(7x-2)
solve for x
5x+8=7x-2
7x-5x=8+2
2x=10
x=5
Find the measure of arc AC
arc AC=(7(5)-2)=33°
Final answer:
The measure of arc AC can be calculated by using the inscribed angle theorem and solving the equation 2×(2.5x + 4) = 7x - 2, which represents the relationship between the inscribed angle and its intercepted arc.
Explanation:
To determine the measure of arc AC, we need to consider the relationship between the inscribed angle of a circle (ABC in this case) and the corresponding arc (arc AC).
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This relationship allows us to set up the equation (2.5x + 4) degrees = 0.5×((7x-2) degrees).
By solving this equation, we can find the value of x, and consequently, the measure of arc AC.
substitute the values
(2.5x+4)=(1/2)(7x-2)
solve for x
5x+8=7x-2
7x-5x=8+2
2x=10
x=5
Find the measure of arc AC
arc AC=(7(5)-2)=33°
Which polygon has an interior angle sum of 1080°?
Step-by-step explanation:
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent.Answer:
Octagon
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides, so
180° (n - 2) = 1080° ( divide both sides by 180° )
n - 2 = 6 ( add 2 to both sides )
n = 8 ← octagon
Joshua likes to read he read 6 books when he was 6 years old every year he doubled the number of book he read the previous year how many total books did he read between the ages of 6 and 10?
When Joshua Is 6 he reads 6 books, when he is 7 he reads 12 books, when he turns 8, he reads 24 books, when he turns 9 he reads 48 books, when Joshua turns 10 he reads 96 books
6+12+24+48+96=186
The answer is C
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Answer:
Joshua read 186 books form 6 to 10 years of age.
Step-by-step explanation:
Joshua reads 6 books at the age of 6.
He doubled the number of books he read the previous years.
Now the sequence will be a geometric sequence as
6, 12, 24, ......
We have to calculate the number of books he read from 6 years to 10 years of his age.
Since sum of n terms of a geometric sequence is given by
[tex]S_{n}=\frac{a(r^{n}-1 )}{r-1}[/tex]
where a = first term
r = common ratio
n = number of terms
[tex]S_{5}=\frac{6(2^{5}-1 )}{2-1}[/tex]
= [tex]\frac{6(32-1)}{1}[/tex]
= 6×31
= 186 books
Therefore Joshua read 186 books form 6 to 10 years of age.
subtract the polynomials (3x^2-11x-4)-(x-2)(2x+3)
Answer:
[tex]x^2-10x+2[/tex]
Step-by-step explanation:
Multiply out the two monomials first because of PEMDAS.
[tex](-x + 2) * (2x + 3)=-2x^2+x+6[/tex]
Now add them together.
[tex]3x^2-11x-4-2x^2+x+6=x^2-10x+2[/tex]
The four folded parts of an envelope are opened up to create this figure. What is the surface area of one side of the unfolded envelope?
A. 25 square centimeters
B. 37 square centimeters
C. 50 square centimeters
D. 64 square centimeters
Answer:
Option C. 50 square centimeters
Step-by-step explanation:
we know that
The surface area is equal to the area of four triangles plus the area of rectangle
so
[tex]SA=2[\frac{1}{2}(4)(2)]+2[\frac{1}{2}(6)(3)]+(6)(4)[/tex]
[tex]SA=8+18+24[/tex]
[tex]SA=50\ cm^{2}[/tex]
Answer:
C
Step-by-step explanation:
The total area comprises of the rectangle (area is base * height) and the 4 triangles (area = 1/2 * base * height).
Area of rectangle = 6 * 4 = 24
Area of top triangle = 1/2 * 6 * 3 = 9
Area of bottom triangle = 1/2 * 6 * 3 = 9
Area of rightside triangle = 1/2 * 4 * 2 = 4
Area of leftside triangle = 1/2 * 4 * 2 = 4
Let's add them up and find the correct answer:
Area = 24 + 9 + 9 + 4 + 4 = 50