Complete question is;
Which of these is an exponential parent function?
A. f(x) = x
B. f(x) = 2^(x)
C. f(x) = x²
D. f(x) = |x|
Answer:
B. f(x) = 2^(x)
Step-by-step explanation:
> In option A, f(x) = x
This function depicts a straight line with intercept as 0 and slope as 1.
> In option C, f(x) = x²
This function depicts a parabola open up since the leading coefficient is greater than 0.
> In option D: f(x) = |x|
This function depicts a straight line y = x for x > 0 and y = -x for x < 0
In option B f(x) = 2^(x)
This function depicts an exponential function because the x is in the exponent form with a base of 2.
A rectangle has a perimeter of 80 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of the perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is ? Cm. Part d: The width is? Cm.
Answer: (a) P = 6W + 2
(b) L = 2W + 1
(c) Width = 13cm
Length = 27cm
Step-by-step explanation:
The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:
L = (2 × W) + 1
(b) L = 2W + 1
Therefore, P = 2(L + W)
P = 2( 2W + 1) + 2W
P = 4W + 2 + 2W
(a) P = 6W + 2
Since perimeter is given as 80cm. Therefore,
P = 6W + 2
6W + 2 = 80
6W = 80 - 2
6W = 78
W = 78/6
W = 13
Width is 13cm
Length = 2W + 1
Length = 2(13) + 1
Length = 27cm
The width of the rectangle is 13cm and the length is 27cm.
Description of a rectangleA rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.
The formula for determining the perimeter of a rectangle = 2x (length + width)
P = 2(L + W)
Perimeter = 80 length = 1 + 2w Width = w Determining the values of width and length80 = 2(1 + 2w + w)
80 = 2(1 + 3w)
40 = 1 + 3w
40 - 1 = 3w
39 = 3w
w = 13cm
Length = 1 + 2(13) = 27cm
To learn more about rectangles, please check: https://brainly.com/question/16595449
What is the sum of the 15th square number and the 5th cube number?
The sum of the 15th square number and the 5th cube number is 350.
The 15th square number will be:
15² = 15 × 15
= 225
The 5th cube number will be:
5³ = 5 × 5 × 5
= 125
The sum of the numbers will be:
225 + 125
= 350
Therefore, we get that, the sum of the 15th square number and the 5th cube number is 350.
Learn more about sum here:
https://brainly.com/question/17695139
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BRAINLIEST FOR EXPLANATION (my own question)
SO when you have a point on a graph, say it's at (-3,7), and you have to graph the dot after a rotation of 90 degrees counterclockwise around the origin, how would you know what to do?
So I know it is (x,y)--> (-y,x), but having the dot as (-7,3) wouldn't work if you followed that equation. Am I doing it right? If not, how would you apply that 'equation' to (-3,7)?
Answer:
(-7, -3)
Step-by-step explanation:
So the formula is (x, y) --> (-y, x) for a 90 degrees counterclockwise rotation.
To apply this formula to (-3,7), first identify which is the x-coordinate and which is the y-coordinate.
x-coordinate is -3 & y-coordinate is 7
Then you literally just substitute it into the formula like so:
(-y, x) -->(-(7), (-3)) --> (-7, -3)
Try to put parantheses around the coordinate when substituting to prevent confusion & incorrect negative signs.
Hope it helps and good luck (●'◡'●)
Answer:
(-7,-3)
Step-by-step explanation:
You could read (x,y)->(-y,x) as if I have the point (x,y), the image point is (opposite of y,x).
So shorthand the rule is just saying
(x,y)->(opposite of y, x)
(-3,7)->(-7,-3)
A few more examples:
(5,7)->(-7,5)
(-5,7)->(-7,-5)
(-5,-7)->(7-,5)
(5,-7)->(7,5)
This whole explanation comes down to reading-u as opposite of u.
Opposite just means to change the sign.
Another way to read -u is -1×u.
Example:
Q: evaluate -u if u=8
A: -8
Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×8=-8 or the opposite or 8 is -8.
Example:
Q: evaluate -u if u=-8
A: 8
Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×-8=8 or the opposite or -8 is 8.
which eqation represents the line that passes through (-6, 7) and (-3, 6)
Answer:
The answer is y= - ⅓x + 5 in slope intercept form and y-7 = - ⅓ (x + 6) in point slope form.
Please help I don't understand this at all
Answer:
The answer is 48in
Step-by-step explanation:
Lim x->-5(((1)/(5)+(1)/(x))/(10+2x))=
correct answer 1/10x = -1/50
explain:
Given:
The limit problem is:
[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]
To find:
The value of the given limit problem.
Solution:
We have,
[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]
It can be written as:
[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]
[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]
[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]
[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]
Applying limit, we get
[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]
[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]
Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].
Carlos is 46 years old, 5’10” and weighs 225 pounds. He has diabetes and dislikes taking his diabetes medications. What wellness strategy would his doctor most likely recommend to help him reduce his diabetes medications?
A.
lose weight
B.
use stress management techniques
C.
get immunized
D.
brush his teeth regularly
E.
increase his daily fruit intake
What is the vertex of the parabola?
y - 3 = 1/2 (x + 5)²
( __ , __ )
Answer:
(-5,31/2)
Step-by-step explanation:
open bracket
y=1/2x^2+5x+28
compare with y=ax2+bx+c
use formula (-b/2a,4ac-b2/4a)
I need to find angle BAC
Answer:
m<BAC = 60°
Step-by-step explanation:
Theorem:
In a triangle, the measure of an exterior angle equals the sum of the measures of its remote interior angles.
m<ACD = m<A + m<B
130° = m<A + 70°
m<A = 60°
m<BAC = 60°
please someone explain this
Answer: 68
Step-by-step explanation: Complementary angles are angles that add up to 90. So, you need to do 90-22=68.
Mark had 3/2 cans of paint and used 1/2 cans for his room. What fraction of the paint did he use
Help I’m slowww
Answer:
1/3 fraction of whole paint is used by mark
Step-by-step explanation:
Mark used 1/2 out of 3/2 cans.
[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{2} = \frac{1}{2}*\frac{2}{3}=\frac{1}{3}[/tex]
Graph the image of T(
–
10,
–
7) after a rotation 270° counterclockwise around the origin.
Answer:
[tex]T' = (-7,10)[/tex]
Step-by-step explanation:
Given
[tex]T = (10,7)[/tex]
[tex]r = 270^o[/tex] counterclockwise
Required
Graph of T'
The rule to this is:
[tex](x,y) \to (-y,x)[/tex]
So, we have:
[tex]T(10,7) \to T' (-7,10)[/tex]
Hence:
[tex]T' = (-7,10)[/tex]
See attachment for graph
In the diagram, what is AC?
find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex] ; now find AD=AB-DB=21-15=6 .Then AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]
Answer:
C
Step-by-step explanation:
Using Pythagoras' identity in both right triangles
To find BD
BD² + CD² = BC²
BD² + 8² = 17²
BD² + 64 = 289 ( subtract 64 from both sides )
BD² = 225 ( take the square root of both sides )
BD = [tex]\sqrt{225}[/tex] = 15
Then
AD = AB - BD = 21 - 15 = 6
To find AC
AC² = AD² + CD²
AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )
AC = [tex]\sqrt{100}[/tex] = 10 → C
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/12
There are 84 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
49
Step-by-step explanation:
The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.
Therefore, let the number of red marbles be [tex]x[/tex].
We have the following equation:
[tex]\frac{x}{84}=\frac{7}{12}[/tex]
Cross-multiplying, we get:
[tex]12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}[/tex]
Therefore, there are 49 red marbles in the bag.
Um criador de ovelhas possui um total de 36 ovelhas e resolveu vender alguma delas no primeiro dia vendeu metade das ovelhas no segundo dia vendeu um terço e no terceiro dia vendeu a nona parte quantas abelhas sobraram?
Answer:
2 sheep
Step-by-step explanation:
If you have 36 sheep and you sell:
first day 1/2 of them you sold 18
second day 1/3 them you sold 12
On thhe third day 1/9 them you sold 4
Therefore you sold 18 + 12 + 4 = 34
And you still have 2 sheep
Let $S$ be the set of points $(a,b)$ in the coordinate plane, where each of $a$ and $b$ may be $-1$, 0, or 1. How many distinct lines pass through at least two members of $S$
Answer:
20 Lines
Step-by-step explanation:
According to the Question,
Given That, Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1.Now, the total pairs of points which can be formed is 9
And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9x4 ⇒ 36
Here, We have overcounted all of the lines which pass through three points.
And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times
Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.
Therefore, the distinct lines pass through at least two members of S is 3 horizontal, 3 vertical, and 2 diagonal lines, so the answer is 36 - 2(3+3+2) = 20 Linestwo significant figures, 18.96 x 2.03 is
Solve for x.
Help me please
Answer:
x = 24
Step-by-step explanation:
Mathematically, in a cyclic quadrilateral; two opposite angles are supplementary
what this mean is that the opposite angles add up to equal 180 degrees
mathematically, we have this as;
(4x + 9) + (3x + 3) = 180
4x + 3x + 3 + 9 = 180
7x + 12 = 180
7x = 180-12
7x = 168
x = 168/7
x = 24
William needs to work out the size of angle Y in this diagram
One of William’s reasons are wrong.
Write down the correct reason.
Answer:
because internal staggal angles are equal
Step-by-step explanation:
The first reason is wrong.
Angle EGH and DEG are internal staggal angles:
the two angles are on both sides of the cut line EG, and the two angles are between the two divided lines.
{the definition of internal staggal angle}
The value of the expression 10 - 1/2^4 x 48
A = 2
B = 4
C = 5
D = 7
Answer:
option d is correct answer
Which of the following values of r will result in a true statement when substituted into the given equation?
2(4r + 4) = -16
A. r = -3
B. r = -2
C. r = 2
D. r = 3
Name a pair of vectors that are orthogonal but not perpendicular.
Answer:
For two vectors to be orthogonal it means that their dot product must be equal to zero.
Usually dot product of perpendicular vectors is zero and thus all perpendicular vectors are orthogonal.
The sum of two numbers is -5 and their difference is -1. Find the two
numbers.
Answer:
x=-3 and y=-2
Step-by-step explanation:
let the numbers be x and y
x+y=-5
x-y=-1
therefore x=-5-y
-5-y-y=-1
-2y=-1+5
-2y=4
y=-2
×=-5-(-2)
x=-5+2
x=-3
Answer: -2 and -3
Step-by-step explanation:
Number #1 = xNumber #2 = yx + y = -5
x - y = -1 -> x = y - 1
(y - 1) + y = -5
y - 1 + y = -5
2y = 1 - 5
2y = -4
y = -2
x = y - 1 = -2 - 1 = -3
FOR EASY BRAINLIEST ANSWER QUESTION BELOW!
1. Solve each word problem .twice a number added three times the sum of the number and 2 is more than 17. Find the numbers that satisfy condition
Answer:
28
Step-by-step explanation:
Given: triangle RST is circumscribed about circle A.
m∠APT = _____°
Answer:
90
Step-by-step explanation:
From the given drawing, we have;
ΔRST is circumscribed about circle A
The center of the circle A = The point A
The line RT = A tangent to the circle A
The radius to the circle A = The line AP
According to circle theory, a line which is tangent to a circle is perpendicular to the radius of the circle drawn from the point of tangency
Where two lines are perpendicular to each other, then the angle formed between them = 90°
The angle formed between a tangent and the radius of the circle = m∠APT
Therefore;
m∠APT = 90°
PLEASE HELP!!! Which choice is a solution to the system of equations below?
A. There are infinitely many solutions
B. (-4, 1)
C. (4, -1)
D. (3, 4)
Answer:
A.
Step-by-step explanation:
4y = 12x + 16
3x = y - 4
=>
y = 3x + 4
using that in the first equation
4(3x+4) = 12x + 16
12x + 16 = 12x + 16
=> both lines/equations are identical, so they have infinitely many solutions.
Which inequality is true?
A.
|-15| > |-19|
B.
|-16| < |13|
C.
|-15| > |12|
D.
|12| < |-8|
E.
|-19| > |-20|
Answer:
I don't know I don't know about question
how do i answer this?
Step-by-step explanation:
here is the answer. Hope that helps.
x + y = 3, 4y = -4x - 4
System of Equations
Answer:
no solutions
Step-by-step explanation:
Hi there!
We're given this system of equations:
x+y=3
4y=-4x-4
and we need to solve it (find the point where the lines intersect, as these are linear equations)
let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable
we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4
y=-x-1
now we have y set as an expression containing x
substitute -x-1 as y in x+y=3 to solve for x
x+-x-1=3
combine like terms
-1=3
This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.
Therefore the answer is no solutions
Hope this helps! :)
The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution
Solve for x.
Help me please
Answer:
x = 24
Step-by-step explanation:
mathematically, in a cyclic quadrilateral, two opposite angles are supplementary
what this mean is that they add up to be 180
From what we have in the question, the two angles are supplementary and that means they add up to equal 180 degrees
thus, we have it that;
(4x + 9) + (3x + 3) = 180
4x + 3x + 9 + 3 = 180
7x + 12 = 180
7x = 180-12
7x = 168
x = 168/7
x = 24
