Answer: D. Horizontal stretch by a factor of 3.
Step-by-step explanation:
Below are some transformations for a function [tex]f(x)[/tex]:
If [tex]f(x)-k[/tex], then it is shifted "k" units down.
If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.
If [tex]-f(x)[/tex], then it is reflected across the x-axis.
If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".
If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].
Based on this, the transformations done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] are:
- It is shifted 7 units down.
- It is shifted rigth 4 units.
- It is reflected over the x-axis.
- It is vertically stretched by a factor of 3.
Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] is:
Horizontal stretch by a factor of 3.
-3x-3y=3
y=-5x-17
solve the system of equations by substitution or elimination
Consider the paragraph proof.
Given: D is the midpoint of AB, and E is the midpoint of AC.
Prove:DE = BC
It is given that D is the midpoint of AB and E is the midpoint of AC. To prove that DE is half the length of BC, the distance formula, d = , can be used to determine the lengths of the two segments. The length of BC can be determined with the equation BC = , which simplifies to 2a. The length of DE can be determined with the equation DE = , which simplifies to ________. Therefore, BC is twice DE, and DE is half BC.
Which is the missing information in the proof?
a
4a
a2
4a2
Answer:
a
Step-by-step explanation:
You're trying to find the distance between D and E so u use the distance formula.
sqrt (a+b-b^2)+(c-c)^2=sqrt a^2=a
Answer:
a
Step-by-step explanation:
We are given that
D is the mid-point of AB and E is the mid-point of AC.
We have to find the missing information in given proof of DE is equal to half of BC.
Proof:
D is the mid-point of AB and E is the mid-point of AC.
The coordinates of A are (2b,2c)
The coordinates of D are (b,c)
The coordinates of E are (a+b,c)
The coordinates of B are (0,0)
The coordinates of C are (2a,0)
Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
Length of BC=[tex]\sqrt{(2a)^2+(0-0)^2}=2a[/tex] units
Length of DE=[tex]\sqrt{(a+b-b)^2+(c-c)^2}=a[/tex] units
[tex]BC=2a=2\times DE[/tex]
[tex]DE=\frac{1}{2}BC[/tex]
Hence, proved.
Option A is true.
66=1/2 h(5+6)
Solve for h
Answer:
h= 12
Step-by-step explanation:
Given
66 = [tex]\frac{1}{2}[/tex] h(5 + 6)
Multiply both sides by 2 to eliminate the fraction
132 = h(5 + 6)
132 = 11h ( divide both sides by 11 )
12 = h
Can someone help me plz and the last two that you couldn’t see was ( c- 1 1/3 ) and ( D- 1 1/9)
Answer:
B 9/10
Step-by-step explanation:
3/5 ÷2/3
Copy dot flip
3/5 * 3/2
9/10
Explain how you can use equivalent fractions to find the quotient of 2 3 ÷ 4.
Answer:
see below
Step-by-step explanation:
2/3 ÷ 4
We use copy dot flip
The flip means make a reciprocal of the second number
2/3 * 1/4
Multiply the numerators
2*1 = 2
Multiply the denominators
3*4 =12
Put the numerator over the denominator
2/12
Simplify
1/6
To use equivalent fractions to find the quotient of \( \frac{2}{3} \) ÷ 4, follow these steps:
### Step 1: Understand the Operation
Division of fractions can be thought of as multiplying by the reciprocal. The reciprocal of a number a is simply \( \frac{1}{a} \).
### Step 2: Find the Reciprocal of the Divisor
The divisor here is the whole number 4. Its reciprocal is \( \frac{1}{4} \).
### Step 3: Multiply the Dividend by the Reciprocal of the Divisor
Instead of dividing \( \frac{2}{3} \) by 4, you can multiply \( \frac{2}{3} \) by \( \frac{1}{4} \).
### Step 4: Perform the Multiplication
Now, multiply the two fractions:
\[ \frac{2}{3} \times \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} \]
This results in a new fraction:
\[ \frac{2}{12} \]
### Step 5: Simplify the Resulting Fraction
Finally, you need to simplify the fraction to its simplest form. To do that, find the greatest common factor (GCF) of the numerator and the denominator and divide both by this number.
For \( \frac{2}{12} \), the greatest common factor is 2. So we divide both the numerator and the denominator by 2:
\[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]
### Conclusion
Therefore, the quotient of \( \frac{2}{3} \) ÷ 4 is \( \frac{1}{6} \). This is the simplest form of the fraction you obtain when \( \frac{2}{3} \) is divided by 4.
What is the solution of the graph?
Answer:
no solution
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 graphs.
The given lines are parallel ( both have a slope = 2 )
Hence the lines never intersect thus there is no solution.
What is the greatest common factor of 22a2 and 32a
Step-by-step explanation:
Write the prime factorization for each:
22a² = 2×11×a²
32a = 2⁵×a
So the greatest common factor is 2a.
Your phone plan charges you an initial fee and then a certain amount depending on the amount of data you use they send you periodic updates of your insiste and your current bill cost. After using 3 GB of data you owe $30. After 5 GB of data you owe $40. What is the initial fee prior to the data usage charge ?
Answer:
5
Step-by-step explanation:
dot
A sequence is defined by the recursive function
f(n + 1) = f(n) - 2
if f(1) = 10, what is f(3)?
1
6
8
30
Answer:
6Step-by-step explanation:
[tex]f(n+1)=f(n)-2\\\\f(1)=10\\f(2)=f(1)-2=10-2=8\\f(3)=f(2)-2=8-2=6[/tex]
Answer:
B) 6
Step-by-step explanation:
The table below relates the number of rats in a population to time in weeks. Use the table to write a linear equation with w as the input variable.
P(w)=
Answer:
C(w) = 6w + 9
Step-by-step explanation:
Anytime 0 is given somewhere, it should be given close scrutiny. In an equation whose general form is
y = mx + b
0 will determine the y intercept immediately.
So when x = 0, y will equal
y = 0*m + 9
So b = 9
y = mx + 9 Now we need to find m
I should start using your variables.
C(w) = m*w + 9
when w = 3 then C(3) = 27
27= 3m +9
27-9 =3m + 9 -9
18 = 3m
18/3 = 3m/3
x = 6
So the complete equation is
C(w) = 6w + 9
Answer:
[tex]P(w)=6w+9[/tex]
Step-by-step explanation:
To find the linear equation, first we need to calculate the slope of that line, we is defined as
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
Where we need to use two points from the table: (0,9) and (4,33).
Replacing these points, we have
[tex]m=\frac{33-9}{4-0}=\frac{24}{4} =6[/tex]
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-9=6(x-0)\\y=6x+9[/tex]
Let's call [tex]y=P(w)[/tex] and [tex]x=w[/tex].
The equation that models the given table is
[tex]P(w)=6w+9[/tex]
The area of a compact disc is 452 4/7 square centimeters. What is the diameter of a compact disc ? Use 22/7 as an approximation for pie?
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=452\frac{4}{7} \end{cases}\implies 452\frac{4}{7}=\pi r^2\implies \cfrac{3168}{7}=\pi r^2 \implies \cfrac{3168}{7\pi }=r^2 \\\\\\ \stackrel{\pi =\frac{22}{7}}{\cfrac{3168}{7\cdot \frac{22}{7}}}=r^2\implies \cfrac{3168}{22}=r^2\implies 144=r^2\implies \sqrt{144}=r\implies 12=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{diameter=2r}{d=24}~\hfill[/tex]
Ms. Cassidy plotted the point (2, 3) on Miguel’s graph of y < 2x – 4. She instructed him to change one number or one symbol in his inequality so that the point (2, 3) can be included in the solution set. Which equations might Miguel write? Check all that apply
Answer:
C, D,F
Step-by-step explanation:
Answer:
Its C
Step-by-step explanation:
hello! i’m currently working on some practice questions, and i was wondering how you would solve this expression!
Answer:
7
Step-by-step explanation:
Givens
x = 4
y = 2
z =-3
equation
xy - z^y
Solution
(4)(2) - (-3)^2 be sure and add the brackets. Otherwise it won't come out correctly.
16 - (9) = 7
what is the probability of rolling a 6 sided die and getting a 1 or a prime number
Answer:
P = 4 / 6 = 2/3 = 0.66 = 66%
Step-by-step explanation:
Assuming the die is numbered 1 to 6.
To answer the question, we first need to know many prime numbers can be represented on the die. What are the prime numbers equal to 6 or lower?
We have 2, 3 and 5. (since 4 and 6 are not prime numbers). So we have 3 prime numbers, plus the number 1... so there are 4 possibilities valid for rolling a 1 or a prime number: 1,2,3 and 5.
4 possibilities out of 6 total possible outcomes, so...
P = 4 / 6 = 2/3 = 0.66 = 66%
Answer:
The probability of rolling a 6 sided die and getting a 1 or a prime number = 2/3
Step-by-step explanation:
The numbers on the die are 1, 2, 3, 4, 5 and 6
To find the probability
Total outcomes of rolling a die = 6
Prime numbers less than 6 are 2, 3 and 5
Possible outcomes(getting 1 or a prime number) = 1, 2, 3 and 5
Probability of getting 1 or prime number when rolling a die = 4/6 = 2/3
cos^2x+cos^2(120°+x)+cos^2(120°-x)
i need this asap. pls help me
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Using the addition formulae for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
---------------------------------------------------------------
cos(120 + x) = cos120cosx - sin120sinx
= - cos60cosx - sin60sinx
= - [tex]\frac{1}{2}[/tex] cosx - [tex]\frac{\sqrt{3} }{2}[/tex] sinx
squaring to obtain cos² (120 + x)
= [tex]\frac{1}{4}[/tex]cos²x + [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x
--------------------------------------------------------------------
cos(120 - x) = cos120cosx + sin120sinx
= -cos60cosx + sin60sinx
= - [tex]\frac{1}{2}[/tex]cosx + [tex]\frac{\sqrt{3} }{2}[/tex]sinx
squaring to obtain cos²(120 - x)
= [tex]\frac{1}{4}[/tex]cos²x - [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x
--------------------------------------------------------------------------
Putting it all together
cos²x + [tex]\frac{1}{4}[/tex]cos²x + [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x + [tex]\frac{1}{4}[/tex]cos²x - [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x
= cos²x + [tex]\frac{1}{2}[/tex]cos²x + [tex]\frac{3}{2}[/tex]sin²x
= [tex]\frac{3}{2}[/tex]cos²x + [tex]\frac{3}{2}[/tex]sin²x
= [tex]\frac{3}{2}[/tex](cos²x + sin²x) = [tex]\frac{3}{2}[/tex]
Which is correct? I am marking Brainliest.
Answer:
A. concave hexagon
Step-by-step explanation:
It has 6 sides, so it's a hexagon. (A heptagon has 7 sides.)
If all interior angles are less than 180 deg, then it is convex. There is one interior angle on the left side that is more than 180 deg, so it is concave.
Answer: concave hexagon
Divide simplify your answer
Answer:
[tex]\large\boxed{\dfrac{2s-6}{s+3}}[/tex]
Step-by-step explanation:
[tex]s^2-9=s^2-3^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(s-3)(s+3)\\\\s^2+6s+9=s^2+2(s)(3)+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\=(s+3)^2[/tex]
[tex]\dfrac{s^2-9}{2s}\div\dfrac{s^2+6s+9}{4s}=\dfrac{s^2-9}{2s\!\!\!\!\diagup_1}\cdot\dfrac{4s}{s^2+6s+9}\\\\=\dfrac{(s-3)(s+3)}{2s\!\!\!\!\!\diagup_{_1}}\cdot\dfrac{4s\!\!\!\!\!\diagup^{^2}}{(s+3)^2}=\dfrac{2(s-3)(s+3)}{(s+3)(s+3)}\qquad\text{cancel}\ (s+3)\\\\=\dfrac{2(s-3)}{s+3}=\dfrac{2s-6}{s+3}[/tex]
Which expression will simplify to 1?
Let us check each Option :
[tex]\mathsf{First\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}[/tex]
[tex]\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}[/tex]
[tex]\mathsf{Second\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{m + 9}\right)}[/tex]
[tex]\mathsf{\implies 1}[/tex]
[tex]\mathsf{Third\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 + m}{9 - m}\right)}[/tex]
[tex]\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{-(m - 9)}\right)}[/tex]
[tex]\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}[/tex]
[tex]\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}[/tex]
[tex]\mathsf{Fourth\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 - m}{9 + m}\right)}[/tex]
[tex]\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{-(m - 9)}{9 + m}\right)}[/tex]
[tex]\mathsf{\implies -\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{9 + m}\right)}[/tex]
[tex]\mathsf{\implies -1\;\neq\;1}[/tex]
Answer : Option (2)
Answer:
B.⁽[tex](\frac{m}{m}\frac{+9}{-9} ) (\frac{m}{m} \frac{- 9}{+ 9} )[/tex]
Step-by-step explanation:
6x - 26 = 58 + 4x, 15 points to whoever solves this
Answer:
x=42
Step-by-step explanation:
Add by 26 from both sides of equation.
6x-26+26=58+4x+26
Simplify.
6x=4x+84
Subtract by 4x from both sides of equation.
6x-4x=4x+84-4x
Simplify.
2x=84
Divide by 2 from both sides of equation.
2x/2=84/2
Simplify, to find the answer.
84/2=42
x=42 is the correct answer.
I hope this helps you, and have a wonderful day!
what is the solution set of 7x^2 + 3x = 0
Answer:
the answer is x=0,-(3/7)
Step-by-step explanation:
Answer:
x = { - [tex]\frac{3}{7}[/tex], 0 }
Step-by-step explanation:
Given
7x² + 3x = 0 ← factor out x from each term
x(7x + 3) = 0
Equate each factor to zero and solve for x
x = 0
7x + 3 = 0 ⇒ 7x = - 3 ⇒ x = - [tex]\frac{3}{7}[/tex]
what is the eighth term in the sequence x+3, - 2x^2 - 6x, 4x^3 +12x^2
Answer:
[tex]a_8=-128x^8-384x^7[/tex]
Step-by-step explanation:
The terms of the sequence are:
[tex]x+3,-2x^2-6x,4x^3+12x^2,...[/tex]
We can rewrite the terms in factored form to get;
[tex]x+3,-2x(x+3),4x^2(x+3),...[/tex]
We can see that the subsequent terms are obtained by multiplying the previous term by [tex]-2x[/tex]. This is called the common ratio.
Therefore the first term of this geometric sequence is [tex]a_1=x+3[/tex] and the common ratio is [tex]r=-2x[/tex].
The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex].
Let us substitute the first term, the common ratio, and [tex]n=8[/tex] to obtain:
[tex]a_8=(x+3)(-2x)^{8-1}[/tex]
[tex]a_8=(x+3)(-2x)^{7}[/tex]
[tex]a_8=-128x^7(x+3)[/tex]
[tex]a_8=-128x^8-384x^7[/tex]
Classify the following triangle
Answer:
Isosceles and obtuse
Step-by-step explanation:
It is not a scalene triangle because it has two same lengths 41 degrees and 41 degrees.
It is a Isosceles triangle because two of the sides have the same lengths 41 degrees and 41 degrees
It is an obtuse triangle because it has on obtuse angle which is 98 and two acute angles that are 41 degrees
It is not an equilateral because not all of the sides are the same lengths
It is not a right triangle because there are 90 degree angles
It is not an acute triangle because not all the angles are acute angles
A triangle can be classified based on its angles and sides. A Trigonal Bipyramidal triangle has angles of 90 degrees or 120 degrees, and atoms can be positioned equatorially (in the plane of the triangle) or axially (above or below the plane). Always remember that the sum of all interior angles of a triangle is 180°.
Explanation:The classification of a triangle depends on its angles and sides. If you have a triangle like a Trigonal Bipyramidal, the angles of such a triangle can be 90 degrees or 120 degrees. This relates to a three-dimensional trigonal bipyramidal molecular geometry where three atoms or groups of atoms are positioned in a flat triangle around a central atom, symmetrically positioned with 120° angles between each pair.
Another element you mentioned is the position of an attached atom in a triangle. This can be either equatorial (in the plane of the triangle) or axial (above or below that plane).
For detailed classification, always keep in mind that the sum of all interior angles of a triangle is always 180°. A triangle with one angle measuring 90° is a right triangle. An equilateral triangle has all angles measuring 60°. In the trigonal planar case, all atoms are in one plane, and bond angles are 120°.
Learn more about Triangle Classification here:https://brainly.com/question/4028542
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Given ƒ(x) = 7x + 1 and g(x) = x^2, find (g ○ ƒ)(x)
For this case we have the following functions:
[tex]f (x) = 7x + 1\\g (x) = x ^ 2[/tex]
We must find[tex](g_ {0} f) (x).[/tex]
By definition of composition of functions we have to:
[tex](g_ {0} f) (x) = g (f (x))[/tex]
So:
[tex](g_ {0} f) (x) = g (f (x)) = (7x + 1) ^ 2 = 49x ^ 2 + 2 (7x) (1) + 1 = 49x ^ 2 + 14x + 1[/tex]
ANswer:
[tex](7x + 1) ^ 2 = 49x ^ 2 + 14x + 1[/tex]
Simplify the expression.
(7.46)** . (7.46)
Answer:
D. 7.46
Hope this helps and have a nice day!!
If I'm wrong pleaseeee tell me
Step-by-step explanation:
A vertex a is at (-1, -2)
Answer:
A'(-4,4)
B'(-2,11)
Step-by-step explanation:
6 unit up and 3 unit left
A (-1,-2) : 6 unit up → (-1,4) → 3 unit left → (-4,4)
A'(-4,4)
B (1,5) : 6 unit up → (1,11) → 3 unit left → (-2,11)
B'(-2,11)
Simplify 3x3+27×2-15x÷3x
[tex]\bf 3x^3+27x^2-15x\div 3x\implies \cfrac{3x^3+27x^2-15x}{3x}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{3x^3}{3x}+\cfrac{27x^2}{3x}-\cfrac{15x}{3x}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x^2+9x-5~\hfill[/tex]
63-5x
So you do PEMDAS
There aren’t any parenthesis
There aren’t any exponents
So you multiply 3*3 and get 9
Multiply 27 by 2 and get 54
And divide 15x by 3x
Now moving on to addition/subtraction
The equation is now 9+54-5x
9+54 is 63
So the answer is 63+5x
On which number line are -3 and its opposite shown?
Answer:
The number line should look like this;
<---- -3 -------- 0 ------- 3 ----->
It must have both 3 and -3 shown
Step-by-step explanation:
Step-by-step explanation:how do you feguire this out because the left of a number line is always negative and the right is always posittive easy right i hope it helped you just like when i learned it it helped me.
Which congruence theorems prove tht
MNP and QRS are be congruent?
Word Bank:
AAS theorem, ASA postulate, SAS postulate,
SSS postulate, HA, AA, HL, LA, LL, HH
Answer
AAS
Step-by-step explanation:
Classify the following triangle check all that apply
Answer: B and F
Hope it helps!!!
Answer: OPTION B AND OPTION D.
Step-by-step explanation:
Analyze the triangle provided.
You can observe that the lenghts of its sides are: 10.9, 15, 14
Then the lenghts of its sides are not equal.
By definition, when all sides of a triangle are different this is called: "Scalene".
You can notice that the measures of its angles are: 63°, 44° and 73°
Then, all its angles are less than 90 degrees.
By definition if all three angles of a triangle are less than 90 degrees, then is called: "Acute".
A polynomial function can be written as (x − 1)(x − 4)(x + 7). What are the x-intercepts of the graph of this function? (4 points) (1, 0), (4, 0), (7, 0) (−1, 0), (−4, 0), (−7, 0) (1, 0), (4, 0), (−7, 0) (−1, 0), (−4, 0), (7, 0)
Answer:
Option C is correct.
Step-by-step explanation:
The x-intercepts of the function (x − 1)(x − 4)(x + 7) can be found by putting this function equal to zero
(x − 1)(x − 4)(x + 7) = 0
Now,
x-1 = 0
x-4 = 0
and x+7 = 0
Now finding the values of x
x-1 = 0 + 1
x - 1 + 1 = 1
=> x = 1
or (1,0)
x - 4 = 0
x -4 + 4 = 0 + 4
x = 4
or (4,0)
x + 7 = 0
x +7 -7 = 0 -7
x = -7
or (-7,0)
SO, the x-intercepts of the function (x − 1)(x − 4)(x + 7) are (1,0),(4,0) and (-7,0)
Option C is correct.
Answer:
+ 1 + 4 -7
Step-by-step explanation:
when they ask for x intercepts you simply have to set the function to 0 and then solve for x or in other words just reverse the number for example. here we have -1 -4 and +7 so just reverse the negative and positive signs