Answer:
f(x) = (x − 3)² − 11
Step-by-step explanation:
To convert to vertex form, complete the square.
f(x) = x² − 6x − 2
f(x) = x² − 6x + 9 − 9 − 2
f(x) = (x − 3)² − 11
We need to complete the square: if we add and subtract 11 from the expression, we have
[tex]f(x)=x^2-6x-2=x^2-6x-2+11-11=x^2-6x+9-11=(x-3)^2+11[/tex]
if line p is (2x+40)°and line q is (3x-85) what is the value of x
Solve for x: (2x + 40)° = (3x - 85)°. The solution is x = 125.
To find the value of x, you can set the expressions for the angles equal to each other since the two lines are parallel and corresponding angles are equal.
The given angles are:
- Line p: [tex]\(2x + 40\)[/tex] degrees
- Line q: [tex]\(3x - 85\)[/tex] degrees
Set them equal to each other and solve for x:
[tex]\[ 2x + 40 = 3x - 85 \][/tex]
Combine like terms:
[tex]\[ 40 + 85 = 3x - 2x \][/tex]
[tex]\[ 125 = x \][/tex]
So, the value of x is 125 degrees.
The complete question is here:
if line p is (2x+40)°and line q is (3x-85) what is the value of x
The value of ( x ) is [tex]\( 125^\circ \)[/tex].
To find the value of ( x ), we can use the properties of parallel lines cut by a transversal. When two parallel lines are cut by a transversal, alternate interior angles are congruent.
Given:
- Angle [tex]\( 2x + 40^\circ \) and angle \( 3x - 85^\circ \)[/tex] are alternate interior angles.
So, we can set up an equation:
[tex]\[ 2x + 40^\circ = 3x - 85^\circ \][/tex]
Let's solve for ( x ):
[tex]\[ 2x - 3x = -85^\circ - 40^\circ \][/tex]
[tex]\[ -x = -125^\circ \][/tex]
To isolate ( x ), we divide both sides by -1:
[tex]\[ x = \frac{-125^\circ}{-1} \][/tex]
[tex]\[ x = 125^\circ \][/tex]
So, the value of ( x ) is [tex]\( 125^\circ \)[/tex].
complete question given below:
In the diagram, parallel lines P and Q are cut by transversal R.
(2x + 40°
(3x - 85)°
What is the value of x?
What is 3 In3-In9 expressed as a single natural logarithim
[tex] 3 \ln 3 - \ln 9 = 3 \ln 3 - \ln 3 ^2 = 3 \ln 3 - 2 \ln 3 = \ln 3[/tex]
Answer: [tex]\ln 3[/tex]
Answer:
ln 3
Step-by-step explanation:
Using the rules of logarithms
• log [tex]x^{n}[/tex] ⇔ n logx
• log x - log y = log ([tex]\frac{x}{y}[/tex] )
Given
3 ln3 - ln9, then
= ln 3³ - ln 9
= ln 27 - ln 9
= ln ([tex]\frac{27}{9}[/tex] ) = ln 3
choose yes or no to indicate which of the equations can be used to describe the pattern in the table (am i correct??????)
the only equation that seems to describe the pattern is:
[tex]\( b = a - 5 \)[/tex]. Therefore, option C is correct
To determine whether the given equations can describe the pattern in the table, we need to look at the values in the table and see if they satisfy the equations. However, the provided image is not completely clear, and it seems like part of the table or the values might be missing.
From what is visible in the image, it seems we have a table with two columns labeled 'a' and 'b', with 'a' taking on values from 5 to 9 and 'b' from 0 to 4. We need to check if the equations given describe the relationship between 'a' and 'b' according to the table.
The equations given are:
1. [tex]\( b + a = 5 \)[/tex]
2. [tex]\( b = a + 5 \)[/tex]
3. [tex]\( b = a - 5 \)[/tex]
4. [tex]\( a = b - 5 \)[/tex]
Without the complete table, we can't perform a full analysis, but we can explain how you would generally approach this:
- For equation 1 [tex](\( b + a = 5 \))[/tex], check if the sum of each pair of 'a' and 'b' equals 5.
- For equation 2 [tex](\( b = a + 5 \))[/tex], check if 'b' is always 5 more than 'a'.
- For equation 3 [tex](\( b = a - 5 \))[/tex], check if 'b' is always 'a' minus 5.
- For equation 4 [tex](\( a = b - 5 \))[/tex], check if 'a' is always 'b' minus 5.
Given the values for 'a' and 'b' in the table:
a | 5 | 6 | 7 | 8 | 9
b | 0 | 1 | 2 | 3 | 4
We can analyze each equation to see if it describes the pattern in the table.
1. [tex]\( b + a = 5 \)[/tex]
Let's check if the sum of 'a' and 'b' equals 5 for each pair:
- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 0 = 5 \)[/tex] (True)
- For [tex]\( a = 6 \), \( b = 1 \): \( 6 + 1 = 7 \)[/tex] (False)
- Since it is false for [tex]\( a = 6 \), \( b = 1 \)[/tex], we can already conclude that this equation does not describe the pattern.
2. [tex]\( b = a + 5 \)[/tex]
Let's check if 'b' equals 'a' plus 5:
- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 5 = 10 \)[/tex] (False)
- Since it is false for [tex]\( a = 5 \), \( b = 0 \)[/tex], this equation does not describe the pattern.
3. [tex]\( b = a - 5 \)[/tex]
Let's check if 'b' equals 'a' minus 5:
- For [tex]\( a = 5 \), \( b = 0 \): \( 5 - 5 = 0 \)[/tex] (True)
- For [tex]\( a = 6 \), \( b = 1 \): \( 6 - 5 = 1 \)[/tex] (True)
- Continuing this pattern, this equation seems to be true for all given pairs of 'a' and 'b'.
4. [tex]\( a = b - 5 \)[/tex]
This is not likely to be true since subtracting 5 from 'b' would result in negative numbers, which are not present in the 'a' values.
From the analysis, the only equation that seems to describe the pattern is:
[tex]\( b = a - 5 \)[/tex]
Let's confirm that this equation is true for all pairs of 'a' and 'b'.
The equation [tex]\( b = a - 5 \)[/tex] holds true for all pairs of 'a' and 'b' values in the table. Therefore, this equation correctly describes the pattern in the table.
3.) The cube of 1-1/3 is.
A) 1-1/9 B) 1-1/27
© 8/27
D) -8/27
Answer:
3*3*3=27
The answer is B 1 1/27
Step-by-step explanation:
As a formula:
volume = s3
where:
s is the length of any edge of the cube.
Read as "s to the power 3"
What is the missing information in the paragraph proof?
inscribed angle
polygon interior angle sum
quadrilateral angle sum
angle bisector
Answer:
Inscribed angle
Step-by-step explanation:
What is 1.16, 1 1/4, 1.37, and 1 1/10 from greatest to least?
Answer 1.37, 1 1/4, 1.16, 1 1/10
Step-by-step explanation:
1.37
1 1/4 (1.25)
1.16
1 1/10 (1.1)
Hello There!
-Ordered From Least To Greatest-
1 1/10 - 1.16 - 1 1/4 - 1.37
At a large university, 15% of students are business majors and 20% are communications majors. If two students are selected at random, what is the probability the first is a communications major and the second is a business major?
Express your answer in decimal form using two decimal places.
Answer:
Probability the first is a communications major and the second is a business major = 0.03
Step-by-step explanation:
let the total number of students be 100
Event A= Business Majors = 15%
Event B = Communication Majors = 20%
P(A) = [tex]\frac{15}{100}[/tex] ⇒ P(A) = 0.15
P(B) = [tex]\frac{20}{100}[/tex] ⇒ P(B) = 0.2
P( A and B) = P(A) × P(B)
= 0.15 × 0.2
= 0.03
8/ 2(2+2)
Trying to prove something
the correct answer would be 16 you add (2+2) first and the do 8/2 then multiple 4 x 4 and you get 16
[tex]\bf 8\div 2(2+2)\implies 8\div 2(\stackrel{\downarrow }{4})\implies \stackrel{\downarrow }{4}(4)\implies 16[/tex]
recall PEMDAS
Parentheses first off
MD multiplication and division from left-to-right.
Solve for the variable x in the following equation. x2 = 100 x =±
Answer:
x = ±10
Step-by-step explanation:
x^2 = 100
Take the square root of each side
sqrt(x^2) = sqrt(100)
x = ±10
If angle g measures 117º, what is the measure of angle h?
The complete question is given below.
If angle g measures 117º, what is the measure of supplementary angle h?
Angle g and angle h are the Supplementary angles. Then the measure of the angle ∠h will be 63°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
If angle g measures 117º.
Then the measure of angle h will be
We know that angle g and angle h are the Supplementary angles. Then we have
∠g + ∠h = 180°
117° + ∠h = 180°
∠h = 63°
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ2
I need help with this question
Answer:
The answer should be D. It is -2 on the inside because it is backwards of what you may think and because it is inside the square root. The -3 represents a down shift of 3
Answer: Last option.
Step-by-step explanation:
Below are shown some transformation for a function f(x):
[tex]f(x) + k[/tex] shifts the function k units upward.
[tex]f(x) - k[/tex] shifts the function k units downward.
[tex]f(x+k)[/tex] shifts the function k units to the left.
[tex]f(x-k)[/tex] shifts the function k units to the right.
Then, knowing that the graph of the function [tex]y=\sqrt{x}[/tex] is shifted 3 units down and 2 units rights, the function that represents the new graph is:
[tex]y=\sqrt{x-2}-3[/tex]
Which is the last option.
Which functions represent a horizontal translation to the left of the parent function f(x) = ln x?
Check all that apply.
g(x) = 3 ln(x − 1) + 6
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
s(x) = −3 ln(x) − 3
p(x) = ln(x + 2) − 2
A horizontal shift happens when you add or subtract a value from the input value of x.
To shift left the number would be added to the x.
The answers are:
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
p(x) = ln(x + 2) − 2
Answer:
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
p(x) = ln(x + 2) − 2
Step-by-step explanation:
The parent function given to us is: [tex]f(x)=\ln x[/tex].
A horizontal translation to the left k units is of the form [tex]y=\ln (x+k)[/tex].
This implies that;
h(x) = 3 ln(x + 3) + 1, is a horizontal translation to the left by 3 units.
r(x) = −3 ln(x + 1) + 3, is a horizontal translation to the left by 1 unit.
p(x) = ln(x + 2) − 2, is a horizontal translation to the left by 2 unit.
The price of a ring was increased by 30% to £325. What was the price before the increase?
Divide the new price by 1 + percent of increase:
325 / 1.30 = 250
The original price was £250
Which of the following equations describes a relationship of inverse variation between x and y
Answer:
I think its D
Step-by-step explanation:
Forgive me if im wrong.
Use the expression below to write an equivalent expression in standard form, and collect like terms.
Show all of the steps in your process.
(1.) 5x + 5 ( x-3y ) + 1/2 (4x - 6y)
The expression 5x + 5 ( x-3y ) + 1/2 (4x - 6y) simplifies to 12x - 18y by distributing the multiplication over addition, combining like terms, and checking the answer for reasonableness.
Explanation:To simplify the algebraic expression 5x + 5 ( x-3y ) + ½ (4x - 6y), let's start by distributing the multiplication over addition for each term inside the parentheses:
Multiply 5 by each term inside the first set of parentheses: 5 × x and 5 × (-3y), which gives us 5x - 15y.
Multiply ½ by each term inside the second set of parentheses: ½ × 4x and ½ × (-6y), resulting in 2x - 3y.
Now, combine the like terms:
The x-terms: 5x + 5x + 2x = 12x.
The y-terms: -15y - 3y = -18y.
So, the expression in standard form is 12x - 18y.
Lastly, we should check the answer to see if it is reasonable:
No like terms are left to combine.
The coefficients are summed up correctly.
The expression is simplified as much as possible.
Simplify √25. please answer
Your answer is 5! (:
Answer:
5
Step-by-step explanation:
A square root of a number n is a number r such that r2=n. in the case 25 we find that 52=25 , so 5 is a square root of 25. sorry if this is confusing. found this from google.
Replacing only the minimum value in a data to a smaller number will also change the mean
A.always
B. Sometimes
C.never true
Answer:
Always.
Step-by-step explanation:
I can think of no example that makes always false.
Replacing the minimum value in a dataset with a smaller number can sometimes change the mean. Hence, the correct answer is B.
Sometimes, replacing only the minimum value in a dataset with a smaller number may change the mean.
For example, if the dataset is {1, 3, 4, 5} and you replace the minimum value 1 with 0, the mean changes from 3.25 to 3.
PLEASE ANSWER RIGHT AWAY
Answer:
The sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is t2 = 4 and recursive definition is tn+1 = 2 tn - 2 ⇒ 4th answer
Step-by-step explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ The recursive definition is tn+1 = 2 tn - 2 and t2 = 4
- Look to the answer we have three answer with second term = 4,
1st , 2nd and 4th
- Lets find the 1st term
∵ t2 = 2 t1 - 2
∵ t2 = 4
∴ 4 = 2 t1 - 2 ⇒ add 2 to the both sides
∴ 6 = 2 t1 ⇒ divide the two sides by 2
∴ t1 = 3
- We have two answer with first term = 3, 2nd and 4th answers
* Lets find the third term
∵ t3 = 2 t2 - 2
∵ t2 = 4
∴ t3 = 2 (4) - 2 = 8 - 2 = 6
∴ The 4th answer has the third term = 6
* The 4th sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is
t2 = 4 and recursive definition is tn+1 = 2 tn - 2
Which integers are opposites
14 and -4
17 and -17
33 and -23
15 and -51
17 and -17. The opposite of a number is usually the negative or positive version of that #
for 6 days in a row, alyssa recorded the total amount of rain
Answer
if your looking for an answer try to be smart and actually show a picture I cant do nothing with just a name thats how we us experts find answers pictures.
Step-by-step explanation:
Please help me with this!!
Step-by-step explanation:
To find the y-coordinate points we need to evaluate the function for all the [tex]x[/tex] values in the table. In other words, we need to replace [tex]x[/tex] with each value in our given function and simplify.
- For x = 0
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(0)=(0-2)^2-5[/tex]
[tex]f(0)=(-2)^2-5[/tex]
[tex]f(0)=4-5[/tex]
[tex]f(x)=-1[/tex]
Since [tex]x=0[/tex] and [tex]y=-1[/tex], our first point is (0, -1)
- For x = 1
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(1)=(1-2)^2-5[/tex]
[tex]f(1)=(-1)^2-5[/tex]
[tex]f(1)=1-5[/tex]
[tex]f(x)=-4[/tex]
Our second point is (1, -4)
- For x = 2
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(2)=(2-2)^2-5[/tex]
[tex]f(2)=(0)^2-5[/tex]
[tex]f(x)=-5[/tex]
Our third point is (2, -5)
- For x = 3
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(3)=(3-2)^2-5[/tex]
[tex]f(3)=(1)^2-5[/tex]
[tex]f(3)=1-5[/tex]
[tex]f(x)=-4[/tex]
Our fourth point is (3, -4)
- For x = 4
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(4)=(4-2)^2-5[/tex]
[tex]f(4)=(2)^2-5[/tex]
[tex]f(4)=4-5[/tex]
[tex]f(x)=-1[/tex]
Our fifth point is (4, -1)
Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.
Oliver plans to purchase a $1,500 certificate of deposit (CD) at his bank. The CD will earn 2.3% interest, compounded semi-annually.
Write an exponential expression in the form a(b)c, where b is a single value, to find the value of the CD, in dollars, after t years. Round any decimals to the nearest ten-thousandth. Do not include dollar signs or percent symbols in the expression.
Answer:
1500(1.0115)^(2t)
Step-by-step explanation:
The formula for the balance in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.
__
Using the given values in the formula, we have ...
A = 1500(1 +0.023/2)^(2t)
Simplifying a bit, this is ...
A = 1500(1.0115)^(2t) . . . . . CD value after t years
a certain project can be completed by 28 men in 90 days. the numbers of men needed varies inversely to the time needed to complete the project. if the contractor wants to complete the project in 72 days how many men does he have to have working?
A. 30 men
B. 270 men
C. 35 men
D. 28 men
ANSWER
C. 35 men
EXPLANATION
Let m represent the number of men needed and d represent the number of days.
From the question,the number of men needed varies inversely to the time needed to complete the project.
We can write the inverse variation equation.
[tex]m = \frac{k}{d} [/tex]
where k is the constant of variation.
When m=28, d =90.
We substitute these values into the variation equation to determine the value of k.
[tex]28 = \frac{k}{90} [/tex]
[tex]k = 90 \times 28[/tex]
[tex]k = 252[/tex]
Now the equation becomes:
[tex]m= \frac{2520}{d} [/tex]
When d=72,
[tex]m = \frac{2520}{72} [/tex]
[tex]m = 35[/tex]
Therefore he needs to have 35 men working.
In the figure, the combined measurement of angles A, E, and K is 127° and angle G measures 90°. What is the measurement of angle B?
A.40°
B.45°
C.53°
D.90°
Answer:
first things first which one is angle B. if would be easier if you labeled them .
Step-by-step explanation:
but any ways see if the image attached can help out
Answer:
b
Step-by-step explanation:
Which of the following describes the roots of the polynomial function K x) - (x+ 2)(x-4)(x+1)3?
Answer:
It's the first option.
Step-by-step explanation:
(x + 2)^2 gives a duplicate (multiplicity 2) root. (because (x + 2)^2 = 0 so x = -2 multplicity 2)
(x - 4) gives one root of 4.
(x + 1)^3 gives x = -1 with multiplicity 3.
Answer:
-2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.
Step-by-step explanation:
The given polynomial function is: [tex]f(x)=(x+2)^2(x-4)(x+1)^3[/tex].
To find the roots of this polynomial, we equate each factor to zero.
This implies that;
i. [tex](x+2)^2=0[/tex], [tex]\implies x=-2[/tex], the multiplicity of this root is 2, because the factor repeats twice
ii. [tex]x-4=0[/tex], [tex]\implies x=4[/tex], the multiplicity of this root is 1, because the factor repeats once.
ii. [tex](x+1)^3=0[/tex], [tex]\implies x=-1[/tex], the multiplicity of this root is 3, because the factor repeats three times.
Which is the better buy?
A. 12-quart container of disinfectant for $44.04
B. 2-gallon container of disinfectant for $23.04
Answer: B
Step-by-step explanation:
There are 4 quarts in a gallon. 12 / 4 = 3.
A contains 3 gallons. B contains 2 gallons. If you divide the price by the number of gallons, b will be cheaper.
Answer:
B.
Step-by-step explanation:
A quart is approximately 1/4 of a gallon. Therefore 8 quarts is 2 gallons. 8/12 is 2/3
2/3 of $44.04 is $29.36. Therefore A is more expensive and B is the better buy.
Justin and David were comparing text messages. For every 8 messages Justin sent, David sent 12 messages. Together Justin and David have sent 450 messages last month. How many messages did each person send?
Answer:
The number of messages sent by Justin was [tex]180\ messages[/tex]
The number of messages sent by David was [tex]270\ messages[/tex]
Step-by-step explanation:
Let
x-----> number of messages sent by Justin
y----> number of messages sent by David
we know that
[tex]\frac{x}{y}=\frac{8}{12}[/tex]
[tex]x=\frac{8}{12}y[/tex] ----> equation A
[tex]x+y=450[/tex] -----> equation B
substitute equation A in equation B and solve for y
[tex]\frac{8}{12}y+y=450[/tex]
[tex]\frac{20}{12}y=450[/tex]
[tex]y=450*12/20=270\ messages[/tex]
Find the value of x
[tex]x=\frac{8}{12}(270)=180\ messages[/tex]
therefore
The number of messages sent by Justin was [tex]180\ messages[/tex]
The number of messages sent by David was [tex]270\ messages[/tex]
Which graph has a slope of 13?
The top right graph has a slope of 1/3
Answer:
top right
Step-by-step explanation:
tell whether the angles are adjacent or vertical.
The angels are ADJACENT ANGELS
Answer:
21
(Side Note: I solved this for anyone who needs the answer.)
Definitions:
Adjacent: Congruent meaning same measure.
Vertical: Two angles that have a common side.
Explanation:
This equation is adjacent.
If we look at this problem and look to the bottom and see that tiny square, that means it is a right angle, right angles equal to 90 degrees.
Step-By-Step:
To solve for x, we need to put 25 degrees and x into a formula.
x + 35 = 90
Next and the last step is to subtract 90 and 35:
90 - 35 = 21
Our final answer is 21.
Hope this helps!
~Hocus Pocus
Someone please help I will mark brainlest!!
Answer:
I would say A, binocular vision. ((Not sure though.))
Step-by-step explanation:
Process of elimination. Opposable thumbs could help, but not as much as being able to spot your prey from far away. And what does singular births and just being a mammal help with being a predator? The answer that makes most sense is A. Hope this helps.
Answer:
I believe binocular vision or opposable thumbs
Step-by-step explanation:
Probably opposable thumbs because it helps predators grab things