Answer:
7
Step-by-step explanation:
Concepts:
Division: a system of distributing a collection of things into equal partsFractions: #s that represent a part of a wholeDividing Fractions: dividing a fraction by another fraction = multiplying the fraction by the inverse (reciprocal) of the other oneInverse Operations: operations that are opposite of each other (e.g. inverse of addition is subtraction)Solving:
1. First, let's set up the equation:
7/8 ÷ 1/8
2. We can get the reciprocal of 1/8 by doing the opposite of division; multiplication. 1/8 becomes 1 · 8, and that's equal to 8.
3. Now, since we know dividing a fraction by another one is exactly the same as multiplying the fraction by the reciprocal of the other, let's multiply 7/8 by the inverse of 1/8, which is 8.
7/8 · 8 = 56/8 = 7
Therefore, 7/8 divided by 1/8 is equal to 7.
Form a third-degree polynomial function with real coefficients, with leading coefficient 1, such that 6+i and 5 are zeros.
Answer:
A third-degree polynomial can be written as:
f(x) = a*x^3 + b*x^2 + c*x + d
Where the leading coefficient is a, and all the coefficients are real.
If we know that the leading coefficient is 1, then the equation becomes:
f(x) = x^3 + b*x^2 + c*x + d
Now, we also know that:
(6 + i) and 5 are zeros.
This means that:
(6 + i)^3 + b*(6 + i)^2 + c*(6 + i) + d = 0
remember that:
i^2 = - 1
This is equal to:
(6 + i)*(36 + 2*6*i + i^2) + b*(36 + 2*6*i + i^2) + c*(6 + i) + d = 0
(6 + i)*(35 + 12i) + b*(35 + 12i) + c*(6 + i) + d =0
(210 + 35i + 72i - 12) + b*(35 + 12i) + c*(6 + i) + d = 0
198 + 107i + b*(35 + 12i) + c*(6 + i) + d = 0
sparating in real and imaginary part, we get:
(198 + b*35 + c*6 + d) + (107 + b*12 + c)*i = 0
Then each parentheses needs to be zero, this means that:
198 + b*35 + c*6 + d = 0
107 + b*12 + c = 0
Knowing that 5 is another zero, we have:
5^3 + b*5^2 + c*5 + d = 0
125 + b*25 + c*5 + d = 0
Then we have a system of 3 equations and 3 variables:
198 + b*35 + c*6 + d = 0
107 + b*12 + c = 0
125 + b*25 + c*5 + d = 0
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate d in the last one, so we get:
d = -125 - b*25 - c*5
now we can replace this in the first equation to get:
198 + b*35 + c*6 + d = 0
198 + b*35 + c*6 + ( -125 - b*25 - c*5) = 0
70 + b*10 + c = 0
So now we have two equations:
70 + b*10 + c = 0
107 + b*12 + c = 0
Again, now we can isolate the one variable in one of the equations, this time let's isolate c in the first one.
c = -70 - b*10
now we can replace this in the other equation:
107 + b*12 + c = 0
107 + b*12 + (-70 - b*10) = 0
38 + b*2 = 0
now we can solve this for b
b*2 = -38
b = -38/2 = -19
Now, with the equation c = -70 - b*10 we can find the value of c.
c = -70 - b*10 = c = -70 - (-19)*10 = 120
And with the equation d = -125 - b*25 - c*5
we can find the value of d:
d = -125 - b*25 - c*5 = -125 - (-19)*25 - (120)*5 = -250
Then we have:
a = 1
b = -19
c = 120
d = -250
The eqation is:
f(x) = 1*x^3 - 19*x^2 + 120*x - 250
Givenl || m | n, find the value of x.
. m
44°
77
By
Answer: 0
Submit Answer
attempt 1 out of 2
Can someone pls help
Answer:
x = 136
Step-by-step explanation:
x and 44 are same- side interior angles and sum to 180° , that is
x + 44 = 180 ( subtract 44 from both sides )
x = 136
What is the sum of the polynomials?
(7x3 – 4x2) + (2x3 – 4x2)
9x3 – 8x2
5x3
5x3 – 8x2
9x3
Answer:
9x3 - 8x2
Step-by-step explanation:
7x3+2x3 = 9x3
-4x2+(-4x2) = -8x2
Answer:
D
Step-by-step explanation:
The Cave of Swallows is a natural open-air pit cave in the state of San Luis Potosí, Mexico. The 1220-foot-deep cave was a popular destination for BASE jumpers. The function 1/4sqrt(d) represents the time t (in seconds) that it takes a BASE jumper to fall d feet. How far does a BASE jumper fall in 3 seconds? Pls answer this as quickly as possible. Thanks.
Answer:
The depth to which a BASE jumper jumps in 3 seconds is 144 feet
Step-by-step explanation:
The details of the Cave of Swallows are;
The depth of the cave = 1,220 ft.
The function that represents the duration, t, in seconds it takes to fall d feet is given as follows;
[tex]t = \dfrac{1}{4} \cdot\sqrt{d}[/tex]
The distance a BASE jumper jumps in 3 seconds = Required
By substituting t = 3 in the given function, we get;
[tex]t = 3 = \dfrac{1}{4} \cdot\sqrt{d}[/tex]
Therefore;
4 × 3 = 12 = √d
d = 12² = 144
The distance a BASE jumper jumps in 3 seconds is d = 144 feet.
What is the difference quotient for the function f(x) = 8/ 4x + 1
Answer:
Last option (counting from the top)
Step-by-step explanation:
For a given function f(x), the difference quotient is:
[tex]\frac{f(x + h) - f(x)}{h} = \frac{1}{h}*(f(x + h) - f(x))[/tex]
In this case, we have:
[tex]f(x) = \frac{8}{4x + 1}[/tex]
Then the difference quotient will be:
[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1})[/tex]
Now we should get a common denominator.
We can do that by multiplying and dividing each fraction by the denominator of the other fraction, so we will get:
[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1}) = \frac{1}{h}*(\frac{8*(4x + 1)}{(4(x + h) +1 )*(4x + 1)} - \frac{8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)})[/tex]
Now we can simplify that to get:
[tex]\frac{1}{h}*\frac{8*(4x + 1) - 8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)}} = \frac{1}{h}*\frac{-32h}{(4(x + h) +1 )*(4x + 1)}} = \frac{-32}{(4(x + h) +1 )*(4x + 1)}}[/tex]
Then the correct option is the last one (counting from the top)
8
20
х
18
Solve for x.
O A) 40
B) 38
C) 45
D) 46
Answer:
its A
Step-by-step explanation:
What is the quotient?
(-3)
(-3)²
O-9
1
o
1
9
100
O 9
Answer:
(-3)
Step-by-step explanation:
follow me if you want
Which statements are true about David's work? Check all that apply. The GCF of the coefficients is correct. The GCF of the variable b should be b4 instead of b2. The variable c is not common to all terms, so a power of c should not have been factored out. The expression in step 5 is equivalent to the given polynomial. In step 6, David applied the distributive property.
Answer:
The GCF of the coefficients is correct.
The variable c is not common to all terms, so a power of c should not have been factored out.
In step 6, David applied the distributive property.
Step-by-step explanation:
Given the polynomial :
80b⁴ – 32b²c³ + 48b⁴c
The Greatest Common Factor (GCF) of the coefficients:
80, 32, 48
Factors of :
80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80
32 : 1, 2, 4, 8, 16, and 32
48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
GCF = 16
b⁴, b², b⁴
b⁴ = b * b * b * b
b² = b * b
b⁴ = b * b * b * b
GCF = b*b = b²
GCF of c³ and c
c³ = c * c * c
c = c
GCF = c
We can see that David's GCF of the coefficients are all correct
From the polynomial ; 80b⁴ does not contain c ; so factoring out c is incorrect
In step 6 ; the distributive property was used to obtain ; 16b²c(5b² – 2c² + 3b²)
Chase buys a bag of cookies that contains 6 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cookies. What is the probability that Chase randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a chocolate chip cookie
Answer:
0.0652173
Step-by-step explanation:
Given that :
6 chocolate chip cookies
6 peanut butter cookies
6 sugar cookies
6 oatmeal cookies
Total number of cookies purchased = (6+6+6+6) = 24
Probability, P= required outcome /total possible outcomes
This is a selection without replacement probability problem :
P(peanut butter cookies) = 6/24 = 1/4
Then ;
P(chocolate chip cookie) = 6/23
Hence,
P(peanut butter cookies then chocolate chip cookie) = 1/4 * 6/23 = 0.0652173
From a group of three boys and six girls a boy and a girl will be selected to attend a conference and how many ways can the selection you made
Answer:
18
Girl = g
Boy = b
1g 1b 1g 2b 1g 3b
2g 1b 2g 2b 2g 3b
3g 1b 3g 2b 3g 3b
4g 1b 4g 2b 4g 3b
5g 1b 5g 2b 5g 3b
6g 1b 6g 2b 6g 3b
---------------------------------------
Another way you can do this,
6 × 3 = 18
In the end there will be 18 selections.
if my mine craft house was burning leaves irl and i was watering my boat on a Wednesday on a weekend in December when its summer how many fish will become orphans late nights in the middle of june?
Can someone please help me to evaluate
Answer:
1
Step-by-step explanation:
a*log(b) = log(b^a), so (1/2)*log(196)=log(14)
So 1+log(15)-log(14)=1
Determine the y-intercept of the quadratic equation Y = x^2 - 4x + 8
9514 1404 393
Answer:
(0, 8)
Step-by-step explanation:
The y-value of the y-intercept is the function value when x=0. That is the constant in the equation, since x=0 will make all of the x-terms be zero.
y-intercept = 8
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah, a total of 8 people took the trip. She was able to purchase coach tickets for $300 and first-class tickets for $1060. She used her total budget for airfare for the trip, which was $6960. How many first-class tickets did she buy?
How many coach tickets did she buy?
number of first-class tickets bought nothing number of coach tickets bought nothing
Answer:
She bought 6 first class tickets and 1 coach ticket
Step-by-step explanation:
1060(6)= 6360 and 6960-6360=300 and 300 is the price for a coach ticket.
How would two billion, nine hundred seventy-six million, twelve thousand, eight be written
Which algebraic expression represents the phrase "six less than a number"?
Answer:
[tex]x-6[/tex]
Step-by-step explanation:
We can let the 'number' in the expression be equal to [tex]x[/tex]. Something 6 less than x would x minus 6, or [tex]x-6[/tex].
Answer:
x-6
Step-by-step explanation:
Let the number be x
Less than means subtract from
x-6
State the quadrant in which the terminal side of the given angle lies.
0
=
Зл
5
determine the equation of a line that is vertical and goes through (-5,6)
Answer:
x = -5
Step-by-step explanation:
A vertical line is a line that goes up and down. It is of the form x = constant
To go through (-5,6) is has to have the value of the x coordinate
x = -5
Given the following coordinates complete the reflection transformation.
Answer:
For a general point (x, y), a reflection across the line x = a transforms the point into:
(a + (a - x), y) = (2a - x, y)
So if we first do a reflection across the line x = 1, the new point will be:
(2*1 - x, y) = (2 - x, y)
And if we now do a reflection across the line x = 3, the new point will be:
(2*3 - (2 - x), y) = (6 - 2 + x, y) = (4 + x, y)
Now that we have the general formula we can solve the question.
For the point (-5, 2)
The generated point after the reflections is:
(4 + (-5), 2) = (-1, 2)
For the point (-1, 5)
The generated point after the reflections is:
(4 + (-1), 5) = (3, 5)
For the point (0, 3)
The generated point after the reflections is:
(4 +0, 3) = (4, 3)
Find the measures of
Answer:
Step-by-step explanation:
Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.
From the picture attached,
m(∠A) = [tex]\frac{1}{2}m(\text{arc BD})[/tex]
= [tex]\frac{1}{2}[m(\text{BC})+m(\text{CD}][/tex]
= [tex]\frac{1}{2}[55^{\circ}+145^{\circ}][/tex]
= 100°
m(∠C) = [tex]\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})][/tex]
= [tex]\frac{1}{2}(360^{\circ}-200^{\circ})[/tex]
= 80°
m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]
115° + m(∠D) = 180°
m(∠D) = 65°
m(arc AC) = 2[m(∠D)]
m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]
m(arc AB) + 55° = 130°
m(arc AB) = 75°
m(arc ADC) = 2(m∠B)
m(arc AD) + m(arc DC) = 2(115°)
m(arc AD) + 145° = 230°
m(arc AD) = 85°
A square has a perimeter of 80 m. What is the length of each side?
Answer:
20 m
[tex]p = 4a \: thus \: a = p \div 4 = 80 \div 4 = 20 \: m[/tex]
Answer:
20
Step-by-step explanation:
P=4L
80=4L
L=80/4
L=20m
If 2^x-4 = 4^x-6 , then value of x is?
Answer: [tex]x=1[/tex]
Step-by-step explanation:
[tex]2^x-4=4^x-6[/tex] is the equation that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (1,-2). Therefore meaning that [tex]x=1[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]2^x-4[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]2^1-4[/tex]
Step 3: Find the square of [tex]2^1[/tex], which is itself, 2.
[tex]2-4[/tex]
Step 4: Subtract 2 from 4. Which is a negative number, thus being -2.
[tex]-2[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]4^x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]4^1-6[/tex]
Step 3: Find the square of [tex]4^1[/tex], which is itself, 4.
[tex]4-6[/tex]
Step 4: Subtract 4 from 6. Which is a negative number, thus being -2.
[tex]-2[/tex]
We know that [tex]x=1[/tex] because when substituting x with 1, we get -2 on both sides. Therefore making this statement true and valid.
[tex]-2=-2[/tex]
Given that the days are the independent variable, which dependent variable has a constant rate of change?
Find the slope of the line
Answer:
The slope is 0.84
Step-by-step explanation:
View solution from above uploaded photos
40 POINTS- please help me
Answer:
a, c, d,
Step-by-step explanation:
I'm not sure if this is right but i think.
First you cant have exponents in a linear equation, so its not e or f. Then i just graphed the rest.
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
There are 50 applicants for two Systems Engineer positions at a local company.
Answer:
you did not provide the numbers to answer any question...
but the formula that you want is probably this one
Combination Formula nCr=n!(n−r)!r!
Step-by-step explanation:
Mike has a total of 1371 coins in his piggy bank if the total value of his coins is $230.25 and make it only has dimes and quarters how many more times than quarters does Mike have
Answer:129
Step-by-step explanation:(621 x 0.25) + (750 x 0.10) = 230.25
750 - 621 = 129 more dimes than quarters
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used
Answer:
[tex]n=35[/tex]
Step-by-step explanation:
From the question we are told that:
Standard Deviation [tex]\sigma=4min[/tex]
Let
[tex]CI=95\%[/tex]
Since
Significance level [tex]\alpha[/tex]
[tex]\alpha =1-CI[/tex]
[tex]\alpha =1-0.95[/tex]
Therefore
[tex]Z_{\alpha/2}=Z_{0.025[/tex]
[tex]Z_{\alpha/2}}=1.96[/tex]
Generally the equation for Sample size is mathematically given by
[tex]n = (Z_{\alpha/2}* \frac{\sigma}{E})^2[/tex]
[tex]n= \frac{1.96 * 3}{1}^2[/tex]
[tex]n=35[/tex]
Does this graph represent a function? Why or why not?
A. Yes, because it passes the vertical line test.
B. No, because it is not a straight line.
C. No, because it fails the vertical line test.
D. Yes, because it has two straight lines.
Answer:
with my own opinion the answer is b
help me with this math question pls!! Find the value of x
Answer:
x = 3
Step-by-step explanation:
using the mid segment formula since quadrilateral WZYP is similar to that of MZYT, this is expressed as;
29 = 1/2(23 +11x+2)
Cross multiply
2(29) = 23+11x+2
58 = 25 + 11x
11x = 58 - 25
11x = 33
Divide both sides by 11
11x/11 = 33/11
x = 3
Hence the value of x is 3
