Answer:
Step-by-step explanation:
We will first find the slope of the line from those 2 points, then write the equation of the line in slope-intercept form, solving for b, the y-intercept.
[tex]m=\frac{13-19}{6-(-3)}=-\frac{6}{9}=-\frac{2}{3}[/tex]
So the slope is -2/3. We will choose a point now to use in the slope-intercept equation. I'm picking the one with no negatives (cuz who likes negatives!?).
[tex]13=-\frac{2}{3}(6)+b[/tex] which simplifies down to
13 = -4 + b so
b = 17
The y-intercept of the line that goes through those 2 points is (0, 17)
If function g has the factors (x − 7) and (x + 6), what are the zeros of function g?
A.
-7 and 6
B.
-6 and 7
C.
6 and 7
D.
-7 and -6
Answer:
B)
Step-by-step explanation:
Do the zero property.
x-7=0, x+6=0
x=0+7=7,
x=0-6=-6
Answer:
b 100% true
Step-by-step explanation:
Which equation is equivalent to 3logx+log2=log3x-log2
Step-by-step explanation:
[tex]3\log x+\log2=\log3x-\log2\\\\\text{Domain:}\ x>0\\\\\text{Use}\\\\\log_ab^c=c\log_ab\\\\\log_ab+\log_ac=\log_a(bc)\\\\\log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\===================\\\log x^3+\log2=\log\left(\dfrac{3x}{2}\right)\\\\\log(2x^3)=\log\left(\dfrac{3}{2}x\right)\iff2x^3=\dfrac{3}{2}x\qquad\text{subtract}\ \dfrac{3}{2}x\ \text{from both sides}\\\\2x^3-\dfrac{3}{2}x=0\qquad\text{multiply both sides by 2}\\\\4x^3-3x=0\qquad\text{use distributive property}\\\\x(4x^2-3)=0\iff x=0\ \vee\ 4x^2-3=0[/tex]
[tex]x=0\notin\ \text{Domain}\\\\4x^2-3=0\qquad\text{add 3 to both sides}\\\\4x^2=3\qquad\text{divide both sides by 4}\\\\x^2=\dfrac{3}{4}\Rightarrow x=\pm\sqrt{\dfrac{3}{4}}\\\\x=\pm\dfrac{\sqrt3}{\sqrt4}\\\\x=-\dfrac{\sqrt3}{2}\notin \text{Domain}\\\\\boxed{x=\dfrac{\sqrt3}{2}}\in \text{Domain}[/tex]
The equivalent equation to 3logx + log2 = log3x - log2 is x² = 3/4, which is derived by applying properties of logarithms such as combining log terms and setting the resulting expressions equal to each other.
The equation 3logx + log2 = log3x - log2 can be simplified using the properties of logarithms. To find the equivalent equation, we use the property that log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b). Applying these properties:
Combine the terms on the left: 3logx + log2 = log(2x³).Combine the terms on the right: log3x - log2 = log(3x/2).Set the expressions equal to each other: log(2x³) = log(3x/2).Remove the logarithms since if log(a) = log(b), then a = b: 2x³ = 3x/2.Multiply both sides by 2 to remove the fraction: 4x³ = 3x.Divide both sides by x, assuming x ≠ 0: 4x² = 3.Finally, divide by 4: x² = 3/4.The solutions are x = ±√(3/4).The equivalent equation is x² = 3/4 or x = ±√(3/4), provided that x ≠ 0 since the logarithm of zero is undefined.
If you awnser this question please include work
Answer:
B and D
Step-by-step explanation:
2 divided by 1
1 3
Keep Change Flip
2 * 3 = 6
1 1
3/4 divided by 2/3= 1 1/8
6 and 1 1/8 is greater than 1.Answer:
B and DStep-by-step explanation:
[tex]\dfrac{a}{b}\times c=\dfrac{a\times c}{b}\\\\a\times\dfrac{b}{c}=\dfrac{a\times b}{c}\\\\\dfrac{a}{b}:c=\dfrac{a}{b}\times\dfrac{1}{c}=\dfrac{a}{b\times c}\\\\a:\dfrac{b}{c}=a\times\dfrac{c}{b}=\dfrac{a\times c}{b}\\\\\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{a\times c}{b\times d}\\\\\dfrac{a}{b}:\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}=\dfrac{a\times d}{b\times c}\\\\============================[/tex]
[tex]\bold{A}\\\\\dfrac{1}{3}\times2=\dfrac{1\times2}{3}=\dfrac{2}{3}<1\\\\\bold{B}\\\\2:\dfrac{1}{3}=2\times\dfrac{3}{1}=2\times3=6>1\\\\\bold{C}\\\\\dfrac{1}{4}\times\dfrac{2}{3}=\dfrac{1\times2}{4\times3}=\dfrac{2}{12}<1\\\\\bold{D}\\\\\dfrac{3}{4}:\dfrac{2}{3}=\dfrac{3}{4}\times\dfrac{3}{2}=\dfrac{3\times3}{4\times2}=\dfrac{9}{8}=1\dfrac{1}{8}>1\\\\\bold{E}\\\\\dfrac{2}{3}\times\dfrac{3}{4}=\dfrac{2\times3}{3\times4}=\dfrac{6}{12}<1\\\\\bold{F}\\\\\dfrac{2}{3}:\dfrac{3}{4}=\dfrac{2}{3}\times\dfrac{4}{3}=\dfrac{2\times4}{3\times3}=\dfrac{8}{9}<1[/tex]
Annie brought 10 bagels to school, 7 of which are Asiago cheese.
If Annie randomly gives away 5 bagels to teachers, what is the probability that e
the chosen bagels are Asiago cheese?
Answer:
The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%
Step-by-step explanation:
Given:
Total bagels brought to school = 10
Number of Asiago cheese bagels = 7
To find the probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese.
Solution:
Let probability of choosing an Asiago cheese bagel be the successful event.
Probability of choosing one Asiago cheese bagels = [tex]\frac{7}{10}=0.7[/tex]
Probability of success = 0.7
Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success = [tex]1-0.7=0.3[/tex]
Using Bernoulli Trials
To calculate the binomial probability of obtaining exactly [tex]r[/tex] events in [tex]n[/tex] trials the formula used is:
⇒ [tex]nCr.p^r.q^{(n-r)}[/tex]
where [tex]p\rightarrow[/tex] Probability of success
[tex]q\rightarrow[/tex] Probability of failure
Thus, probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :
⇒ [tex]5C3(0.7)^3(0.3)^2[/tex]
⇒ [tex]\frac{5!}{(5-3)!3!}(0.343)(0.09)[/tex]
⇒ [tex]\frac{5!}{(2)!3!}(0.343)(0.09)[/tex]
⇒ [tex]10(0.343)(0.09)[/tex]
⇒ [tex]0.3087\ or\ 30.87\%[/tex] (Answer)
A culture started with 3,000 bacteria. After 8 hours, it grew to 3,300 bacteria. Predict how many bacteria will be present after 12 hours. Round your answer to the nearest whole number.
Answer:
[tex]3,462\ bacteria[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
x is the time in hours
y is the numbers of bacteria
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
we have that
[tex]a=3,000\ bacteria[/tex]
For x=8, y=3,300
substitute in the exponential function
[tex]3,300=3,000(b^8)[/tex]
solve for b
[tex]1.1=(b^8)[/tex]
[tex]b=\sqrt[8]{1.1}[/tex]
[tex]b=1.0120[/tex]
Find the value of r
[tex]r=b-1=1.0120-1=0.0120=1.20\%[/tex]
The equation is equal to
[tex]y=3,000(1.012^x)[/tex]
For x=12 hours
substitute the value of x in the equation
[tex]y=3,000(1.012^{12})[/tex]
[tex]y=3,462\ bacteria[/tex]
For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?
Answer: 31.43 cm
Step-by-step explanation:
The length of an arc is calculated using the formula:
[tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r
where : theta is the angle in degree
r = radius
If the angle is given in Radian , the length can be calculated using the formula:
L = r∅
Since , the angle is given in degree , we will use the first formula.
L = [tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r
L = [tex]\frac{120}{360}[/tex] X 2 X π X 15
L = [tex]\frac{1}{3}[/tex] X 2 X [tex]\frac{22}{7}[/tex] X 15
L = [tex]\frac{660}{21}[/tex]
L = 31.42857143
L ≈ 31.43 cm
A boy has 10 cookies. His sister has 2.5 times as many. How many does the sister have?
If the boy has 10, and his sister has 2 1/2 times as many as him, you would first multiply 10 times 2 to get 20. After that you would automatically 1/2 of 10 is 5, which would bring you to the conclusion that his sister has 25 cookies. Thus, you answer is 25 cookies.
Answer:
25
Step-by-step explanation:
10×2.5=25
and heres some other random stuff so brainly will let me tell you this
How is 0.624 written in a expanded form?
0+6/10+2/100+4/100
Hope this helped! (plz mark me brainliest)
Solve for z.
In 63 = In z + In 7
ln z + ln 7 = ln 63
When adding two logarithms of the same base, you can combine them into a single logarithm where the input is the product of both previous inputs
ln 7z = ln 63
Take the exponential of e to both sides
7z = 63
Divide both sides by 7
z = 9
Let me know if you need any clarifications, thanks!
6) When a teacher counted her students in groups of 4, there were 2 students left over. When she counted them in groups of 5, she had 1 student left over. If 15 of her students were girls, and she had more girls than boys, how many students did she have??
This needs to be shown full work for full credit on my college math class I need help it’s due this Wednesday!!!
Answer:
The solution is that there are 26 students in her class
Step-by-step explanation:
We know that 15 of her student are girls, and since there are more girls than boys in the class, there can at most be 15+14= 29 students in her class.
We need to find a number x between 16 (in the case where there is only one boy in the class) and 29, for which x/4 gives a remainder of 2, and x/5 gives a remainder of 1.
The numbers between 16 and 29, which when divided by 4 gives a remainder of 2 are:
18, 22, and 26
You can check yourself that these give a remainder of 2.
So it is one of these numbers. But the solution must also fulfill that the number divided by 5 gives a remainder of 1.
18/5 = 15 + remainder=3
22/5 = 4 + remainder=2
26/5 = 5 + remainder=1
Thus the only possible solution is 26.
To find the total number of students, we can use modular arithmetic and the Chinese Remainder Theorem. The number of students is 40k + 27, where 'k' is an integer.
To solve this problem, we can use the concept of modular arithmetic. Let's assume the number of students as 'x'. We are given that when the students are divided into groups of 4, there are 2 students left over. This can be written as x % 4 = 2. Similarly, when the students are divided into groups of 5, there is 1 student left over, which can be written as x % 5 = 1.
To find the value of 'x', we can solve these congruences simultaneously. One way to solve this is by brute force by trying different values of 'x'. However, a more efficient approach is to use the Chinese Remainder Theorem. By solving the congruences, we get x ≡ 21 (mod 20). This means that the number of students can be expressed as x = 20k + 21, where 'k' is an integer.
Since we are given that there are 15 girls and more girls than boys, we can say that the number of boys is 'x - 15'. Substituting the value of 'x' from the previous equation, we get the number of boys as 20k + 21 - 15 = 20k + 6. Therefore, the total number of students is 20k + 21 + 20k + 6 = 40k + 27.
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26 eggs in a carton were broken. this was 5% of the total number of eggs in the carton. how many eggs were in the carton altogether?
Answer:
520 eggs
Step-by-step explanation:
5%*2 is 10%.
10%*10 is 100%,that is the full carton of eggs.
26*2*10 is 520.
There were 520 eggs in the carton altogether.
Hope this helps :)
To find the total number of eggs in the carton, we use the information that 26 eggs (5% of the total) were broken. By solving the equation 0.05x = 26, we determine there were 520 eggs in the carton.
The question at hand is, "26 eggs in a carton were broken. This was 5% of the total number of eggs in the carton. How many eggs were in the carton altogether?"
To solve this problem, let us consider the total number of eggs in the carton as x. Given that 5% of x is equal to 26 eggs, we can write this relationship as an equation: 0.05x = 26. To find x, we divide both sides of the equation by 0.05, yielding x = 26 / 0.05. Calculating this result, we find that x = 520.
Therefore, there were 520 eggs in the carton altogether.
The school store sells packs of 12 pens for $2.40.
Select the three unit rates that describe this sale.
CLEAR CHECK
$0.20 per pen
$2.40 per pack of pens
5 pens per dollar
120 pens per $24
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For this case we can express the rates as:
[tex]\frac {2.40} {12} * \frac {dollars} {pen} = 0.2 \frac {dollars} {pen}[/tex]
Option A
[tex]\frac {12} {2.40} * \frac {pen} {dollars} = 5 \frac {pens} {dollar}[/tex]
Option C
If the pen package contains 12, then the cost of the package is $2.40.
Option B
Answer:
Option A, B, C
Answer: 1, 2, and 3
Step-by-step explanation: I did the question
NEED HELP ASAP!!
why we can multiply by the reciprocal of a fraction when completing a division problem?
Answer:we multiply by the reciprocal of a fraction when completing a division problem because it is a rule in mathematics that when you divide two fraction, you change the division sign to multiplication and flip the fraction at the right of the multiplication sign.
Step-by-step explanation:
For example if you have 4÷ 1/2. It basically means how many 1/2 can one get in 4. And the answers is 8.
Therefore multiplying by the reciprocal of a fraction when completing a division problem is a short cut method that has been tested and proven to be correct.
which line is parallel to the line given below? y= -4/3x + 1
Answer:
The line which is parallel to the given line [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 1}[/tex] is [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 2}[/tex]
Step-by-step explanation:
Given that the equation of the line is
[tex]y=-\frac{4}{3}x+1\hfill (1)[/tex]
To find the equation of the line is parallel to the given line equation.
We know that the given equation is in the slope intercept form
y=mx+c where m is the slope and c is the intercept.
Compare with given equation(1) we get
[tex]m=-\frac{4}{3}[/tex] and c=1
Now change the y intercept c=1 to a intercept of c= 2
Therefore (1) becomes
[tex]y=-\frac{4}{3}x+2[/tex]
The above equation of the line is the parallel line to the given equation of the line
Answer:
3x - 4y = -28
Step-by-step explanation:
Three-fourths of a number multiplied by seven
Answer:
5 1/4 or 5.25
Step-by-step explanation:
Multiplying fractions means that we can multiply the numerator by the numerator and the denominator by the denominator straight across without needing a common denominator.
3*7 = 21
4*1 = 4
We end up with the improper fraction 21/4. We can convert this into a mixed number.
Because 4 goes into 21 a total of 5 times with 1 left over, we end up with the mixed number of 5 1/4, or as a decimal, 5.25
Find the interquartile range.
6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93
Based on the calculations, the interquartile range of a data set is equal to 53.
In order to determine the statistical measures or the five-number summary, we would arrange the data set in an ascending order:
6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93
Based on the data set, the first quartile can be calculated as follows;
First quartile = [(n + 1)/4]th term
First quartile = (13 + 1)/4
First quartile = 3.5th term
First quartile = (30+9)/2
First quartile = 19.5.
For the third quartile, we have:
Third quartile = [3(n + 1)/4]th term
Third quartile = 3 × 3.5th term
Third quartile = 10.5th term
Third quartile = (75+70)/2
Third quartile = 72.5
Mathematically, the interquartile range of a data set is the difference between third quartile (Q₃) and the first quartile:
Interquartile range of data set = Third quartile - First quartile
Interquartile range of data set = 72.5 - 19.5
Interquartile range of data set = 53.
if a rectangle has an area of 6 2/3 and a length of 2 1/2 inches what is the width of the rectangle
Answer:
Step-by-step explanation:
HELP PLEASE I NEED HELP I DONT UNDERSTAND THIS
Answer:
t=44°
Step-by-step explanation:
The sum of the interior angles of any pentagon is always 540 degrees.
Let's set up an equation with this information: (all figures are in degrees)
[tex]t+3t+t+32+149+139=540[/tex]
Now we combine all like terms.
[tex]5t+320=540[/tex]
Now begin to isolate t be subtracting 320 from both sides.
[tex]5t=220[/tex]
Finally divide both sides by 5 to isolate t.
t=44°
The inside dimensions of a box are 12 inches long, 5 inches wide, and 2 inches deep. How many cubic inches does it contain?
The answer is 120 cubic inches.
There are 120 cubic inches contained inside the box.
What is meaning of volume?The volume of space occupied by a substance or item, or the space enclosed within a container.
What is the volume of cuboid?Volume = L * B * H (unit^3)
Given length of the cuboid = 12 inches
Given breadth of the cuboid = 5 inches
Given height of the cuboid = 2 inches
Volume of cuboid = 12 * 5 * 2 = 120 inch^3
Hence there are 120 cubic inches contained inside the box.
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what is 3+ 11t - 9u when t = 9 and u = 11.
Answer:
3
Step-by-step explanation:
3+11t-9u=3+11(9)-9(11)=3+99-99=3
Dave walked to his friend's house at a rate of 4 mph and returned back biking at a rate of 10 mph. If it took him 18 minutes longer to walk than to bike, what was the total distance of the round trip?
I need help on it
Answer:
4 miles
Step-by-step explanation:
Walking:
Distance = d miles
Rate = 4 mph
Time = t hours
[tex]d=4\cdot t[/tex]
Biking:
Distance = d miles
Rate = 10 mph
Time [tex]=t-\dfrac{18}{60}=t-0.3[/tex] hours (convert minutes to hours)
[tex]d=10\cdot (t-0.3)[/tex]
Hence,
[tex]4t=10(t-0.3)\\ \\4t=10t-3\\ \\4t-10t=-3\\ \\-6t =-3\\ \\6t=3\\ \\t=\dfrac{3}{6}=\dfrac{1}{2}=0.5\ hour[/tex]
Therefore, the distance to friend's house is
[tex]d=4\cdot 0.5=2\ miles[/tex]
and the total distance of the round trip is
[tex]2+2=4\ miles[/tex]
1. Write the first ten multiples of these pairs of number and find their LCM
a) 2, 3
Answer:
Multiples:
2: 2 4 6 8 10 12 14 16 18 20
3: 3 6 9 12 15 18 21 24 27 30
The LCM is 6 (underlined)
How many yards are in 7 3/5 feet?
A. 15 1/5
B. 3 4/5
C. 2 8/15
D. 22 4/5
Please help me!
Answer:
22 4/5 yards
Step-by-step explanation:
(7 3/5) x 3 = 22 4/5
To convert 7 3/5 feet to yards, you use the conversion 1 yard = 3 feet. After converting the mixed number to an improper fraction, you divide by 3, yielding the answer 2 8/15 yards, which corresponds to option C.
To convert feet to yards, we can use the conversion factor that 1 yard is equal to 3 feet. Since the student needs to find out how many yards are in 7 3/5 feet, we can convert mixed numbers to improper fractions to simplify the calculation.
The mixed number 7 3/5 can be converted to an improper fraction by multiplying the whole number 7 by the denominator 5 and adding the numerator 3, then placing the result over the original denominator: (7 * 5) + 3 = 35 + 3 = 38, so 7 3/5 becomes 38/5.
To convert 38/5 feet to yards, divide by 3 because there are 3 feet in 1 yard:
38/5 feet * 1 yard/3 feet = (38/5)/3 = 38/5 * 1/3
This simplifies to 38/5 * 1/3 = 38/15 yards
Then divide 38 by 15 to get 2 with a remainder of 8, so we have 2 and 8/15 yards.
Therefore, the answer is C. 2 8/15 yards.
593.5625 as a whole number and remainder.
Answer:
whole number: 593remainder: 0.5625Step-by-step explanation:
Here, the "whole number" is the portion of the number to the left of the decimal point: 593.
The "remainder" is the portion left after the whole number is subtracted: 0.5625.
Find X if possible please?
Check the picture below.
Can someone tell me the answer to this please!!!
the answer is 38
16+18+4
Answer:
46
Step-by-step explanation:
The picture are irrelevant and is used to trick you.
Let swirly hair = s
Let curly hair = c
Let flat hair = f
Ok, now we can rewrite the picture in math terms
s = 16
c = 2 + s = 2 + (16) = 18
s = 4 + f → f = s - 4 = (16) - 4 = 12
s + c + f = 16 + 18 + 12 = 46
Item 14 Question 1 You have at most $60 to spend on trophies and medals to give as prizes for a contest. A drawing of a trophy and some medals are shown. The trophy is labeled 12 dollars each and the medals are labeled 3 dollars each. a. Write an inequality that represents the numbers of trophies x and medals y you can buy. The inequality is:
Answer:
[tex]12x+3y\leq 60[/tex]
Step-by-step explanation:
Let
x ----> the numbers of trophies you can buy
y ----> the numbers of medals you can buy
we know that
The term "at most" means "less than or equal to"
so
The number of trophies multiplied by $12 plus the number of medals multiplied by $3 must be less than or equal to $60
The inequality that represent this situation is
[tex]12x+3y\leq 60[/tex]
[tex]3x + 12y\leq 60[/tex]
Step-by-step explanation:
86 as a fraction in simplest form
Answer:
86/1
Step-by-step explanation:
The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour. There were initially 500
bacteria.
Which expression gives the number of bacteria after 3 hours?
The expression that gives the number of bacteria after 3 hours is
500 x 1.2³.
Given,
The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.
There were initially 500 bacteria.
We need to find an expression that gives the number of bacteria after 3 hours.
How do we get the final value of a number that gets multiplied by 2 every interval of time?Suppose we have a number 3 that gets multiplied by 2 every 1 minute.
So in 3 minutes, we have,
3 x 2 = 6
6 x 2 = 12
12 x 2 = 24
We see that we need to multiply the previous answer by the required factor till the required number of times.
We have,
The initial number of bacteria = 500
The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.
This means the number of bacteria after one hour:
= 500 x 1.2
= 600 bacteria
After two hours,
= 600 x 1.2
= 720 bacteria
After 3 hours
= 720 x 1.2
= 864 bacteria
The expression that gives the number of bacteria is 500 x [tex]1.2^{h}[/tex] where h is the number of hours.
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The number of bacteria after 3 hours, given an initial count of 500 and a growth factor of 1.2 per hour, can be calculated as 500 × 1.2^3, resulting in 864 bacteria.
Explanation:The number of bacteria in a petri dish growing exponentially can be modeled mathematically. If the number of bacteria is multiplied by a factor of 1.2 every hour, and we began with 500 bacteria, the expression for the number of bacteria after 3 hours can be found using exponential growth formula.
To find the number of bacteria after 3 hours, we would start with the initial amount of 500 bacteria and multiply it by 1.2 for each hour that passes. Therefore, after 3 hours, the expression would be:
Number of bacteria after 3 hours = Initial number × (growth factor)number of hours = 500 × 1.23
Using a calculator, we can compute this to find:
500 × 1.23 = 500 × 1.728 = 864
Thus, there would be 864 bacteria in the petri dish after 3 hours.
write the ratio as a fraction in simplest form
30 to 18
Answer:
5/3
Step-by-step explanation:
30/18=5/3