The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
In the question ,
Four equations are given , we need to find the equation that represents the identity property of multiplication .
we know that the identity property of multiplication states that the product of any number and 1 is the same given number .
For Example : the product of a number 'a' and 1 is = a , that is a×1 = a .
So , by the applying the definition of Identity property of multiplication we get that the equation that models the identity property is
(a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi)
Therefore , The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
The given question is incomplete , the complete question is
Which equation illustrates the identity property of multiplication?
(a) (a + bi) × c = (ac + bci)
(b) (a + bi) × 0 = 0
(c) (a + bi) × (c + di) = (c + di) × (a + bi)
(d) (a + bi) × 1 = (a + bi)
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a dog breeder is planning to buy more dog food. he makes a table showing how many pounds of food he will have after shopping the table is based on.how much he spends and how much food he already has which equation generates the table
The linear function that models the data-set is given as follows:
v = 4 + 0.4x.
What is a linear function?The slope-intercept representation of a linear function is presented as follows:
y = mx + b
The coefficients of the function and their meaning are obtained as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the output y of the function when the input variable x assumes a value of 0.For this problem, the values of these parameters are given as follows:
Slope of m = 0.4, as when the input increases by 20, the output increases by 8, hence m = 8/20 = 0.4.Intercept of b = 4, as when the input is of zero, the output is of 4.Hence the equation is given as follows:
v = 4 + 0.4x.
Missing InformationThe table is given by:
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
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a stats 10 test has 4 multiple choice questions with four choices with one correct answer each. if we just randomly guess on each of the 4 questions, what is the probability that you get exactly 1 question correct? find the nearest answer.
if we just randomly guess on each of the 4 questions, Then the probability that you get exactly 1 question correct is 1/4.
Probability formula: P(E) = favourable outcomes/Total outcomes
The number of questions is 10
The options for each question are 4.
Possible answers are 1.
Then,
favourable events = 1 × 10= 10
Total events = 4× 10= 40
Now, find the probability by putting the values as follows:
P(E) = favourable outcomes/Total outcomes
P(E) = 10/40
P(E) = 1/4
Therefore, the probability of doing all questions correct is 1/4
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Below, the two-way table is given for a class
of students.
Sophomore
Freshmen
Male
4
Female 3
Total
6
4
17
Juniors Seniors Total
2
6
2
3
If a female student is selected at random, find the
probability that the student is a senior.
P(Senior | Female ) = [? ]%
Round to the nearest whole number.
Enter
Answer:
19%
Step-by-step explanation:
Of the female students, there are:
3 freshmen4 sophomores6 juniors3 seniorsOut of 16 total students, 3 are juniors, so the probability is [tex]\frac{3}{16} \approx 19\%[/tex]
A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?
Answer:
4
Step-by-step explanation:
Let x be the unknown number.
[tex]\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}[/tex]
Solve the found equation for x:
[tex]\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}[/tex]
Therefore, the number squared is:
[tex]\implies x^2=2^2=4[/tex]
24) The cost in millions of dollars for a company to manufacture x thousand automobiles is given by
the function C(x) = 3x^2 - 30x + 200. Find the number of automobiles that must be produced to
minimize the cost.
A) 15 thousand automobiles
C) 5 thousand automobiles
B) 125 thousand automobiles
D) 10 thousand automobiles
For minima,
C'(x) = 0
6x-30 = 0
x = 5
If C"(x) >0, then minima
So, C"(x) = 6 > 0
So, for x = 5 , thr value of C(x) will be minimum.
Option C is correct
Help me solve this please
Step-by-step explanation:
let's use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
so,
5.4/sin(K/2) = 12.3/sin(M1)
8.2/sin(K/2) = x/sin(M2)
M1 + M2 = 180 (as complementary angles or linear pair)
M2 = 180 - M1
sin(K/2) = 5.4×sin(M1)/12.3
sin(K/2) = 8.2×sin(M2)/x
therefore
5.4×sin(M1)/12.3 = 8.2×sin(180 - M1)/x
since sin(a) = sin(180 - a)
5.4×sin(M1)/12.3 = 8.2×sin(M1)/x
and then
5.4/12.3 = 8.2/x
x×5.4 = 8.2×12.3
x = 8.2×12.3/5.4 = 18.67777777... ≈ 18.7
Step-by-step explanation:Step-by-step explanation:
let's use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
so,
5.4/sin(K/2) = 12.3/sin(M1)
8.2/sin(K/2) = x/sin(M2)
M1 + M2 = 180 (as complementary angles or linear pair)
M2 = 180 - M1
A 2-pint bucket of paint costs $11.08. What is the price per cup?
The price per cup for a 2-pint bucket of paint costs $11.08 is $2.77.
How to calculate the price per cup?It should be noted that 1 pint = 2 cup
In this case, 2-pint bucket will be:
= (2 × 2)
= 4 cups.
Therefore, 4 cups cost $11.08.
The price per cup will be:
= Total cost / Number of cups
= $11.08 / 4
= $2.77
The price is $2.77.
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There are 50 tudent in cla. Boy make up 20% of the cla. 60% of the boy wear glae. How many boy in the cla wear glae?
The boys in the class that wear glae are 6 people.
The boys in the class that wear glae can be calculated as follows:
First we should calculate how many boys there are in the class. We can calculate it by multiplying the percent of the boys to the total students.
Boys in the class = [tex]\frac{20}{100} X 50[/tex] = 10 people.
Thus, we can calculate the boys who wear the glae by multiplying the percent of the boys wearing glae of the boys in the class.
Boys wear glae = [tex]\frac{60}{100} X 10[/tex] = 6 people.
Hence, The boys in the class that wear glae are 6 people.
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Write 8128 as the sum of consecutive odd cubes.
The sum of consecutive odd cubes of 8128 is 1³+3³+5³+7³+9³+11³+13³+15³
Therefore, 1+27+125+343+729+1331+2197+3375=8128
What are consecutive numbers?Consecutive numbers are those that come after each other in descending order from the smallest to the largest. The difference between consecutive numbers is always fixed and follows a predictable pattern. For example, the first three consecutive natural numbers are 1, 2, 3. The simplest way to find consecutive numbers is to look at the number set and find the number that is either before or after the term of interest.
We know that consecutive odd numbers are 1,3,5,7,9,11,13,15,17..
Here 8128 is a perfect square
And it can be written as the sum of consecutive odd cubes as follows:
1³=1
3³=27
5³=125
7³=343
9³=729
11³=1331
13³=2197
15³=3375
The sum of consecutive odd cubes of 8128 is
=1³+3³+5³+7³+9³+11³+13³+15³
=1+27+125+343+729+1331+2197+3375
=8128
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13. At Greenville High School 1/3 of the students
are involved in sports. Of the students
involved in sports 20% play football. If there
are 3,000 students at the school, how
many play football? (Example 5)
Out of 3000 students at the school , 200 student plays foot ball .
In the question ,
it is given that ,
fraction of students that are involved in sports at Greenville High School = 1/3 of total students ,
percent of students that plays football = 20% of sports students .
given that the total number of students present at the school = 3000
So , the number of students involved in sports = (1/3) × 3000
= 1000
number of students who plays football = 20% of 1000
= 0.20 × 1000 ....because 20% = 0.20
= 200
Therefore , Out of 3000 students at the school , 200 student plays foot ball .
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suppose that the radius is expanding at a rate of 0.6 inches per second. how fast is the volume changing when the radius is 2.3 inches? use at least 5 decimal places in your answer.
Using the theories of Application of derivative,we got that 59.11221inches³/sec is rate of volume changing when the radius is 2.3 inches.
We are given rate of change of radius (dr/dt)=0.6inches
We know very well that volume of sphere is given by (4/3)πr³
where r is the radius of the sphere.
Now, differentiating the volume with respect to radius, we get
=>dV/dr=4πr²
=>dV/dt=(dv/dr)·(dr/dt)
=>dV/dt=4πr².(dr/dt)
We are given that dr/dt=0.6inches/sec
So, dV/dt=4πr²·(0.6)
Now, putting values of r=2.3
dV/dt=4π(2.3)²×(0.6)
=>dV/dt=4×3.14×2.3×2.3×0.6
=>dV/dt=59.11221inches³/sec
Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.
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Can someone please help
After solving the value of x is 2.
From the figure:
Let ABCDE be the figure such that:
AB = 6x , BC = 6 , CD = 4,and DE = CE - CD = 12 - 4 = 8.
BD and AE are parallel lines such that:
AB/BC = ED/CD
6x/6 = 8/4
x = 8/4
x = 2.
Therefore After solving the value of x is 2.
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The tap can fill up the bathtub in 22 minutes. The capacity of the bathtub is 176 L
How much water is added to the tub per minute?
Answer:
8.8 L
Step-by-step explanation:
volume/time
176/22
=8.8
Maria is renting kayaks from a local shop that charges a $10 fee, plus an hourly rate of $7. 50. For how long can maria rent the kayak if she pays a total of $70?.
Answer:
8 hours
Step-by-step explanation:
We can use an algebraic equation to solve this problem.
7.5x + 10 = 70
7.5x + 10 (-10) = 70 (-10)
7.5x (/7.5)= 60 (/7.5)
x = 8
5. Gabi will graph f(x) = x and m(x) = f(x). Mark each statement as true or false. If false,
rewrite as true in the space below.
a. The slope of m(x) will be steeper than f(x).
_b. The y-intercept of m(x) will be units up from f(x).
d. g(x) = f(x − 3)
The Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function
What is a Slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.
Take notice that tan = y/x.
In the given question, we have: two functions:
So, finding the slope of each of the functions;
The slope of the first function; f(x) =x is 1;
The slope of the second function: m(x) =[tex]\frac{3}{5} f(x)[/tex];
Since the Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function because the graph depends on the slope.
Hence,
the Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function.
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Correct answer get's free 50 points
The correct statement regarding the solution of the inequality 8x - 6 < 3x + 19 is given as follows:
D. She knows that the solution must be either all the values less than 5 or all the values greater than 5.
What is the solution to the inequality?The inequality is presented as follows:
8x - 6 < 3x + 19.
Lin finds the value of x = 5 for which the two sides of the inequality are equal. Then, there are only two cases for the solution, which are listed as follows:
All values that are less than 5.All values that are greater than 5.Thus option D gives the correct option regarding how to find the solution.
The justifications for the other options being wrong are given as follows:
Options A, C and D: an inequality gives a range of values as a solution, not a single value, hence substituting the value on the inequality you verify if the value is a solution, but you do not solve, that is, you do not find all the values that are solutions to the inequality.Option E: The inequality is an open inequality, meaning that x = 5 is not a solution to the inequality.More can be learned about inequalities at https://brainly.com/question/25275758
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Answer:
I think its D.... id/k I think it is.
Step-by-step explanation:
……………………………………………………..
Answer:
-11, -2, 3, 6
-16, -5, 19, 21
Step-by-step explanation:
The velocity, V, of a specific object being dropped from a particular height, h, can be found by the radical function V equals the square root of the quantity 2 times h times a end quantity where a represents the acceleration in ft/sec2. If the acceleration due to gravity is 32.2 ft/sec2, at what height should you drop an object in order for it to have a velocity of 60 ft/sec?
0.9 feet
55.6 feet
55.9 feet
3,864 feet
The height should you drop an object in order for it to have a velocity of 60 ft/sec is 55.9 feet
How to find the heightThe equation given in the problem is written below
v = √2ha
velocity, v = 60 ft/sec
height, h = ?
acceleration due to gravity, a = 32.2ft/sec^2
The problem asks for height hence we make h the subject of the formula
v = √2ha
v^2 = 2ha
h = v^2 / 2a
substituting the values in to the equation
h = 60^2 / (2 * 32.2)
h = 3600 / 64.4
h = 55.9 feet
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Meshea sold 12 dresses in 120 minutes at this rate how many hours will it take her to sell 144 dresses
Answer: 144 dresses in 1440 minutes.
Step-by-step explanation:
Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.
The rate is 120min/12dresses. Let's simplify it.
12/120 = 10min/1dress (or just 10)
Lets use this rate for 144 dresses
10 x 144 = 1140
It will take 1440 minutes to sell 144 dresses.
what is the value of x in the equation 0.5x+3=4.5?
Answer:
x = 3
Step-by-step explanation:
Collect like terms
0.5x = 4.5 - 3
0.5x = 1.5
Divide both sides by 0.5
0.5x/0.5 = 1.5/0.5
x = 3
Using fractions,
1/2x = 9/2 - 3
1/2x = 3/2
Divide both sides by 1/2
x = 3/2÷1/2
Reciprocate
x = 3/2 × 2/1
x = 6/2
x = 3
Put the following equation of a line into slope-intercept form, simplifying all fractions. 9y−3x= −54
The equation of the line into slope-intercept form is y = x/3 - 6
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to put the equation of a line into slope-intercept form?From the question, we have the following equation that can be used in our computation:
9y−3x= −54
Rewrite properly
This gives
9y - 3x = -54
Divide through the equation by 3
So, we have the following representation
9y/3 - 3x/3 = -54/3
Evaluate
3y - x = -18
To rewrite as slope-intercept form is to make y the subject
So, we have
3y = x - 18
Divide through the equation by 3
So, we have the following representation
y = x/3 - 6
Hence, the equation is y = x/3 - 6
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A shop sells tins of paint in 2 litre and 5 litre cans. The manager checks the amount of paint he
has in stock, and finds that there are 500 cans altogether. These cans hold a total of 1420 litres of
paint. By forming and solving a pair of simultaneous equations, find the number of each size of
can in stock.
Answer:
360 of 2 liter cans and 140 of 5 liter cansStep-by-step explanation:
Let the number of 2 liter cans be x and 5 liter cans be y.
Number of cans:
x + y = 500Amount of paint:
2x + 5y = 1420Solve the system by elimination, double the first equation and subtract from the second one:
2x + 5y - 2x - 2y = 1420 - 2*5003y = 420y = 420/3y = 140Find x:
x + 140 = 500x = 500 - 140x = 36021. A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n+4) apples. How many apples do you and your friend pick together?
How many baskets do you need to carry all the apples? Justify your answer.
Answer:
21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n+4) apples. How many apples do you and your friend pick together?
How many baskets do you need to carry all the apples? Justify your answer.
Step-by-step explanation:
(2n - 3)(n + 4) binomial times a binomial equals
2n^2 + 5n - 12
Can anyone please help me with this? I don't get it.
Answer:
739
Step-by-step explanation:
2217 (weight) / 3 ( # of blocks)
Piper invested $4,700 in an account paying an interest rate of 4. 8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 19 years?.
Assuming no deposits or withdrawals are made, the amount in the account after 19 years is: 11,454. 133.
How to find the amount in the account?Using this formula
A = P(1+r/100)ⁿ
Where:
A = Amount =?
P = Principal = $4700
r = Interest rate =4.8%
n = the number of periods =19 years
Let plug in the formula
A = 4,700 (1 + 4.8/100)¹⁹
A = 4,700 (1 + 0.048)¹⁹
A = 4,700 (1.048)¹⁹
A = $11,454. 133
Therefore the amount is $11,454. 133.
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Write 36 a product of it' prime factor. Write the factor in order, from mallet to larget
The factor of 36 in order from smallest to largest is 2 × 2× 3× 3.
Prime factor:
Factors are the numbers you multiply together to get another number. In simple words, a prime factor is finding which prime numbers multiply together to make the original number.
Here we have to find the prime factor 36.
That is we have to find the smallest multiplication of digits to get the value.
36 = 2 × 2 × 3 × 3
Therefore the prime factor is 2 × 2×3×3.
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Nolan has five more quarters and dimes and seven fewer nickels and dimes. He has 25 coins. How many of each coin does he have? How much money in dollars and cents is it worth?
Answer:
9 dimes, 4 nickels, 12 quarters
90 cents + 20 cents + 300 cents = 410 cents = $6.83
Step-by-step explanation:
q=5+d
n=d-7
q+n+d=25
5 + d + d - 7 + d = 25
3d-2=25
3d=27
d=9
25 - 9 = 16 nickels and quarters
q + n = 16 ---> q=16-n
n=d-7 ---> d=n+7
q=5 + n + 7
q=n+12
n+12 = 16-n
2n=4
n=4
25-(9+4)= 12 quarters
He has 2 nickels, 9 dimes, and 14 quarters, with a total value of $4.50
Step-by-step explanation:I am going to assume that the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than" because otherwise, there is no context in this question. If my answer is incorrect, please tell me how to correctly interpret this question.
In this scenario, the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than."
Amount of nickels - x
If there are seven fewer nickels than dimes, the amount of dimes is x + 7. There are five more quarters than dimes, so the amount of quarters is x + 7 + 5, which equals x + 12.
x + x + 7 + x + 12 = 253x + 19 = 253x = 6x = 2
Therefore, there are 2 nickels. Now we must figure out the number of quarters and dimes.
x + 7 = 9
x + 12 = 14
There are 9 dimes and 14 quarters.
Nickels are each worth 5 cents. 2 times 5 is 10 cents.
Dimes are each worth 10 cents. 9 times 10 is 90 cents.
Quarters are each worth 25 cents. 14 times 25 is 350 cents.
Now, we add. 10 + 90 + 350 = 100 + 350 = 450.
REMEMBER, THIS IS IN CENTS. WE MUST STILL CONVERT IT INTO DOLLARS.
450 divided by 100 is $4.50
Which of the following are two-dimensional shapes? Select three options.
circle
cube
cylinder
hexagon
oval
pyramid
Answer:
Circle, hexagon, and oval
Step-by-step explanation:
They are all 2d.
Please answer this question
Answer:
x=9
y=-5
Or
(9,-5)
Step-by-step explanation:
-x+y=-14
+x. +x
y=x-14
2x-3(x-14)=33
2x-3x+42=33
-x+42=33
-42. -42
-x=-9
/-1. /-1
x=9
-(9)+y=-14
+9. +9
y=-5
Hopes this helps please mark brainliest
-0.6a^2b * (-10ab^2)
please help :)
Answer:
evaluation or perhaps difference
Step-by-step explanation:
ex: 6b 2a 2b+1
diff: 6(2b+1)b 2 a 2b