Step-by-step explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
7/8 x 8/3 = ?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
7 x 8
8x3
56/24
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 56 and 24 using
GCF(56,24) = 8
56/8 = 7
24/8 = 3
The fraction 7/3 is the same as 7 divided by 3
Convert to a mixed number using long division for 7 ÷ 3 = 2R1, so
Therefore:
7/3 = 2 1/3
2 1/3
The required quotient is 7/3 when 7/8 is divided by 3/8.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
The division operation is given in the question following as:
⇒ 7/8 ÷ 3/8
We have to determine the quotient when 7/8 is divided by 3/8
As per the given question, we have
⇒ 7/8 ÷ 3/8
⇒ (7/8) / (3/8)
Reciprocal the terms in the numerator, and we get
⇒ (7/8) × (8/3)
Apply the multiplication operation,
⇒ 56/24
Reduce the above fraction to the simplest form
⇒ 7/3
Therefore, the required quotient is 7/3 when 7/8 is divided by 3/8.
Learn more about the quotient here:
brainly.com/question/27796160
#SPJ5
Does the bowling ball have more potential energy or kinetic energy as it sit on top of the building? Why?
Answer:
The bowling ball has only potential energy as it sits on top of a building.
The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.
The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.
Therefore the bowling ball will have more potential energy as it sits on top of the building.
Step-by-step explanation:
The bowling ball has only potential energy as it sits on top of a building.
The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.
The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.
Therefore the bowling ball will have more potential energy as it sits on top of the building.
Answer:
Before the ball hits the ground it has more potential energy but when is going down it looses potential energy and creates kinetic energy so when the ball hits the floor it would have more kinetic energy.
Step-by-step explanation:
Mofor’s school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 6 student tickets for a total of $96. The school took in $202 on the second day by selling 8 senior citizen tickets and 13 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.
Answer:
Senior citizen tickets = 9
Student tickets = 10
Step-by-step explanation:
We begin by converting the question into simultaneous linear equations;
Senior citizen tickets = a
Student tickets = b
4a + 6b = 96
8a + 13b = 202
to find a,
if 4a +6b = 96
a = 96/4 - 6b/4
a = 24 - 1.5b
We now substitute this into the second equation
8(24 - 1.5b) + 13b = 202
192 - 12b + 13b = 202
b = 202 - 192
b = 10
We now put the value of b in either equation
4a + 6b = 96
4a + 6(10) = 96
4a + 60 = 96
4a = 96 - 60
4a = 36
a = 9
a recycling plant processes an average of 1/3 ton of glass each minute.At approximately what rate does the recycling plant process glass,in tons per day?
Answer:
480 tons
Step-by-step explanation: You have to figure out how many minutes are in 24 hours. (1440 min) Then, you multiply 1440 x 1/3.
Answer:
the answer is 480
Step-by-step explanation:
it is common sense but in your case it is uncommon sense
2. What can you conclude about two triangles when you know that two pairs of
corresponding sides and the corresponding included angles are congruent?
We can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.
Given that, two pairs of corresponding sides and the corresponding included angles are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
If two pairs of corresponding sides are equal and corresponding included angles are equal.
By SAS congruence theorem, two triangles are congruent.
Therefore, we can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.
To learn more about the congruent theorem visit:
https://brainly.com/question/24033497.
#SPJ2
Expand to write an equivalent expression: -1/4(8x+12y)
Answer:
-2x-3y
Step-by-step explanation:
-1/4(8x+12y)
-8/4x-12/4y
-2x-3y
Final answer:
The expression -1/4(8x+12y) is expanded by distributing -1/4 to both 8x and 12y, resulting in the equivalent expression -2x - 3y.
Explanation:
To expand the expression -1/4(8x+12y), you need to distribute the term outside the parenthesis (-1/4) to each term inside the parenthesis. This process is known as the distributive property of multiplication over addition. Here's the step-by-step process:
Multiply -1/4 by 8x to get -2x.Multiply -1/4 by 12y to get -3y.Combine these two products to get the expanded expression: -2x - 3y.In conclusion, the equivalent expression after expanding -1/4(8x+12y) is -2x - 3y.
does anyone know the answer ?
Answer:
15.7cm
Step-by-step explanation:
2 + 1.4 + 1.3 + 1.2 + 4.1 + 1.3 + 1.4 + 3
How do you divide a decimal by a whole fraction
Answer
wherever the decimal is, put it directly on top of the dividing line thing. Now that the decimal looks like a regular whole number you can divide like you usually would. Whenever you do regular long division, your answer is always going to be on the top of the line. Your answer should have a decimal in it ... and that should be your answer.
Nara multiplied two whole numbers together to equal a product of 90.
Then she accidentally spilled ketchup on her work.
Select the three responses below that could be one of the numbers Nara multiplied.
Answer:
30×3=90 10×9=90 45×2=90 . .
Answer: 5, 10, 18
Step-by-step explanation:
How many times can 27 go into 224
Answer:
27 can go into 224 8 times by dividing 224 by 27 .
SHOW ALL WORK: Graph each lineby plotting its intercepts or by using the y intercept and slope. {2x-y=4 {3y-3x=6
Answer:
x-y=-2
Step-by-step explanation:
Divide both sides if the equations by 3.
(3y-3x)÷3=6÷3
y-3x÷3=2
calculate the quotient
y-x=2
multiply both sides of the equation bub -1
-1x(-x)-1y=-1x2
any expression multiplied by -1
x-1y=-1x2
any expression multiplied by 1 remains the same.
x--y=-1x2
x-y=-2
Jeannie needs 2 cups of milk to make her homemade brownies. How many fluid ounces does Jeannie need?
Answer:
16 fluid ounces=2 cups
Hope this helps!
Step-by-step explanation:
Answer:
16 fluid ounces
Step-by-step explanation:
1 cup is equal to 8 fluid ounces, so 2 cups is 16 fluid ounces.
Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor. How much more per hour does Maddy’s neighbor pay than her aunt?
Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5
Step-by-step explanation:
In a triangle, one angle measures 68° and another
angle measures 38°. What is the measure of the third
angle?
Answer:
74°
Step-by-step explanation:
all angles of a triangle will always end up equal to 180°
68 + 38 = 106
180 - 106 = 74
Joe's annual income has been increasing in the same dollar amount. The first year his income was $15,200, and the 4th year his income was $17,900. In which year was his income $19,700?
Answer:
Therefore 6th year his income was $19,700.
Step-by-step explanation:
Given, Joe's annual income has been increasing in some dollar amount . The first year his income was $15,200 and 4th year his income was $17,900.
A=$17900, P= $15,200 and n = 3 year
[tex]A= P(1+\frac{r}{100} )^n[/tex]
[tex]\Leftrightarrow 17900=15200(1+\frac{r}{100})^3[/tex]
[tex]\Leftrightarrow (1+\frac{r}{100})^3=\frac{17900}{15200}[/tex]
[tex]\Leftrightarrow (1+\frac{r}{100})=(\frac{17900}{15200})^{\frac{1}{3} }[/tex]
[tex]\Leftrightarrow \frac{r}{100}=(\frac{17900}{15200})^{\frac{1}{3} }-1[/tex]
[tex]\Leftrightarrow r=5.60[/tex]
Let [tex]t^{th}[/tex] year Joe's income was $19,700.
[tex]\therefore 19700=15,200(1+\frac{5.60}{100} )^{t-1}[/tex]
[tex]\Leftrightarrow 1.296= (1+0.056)^{t-1}[/tex]
[tex]\Leftrightarrow 1.296= (1.056)^{t-1}[/tex]
[tex]\Leftrightarrow log(1.296)= (t-1)log(1.056)[/tex]
[tex]\Leftrightarrow \frac{log(1.296)}{log(1.056)}= (t-1)[/tex]
[tex]\Leftrightarrow t-1= 4.75[/tex]
[tex]\Leftrightarrow t= 4.75+1[/tex]
[tex]\Leftrightarrow t = 5.75[/tex] ≈6
Therefore 6th year his income was $19,700.
If the number of professors in a college is P and the number of students is S, and there are 19 times as many students as professors,write an algebraic equation that shows the
Answer:
[tex]S =19P\\S-19P = 0[/tex]
Step-by-step explanation:
We are given the following in the question:
Let P be the number of professor and S be the student in a college.
According to the question:
There are 19 times as many students as professors.
We have to write an equation to show the given relationship between professors and students.
[tex]S =19P\\S-19P = 0[/tex]
The above situation is the situation that represents the given relationship.
9. A relation contains the points ( -5,-10),( -2,-4)(-1,-2),(4,8) and (5,10) . Is this a function? Explain. (2 points)
Answer:
Yes it is a function given by f(x) = 2x
Step-by-step explanation:
Any function can approximated as series or a polynomial. For example,
[tex]e^{x} = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} ...[/tex] (exponential function)
(n! or n factorial is equal to n(n-1)(n-2)...3.2.1 ; 3! = 3.2.1 = 6)
and for the series to converge(the sum does not go to infinity), higher order terms must tend to zero.
General form of a polynomial/series: [tex]f(x) = a + bx +cx^{2} + ...[/tex]
For the given set of points, we can start with the straight line equation:
[tex]f(x) = y = a + bx[/tex] ........(1)
Let us take two points from the given relation: (-5, -10), (-1, -2)
and put the respective x and y values in equation (1), we get two equations, which we can then solve simultaneously to get values of [tex]a[/tex] and [tex]b[/tex]:
[tex]-10=a-5b[/tex] ........(2)
[tex]-2=a-b[/tex] ..........(3)
Now (3) - (2) gives us: [tex]b=2[/tex] and putting the value of [tex]b[/tex] in any of the above equation gives us [tex]a=0[/tex]
Hence, we get the equation, [tex]f(x)=y=2x[/tex]
It can be seen that all the given points satisfies this relation and since we get a unique [tex]y[/tex] for every [tex]x[/tex], we can call this a function.
Final answer:
The provided relation is a function because each x-value is unique and maps to exactly one y-value, fulfilling the criterion that every element of the domain is associated with exactly one element of the range.
Explanation:
The question asks if a relation containing the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10) is a function. To determine if this relation is a function, we need to examine if any x-value (the first number in each pair) repeats with a different y-value (the second number in each pair). Upon inspection, we see that each x-value is unique to a single y-value, which means that each element of the domain maps to a unique value in the range. Therefore, we can conclude that this relation is indeed a function.
In general, a function is defined as a relation in which every element of the domain (set of all first elements) is associated with exactly one element of the range (set of all second elements). This criterion is met in the relation provided as each x-value is unique and paired with only one y-value.
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
5x + 3y = 9
-10x – 6y = -18
Answer:
The system has infinitely many solutions
Step-by-step explanation:
we have
[tex]5x+3y=9[/tex] ----> equation A
[tex]-10x-6y=-18[/tex] ----> equation B
Multiply by -2 both sides equation A
[tex]-2(5x+3y)=-2(9)[/tex]
[tex]-10x-6y=-18[/tex] ----> equation C
Compare equation B and equation C
The equations are identical (is the same line)
therefore
The system has infinitely many solutions
Is a consistent dependent system
If the circumference of each tire on a vehicle is approximately 88 in., how many miles will the vehicle travel when the tires make
23
23,000 revolutions?
Answer:
31.94 miles
Step-by-step explanation:
we know that
The circumference of a tire represents the distance traveled by the vehicle in one revolution
so
by proportion
Find out the distance traveled by the vehicle in 23,000 revolutions
[tex]\frac{88}{1}\ \frac{in}{rev}=\frac{x}{23,000}\ \frac{in}{rev}\\\\x=88(23,000)\\\\x=2,024,000\ in[/tex]
Convert inches to miles
Remember that
[tex]1\ mile=63,360\ inches[/tex]
To convert inches to miles divided by 63,360
therefore
[tex]2,024,000\ in=2,024,000/63,360=31.94\ miles[/tex]
Suppose h(t)= -0.2 + 2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds
The maximum height of the ball is found at 64 feet
Explanation:Hello! remember to write complete and clear questions in order to get good and exact answers. I've found a similar question so I have written it in a comment above. We know that h(t) models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds. This equation follows a quadratic function so from math we know that the maximum or minimum of this type of functions is found at the vertex of its graph. So:
[tex]f(x)=ax^2+bx+c \\ \\ \\ Vertex \ (h,k): \\ \\ h=-\frac{b}{2a} \\ \\ k=f(-\frac{b}{2a}) \\ \\ \\ Our \ function \ is: \\ \\ h(t)=-16t^2+64t \\ \\ \\ Comparing: \\ \\ a=-16 \\ \\ b=64 \\ \\ c=0 \\ \\ \\ h=-(\frac{64}{2(-16)})=2 \\ \\ k=-16(2)^2+64(2) \\ \\ k=64[/tex]
Finally, the maximum height of the ball is found at 64 feet
Learn more:
Volume of a box: https://brainly.com/question/10501080
#LearnWithBrainly
PLEASE HELP ME THIS IS DUE TODAY! TYSM IF YOU CAN. a.) Lines AD and BE intersect at point C, as shown. Create an expression that represents the measure of angle DCE in terms of X. b.) Using your expression, solve for the missing value of X if DCE was 120 degrees.
Answer:
1) ∠DCE = (180 - x)°
2) x = 60°
Step-by-step explanation:
Here, given : Lines AD and BE intersect at point C
(a) Now, as we know, c BE is a straight line.
⇒∠BCD + ∠DCE = 180 ° (LINEAR PAIR)
⇒x ° + ∠DCE = 180 °
or, ∠DCE = (180 - x)° ....... (1)
(b) ∠DCE = 120°
Putting the value in the equation (1), we get:
120° = (180 - x)°
or, x = 180 - 120° = 60°
or, x = 60°
What is the degree of the polynomial below?
2х^2 + 3x +1
Answer:
the degree for the polynomial is 2
What is the value of y if formula is 4/5
Step-by-step explanation:
The complete question:
What is the value of y in the formula shown when x = [tex]\dfrac{4}{5}[/tex] ?
[tex]y=\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]
We have,
[tex]\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex] ...... (1)
To find, the value of y = ?
Put x = [tex]\dfrac{4}{5}[/tex] in equation (1), we get
[tex]y=\dfrac{4}{\dfrac{4}{5}}+\sqrt{\dfrac{4}{5}+0.2}-5(\dfrac{4}{5})[/tex]
[tex]=5+\sqrt{0.8+0.2}-4[/tex]
[tex]=1+\sqrt{1}[/tex]
= 1 + 1
= 2
Thus, the value of y is equal to 2.
How to divide 704 by 3 using long division
Answer:
Step 1: D for Divide. How many times will 5 go into 65? ...
Step 2: M for Multiply. You multiply your answer from step 1 and your divisor: 1 x 5 = 5. ...
Step 3: S for Subtract. Next you subtract. ...
Step 4: B for Bring down. ...
Step 1: D for Divide. ...
Step 2: M for Multiply. ...
Step 3: S for Subtract.
Step-by-step explanation:
1. What is the solution to the equation -5(s - 30) = -10?
Answer:
s = 32
Step-by-step explanation:
-5(s - 30) = -10
-5s + 150 = -10
-5s = -10 - 150
-5s = -160
s = -160/-5
s = 32
Find the area of the figure.
triangle with base 27.5 m and height 4.8 m
Answer:66
Step-by-step explanation:
27.5x4.8/2
Answer:
66 meters squared
Step-by-step explanation:
You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.
A figure is dilated by a factor of 3. which statement about the mesurements of the image is true
A Dilation factor of 3 means that all dimensions of the figure are three times larger than those of the original figure. This applies to every dimension of the figure including height, width, and depth (if applicable). An example is a rectangle with original measurements 2 cm by 4 cm becoming 6 cm by 12 cm after dilation.
When a figure undergoes a dilation, all its dimensions are altered by the dilation factor.
In this case, the dilation factor is 3, which means that each dimension of the figure is three times larger than before.
It is important to note that this applies to all dimensions: height, width, and depth (if applicable).
For instance, suppose you have a rectangle with a height of 2 cm and width of 4 cm.
If the rectangle is dilated by a factor of 3, the new dimensions would be 6 cm (2 cm * 3) for height and 12 cm (4 cm * 3) for width.
Learn more about Dilation here:
https://brainly.com/question/29811168
#SPJ6
The question probable may be:
Explain the concept of dilation and provide an example illustrating how the dimensions of a figure change when subjected to a dilation factor. In particular, discuss the scenario where a rectangle with a height of 2 cm and width of 4 cm undergoes a dilation by a factor of 3. What are the new dimensions, and how does this align with the general principle of dilation?
Solve this equation 3x4x4x15-14+1= ?
Answer:
my answer is 707
Step-by-step explanation:
i used a calculator lol
Answer:
707
Step-by-step explanation:
can someone help me one the questions I have not answered?
Answer:
[tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex] 391 = 17×23391 is not a Prime NumberExplanation:
391[tex]391\:\mathrm{divides\:by}\:17\quad \:391=23\cdot \:17[/tex]
[tex]=17\cdot \:23[/tex]
17, 23 are all prime number. So no further factorization possible
[tex]=17\cdot \:23[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex] 391 = 17×23391 is not a Prime Number Q # 3Answer:
[tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]291 = 3×97291 is not a Prime NumberExplanation:
291[tex]291\:\mathrm{divides\:by}\:3\quad \:291=97\cdot \:3[/tex]
[tex]=3\cdot \:97[/tex]
3, 97 are all prime number. So no further factorization possible
[tex]=3\cdot \:97[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]291 = 3×97291 is not a Prime Number Q # 4Answer:
[tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]37=37Yes, 37 is a Prime NumberExplanation:
3737 is a prime number. So no further factorization possible
[tex]=37[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]37=37Yes, 37 is a Prime Number Q # 6Answer:
[tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]411 = 3×137 411 is not a Prime NumberExplanation:
411[tex]411\:\mathrm{divides\:by}\:3\quad \:411=137\cdot \:3[/tex]
[tex]=3\cdot \:137[/tex]
3, 137 are all prime number. So no further factorization possible
[tex]=3\cdot \:137[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]411 = 3×137 411 is not a Prime Number Q # 7Answer:
[tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]387 = 3×3×43387 is not a Prime NumberExplanation:
387[tex]387\:\mathrm{divides\:by}\:3\quad \:387=129\cdot \:3[/tex]
[tex]=3\cdot \:129[/tex]
[tex]129\:\mathrm{divides\:by}\:3\quad \:129=43\cdot \:3\\=3\cdot \:3\cdot \:43[/tex]
3, 43 are all prime number. So no further factorization possible
[tex]=3\cdot \:3\cdot \:43[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]387 = 3×3×43387 is not a Prime Number Q # 9Answer:
[tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]113 = 113Yes, 113 is a Prime NumberExplanation:
113113 is a prime number. So no further factorization possible
[tex]=113[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]113 = 113Yes, 113 is a Prime Number Q # 16Answer:
[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]293 = 293 Yes, 293 is a Prime NumberExplanation:
293
[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]
[tex]=293[/tex]
[tex]293\mathrm{\:is\:a\:prime\:number,\:therefore\:no\:factorization\:is\:possible}[/tex]
[tex]=293[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]293 = 293 Yes, 293 is a Prime Number Q # 17Answer:
[tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]451=11×41 451 is not a Prime NumberExplanation:
451[tex]451\:\mathrm{divides\:by}\:11\quad \:451=41\cdot \:11[/tex]
[tex]=11\cdot \:41[/tex]
11, 41 are all prime number. So no further factorization possible
[tex]=11\cdot \:41[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]451=11×41 451 is not a Prime Number Q # 18Answer:
[tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]459 = 3×3×3×17459 is not a Prime NumberExplanation:
459[tex]459\:\mathrm{divides\:by}\:3\quad \:459=153\cdot \:3[/tex]
[tex]=3\cdot \:153[/tex]
[tex]153\:\mathrm{divides\:by}\:3\quad \:153=51\cdot \:3[/tex]
[tex]=3\cdot \:3\cdot \:51[/tex]
[tex]51\:\mathrm{divides\:by}\:3\quad \:51=17\cdot \:3[/tex]
[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]
3, 17 are all prime number. So no further factorization possible
[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]459 = 3×3×3×17459 is not a Prime Number Q # 19Answer:
[tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]385 = 5×7×11385 is not a Prime NumberExplanation:
385[tex]385\:\mathrm{divides\:by}\:5\quad \:385=77\cdot \:5[/tex]
[tex]=5\cdot \:77[/tex]
[tex]77\:\mathrm{divides\:by}\:7\quad \:77=11\cdot \:7[/tex]
[tex]=5\cdot \:7\cdot \:11[/tex]
5, 7, 11 are all prime number. So no further factorization possible
[tex]=5\cdot \:7\cdot \:11[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]385 = 5×7×11385 is not a Prime Number Q # 20Answer:
[tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]162 = 2×3×3×3×3 162 is not a Prime NumberExplanation:
162[tex]162\:\mathrm{divides\:by}\:2\quad \:162=81\cdot \:2[/tex][tex]=2\cdot \:81[/tex][tex]81\:\mathrm{divides\:by}\:3\quad \:81=27\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:27[/tex][tex]27\:\mathrm{divides\:by}\:3\quad \:27=9\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:9[/tex][tex]9\:\mathrm{divides\:by}\:3\quad \:9=3\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex][tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex]So,
[tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]162 = 2×3×3×3×3 162 is not a Prime NumberKeywords: prime factor
Learn more about prime factor from brainly.com/question/387724
#learnwithBrainly
Sidneys made $38 more than 3 times Casey’s weekly salary. If x represents Casey’s weekly salary , write an expression for sidneys weekly salary
y=3x+38 is the expression for Sidney's weekly salary.
Step-by-step explanation:
Given,
Casey's weekly salary = x
Let,
y be the weekly salary of Sidney's.
According to given statement;
Sidney makes $38 more than 3 times Casey's weekly salary.
Sidney's weekly salary = 3 times Casey's weekly salary + $38
[tex]y=3x+38[/tex]
y=3x+38 is the expression for Sidney's weekly salary.
Keywords: variable, addition
Learn more about variables at:
brainly.com/question/11207748brainly.com/question/11280112#LearnwithBrainly
The stock of Company A gained 4% today to $47.84. What was the opening price of the stock in the beginning of the day?
Answer:
46
Step-by-step explanation:
47.84 / 1.04, which is 46
The opening price of Company A's stock before the 4% increase to the closing price of $47.84 was $46.00.
To calculate the opening price of Company A's stock at the beginning of the day, before the 4% gain, we need to work backwards from the closing price. Since the stock closed at $47.84 after gaining 4%, we can represent the closing price as 104% of the opening price. Thus, the equation to find the opening price (OP) is:
OP x1.04 = $47.84
Now we solve for OP:
OP = $47.84 / 1.04
OP = $46.00
The opening price of Company A's stock at the beginning of the day was $46.00.