Using the rule of exponents, the expression is 12x^4 × 35y^5
What are the rules of exponents?The rules of exponents are given as:
Product of powers rule — When they are like bases, add the powersQuotient of powers rule — When they are like bases dividing, subtract the powersPower of powers rule — Multiply the powers together when a power is raised by another exponent.Given the expression;
3x^3 * 7y^2 * 4x * 5y ^3
collect the like bases
3x³ × 4x × 7y² × 5y³
Add the powers
12x^3 + 1 × 35^ 2 + 3
We then have;
12x^4 × 35y^5
Thus, using the rule of exponents, the expression is 12x^4 × 35y^5
Learn more about rules of exponents here:
https://brainly.com/question/847241
#SPJ1
Priya has some money to spend at a fair. It costs $6 to get in and $0.50 per ride ticket. Write an expression to represent how much Priya spends at the fair, in dollars. Let `x` represent the number of ride tickets Priya buys.
Answer
.50x + 6
If you need a step-by-step explanation or just the explanation tell me
I will mark BRAINLIEST AND GIVE EXTRA POINTS TO WHOEVER ANSWERS
I really don't understand this please help meh thanks :)
Draw a rectangle that has a diagonal twice as long as its width. Then write an equation to find the length of the rectangle.
The drawing of rectangle that has diagonal twice as long as its width is attached with this.
The equation for the length of the rectangle is l = [tex]\sqrt{3} x[/tex]
Given,
Width of rectangle, w= x
Diagonal of rectangle, d = 2x
We have to find the equation for length of rectangle.
We know that d² = l² + w²
Here,
(2x)² = l² + x²
4x² = l² + x²
l² = 4x² – x²
l² = 3x²
l = [tex]\sqrt{3}[/tex]x
That is the equation for length of rectangle is l = [tex]\sqrt{3}[/tex]x
Lets take width of rectangle, x = 3
Diagonal of rectangle, d = 2 × 3 = 6
L = [tex]\sqrt{3}[/tex] × 3 = 5.20
Here we proved that the equation is correct.
Learn more about rectangle here: https://brainly.com/question/12493568
#SPJ4
Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 2+6+18+ . . . . . . ; n=6
The given series is a geometric series. The sum of its first 6 terms is 728.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given series is:
2+6+18+ . . . .
and the number of terms is 6.
In the given series:
a(1) = 2
a(2) = 6
a(3) = 18
Notice that
a(2)/a(1) = 6/2 = 3
a(3)/a(2) = 18/6 = 3
Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 3
Sum formula for the first n term of a geometric series is:
S(n) = a(1) . (rⁿ -1)/(r -1)
Substitute n = 6, a(1) = 2, and r = 3
S(6) = 2 . (3⁶ - 1)/(3 - 1)
S(6) = 2. 364
= 728
We can also evaluate the sum directly. Write all the terms until n = 6.
a(4) = 18 . 3 = 54
a(5) = 54 . 3 = 162
a(6) = 162 . 3 = 486
Hence, the series is:
2+6+18+54+162+486 = 728
Learn more about series here:
https://brainly.com/question/28108001
#SPJ4
Solve the quadratic equation by compeleting the square. x^2 + 8x = 10
The value of x for the quadratic equation is 1.099 or -9.099 .
What is completing the square?
Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
To solve ax²+bx+c=0 by completing the square:
1. Transform the equation so that the constant term, c , is alone on the right side.
2. If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .
3. Add the square of half the coefficient of the x -term, to both sides of the equation.
4. Factor the left side as the square of a binomial.
5. Take the square root of both sides. (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)
6. Solve for x .
According to the question
Quadratic equation by completing the square
x² + 8x = 10
As we will try to make complete square of left side
for that
we have to add to both sides of the equation
As
a = 1
2ab = 8
b = 4
x² + 8x + 4² = 10 + 4²
By using the identity ( )
(x + 4)² = 10 + 16
(x + 4)² = 26
x + 4 = ±
x + 4 = ± 5.099
x = 5.099 - 4
x = 1.099
or
x = -5.099 - 4
x = -9.099
Hence, The value of x for the quadratic equation is 1.099 or -9.099 .
To know more about completing the square here:
brainly.com/question/4822356
#SPJ2
If x in {- 2, - 1, 0, 1, 2} find the solution set of x + 2 > 1
Answer:
if x is an element of that set therefore after solving the inequality we will determine the solutions according to the given set of numbers.x+2>1
x>1-2
x>-1
now from the set choose ot the numbers which are greater that -1
we find that x=0,1 and 2
Answer:
{0, 1, 2}.
Step-by-step explanation:
x + 2 > 1
x > 1 - 2
x > -1.
So, the solution set is:
{0, 1, 2}
Click the pair of numbers that are relatively prime.
11 and 121
35 and 125
39 and 75
34 and 49
34 and 49 is pair of numbers that are relatively prime.
What is relatively prime example?
If there isn't an integer bigger than one that divides two integers, then those two numbers are substantially prime (or coprime) (that is, their greatest common divisor is one). For instance, 12 and 13 are not very prime numbers, whereas 12 and 14.What do you mean by relatively prime?
If there are no other positive factors (divisors) between two integers other than 1, they are considered to be relatively prime. Two integers and are said to be relatively prime if using the notation to represent the greatest common divisor.34 and 49 is the pair of numbers that are relatively prime.
The numbers have no common prime factors.
Learn more about prime
brainly.com/question/20532807
#SPJ9
Answer:
D
Step-by-step explanation:
Just did it on T4L
Is it possible to find a value of $x$ so that the value of the surface area (in square inches) is equal to the value of the volume (in cubic inches)? a rectangular prism with length labeled 9 inches, width labeled 4 inches, and height labeled x inches.
A rectangular prism can have a surface area equal to its volume given the dimensions are 9 inches long, 4 inches wide and x inches high, where x is equal to 7.2 inches.
A rectangular prism is a three-dimensional figure with 8 vertices, 12 edges, and 6 rectangular faces.
If the dimensions of a rectangular prism is:
L = 9 inches
W = 4 inches
H = x inches
then the value of its surface area is equal to the value of its volume.
SA = V
2(lw + wh + lh) = lwh
Substitute the values and solve for x.
2(lw + wh + lh) = lwh
2[(9)(4) + 4x + 9x] = (9)(4)x
2(36 + 13x) = 36x
72 + 26x = 36x
10x = 72
x = 7.2 inches
Learn more about rectangular prism here: https://brainly.com/question/24284033
#SPJ4
This is for physical science
You call your parents to explain your issue with having a smashed phone and your parents travel at 0 meters in 2.5 hours. How fast did your parents rush to get here?
After calling the parents, and explaining them the issue of smashed phone, they travelled at a speed of 2.223 m/s = 8.0028 km/hr
As per the question statement, we are given that we call our parents to explain our issue with having a smashed phone and your parents travel at 20000 meters in 2.5 hours. We are supposed to find out that how fast did the parents rush to get here. Basically we have to find their speed of travelling.
Before solving the question, we must be aware that what is speed.
[tex]speed = \frac{distance}{time}[/tex]
and distance and time should be in SI units.
Given distance = 20,000 meters
Given time = 2.5 hours
[tex]1 hour = 60 min\\2.5 hour = 2.5*60\\2.5 hour = 150 min[/tex]
[tex]1 min = 60 sec\\150 min = 150*60 sec\\150 min= 9000 sec[/tex]
Therefore given time = 9000 sec
Therefore speed = [tex]\frac{distance}{time} = \frac{20000}{9000}[/tex]
Speed= 2.223 m/sec
Hence they travelled at a speed of 2.223 meters per second
2.223 m/s = 8.0028 km/hr
Speed: The speed it the distance covered by an object or body or person per unit time or time taken by him/her to cover the given distance. SI Unit: [tex]m/sec[/tex]To learn more about speed, distance and time, click on the link given below:
https://brainly.com/question/7359669
#SPJ1
The perimeter of a rectangle is 398 meters.
The perimeter of a rectangle is 398 meters. The rectangle has a length of (12x-3) meters and a width of (8x+2) meters. What are the dimensions of the rectangle?
The value of perimeter of the rectangle is 398, So the length is 177m and breadth is 82m.
What is perimeter of rectangle?
The complete length of a rectangle's outside edge is known as its perimeter. The formula P=2l+2w, where l is the rectangle's length and w is its width, determines the perimeter P of a rectangle.
Given the perimeter of the rectangle = 398
perimeter of rectangle = 2 × (L + B)
Length of rectangle = (12x-3)
Breadth of rectangle = (8x+2)
⇒ perimeter of rectangle = 2 × (12x-3 + 8x+2)
⇒ 398 = 2 × (20x - 1)
⇒ 199 = 20x - 1
⇒ x = 200/20
⇒ x = 10
Length = 120 . 10 - 3
Length = 117
Breadth = 8.10+2
Breadth = 82
To learn more about perimeter of the rectangle from given link
https://brainly.com/question/10452031
#SPJ1
Answer:
length = 117
width = 82
Carla puts $625 into a savings account at an annual interest rate of 2.5%. If she does not withdraw or deposit any money, what is the interest that Carla will earn at the end of 6 months?
The formula is I=prt
Please dont put random answers
Ill give brainlyist to the correct answer
Answer: 7 81 cents
Step-by-step explanation:
yes
A student incorrectly claims that 2/3 divided by 5/9 = 5/6 find the correct quotation.What was the students error
Answer:
See explanation
Step-by-step explanation:
2/3 / 5/9=
2/3 * 9/5= ==> Dividing by a number is basically multiplying by its reciprocal.
(2*9)/(3*5)=
18/15=6/5 ==> The student just switched the numerator and denominator.
Answer:
6/5
Step-by-step explanation:
2/3÷5/9=2/3x9/5=2/1x3/5=6/5
-|10-7•5+8•-4+2•2| helppppppppp
Answer: -53
Step-by-step explanation:
-|10-7•5+8•-4+2•2|=
-|10-7•5+8•(-4)+2•2|=
-|10-35+(-32)+4|=
-|-25-32+4|=
-|-25-28|=
-|-53|=
-(53)=-53
you earn $10 per hour babysitting and you babysit 25 hours each week. You also help your neighbor with household chores and are paid $8 per hour. If you spend 12 hours helping your neighbor, how much will you earn in one week?
Answer:
$346
Step-by-step explanation:
Babysitting = $250
($10 × 25 hrs)
Neighbour's Chores = $96
($8 x 12 hrs)
Total Earning = $346
($250 + $96)
Fred started a new e-Commerce business and borrowed $13,100 for 13 years to get the business up and running. The interest is $3916.90. Find the rate.
Round to two decimal places, if necessary.
Simple Interest
The rate of interest is 0.26%
Given,
The amount borrowed by Fred to start a new e-commerce business = $13100.
Time of investment = 13 years.
Interest for the money = $3916.90
We have to calculate the rate of interest.
For simple interest, equation is:
P = IRT
Where,
P = Principal amount
R = Rate of interest
I = Interest
T = Time period
Here,
P = 13100
I = 3916.90
T = 13
Then,
R = P / IT
R = 13100 / (3916.90 × 13)
R = 13100 / 50919.7
R = 0.26%
Therefore, the rate of interest is 0.26%
Learn more about Interest here:
https://brainly.com/question/18766194
#SPJ1
Write the equation of the line in slope-intercept form.
3y+9=-6x
The equation of the line in slope-intercept form is y = (-2)x + (-3) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 3y + 9 = -6x .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
3y + 9 = -6x
3y = -6x - 9
On dividing both sides of above equation by 3, we will get
y = (-2)x + (-3) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = -2
Intercept = c = -3
The equation of the line in slope-intercept form is y = (-2)x + (-3) .
To know more about Slope Intercept form refer to the link:
https://brainly.com/question/19440459
#SPJ4
find the exact length of the line segments whose endpoints are (10, 1) and (9, -4)
The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37
How to find the exact length of the line segments whose endpoints are (10, 1) and (9, -4)?The points are given as (10, 1) and (9, -4)
The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is calculated as
d = √[(x2 - x1)^2 + (y2 - y1)^2]
So, we have
d = √[(10 - 9)^2 + (1 + 5)^2]
Evaluate
d = √37
Hence, the exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37
Read more about distance at
https://brainly.com/question/7243416
#SPJ1
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
A basketball player plays 2, 181 minutes the first year of his career, 2, 583 minutes the second year of his career, and 2, 716
minutes the third year of his career. How many minutes has he played in three years?
He played 7480 minutes across three years.
The information provided, expressed in minutes per year, is as follows:
The first year is 2181 minutes, the second is 2583 minutes, and the third is 2716 minutes.
Add that now to determine the total amount of time:
The sum of the three years is 7480 minutes (2181 + 2583 + 2716).
The gamer used 7480 minutes throughout the course of three years.
How much time in total?The measurement of continuously occurring events is done in terms of time. In hours, seconds, and minutes, it is measured. The well accepted established formulae can be used to compute it.
To learn more about the time from the given link:
https://brainly.com/question/26046491
#SPJ9
Simplify (2y-5)(2y+5)
Answer:-10
Step-by-step explanation:
Answer: 4y^2-25
Step-by-step explanation:
what si the answer for 2+2
Answer:
4
Step-by-step explanation:
2+2=4
In this problem, you will investigate the relationship between same-side exterior angles.
e. Write a proof of your conjecture.
Eight angles are formed when two parallel lines are intersected by a third line that intersects them at an acute angle, known as a transversal line. These angles interact in a number of ways, one of which is the same-side exterior. Both angles are on the same side of the transversal line, as indicated by the word "same-side," and both are "external," or "outside," of the parallel lines, as represented by the term "outside."
When a transversal crosses two parallel lines, it creates an angle between the lines and outside the lines on the same side. Because the alternate interior and alternate exterior angles are the same, and because linear pairs of angles are supplementary, the identical side angles are also supplementary.
Learn more about exterior angles at https://brainly.com/question/26969915
Instructions for roasting meat: Cook for 30 minutes at 230°C. Turn down the heat to 180 °C. Allow 30 minutes cooking time for every 450g. A piece of meat takes 2 hours altogether to cook. How heavy is it?
The piece of meat has a weight of 1,800g.
What is the definition of a mathematical operation?The principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action on each function.So, as the question says allow 30 minutes of cooking to each 450g.
Total time is taken = 2 hours.30 × 4 = 120 minutes is, 2 hours.Similarly,
450 × 4 = 1,800Therefore, the piece of meat has a weight of 1,800g.
Know more about mathematical operations here:
brainly.com/question/28294142
#SPJ9
Answer:
1800
Step-by-step-explanation:
How many books does Jeff own if he has more than 14 books? Describe the number of books that Jeff owns if you add the constraint that he owns fewer than his sister, who owns 19 books.
Jeff can own 15,16,17 or 18 books as per the given question
The following question is based on inequality. Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. In this type of question, we will get a range of answers and not a specific answer.
No. of books owned by Jeff > 14
No. of books owned by his sister = 19 books
As per the question "He owns books fewer than his sister"
So, he owns >14 and <19 books
Therefore, he can own 15, 16, 17 or 18 books as per the given inequality.
Learn more about inequality:
https://brainly.com/question/20383699
#SPJ4
331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Create equation here.
The required equation is 6x+7=331 and the no. of students traveling on each bus is 54.
What is an equation?A mathematical equation can be defined in a variety of ways. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. One or more variables are used in the most basic and simple algebraic equations in mathematics.
Given data:
Total no. of students: 331
Number of students on bus = 7
No. of buses = 6
Let the no. of the students on each bus be x.
So according to the given condition,
6x+7=331
6x=331-7
6x=324
x=324/6
x=54
Therefore, the required equation is 6x+7=331 and the no. of students travelling on each bus is 54.
To know more about this equation visit:
https://brainly.in/question/24791936
#SPJ9
Using the function you entered in Activity 1, set up the table as shown.
Scroll to x- values less than 3 . Do they make the inequality true?
Answer:
yes
yjnujhhhbhhhjhhbhhbhhhjj
Find each sum.
-1.95+10
A 36-inch diameter pie is cut into 6 slices. What is the area of one of the slices?
A. 54pi inches
B. 216pi inches
C. 6pi inches
D. 24pi inches
E. None of the above
The area of one of the slices is 54π square inches
What is the area of one of the slices?The given parameters are
Diameter = 36 inches
Number of slices = 6
The pie represents take the shape of a circle
And the area (A) of a circle using the diameter (d) is
A= π(d/2)^2
Multiply the above area by 1/6 to get the area of a slice of the pie
So, we have
Area = 1/6 * π(d/2)^2
This means that the area of one of the slices is calculated by
Area = 1/6 * π(d/2)^2
Where
d represents the diameter of the pie i.e. d = 36 inches
So, we have
Area = 1/6 * π * (36/2)^2
Evaluate
Area = 54π
Hence, the area of one of the slices is 54π square inches
Read more about area at:
https://brainly.com/question/22972014
#SPJ1
help please with all answers !☹️
Answer:
Here are the answers!
Step-by-step explanation:
When there are two angles on a line that are touching you can subtract what you know from 180° (Ex: 138° and angle 4)
The angles across from each other are the same.
The total of all three angles in a triangle should be 180°
Betsy has a bag with three mint sticks eight jelly treats and nine fruit tart chews if she eats one piece every three minutes what is the probability her first two pieces will be a fruit tart chew and a jelly treat
If Betsy has a bag with three mint sticks, eight jelly treats, and nine fruit tart chews and she eats one piece every three minutes, the probability her first two pieces will be a fruit tart chew and a jelly treat is 18.9%.
The probability of her first two pieces being a fruit tart chew and a jelly treat can be calculated as follows,
First, we divide the expected outcomes by the total possible outcomes.
Total possible outcomes = 3(mint sticks) + 8(jelly treats) + 9(fruit tart chews) = 20
Hence,
Probability for fruit tart chew: 9 ÷ 20
Probability for jelly treat: 8 ÷ 19 (as one possibility is considered to be fruit tart chew)
The probability of her first two pieces to be fruit tart chew and jelly treat can be determined by multiplying the probability for fruit tart chew with the probability for jelly treat,
Probability = (9/20)(8/19)
Probability = 72/380 = 0.189
Converting into percentage,
Probability = 0.189 × 100 = 18.9%
Hence, the probability that her first two pieces will be a fruit tart chew and a jelly treat is equal to 18.9%.
To learn more about probability, click here:
https://brainly.com/question/251701
#SPJ4
Determine whether Δ P Q R ≅Δ X Y Z . (Lesson 4-4)
P(8,1), Q(-7,-15), R(9,-6), X(5,11), Y(-10,-5) , Z(6,4)
The measurement of triangle ΔPQR ≇ ΔXYZ.
What do we mean by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
To prove: ΔPQR ≅ ΔXYZ
P(8,1) ≠ X(5,11)Q(-7,-15) ≠ Y(-10,-5)R(9,-6) ≠ Z(6,4)So, we can say that ΔPQR ≇ ΔXYZ.
Therefore, ΔPQR ≇ ΔXYZ.
Know more about the congruency of a triangle here:
brainly.com/question/2938476
#SPJ4
