(i) 1050 as the product of its prime factors is 1050 = 2 x 3 x 5² x 7.
(ii) The two numbers having a highest common factor of 21 and
lowest common multiple of 1050 are (760,1160).
What is a prime factor?
A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. Now, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers.
To get the prime factors of 1050, start dividing the number by its primes -
1050 ÷ 525 = 2
525 ÷ 175 = 3
175 ÷ 35 = 5
35 ÷ 7 = 5
7 ÷ 1 = 7
So here the prime factorisation of 1050 -
= 2 x 3 x 5 x 5 x 7
= 2 x 3 x 5² x 7
Therefore, the prime factors are 2, 3, 5, and 7.
Now, it is given that HCF of numbers = 21
LCM of numbers = 1050
Calculate the two numbers by using the following procedure -
Let the two numbers be 40x and 40y respectively.
Product of numbers = LCM × HCF
Now, the equation will be -
40x × 40y = 1050 × 21
40(x × y) = (1050 × 21)
xy = 22050/40
xy = 551.25 ≈ 551
So, the co-primes with product 551 are (1,551) and (19,29).
So, the prime numbers are (40×1,40×551) and (40×19,40×29).
Therefore, the most suitable pair is (40×19,40×29) = (760,1160).
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David has $540 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $298.79. He buys 3 bicycle reflectors for $8.13 each and a pair of bike gloves for $21.79. He plans to spend some or all of the money he has left to buy new biking outfits for $79.43 each. Which inequality can be used to determine xx, the maximum number of outfits David can purchase while staying within his budget?
Maria score 70% on a spelling test if there are 40 total words how many did he get right?
Answer:
28 words Maria got right
Step-by-step explanation:
70% of total words Maria got right
Therefore:
[tex]\frac{70}{100} *40= 28[/tex]
help! Plot the image of triangle
△
�
�
�
△ABCtriangle, A, B, C under a reflection across line
ℓ
ℓell.
Check the picture below.
A plant 3 centimeters tall is placed by a window. If it grows 4 centimeters a day, how many days will it take to be
51 centimeters tall?
A. 12
B. 17
C. 12.75
A1= -2 and a5= -512; given two terms in a geometric sequence find the 8th term and the recursive formula. Please help
The 8th term and the recursive formula is ar⁷= 32768
What is geometric progression?A geometric progression is said to be a type of sequence in which the subsequent terms are gotten by the multiplication of a term by the constant ratio.
The parameters that will help us to solve the terms are
The first term (a)= -2
The fifth term ar⁴ = -512
by substituting a in equation 2 we have
-2 * r⁴ = -512
Dividing by -2 to get
r⁴= 256
Making r the subject of the relation
r=4th root of 256
r=4
This implies that T₈ = -2 * 4⁷
T₈ = -2*16384
In conclusion, the T₈ = 32768
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IInvestments in debt securities classified as trading are reported on the balance sheet at
Investments in debt securities classified as trading are reported on the balance sheet at fair value and held to maturity securities.
What do you mean by the investments?
An asset or object acquired with the intention of creating income or recognition is referred to as an investment.
A purchase of products that are not consumed right away but will be utilized to create wealth down the road is referred to as an investment in an economic outlook.
Equity and debt investments that are recorded using the cost method are divided into three categories: trading securities, available-for-sale securities, and held-to-maturity securities for debt investments.
Unrealized gains and losses are reflected in net income each period for debt securities that are classed as trading and reported at fair value.
Therefore, Investments in debt securities classified as trading are reported on the balance sheet at fair value and held to maturity securities.
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Ill give brainliest for the answer
Answer:
m<3 is 95 degrees.
Step-by-step explanation:
m<2 is 55*, the other angle is 30* because 180-150 is 30, and so by process of elimination it is 95*
Hope this helps!
Answer:
m<3=95°
Step-by-step explanation:
m<2 is vertically opposite an angle of 55°, and since vertically opposite angles are equal, we can say m<2=55°.
The unmarked angle in the triangle containing m<2 and m<3 is on a straight line with an angle of 150°. Since the angles along a straight line add to 180°, this unmarked angle=180-150°=30°.
The angles in a triangle always add to 180°, so the sum of m<3, m<2 and the unmarked angle should be 180°:
m<3+55°+30°=180°
m<3+85°=180°
m<3=95°
Elly and Julie are 18 miles apart on a path when they start moving toward each other. Elly runs at a constant speed of 4 miles per hour, and Julie walks at a constant speed of 6 miles per hour. How long does it take until Elly and Julie meet?
Elly and Julie meet 12km long distance.
How is the distance rate formula calculated?The relationship between distance, rate, and time is shown by the equation: distance=ratetimed=rt. You will have travelled 180 miles if, for instance, your speed is 60 mph and you drive for three hours.
Use the formula d = st, which says that distance is equal to speed times time, to calculate speed, distance, or time.
Speed is calculated as distance divided by time. You can also calculate the time by dividing the distance travelled by the speed. The third input can be calculated if you know two of the inputs. Using the formula 120 x 2 = 60 mph, we can calculate the speed of a car that travels 120 miles in two hours.
18*4 = 60
72-60 = 12 km.
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It would take Elly and Julie 1.8 hours to meet from their respective distance.
How is the distance rate formula calculated?The relationship between distance, rate, and time is shown by the equation: distance=ratetimed=rt. You will have travelled 180 miles if, for instance, your speed is 60 mph and you drive for three hours.
Use the formula d = st, which says that distance is equal to speed times time, to calculate speed, distance, or time.
Let's call the time (in hours) that it takes for Elly and Julie to meet as "t".
We know that Elly runs 4 miles per hour, so in "t" hours, she would have run 4 * t miles.
Similarly, Julie walks 6 miles per hour, so in "t" hours, she would have walked 6 * t miles.
Since they started 18 miles apart, they would meet when the sum of the distances that each of them has covered is equal to 18 miles:
4 * t + 6 * t = 18
Solving for "t":
10 * t = 18
t = 18 / 10
t = 1.8 hours
So, it would take Elly and Julie 1.8 hours to meet.
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Your business requests a 3-month loan for
$550,000. What will be the interest paid at the
end of the term if the business risk percentage is
assessed at 2.0% and LIBOR is at 2.8%?
interest paid = $ [?]
Round to the nearest hundredth.
Enter
PH
Skip
The interest paid on a loan can be calculated using the formula:
What does money interest mean?
You pay interest on any loans or borrowings of money. the portion of the loan's value that lenders use to calculate interest. Consumers can earn interest by lending money (via a bond or certificate of deposit, for example), or by putting money into an interest-bearing bank account.
Interest = Principal x Risk Percentage x Term (in months) x LIBOR
In this case, the principal is $550,000, the risk percentage is 2.0%, the term is 3 months, and LIBOR is 2.8%. So the interest paid at the end of the term is:
Interest = $550,000 x 2.0% x 3 x 2.8% = $15,660
Therefore, the interest paid at the end of the term is $15,660.
Note: I have used the risk percentage and LIBOR to calculate the interest rate which is (2.0%+2.8%) and then multiplied it with the principal and term to get the interest paid.
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Arrange each set of numbers in increasing order
the increasing order of the given numbers will be 2.2*10^3<310000<3.1*10^7<216000000.
What is increasing order?
Ascending order is the term used in mathematics to describe the ordering of integers from smallest value to highest value. A way to arrange numbers from smallest value to highest value is by using ascending order. From left to right, the order is given. Increasing order may also be used to refer to ascending order. As an illustration, consider a set of natural numbers that are arranged in ascending order: 1, 2, 3, 4, 5, 6, 7, 8, and so forth. The rising order is indicated by the less than symbol (). Descending order is the opposite of ascending order, where the numbers are organized according to decreasing value.
The given values are
216000000, 2.2*10^3, 3.1*10^7 and 310000
The increasing order:
2.2*10^3<310000<3.1*10^7<216000000
Hence the increasing order of the given numbers will be 2.2*10^3<310000<3.1*10^7<216000000.
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2. What value of m gives the system infinitely many solutions?
y = mx + 3
(-x+3y=9
Answer: When m = 3/1 = 3
Step-by-step explanation:
A system of equations will have infinitely many solutions when the equations are equivalent, that is, they represent the same line. This can happen when the equations are multiples of each other.
In this case, the first equation y = mx + 3 is a standard form equation of a line with slope m and y-intercept (0,3). The second equation -x + 3y = 9 can be written in slope-intercept form as y = (3/1)x + (-9/1).
To find the value of m that gives the system infinitely many solutions, we have to compare the slope of the two equations. The slope of the first equation is m, and the slope of the second equation is 3/1. Thus, the system will have infinitely many solutions when m = 3/1 = 3.
A coach is buying snacks for 22 players at a soccer match.She pays a total of $77to buy each player a bottle of water and an energy bar.The price for one energy bar is $2
Answer:
22
Step-by-step explanation:
TBH i think this is correct
Answer:
It isn't clear what the question is but if you're trying to find the missing info for how much a bottle of water is, it'd be $1.50 per bottle.
Trey is taking out a loan for $85,000. It is a 10-year loan with an APR of 6.75% What will his monthly payment be? Use the table provided for help.
The monthly payment that Trey will make is $976.
How is the monthly payment determined?The monthly payment represents the equal periodic payment that must be made to settle the 10-year loan at an annual percentage rate (APR) of 6.75%.
The monthly payment can be determined using an online finance calculator that sets the following parameters.
N (# of periods) = 120 months (10 years x 12)
I/Y (Interest per year) = 6.75%
PV (Present Value) = $85,000
FV (Future Value) = $0
Results:
Monthly Payments (PMT) = $976.00
Sum of all periodic payments = $117,120.60
Total Interest = $32,120.60
Thus, Trey should pay $976 monthly to settle the loan and compounded interest.
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Solve for the approximate solutions in the interval [0, 2m). List your answers separated by a comma, round to
two decimal places. If it has no real solutions, enter DNE.
As you probably know, trinomials of the form y=ax²+bx+c,a≠1 can be solved by finding two numbers that multiply to a×c and that add to b.
∴ Two numbers that multiply to −2 and that add to −1 are −2 and +1.
(2cos²θ−2cosθ)+(cosθ−1)=0
(2cosθ+1)(cosθ−1)=0
cosθ=−1/2andcosθ=1
By special angles:
θ=120˚,240˚and0˚,or3π/2+2nπ,4π/ 3+2nπ and 2nπ, n being an integer.
What is trinomals?A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms. These expressions use symbols or operations as separators such as +, –, ×, and ÷. A trinomial along with monomial, binomial, and polynomial are categorized under this algebraic expression. Let us learn more about trinomials, factoring trinomials, the formula for factoring trinomials along solving a few examples.A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression. A trinomial is a type of polynomial but with three terms. A polynomial is an algebraic expression that has one or more terms and is written as a0xn + a1xn-1 + a2xn-2 + ... + anx0 in the standard form.To learn more about polynomial refer to:
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What can we do to create more energy?
A: Nothing, energy cannot be created or destroyed
B: destroy old energy and create new energy with power plants
C: Whenever energy changes from one form to another, more energy is created
To produce more energy, we do energy cannot be generated or destroyed but can only alter its forms.
Energy production and destruction are both possible.Energy can only be changed from one type of energy to another, according to the rule of conservation of energy, and cannot be created or destroyed. Accordingly, until additional energy is added from outside, a system always possesses the same amount of energy.Energy cannot be generated or destroyed but can only alter its forms. It is possible to transfer energy from one system to another, but it is not possible to create energy from scratch. The same holds true for energy; it cannot be destroyed by a system but can be transferred to another.To produce more energy, we do energy cannot be generated or destroyed but can only alter its forms.To learn more about energy refer to:
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On a math test the students are given a right triangle. One of the acute angles has a measure of 53°. One student says that the measure of the other acute angle is 127°. What is the measure of the other acute angle? What error might the student have made?
The other acute angle is 37°.
The student made two errors. First of all, a triangle doesn't have two angles, it has three. Since it's a right triangle, there's an immediate 90° angle that's a part of the triangle. Secondly, an acute angle is lower than 90°. 127° is an obtuse angle. Anyway, we know that the other acute angle is 37° because 53° + 37° = 90, and since we have a right triangle, 90° + 90° = 180°.
i need help with #4 please!!
By calculating , the values of gof(-4) = -67 , f(g(-4)) = -57 ,
g(f(x)) = -3x^2 - 19 and -f(x) + 3g(x) = = x^2 + 9x + 24 .
What is a function ?
function can be defined as which related an input to the given any output of the following.
Given ,
functions
f(x) = -x^2- 8
g(x) = 3x+5
So , the value of (gof)(-4) =
gof(x) = 3 (-x^2 - 8 ) + 5
= -3x^2 - 24 + 5
= -3x^2 - 19
gof(-4) = -3 (-4*-4) -19
= -3 (16 ) - 19
= -48- 19
= -67
gof(-4) = -67
g(x) = 3x+5
g(-4) = 3*-4 + 5
= -12 + 5
= -7
f(g(-4)) = - (-7*-7) - 8
= -49 - 8
= -57
g(f(x)) = gof(x) = 3 (-x^2 - 8 ) + 5
= -3x^2 - 24 + 5
= -3x^2 - 19
-f(x) = -(-x^2-8) = x^2 + 8
3g(x) = 3 * (3x+5)
= 9x + 15
-f(x) + 3g(x) = x^2 + 8 + 9x + 15
= x^2 + 9x + 24
Hence, By calculating , the values of gof(-4) = -67 , f(g(-4)) = -57 ,
g(f(x)) = -3x^2 - 19 and -f(x) + 3g(x) = = x^2 + 9x + 24 .
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2x-5y=8
5y=-2x+8
What Is the best way to describe the solution of this system of equations?
Answer: The solution of this system of equations is the ordered pair (x, y) that satisfies both equations. This can be found by solving for one variable in one equation and substituting that value into the other equation, or by using elimination or substitution methods. The solution can also be represented graphically as the point of intersection of the two lines represented by the equations.
Step-by-step explanation:
Math
Sixth grade W.3 Find start and end times BAJ
2:00 P.M.
Recommendations
Emily made oatmeal cookies to take to a party. It took her 30 minutes to make the dough
and 1 hour to bake all of the cookies. It was 1:30 P.M. when Emily finally took the last batch
of cookies out of the oven. What time was it when Emily started making the cookies?
Submit
12:00 P.M.
Skill plans
1:00 P.M.
12:30 P.M.
Answer:
12:30 P.M.
Step-by-step explanation:
Emily took 30 minutes to make the dough and 1 hour to bake all of the cookies. In total, that's 30 minutes + 1 hour = 90 minutes (1 hour and 30 minutes). If it were 1:30 P.M. when Emily took the last batch of cookies out of the oven, then 90 minutes before that would be 1:30 P.M. - 90 minutes = 12:30 P.M. So, Emily started making the cookies at 12:30 P.M.
Combine like terms in the expression: 2x + 3y + 6x –y
Answer:
The answer is 8x + 2y.
Step-by-step explanation:
First, you're gonna add both 2x and 6x. (2x + 6x = 8x)
Then you're gonna subtract 3y and y. (3y - y = 2y)
*Just because there is no number on the y doesn't mean it doesn't have a number. And the number for y is 1.
Since both 8x and 2y are both positive, the answer will be 8x + 2y.
the question is 4 1/5 x 5/14
Answer:
3/2
Step-by-step explanation:
Simplify the following:
((4 + 1/5)×5)/14
((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:
((4 + 1/5)×5)/14
Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:
(((5×4)/5 + 1/5) 5)/14
5×4 = 20:
((20/5 + 1/5)×5)/14
20/5 + 1/5 = (20 + 1)/5:
(((20 + 1)/5)×5)/14
20 + 1 = 21:
(21/5×5)/14
21/5×5 = (21×5)/5:
((21×5)/5)/14
((21×5)/5)/14 = (21×5)/(5×14):
(21×5)/(5×14)
(21×5)/(5×14) = 5/5×21/14 = 21/14:
21/14
The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:
Answer: 3/2
what percentage is 1,580 of 1,738?
Answer:
100/1738*1580 = 90.9090909091
Step-by-step explanation:
Solve the equation and enter the value of y below.
6y+ 3 = 45
Answer here
[B]
Therefore , the solution of the given problem of linear equation comes out to be y = 7.
The definition of a linear equation.A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Despite the fact because both y and x are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases. The equation for a simple linear equation is Y=mx+b, where m stands for the slope and b for the y-intercept. Y=mx+b, where m stands for slopes and b for the y-intercept, is how the equation is expressed.
Here,
Given :
=> 6y + 3 = 45
=> 6y = 45-3
=> 6y = 42
=> y = 42/6
=> y = 7
Therefore , the solution of the given problem of linear equation comes out to be y = 7.
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[tex]6y+3=45[/tex]
Subtract 3 from both sides:
[tex]6y+3-3=45-3[/tex]
[tex]6y=42[/tex]
Divide both sides by 7:
[tex]\dfrac{6y}{6} =\dfrac{42}{6}[/tex]
[tex]\fbox{y = 7}[/tex]
Dwight offers one-hour piano lessons
and one-hour guitar lessons. He works
10 hours a week in all. How many
different ways can he divide his time
giving lessons in both instruments?
He can split the 120 minutes he spends teaching both instruments into various ways.
what is unitary method ?The unit strategy is an approach to problem-solving that involves first figuring out the value of a single unit, then multiplying that value to figure out the required value. Simply described, the unit method is used to extract a single unit value from a specified multiple. For instance, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure might be standardized. one nation. anything has a distinctive element. Its adjoint and reciprocal are equal in terms of mathematics (algebra), linear algebra, mathematical analysis, or mathematics of matrices or operators.
given
Dwight gives hour-long piano and hour-long guitar classes, so he can divide his time in a variety of ways.
There are 60 minutes in an hour.
To convert from minutes to hours, divide the amount of minutes by 60. If 120/60=2, for instance, it signifies that 120 minutes are equivalent to 2 hours.
He can split the 120 minutes he spends teaching both instruments into various ways.
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A survey was conducted to find the possible relationship between age groups and the most favored of three book genres. The data is represented in the frequency table.
Answer: 176
Step-by-step explanation:
1/4=_=_
Plsssssss helppppp
Answer:
0.25
Step-by-step explanation:
Solve for x in the following equation: 6x + 35 = -2x + 11
Answer: X= -3
Step-by-step explanation:
6x +35 = 2x +11
Add 2x to both sides
6x+35+2x=11
Combine 6x and 2x
8x+35=11
Subtract 35
8x=11-35
Subtract 35 from 11
8x=-24
Divide both
X= -24/4
Divide -24 by 8
X=-3
I think
Daryl has a pyramid with a square base. He slices the pyramid with a plane that is
either parallel or perpendicular to the base.
Which shapes are possible cross-sections for Daryl's slice?
Choose all that apply.
A circle
B square
C triangle
The cross-section of an item would be a circle if it were cut through by a plane parallel to its base. The object has made touch in this manner.
What is meant by cross-section triangle?A straight cut through an object yields a shape known as a cross section. Having a triangle as its cross section, this object. It resembles a window produced by cutting through something to see inside.
When you slice or cut through an object, you form a cross section of that object. They enable us to view an object's interior. Conic sections are some of the most well-known cross sections. Conic sections are made by cutting a right cone in several ways.
When a solid (such a cone, cylinder, or sphere) is cut by a plane, a cross-section. For instance, if a plane parallel to an object's base were to cut through it, the cross-section that resulted would be a circle. In this way, the object has come into contact.
Therefore, the correct answer is option C. triangle.
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Box A contains only green and purple counters.
Box B contains only green, purple and orange counters.
Juan picks one counter from box A and one counter from box B.
How many possible ways are there for Juan to pick exactly one purple counter.
Answer:
4
Step-by-step explanation:
If we take 4 as k then
4k = 4(4) = 16 boxes
k + 9 = 4 + 9 = 13 boxes
Hope this helps <3
Step-by-step explanation:
box A green and purple.
box B green, purple and orange.
one pick from A, one pick from B.
there are only 2 picks. both have a chance to get purple.
the possible outcomes regarding purple are
pick 1 pick 2
not purple not purple
purple not purple
not purple purple
purple purple
so, there are exactly 2 possible ways to pick exactly one purple counter :
purple not purple
not purple purple
In a random sample of 7 college students, the mean number of hours per week they exercise was 5.2. Suppose an additional student is added to the sample with exercising time of 2 hours. Find the sample mean for all 8 students.
The sample mean for all 8 students is 4.8 hours per week.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
To find the new sample mean, we need to add the new student's exercising time to the total time for the previous 7 students, and then divide by the total number of students.
The total exercising time for the previous 7 students is 7 x 5.2 = 36.4 hours.
The total exercising time for all 8 students is 36.4 + 2 = 38.4 hours.
So the sample mean for all 8 students is 38.4 / 8 = 4.8 hours per week.
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