b)
What is the Lowest Common Multiple of 42 and 90?

Answer:

You would multiply across and then simplify ur answer. So you would do 6*5 which is 30 and then do 11*8 which is 88.  30/88 reduced is 15/44

Hope this helped  

[tex]\dfrac{6}{11} \times\dfrac{5}{8}[/tex]

When multiplying fractions, you have to multiply the numerator by numerator and the denominator by denominator.

[tex]\dfrac{6\time}{11} \times\dfrac{5}{8}[/tex]

[tex]\dfrac{6\times5}{11\times8}[/tex]

[tex]=\dfrac{30}{88}[/tex]

Reduce to simplest form:

[tex]\dfrac{30\div2}{88\div2}[/tex]

[tex]=\fbox{$\dfrac{15}{44} $}[/tex]

The angle measures : m∠1 = 107° and m∠4= 73°

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

There are 2 parallel lines

A transversal cuts them

∠5 and ∠7 are corresponding angles

Corresponding angles are equal in measures

m∠5 = m∠7

m∠7 = 107°

m∠5 = 107°

∠1 and ∠7 formed a pair of alternate exterior angle.

And m∠1 = m∠7

∠1 and ∠4 formed a pair of linear angle.

The sum of the measures of the linear angles is 180°

m∠1 + m∠4 = 180°

Substitute ∠1 by 107°

m∠4 + 107° = 180°

m∠4 = 180 - 107

m∠4= 73°

Therefore, m∠1 = 107° and m∠4= 73°

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The three variable system is written as (x, y, z).

Here we have to find the definition of three variable system.

basically a solution of a system in three variables is an ordered triple (x, y, z) that makes all three equations true.

On the other hand it is what they all three have in common.

Where as the solution to a system of three equations in three variables (x, y, z) is called an ordered triple.

In order to solve these one we have to do the following:

First we have to pick any two pairs of equations from the system.

And then we have to eliminate the same variable from each pair using the Addition/Subtraction method.

Final step is to solve the system of the two new equations using the Addition/Subtraction method.

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The dilation of the circle with a scale factor 1/r and center at (a,b) will transform the circle into a point at (a,b).

A dilation is a transformation that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.

To solve this we will use the transformation formula for a dilation with center (a,b) and scale factor

k, (x,y) --> (a + k(x-a), b + k(y-b)).

Substituting in our values, we get

(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).

Setting this equal to (a,b), we get

(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).

Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).

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Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

A log graph can be either increasing or decreasing, depending on the function or data being graphed.

A log graph is a type of graph that displays the data on a logarithmic scale. That is, the values of the data are represented on a logarithmic scale, rather than on a linear scale. This type of graph is useful for displaying data or functions that span a wide range of values over a large range of exponents. The direction of the graph depends on the data being graphed or the function being shown. If the values of the data or the function being graphed increase over time, then the graph will be increasing. Conversely, if the values of the data or the function being graphed decrease over time, then the graph will be decreasing.

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All Answers:

1a) The equation that models the situation is: 4.65r + 4.95p = 874.80

1b) Using the equation from part 1a, we know that 4.65r + 4.95p = 874.80. If we know that Alice purchased 87 gallons of regular unleaded gas, we can substitute that value into the equation: 4.65(87) + 4.95p = 874.80. Solving for p, we get: 4.65(87) + 4.95p = 874.80

4.0995 + 4.95p = 874.80

4.95p = 869.805

p = 175.6 gallons

2a) The function that models the number of checked bags, b, as it relates to the total cost, c(b), is: c(b) = 35b + 475.

2b) Number of Bags (b) Total Cost c(b)

0 475

1 510

2 545

3 580

4 615

6 675

8 835

3a) The y-intercept in this scenario represents the total distance travelled when the time spent on the trip is zero. As the distance traveled is 700 miles when time is zero, the y-intercept is (0,700)

3b) The x-intercept in this scenario represents the total time spent on the trip when the distance travelled is zero. As time is zero when the distance traveled is zero, the x-intercept is (0,0)

3c) (2.5, 200) (10, 300)

3d) The domain and range are based on the permissible values of time and distance travelled. Based on the information provided, the domain would be {h | 0 < h < 10} and the range would be {f(h) | 0 < f(h) < 700}

About the last part of the question, it is referring to the fact that life is like a journey, and we should strive to be like runners who run to win the prize, not just to participate. This passage encourages us to put in the hard work and dedication necessary to achieve our goals in life, and to not be satisfied with simply going through the motions. It also reminds us that our ultimate goal should be eternal reward, not temporary ones. In your life, it might mean setting a goal, making a plan, and putting in the effort to achieve it, but also keeping a perspective of what is important in the long run, not just in the short run.

1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.

1. Infinity is an abstract concept and cannot be used in the same way as numeric values.

2. Infinity is not a number or a numerical value.

3. Therefore, it cannot be used in equations or arithmetic operations.

4. Therefore, 1 [infinity] is not defined.

1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.

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Yes , she will be able to buy the PlayStation before Marko as she only needs 5 weeks to collect the remaining amount of money.

Cost of PlayStation given = 700 dollars

Amount of money which Rosaline has = 200 dollars

Now, if she has 200 dollars and deposits 100 dollar every week , this means she will be able to collect 700 dollars in 5 weeks of time.

100 dollar = 1 week

therefore, this relation means that  500 dollars = 5  weeks

Hence , she will be able to buy the PlayStation in about 5 weeks from the time she starts collecting the money.

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There are 12 weeks will Sonja's balance remain above $377.

What is account balance?

The balance is the sum owed on an account in banking and accounting. The term "balance" in bookkeeping refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a given financial period. The account shows a debit balance when total debits exceed total credits.

Given:

Sonja has a bank account balance of $1400. Each week, her balance changes by -$85.25. She wants to keep the balance above $377.

We have to find the number of  weeks will Sonja's balance remain above $377.

Let, $1400 - $377 = $1023.

⇒  $1023 / $85.25 = 12

Hence, there are 12 weeks will Sonja's balance remain above $377.

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Answer:

2 + m

Step-by-step explanation:

2.25×10 times greater is the weight of the elephant than the weight of the lion.

Two or more expressions with an Equal sign is called as Equation.

Given that a zookeeper  weighted an African elephant to be 9 x 10³ pounds.

An African lion to be 4 x 10² pounds

We need to find how many times greater is the weight of the elephant than the weight of the lion

Now, Divide the weighed an African elephant with weighed an African lion to determine times greater is the weight of the elephant than the weight of the lion,

N=9×10³/4×10²

=2.25×10

Hence, 2.25×10 times greater is the weight of the elephant than the weight of the lion.

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By fraction , 3  3/7   will it take 7 men to do the job if they work at the same rate.

What is fraction in maths?

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the proportionate pieces of the whole.

                The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

per person per hour

           1/4*6  = 1/24

7 men per hour

       1/24 * 7 =   7/24

  total times

          1 ÷ 7/24  =  1   *  24/7  

                   =  3  3/7

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The answer to ur question is 1

To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

Consider an example where vertex is (2,1) and y-intercept is (0,-3).

The equation of parabola needs to be deduced using these points.

The equation of a parabola in vertex form is -

y=a(x-h)^2+k

Here, a is a constant and (h ,k) are the coordinates of the vertex.

So, (h,k)=(2,1)

⇒y=a(x−2)^2+1

To obtain the value of a, substitute (0,−3) into the equation -

-3=4a+1

4a=-4

a=-1

⇒y=-1(x−2)^2+1

Now, distribute and simplify -

y=-1(x−2)^2+1

y=-(x^2-4x+4)+1

y=-x^2+4x-4+1

y=-x^2+4x-3

On, graphing this equation a parabola is obtained.

Therefore, to write an equation of parabola vertex form is used.

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280t + 320t = 1,000 is distance equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart.

What does distance mean in a nutshell?

Distance is the overall movement of an object without consideration of direction.

                      Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.

At 10:00 a.m. two planes leave an airport. If the northbound plane flies at 280 mph and the southbound at 320 mph

Let 't' be the time taken when they are 1000 miles apart

the northbound plane flies at 280 mph

Distance  = speed * time

distance covered by northbound plane D1= 280 * t= 280t

the southbound at 320 mph

distance covered by southbound plane D2=320 t

Distance is 1000 miles apart

D1 + D2= 1000

280t + 320t = 1,000

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Parallel programming can improve the performance of an application over sequential programming in certain cases, but it is not a guarantee.

Parallel programming allows for the use of multiple processors or cores to perform tasks simultaneously, which can improve the overall speed of an application. However, parallel programming can also introduce complexity and overhead, which can decrease performance. The potential for improved performance depends on the specific application and the design of the parallel implementation. Some applications may not benefit from parallel programming because they are not computationally intensive or because their data is not easily divided into parallelizable tasks. Additionally, the performance improvement also depends on the number of cores and the communication costs between them.

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If Zoe already has $80 and can save an additional $6 per week using money from her after school job then the total amount of money that Zoe saved after 6 week of saving is $116  and

the expression that represent amount of money Zoe would have saved in w weeks is [tex]80+6w[/tex]  .

The amount that Zoe already saved = $80 ;

the amount that she can additionally save is = $6 per week ,

the amount of money that can be saved after 6 weeks can be written as :

[tex]Amount = \$80+(Amount Saved Per Week)\times(Number Of Weeks)[/tex]

Amount = [tex]80+6\times6[/tex]

= [tex]80+36[/tex]

= $116

and the expression for w weeks will be = [tex]80+6\times w[/tex]

The expression is ⇒ [tex]Amount = 80+6w[/tex].

The given question is incomplete , the complete question is

Zoe is saving up to buy a new bicycle. She already has $80 and can save an additional $6 per week using money from her after school job. How much total money would Zoe have after 6 week of saving ?

Also, write an expression that represent the amount of money Zoe would have saved in w weeks ?

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Step-by-step explanation:

since the height from M (line MB) to the baseline is splitting the baseline into 2 identical halves, the triangle must be an isoceles triangle (both legs are identical long).

and therefore,

5x - 5 = 3x + 1

2x - 5 = 1

2x = 6

x = 6/2 = 3

Answer:

--------------------------

Let the cost of a hotdog be h and pretzel be p.

Set up equations as per question:

Divide the second equation by 2, then subtract from the first one:

Now find the value of p:

Hotdog costs $2 and pretzel costs $0.75.

Answer:

2,30

the difference between 3,45 and 4,60 is 1,15. So if you add 1,15 and 1,15 it will be 2,30. you can't do 1,10 because the rate is 1,15 neither can you do 6,85 because 5,75 plus 1,15 is 6,90 not 6,85 so 2,30 is the final choice.

The simplest form is 15z+ 15x²

In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.

Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.

Given,

(5z+5 x²)3

15z+15x² by simplifying,

3(5z+5 x²)

apply the distributive formula :a (b + c) =ab + ac

3(5z+5 x²) = 5x+3 * 5x²

By simplifying 3 5z+3 , 5x², 15z+15x²

we get

15z+ 15x²

Therefore the simplest form is 15z+ 15x² .

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Answer: 3 grams

Step-by-step explanation:

I just looked up the answer lol- I tried though, (Also I can't guarantee if it's right... But it probably is).

An example that contradicts this definition would be an ellipse that set all points such that the sum of the distances between the point and two other fixed points (called foci) is constant.

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

A circle is defined as the set of all points that are the same distance from one given point, called the center of the circle. An example that contradicts this definition would be an ellipse, which is defined as the set of all points such that the sum of the distances between the point and two other fixed points (called foci) is constant.

An ellipse is not a circle since all points of an ellipse are not equidistant to the center point

To make the definition more accurate, it could be modified to say "A circle is defined as the set of all points that are a fixed distance from one given point, called the center of the circle." or "A circle is defined as the set of all points such that the distance between the point and the center is constant"

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The approximate solutions are -0.28 and -2.28.

Now, According to the question:

Given, the equation is 4x^2 + 3 = -12x

We have to find the approximate solutions to the equation.

Using quadratic formula,

[tex]x = \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]

The equation can be written as 4x^2 + 12x + 3 = 0.

Here, a = 4, b = 12, c = 3

x = [tex]\frac{-12±\sqrt{12^2-4(4)(3)} }{2(4)}[/tex]

x = [tex]\frac{-12±\sqrt{144-48} }{8}[/tex]

x = [tex]\frac{-12±\sqrt{96} }{8}[/tex]

x = [tex]\frac{-12±9.8}{8}[/tex]

Now, x = [tex]\frac{-12+9.8}{8} =\frac{-2.2}{8}[/tex] = -0.275

x = [tex]\frac{-12-9.8}{8} =\frac{-21.8}{8}[/tex] = -2.275

Therefore, the approximate solutions are -0.28 and -2.28.

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The complete question is this :

What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth?

Answer:

Step-by-step explanation:

you have studied this in grade 8 grade 9 and grade 10 if you are studying under CBSE, so, better call textbook

The theoretical likelihood of selecting a heart is 1/16 times higher than the actual likelihood.

In the given question, we have to find the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart.

We are aware that a deck's total number of cards= 52

Total number of hearts = 13

Then the theoretical probability of getting a heart = Number of cards have hearts/Total cards

Then the theoretical probability of getting a heart = 13/52

Then the theoretical probability of getting a heart = 1/4

Then the theoretical probability of getting a heart = 0.25

Cards chosen by Rochelle : Clubs 29, Spades 13, Hearts 15, Diamonds 23

Total cards  = 80

The experimental likelihood of experiencing a heart attack = Number of cards have hearts/Total cards

The experimental likelihood of experiencing a heart attack = 15/80

The experimental likelihood of experiencing a heart attack = 3/16

The experimental likelihood of experiencing a heart attack = 0.185

Since, 0.25 > 0.1875 so, Theoretical probability > Experimental probability

and,

Theoretical probability = 0.25-0.1875

Theoretical probability = 0.0625

Theoretical probability = 625/10000

Theoretical probability = 1/16

Hence, the theoretical likelihood of selecting a heart is 1/16 times higher than the actual likelihood.

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we can use the Triangle inequality Theorem a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side

It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.

1 . Triangle Inequality Theorem

smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.

In this case, a, b, and c are each equal to seven.

2. Check to see if the sum of the first two sides is greater than the third

Check to see if the sum of the first two sides is greater than the third adding the sides a and b yields 17, which is larger than 5, or 7 plus 10. It can alternatively be considered as 17 > 5.

3. Check to see if the sum of the next combination of two sides is greater than the remaining side

just see if the sum of sides a and c are greater than the side b.[4] This means you should see if 7 + 5, or 12, is greater than 10. 12 > 10,

4. Check to see if the sum of the last combination of two sides is greater than the remaining side.

Check to see if side b and side c added together are greater than side a. To accomplish this, you must determine whether 10 Plus 5 is greater than 7. The triangle is complete on all sides since 10 + 5 = 15 and 15 > 7.

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Answer: 8:15pm

Step-by-step explanation:

9+6=15 +105 = 120, 120/60=2 hours (total duration), 6:15 + 1 hour = 7:15 + 1 hour = 8:15pm

For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;

The mathematical function she may use to calculate is given as

f(n)=log1.38(n/200)

Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?

Generally, the equation for the final value is mathematically given as

A=Ao(1+u)^t

Therefore

n=200(1+0.38)*t

log(1.38^t)=log(n/200)

t=log1.38(n/200)

In conclusion, The function she could use to calculate is

f(n)=log1.38(n/200)

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