Write 12 1/3 as an improper fraction.

Step-by-step explanation:

Using Vieta's formula

x²-(sum of roots)x+(product of roots)=0

x²-(5+-1)x+(5×-1)=0

x²-4x-5=0

Alternatively,

if the zeros are 5 and -1 then the quadratic factorizes to (x-5)(x+1) Now expand it

x²+x-5x-5=0

x²-4x-5=0

Identify a quadratic function in standard form with zeros 5 and -1

x (2) + (2)x - 15 = 0

X=3 and x= -5

(x - 3) = 0 and (x + 5) = 0

Compared with the beam, the large cube has the same volume but a smaller surface area.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Given that, there are two sets of eight blocks, each with an edge measurement of 1 cm. Two blocks are placed on top of two other blocks to form a big cube. You assemble the second set into a 1-by-8-block straight beam.

Since the volume is the same.

The surface area of a cube,

=6a²

=6(2)²

=6×4

=24 cm²

The surface area of a beam,

=1 × 8

=8 cm²

Thus, compared with the beam, the large cube has the same volume but a smaller surface area.

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When a line that is externally tangent to both circles intersects ray AB at point C, the value of BC is 12.

A tangent line to a circle in Euclidean plane geometry is a line that touches the circle at exactly one point while never entering the circle's interior. Tangent lines to circles are the topic of various theorems and are used in several geometrical constructions and proofs.

A tangent to a circle is a straight line that touches the circle just once. This is referred to as the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

Let D and E be the tangent points of circles A and B with line CD, AB=8.

Also, set BC to x.

Because ADC and BEC are at right angles,

At the point of tangency, the radius is perpendicular to a tangent line, and both triangles share ACD, ADCBEC.

We can calculate the proportion from this.

BC/AC=BE/AD

x/(x+8)=3/5

5x=3x+24

2x=24

x=12

As a result, the value of BC=12

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"Externally tangent circles with centers at points A and B have radii of lengths 5 and 3, respectively. A line externally tangent to both circles intersects ray AB at point C. What is BC?"

Answer:

45 minutes

Step by step explanation:

60min ÷ 56miles × 42miles = 45mins

Answer: 13

Step-by-step explanation:

7.5 2. debt payments of $700 in two months and $800 in five months are scheduled to be due. If interest at 8.3% is allowed, what single payment today is required to settle the two scheduled payments.

Single payment today is required to settle the two scheduled payment is $1,948.2.

Given Payments of two months = $700

Payments in five months = $800

Interest rate = 8.3%

To find : Single payments of two scheduled payments

Solution:

Interest for 1 month for $700

        = $700 x 8.3%

        = 58.1

Thus, for two months

Interest = 2 x $58.1 = $116.2

Now interest for 1 month for $800

       = $800 x 8.3%

       = $66.4

Thus, for five months

Interest = 5 x $66.4

       = $332

Now total Payments:

       = ($700 + $116.2) + ($800 + $332)

       = $1,948.2

Hence, single payment today is required to settle the two scheduled payment is $1,948.2.

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Answer:

see below

We need to prove that KL ≅ JK .

Given :-

To prove:-

Proof:-

In ∆JKM and ∆LKM ,

Therefore by AAS congruence condition , ∆JKM ≅ ∆LKM .

Therefore,

Hence proved !

If you dealt 4 cards from a shuffled deck of 52 cards without replacement.

The probability that all 4 cards are face cards is 0.00182842367.

The face cards are the King, Queen, and Jack (sometimes known as the Knaves). There are 12 face cards in the 52-card deck of playing cards.

The cards are drawn without replacement,

The probability of getting a face card in first draw is 12/52.

As it is without replacement, in the second draw the probability is 11/51.

In third draw, it is 10/50.

In the fourth draw the probability is 9/49.

We have to draw all the four cards, so we multiply the probabilities, to get the final probability.

=12/52x 11/51 x 10/50 x 9/49

=0.00182842367.

Hence the answer is, the probability that all 4 cards are face cards is 0.00182842367.

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Answer:

The second and the fifth answers are correct.

Step-by-step explanation:

Solving the absolute value equation, it is found that:

The absolute value equation for this problem is given as follows:

p(t) = 0.165| t - 60 | + 4.8.

In which the variables are:

This percentage was of 13% when:

p(t) = 13.

Hence:

p(t) = 0.165| t - 60 | + 4.8.

13 = 0.165| t - 60 | + 4.8.

0.165| t - 60 | = 8.2.

|t - 60| = 8.2/0.165

|t - 60| = 49.7.

Then the solutions are as follows:

For the percentage of four percent, we have that:

4 = 0.165| t - 60 | + 4.8.

0.165| t - 60 | = -0.8.

The absolute value equation can never assume a negative value, hence the percentage will never be of 4%.

The equation is:

p(t) = 0.165| t - 60 | + 4.8

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The graph has rotational symmetry about the y-intercept and y-intercept is 0 when x = 0

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of the function is given:

From the graph:

The graph has rotational symmetry about the y-intercept

The y-intercept is 0 when x = 0

Thus, the graph has rotational symmetry about the y-intercept and y-intercept is 0 when x = 0

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The difference in the payments of Oscar and Felix is given as follows:

$56.

The payment for each of Oscar and Felix is obtained applying proportions, with the multiplication of the finance charge by each of the rates.

As stated in the problem, the balance is of:

800.

Felix rate is of:

14%.

Hence the finance charge for Felix is of:

0.14 x 800 = 112.

Oscar rate is of:

21%.

Hence the finance charge of Oscar is of:

0.21 x 800 = 168.

Then the difference in the payments will be of:

168 - 112 = $56.

Felix and Oscar applied for the same credit card from the same bank. The bank checked both of their FICO scores. Felix had an excellent credit rating, and Oscar had a poor credit rating.

The rates are given as follows:

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The equation that models the scenario is:

80 = 8x + 10y

Where x is the number of pounds of almonds and y is the number of pounds of cashews.

We know that almonds cost $8 per pound and Cashews cost $10 per pound, so if you buy x pounds of almonds and y pounds of cashews, the total cost is:

c(x, y) = x*$8 + y*$10

Now we know that Tamira has $80 to spend, so the total cost will be equal to $80, then the equation that models this scenario is:

$80 = x*$8 + y*$10

Or, removing the units:

80 = 8x + 10y

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Answer:

x = 1

5 x 1 = 5 + 10 = 15

Step-by-step explanation:

Answer: X= 1

Step-by-step explanation: you would do 15 - 10 = 5

then you would do 5x times 5 which would equal 25

The y-intercept of the coordinate plane is y = -5/16x+32

To find the equation or y-intercept, we fist need to find the slope of the equation.

The intercept form of the equation is given by

y-y1 = m(x-x1)

The slope can be find as

m = (y2-y1)/(x2-x1)

Let us consider two points as

x1 = 32, y1 = 22

x2 = 48. y2 = 17

Substitute the values to get the slope

m = (17-22)/(48-32) = -5/16

Now substitute the values to find y-intercept

(y-22) = -5/16(x-32)

⇒ y-22 = -5/16x+10

⇒ y = -5/16x+10+22

⇒ y = -5/16x+32

Hence, y intercept of the given points are y = -5/16x+32

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Answer: 5w plus 23 equals 98

Step-by-step explanation:

This answer is more reasonable because Paula already has $23 and she can save $5 per week.  She only needs 75 dollars more to get the records. So it will take her 17 weeks to get $75.

[tex]\frac{-3}{5} > -2[/tex] indicates that -3/5 is located on the right of -2 on the number line.

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

consider, [tex]\frac{-3}{5} > -2[/tex]

Here, -3/5 = -0.6

-0.6 > -2

-0.6 is the number greater than -2.

So, -3/5 is located on the right side of -2.

Hence, -3/5  is located on the right of -2 on the number line.

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A correlational study can produce one of three outcomes: a positive correlation, a negative correlation, or no correlation at all. A measure of how closely two or more variables are related to one another is known as correlation.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate).It's a common method for describing simple relationships without mentioning cause and effect explicitly. Correlation is a measure of how strongly two variables are related, but it also refers to association. There are three possible results from a correlational study: a positive correlation, a negative correlation, or no correlation at all.

A measure of how closely two or more variables are related to one another is known as correlation.

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The number of permutations and combinations possible for the formation is: [tex]^{31}C_{11} \times ^{12}C_3 \times ^{3}C_1 \times ^{9}C_4 \times ^{7}C_3[/tex]

What are permutations and combinations?

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the elements of a set if the set is already ordered. Nearly all areas of mathematics involve permutations in some form or another. They frequently appear when various orderings on particular finite sets are taken into account.

In the given question: we have;

Total number of PLayers = 31;

Number of goalkeeper = 3;

Number of Defender = 12;

Number of Midfielders = 9;

Number of Strikers = 7;

We have to select 11 players

and in that we should have 3 defenders; 4 midfielders, 3 strikers, and 1 goalkeeper;

So the permutation and combination possible for choosing a defender from 12 players are: [tex]^{12}C_3[/tex]

and,

The number of permutations and combinations possible for choosing 1 goalkeeper are: [tex]^{3}C_1[/tex]

A number of permutations and combinations possible for choosing 4 midfielders are: [tex]^{9}C_4[/tex]

The number of permutations and combinations possible for choosing 3 strikers are: [tex]^{7}C_3[/tex]

So, the total number of ways possible is: [tex]^{31}C_{11} \times ^{12}C_3 \times ^{3}C_1 \times ^{9}C_4 \times ^{7}C_3[/tex]

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The number of candies is 7,and the number of pretzels is 6 that Shaquana bought.

Given:

Shaquana and her children went into a movie theater and she bought $53 worth of candies and pretzels.

Each candy costs $5 and each pretzel costs $3. She bought a total of 13 candies and pretzels altogether.

Let x be the number of candies and y be the number of pretzels.

x + y = 13

x = 13 - y

5x + 3y = 53

susbstitute x value, we get

5(13 - y) + 3y = 53

-5y + 65 + 3y = 53

-2y = 53 - 65

-2y = -12

divide by -2 on both sides

y = -12/-2

y = 6 pretzels

x = 13 - y

= 13 - 6

= 7 candies .

Therefore the number of candies is 7,and the number of pretzels is 6 that Shaquana bought.

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a. The vertical height is y = 100tSinθ - (1/2)9.8t².

b. Time of flight is t = 200sin(theta)/9.8.

A projectile motion is a type of motion that an object or particle experiences when it is launched into a gravitational field, such as from the surface of the Earth, and proceeds along a curved route only under the influence of gravity.

We know At any time t, a projectile's horizontal and vertical displacement are x = V₀tCos θ where V is the initial velocity, θ is the launch angle

y = V₀tSinθ - (1/2)gt².

Given ball was hit with an initial velocity of 100 feet per second

∴ Height in feet is

y = 100tSinθ - (1/2)9.8t².

The time for which the ball will stay in the air is a time of flight which is given by the formula t = 2v₀sin(theta)/g.

t = 200sin(theta)/9.8.

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Answer:

249.40 Option b

Step-by-step explanation:

When multiplying 21.5 x 11.60 you get $249.40

The equation relating C to S will C = 7500+175S and the total cost to transport 14 tons of sugar is $9950.

According to the question,

We have the following information:

It will cost $7500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.

So, we have the following expression:

C = 7500+175S

Now, when S = 14, then the total cost will be:

C = 7500+175*14

C = 7500+2450

C = $9950

Hence, the equation relating C to S will C = 7500+175S and the total cost to transport 14 tons of sugar is $9950.

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Answer:

The area of the shape is 396 square cm.

Step-by-step explanation:

Answer: -1.75

Step-by-step explanation: -7 + 5 + (-9) + 4 = -7, then -7÷4=-1.75

Answer:

Step-by-step explanation:

Answer: 238

Step-by-step explanation:

Bit hard to explain but after some work this is what I got

Hope this helps :)