3. (05.02 LC)
The lengths of two sides of a triangle are 14 inches and 4 inches. Which of the following dimensions is the third side of this triangle? (5 points)
10 inches
O11 inches
O 8 inches
O9 inches

The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).

Hence, the missing values are 3 and 2 respectively.

Given the expression: 2x² - x - 6

First, we factor -1 out of -x

2x² - x - 6

2x² -1(x) - 6

Not that, -1 can also be written as 3-4

2x² + (3-4)x - 6

2x² + 3x - 4x - 6

Next, we group the first two terms and the last two terms and factor out the GCF

(2x² + 3x) - 4x - 6

x(2x + 3) - 2( 2x + 3)

Factor out the GFC which is ( 2x+3 )

We have; ( 2x + 3 )( x - 2 )

The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).

Hence, the missing values are 3 and 2 respectively.

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A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.

To gauge the strength of the linear link between two variables, correlation coefficients are used.

For a value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.

Zero correlation coefficient means there is no correlation between the two variables under comparison.

A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.

Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.

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The rational function that meets all the conditions is:

[tex]f(x) = \frac{-15}{(x - 3)*(x + 5)}[/tex]

A rational function is of the form:

[tex]f(x) = \frac{p(x)}{q(x)}[/tex]

As the horizontal asymptote is at y = 0, we know that the numerator can't depend on x, so it is just a constant.

p(x) = a

And we want to have two vertical asymptotes at x = 3 and x = -5, then q(x) becomes zero at these values, so we have:

q(x) = (x -3)*(x + 5)

At this point, the function is:

[tex]f(x) = \frac{a}{(x - 3)*(x + 5)}[/tex]

Finally, we know that the y-intercept is 1, then we need to solve:

[tex]f(0) = 1 = \frac{a}{(0 - 3)*(0 +5)} = \frac{a}{-15} \\\\-15 = a[/tex]

Then we conclude that our function is:

[tex]f(x) = \frac{-15}{(x - 3)*(x + 5)}[/tex]

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Step-by-step explanation:

The equation of a parabola that relates it focus is

[tex] {x}^{2} = 4py[/tex]

So here, we isolate x^2.

[tex]y = \frac{1}{32} {x}^{2} [/tex]

[tex]32y = {x}^{2} [/tex]

Next, we factor out 4.

[tex] {x}^{2} = 4(8)(y)[/tex]

Our p=8 so this tells us the distance of the vertex to the focus.

The sample space neeeded for the experiment to find the face cards is 52.

Given there is a standard deck of cards.

We have to finf the sample space needed for the experiment of finding the probability of face cards.

Probability is the chance  of happening an event among all the events that are possible. It lies between 0 and 1. The probability is the number of items divided by the total items.

Sample is a part of population. It is studied when the study of whole population is difficult to do.

Cards in a deck=52

Number of face cards is 12.

When we  draw a card from the deck then it might be a face card or not. So we have to draw all the cards of a standard deck because it might possible that face card is present at the end of deck.

Hence the sample size needed in the experiment is 52.

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Answer:

1:2

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

Answer:

$1265

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here length = 40 and  A = 2800 , then

2800 = 40 × width ( divide both sides by 40 )

70 = width

the perimeter (P) is calculated as

P = 2(length + width) = 2(40 + 70) = 2 × 110 = 220 ft

cost = 220 × $5.75 = $1265

Answer:

$1265

Step-by-step explanation:

area = length × width

area = 2800

length = 40

2800 / 40 = 70

So, the width of the lot is 70ft , and the length is 40

when building a fence, it would surround the entire property's perimeter (which is the length of the outside edges/sides of the shape added together)

so, it would need to cover 70 + 40 + 70 + 40

(the perimeter = 70 + 40 + 70 + 40)

= 220

so, if each foot costs 5.75, we can multiply 220 × 5.75 to find the cost:

220 × 5.75 = 1265

So, this will cost him $1265

hope this helps! have a lovely day :)

Answer:

57 yd²

Step-by-step explanation:

See image

Answer:

(0, 5)

(1, 6)

(4, 7)

(9, 8)

Step-by-step explanation:

y = √x + 5

y = √0 + 5

= 5

y = √1 + 5

= 6

y = √4 + 5

= 2 + 5

= 7

y = √9 + 5

= 3 + 5

= 8

The profit percent of supplier is 17.972 %

The given parameters are:

Start by calculating the selling price without VAT

Selling price = Rs 47460 * (1 - 13%)

Evaluate

Selling price = Rs 41290.2

The percentage profit is then calculated as:

Percentage profit = (Selling price - Cost price)/Cost price * 100%

This gives

Percentage profit = (41290.2 - 35000)/35000 * 100%

Evaluate

Percentage profit = 17.972 %

Hence, the profit percent of supplier is 17.972 %

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The solution of the inequality is x ≥ -3 and the graph is shown below

From the question, we are to determine the graph that represents the given inequality

The given inequality is

−3x + 1 ≤ 10

First, we will solve the inequality

−3x + 1 ≤ 10

Subtract 1 from both sides

−3x +1 -1 ≤ 10 - 1

−3x ≤ 9

Divide both sides by -3 and flip the sign

x ≥ -3

The graph of the inequality is shown below

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Answer:

y + 6 = [tex]\frac{3}{5}[/tex] (x - 4)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = [tex]\frac{3}{5}[/tex] and (a, b ) = (4, - 6 ) , then

y - (- 6) = [tex]\frac{3}{5}[/tex] (x - 4) , that is

y + 6 = [tex]\frac{3}{5}[/tex] (x - 4)

If the graph is translated 3 up, reflected across the x-axis, and is narrower than the graph y = x², we have; y = -(x² + 3)

We are given the original equation of the function as;

y = x²

Now, when we translate the graph 3 units upwards, it means we add 3 units to the function to get;

y = x² + 3

Now, when we reflect across the x-axis, it means we just change the sign of the function to get;

y = -(x² + 3)

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The internet service provider charges 40 cents for each extra hour used.

Also, he provides 40 hours of free service for every account.

Solved using linear equations.

Let the number of free hours provided by the internet service provider be x, and the charge for each extra hour be p cents.

Let the time consumed by Wells, Ted, and Vino be t1, t2, and t3 respectively.

Chargeable time used by Wells = t1 - x.

Cost for Wells = p(t1 - x).

Chargeable time used by Ted = t2 - x.

Cost for Ted = p(t2 - x).

Chargeable time used by Vino = t3 - x.

Cost for Vino = p(t3 - x).

Now, we are given that Wells and Ted, in total used 105 hours, that is, t1 + t2 = 105.

The cost for them together is $10 or 1000 cents.

This can be shown as the linear equation:

p(t1 - x) + p(t2 - x) = 1000.

or, p{(t1 - x) + (t2 - x)} = 1000,

or, p{(t1 + t2) - 2x} = 1000,

or, p(105 - 2x) = 1000,

or, p = 1000/(105 - 2x) ... (i).

Time consumed by Vino is given as 105 hours, thus, t3 = 105.

The total cost to Vino is given as $26 or 2600 cents.

This now can be shown as the linear equation:

p(t3 - x) = 2600,

or, {1000/(105 - 2x)}(105 - x) = 2600 {Substituting t3 = 105, and p = 1000/(105 - 2x)}.

This is the required linear equation in one variable.

It can be solved as follows:

{1000/(105 - 2x)}(105 - x) = 2600,

or, 105000 - 1000x = 273000 - 5200x,

or, 5200x - 1000x = 273000 - 105000,

or, 4200x = 168000,

or, x = 168000/4200 = 40.

Substituting x = 40 in (i), we get:

p = 1000/(105 - 2x),

or, p = 1000/(105 - 2(40)),

or, p = 1000/(105 - 80),

or, p = 1000/25,

or, p = 40.

Thus, the internet service provider charges 40 cents for each extra hour, and he provides 40 hours of free internet on every account.

The provided question is incomplete. The complete question is:

"An Internet service provider allows a certain number of free hours each month and then charges for each additional hour used. Wells, Ted, and Vino each have separate accounts. This month the total hours used by Wells and Ted was 105, and each used all of their free hours. Their total cost was $10. Vino used 105 hours by himself and had to pay $26. What is the number of cents charged for each extra hour?"

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The mean of the number of free throws made is 79.9

The standard deviation of throws is 3.46

Karissa is a college basketball player who makes 85% of her free throws. If Karissa takes 94 free throws then,

For binomial distribution B(94,0.85)

n  = no. of throws

P = probability of the success

mean = np

         = 94*0.85

         = 79.9

standard normal = (npq)^0.5

                            = (94*0.85*0.15)^0.5

                            = 3.46

the mean of the number of free throws made is 79.9

and standard devation of trows is 3.46

mean = np

standard deviation = (npq)^0.5

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Answer:

30 degrees

Step-by-step explanation:

180-56-90=34

34 rounded off to nearest tenth is 30

Part A

If the number is n, then the expression is 7n+6.

Part B

Three times the sum of a number and 8.

Answer:

Step-by-step explanation:

Answer:

[tex](x + 5) ^{2} + {(y - \frac{1}{2}) }^{2} = 1[/tex]

Step-by-step explanation:

the formula of a circle is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

knowing the values of h, k, and r we can substitute them into the formula

knowing the

The likelihood that it contains a letter just after an odd number is 1/2 . D's likelihood of being in the code but not at the first position is 1/4.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

A three-digit code is needed to unlock the lock on a locker. One letter and two numbers are required for the code, and neither a letter nor a number may be repeated.

Four letters, A, B, C, and D, as well as two numerals, 5 and 6, are available for selection.

The sample space has a size of (8, 16, 20, and 24)

If a random code is chosen,

The likelihood that it contains a letter after an odd number (1/8, 1/6, 1/3, 2/5, or 2/3)

= 1/2

If a random code is chosen,

Probability (1/8, 1/6, 1/3, 2/5, 2/3) that D is in the code but not at the first position.

= 1/4

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14  triangles with exactly two equal sides can be formed

The triangles will be isosceles as there have to be 2 equal sides.

The possible triangles are :

2 2 3      3 3 2        5 5 2       7 7 2         11  11  2

             3 3 5        5 5 3       7 7 3         11  11  3

                             5 5 7       7 7 5         11  11  5

                                            7 7 11       11  11  7

So 14   triangles are possible

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The point (6, 4) is the same distance from the y-axis as point G(-6, 4) but on the opposite side of the y-axis

An equation is an expression that shows the relationship between two or more numbers and variables.

Point G on the coordinate plane is at G(-6, 4).

The point (6, 4) is the same distance from the y-axis as point G(-6, 4) but on the opposite side of the y-axis

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Answer:

if x=0 then they have same value

1st and 2nd options are out

for x=-1

g(-1)=1

h(-1)=-1

3rd is true

4th

false

for all values except zero, g(x)>h(x)

correct ones are

ANSWER: g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

Answer:

k = - 3 1/6

Step-by-step explanation:

-8-3k(2)=11

-8-6k = 11

8 - 8 - 6k = 11 + 8

-6k = 19

-6k/-6 = 19/-6

k = -3.16667

k = -3 1/6

Answer:

62.9643082106 degrees

Step-by-step explanation:

First, notice that triangle ABC is a right triangle. This allows us to use SIN, COS, and TAN to find the measure of angle A. Recall SOH CAH TOA, so SIN = OPPOSITE / HYPOTENUSE, COS = ADJACENT / HYPOTENUSE, and TAN = OPPOSITE / ADJACENT.

Looking at angle A, sides c and b correspond to hypotenuse and adjacent respectively. Therefore, we can use COS to set up an equation.

cos(A) = b/c

cos(A) = 5/11

A = arccos(5/11)

A = 62.9643082106 deg

The degree the tree was leaning is 70 degrees.

Using cosine law,

c² = a² + b² - 2ab cos C

Therefore,

6² = 2² + 5² - 2 × 2 × 5 cos C

36  = 4 + 25  - 20 cos C

36  = 29 - 20 cos C

36  - 29 = - 20 cos C

7 = - 20 cos C

cos C = 7 / - 20

cos C = -0.35

C = cos⁻¹ 0.35

C = 69.5126848853

C = 70 degrees.

Therefore, the degree the tree was leaning is 70 degrees.

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Answer:

B. One

Step-by-step explanation:

Since the two angles are already given, the value of the third angle is already fixed. The third angle can be found by the sum of both angles subtracted from 180. Since 2 angles and lengths are already given, there can only be 1 triangle.

Hope this helps!

If not, I am sorry.

The statement is " It was said that the circumstance was represented by the fact that the supper meal has 1500 calories."

Generally, the equation for Calories consumed  is  mathematically given as

x = 2/3 of daily calorie

The calories consumed during breakfast and lunch

Cbl=1 - 2/3

Cbl = 1/3

Hence, calories consumed per day

1/3 * cc = 750

cc/3 = 750

cc = 750 * 2

cc= 2250 calories

Calories consumed at dinner

cd= (2250 - (750))

cd= 1500 calories

In conclusion, It was said that the circumstance was represented by the fact that the supper meal has 1500 calories.

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