solve by completing the square
-x^2=5x-14

Answer:

Jack has 8 jellybeans and his brother has 17 jellybeans

Step-by-step explanation:

Jack+Jack's Brother= total

x+(2x+1)=25

3x+1=25

3x=24

x=8

2*8+1=16+1=17

Jack has 8 jellybeans and his brother has 17 jellybeans.

"It is a statement which consists of equal symbol between two mathematical expressions."

"It is a finite set of equations for which we find a common solution."

For given example,

Let Jack has 'x' jellybeans and his brother has 'y' jellybeans.

Jack split 25 jellybeans between his brother and himself.

⇒ x + y =25                          ...........................(1)

his brother has one more jellybean than twice the number Jack has.

⇒ y = 2x + 1                         ...........................(2)

So, we get system of equations,

x + y =25

y = 2x + 1

Now, substitute the value of y [from equation (2)] in the equation (1),

⇒ x + (2x +  1) = 25

⇒ 3x + 1 = 25

⇒ 3x = 24

⇒ x = 8

Substitute this value of 'x' in the equation (2),

⇒ y = 2(8) + 1

⇒ y = 17

Therefore Jack has 8 jellybeans and his brother has 17 jellybeans.

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Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).

The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.

Here,

Sinx = perp./hypo.

Cosx equals base/hypo.

So,

Sin = B/C

A= cos(90 -∅ ) = BC/AC

So,

Cos(90 -∅ ) = Sin(BC/AC)

And,

cos = AC/AB

AB/AC = sin(90 -∅ )

So,

cos AB/AC = sin (90 -∅ )

Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).

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Answer:

[tex]\huge\boxed{\text{4.2 feet}}[/tex]

Step-by-step explanation:

In order to solve this problem, we can use the basic trigonometric functions.

Let's first start to break down the triangle scenario we're given.

Now we know the three angles of the triangle and one side.

We can find the other two sides (or just the base side, in our case), using trigonometric functions such as sin, cos, and tan. We can substitute in their formulas and find lengths based on angle measures.

We know using SOH CAH TOA the relationships between opposites, adjacents, and hypotenuses with these functions. SOH CAH TOA states that:

Using the triangle, we want to find a relationship that has the base we need as an opposite/adjacent that can use the hypotenuse (since it's the only side length we know.

Well, we can take the sin of the 25 degree angle - it's opposite is the base leg and the hypotenuse is 10.

We can then represent this using an equation:

Therefore, the length of the base leg is 4.2 feet

Hope this helped!

Answer:

4.2 feet

Step-by-step explanation:

.................

Answer:

7

Step-by-step explanation:

hope this helps:))))))

Answer:

Degree measure of each angle is 90⁰, 47⁰ and 43⁰

Step-by-step explanation:

since the triangle is right angled, we assume that Q and S are the other angles of this triangle R

Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰

5x - 13 + 4x - 5 = 90⁰

9x = 108

x = 12

We now replace x in Q and S to get the angles

Q = 5(12) -13

= 47⁰

S = 4(12) - 5

= 43⁰

The cartoonist's purpose of the given cartoon is C: "to make people laugh at a play on the words".

Though the cartoon in the picture is designed based on the concept that fungal bands are an effective way of the biological control of Asian longhorn beetles, the core purpose of the cartoonist in designing this cartoon is to portray the idea in a comical way, indicating how these fungi actually form a music band called 'the fun guy' and they remove the beetles by playing their music, that awful racket as the beetle says.

Thus, the cartoonist's purpose of this cartoon is to make people laugh at a play on the words.

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Answer:

65

Step-by-step explanation:

We are given f(x) = 9

Substitute 9 for x in f(x) = 8x - 7

f(x) = 8 (9) - 7

f(x) = 72 - 7

f(x) = 65

Answer:

B. y ≥ 3x – 4

Step-by-step explanation:

Answer:

area=12cm

perimeter=16 cm

Step-by-step explanation:

a=bh/2

a=6(4)/2

a=24/2

a=12 cm

p=5+5+6

p=16 cm

In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.

The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.

Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.

Using the law of ins we can state that:

Sin 8°/x = sin 15°/90

90 (Sin 8°) /x = Sin 15°

90 Sin 8° = x Sin 15°

90 Sin 8° / Sin 15° = x

90 (0.13917310096)/ 0.2588190451 = x

Thus,

x = 48.3951213156

x [tex]\approx[/tex] 48.4

Thus, the distance of the flight is approximately 48.4 miles.

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On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Total Surface Area = 2(lw + bw + lb)

Total Surface Area = [tex]2(24 + 30 + 20)[/tex]

Total Surface Area = [tex]148cm^2[/tex]

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On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²

what is surface area ?

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Total Surface Area = 2(lw + bw + lb)

Total Surface Area = - 148cm²

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Answer:

30

Step-by-step explanation:

Answer:

Option D. {7 + i√71 / 20, 7 – i√71 / 20}

Step-by-step explanation:

10m² – 7m + 3 = 0

Using formula method, the solution to equation can be obtained as follow:

10m² – 7m + 3 = 0

Coefficient of m² (a) = 10

Coefficient of –7m (b) = –7

Constant (c) = 3

m = –b ±√(b² – 4ac) / 2a

= – –7 ±√((–7)² – 4 × 10 × 3) / 2 × 10

= 7 ±√(49 – 120) / 20

= 7 ±√(–71) / 20

Recall:

–17 = –1 × 17

Thus,

7 ±√(–71) / 20 = 7 ±√(–1 × 71) / 20

Recall:

√–1 = i

Thus,

7 ±√(–1 × 71) / 20 = 7 ± i√71 / 20

= 7 + i√71 / 20 or 7 – i√71 / 20

Therefore, the solutions to the equation are:

{7 + i√71 / 20, 7 – i√71 / 20}

An ordered pair function is a type of mathematical function that associates certain pairs of elements (called ordered pairs) with a single output. For example, the function f(x,y) = x+y associates the ordered pair (2,3) with the output 5.

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions such as print(), etc. but you can also create your own functions. These functions are called user-defined functions.

This is because 2+3 = 5. Another example is the function f(x,y) = x×y,

which associates the ordered pair (3,4) with the output 12, since 3×4 = 12.

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On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.

Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.

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Answer:

0+90=90 thank me later

Step-by-step explanation:

Answer:

she has rode 16 miles this week

Step-by-step explanation:

3 miles on monday 3 times that many on tuesday plus 4 miles one wensaday add them all up

3 times 3 is 9 plus 3 is 12 plus 4 is 16 there fore 16 miles in totale

sorry for my speling erros

She rode a total distance of 16 miles this week.

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

The distance rode by Lexi per day is mentioned below -

Monday - Lexi rode 3 miles on a bike.

Tuesday - Lexi rode 3 times more than she did Monday.

Wednesday - Lexi rode an additional 4 miles.

We can write the expression to find the total distance in miles covered by Lexi as -

d = d{M} + d{T} + d{W}

d = 3 + (3 + 3) + 4

d = 3 + 6 + 4

d = 13 miles

Therefore, she rode a total distance of 16 miles this week.

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Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.

score / total points = percentage / 100

To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:

score * 100 = percentage * total points

We know that percentage=80 and total points =50, so we can substitute these values:

score * 100 = 80 * 50

score = (80*50) / 100 = 40

So Lyda needs to score 40 points to accomplish her goal of 80%.

The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10

It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.

Step-by-step explanation:

Answer:

If we substitute pi as 3.14 we would be doing -

56.52/3.14 = 18

18/2 = 9.

So the circle's radius would be 9.

BUT if you want it with PI. . .

The answer would be 8.995437385

On solving the provided question, we can say that - the answer of the following sequence 1.9, 3x , 8x will be 13.78x

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

sequence 1.9, 3x , 8x

answer is = 13.78x

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Answer:

C

Step-by-step explanation:

6:4=8:12

6x3=8

4x3=12

Answer:

value of 10^-3= 0.001

hope it helps.

Answer:

Step-by-step explanation:

10^(-3) is equivalent to

   1

---------  which in turn is equivalent to 1/1000, or 0.001.

 10^3

Answer:

Q1 - 5

Q3 - 12.75

Interquartile Range = 7.75

(i think)

Step-by-step explanation:

Answer:

the x =2 cant be a solution for (x+3)^2 =5.

hope it helps.

Answer:

1.   f(x)=1-1/2

4.   y=10x

5.   yes

Step-by-step explanation:

1)
f(x) = 4(2 + 3x) + 3 is a linear function.

2)

The slope of the function is 6.

3)

The linear function is (1/2)x - 4.

4)

y = x² + 2 is not a linear function.

5)

No, it is not a linear function.

6)

Graph D does not represent a linear function.

7)

Graph B does not represent a linear function.

8)

Table D is a linear function.

9)

Table B is not a linear function.

10)

3x + 2y = 6 is a linear function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

1)

f(x) = 4(2 + 3x) + 3

f(x) = (1/2)x² - 5

f(x)= 5 - x²

f(x) = 1 - 1/x

The graph of each function is given below.

The red line in the graph represents f(x) = 4(2 + 3x) + 3.

This is a straight line which means it is a linear function.

2)

f(x) = 2(3x - 7)

f(x) = 6x - 14

It is in the form of y = mx + c where m is the slope.

So,

m = 6

3)

f(x) = (1/2)x - 4

f(x) = x³ - 2

The graph is given below.

The red line represents f(x) = (1/2)x - 4.

This is a linear function.

4)

y = 3x + 12

y = x² + 2

y = 10x

y = 9

The graph is shown below.

The green curve is y = x² + 2.

This is not a linear function.

5)

y = 2x² - 6

This is not a linear function because we have x².

The graph is given below.

6)

Graph D represents a non-linear function.

7)

Graph B represents a non-linear function.

8)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table D has the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

= (4 - 7) / (-1 + 2)

= -3/1

= -3

Table D is a linear function.

9)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table B does not have the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

Table B is not a linear function.

10)

The green line on the graph represents a straight line.

The green line is a linear function.

The green line is 3x + 2y = 6.

Thus,

The answers are given above.

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Answer:

c

Step-by-step explanation:

the answer is c

hope it helps

Answer:

8 seats

Step-by-step explanation:

n = 8 ---booths

r = 1 --- hostess

Order is required

Important Order? We solve using permutation.

nPr = n!/(n - r)!

So we have:

8p1 = 8!/(8 - 1)!

IF we do the math correctly, we get this:

8p1 = 8/7!

Finally let's expand to come up with the solution.

8p1 = 8 x 7/7

8p1 = 8

So the answer is 8!

I hope this helps! Have a good day (PLS GIVE BRAINLIEST)

There are 8 types of different arrangements possible for the hostess to seat customers at the waiter’s booths if order is important.

What is Permutation and Combination ?

The various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

Total number of booths = 8

To determine we will use the generalized expression

How many ways can you arrange 'r' from a set of 'n' if the order matters

P(n,r) = n! / (n-r)!

P(8,1) = 8!/ (8-1)!

= 8!/7!

= 8

So there are 8 types of different arrangements possible for the hostess to seat customers at the waiter’s booths if order is important.

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Given:

The variable cost per unit is $3, fixed costs are $2.

The revenue function is:

[tex]Y_{TR}=5\sqrt{q}[/tex]

where q is the number of thousands of units of output produced.

To find:

The break - even points for company X.

Solution:

The variable cost per unit is $3, fixed costs are $2.

So, the cost function is:

Total cost = Fixed cost + Variable cost × Quantity

[tex]Y_{TC}=2+3q[/tex]

The revenue function is:

[tex]Y_{TR}=5\sqrt{q}[/tex]

At break - even points the profit is zero. It means the cost and revenue are equal.

[tex]Y_{TC}=Y_{TR}[/tex]

[tex]2+3q=5\sqrt{q}[/tex]

Squaring both sides, we get

[tex](2+3q)^2=(5\sqrt{q})^2[/tex]

[tex]2^2+2(2)(3q)+(3q)^2=25q[/tex]

[tex]4+12q+9q^2-25q=0[/tex]

[tex]4-13q+9q^2=0[/tex]

Splitting the middle term, we get

[tex]4-4q-9q+9q^2=0[/tex]

[tex]4(1-q)-9q(1+q)=0[/tex]

[tex](4-9q)(1-q)=0[/tex]

Using zero product property, we get

[tex]4-9q=0[/tex] and [tex]1-q=0[/tex]

[tex]q=\dfrac{4}{9}[/tex] and [tex]q=1[/tex]

[tex]q\approx 0.444[/tex] and [tex]q=1[/tex]

Therefore, the break even points are 0.444 and 1.

To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.

Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.

The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.