What type of number is
5
6
A) rational
B) irrational
C) integer
D) whole
I don't know

The solutions to the quadratic function y = x² + 4x + 3, using the quadratic formula, are given as follows:

x = -1 and x = -3.

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

In which the leading coefficient a must assume a value different of zero.

The solutions to the quadratic function ax² + bx + c = 0 are obtained using the quadratic formula, as follows:

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

The quadratic function for this problem is defined as follows:

x² + 4x + 3 = 0.

Hence the coefficients are:

a = 1, b = 4, c = 3.

The first solution is:

[tex]x = \frac{-4 - \sqrt{4^2 - 4(1)(3)}}{2} = -3[/tex]

The second solution is:

[tex]x = \frac{-4 + \sqrt{4^2 - 4(1)(3)}}{2} = -1[/tex]

This problem was incomplete, hence the quadratic formula is used to solve y = x² + 4x + 3, as an example.

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Answer:

C is a function

Step-by-step explanation:

for a relation to be a function each value of x must map to exactly one unique value of y

A

2 → 5 and 2 → 2 ← not a function

B

- 1 → 6 and - 1 → 7 ← not a function

C

all values of x map to exactly one unique y ← function

D

3 → 1 and 3 → 2 ← not a function

Answer:

Isosceles triangle

Step-by-step explanation:

Thorough explanation: Through the angles in the triangle ABC.

First, observe that angle ACD = 50 degrees (given)

Since lines AB and DE are parallel to each other,

angle BAC = angle ACD = 50 degrees (by the property of alternate angles)

It is also given that angle ABC = 80 degrees.

Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.

Angle BAC + Angle ABC + Angle ACB = 180 degrees

50 + 80 + Angle ACB = 180

Angle ACB = 180 - 50 - 80

                   = 50 degrees

Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)

Answer:

[tex]v=-18,14[/tex]

Step-by-step explanation:

[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]

The values of x are 5 or 13.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] = -8+x

Squaring both sides,

2x-1 = x²+64-16x

x²-16x-2x+1+64 = 0

x²-18x+65 = 0

Factorizing the equation,

x²-18x+65 = 0

x²-13x-5x+65 = 0

x(x-13)-5(x-13) = 0

(x-5)(x-13) = 0

x = 5 or 13

Hence, the values of x are 5 or 13.

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The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

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The graph of the given equation y=2x+1 is attached below.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The equation y=2x+1 gives the following information:

The slope is 2

The line intercepts is 1 on the y axis

First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.

By using my slope we know that (1,3) and (-1,-1).

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A line segment is merely a portion of a line, one with definite ends and a finite length.

A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.

An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.

O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.

Given the following details as:

N is between M and O.

O is between N and P .

NO=6 and NP = 8.

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Each will get 3/5 cups of nuts by ratio and proportion concepts.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

We have to divide total nuts within 5 people.

so,

3 3/5 : 5

but first convert,

3 3/5 = 15/4

substitute,

15/4 : 5 = 15/20cups of nuts

simplify,

3/5 cups

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Answer:

y = 90°

Step-by-step explanation:

a) The probability that a student will study and will pass is 0.765.

b) The probability that a student will pass is 0.715.

What is probability?

Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.

Define some events -

A: A  student studies.

B: A student will pass.

Given that P(A)=0.85 and

P(B|A)=1-P([tex]\bar{B}[/tex]|A)

=1-0.10

=0.90

a) P(a student will study and will Pass)= P(A∩B)

= P(A)·P(B|A)

= 0.85×0.90

= 0.765

b) Given that P( student will either study or pass), the probability is -

=P(A∪B)= 0.8 then P(a student will pass)

=P(B)

It is known that P(A∪B)= P(A)+P(B)-P(A∩B)

Then P(B)=P(A∪B) -P(A) +P(A∩B)

=0.8-0.85 + 0.765

=0.715

Therefore, the probabilities are 0.765 and 0.715.

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The arithmetic expression may be used to get the formula T = (11 + w)/4, which is the distance Kane runs in a training session after w weeks.

Every training session, Kane begins out by running 3 miles, and he has a plan to improve that distance by 1/4 mile each week.

The number of weeks is w.

The arithmetic progression may be used to calculate an expression that displays the distance Kane runs during a training session after w weeks.

T = A + (n-1)d is the formula for the nth term in an arithmetic operation, where an is the first term, which is 3, d is the difference between two consecutive terms, which is, is the last term, and n is the total number of terms.

We get, T = (11+w)/4

This is the expression to show the distance Kane runs in a training session after w weeks.

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Complete question - Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance Kane runs in a training session after w weeks

Observational data collection might be best to study how voters might decide an upcoming ballot issue.

The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).

In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.

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When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.

The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

Let x be the price of a single tulip bag.

Y should equal the price of one bag of daffodil bulbs.

Grace = 14x + 12y = 254

ava = 6x + 12y = 198

- 8x = - 56

x = - 56/-8

x = 7.

Equation 1 becomes

6* 7 + 12y = 198

42 + 12y = 198 when x = 7 is substituted.

12y = 198 - 42

12y = 156

y = 156/12

y = 13

When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.

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Answer:

infinity/undefined (both are acceptable)

Undefined is actually the best answer in college but your answer key might put it as infinity.

Step-by-step explanation:

Observe that the x coordinates of the two points are exactly the same at 12.

This reduces the possibility of the line being a horizontal or a vertical line.

Imagine, if x coordinates is always the same, it means that you are only varying y and that happens when you move up and down the graph.

Hence, the line is a straight vertical line. (Line equation: x = 12)

Gradient/Slope of a vertical line = infinity/undefined.

The slope of the given line is Undefined

The slope of the line when two points in the line is given is given by

m=(y₂-y₁)/(x₂-x₁)

The points are (12,0) and (12,9)

m=(9-0)/(12-12)

  = 9/0

  =Undefined

The slope of the line is Undefined

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The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].

As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]

The polynomial is zero polynomial if x is 2

The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).

Replace x with 2 we get

Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]

[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0

[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0

[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0

Add -12 on both sides we get

12 + 5 (a) - 12 = 0 - 12

5 (a) = -12

Divided by 5 into both sides we get

a = [tex]-\frac{12}{5}[/tex]

Therefore the value of a is [tex]-\frac{12}{5}[/tex]

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Answer:

It's B, -2, v/5 4, and 3².

Answer:

2.50 × 19 = 47.5

Therefore, she would get $47.5 if she sold 19 cups.

The number of hours that Julius can spend online this week is 1 1/3 hours.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.

This will be Illustrated as x.

x + 1 2/3 ≤ 3.

x ≤ 3 - 1 2/3

x ≤ 1 1/3.

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The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.

Let's write the terms in the order x, y therefore,

y - 2x + 5 = 0

- 2x + y = - 5.

2x - y = 5.

And

y + 4x + 1 = 0.

4x + y = - 1.

The graph of the system of equations is attached in the image.

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Answer:legs

Step-by-step explanation: I cannot give a explanation since it is simply math, anything adjacent to a right angle is called a leg.

Answer: the legs? or opposite and hypotenuse.

Step-by-step explanation:

Answer:

x = 4, y = 12

Step-by-step explanation:

xy = -16

y = x + 8

substitute y = x + 8 into xy = -16

x(x + 8) = -16

x^2 +8x + 16 = 0

x = 4

sub x = 4 into y = x + 8

y = 4 + 8

y = 12

The Petronas tower is 1483.811 feet tall.

One of the six fundamental functions in trigonometry is the tangent function. As stated, Tan A = Opposite Side/Adjacent Side is the Tangent Formula. Tangent may be modeled using sine and cosine as follows: Tan A = Sin A / Cos A.

Given:

Angle of elevation: In 2001, the tallest building in the world was the Petronas Tower in Kuala Lumpur, Malaysia.

For a person standing 25.9 ft from the base of the tower.

The angle of elevation to the top of the tower is 89°.

Let c = height of the tower,

and a = distance from the base of the tower to x.

a = 25.9 feet.

The formula:

Tangent (angle) = opposite side / adjacent side.

tan89° = c / a

57.29 = c / 25.9

c = 57.29 x 25.9

c = 1483.811 feet

Therefore, 1483.811 feet is the height of the Petronas tower.

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Answer:

Step-by-step explanation:

good

Given that,

Perimeter of kite -  38 cm

Let "x" be the one side of kite

Both of the top sides are equal

Therefore, other side = x

One side of a kite is 2 cm less than 2 times the length of another

Therefore,

One of bottom side = 2x - 2

Bottom sides are also equal

Thus, other bottom side = 2x - 5

We know that,

Perimeter = sum of all sides

38 = x + x + 2x - 2 + 2x - 2

38 = 6x - 4

6x = 38 + 4

6x = 42

x = [tex]\frac{42}{6}[/tex]

x = 7

Thus length of each side of kite is:

x = 7

2x - 2 = 2(7) - 2 = 14 - 2 = 12

Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm

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The family's monthly payment for their new minivan is $6,664.52

To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.

Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:

Monthly Payment = Financed Amount * Monthly Payment Factor

So in this case:

Monthly Payment = $33,000 * 0.202764 = $6,664.52

Therefore, the family's monthly payment for their new minivan is $6,664.52

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The probabilities are given as follows:

a) No injuries: 0.4493 = 44.93%.

b) More than two injuries: 0.0474 = 4.74%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The mean for this problem is of:

[tex]\mu = 0.8[/tex]

The probability of no injuries is of P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

The probability of more than two injuries is of:

P(X > 2) = 1 - P(X <= 2)

In which:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

Hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]

[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]

Then:

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The inequality that represents the situation is 45x + 1240 ≥ 6000

There are 45 members overall.

If one individual contributes $x, then

The sum that 45 individuals together raised is then equal to 45x.

$6000 is the bare minimum necessary to enter the competition.

$1240 is the amount they already have.

Therefore, the amount they need to raise is $6000 minus $1240.

Inequality can be displayed as:

45x ≥ 6000 - 1240

This demonstrates that the total amount raised by 45 individuals (45x) should be equal to or more than the sum they need to raise ($6,000 - $1240).

change the equation's order;

45x + 1240 ≥ 6000

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6=3

6÷3

2 is the required answer for this question

The ratio of days in May and days in a year is 31 to 365 or 31:365

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We need to find the days in May and days in a year as a ratio

Therefore, Days in may = 31

Days in a year = 365

Thus, the expected ratio = 31/365

Or

31:365

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Answer:

Gain: $415

Loss: $10

Step-by-step explanation:

money earned - money spent = gain/loss

The gain is when the participant wins the telescope:

telescope = $425  ==> money earned

10 tickets * $1 = $10 for tickets  ==> money spent

$425 - $10 = $415

Loss is when the participant doesn't get the telescope:

$0 ==> money earned (No money earned)

10 tickets * $1 = $10 for tickets  ==> money spent

$0 - $10 = -$10 gained

-$10 gained ==> $10 lost