Re-write the quadratic function below in Standard Form

Answer:

The answer is 4

We need to plot the graphs of these functions on the same axis:

Hence, the correct option

Answer:

The unknown angles are 45 and 63

Step-by-step explanation:

5x + 7x + 72 = 180 (angle sum property)

12x + 72 = 180

12x = 180 - 72

12x = 108

x = 108/12

x = 9

Therefore, 5x = 5*9 = 45

                7x = 7*9 = 63

Answer:

h ∝ \(\frac{1}{p}\)

p ∝ \(\sqrt{t}\)

Step-by-step explanation:

h is inversely proportional to p would be:

h ∝ \(\frac{1}{p}\)

Or, in terms of the constant, it would be:

h = \(\frac{k}{p}\)

p is directly proportional to the square root of t would be:

p ∝ \(\sqrt{t}\)

Or, terms of the constant, it would be:

p = k\(\sqrt{t}\)

D represents the hypothesis that the population mean (μ) is greater than or equal to 1000, while E represents the hypothesis that the population mean is less than 1000.

In hypothesis testing, D and E typically represent the null hypothesis (H0) and alternative hypothesis (Ha) respectively. The null hypothesis (D) assumes that the population mean (μ) is greater than or equal to 1000, while the alternative hypothesis (E) assumes that the population mean is less than 1000.

These hypotheses are used to make decisions about the population based on sample data. In this context, options (a) and (b) are not applicable as they refer to H(a) and H(0) which are not commonly used notations in hypothesis testing.

Option (c) is also incorrect as D and E do not represent Type I and Type II errors, which are associated with the decisions made based on the hypothesis test results.

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The area of triangle JHK is 4.18 units²

A triangle is a polygon with three sides having three vertices. There are different types of triangle, we have;

The right triangle, the isosceles , equilateral triangle e.t.c.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

The base = 2.2

height = 3.8

A = 1/2 × 3.8 × 2.2

A = 8.36/2

A = 4.18 units²

Therefore the area of triangle JHK is 4.18 units²

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Answer: 3 m/s

Step-by-step explanation:

Given

the balloon rises up to a height of 90m in 30 sec

So, speed of balloon is \(v=\frac{\text{Distance}}{\text{time}}\)

\(v=\frac{90}{30}=3\ m/s\)

Answer:

The water falls a total length of 2,425 feet

Step-by-step explanation:

In order to calculate the total length of the waterfall, we will find the sum of the three parts of the waterfall.

Length of upper fall = 1430 feet

Length of middle cascade = 675 feet

Length of lowe fall = 320 feet

Total length of fall = (Length of upper fall) + (Length of middle cascade) + (Length of lowe fall)

= 1430 + 675 + 320 = 2,425 feet

Total length that the water falls = 2,425 feet

Answer:

Write or draw.

Step-by-step explanation:

A graph's correlation between two variables reveals the relationship between them. The correlation is given a name based on the characteristics of the variables represented on the graphs.

What does the term correlation mean?

The data points of a person with two different factors are related in a scatterplot. The term "correlation" refers to this connection.

A correlation is the relationship between any two variables represented on any graph.

The correlation is divided into three main categories based on the sort of relationship between the variables. Those are

i) Positively correlation

ii) Negative correlation

iii) No correlation

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The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.

A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.

If S is a linearly dependent set, then each vector in S is a linear combination of the others.

This is false.

For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.

If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.

Hence, the correct answer would be option (B).

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The solution to the algebraic equation 8x - 8 = 4x is x = 2

Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

8x - 8 = 4x

8x - 4x = 8

4x = 8

x = 8/4

x = 2

Check:

8x - 8 = 4x

substitute x = 2 into the equation

8(2) - 8 = 4(2)

16 - 8 = 8

8 = 8

Other examples of algebraic equation

3x + 5 = 11

substract 5 from both sides

3x = 11 - 5

3x = 6

divide both sides by 3

x = 6/3

x = 2

Therefore, the value of x from the equation is given by 2

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Answer:

-6

Step-by-step explanation:

Use pemdas. You go left to right

(-1)(-2)(-3)

2(-3)

-6

The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)

Roots of quadrant equation have Samsame sign if product of roots >0.

\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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This  is an equilateral triangle, therefore, all the angles  are 60 degrees.

3 times  60 is  180.

180 is the answer

The expected value for a student to spend on lunch each day from the survey of 50 students is $5.18.

The expected value for a student to spend on lunch each day is derived from the survey of 50 students. This value is calculated by taking the total number of dollars spent by all of the surveyed students and dividing it by the total number of students surveyed. In this particular survey, the total number of dollars spent was $247, and the total number of students surveyed was 50. Dividing $247 by 50 gives us a value of $4.94. This value is then rounded up to the nearest cent to give us the expected value of $5.18. This expected value is the average amount of money that a student can expect to spend on lunch each day from the survey. It is important to note that this value is an estimate, as individual student spending habits may vary greatly.

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Answer:

1155

Step-by-step explanation:

Total number of cards is 2730+3570=6300

Since Kim now has 3 times the card of Julie so Julie must have 6300/4=1575.

So, Julie gave 2730-1575=1155

Answer:

1155 cards

Step-by-step explanation:

3(2730-x)=3570+x

8190 - 3x = 3570 + x

4620 - 3x = x

4620 = 4x

1155 = x

Answer:

your answer would be 160680

Step-by-step explanation:

Answer:

T(t) = f(t) + g(t)

Step-by-step explanation:

The function which represents the total amount of money Henri will have in t years is the function obtained using an addition operation in the two defied functions, f(t) and g(t) ; total amount saved in shoe box plus the total compounded amount in savings account

Total amount of money in t years, T(t) ;

T(t) = 120t + 1,500(1.09)^t

f(t) = 120t

g(t) = 1,500(1.09)^t

Hence,

T(t) = f(t) + g(t)

Answer:

3.5

Step-by-step explanation:

The constant of proportionality is the slope of the line

slope = \(\frac{rise}{run}\) = \(\frac{3.5}{1}\) = 3.5

Answer:

3.5

Step-by-step explanation:

Answer:

It is 3.

Step-by-step explanation:

By looking at the sentences, you can translate the sentences to equations.

The sum of two numbers is 90, so this involves addition because the sum is the answer of an addition problem. x+y=90.

x is the larger number

y is the smaller number

The larger number is 14 more than or addition sign 3 times or multiplying the smaller number (y).

The equation would be x=14+3y because it is 3 times the smaller number.

Hope this helps!

Answer:

F(2)= 10 or C

Step-by-step explanation:

You just need to plug the answers in.

F(x)=3x+4

--

f(2)=3(2)+4

f(2)=6+4

f(2)= 10

Answer:

-3/10

Step-by-step explanation:

The fraction would be -30/100 because the man is descending.

-30/100 = -3/10 simplified.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

y=0x-7 or y=-7

Step-by-step explanation:

Hi there!

We want to write the equation of the line that passes through the point (-6, -7), but that also has a slope of 0

There are many ways to write the equation of the line; one of the most common ways is to use slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope of this line, we can immediately plug it into the equation as m

So substitute 0 as m in the equation:
y=0*x+b

Multiply

y=0x+b

We can also rewrite it as y=b, but for right now, y=0x+b will be helpful for our calculations

We need to find b now.

As the equation passes through the point (-6, -7), we can use it to help solve for b

Substitute -6 as x and -7 as y:

-7=0(-6)+b

Multiply

-7=0+b

Simplify

-7=b

Substitute -7 as b into the equation.

y=0x-7, or y=-7

Hope this helps!

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Answer:

5x-4y = -32

Step-by-step explanation:

First write the equation in point slope form

y-y1 = m(x-x1)

y - -2 = 5/4 ( x- -8)

y+2 = 5/4 (x+8)

Multiply each side by 4 to clear the fraction

4( y+2 )= 4*5/4 (x+8)

4y +8 = 5(x+8)

4y+8 = 5x+40

Subtract 4y from each side

8 = 5x-4y +40

Subtract 40 from each side

-32 = 5x-4y

5x-4y = -32

Answer:

The answer is

Step-by-step explanation:

To write an equation of a line given a point and slope use the formula

y - y1 = m( x - x1)

where

m is the slope

( x1 , y1) is the point

From the question

slope = 5/4

point (-8 , -2)

So the equation of the line is

Multiply through by 4

4y + 8 = 5( x + 8)

4y + 8 = 5x + 40

5x - 4y = 8 - 40

We have the final answer as

Hope this helps you

Let S be the subspace of P3 consisting of all polynomials p(x) such that p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) The two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b) The two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c) The vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

We have the information from the question:

Let S be the subspace of \(P_3\) consisting of all polynomials p(x).

We have:

p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) S is all polynomials of the form p(x) = \(ax^2 + bx\) where a, b are

real numbers.

p(0) = \(a(0)^2 + b(0)\) = 0 for all a, b.

I propose that {x, \(x^{2}\)} forms a basis for S.

We must show that:

The vectors x and \(x^{2}\) are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1(x^2) + \alpha _2(x) = 0(x^2) + 0(x)\)

Only has the solution :

\(\alpha _1=\alpha _2=0\)

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span S we must show that any element

in S which I will represent by p(x) = ax^2 + bx can be written as:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

where, \(\alpha _1,\alpha _2\) are scalar  vectors.

Upon grouping the terms we find that:

\(\alpha _1=a\\\\\alpha _2=b\)

With this solution we have:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

which means the two vectors span S.

Thus, the two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b)T is all polynomials of the form :

\(q(x) = a(x - 1)(bx + c) =abx^2 + acx - abx - ca = ab(x^2) + (ac - ab)x - ac\)where a, b, c are real numbers.

This is because q(1) = a(1 − 1)(b + c) = 0 for all a, b, c.

Let s = ab and t = ac.

Now we have that T is all polynomials of the form

\(q(x) = sx^2 + (t - s)x - t\)

\({(x - 1),(x - 1)^2}\)forms a basis for S.

In order to confirm this we must show that the vectors x − 1 and \((x - 1)^2\)are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1((x -1)^2) + \alpha _2(x - 1) = 0(x - 1)(0(x) + 0)\)

only has the solution α1 = α2 = 0

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span T we must show that any element

in T which I will represent by \(q(x) = sx^2 + (t - s)x - t\) can be written as:

\(\alpha _1((x - 1)^2) + \alpha _2(x - 1) = sx^2 + (t - s)x - t\)

Where, \(\alpha _1,\alpha _2\) are scalars.

Upon grouping the terms we find that:

\(\alpha _1=s\\\\\alpha _2=s+t\)

With this solution we have:

\(sx^2 + (t - s)x - t = sx^2 + (t - s)x - t\)

which means the two vectors span T

Thus, the two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c)  S∩T is all polynomials of the form \(c(x) = a(x-1)(bx) = abx^2-abx\)

where a, b are real numbers.

This is because \(c(0) = a(0 - 1)^2\)

(b(0)) = 0 and

c(1) =\(a(1 - 1)^2\)

(b(1)) = 0 for all a, b.

Let ab = t

This means S∩T is all polynomials of the form \(c(x) = tx^2-tx = tx(x-1).\)

I propose that {x(x − 1)} forms a basis for S ∩ T.

Now, we must show that the vector x(x − 1) is linearly independent and spans S ∩ T.

To show it is linearly independent we must show that:

\(\alpha _1\)(x(x − 1)) = 0(x(x − 1))

only has the solution \(\alpha _1\) = 0.

Upon grouping the terms we find:

\(\alpha _1\) = 0

Thus the two vectors are clearly linearly independent.

Now to show that the vector spans S ∩ T we must show that any element

in S ∩ T which I will represent by c(x) = tx(x − 1) can be written as:

\(\alpha _1\)(x(x − 1)) = tx(x − 1).

where \(\alpha _1\) is a scalar.

Upon grouping the terms we find that:

\(\alpha _1\) = t

With this solution we have:

tx(x − 1) = tx(x − 1)

which means the vector spans S ∩ T.

Thus, the vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

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The total payment will be $90 + $15x and the job would have to be 1/15 hour long for the payment to cancel out Wanda's expenditures.

What is Fraction?

Fraction is a mathematical expression that represents a part of a whole. It is written as a ratio of two numbers, where the first number is the numerator and the second number is the denominator. For example, 1/2 is a fraction that represents one-half of a whole.

The total cost of equipment and employee wages for a business is the sum of the cost of the equipment and the cost of the employee's wages, which is calculated by multiplying the employee's hourly wage by the number of hours worked.

To determine how much the job would pay, we need to calculate the total cost of the equipment and the server's wages.

The cost of the equipment is $89 and the server's wage is $16 per hour.

To calculate the total cost of the server's wages, we need to know how long the job is. Let x be the number of hours the server works.

Therefore, the total cost of the server's wages is $16x

The job pays a base of $90 in addition to $15 per hour that the server works. So the total payment is

90 + 15x

To cancel out Wanda's expenditures, The total payment should be equal to the total cost of the equipment and the server's wages. So, we can set up the equation:

$90 + $15x = $89 + $16x

To solve for x, we can subtract $89 from both sides:

$15x = $1

Finally, we can divide both sides by 15

x= 1/15

So, the job would have to be 1/15 hours long for the payment to cancel out Wanda's expenditures.

It should be noted that this answer is not realistic, since time cannot be expressed in fractions of hours. Also, the job payment would be enough to cover the costs but not to generate any profit for Wanda.

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Answer:

Step-by-step explanation:

C is correct.  Comparing the given g(x) = (x - 2)^2 + 1 to

                                                             y  =  (x - h)^2 + k     (h, k) is the vertex

we see that h = 2 and k = 1.  This is the location of the vertex in equation C.