Use the vertex and intercepts to sketch the graph of each quadratic function give the equation of the parabola axis of symmetry use the graph to determine the function domain and range f(x)=(x-1)^2+2

Answer:

0.65 pens

2.25 rubber

Step-by-step explanation

You can make two equations with the information given and solve them simultaneously to find x and y. Assume x is pens and y is rubber.

Answer:

  7.2 cm

Step-by-step explanation:

You want the value of C to the nearest tenth centimeter, given that 4^2 + 6^2 = C^2.

Simplifying gives ...

  4^2 + 6^2 = C^2

  16 +36 = C^2 = 52

  C = √52 ≈ 7.2

The length of the missing side is about 7.2 cm.

Answer:

Answer is y = 11

Step-by-step explanation:

8 = y - 3

or, 8 + 3 = y - 3 + 3

or, 11 = y

or, y = 11

As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the information given in the question,

The given equation is,

y= -1/4 x + 2

Now, let's take y = 0 for x- intercept,

So, the equation will be,

0 = 1/4x + 2

1/4x = -2

x= -8

The x-intercept is (-8, 0).

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The question sees incomplete, your question may be:

Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?

After 81 minutes of driving the distance to destination is 32.8 miles.

Th function that has two variables with first order term is called linear function.  While plotting on the XY coordinate system we get a straight line.

Why do we use linear equation in this problem?

as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.

given, distance to destination in miles is a linear function of total driving time in minutes.

y=mx+b

in the equation, y denotes the distance to destination in miles

                 x is the total driving time in minutes

         m is the slope of linear equation

      b is the y intercept

Milan has 68 miles to his destination after 37 minutes of driving

68 = mx37+b

he has 45.6 miles to destination after 65 minutes of driving

45.6=mX65+b

solving the two equations by addition method

slope, m= -0.8

from the above two equation

we get b=97.6

now, after 81 minutes of driving the distance to destination, y=mx+b

                                               y= -0.8x81+97.6

                               distance = 32.8 miles

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The graph that shows the linear relationship of the table is attached below.

To determine the graph of a linear relationship, do the following:

Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:

Slope = change in y / change in x = (1 - 0) / (2 - 0)

Slope = 1/2.

The y-intercept (b) = 0.

Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.

Thus, the graph is shown below.

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The equivalent expression for the given expression is 29/3.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given mixed fraction [tex]9\frac{2}{3}[/tex].

There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.

Convert mixed fraction to improper fraction as follows

Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator

[(9×3)+2]/3

=[27+2]/3

= 29/3

Therefore, the equivalent fraction for the given mixed fraction is 29/3.

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The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given

A line passes through the point (-6,3)

and has a slope of 3/2

Slope intercept form

y = mx + b

Equation,

y - 3 = 3/2(x - (-6))

y - 3 = 3/2(x+6)

2y - 6 = 3x + 18

2y = 3x + 24

y = 3/2x + 12

The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.

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Answer:

x is 44 Hope that helps.

The degree to turn before walking 673 paces is 59 degrees

From the question, we have the following parameters that can be used in our computation:

Lengths = 989 paces, 673 paces and 861 paces

These paces can be represented as

x = 989

y = 673

z = 861

The measure of the required angle (angle Z) i.e.  the degree to walk can be calculated using the following cosine rule

z² = x² + y² - 2xy * cos(Z)

Substitute the known values in the above equation, so, we have the following representation

861² = 989² + 673² - 2 * 989 * 673 * cos(Z)

Evaluate the exponents, the products and the summation

So, we have the following representation

741321 = 1431050 - 1331194 * cos(Z)

Evaluate the like terms

- 1331194 * cos(Z) = -689729

Divide both sides by  - 1331194

cos(Z) = 0.51812808651

Take the arc-cos of both sides

Z = 58.7

Approximate

Z= 59 degrees

Hence, the measure of the angle is 59 degrees

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a. The blue line represents g(x) = 250,000csc(π30x).

b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.

c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).

d. The equation has a vertical asymptote at x = 30/π.

a. Graph g(x):

To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).

b. Evaluate g(5):

The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.

c. Minimum distance between the comet and Earth:

The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.

d. Vertical Asymptotes:

The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.

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The interest accrued in the first four years is $1.69 and a half years is $0.21.

What is interest rate?

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.

The rate is 4.3%.

We have to find the interest accrued in the first four-and-a-half years.

First to find the interest for first four years.

p = $9.800,  r  = 4.3% = 0.043,  t = 4

⇒ I = P x r x t

   I = 9.800 x 0.043 x 4

   I = 1.6856

   I = $1.69

Now to find the interest for a half years.

p = $9.800 ,  r = 4.3% = 0.043,  t = 1/2

I = p x r x t

I = 9.800 x 0.043 x 1/2

I = 0.2107

I = $0.21

Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.

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the measure of ∠LPM is 90°

the measure of ∠PMN is 102°

the length of LN is 10 units.

Define Rhombus.

A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.

For a Rhombus, LMNO

∠LON = 102°

NP = 5 units

By the properties of Rhombus, we know that

All sides of a rhombus are congruent (equal)

So, LM = MN = NO = OL

and

Opposite angles are equal and the opposite sides are parallel.

So, ∠LON = 102° = ∠LMN

Since Adjacent angles add up to 180°.

Therefore ∠L + ∠M = 180°

                 ∠M + ∠N = 180°

                 ∠N + ∠O = 180°

                 ∠O + ∠L = 180°

So, ∠N = 180° - ∠O = 180° - 102° =78°

      ∠L = 180° - ∠O = 180° - 102° =78°

      ∠M = 180° - ∠L = 180° - 78° =102°

Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.

So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°

Thus, the measure of ∠LPM is 90°

         the measure of ∠PMN is 102°

         the length of LN is 10 units.

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Answer:

Lpm= 90

PMN=51

LN= 10

Step-by-step explanation:

The equation of a hyperbola can be written in the form:

(x-h)^2/a^2 - (y-k)^2/b^2 = 1

where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices on the x-axis, and b is the distance from the center to the vertices on the y- axis.

In this case, the vertices of the hyperbola are (6,4) and (0,4), and the center of the hyperbola is at (3,4). The distance from the center to the vertices on the x- axis is 3, and the distance from the center to the vertices on the y- axis is 0.

Plugging these values into the equation for a hyperbola, we get:

(x-3)^2/3^2 - (y-4)^2/0^2 = 1

This equation is not defined, because the value of b is 0. This means that the hyperbola has a horizontal orientation, and its vertices are on the y-axis.

To find the equation of the hyperbola, we need to rewrite the equation in a different form. We can do this by using the fact that the distance between the center of the hyperbola and a point on the hyperbola is given by:

√ ((x-h)^2 + (y-k)^2) = a*√ (1 + (y-k)^2/b^2)

Substituting in the values for h, k, and a, we get:

√ ((x-3)^2 + (y-4)^2) = 3*√ (1 + (y-4)^2/0^2)

This equation can be simplified to:

√ ((x-3)^2 + (y-4)^2) = 3*√((y-4)^2/0^2)

The value of b is still 0, so the equation for the hyperbola is:

(x-3)^2 = 9*(y-4)^2

This is the equation for a horizontal hyperbola with vertices (3,4) and (9,4) and asymptotes y = 1/3x + 3 and y = -1/3x + 5.

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces which is known as connected components, that are mirror images of each other and resemble two infinite bows.

Therefore, the correct answer is as given above

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Answer:

B, F

Step-by-step explanation:

[tex]2x^2(x-4)^2=0 \\ \\ \implies x^2=0, (x-4)^2=0 \\ \\ \implies x=0,4[/tex]

Answer:

Y=6x-12

Step-by-step explanation:

whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.

The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.

The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given statement for the problem is, " 20 divided by 1 plus 4".

It can be written in the form of expression as follows,

The sign of plus is given as '+'.

And, for divide it is '÷'.

Now, 20 divided by 1 plus 4 can be written as,

20 ÷ 1 + 4

Which is evaluated  by BODMAS to give,

20 + 4 = 24.

Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.

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The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.

A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.

The expression for the volume of a regular pentagon is given as V =  5/2 × abh

Where h is the height and a and b are the length of the sides.

Now, the value of a, b and h as per the question is given as,

a = b = h = 1.

Then, the volume can be calculated as,

V = 5/2 × 1 ×1 × 1
   = 2.5

Hence, the volume of the regular pentagonal prism  is given as 2.5 cm³.

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The two polynomials whose difference is 2x^2 + x + 4 are

6x² + 3x + 5 and 4x² + 2x + 1.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The difference between the two polynomials is 2x² + x + 4.

The two polynomials are:

6x² + 3x + 5 _____(1)

4x² + 2x + 1 ______(2)

The difference between (1) and (2)

6x² + 3x + 5 - 4x² - 2x - 1

2x² + x + 4

Thus,

The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.

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The total income from the machines over the first 5 years is $185.89

From the question, we have the following parameters that can be used in our computation:

f(t) = 160e0.03t

Where

Rewrite the function properly

so, we have the following representation

f(t) = 160e⁰.⁰³ⁿ

The above function is an exponential function

So: In the first 5 years, we have the value of t to be 5

This is represented as follows

t = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 160e⁰.⁰³ ˣ ⁵

Evaluate the product of the exponents

f(5) = 160e⁰.¹⁵

The products above give

f(5) = 185.89

Hence, the total income is $185.89

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There are 21 days for there to be 150 frogs in the pond.

There are 37 days for there to be 1400 frogs in the pond.

What is exponential growth?

Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.

Given:

There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.

The exponential equation for the given problem is,

[tex]A(t) = Ar^t^/^1^0[/tex]

To find the number of days for there to be 150 frogs in the pond.

Here,

A(t) = 250, A = 25, r = 3

⇒

[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]

t ≈ 21

Hence, there are 21 days for there to be 150 frogs in the pond.

Now to find how long for there to be 1400 frogs in the pond, we solve:

[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]

t ≈ 37

Hence, there are 37 days for there to be 1400 frogs in the pond.

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Answer:

x = - 3

Step-by-step explanation:

2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify

2x - 12 + 2 = 4x - 4

2x - 10 = 4x - 4 ( subtract 4x from both sides )

- 2x - 10 = 4x - 4 ( add 10 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer:

SOLUTION

2(X-6)+2=4X-4

open the blanket by multiplication

2x-12+2=4x-4

2x-10=4x-4

collect like term

2x+4x=-4+10

6x=6

divide both side by 6

x=1

Answer:

Below

Step-by-step explanation:

2^9 possibilities =512

9 possibles with only ONE tails  (9 C 1)

36 possibles with TWO tails     ( 9 C 2)

45 out of 512       45/512 = .088  

The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²

An expression is combination of variables, numbers and operators.

(4c − 3d)(3c + d) is the given expression.

Four times c minus three times d into three times f c plus d.

In the given expression c and d are variables.

Plus and minus are operators.

We need to find the equivalent expression of (4c − 3d)(3c + d).

(4c − 3d)(3c + d)

4c(3c+d)-3d(3c + d)

Apply the distributive property.

12c² + 4cd - 9cd - 3d²

Add the like terms

12c² - 5cd - 3d²

Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).

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Answer:

Hope this helps!

Answer:

-41.328

Step-by-step explanation:

Answer:

-41.328

Step-by-step explanation:

Addition multiplied by subtraction gets you subtraction. +-=-

so now, ()= multiplication

so now all you have to do is 17.22 times 2.4 which gets us 41.328

then, add the negative sign which gives you -41.328

yw :)

The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)

The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.

Here we have given the inequality (x² - 5)/ (x - 36) < 0

And we need to find the solution in inequality notation and in interval notation.

In order to find the inequality notation, we have to solve the given inequality, then we get.

(x² - 5)/ (x - 36) < 0

(x² - 5) < 0

x² < 5

x < √5

While we looking into the inequality we must know that the denominator must not be 0.

So, the interval notation can be written as,

=>  (-∞ . -√5]∪[√5,36)

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A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c)  (0.4901, 0.6699)

According to the question,

A professor wanted to know what proportion of college students believe in ghosts.

For that he drawn a sample from the college.

Sample size : n = 200

Proportion of students that believed in ghosts in sample = 58%

=> p = 0.58

Proportion of students who does not believe in ghost : q = 1 - p

=> q = 0.42

We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts

Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]

Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size

C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200

=> 0.58 ± 2.576 √0.001218

=>  0.58 ± 2.576 × 0.035

=> 0.58 ± 0.08958

C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)

Hence, Option (c) is correct

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Answer:

41%

Step-by-step explanation:

Answer: 2 complete games

Step-by-step explanation:

add shoes and game charge

$10.00 + 2.75 = 12.75 <— that’s 1 complete game

subtract it from $30.00

$30.00 - 12.75 = 17.25.

A complete game costs 12.75. so, Kim had enough money for one more game.

17.25 - 12.75 = $4.50 remaining after 2 complete games

Answer: 7 games

Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.