Claudia is considering taking a vacation but she's not sure if she wants to drive or fly somewhere. She realized that it would take her the same amount of time to drive 150 miles as it would take a plane to fly 1350 miles. If the plane is flying 400 mph faster than the car, how fast is each traveling?

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y = x² -14 x + 48[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.

So, the values of x, when y = 0 are the roots of the given quadratic function.

that is : x = 6 and x = 8

And it can be represented as :

[tex]\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0[/tex]

[ h1 and h2 represents roots of the quadratic function ]

[tex]\qquad \tt \rightarrow \: (x - 6)(x - 8) = 0[/tex]

It can be further simplified as :

[tex]\qquad \tt \rightarrow \: {x}^{2} -8x - 6x + 48 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x {}^{2} - 14x + 48 = 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The new quantity supplied when the price is $348 per cord is  424.

The supply curve is a graph that shows the relationship between price and quantity supplied. The supply curve has a positive slope.

The slope of the supply curve is the ratio of the change in the value of price divided by the change in the value of the quantity supplied.

Slope = change in price / change in quantity supplied

0.75 = ($348 - $255) /  change in quantity supplied

0.75 = $93 /  change in quantity supplied

change in quantity supplied = 93 / 0.75 = 124

The new quantity supplied = 300 + 124 = 424

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The graph has the horizontal tangent line at the the turning point(stationary point) And we know that at the turning point the gradient is 0. We can find the gradient of f(x0 by the first derivative. As  I said the gradient a the turning point is 0 meaning since f'(x) =m  and m=0 ∴f'(x)=0

[tex]f'(x)=4x-2\\0=4x-2\\4x=2\\\frac{4x}{4}=\frac{2}{4} \\x=\frac{1}{2}[/tex]

Now we know that in order to find the point where x = [tex]\frac{1}{2}[/tex]  we can substitute the value of x in the original equation

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

The answer is [tex](\frac{1}{2} ,-\frac{3}{2} )[/tex]

Hope I helped.

The corresponding values of expressions 1, 2,3,4 and 5 when evaluated are -2, -0.65, -7/48, 67 1/2 and 2 2/33

1. To evaluate (a-2b)^3 when a = -3 and b = - 1/2,  put a = -3 and b = - 1/2 into the expression (a-2b)^3:

(a-2b)^3 = ( -3 - 2(-1/2) )

              = (-3 + 1) = -2

2. To evaluate (jk - 1) ÷ j when j = -4 and k = -0.9, put  j = -4 and k = -0.9 into the expression (jk - 1) ÷ j:

(jk - 1) ÷ j = ( -4(-0.9) - 1) ÷ (-4)

              = (3.6 -1) ÷ (-4) = (2.6) ÷ (-4) = -0.65

3. To evaluate -|a+b| / 2-c when a =1 7/8 , b = -1 , and c = -4 , put b = -1 , and c = -4 into the expression -|a+b| / 2-c:

-|a+b| / 2-c  = -|1 7/8 + (-1)|/ 2 -(-4)

                  = -| 7/8 | / 6 = -7/48

4. To evaluate (w^2 / x - 3) ÷ 10 multiplied by z when w = -9 , x = 2.7 , and z= -2/5:

(w^2 / x - 3) ÷ 10z = ((-9)²/ 2.7 -3)  ÷ 10(-2/5)

                            = (81/(-0.3))  ÷  (-4) = -270/-4 = 67 1/2

5. To evaluate (2a - 1/3) ÷ b/15 when a = -2/5 and b = -8.25:

(2a - 1/3) ÷ b/15 = (2(-2/5) - 1/3) ÷ -8.25/15

                          = (-4/5 - 1/3) ÷ (-11/20) = -17/5 ÷ (-11/20) = 2 2/33

Therefore, the expressions 1, 2,3,4 and 5 evaluate to -2, -0.65, -7/48, 67 1/2 and 2 2/33 respectively

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The weighted dollar amount of the savings account as per the an investment portfolio given is equal to $67.20.

As given in the question,

An investment portfolio is shown below.

Investment Amount Invested ROR

Savings Account $3,200     2.1%

Municipal Bond $4,900       4.5%

Preferred Stock  $940         10.5%    

Common Stock A $1,675     -3.5%

The weighted dollar amount of the savings account is equal to :

= 2.1% of $3200

=  ( 2.1 / 100)  × $3200

= ($6720) /100

= $ 67.20

Therefore,  the weighted dollar amount of the savings account  as per the an investment portfolio given is equal to $67.20.

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iN linear equations, store 1 jeans is cheaper than store 2.

What are instances of linear equations?

one store the jeans are selling for 1/5 off the original price of $70

              $70 * 1/5  = 14

second store the same jeans are selling for 1/3 off the original price $81

                 $81 * 1/3  = 27

So, store 1 jeans is cheaper than store 2.

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The ratio of 5 to 6 means that for every 5 girls on the track team there are 6 boys.

So, if there are n groups of 5 girls, there should be also n groups of 6 boys. Thus, we have the proportion:

Then, let's check each item to find out which one shows possible numbers of girls to boys on the track team.

A. 24 girls, 20 boys

B. 50 girls, 56 boys

C. 60 girls, 50 boys

D. 20 girls, 24 boys

Therefore, option D is correct.

Answer: I am 97% sure it's D

Step-by-step explanation:

9. To draw the rise, you can follow these steps:

- Identify a point on the line. In this case, this can be:

- Draw a vertical line that rises from that point. See the picture below:

10. To draw the line that represents the run, you need to Draw a horizontal line that goes from the endpoint of the line that represents the rise and extend it until it touches the function. See the picture below:

Therefore, the answers are (See the picture):

From the diagram we notice that the angle of 55° is vertical opposite to angle 3, hence they are equal.

Also from the diagram we notice that angles 3 and 6 are alternate interior angles and since lines A and B are parallel then they are equal.

Finally angle 6 and angle 7 are vertical opposite, which means they are equal.

Therefore, the value of angle 7 is 55°

iven:

heere are given that the population in the year 2000 was 12000 and the growth rate is 7% per year.

xplanation:

ccording to the question:

For t =0 which is the year 2000:

For t = 1:

If we say r is the rate, then:

Then,

For t = 2:

And,

For t = 3:

Therefore our function should be:

(a):

he population function:

Now,

(b):

ccording to the question:

2008 is 8 year from year 2000:

Therefore, t = 8:

Then,

Put the value 8 for t into the function (a):

inal answer:

The factor of the trinomial 9x² + 30x + 25 is (3x + 5).

When you factor a trinomial, you change an algebraic expression from a trinomial to a binomial. ax² + bx + c, where a and b are coefficients and c is a constant, is the general expression for a trinomial, which is a polynomial with three terms.

Given trinomial: 9x² + 30x + 25

Factoring the trinomial, we get

9x² + 30x + 25

9x² + 15x + 15x + 25

3x(3x + 5) + 5(3x + 5)

(3x + 5)²

Therefore, (3x + 5) is the factor of the given trinomial.

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Answer:

30

Step-by-step explanation:

200/40=5

5x6=30

therefore there are 30 tickets you could get with 400$

hope this helped

have a great day ^^

Answer:

30 tickets

Explanation:

One ticket can be represented as variable t.

Using t, we can set up an equation (proportion) using the given information:

[tex]6t = \$ 40[/tex]

Then, we can multiply both sides of the equation (proportion) by something such that the number of dollars on the right side is $200.

[tex]6t \ = \ \$ 40 \\\times 5 \ \ \ \times 5[/tex]

[tex]30t = \$ 200[/tex]

So, we can get 30 tickets for $200.

Solution

The total number nof cookies in the bag is:

- Thus, we can write the probabilities of choosing any of the cookies are given as:

- Now, let us analyze Trey's random choices

Choice 1:

He chose a sugar cookie at first.

- Thus, the probability of this choice is

Choice 2:

- He chose an oatmeal cookie in the second choice.

- But he already had one cookie before this choice, thus, the total number of cookies is one less. That is, 23 not 24.

- Thus, the probability of choosing the oatmeal cookie is given as:

- Because these choices do not interfere with one another (i.e. they are mutually exclusive), we can apply the AND probability formula to calculate the probability that Treys chose a Sugar Cookie first, and then an Oatmeal cookie next.

- The AND probability is given as

- Thus, we can find the probability that Trey chooses Sugar Cookies first and Oatmeal Cookie next as follows:

Final Answer

The answer is

Answer:

congruent: a° and c°; d° and b°

Supplementary: c° and b°; a° and b°; a° and d°; c° and d°

Step-by-step explanation:

The method that she could use to measure an equivalent amount is to remove 25% from the measurement used.

From the information, the chef needs 3/4 of a cup of flour for her recipe, but her 1/4 cup measure is missing.

Therefore, the method that she could she use to measure an equivalent amount will be to subtract 25% from whatever value that she is using.

It should be noted that 3/4 to percentage will be:

= 3/4 × 100.

= 75%

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = [tex]\frac{-2-0}{0-(-3)}[/tex] = [tex]\frac{-2}{0+3}[/tex] = - [tex]\frac{2}{3}[/tex]

(b)

the y- intercept is the point on the y- axis where the line crosses, that is

y- intercept c = - 2

(c)

y = - [tex]\frac{2}{3}[/tex] x - 2 ← equation of line

The rocked was launched at an initial height of 325 meters

The equation of the function is given as

h ( t ) = − 4.9 t 2 + 226 t + 325 .

Rewrite the above equation properly

So, we have the following equation

h(t) = −4.9t^2 + 226t + 325

At the initial height of the launch, the time is 0

This is represented as

t = 0

Substitute the known values in the above equation

So, we have the following equation

h(0) = −4.9(0)^2 + 226(0) + 325

Evaluate the exponent in the above equation

So, we have the following equation

h(0) = −4.9(0) + 226(0) + 325

Evaluate the product in the above equation

So, we have the following equation

h(0) = 0 + 0 + 325

Evaluate the sum in the above equation

So, we have the following equation

h(0) = 325

Hence, the initial height of the launch is 325 meters

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Possible question

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9 t 2 + 226 t + 325 .

Calculate the height of launch of the rocket

The subsets of the set {-3, 6}, which are proper subsets is the option;

A set is a model that represents a collection of mathematical objects such as numbers, lines, symbols, points, other sets, variables, or shapes.

In set theory, a set A is a subset of the set B if all the elements or members present in set A can be found in set B. Therefore, set B is said to contain set A or set A is contained in set B.

The above relationships can be expressed using examples as follows;

Let set A = {X, Y} and let set B = {X, Y, Z}, then set A is a subset of set B because the elements, X, Y, contained in set A, are also contained in set B,

Generally, the number of proper subsets of a set that contains n elements is [tex] {2}^{n} - 1[/tex]

Given that the subset of a set which is not a proper subset is the set of itself.

The given set is; {-3, 6}

The number of elements in the set, n = 2

Therefore;

The number of proper subsets = 2² - 1 = 3

All the subsets of {-3, 6} are therefore;

∅, {-3}, {6}

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Answer:

14, 9, 16

Step-by-step explanation:

from 3 to 10, you add 7

from 10 to 5, you minus 5

from 5 to 12, you add 7

from 12 to 7, you minus 5

so the pattern is add 7, minus 5

7 plus 7 is 14

14 minus 5 is 9

9 plus 7 is 16

Answer:

A and D (the top one and the bottom one)

Step-by-step explanation:

You do not multiply the exponents when the two terms are be multiplied. Instead, you add the exponents. For example, in the first problem, the terms being multiplied are [tex]5y^4[/tex] and [tex]2y^5[/tex]. The exponents are 4 and 5, and when you add them together, that is the exponent that y should carry in the answer.

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olution

Basically, the number of asymptotes will be the number of solutions the denominator of the function has

We are given the function

Solving the denominator

he answer is 3 vertical asymptotes

Answer:

1, 7, 13, 19, 25, 31, 37, 43

Step-by-step explanation:

it is increasing by 6 each time so you add 6 three more times.

Answer:

The original price was 18 dollars.

Step-by-step explanation:

Givens

Final price = 15 dollars

Discount = 20%

Original Price = x

Formula

x = 15 + 20/100 15

Solution

x = 15 + 300/100                     Multiply 20 * 15. Divide by 100

x = 15 + 3

x = 18

Answer:

Using the data under D1 and D2, calculate the cross elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.) At $50, cross elasticity = -2.40 ± 0.05At $35, cross elasticity = -3.00 ± 0.05At $20, cross elasticity = -4.00 ± 0.05Is the cross elasticity the same at all three prices? No. Are movies and golf substitute goods, complementary goods, or independent goods? Complementary goods.b. Using the data under D2 and D3, calculate the income elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the income elasticity of demand.) At $50, income elasticity of demand = 1.40 ± 0.05At $35, income elasticity of demand = 2.33 ± 0.05At $20, income elasticity of demand = 3.00 ± 0.05Is the income elasticity the same at all three prices? No. Is golf an inferior good? No, it is a normal good.

The required statement is given as the data tends to the normal good.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Calculate the cross elasticity of demand for golf at each of the three prices using the information under D1 and D2.

At $50, the cross elasticity is equal to -2.40 ± 0.05;
At $35, it is - 3.00± 0.05;
At $20, it is - 4.00 ±0.05.
No golf and movies complementary, independent, or alternative goods complementing products b.

Calculate the income elasticity of demand for golf at each of the three prices using the information under D2 and D3.
At $50, the income elasticity of demand is equal to 1.40±0.05
At $35, it is 2.33± 0.05
At $20, it is 3.00± 0.05

Thus, the required statement is given as the data belong to the normal good.

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Answer: (a) only

Step-by-step explanation:

For there to be inverse proportion, the product of x and y must be constant.