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Assume that lines that appear tangent are tangent. Find the value of each variable.

Answer:

The inequality is [tex]0.6x < 12.5[/tex]

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Step-by-step explanation:

14 gallons-1.5 gallons=12.5 gallons  

we know that

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on  

so

Let

x ----> the number of days

[tex]0.6x < 12.5[/tex] ----> inequality that represent the situation

Solve for x

[tex]x < 12.5/0.6[/tex]

[tex]x < 20.8\ days[/tex]

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

An inequality is similar to an equation in that they both describe the relationship between two expressions.

The inequality represents the number of days Diego's father can drive the car without the warning light coming on is [tex]\rm x<20.8[/tex].

Diego's family car holds 14 gallons of fuel.

Each day the car uses 0.6 gallons of fuel.

A warning light comes on when the remaining fuel is 1.5 gallons or less.

An inequality is similar to an equation in that they both describe the relationship between two expressions.

The inequality represents the number of days Diego's father can drive the car without the warning light coming on is,

The remaining fuel is greater than 1.5 gallons Diego's father can drive the car without the warning light coming on.

Here, x represents the number of days.

Therefore,

The inequality represents the number of days Diego's father can drive the car without the warning light coming on is,

[tex]\rm 0.6x<12.5\\\\x < \dfrac{12.5}{0.6}\\\\x<20.8[/tex]

Hence, The inequality represents the number of days Diego's father can drive the car without the warning light coming on is [tex]\rm x<20.8[/tex].

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Answer:

F. (0, 5) and (-4, 2)

Step-by-step explanation:

We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:

F. (0,5) and (-4,2)  As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4.  This is the line with slope 3/4.

Answer:

2.78

Step-by-step explanation:

We are given the expression [tex]x^2-1.78x[/tex]

As we know that x=2.78, we can plug that value into the expression and simplify it

[tex](2.78)^2-1.78(2.78)\\\\7.7284-4.9484\\\\2.78[/tex]

Answer:

See below.

Step-by-step explanation:

The 2 functions have the same output value when x = 7  ( that is what m(x) = p(x) at x = 7 means).

Answer:

C. 3 in x 6 in

Step-by-step explanation:

Jammal cuts the block in a straight line parallel to one side... so the section revealed when he finishes his cut will be identical as the parallel side to which the cut is done.

We know the the left side of the prism on the image is 3 inches wide and 6 inches high... so that will also be the dimensions of the exposed cross section.

The answer is then 3 inches y 6 inches. The thickness of the block (5 inches) has no impact on the exposed area of the cross-section.

Answer:

  x² +y² = 14x

Step-by-step explanation:

Making the usual substitution x = r·cos(θ) and r² = x² +y², we can get there this way:

Substitute cos(θ) = x/r:

  r = 14·x/r

Multiply by r:

  r² = 14x

Substitute for r²:

  x² + y² = 14x

_____

The original equation is shown dotted; the rectangular version is shown as a solid line. The graphs are identical.

x2 + y3 = 14x is the soulution of your answer (sorry for bad grammar)

Answer: $965

Step-by-step explanation:

The used car is priced at $2,695.

If you borrow the money for the car, your payments will be $122 a month for 30 months. This means that the total amount of money that you would have paid at the end of 30 months at a rate of $122 per month is the amount paid per month multiplied by the total number of months. It becomes

Total payment = 122×30 = $3660

This means that you ended up paying higher than you would have paid if you paid cash.

Amount that you would have saved = amount paid over 30 months - cost of the car

Amount that you would have saved

= 3660 - 2695 = $965

By paying cash for the used car priced at $2,695, you will save $965. Option C is correct.

The total amount paid when financing the car can be found by multiplying the monthly payment by the number of months:

Total amount paid when financing = Monthly payment × Number of months

= $122 × 30

= $3,660

To find the savings, we subtract the total amount paid when financing from the total cost of the car when paying cash:

Savings = Total cost of the car when paying cash - Total amount paid when financing

= $2,695 - $3,660

= -$965

Since the result is negative, it means you would actually be paying more when financing the car compared to paying cash.

Absolute value of savings = |- $965|

= $965

Therefore, the correct answer is  $965.

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Answer the answer is c

Step-by-step explanation:

I also got C for this answer

Answer:

100.

Step-by-step explanation:

The percentage of children's watches = 100 - 20 - 40 = 100-60

= 40%.

40% = 0.40 as a decimal fraction.

So the number of children's watches

= 0.40 * 250

= 100.

CCCCCCCCCCCCCCCCCCCCCC

Answer:

The correct answer is option "C"

"The interquartile range increases"

The value of the (RIC) will increase from 4 to 5.75, that is, 44%

Step-by-step explanation:

The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin

The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.

Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%

The answer is C: Three real zeros and 2 imaginary zeros

Answer:  C) 3 real zeros & 2 imaginary zeros

Step-by-step explanation:

Since the function has a degree of 5, then there must be 5 zeros.  

If each of the 3 given zeros crosses the x- axis (which is what happens when it has an odd-numbered multiplicity), then there are 2 zeros missing.

The missing zeros are imaginary.

(3 zeroes × multiplicity of 1) + (2 imaginary)

                  3                         +          2           = 5  [tex]\large\checkmark[/tex]

Answer:

A. -25° 29' 24"

Step-by-step explanation:

It is easier to talk about this by considering the magnitude of the angle, then applying the sign to the result.

The fractional part, 0.49°, can be multiplied by 60' per degree to get the number of minutes:

0.49° × 60'/1° = 29.4'

The fractional part of this, 0.4', can be multiplied by 60" per minute to get the number of seconds:

0.4' × 60"/1' = 24"

Then the angle is ...

-25.49° = -25° 29' 24"

_____

Alternate solution

You can recognize this is 0.01° less than 25° 30', so is ...

0.01° × 60' = 0.6' = 0.6 × 60" = 36"

When 36" is subtracted from 25.5° = 25° 30', the result is 25° 29' 24". Of course, your angle is negative: -25° 29' 24".

_____

Comment on base-60 arithmetic

In base-10 arithmetic, when you borrow 1 from the next higher place in the number, you are borrowing ten of the current place. For example, when you are doing arithmetic with hundreds, and you borrow 1 from the thousands place, you have effectively borrowed 10 hundreds.

In base-60 arithmetic, when you borrow one from the next higher place, you borrow 60 of the current unit. That is, borrowing one minute gives you 60 seconds. Thus, 30 minutes is the same as 29 minutes and 60 seconds. Subtracting 36 seconds from this value gives 29 minutes and 24 seconds.

The term "borrowing" was used when I learned arithmetic. More recently, I've seen it called "rewriting" the number. I also think of it as "making change": changing a higher unit to an equivalent number of smaller units.

The calculated area of the triangle is 18 square units

How to calculate the area of the triangle in square units?

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

(–2, –1), (4, –1), (6, 5)

The area of the triangle in square units is calculated as

Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|

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

Area = 1/2 * |-2 * -1 - 4 * -1 + 4 * 5 - 6 * -1 + 6 * -1 - 5 * -2|

Evaluate the sum and the difference of products

Area = 1/2 * 36

So, we have

Area = 18

Hence, the area is 18 square units

They left the park at 3:05

Answer:

I think it's the last one, BD/AE

Step-by-step explanation:

Answer:

Option C. w=5×15

Step-by-step explanation:

Let

w ----> the amount of dollars to buy 5 tickets

we know that

The variable w is equal to multiply the numbers of tickets by the cost of each ticket

so

The equation that represent this situation is

w=5(15)

Answer:

Thus, the required equation is W=15×5

Step-by-step explanation:

Consider the provided information.

Gina wants to go to the water park with her friends. They have a total of w dollars.

W represents the total money they have.

They buy 5 tickets and each ticket cost 15 dollars.

Thus the total cost for 5 tickets is:

15×5

She had W dollars. That means the above expression is equal to W.

W=15×5

Thus, the required equation is W=15×5.

Answer:

Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.

Step-by-step explanation:

The result of subtracting two or more numbers in mathematics is called the difference. In vector subtraction, this applies as we add the first vector to negative of the vector that needs to be subtracted, resulting in a difference vector. This is equivalent to subtracting scalar values.

In mathematics, the result of subtracting two or more numbers is known as the difference. This concept also applies to vectors in a process called Vector Subtraction.

For instance, if we have two vectors A and B, and we wish to subtract B from A (usually written as A - B), we do so by adding the first vector, A, to the negative (-) of the second vector, B (written as A + (-B)). Here, -B (negative B) represents the same vector as B but in the opposite direction. The subtraction of A and B results in a difference vector, D, i.e., D = A - B.

The same principle is true for ordinary numbers. Take the numbers 5 and 2 for example. If we subtract 2 from 5 (5 - 2), it's equivalent to adding 5 and -2 (5 + (-2)). Here, the difference is 3.

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Answer:

5 seconds

Step-by-step explanation:

In order to find the time when it landed, we will have to find the x-intercepts.

Equation given to us : -16t² + 48t + 160

Let's take the GCD, which is -16.

-16( t² - 3t - 10 )

Factoring what's inside the brackets, we get the x-intercepts.

What multiples to -10 but adds up to -3? The numbers are -5 and 2

-16 ( t - 5 ) ( t - 2 )

X-intercepts are t - 5 and t - 2

Which is 5 and 2 seconds. But one of this is an extraneous solution and that is 2.

If we substitute the value of 2 in the equation, we will not get 0.

During the x-intercept, the x has a value and y is 0. If we substitute 5 ans x. we will get y as 0.

Hence, the answer is 5 seconds.

Answer:

4:The denominator can't be equal to 0, therefore -  5

5: 4)The denominator can't equal to 0 -4

Answer:

Question 4:

(x² - 25) / (x - 5)

= (x² - 5²) / (x - 5)

= [(x - 5) · (x + 5)] / (x - 5)

= x + 5

The denominator can't be equal to 0, therefore:

x - 5 ≠ 0 ⇔ x ≠ 5

Question 5:

(3x² - 6x) / (x² - 2x - 8)

= [3x (x - 2)] / (x² + 4x - 2x - 8)

= [3x (x - 2)] / [x (x + 4) - 2 (x + 4)]

= [3x (x - 2)] / [(x - 2) (x + 4)]

= 3x / (x + 4)

The denominator can't equal to 0, therefore:

x + 4 ≠ 0 ⇔ x ≠ -4

Answer:

660

Step-by-step explanation:

Because the ration is 1:5, then 132 chaperones times 5 is 660 students. Please like me and rate!!

Answer:

[tex](-\frac{3}{8},2)[/tex]

Step-by-step explanation:

Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y.  That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8).  Our k value is 5/8.  Now we will find the rise and run values which is the slope of this line segment:

[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]

Coordinates are found in this formula:

[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]

Filling that in:

[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]

which simplifies to

[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]

which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]

Answer:

[tex]y=0.2x+3[/tex]

Step-by-step explanation:

Let

x ----> the number of stickers

y ----> the price of the boxes

we have the points

[tex]A(15,6),B(25,8)[/tex]

Find the slope

[tex]m=(8-6)/(25-15)[/tex]

[tex]m=2/10=0.20[/tex]

Find the equation of the line into point slope form

The equation is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute the value of m and the point A

[tex]y-6=0.2(x-15)[/tex]

[tex]y=0.2x-3+6[/tex]

[tex]y=0.2x+3[/tex] ----> linear equation that represent the situation

Answer:

51

Step-by-step explanation:

Given

P(x) = 2x³ + 4x² - 10x - 9, then

P(a) = 2a³ + 4a² - 10a - 9 ← substitute x = a into P(x)

To evaluate P(3) substitute a = 3 into P(a)

P(3) = 2(3)³ + 4(3)² - 10(3) - 9 = 54 + 36 - 30 - 9 = 51

Since P(3) ≠ 0 then (x + 3) is not a factor of P(x)

Answer:

51

Step-by-step explanation:

2(3)³ + 4(3)² - 10(3) - 9

= 51

Answer:

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3

Step-by-step explanation:

The expansion of the given (4x – 2)(2x 2 + 3) is

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.

We have given that the (4x – 2)(2x 2 + 3)

We have to determine the expansion of the(4x – 2)(2x 2 + 3)

the act of expanding or the state of being expanded · something expanded; an expanded surface or part · the degree, extent, or amount by which something expands.

Therefore the expansion is given by

[tex](4x -2)(2x^ 2 + 3)=4x*2x^2+4x*3+(-2)*2x^2+(-2)*3[/tex]

Therefore we get the expansion of the given (4x – 2)(2x 2 + 3) is

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.

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Answer:

65/4 cm³, or 16.25 cm³

Step-by-step explanation:

Here, Volume V = (length)(width)(height).  Those measurements are included here:

V = (1  1/4 cm)(4 cm)(3  1/4 cm), or

V  = (5/4 cm)(4 cm)(13/4 cm)

V  =    (5 cm²(13/4 cm) = 65/4 cm³, or 16.25 cm³

Answer A becaus descriminant =16-4*3*2=-8

ANSWER

A. There are two complex roots.

EXPLANATION

The given quadratic equation is

[tex]3x^2+4x+2=0[/tex]

when we compare this to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=3,b=4 and c=2.

We use the discriminant to determine the nature of roots.

[tex]D= {b}^{2} -4ac [/tex]

[tex]D= {4}^{2} -4(3)(2) [/tex]

[tex]D= 16-24[/tex]

[tex]D= - 8[/tex]

Since the discriminant is less than zero, the equation will have 2 complex roots.

(3√-3)(3√-5)  multiply 3 and 3, and multiply √-3 and √-5 together, the √ stays

9√15   Your answer is A

Answer:

The correct answer is option A.  9 √15

Step-by-step explanation:

It is given that, 3√-3 and 3 √-5

To find the product

we have, 3√-3 and 3 √-5

(3√-3) * (3 √-5) = 3√-3 * 3 √-5

 = (3 * 3) (√-3 * √-5)

 = 9 * √(-3 * -5)

 = 9* √15

 = 9√15

Therefore the correct answer is option A.  9√15

Answer:

  151.4496 cm²

Step-by-step explanation:

The area of a trapezoid is found using the formula ...

  A = (1/2)(b1 +b2)h

where b1 and b2 are the lengths of the parallel bases and h is the distance between them. Fill in the numbers and do the arithmetic.

  A = (1/2)(22.2 cm + 8.52 cm)(9.86 cm) = 151.4496 cm²

Answer:

B

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

To obtain this form use the method of completing the square

Given

x² - 8x + y² - 2y - 8 = 0 ( add 8 to both sides )

x² - 8x + y² - 2y = 8

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 8 + 16 + 1

(x - 4)² + (y - 1)² = 25 → B

Final answer:

The standard form of the given circle equation is (x - 4)^2 + (y - 1)^2 = 25, which is option (B).

Explanation:

To rewrite the given equation of a circle in standard form, we need to complete the square for both x and y terms. The equation is given as:

x² − 8x + y² - 2y - 8 = 0

We organize the equation by grouping x and y terms:

(x² − 8x) + (y ² - 2y ) = 8

To complete the square, we add to each side (½ the coefficient of x) ² for the x-terms and (½ the coefficient of y) ² for the y-terms:

For the x terms: (½ × -8)² = (-4)² = 16. Add 16 to both sides.

For the y terms: (½ × -2)² = (-1)² = 1. Add 1 to both sides.

Our equation becomes:

(x² − 8x + 16) + (y² - 2y + 1) = 8 + 16 + 1

Which simplifies to:

(x - 4)² + (y - 1)² = 25

Therefore, the standard form of the given equation is (x - 4)² + (y - 1)² = 25, and the correct answer from the options is (B).

I used 3,14 for pi since it was only way it made sense based on the answers.

The question probably provided you with this.

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The probability that a point picked at random in the square is in the shaded region will be 86/314. Thus option C is correct.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given:

A circle with a diameter of 20 m is inscribed in a square .

Thus side of square = 20 m

Now, area of square = 20 x 20

                                   = 400 sq m

The radius of circle = 10 m

Area of circle

[tex]A = \pi r^2\\\\A = 3.14 \times 10^2\\\\A = 314 m^2[/tex]

Now, Area of shaded region = Area of the square - an area of circle

Area of shaded region = 400 - 314

                                      = 86

The probability that a point picked at random in the square is in the shaded region will be 86/314. Thus option C is correct.

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