7x+23+21x-11=180 how do you set up the equation right?

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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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

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:

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 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:

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 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.

Answer:

14 feet below. the deck.

Step-by-step explanation:

That would be (20 + 78 - 85 +103 - 110 )  feet above the ground

= 6 feet above the ground.

That is 20 - 6 = 14 feet below the deck.

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 the answer is c

Step-by-step explanation:

I also got C for this answer

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).

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:

50.8%

Step-by-step explanation:

That is the one my friend and I chose. It is 31/61 when all the stuff is added together and that is put to 50.8 as a percentage..

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.

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.

If you have any more questions do not hesitate :)

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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The greatest common factor of 8m^3 and 6m^4 is 2m^3. This is found by determining the highest number or term that can divide both terms exactly, considering both the coefficients and the power of the variable.

The question asks for the greatest common factor of the terms 8m3 and 6m4. The greatest common factor (GCF) is the highest number or term that divides both numbers exactly. Ignoring the coefficients (8 and 6), we can easily see that these terms both contain the variable 'm', raised to the powers 3 and 4, respectively.

The rule for dealing with variables when finding the GCF is to take the variable to the power which is the lesser of the two. In this case, that would be m3. Now, looking at the coefficients (8 and 6), the highest number that can divide them both exactly is 2. Therefore, the greatest common factor of 8m3 and 6m4 is 2m3.

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The greatest common factor of 8m³ and 6m⁴ is 2m³, which is found by identifying the shared prime factors and the lowest power of 'm' present in both terms.

To find the greatest common factor (GCF) of 8m³ and 6m³, we need to find the highest power of each prime number and the variable that is contained in both terms. The prime factorization of 8 is 23, and for 6, it is 2 × 3. Since both have at least one factor of 2, we'll use that in our GCF. Additionally, since the lowest power of 'm' that appears in both terms is m3, we will also use that.

The GCF is the product of these shared factors. So, we have:

2 (the common prime factor)

m3 (the lowest power of 'm' in both terms)

Therefore, the GCF of 8m³ and 6m⁴ is 2m³.

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.

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:

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:

  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:

[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:

Choice A is the correct answer

Step-by-step explanation:

[tex]2x\sqrt{2x}[/tex]

Find the attachment below for the explanation

For this case we must indicate an expression equivalent to:

[tex]\sqrt {18x ^ 3} - \sqrt {9x ^ 3} +3 \sqrt {x ^ 3} - \sqrt {2x ^ 3}[/tex]

So, rewriting the terms within the roots we have:

[tex]18x ^ 3 = (3x) ^ 2 * (2x)\\9x ^ 3 = (3x) ^ 2 * (x)\\x ^ 3 = x ^ 2 * x\\2x ^ 3 = (2x) * x ^ 2[/tex]

So:

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

Removing the terms of the radical:

[tex]3x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} -x \sqrt {2x} =[/tex]

We simplify adding terms:

[tex]3x \sqrt {2x} -x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} =\\2x \sqrt {2x} + 0 =\\2x \sqrt {2x}[/tex]

Answer:

Option A

Answer:

270

Step-by-step explanation:

The mean is 228 and the standard deviation is 18.

2.3 standard deviations above the mean is:

228 + 2.3×18

228 + 41.4

269.4

Since scores are usually integers, we round up to 270.

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: $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:

  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:

A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.

Step-by-step explanation:

The answer choice speaks for itself.

The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.

The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.

Clearly, the given leg lengths match the second set of ratios more closely:

10 : 17.32 : 20 ≈ 1 : √3 : 2.

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%

Answer:

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

Step-by-step explanation:

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.