8. The smaller of two numbers is five less than half the larger number. Their sum is 13. Find the numbers,​

The line should be perpendicular to x = -4

x= -4 is a vertical line crossing the x axis at x= -4

The slope is undefined in x =-4

For an equation in slope intercept form, the general form is ;

y= mx + b where m is the slope and b is the y-intercept

So for any y value, x is always -4

Thus the slope for line x = -4 is not defined

A line perpendicular to x = -4 will thus be a horizontal line with slope 0

For the equation of this line

0= y--5/x-4

0 = y+5 /x-4

0{x-4} = y +5

0 = y+5

y= - 5

The equation is = because 1 makes a denominator equal zero and is a solution of the equation derived from cross multiplying. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.

An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.

We have to open the equation by using cross multiplication

10(3x - 3) = 15(x² - 1)

= 30x - 30 = 15x² - 15

we would have to factorize

30(x-1) = 15(x-1)(x+1)

We have to divide by 15(x-1)

2 = x + 1

take the like terms

2 -1 = x

x = 1

Hence the equation that has the extraneous solution is option a because the solution is 1.

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We can define the percent error as the difference between the estimated value and the actual value, divided by the actual value.

In this case, the estimated value (what Jimmy thought he had purchased) is 7 and the actual value is 6.

Then, the percent error is:

The percent error is 16%.

Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769

Proportion means a share from total set being discussed.

Data from the given case:

- The assembly has 769 team members.

- The assembly has 353 stations

- At each station, there are 2 shifts operations.

Assuming that 1 person is assigned to 1 shift operation, then there will:

353 x 2 = 706 person assigned.

The remaining team members that not assigned is:

769 - 706 = 63 person.

Therefore, the share or the proportion of unassigned team members is:

63/769

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Answer:

First answer is obtuse

The second answer is scalene

Step-by-step explanation:

Obtuse is when an angle is over 90

Scalene since all the angles are different, all the side lengths are different.

An inscribed circle is the largest circle contained in the polygon (triangle):

• Bisects two angles of the triangle.

• The angle bisector will intersect at the intercenter.

Procedure

To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.

Answer: the Equation is y-3=0.4(x-1) or y-5=0.4(x-6).

Step-by-step explanation: I hope this helps.

Answer:

-44.09

Step-by-step explanation:

Trust bro i am passing collage math at 15

Answer:2 is the scale factor

Step-by-step explanation:

The height of plant will be 7.56cm tall after 2 weeks

The original height of the plant is 6.2cm

The height increases by 11% each week

= 11/100

= 0.11

The increase of the plant in a week

= 0.11 × 6.2

= 0.682

The height of the plant after two weeks can be calculated as follows

= 0.682 + 0.682

= 1.364

= 6.2 + 1.364

= 7.56

Hence the height of the plant after 2 weeks is 7.56cm

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Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).

What does the triangle's angle relationship mean?

Angles and sides in relation to one another The biggest side and angle in any triangle are in opposition to one another. The smallest side and angle in every triangle are on opposing sides. The middle side and middle angle are always in opposition to one another in triangles.

A congruent triangle ,

if all of two triangles' sides match, then they are said to be congruent.

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Answer:

0.14 meters, or 140 mm

Step-by-step explanation:

(1/40) means that the model car will have dimensions that are (1/40) the original car.

Real car = 5.5 meters.

Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm

The angle x of the triangle is 60 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.

A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.

Therefore, the angle x of the triangle can be found as follows:

x + x + x = 180

3x = 180°

divide both sides of the equation by 3

3x / 3 = 180 / 3

x = 180 / 3

x = 60 degrees.

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Answer:

the person below or above me is the answer. Yeah

Step-by-step explanation:

The center of the hyperbola is (2, -3)

A hyperbola is a curve that is open and that has two branches and it is symmetrical

The equation is given as

(y + 3)²/9 − (x − 2)²/2 = 1

A hyperbola is represented as

(y - k)²/a² − (x − h)²/b² = 1

Where the center of the hyperbola has the coordinates of (h, k)

The values of h and k in the given equation (y + 3)²/9 − (x − 2)²/2 = 1 are

h = 2 and k = -3

This means that:

(h, k) = (2, -3)

So, we have coordinates of the center to be (2, -3)

Hence, the center is (2, -3)

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Based on the package of boondins and the package of rews, the package of rews will have a weight in relation to the package of boondins that is 3.77 ounces

To find how much more that the package of rews weighs over the boondins, deduct the weight of the package of boondins from the weight of a package of rews.

Weight of package of rews = 9.97 ounces

Weight of package of boondins = 6.2 ounces

The difference in the weight of the packages is:

= 9.97 - 6.2

= 3.77 ounces

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The required difference in the package of the bodies and rews is 3.77 ounces.

As per the given in the question,
boudin is 6.2 ounces in weight and rews are 9.97 ounces in weight.

here,
As per observation, rews weighs more than bodies, and the difference between their weights is simply evaluated from the subtraction between the weight. So,
Weigh difference = weigh of rews  - weigh of boodins
Substitute the value in the above equation,
Weigh difference = 9.97 - 6.2 = 3.77.

Thus, the required difference in the package of the bodies and rews is 3.77 ounces.

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The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.

It follows from the task content that the regular train ticket costs, 3.00.

Therefore, the cost for travelling x times with the month is; 3x.

On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;

3x = 18.75

x = 18.75/3

x = 6.25 times.

Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.

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Answer:

y = 3x + 20

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 )

y = 3x + 5 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

to find c substitute (- 8, - 4 ) into the partial equation

- 4 = - 24 + c ⇒ c = - 4 + 24 = 20

y = 3x + 20 ← equation of parallel line

Answer:

Step-by-step explanation: From the given point,

The line is: -8x-4y=0

           viz, 2x+y=0

The required probability is 0.852

Here, n=15

P(X ≤5) = P(X = 1)+...+ P(X = 5)

            = [(¹⁵₀)(0.25)⁰ (1-025)¹⁵⁻⁰ +...(¹⁵₅)(0.25)⁵ (1-0.25)¹⁵⁻⁵]

            = 0.01336+...+0.16515

            = 0.85163

            = 0.852  (Round to 3 decimal place)

Hence, the required probability is 0.852

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Answer:

The answer is |-3|

Step-by-step explanation:

The absolute value of a negative number will always be the same number but positive. Like the absolute value of |-4| will be 4.

   y - 5 = -1 ( x + 3 )  is Equation of a Lin in slope intercept form,.

What is in slope-intercept form?

Slope between the points M(-3, 5) and N(2, 0).

       m = 0 - 5/2 + 3

       m = -5/5  = -1

the equation of   point-slope form

    y - y₁ = m ( x - x₁ )

   y - 5 = -1 ( x - ( -3 ))

   y - 5 = -1 ( x + 3 )

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The money which is expected to spend on new word processors during this year is

The probability distribution is

x:          0            1             2            3

f(x)         [tex]\frac{1}{10}[/tex]           [tex]\frac{3}{10}[/tex]           [tex]\frac{2}{5}[/tex]              [tex]\frac{1}{5}[/tex]

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars

So total money spent in this year is [tex]1200x-50x^2[/tex]          

Then the equation of expenses will be

[tex]\text{Expenses}=E(1200x-50x^2)[/tex]

We can rewrite it as

[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]  

  [tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]   -----------------(1)

Now the mean of the probability distribution is ,

[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]      

The variance of the function is

[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]

        [tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]

        [tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]

        [tex]=\frac{37}{10}[/tex]

        [tex]=3.7[/tex]

On substituting the values in equation (1)

[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]

              [tex]=1200(1.7)-50(3.7)^2[/tex]

              [tex]=2040-684[/tex]

              [tex]=1855[/tex]

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Step-by-step explanation:

you don't a type your question. so if it correct i will be happy to help you

Answer:B

Step-by-step explanation:

Answer:

(C) I and III only.

Step-by-step explanation:

Hello! It's me again! Let's help you with this question too!

Now, let's start understanding what information is given to us.

[tex]a < b < 0[/tex]

This means that, some integer a is lower than some integer b and b is lower than 0. So right out of the gate, both integer a and b are both negative numbers. Here, we can evaluate all 3 possibilities like so:

I. [tex]\frac{a}{b} > 0[/tex]

To start, let's see if this is true. The simplest way is to substitute values into integer a and b to where [tex]a < b < 0[/tex] holds true as well. For this example, we can say [tex]a=-2[/tex] and [tex]b=-1[/tex]. If we evaluate as such, it would be:

[tex]\frac{-2}{-1} > 0[/tex]

[tex]2 > 0[/tex]

From this example, 2 is higher than 0. Meaning this is true. Now, it'll be true for every value due to something called the fraction rule. Fraction rule is simply just stating that, if the numerator and denominator both have a negative sign, they cancel each other out and become a positive fraction. So, we can say I. is true.

II. [tex]-b > -a[/tex]

This is simple to prove, all it's saying is that negative integer b is always going to be higher than negative integer a. Using our same example from I. we can substitute as such and evaluate:

[tex]-(-1) > -(-2)[/tex]

[tex]1 > 2[/tex]

Here, we can see that 1 is not greater than 2 and no matter what numbers you substitute, that will always be the case because you're essentially putting the lowest number first and seeing if it's greater than the lower number. So II. is false.

III. [tex]0 < \frac{b}{a} < 1[/tex]

Now this one is a bit more difficult. However, there isn't much we need to do here. This is saying that 0 is lower than [tex]\frac{b}{a}[/tex] but [tex]\frac{b}{a}[/tex] is lower than 1.  Let's split this into 2 parts.

Part 1: [tex]0 < \frac{b}{a}[/tex]

This isn't the same as I. as the numerator and denominators have switched. Let's use the values we've set back in I. to see if this holds true:

[tex]0 < \frac{-1}{-2}[/tex]

[tex]0 < \frac{1}{2}[/tex]

From here, we find that it is true. And it also holds true that it is less than 1. We can use another set of values to see if this still holds. Let's try [tex]a=-7[/tex] and [tex]b=-3[/tex]:

[tex]0 < \frac{-3}{-7}[/tex]

[tex]0 < \frac{3}{7}[/tex]

As you can see here, using the fraction rule. So long as there is an integer a and b are different (they always will be because of [tex]a < b < 0[/tex]), regardless of what they will be, it will always give us a fraction answer. And a fraction answer will always be lower than 1. Therefore, III. is also true.

So, the answer to this question is C. I and III only

Given:

Required:

To find the quotient and remainder using synthetic division.

Explanation:

Consider

Here the quotient is

And the remainder is

Final Answer:

Quotient :

Remainder : -9.

Assuming that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee, there are b. 1211760 ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors. The committee can be selected in 1,211,760 ways.

Combination formula:

Cn,x is the number of different combinations of x objects from a set of n elements, given by:

Cnₓ= n!÷ x! (n-x!)

In this problem:

2 sophomores from a set of 18.

2 juniors from a set of 12.

3 seniors from a set of 10.

They are independent, so we can just multiply them, thus:

T= C₁₈,₂ × C₁₂,₂× C₁₀,₃ = 18! ÷2!6! × 12!÷ 2!10! × 10!÷ 3!×7! = 1211760

The committee can be selected in 1,211,760 ways.

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Answer:

The three options you would pick is
y2 – 5y = 750
750 – y(y – 5) = 0
(y + 25)(y – 30) = 0

Step-by-step explanation:

Hope this helps! :))

Answer:

We have been given an equation . We are also told that x is greater than 0. We are asked to choose the equation that can be written as our given equation.

Since x is greater than, so we will take positive root on both sides of our given equation as:

Upon looking at our given choices, we can see that option C is same as our answer.

Step-by-step explanation:Therefore, option C is the correct choice.

Answer:2=x

Step-by-step explanation:

x+4=x^2

0+4=x^2

Square root 4 = square root x^2

2=x

Given:

There are given that the number of people who said yes is 191 and who said no is 485.

Explanation:

According to the given question:

The total number of people is:

That means the total outcome is 676.

Now,

The probability that the person is chosen own dog is:

So,

Final answer:

Hence, the correct option is C.

Answer:

191/676.

Step-by-step explanation:

The total number of people asked is 191 + 485

= 676.

So. the required probability

= number of people owning a dog/ total number of people

= 191/676.