Solve the following system by substitution. m+n=5 and 5m+5n=25. Solve.​

Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x+5}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 4x+2y=1.\ \text{Convert to the slope-intercept form y = mx + b:}\\\\4x+2y=1\qquad\text{subtract 4x from both sides}\\\\2y=-4x+1\qquad\text{divide both sides by 2}\\\\y=-2x+\dfrac{1}{2}\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{2}x+b.\\\\\text{The line passes through }(-4,\ 3).[/tex]

[tex]\text{Put the coordinates of the point to the equation.}\ x=-4,\ y=3:\\\\3=\dfrac{1}{2}(-4)+b\\\\3=-2+b\qquad\text{add 2 to both sides}\\\\b=5[/tex]

Answer:

Dividing mixed numbers is very similar to multiplying mixed numbers. You just add one step—after changing the divisor into an improper fraction, you then find its reciprocal and multiply. ... First step: Write the whole number and the mixed number as improper fractions.

Step-by-step explanation:

Dividing mixed numbers is essentially similar to dividing whole numbers, with an extra step of converting mixed numbers into improper fractions. The core concepts remain the same but it extends division into fractions.

Dividing mixed numbers is related to dividing whole numbers because the fundamental concepts remain the same. In dividing whole numbers, we take a number (dividend) and distribute it into equal parts. For instance, dividing 6 by 2, we are distributing 6 into 2 equal parts, which will give us 3 in each part.

Similarly, when dividing mixed numbers, we proceed in the same manner. However, it adds an extra step of converting mixed numbers into improper fractions first before proceeding with the division. For example, when dividing 2 1/2 by 1 1/2, we would first convert these into improper fractions and then proceed with the division as we would do with whole numbers.

Therefore, the concept for dividing mixed numbers is essentially an extension of the concept for dividing whole numbers.

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Answer nica  me ayudan a mi pliss...oh mana nose

Step-by-step explanation:

Answer:

33/56 inches

Step-by-step explanation:

2.75(3/14)=33/56

Answer:

[tex] 8\frac { 1 5 } { 1 6 } [/tex] inches or 8.94 inches

Step-by-step explanation:

We know that the current height of the photo is [tex]3\frac{1}{4}[/tex] inches and the customer wants it to be enlarged by a factor of [tex]2\frac{3}{4}[/tex] its current height.

[tex]  3\frac { 1 } { 4 } = 3.25 [/tex]

[tex] 2 \frac { 3 } { 4 } = 2.75 [/tex]

Multiplying this scale factor with the current height of photo to find the enlarged height.

Enlarged height = [tex]3.25 \times 2.75 = 8\frac{15}{16}[/tex] inches or 8.94 inches

ANSWER

E.

[tex]y = 2 \sin( \theta) - 3[/tex]

EXPLANATION

The parent function

[tex]y = \sin( \theta) [/tex]

can be shifted down by 3 units to obtain

[tex]y = \sin( \theta) - 3[/tex]

Also, when the basic sine function is stretched vertically by a factor of 2, the equation becomes,

[tex]y = 2 \sin( \theta) [/tex]

Therefore, a vertical shift down 3 units and stretch factor of 2 gives the equation:

[tex]y = 2\sin( \theta) - 3[/tex]

The correct choice is E.

Answer: no

Step-by-step explanation:

Because of the angles

This is an incomplete question.

Answer:

Step-by-step explanation:

This is incomplete

Answer:

50%

Step-by-step explanation

Each quartile of a box plot contains 25% of the data.

45-48 minutes is 25%

48-53 minutes is 25%

53-56 minutes is 25%

56-64 minutes is 25%

The questions asks for the percentage from 48-56.

48-53 is 25% and 53-56 is 25%. If you add 25% + 25%, you get 50%

Therefore, the percentage of village women who took 48-56 minutes to collect one container of water if 50%.

Hope this helps!

Answer:

the correct option is option c.

Step-by-step explanation:

We have the expression: (160*243)^1/5

First, we know that 160 = 5(2^5)

And, 243 = 3^5

Then we have: (160*243)^1/5 = [5(2^5)(3^5)]^1/5 = 6(5)^1/5

So the correct option is option c.

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=81\pi \end{cases}\implies 81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies \boxed{9=r}~\hspace{10em}\stackrel{\textit{diameter = twice the radius}}{18}[/tex]

[tex]

A=81\pi \\

A=\pi r^2 \\

81\pi=\pi r^2\Longrightarrow r^2=81

radius=\sqrt{81}=\boxed{9} \\

diameter=2radius = 2\cdot9=\boxed{18}

[/tex]

Measure of an angle is usually in degrees or radians. The measure of angle M is [tex]36^\circ[/tex]. Thus, [tex]m\angle M = 36^\circ[/tex]

It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex].

Suppose that two angles are given as [tex]a^\circ[/tex] and [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]

Then, by the aforesaid theorem, we get:

[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]

For the given case, we have:

[tex]m\angle S = 84^circ\\\\m\angle A = 60^\circ\\\\m\angle M = x^\circ \text{ (say)}[/tex]

Thus,

[tex]x^\circ = 180^\circ - (60+84)^\circ\\\\x^\circ = 36^\circ[/tex]

Thus,

The measure of angle M is [tex]36^\circ[/tex]. Thus, [tex]m\angle M = 36^\circ[/tex]

Learn more about triangle's angles here:

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Answer: FIRST OPTION.

Step-by-step explanation:

To know which is the solution set given the inequality [tex]3x < -6[/tex] you need to solve for the variable "x".

You must divide both sides by 3:

[tex]3x < -6\\\\\frac{3x}{3}=\frac{-6}{3}[/tex]

Therefore, you get:

[tex]x<-2[/tex]

Then, the solution set is the following:

{[tex]x | x < -2[/tex]}

You can observe that this solution set matches with the first option.

Answer: First option

Step-by-step explanation:

For this case we must solve the following inequality:

[tex]- \frac {t} {5}> 15[/tex]

We follow the steps below:

We multiply by 5 on both sides of the inequality:

[tex]-t> 15 * 5\\-t> 75[/tex]

We multiply by -1 on both sides of the inequality. We must bear in mind, that when multiplying by -1, the sense of the inequality changes.

[tex]t <-75[/tex]

Answer:

Option A

Answer:

C(x) = 2

Step-by-step explanation:

The graph of the average cost is shown in the attached image.

Note that, as is to be expected, when the number of booklets produced x increases, then the average cost per booklet decreases.

To calculate the expected cost of producing a booklet when x is very large, look at the graph.

Note that when x = 2 then the average cost is equal to 4, then when x = 5 the average cost is 2.5.

In this way, the bigger x is made, the more the cost approaches 2.

Therefore it can be said that

[tex]\lim_{x \to \infty}C(x)= 2[/tex]

Finally, the expected average cost when the number of booklet  produced is very large is C (x) = 2

Answer:

[tex]13C10 =286[/tex]

Step-by-step explanation:

To solve this problem we must use the formula of combinations.

[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]

Where n is the number of players that there are and elect r of them

In this case there are [tex]7 + 6 = 13[/tex] players and you choose 10 of them

Then we look for  13C10

[tex]13C10 =\frac{13!}{10!(13-10)!}[/tex]

[tex]13C10 =\frac{13!}{10!*3!}[/tex]

[tex]13C10 =286[/tex]

There are 286 possible combinations

Answer:

D. Opposite angles are congruent

With option A, we can see that it is clearly wrong, in a parallelogram, only the opposite sides are congruent, if all of the sides are congruent then the shape is more likely to be a square or a rhombus.

With option B, only the opposites angles are congruent. If all four angles are congruent, that will be more likely to be true when we consider a square or a rectangle.

With option C, it is also wrong, unless the shape is a rhombus, square or rectangle.

That leaves us with the last option which is D.

Answer:

Option A, The pen cost less than $0.35.

Step-by-step explanation:

The given inequality is d ∠ 0.35

Now we have to define this inequality with the help of given options.

If d represents the cost of pen, then cost of pen should be less than 0.35.

Option A, The pen cost less than $0.35. is the answer.

Answer:

A

Step-by-step explanation:

Answer is

(-16 , 14)

Answer:

-16, 14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Percent decrease =

(difference in prices)/(original price) × 100

(2.89 - 2.82)/2.89 × 100

= (0.07)/2.89 ×100 ≈ 2.4%

The price of unleaded gas has increased by 2.2% from yesterday to today. This percentage was calculated by finding the price increase ($0.06), dividing it by yesterday’s price ($2.79), and multiplying by 100. The result was then rounded to the nearest tenth of a percent.

To find the percentage increase in the price of a gallon of unleaded gas, you first need to find the difference in the price. In this case, today's price is $2.85 and yesterday's price was $2.79, so the difference is $2.85 - $2.79 = $0.06.

Then, to find the percentage increase, you divide this difference by the original price (which is yesterday's price) and multiply by 100 to turn it into a percentage. So, percentage increase = ($0.06 / $2.79) * 100 = 2.15053.

Finally, you round this to the nearest tenth of a percent, which gives you 2.2%. So, the price of unleaded gas has increased by 2.2% from yesterday to today.

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Answer:the answer is 10 min hope this helped:)

Step-by-step explanation:

the answer is 6 minutes

Answer:

[tex]\large\boxed{\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x^2}{4}-\dfrac{y^2}{4}=\dfrac{x^2}{2^2}-\dfrac{y^2}{2^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x}{2}\right)^2-\left(\dfrac{y}{2}\right)^2\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}[/tex]

For this case we must find the unit cost of juice box of each option and compare:

Option A: 2 juice boxes for $ 0.66

[tex]\frac {0.66} {2} = 0.33 \frac {dollars} {box}[/tex]

Option B: 6 juice boxes for $ 1.92

[tex]\frac {1.92} {6} = 0.32 \frac {dollars} {box}[/tex]

Option C: 9 juice boxes for $ 2.97

[tex]\frac {2.97} {9} = 0.33 \frac {dollars} {box}[/tex]

Option D: 12 juice boxes for $ 4.20

[tex]\frac {4.20} {12} = 0.35 \frac {dollars} {box}[/tex]

The most feasible option is B. That is, buy 6 boxes for $1.92

Answer:

Option B

Answer: Option A: 2 juice boxes for $ 0.66Option B: 6 juice boxes for $ 1.92Option C: 9 juice boxes for $ 2.97Option D: 12 juice boxes for $ 4.20The most feasible option is B. That is, buy 6 boxes for $1.92

Step-by-step explanation:

Answer:

volume = 3.5 m * 4.5 m * 2 m

Step-by-step explanation:

The volume of a rectangular prism is

volume = length * width * height

volume = 3.5 m * 4.5 m * 2 m

The total space bought for the two ads in the newspaper is 3/4 of a page. This is determined by adding the fractions representing the size of each ad together: 5/8 + 1/8 = 6/8, which simplifies to 3/4.

You are dealing with fractions in this mathematics problem. If you bought two ads, one taking 5/8 of a page and the other taking 1/8 of a page, you need to add these fractions together to find out how much space you bought for ads overall.

Adding the fractions 5/8 and 1/8 would give you:

5/8 + 1/8 = 6/8

The fraction 6/8 can be simplified further by dividing both numbers by their greatest common divisor (which is 2), resulting in:

6/8 = 3/4

Therefore, the ads took up 3/4 of a page in total.

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you bought a total of 3/4 of a page for ads.

To calculate the total space bought for ads in a newspaper, simply add the proportions of the page that each ad takes up. The first ad covers 5/8 of a page, while the second ad occupies 1/8 of a page. Adding these together:

5/8 + 1/8 of a page

This can be calculated by adding the numerators and keeping the denominator the same since both fractions have the same denominator.

Add the numerators: 5 + 1 = 6

Keep the denominator the same: 8

Combine them to get the new fraction: 6/8 of a page

However, notice that 6/8 can be simplified to 3/4, because both the numerator and the denominator can be divided by 2.

Therefore, you bought a total of 3/4 of a page for ads.

[tex]\bf 3^{4x}=27^{x-3}\implies 3^{4x}=(3^3)^{x-3}\stackrel{~\hfill \textit{same base, the exponents must also be the same}}{\implies 3^{4x}=3^{3(x-3)}\implies 3^{4x}=3^{3x-9}\qquad } \\\\\\ 4x=3x-9\implies x=-9[/tex]

For the six numbers in the cube, we have.

So, only two of the numbers in the cube are composite. This means that you have a chance of

[tex]\dfrac{2}{6}=\dfrac{1}{3}[/tex] of rolling one of them.

Answer:

So,  the experimental probability of tossing heads using lynn and dawn's results is 2/5

Step-by-step explanation:

No of times the coin is tossed = 30

No of times head came = 12

Probability of tossing heads = No of times head came / No of times the coin is tossed

                                              = 12/30

                                              = 4/10

                                              = 2/5

So,  the experimental probability of tossing heads using lynn and dawn's results is 2/5

B, because a rational number is a number that goes on forever. Ex : pi

Answer:

Step-by-step explanation:

(jk^-2/j^-1k^-3)^3

(-2)(-1)^-2

-------------               ^3

(-2)^-1(-1)^-3

switch negative exponenst to other side

(-2)(-2)(-1)^3

__________

(-1)^2

4(-1)

-----

1

= -4

REMEMBER all to the 3rd power!

(-4)^3

-64

Answer

B is the answer to this question

Answer:

D=2162 or answer B

Step-by-step explanation:

1.) C=Dpi

2.)6790=D pi

3.)6790/pi = D pi/pi

4.) D= 2161.32412719

5.) D=2162