Find the missing length. The triangles are similar.

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

9514 1404 393

Answer:

Step-by-step explanation:

Let b represent the length of the base. Then (b+4) is the height and the area of the triangle is ...

  A = 1/2bh

  70 = 1/2(b)(b+4)

  b² +4b -140 = 0 . . . . . multiply by 2, put in standard form

  (b +14)(b -10) = 0 . . . . factor

  b = 10 . . . . the positive solution

The base of the triangle is 10 yards; the height is 14 yards.

Answer:

2 2/3

Step-by-step explanation:

hope this helps :)

don't be afraid to ask questions

Answer:

$480

Step-by-step explanation:

Let original price be x

{Original price - discount amount = sale price}

So, x - (x * 35/100) = 312

x - 35x/100 = 312

100x - 35x / 100 = 312

65x/100 = 312

65x = 31200

x = 31200/65

x = $480

So I think the original price of desk was $480

The original price of the desk is $480.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a desk is being sold for $312.

Let the original price of the desk be x.

Here, x-35% of x =312

x- 35/100 ×x=312

x-0.35x=312

0.65x=312

x=312/0.65

x=480

Therefore, the original price of the desk is $480.

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Answer:

(42% ; 48%)

We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%

Step-by-step explanation:

The confidence interval is used to estimate the range of values for which the population value may lie at a certain level of confidence.

Given that :

Phat = 45%

Margin of error = ±3%

The confidence interval is defined as :

C. I = Phat ± margin of error

C. I = 45% ± 3%

Lower boundary :

45% - 3% = 42%

Upper boundary :

45% + 3% = 48%

C.I = (42% ; 48%)

We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%

Answer: -21/2

Concept:

Usually, when doing mathematics operation, it goes by the PEMDAS order:

However, since the question asks to solve the order of operation from left to right, then we would be doing [addition] --> [Divison]

Solve:

Given

(-5/2) + 3/4 ÷ 1/6

Operate with addition

=(-10/4) + 3/4 ÷ 1/6

=(-7/4) ÷ 1/6

Operate with division

=(-7/4) × 6/1

=-42 / 4

=-21 / 2

Hope this helps!! :)

Please let me know if you have any questions

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

Answer:

Carmen:27

Abdul:17

David=34

Step-by-step explanation:

Carmen+Abdul+David = 78

Carmen-Abdul=10

David=2Abdul

Carmen=Abdul+10

Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78

4Abdul=68

Abdul = 68/4=17

Carmen = 17+10=27

David = 2 * 17 = 34

27+17+34=78

Answer:

3

Step-by-step explanation:

2x-xy

2(x)-(x)(y)

2(-1/2)-(-1/2)(8)

-1 - (-4)

-1 + 4

3

Answer:

3

Step-by-step explanation:

2x-xy

Let x = -1/2 and y = 8

2(-1/2) - (-1/2)(8)

Multiply

-1 - (-4)

Subtracting a negative is like adding

-1+4

Add

3

Answer:

Step-by-step explanation:

Total amount = 200 mg + (13 days)×(180 mg)/day = 2620 mg

One 35 mL bottle contains (35 mL)×(10 mg)/mL) = 350 mg of medication.

(2620 mg)×(1 bottle)/(350 mg) ≈ 7.5 bottles

8 bottles are needed.

Answer:

B. The question may not be directly stated.

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The demand equation illustrates the price of an item and how it relates to the demand of the item.

From the question, we have:

[tex]Plates = 300[/tex]

[tex]Price = 20[/tex]

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{25-20}{290-300}[/tex]

[tex]m = \frac{5}{-10}[/tex]

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

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]

Open the brackets to calculate the maximum revenue

[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]

[tex]R(x) =6000 + 1300x - 50x^2[/tex]

Equate to 0

[tex]6000 + 1300x - 50x^2 =0[/tex]

Differentiate with respect to x

[tex]1300 - 100x =0[/tex]

Collect like terms

[tex]100x =1300[/tex]

Divide by 100

[tex]x =13[/tex]

So, the price at maximum revenue is:

[tex]Price= 20 + 5x[/tex]

[tex]Price= 20 + 5 * 13[/tex]

[tex]Price= 85[/tex]

In conclusion:

Read more about demand equations at:

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Answer:

24n^7/m^16

Step-by-step explanation:

Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.

Answer:

should be 192

Step-by-step explanation:

Answer:

45 days

Step-by-step explanation:

Based on the giving information, 30*15/10.

Reduce the fraction by canceling the greatest common factor: 3*15 = 45

9514 1404 393

Answer:

  1/63

Step-by-step explanation:

There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:

  4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63

The larger fraction is 1/63 unit larger than the smaller fraction.

One piece will be length x and the other piece will be 20 cm longer, so it will be x + 20 cm long.  

Added together the length of these two boards will equal 86 cm. So you can write an equation:  

x + (x + 20) = 86  

Remove the parentheses and add the two x's together to get:  

2x + 20 = 86

Subtract 20 from both sides:  

2x = 66  

Divide both sides by 2 and you have:  

x = 33  

The short piece is 33 cm and the other piece is 20 cm longer or 33 + 20 = 53 cm.

Answer:

Answer:

The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8

Step-by-step explanation:

√50 + √98​ ​= √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

The process of copying an angle through construction involve ensuring

that the distance between the two rays forming the angle is the same or

equal in the original and copy of the angle at a given equal distance from

the vertex of both angles

The step where the error occur is step 4. She measured the incorrect length

The reason for the above selection is as follows:

The steps to copy an angle are as follows;

A critical step in the copying process involves the finding the distance

between the initial line and the terminal line EF at a given distance DG =

AE from the angle vertex

The step where the error occur is in step 4. by opening the compass

between points A and E which are points on the same line and placing the

compass at point G on line l to draw an arc intersecting the arc created

from point D at H, thereby making the radial distance between the two lines

forming the angle, in the copied angle at a distance E from the vertex,

equal to AE rather than EF

Therefore, the error occurred in step 4. She measured the incorrect length

Learn more about the steps to copy an angle here:

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Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

2 and 3 are the common factor of 24 and 60

.

.

..

.

.............

Answer:

[tex]13+19=n+25[/tex]

[tex]n+25=13+19[/tex]

Add 13+19= 32

[tex]n+25=32[/tex]

Now Subtract 25 from both sides

[tex]n+25-25=32-25[/tex]

[tex]n=7[/tex]

OAmalOHopeO

Answer:

The probability is 0.51

Step-by-step explanation:

We want to find the of choosing a red card for the second card drawn, given that the first card drawn without replacement, was a club.

Then we need to assume that the first card drawn was a club, so now we have a deck of 51 cards with:

13 hearts

13 diamonds

13 spades

12 clubs.

Now with this deck, the probability of drawing a red card is equal to the quotient between the number of red cards and the total number of cards in the deck.

We have 26 red cards (13 hearts  + 13 diamonds)

And there is a total of 51 cards in the deck, then the probability of drawing a red card now is:

P = 26/51 =0.51

The probability is 0.51

Answer:

the the 3rd one Is the one

Answer:

20 km

Step-by-step explanation:

We can use ratios to solve

1 cm          4 cm

--------  = ------------

5 km          x km

Using cross products

1 * x = 4 * 5

x = 20

20 km

Answer:

1/5 = 4/x

Step-by-step explanation:

Each cm on the map represents 5 km. If it shows 4 cm apart of the map, you can use the proportion 1 cm : 5 km = 4 cm : x km.