Please help this is for math....

Answer:

\(x = 2\)

Step-by-step explanation:

\( - 5(4x - 2) = - 2(3 + 6x) \\ - 20x + 10 = - 6 - 12x \\ 20x - 12x = 10 + 6 \\ 8x = 16 \\ \\ x = \frac{16}{8} \\ \\ x = 2\)

Hey there!

Solve for x :

x = 2 ✅

Distributive property: A(B + C) = AB + AC

-5(4x - 2) = -2(3 + 6x)

>> Distribute the -5 to the 4x and to the -2 :

-5(4x) + (-5)(-2) = -2(3 + 6x)

-20x + 10 = -2(3 + 6x)

>> Distribute the -2 to the 3 and to the 6x :

-20x + 10 = -2(3) + (-2)(6x)

-20x + 10 = -6 - 12x

>> Substract 10 from both sides :

-20x + 10 - 10 = -6 - 12x - 10

-20x = -12x - 16

>> Add 12x to each side :

-20x + 12x = -12x - 16 + 12x

-8x = -16

>> Divide both sides by -8 :

-8x / -8 = -16 / -8

x = 2

▪️Let's verify :

-5(4(2) - 2) ⇔ -5(8 - 2) ⇔ -5(6) ⇔ -30

-2(3 + 6(2)) ⇔ -2(3 + 12) ⇔ -2(15) ⇔ -30

Therefore, your answer is x = 2

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Balloon's altitude = 43.7ft as

change in altitude/500 = tan 5°  

change in altitude = .0875*500

                              =43.7ft

Answer:

127:97:86

Step-by-step explanation:

The yankees won 125 games

The Red Sox won 97 games.

The Mets won 86 games

Therefore the ratio of wins of the Yankees to the red Sox to the Mets can be shown as follows

127:97:86

Answer:

A

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 )

Here m = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute (7, 8) into the partial equation

8 = - 21 + c ⇒ c = 8 + 21 = 29

y = - 3x + 29 → A

Answer:

True.

Step-by-step explanation:

True.

The two smaller segments added together are greater than the longest segment.

Answer:

True

Step-by-step explanation:

The Triangle Inequality Theorem says that the sum of any two sides must be greater than the third side.

a = 6

b = 5

c = 8

a + b

6 + 8 = 14>5

a + c

6 + 5 = 11>8

c + b

8 + 5 = 13>6

Answer:

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Step-by-step explanation:

Since the stew is composed of shrimps and potatoes, then the sum of the weighs of these ingredients must be equal to the weigh of the stew, so we have:

\(shrimp + potato = 5\)

We also know that he bought three times more potatoes than shrimps, therefore:

\(potato = 3*shrimp\)

Using the second equation on the first one, we have:

\(shrimp + 3*shrimp = 5\\4*shrimp = 5\\shrimp = \frac{5}{4} = 1.25\)

\(potato = 3*shrimp = 3*1.25 = 3.75\)

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Answer:

Approximately 16.67 liters concentration of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

Step-by-step explanation:

Let's denote the amount of the 6% solution as x liters and the amount of the 15% solution as y liters. We need to find the values of x and y that satisfy the conditions.

Since we want to make 30 liters of a 10% solution, we can set up the following equations:

Equation 1: x + y = 30 (total volume equation)

Equation 2: (0.06x + 0.15y) / 30 = 0.10 (concentration equation)

From Equation 1, we have x = 30 - y. Substituting this into Equation 2, we get:

(0.06(30 - y) + 0.15y) / 30 = 0.10

Simplifying the equation gives:

(1.8 - 0.06y + 0.15y) / 30 = 0.10

1.8 + 0.09y = 3

0.09y = 1.2

y ≈ 13.33

Substituting y back into Equation 1, we find:

x + 13.33 = 30

x ≈ 16.67

Therefore, approximately 16.67 liters of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

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Answer:

This is gebber gabber but yes

Step-by-step explanation:

LCL for the p-control chart: 0.033

UCL for the p-control chart: 0.287

To calculate the Lower Control Limit (LCL) and Upper Control Limit (UCL) for the p control chart, we need to use the formulas:

LCL = p - 3√(p(1-p)/n)

UCL = p + 3√(p(1-p)/n)

Where p is the overall proportion of defective items, and n is the number of observations in each sample.

First, let's calculate p:

Total defective items = 2 + 5 + 3 + 4 + 1 + 2 + 3 + 6 + 2 + 4 = 32

Total observations = 10 * 20 = 200

p = Total defective items / Total observations = 32 / 200 = 0.16

Next, let's calculate the LCL and UCL:

LCL = 0.16 - 3√(0.16(1-0.16)/20)

UCL = 0.16 + 3√(0.16(1-0.16)/20)

Now we can calculate the values:

LCL = 0.16 - 3√(0.160.84/20) = 0.16 - 0.127 = 0.033

UCL = 0.16 + 3√(0.160.84/20) = 0.16 + 0.127 = 0.287

The LCL for the p-control chart is 0.033 and the UCL is 0.287.

To draw the p chart, you can use the number of defective items (red chocolates) in each sample (s1 to s10) divided by the total observations in each sample (20). Plot these proportions on the y-axis and the sample number (s1 to s10) on the x-axis.

To determine if there are any points out of control, you need to check if any data points fall outside the calculated control limits (LCL and UCL). If any point falls outside these limits, it indicates a potential out-of-control situation.

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Answer:

\(B=-\frac{3}{4}x^6y^4\)

Step-by-step explanation:

One is given the following equation:

\(B=(\frac{-3}{16}x^2y)(4x^4y^3)\)

Multiply each term in one of the parenthesis by its like term in the other. Bear in mind, since all of the operations in this equation are multiplication, one doesn't have to multiply every single term by another in the parenthesis, one only has to multiply like terms to simplify.

\(B=(\frac{-3}{16}x^2y)(4x^4y^3)\)

\(B=(\frac{-3}{16})(4)(x^2)(x^4)(y)(y^3)\)

Simplify further, remember, when multiplying two terms with the same base, one can add their exponents to simplify,

\(B=(\frac{-3}{16})(4)(x^2)(x^4)(y)(y^3)\)

\(B=(\frac{-3*4}{16})(x^2^+^4)(y^1^+^3)\)

\(B=(\frac{-3*4}{16})(x^6)(y^4)\)

Now simplify the fraction, remove like terms found in both the numerator and denominator. Remember, (4) is a factor of both (4) and (16):

\(B=(\frac{-3*4}{16})(x^6)(y^4)\)

\(B=(-\frac{3}{4})(x^6)(y^4)\)

\(B=-\frac{3}{4}x^6y^4\)

9 meters cost P600

Step-by-step explanation:

3×3 = 9

p200×3 =P600

Answer:9

Step-by-step explanation:when an absolute value has a negative it turns to a positive which makes this problem 3x3

Answer:

9

Step-by-step explanation:

3×-3= -9

absolute value of -9 is 9

Answer:

the number of cars is 20

the number of vans is 13

All the ratios 25:5, 10:2, 5:1, and 15:3 are equivalent to each other.

Ratio:

Ratio is referred as the an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Here we have the ratio 25:5 and 10:2 equivalent ratios to 5:1 and 15:3.

Basically, the equivalent ratios are calculated as by either dividing or multiply with some other real numbers in order to simplify it.

First, we have to take the ratio 25: 5,

When we simplify it by dividing the term by 5, then we get, 5:1.

So, the term 25: 5 is equivalent to 5:1.

Similarly, when we take 10:2 and then we simply divide it by 2, then we get 5:1.

So, both ratio are equivalent one with 5:1. But not associated with the other ratio 15:3.

But when we simplify 15:3 by dividing it using 3, then we get 5:1.

Therefore, all the ratios 25:5, 10:2, 5:1, and 15:3 are equivalent to each other.

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Answer:

6x-5y-40 = 0

Step-by-step explanation:

y-(-2)=6/5(x-5)

5(y+2)= 6(x-5)

5y+10 =6x-30

6x-5y-40 = 0

6x-5y-40 = 0 is the answer

Answer:

Taxi Cost = $47.78

Step-by-step explanation:

Taxi Cost = Cost of the ride + (Cost of the ride × sale tax %)        5% = .05 as a

                                                                                                          decimal

Taxi Cost = $45.50 + (45.50 × .05)

 Taxi Cost = $45.50 + $2.275)

  Taxi Cost = $47.775

   Taxi Cost = $47.78

Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins to solve the equation for h but runs out of time. Her partial work is shown below:

p = 4l + 4w + 4h

2. StartFraction p Over 4 EndFraction equals StartFraction 4 l plus 4 w plus 4 h Over 4.

3. StartFraction p Over 4 EndFraction equals l plus w plus h. = l + w + h

h = 4. h equals StartFraction p Over 4 EndFraction minus blank. –

Which expression should follow the subtraction in Hallie’s equation?

(l + w)

(l – w)

left-parenthesis StartFraction l plus w Over 4 right-parenthesis.

left-parenthesis StartFraction l plus w Over 4 EndFraction right-parenthesis.

The expression (w + h) + p/4 should follow the subtraction if Hallie's equation is

p = 4l + 4w + 4h

p/4 = l + w + h

h = -

Hallie can use the following equation to solve the problem

p = 4l + 4w + 4h

She can proceed to make h the subject of the formula.

p = 4l + 4w + 4h

When we factor out 4 on the right hand side, we get:

p = 4(l + w + h)

We then divide both side by 4, we have

p/4 = l + w + h

Then, subtracting (l + w) from both sides, we get:

p/4 - (l + w) = h.

We can write it as:

h = - (l + w) + p/4

And that is what Hallie wanted to obtain.

Answer:

Correct answer is 54.82 ft.

Step-by-step explanation:

First of all, let us label the diagram and do the construction as per the attached answer image.

Let us consider \(\triangle ABC\):

\(\angle B = 90^\circ\\\angle ACB = 180-110 = 70^\circ\)

Let side AB = d ft and let side BC = x ft

We need to find AB to find the shortest distance across the river.

Using trigonometric identity of tangent:

\(tan\theta = \dfrac{Perpendicular}{Base}\)

\(tan 70 = \dfrac{d}{x}\\\Rightarrow x = \dfrac{d}{tan70} = 0.36d ..... (1)\)

Now, let us have a look at another right angled triangle ABD:

Let us consider \(\triangle ABC\):

\(\angle B = 90^\circ\\\angle ADB = 180-150 = 30^\circ\)

side AB = d ft and side BD = x+75 ft

Using trigonometric identity of tangent:

\(tan\theta = \dfrac{Perpendicular}{Base}\)

\(tan 30 = \dfrac{d}{x+75}\\\text{Using equation (1)}:\\0.577 = \dfrac{d}{0.36d+75}\\\Rightarrow 0.207d + 43.27 = d\\\Rightarrow 0.793d = 43.27\\\Rightarrow d \approx 54.82\ ft\)

Correct answer is 54.82 ft.

Answer: B 58.34

Step-by-step explanation: the angle supplementary to the 150 angle = 30

So the remaining angle is 180-110-30= 40

sin40/75 = sin30/x

solve for x = 58.34

Just did the quiz.

Answer:

40 mph

Step-by-step explanation:

every 1 hour, he travels 40 miles

200/5=40

Answer:

The answer would be 71 because x = 9 so y = 71

Answer:

7

Step-by-step explanation:

Answer:

The length of AB is approximately 6.07 m

Step-by-step explanation:

The given dimensions of the triangle are;

The value of x = 7.7 m

The measure of angle, θ = 52°

The length of side AB = Required

The given triangle ΔABC is a right triangle, with the following sides;

AC = x = The hypotenuse (opposite to right angle) side

(Leg) AB = The opposite side to the reference angle, θ

(Leg) BC = The adjacent side to the reference angle, θ

By trigonometric ratio, we have;

\(sin(\theta) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{AB}{x}\)

Therefore;

\(sin(52^{\circ}) = \dfrac{AB}{7.7}\)

AB = 7.7 × sin(52°) ≈ 6.07

The length of AB ≈ 6.07 m.

Answer:

7x

Step-by-step explanation:

The following statements are proved using mathematical induction:

(b) Prove that for any positive integer n,6 evenly divides \(7^n -1\).

(c) Prove that for any positive integer n,4 evenly divides \(11^n-7^n\).

(e) Prove that for any positive integer n,2 evenly divides \(n^2-5n+2\).

(b) Prove that for any positive integer n, 6 evenly divides \(7^n - 1.\)

Step 1: Base case

Let's check if the statement holds true for the base case, n = 1.

For n = 1, we have  \(7^1 - 1 = 6\), which is divisible by 6. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 6 evenly divides  \(7^k - 1\).

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \(7^{(k + 1)} - 1.\)

We can rewrite it as  \(7 * 7^k - 1.\)

Using the assumption from the inductive hypothesis, we know that \(7^k - 1\)is divisible by 6.

Since 7 is congruent to 1 (mod 6), we have \(7 * 7^k\) ≡ \(1 * 1^k\) ≡ 1 (mod 6).

Therefore,  \(7^{(k + 1)} - 1\) ≡ 1 - 1 ≡ 0 (mod 6), which means 6 evenly divides \(7^{(k + 1)} - 1.\)

By the principle of mathematical induction, we can conclude that for any positive integer n, 6 evenly divides  \(7^n - 1\).

(c) Prove that for any positive integer n, 4 evenly divides  \(11^n - 7^n.\)

Step 1: Base case

For n = 1, we have \(11^1 - 7^1 = 11 - 7 = 4\), which is divisible by 4. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 4 evenly divides  \(11^k - 7^k.\)

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \(11^{(k + 1)} - 7^{(k + 1)}.\)

We can rewrite it as  \(11 * 11^k - 7 * 7^k.\)

Using the assumption from the inductive hypothesis, we know that \(11^k - 7^k\) is divisible by 4.

Since 11 is congruent to 3 (mod 4) and 7 is congruent to 3 (mod 4), we have  \(11 * 11^k\) ≡ \(3 * 3^k\) ≡ \(3^{(k+1)}\) (mod 4) and  \(7 * 7^k\) ≡ \(3 * 3^k\) ≡ \(3^{(k+1)}\) (mod 4).

Therefore,  \(11^{(k + 1)} - 7^{(k + 1)}\) ≡ \(3^{(k+1)} - 3^{(k+1)}\) ≡ 0 (mod 4), which means 4 evenly divides  \(11^{(k + 1)} - 7^{(k + 1)}.\)

By the principle of mathematical induction, we can conclude that for any positive integer n, 4 evenly divides \(11^n - 7^n.\)

(e) Prove that for any positive integer n, 2 evenly divides \(n^2 - 5n + 2.\)

Step 1: Base case

For n = 1, we have  \(1^2 - 5(1) + 2 = 1 - 5 + 2 = -2,\)  which is divisible by 2. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 2 evenly divides  \(k^2 - 5k + 2.\)

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \((k + 1)^2 - 5(k + 1) + 2.\)

Expanding and simplifying, we get  \(k^2 + 2k + 1 - 5k - 5 + 2 = k^2 - 3k - 2.\)

Using the assumption from the inductive hypothesis, we know that 2 evenly divides  \(k^2 - 5k + 2\).

Since 2 evenly divides -3k, and 2 evenly divides -2, we can conclude that 2 evenly divides  \(k^2 - 3k - 2\).

By the principle of mathematical induction, we can conclude that for any positive integer n, 2 evenly divides  \(n^2 - 5n + 2\).

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Answer:

Step-by-step explanation:

where is the swan?

Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

The three externalities, which can either be positive or negative are Pollution from a factory, as more electricity is consumed, more coal is burned in power plants and vaccinations, such as the flu shot, can be advantageous for third parties.

The three externalities, which can either be positive or negative are:

1. Pollution from a factory can affect a community's quality of life and lead to health issues for the population.

2. As more electricity is consumed, more coal is burned in power plants, which contributes to pollution and causes smog, acid rain, and global warming.

3. Vaccinations, such as the flu shot, can be advantageous for third parties since they stop the spread of the illness in the general population, which has positive externalities.

These externalities arise because they provide a benefit or incur a cost to a third party, who may be a society or a consumer who is not using the service. Government intervention can address some of these issues in two ways:

(a) Command and control rules that impose direct restrictions on behavior, such as restricting smokestack emissions or the amount of toxic waste and outlining specific cleanup processes.

(b) Market-based policies that can encourage favorable externalities by offering market players incentives to reach the socially optimal level In order to reduce costs or boost production to improve demand and supply, the government can either provide subsidies to buyers or producers.

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With a ratio of 5 : 3, the amount of cocoa powder used to make the icing is 27g.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other. On the other hand, proportion is the equality of two ratios, such that a : b = c : d.

If the combined weight of the iced cake (batter + icing) is 480 g, of which 15% is cocoa powder, then the total mass of the cocoa powder used is:

total mass of the cocoa powder = 15% of 480g

total mass of the cocoa powder = 0.15(480g)

total mass of the cocoa powder = 72 g

If the amount of cocoa powder used in the batter of a chocolate cake and the amount of cocoa powder used in the icing for the cake is in the ratio 5 : 3, and its total mass is 72g, using proportion, solve for the weight used to make the icing.

a + b = 72   ⇒   a = 72 - b

where a = amount of cocoa powder used in the batter

b = amount of cocoa powder used in the icing

5 : 3 = a : b

5 : 3 = 72 - b : b

5b = 3(72 - b)

5b = 216 - 3b

5b + 3b = 216

8b = 216

b = 27

amount of cocoa powder used in the icing = 27 g

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