What does it mean when two such lines intersect? What can you say about the solution of the two equations? the graphs of x + 2y = 4 and y = 2x - 3

Answer:

115-m = Current Sum

Answer:

\(2 {x}^{2} + 12x + 18\)

\(➳ \: 2 {x}^{2} + 6x + 6x + 18

\)

\(➳2x(x + 3) + 6(x + 3)\)

\(➳ \: (2x + 6)(x + 3)\)

hence in there equation solution

we can solve the value of x

\( \leadsto \: (2x + 6)\)

\( \longrightarrow \: 2x = - 6\)

\(➳x = \frac{ - 6}{2} \)

\(➳ \: x \longrightarrow \: - 3\)

The values of x are -3

The equation is given as:

\(2x^2 + 12x + 18 = 0\)

Expand the equation

\(2x^2 + 6x + 6x + 18 = 0\)

Factorize the equations

\(2x(x + 3) + 6(x + 3) = 0\)

Factor out x + 3

\((2x + 6) (x + 3) = 0\)

Split the equation

\((2x + 6) = 0\ or\ (x + 3) = 0\)

Remove the brackets

\(2x + 6 = 0\ or\ x + 3 = 0\)

Solve for x

\(x = -3\ or\ x =-3\)

Hence, the values of x are -3

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Answer:

Answer 1:$0.15(15 cents) is the unit rate.

Answer 2:Kylie bought 64 fluid ounces.

Step-by-step explanation:

Step 1

2 quarts=4 pints

4 pints=8 cups

8 cups=64 fluid ounces

Step 2

$9.60÷64=0.15$

Answer:

y = 5x + 3

Step-by-step explanation:

You could also plot a line on a graph with this equation to help you even more.

Answer:

\(36x\)

Step-by-step explanation:

\(\left(\frac{x^3}{x^2}\right)* \:6^2\)

Apply exponent rule: \(\frac{x^a}{x^b}\:=\:x^{a-b}\)

\(x^{3-2}*6^2\)

\(x*6^2\)

\(x*36\)

\(36x\)

0.3 so yea i guess....

Answer:

Step-by-step explanation: 380

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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Answer:

48 onces

Step-by-step explanation:

Answer:

48 ounces.

Step-by-step explanation:

Answer:

1) x= 20

2) x= 75

Step-by-step explanation:

In the first problem, we see vertical angles. This means that both angles equal each other: 50= 2x+10

Step 1- Subtract 10 to both sides.

50= 2x+10

-10         -10

40= 2x

Step 2- Divide both sides by 2.

40= 2x

2     2

x= 20

In the next problem we see a straight line and an intersecting point. Now, both of these angles sum up to 180 degrees. So the equation would be:

x-10+2x-35= 180

Step 1- Add common variables.

(x+2x)+(-10-35)= 180

3x-45= 180

Step 2- Add 45 to both sides.

3x-45= 180

   +45  +45

3x= 225

Step 3- Divide both sides by 3.

3x= 225

3      3

x= 75

Input the value of x into the equations.

75-10= 65

2(75)-35= 115

Hope this helps!

Answer:

The answer is -17

Step-by-step explanation:

Add all the numbers together:

-12-10 is -22

Then -22+5= -17

The surface area of the pyramid is approximately 721.04 square feet.

Area is a measure of the size of a two-dimensional region or surface, such as a rectangle, triangle, circle, or any other shape. It is the amount of space inside the boundaries of a closed figure, expressed in square units. The unit of measurement used for area depends on the context and the system of measurement being used, but some common units include square meters, square centimeters, square feet, and square inches.

To calculate the area of a regular shape, such as a square or rectangle, you can multiply the length of the base by the height or width of the shape. For more complex shapes, such as triangles or circles, different formulas can be used depending on the properties of the shape. Area is an important concept in geometry, as well as in many other areas of mathematics, science, engineering, and everyday life.

To find the surface area of the pyramid, we need to find the area of each face and add them up.

Since the base of the pyramid is a square, and the length of each side is 13 ft, the area of the base is:

Area of base = (13 ft) x (13 ft) = 169 sq ft

To find the area of each triangular face, we first need to find the slant height of the pyramid. The slant height is the distance from the apex of the pyramid to the midpoint of one of the sides of the base. We can use the Pythagorean theorem to find the slant height:

Slant height = √( (1/2 x 13 ft)² + 18 ft² )

= √( 169 ft² + 324 ft² )

= √493

≈ 22.18 ft

Now we can find the area of each triangular face using the formula:

Area of triangle = (1/2) x base x height

where the base is one of the sides of the square base, and the height is the slant height we just found. Therefore, the area of each triangular face is:

Area of triangle = (1/2) x 13 ft x 22.18 ft

≈ 143.01 sq f

Since there are four triangular faces, the total surface area of the pyramid is:

Total surface area = 4 x Area of triangle + Area of base

= 4 x 143.01 sq ft + 169 sq ft

≈ 721.04 sq ft

Therefore, the surface area of the pyramid is approximately 721.04 square feet.

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Answer:

c and d

Step-by-step explanation:

c) Housing, savings and food = 54%

d) Housing, food and transportation = 60%

Answer:

c and d

Step-by-step explanation:

The 205th term of the sequence is 768 with a common difference of 4.

So, the sequence is:

-48, -44, -40, -36, -32,... +4

The common difference is: -48 + 4 = - 44 ⇒ 4

Formula: aₙ = a + (n - 1)d

Now calculate as follows:

aₙ = a + (n - 1)d

aₙ = -48 + (205 - 1)4

aₙ = -48 + (204)4

aₙ = -48 + 816

aₙ = 768

Therefore, the 205th term of the sequence is 768 with a common difference of 4.

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To find the change of coordinates matrices P and Q, we need to express the basis vectors of each basis in terms of the other two bases and use these to construct the corresponding change of coordinates matrices.

First, let's express the basis vectors of each basis in terms of the other two bases:

E basis:

1 = 1(1) + 0(t) + 0(t^2) + 0(t^3)

t = 0(1) + 1(t) + 0(t^2) + 0(t^3)

t^2 = 0(1) + 0(t) + 1(t^2) + 0(t^3)

t^3 = 0(1) + 0(t) + 0(t^2) + 1(t^3)

B basis:

1 = 0(1) + 1(1+2t) + 2(2-t+3t^2) + 0(4-t+t^3)

t = 0(1) + 2(1+2t) - 1(2-t+3t^2) + 0(4-t+t^3)

t^2 = 0(1) - 3(1+2t) + 4(2-t+3t^2) + 0(4-t+t^3)

t^3 = 1(1) - 4(1+2t) + 1(2-t+3t^2) + 1(4-t+t^3)

C basis:

1+3t+t^2 = 1(1+2t) - 1(2-t+3t^2) + 0(4-t+t^3)

2+t = 1(1) + 0(t) + 0(t^2) + 1(t^3)

3t-2+4t^3 = 0(1+2t) + 3(2-t+3t^2) + 0(4-t+t^3)

3t = 0(1) + 0(t) + 1(t^2) + 0(t^3)

Now we can construct the change of coordinates matrices P and Q:

P matrix:

The columns of P are the coordinate vectors of the basis vectors of E with respect to B.

First column: [1, 0, 0, 0] (since 1 = 0(1) + 1(1+2t) + 2(2-t+3t^2) + 0(4-t+t^3))

Second column: [1, 2, -3, -4] (since t = 0(1) + 2(1+2t) - 1(2-t+3t^2) + 0(4-t+t^3))

Third column: [0, -1, 4, -1] (since t^2 = 0(1) - 3(1+2t) + 4(2-t+3t^2) + 0(4-t+t^3))

Fourth column: [0, 0, 0, 1] (since t^3 = 1(1) - 4(1+2t) + 1(2-t+3t^2) + 1(4-t+t^3)

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The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Answer: Here is the answer hope that helps ( Thanks for the points) (Btw my teacher helped me with it)

Step-by-step explanation:

Simplifying

b(x) = 18 + -0.5x

Multiply b * x

bx = 18 + -0.5x

Solving

bx = 18 + -0.5x

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Divide each side by 'x'.

b = 18x-1 + -0.5

Simplifying

b = 18x-1 + -0.5

Reorder the terms:

b = -0.5 + 18x-1

Answer:

19, 18, 15.5

Step-by-step explanation:

given :

b(x)=18-0.5x

when x = -2,

b (-2) = 18 - 0.5 (-2) = 18 +1 = 19  (answer)

When x = 0,

b(0) = 18 - 0.5 (0) = 18 - 0 = 18   (answer)

when x = 5,

b(5) = 18 - 0.5(5) = 18 - 2.5 = 15.5  (answer)

Answer:

(4x + 3)(2x + 5)

4x(2x + 5) +3(2x + 5)

8x^2 +20x +6x + 15

8x^2 +26x + 15

so, g(h(x))=8x^2 +26x +15

again

(4x + 3)(2x +5).0

0

so, g(h(0))=0

The equation that represents the scenario is 3500 < 360w + 600.

Here are inequality signs and what they mean:

Total amount Michelle wishes to save < total amount already saved + (number of weeks x amount made weekly)

$3500  < $600 + ($360w)

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Hey,

\( \frac{2}{3} \div \frac{3}{4} = \frac{2}{3} . \frac{4}{3} = \frac{8}{9} \)

`Sorry if it's wrong

Good luck :)

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Solving by factoring in steps shown below

Answer:

\(\textsf{1. \quad $x=1, \quad x=-\dfrac{2}{5}$}\)

\(\textsf{2. \quad $x=1, \quad x=3$}\)

Step-by-step explanation:

Solving quadratic equations by factoring

Given equation:

\(5x^2=3x+2\)

Subtract (3x + 2) from both sides:

\(\implies 5x^2-(3x+2)=3x+2-(3x+2)\)

\(\implies 5x^2-3x-2=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\), and rewrite \(b\) as the sum of these two numbers:

\(\implies ac=5 \cdot -2=-10\)

\(\implies b=-3\)

Therefore, the two numbers are -5 and 2.

Rewrite \(b\) as the sum of the two numbers:

\(\implies 5x^2-5x+2x-2=0\)

Factor the first two terms and the last two terms separately:

\(\implies 5x(x-1)+2(x-1)=0\)

Factor out the common term (x - 1):

\(\implies (5x+2)(x-1)=0\)

Apply the zero-product property:

\(\implies 5x+2=0 \implies x=-\dfrac{2}{5}\)

\(\implies x-1=0 \implies x=1\)

Therefore, the solutions are:

\(\boxed{x=1, \quad x=-\dfrac{2}{5}}\)

Given equation:

\(\implies x^2-4x+3=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\), and rewrite \(b\) as the sum of these two numbers:

\(\implies ac=1 \cdot 3=3\)

\(\implies b=-4\)

Therefore, the two numbers are -3 and -1.

Rewrite \(b\) as the sum of the two numbers:

\(\implies x^2-3x-x+3=0\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-3)-1(x-3)=0\)

Factor out the common term (x - 3):

\(\implies (x-1)(x-3)=0\)

Apply the zero-product property:

\(\implies x-1=0 \implies x=1\)

\(\implies x-3=0 \implies x=3\)

Therefore, the solutions are:

\(\boxed{x=1, \quad x=3}\)

The theory of rational expectations suggests that people will form expectations about future economic conditions based on all available information, including past experiences and government policies.

This means that discretionary monetary and fiscal policy may work in the short run, but not in the long run, as people will adjust their behavior to take into account the expected effects of policy changes. However, it is also possible that new information may change people's expectations and allow them to correctly anticipate policy effects. Overall, the theory of rational expectations suggests that economic policies should be designed with a long-term perspective in mind, as short-term changes may not have the intended effects.

The theory of rational expectations suggests that information may change people's expectations and allow them to correctly anticipate policy effects (Option 3). This implies that individuals use all available information to make predictions about future economic policies and adjust their behavior accordingly, which can affect the overall effectiveness of discretionary monetary and fiscal policies.

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Answer: 19, 21

Step-by-step explanation:

add 2, then, 4. Since 13 is adding two. You must add 4 from fifteen. Making 19. Then two, making 21.

The next term in the sequence  1, 3, 7, 9, 13, 15 is 19, 21, and so on. The sequence is shown below.

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given:

1, 3, 7, 9, 13, 15

Here, the sequence can be determined as,

1, 1 + 2, 3 + 4, 7 + 2, 9 + 4, 13 + 2, 15 + 4, 19 + 2, 21 + 4

As we can see, 2 is added and then 4 is added to the answer,

Thus, the next term is

15 + 4 = 19 and 19 + 2 = 21

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Answer:

Step-by-step explanation:

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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A 6 pack of bouncy ball costs 2.76$ and the unit price of a bouncy ball is $0.46

To find the unit price of the bouncy balls, we need to divide the total cost by the number of bouncy balls in the pack. Since there are 6 bouncy balls in the pack and the cost is $2.76, we can calculate the unit price as follows: Unit price = total cost ÷ number of units

Unit price = $2.76 ÷ 6

Unit price = $0.46

Therefore, the unit price of a bouncy ball is $0.46.

Unit price is a measure of the cost of a single unit of a product. It is calculated by dividing the total cost of a product by the number of units in the package. The unit price is helpful when comparing the costs of different package sizes or brands of the same product. It allows consumers to make informed decisions about their purchases based on the value they receive for their money. Unit pricing is required by law in some countries, including the United States, to ensure transparency in pricing and to protect consumers from deceptive marketing practices. Overall, knowing the unit price of a product can help consumers save money and make more informed purchasing decisions.

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Answer: y = -2x² + 920x - 84168

suppose: the equation of the parabola is y = ax² + bx + c

because the parabola passes through (126,0); (134,3200); (334,0)

=> we have the equations:

126².a + 126b + c = 0

134².a + 134b + c = 3200

334². a + 334b + c = 0

⇒ a = -2

    b = 920

    c = -84168

=>  the equation of the parabola is y = -2x² + 920x - 84168

Step-by-step explanation:

Answer:

yea listen to the other person

Step-by-step explanation: