What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3,−4)?

The equation of a line with an x-intercept of 2 and a y-intercept of -8 is y = 4x - 8, which follows from applying the slope-intercept form and calculating the slope based on the intercepts.

To find the equation of a line with an x-intercept of 2 and a y-intercept of -8, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

We can determine the slope by recognizing that the line crosses the x-axis at (2,0) and the y-axis at (0,-8).

The slope m is the rise over the run, which in this case is (-8 - 0) / (0 - 2) = 4.

Therefore, the equation of the line is y = 4x - 8.

This equation satisfies the given conditions, as plugging in x = 0 gives the y-intercept of -8 and setting y to 0, and solving for x yields the x-intercept of 2.

Answer: The expected value of the number of gram of the sugar in the cereal is 8 grams.

Step-by-step explanation:

When we multiply each of the possible outcomes by the likelihood each outcome will occur and find out the sum of the all values, we get the expected value of an experiment.

Here, the probability of the different brands 4g, 8g and 16g are 1/4, 5/8 and 1/8 respectively.

Thus, by the above definition,

The expected value of the number of grams of the sugar in the cereal = 4 g × its probability + 8 g × its possibility + 16 gram × Its possibility,

[tex]=4\times \frac{1}{4}+8\times \frac{5}{8}+16\times \frac{1}{8}[/tex]

[tex]=1+5 +2 = 8[/tex]

Thus, The expected value of the number of gram of the sugar in the cereal is 8 grams.

The expected value of the number of grams of sugar in cereal is 8 grams and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the expected value of the number of grams of the sugar in cereal:

Step 1 - The probability concept can be used in order to determine the expected value of the number of grams of sugar in the cereal.

Step 2 - According to the given data, the probability of choosing a cereal with 4 grams of sugar is 1/4, the probability of choosing a cereal with 8 grams of sugar is 5/8, and the probability of choosing a cereal with 16 grams of sugar is 1/8.

Step 3 - So, the expected value of the number of grams of the sugar in cereal is:

[tex]\rm Total \;number \;of\; grams\; of\; sugar=4\times \dfrac{1}{4}+8\times \dfrac{5}{8}+16\times \dfrac{1}{8}[/tex]

Step 4 - Simplify the above expression.

Total number of grams of sugar = 8 grams

Therefore, the correct option is C).

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To determine which equation could have been Henry's, we need to compare it to Fiona's equation. Option C, x - (5/4)y = 25/4, has the same solutions as Fiona's equation and could have been Henry's equation.

To determine which equation could have been Henry's, we need to compare it to Fiona's equation, y = (2/5)x - 5. Henry's equation should have the same solutions as Fiona's, which means it should have the same slope and y-intercept.

Comparing the options:

Only option C, x - (5/4)y = 25/4, has the same solutions as Fiona's equation. Therefore, it could have been Henry's equation.

Final answer:

To calculate 6x^2 – 4x when x = 5, you square 5 to get 25, multiply by 6 to get 150, then subtract 4 times 5 which is 20, resulting in a final value of 130.

Explanation:

To find the value of the expression 6x^2 – 4x when x = 5, you need to substitute 5 for x in the expression and perform the arithmetic. First, calculate the value of 6x^2 by squaring x (which is 5) and multiplying by 6:

6 * 5^2 = 6 * 25 = 150.

Next, calculate the value of 4x when x is 5:

4 * 5 = 20.

Now subtract the result of 4x from the result of 6x^2:

150 - 20 = 130.

So, the value of the expression when x = 5 is 130.

Melissa sold 5 Volvos. Given that Jane sold eight times as many Volvos as Melissa, Jane sold 40 Volvos.

In order to solve this problem, we can use a simple equation. Let's denote the number of Volvos Melissa sold as 'x'. Since Jane sells 8 times as many Volvos as Melissa, the number of Volvos Jane sold can be denoted as '8x'. We know from the problem that the difference between the number of cars Jane and Melissa sold is 35, so we can write the equation like this: 8x - x = 35.

By simplifying the equation, we get 7x = 35. Therefore, to find the value of 'x', we divide 35 by 7, which gives us 'x' equals to 5.

But 'x' is the number of Volvos Melissa sold. To find out the number of cars Jane sold, we multiply 'x' by 8. Which gives us 5 multiplied by 8 equals to 40 cars.

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Answer:

C) ASA

Step-by-step explanation:

Let's name the first triangle ABC  and the second triangle DEF.

Statement                                     Reason

∠A ≅∠D                                       Given

AB ≅DE                                        Given

∠B ≅ ∠E                                       Given

In two triangles, if the two angles and the included side of the two triangles are congruent, then the triangles are congruent by the property ASA (Angle-Side-Angle) using corresponding parts of congruent triangles are congruent.

According to the given triangles, the two triangles are congruent by the property of ASA.

Answer:

it's c on edge your welcome

The limit as x approaches negative infinity of (1.001)^x is 0, because as we raise a number slightly larger than 1 to increasingly negative exponents, the results get closer and closer to zero.

The student is asking about the limit of a function as x approaches negative infinity, specifically for the function (1.001)^x. When evaluating this limit, it is essential to understand how exponential functions behave as the exponent becomes very large or very negative. Since 1.001 is greater than 1, raising it to increasingly negative exponents will result in values that approach zero. Therefore, the limit as x approaches negative infinity of (1.001)^x is 0.

Understanding the behavior of functions at infinity can be connected to the general concept where, for example, the reciprocal of a number as it approaches zero from the positive side (1/x) goes to positive infinity and from the negative side (1/x) goes to negative infinity. However, when evaluating the limit at negative infinity for our function, we must consider the base of the exponential function, which dictates that the function's values descend towards zero.

Answer:

The vertex form of the parabola is  [tex]x=(y+5)^2-3[/tex]

C is the correct option.

Step-by-step explanation:

The standard form of the parabola is [tex]x=y^2+10y+22[/tex]

We can write this equation in vertex form by using the completing square method.

For the expression [tex]y^2+10y[/tex], the value of b is 10.

Hence, add and subtract [tex](\frac{10}{2})^2=25[/tex] to the right side of the equation.

Thus, the equation becomes

[tex]x=y^2+10y+25-25+22[/tex]

Now, the expression [tex]y^2+10y+25=(y+5)^2[/tex]

Hence, we have

[tex]x=(y+5)^2-25+22[/tex]

We can simplify further as

[tex]x=(y+5)^2-3[/tex]

Hence, the vertex form of the parabola is  [tex]x=(y+5)^2-3[/tex]

C is the correct option.

Answer:

A, C, E   are not polynomials

Step-by-step explanation:

Identify the expressions that are not polynomials

A. x^2-(square root of x)-3

Polynomial cannot have a square root. so it is not polynomial

B. 4 - 3x + 5x^6

C. 5x^1/2 + 4x^2

A polynomial does not have fractional exponent

D. 14x^7

E. x^2-x-12/x+3

Polynomial cannot have x in the denominator

F. 8x^10 + 2x^5

Answer:

[tex]\sqrt[3]{373248}=\sqrt[3]{18^{3}*64}\\[/tex]

Step-by-step explanation:

A Perfect Cube is an integer number multiple of three that can be expressed as a product of prime factors raised to 3rd power. We have many Perfect Cubes, such as:

15³=3³x5³, and 15 ∈ ={1,3,6,9,12,15,18,..} so 15 is a perfect cube

18³=2³x3³x3³ and 18 ∈ ={1,3,6,9,12,15,18,..} so 18 is a perfect cube.

Finally, for instance, we can rewrite the number 373248 as

cubic root of 18³ times 64. 18 is a perfect cube 64 is not a perfect cube for 64 =[tex]2^{6}[/tex]

Final answer:

The net force required to accelerate a bowling ball weighing 48 N at 3.0 m/s² is 14.7 N, which we round to 15 N using two significant figures.

Explanation:

To find the net force required to accelerate the bowling ball at 3.0 m/s², we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). First, we need to determine the mass of the bowling ball. Since the weight of the bowling ball is given as 48 N and weight can be calculated by multiplying mass with the acceleration due to gravity (weight = mass × gravity), we can find the mass (m = weight / gravity). Assuming the acceleration due to gravity is 9.8 m/s², the mass of the bowling ball would be approximately 4.9 kg (48 N / 9.8 m/s²). Next, we apply Newton's second law to find the net force required for the 3.0 m/s² acceleration by multiplying the mass by the desired acceleration (F = ma).

The calculation is as follows:

F = ma = 4.9 kg × 3.0 m/s² = 14.7 N

Therefore, a net force of 14.7 N must be applied to the bowling ball to achieve the acceleration of 3.0 m/s². We typically round this to two significant figures, giving a final answer of 15 N.

To make 20 cups of Jessica's favorite purple paint, she needs approximately 6.67 cups of blue paint and 10 cups of red paint.

To find the number of cups of blue and red paint Jessica needs to make 20 cups of her favorite purple paint, we need to set up a proportion based on the ratios of blue paint and red paint in her favorite shade.

Since Jessica uses 1/3 cup of blue paint and 1/2 cup of red paint to make her favorite shade, we can set up the proportion:

1/3 cup of blue paint / 1/2 cup of red paint = x cups of blue paint / 20 cups of purple paint.

To solve for x, we can cross multiply and divide:

x = (1/3 cup of blue paint)(20 cups of purple paint) / (1/2 cup of red paint) = 20/3 = 6.67 cups of blue paint.

So, Jessica needs approximately 6.67 cups of blue paint and 10 cups of red paint to make 20 cups of her favorite purple paint.

Answer:

A. [tex]4x(2x^2+3)[/tex].

Step-by-step explanation:

We have been given an expression [tex]8x^3+12x[/tex]. We are asked to factor our given expression.

We can see that both terms of our given expression share a common factor that is 4x.

Upon factoring out 4x from our given expression, we will get:

[tex]4x(2x^2+3)[/tex]

Therefore, the factored form of our given expression would be [tex]4x(2x^2+3)[/tex] and option A is he correct choice.