Help me please Algebra 1

Answer:

1. y = 0

2. f(x) has a horizontal asymptote at y=3/2

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

There is a horizontal asymptote at y = 0 because the degree of the x value in the denominator is greater than the degree of the numerator (since it doesn't exist in the numerator, it counts as 0).

The second question does not have a slant asymptote.

The degree of both numerator and denominator are equal, so the horizontal asymptote is the quotient of the leading coefficients. So, it's 3 divided by 2.

So, the dimensions that give the largest printed area are 6.5 inches by 8 inches, with 1-inch margins at the bottom and sides, and a 2-inch margin at the top.

Let the dimensions of the printed area be x and y. Then we have:

The bottom margin is 1 inch, so the height of the poster is y + 2 + 1 = y + 3 inches.

The side margins are 1 inch each, so the width of the poster is x + 2 inches.

The top margin is 2 inches, so the height of the printed area is y.

Therefore, the total area of the poster is:

A = (y + 3) * (x + 2)

Expanding this expression, we get:

A = xy + 3x + 2y + 6

To maximize the printed area, we need to find the values of x and y that maximize A. To do this, we can use calculus. We differentiate A with respect to x and y, and set the derivatives equal to zero to find the critical points:

dA/dx = y + 3 = 0

dA/dy = x + 2 = 0

Solving these equations simultaneously, we get:

y = -3

x = -2

These values are not physically meaningful, since x and y represent dimensions of a poster and cannot be negative. However, they tell us that A has no local maxima or minima. Therefore, to maximize A, we need to consider the endpoints of the feasible region, which are determined by the margins.

The feasible region is a rectangle with height y = 11 - 2 - 1 = 8 inches and width x = 8.5 - 2 = 6.5 inches. Therefore, the maximum area is:

A = (8 * 6.5) - (3 * 2)

= 46 square inches

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Answer:

r = 3

Step-by-step explanation:

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Answer:

r = 3

Step-by-step explanation:

Step 1: subtract 18 from both sides. Then you have -4r = -12

Step 2: Divide -4 to both sides and you get r= 3

The slope of a line is m= rise / run .

The rise measures the vertical change and the run measures the horizontal change.

Slope of the straight line passing through the points (X1,y1) and ( x2 , y2 ) is given by :-

\(m = \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \)

Slope of the straight line passing through the points ( -3 .2 ) and (-1 , 0 ) is .

\(m = \frac{0 + 2} { - 3 - 1} = - \frac{3}{2} \)

In general, the tallest and shortest plant heights can vary widely depending on the species of plant being considered.

For example, some species of trees can grow over 300 feet tall, while certain species of mosses may only grow a few millimeters in height. The specific environmental conditions, such as the availability of water, sunlight, and nutrients, can also impact the growth and height of plants. Therefore, without more specific information, it is difficult to provide a more precise answer.

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Answer:

acute angle

Step-by-step explanation:

as it right angle have 90•

and acute angles are 180•.

No , 23 x 10⁶ is not written in scientific notation.

Values that are either too huge or too little to be conveniently expressed in decimal form can be expressed using scientific notation (typically would result in a long string of digits).

So 23 x 10⁶ written in exact scientific notation is given by 2.3 × 10⁷ .

Therefore   2.3 × 10⁷ is written in scientific notation whereas  23 x 10⁶  is not in scientific notation.

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Answer:

c.130

Step-by-step explanation: so first you would plus 20 and 10 and that equals 30 then you would multiply 3 times 30 and that equaled 90 now you have 90+40 which equals 130.

Answer:

Step-by-step explanation:

1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.

  \(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}\)

__

2. Using the same idea here, we get ...

  \(\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}\)

Answer:

Step-by-step explanation:To determine the line of reflection, we need to find the equation of the line that is equidistant from each vertex of the original triangle and the corresponding vertex of the reflected triangle.

First, let's find the coordinates of the image of each vertex under the reflection. Since F' is given as (2, 2), we can reflect F across the unknown line of reflection to find the image of D and E. The line of reflection must be equidistant from each of these pairs of corresponding points.

To reflect F across a vertical line, the x-coordinate of F' must be the same as that of F but with the opposite sign. The x-coordinate of F is -2, so the x-coordinate of its image F' must be 2. Similarly, the y-coordinate of F' is 2, which means that the line of reflection must pass through the point (2, 2).

To reflect D across the same line, we can draw a perpendicular bisector between D and its image D', which must intersect the line of reflection at a right angle. The midpoint of DD' lies on the line of reflection, and it is equidistant from D and D'. Using the midpoint formula, we find the midpoint of DD' to be ((-3+2)/2, (5+2)/2) = (-0.5, 3.5). Since this point lies on the line of reflection, we can use the point-slope form of a line to find the equation of the line passing through (2, 2) and (-0.5, 3.5):

(y - 2) = m(x - 2) (where m is the slope of the line of reflection)

Simplifying:

y - 2 = m(x - 2)

y = mx - 2m + 2

To find the value of m, we can use the fact that the midpoint of DE lies on the line of reflection as well. The midpoint of DE is ((-3-10)/2, (5+4)/2) = (-6.5, 4.5). Substituting these values into the equation of the line, we get:

4.5 = m(-6.5) - 2m + 2

2.5 = -8.5m

m = -0.294

Therefore, the equation of the line of reflection is:

y = -0.294x + 2.588

This line is not the x-axis, y-axis or the line y=x. Therefore, the line of reflection is neither the x-axis nor the y-axis, and it is not the line y = x.

Answer:

X-axis

Step-by-step explanation:

I am in the middle of taking the quiz and this is the answer I think would be correct!

Look at the both picture.

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

12 bowls

Step-by-step explanation:

If marry had nine pounds of salad, and each salad bowl holds 3/4 pounds each, then the equation is 9 divided by 3/4, which equals twelve.

Answer:

False

Step-by-step explanation:

The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p7, where n is the number of shots and p is the probability of success.The probability of making 7 consecutive successful shots in exactly k shots is given by Pk = (1-p)k-7 * p7. The expected value of X is given by E(X) = [k=7,] k. We can use the formula for the sum of an infinite geometric series to simplify the expression and evaluate the numerator of the expression. Thus, E(X)  7 / p7.

a) In n shots, the expected number of streaks of 7 consecutive successful shots is given by the formula below:The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p^7, where n is the number of shots and p is the probability of success. In other words, for each block of 7 shots, we have a probability of p^7 of making 7 consecutive successful shots, and there are (n-6) blocks of 7 shots in n shots. Therefore, the expected number of streaks of 7 consecutive successful shots is the product of these two values.

b) We know that X is the number of shots taken until the player makes 7 consecutive successful shots for the first time. Therefore, X is a random variable that follows the geometric distribution with parameter p. The probability of making 7 consecutive successful shots in exactly k shots is given by:Pk = (1-p)^{k-7} * p^7Therefore, the expected value of X is given by:E(X) = Σ[k=7,∞] k * PkWe can use the formula for the sum of an infinite geometric series to simplify this expression:

\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (1 - (1-p)^7)\) We can also use the formula for the sum of a geometric series to simplify the denominator:

\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (p^7 + Σ[j=1,6] (1-p)^j * p^7)\)

\(E(X) = (p^7 * Σ[k=1,∞] k * (1-p)^{k-1}) / (p^7 * (1 + Σ[j=1,6] (1-p)^j))\)

\(E(X) = (1 / p^7) * (Σ[k=1,∞] k * (1-p)^{k-1}) / (1 + Σ[j=1,6] (1-p)^j)\)

We can use the formula for the derivative of a geometric series to evaluate the numerator of this expression:

\(Σ[k=1,∞] k * (1-p)^{k-1} = d/dp\)

Σ[k=1,∞] (1-p)^k

= d/dp (1-p) / (1 - (1-p))²

= 1 / p^2

Therefore, \(E(X) = (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^2) ≤ (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^7) = 1 / p^{14} ≤ 7 / p^7\)

Thus, \(E(X) ≤ 7 / p^7.\)

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Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

Answer:

-6a - 48

4 + 36x

-30n + 42

18m + 20

The candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

Let x be the quantity of 10% fat-content chocolate.

Fat in 10% fat-content chocolate + Fat in 60% fat-content chocolate = Total fat in 25% fat-content chocolate

0.10x + 0.60(100 - x) = 0.25*100

10x + 60*100 - 60x = 25*100

-50x = 25*100 - 60*100

-50x = 100(25 - 60)

50x = 3500

x = 3500/50

x = 70 kg

This is the quantity of 10% fat-content chocolate required.

100 - x = 30 kg

This is the quantity of 60% fat-content chocolate required.

Therefore, we have found that the candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

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Answer:

x = 3.  y = 11

Step-by-step explanation:

The two equations are two simultaneous equations, which can be solved by substitution, elimination or graphical method.

Elimination method:

The coefficients of 'x’ or ‘y’ need to be the same with opposite signs. The coefficients of ‘y’ will be focused:

                  (17x - y = 40) Multiplied by 4

                  (2x + 4y = 50) Multiplied by 1

                  68x - 4y = 160

                   2x + 4y = 50

In the net total, the ‘y’ terms will cancel each other out:

                 70x = 210

                     x = \(\frac{210}{70}\)

                     x = 3

The calculated value of x is substituted in any of the equations to determine the value of y:

                 17(3) - y = 40

                    51  - y = 40

                   51 - y - 40 = 0

                   51 - 40 - y = 0

                   11 - y = 0

                   y = 11

The probability that the sum of two fair six-sided dice is 9 or 99 or higher is 5/36.

To find the probability of whether the sum of two fair six-sided dice is 9 or 99 or higher, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The possible outcomes when rolling two six-sided dice range from 2 (minimum sum) to 12 (maximum sum). We want to calculate the probability of getting a sum of 9 or 99 or higher.

To determine the favorable outcomes, we need to identify all the combinations of dice rolls that meet our criteria. Here are the favorable outcomes:

(3, 6) = sum of 9

(4, 5) = sum of 9

(5, 4) = sum of 9

(6, 3) = sum of 9

(6, 6) = sum of 12

Therefore, we have 5 favorable outcomes.

Now, let's calculate the total number of possible outcomes. Since each die has 6 possible outcomes (numbers 1 to 6), the total number of possible outcomes for rolling two dice is 6 * 6 = 36.

The probability of getting a sum of 9 or 99 or higher is given by:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 5 / 36

Therefore, the probability that the sum of two fair six-sided dice is 9 or 99 or higher is 5/36.

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It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.

Let pi be pipe 1 and pi2 be pipe 2

pi = 1 / 1

pi2 = 1 / 2

together = 1/1 + 1/2 ;

3/2 time ; 2/3 hour.

It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.

Problem-solving is the act of defining a problem; figuring out the motive of the problem; identifying, prioritizing, and deciding on alternatives for a solution; and implementing an answer.

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A p-value of 0.23 in the context of a clinical trial testing a vaccine's effectiveness suggests that the observed reduction in the percentage of individuals catching the virus, when comparing the vaccine group to the control group, is not statistically significant at conventional levels of significance (such as 0.05 or 0.01).

The p-value represents the probability of obtaining the observed data, or data more extreme, under the assumption that the null hypothesis is true.

In this case, the null hypothesis would typically state that there is no difference in the percentage of virus cases between the vaccine and control groups. A p-value of 0.23 indicates that there is a 23% chance of observing the reported reduction in cases or an even more substantial reduction if the null hypothesis were true.

Therefore, based solely on the p-value of 0.23, the best interpretation is that the observed reduction in virus cases could plausibly be due to random variation or chance, rather than a true effect of the vaccine. However, it is important to consider other factors, such as the study design, sample size, and clinical significance of the observed reduction, before drawing final conclusions about the vaccine's effectiveness.

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Answer:

750.88 (rounded to 2 d.p.)

Step-by-step explanation:

100% --- 731

100% + 7% --- \(\frac{100+7}{100}\) × 731 = 782.17

100% --- 782.17

100% - 4% --- \(\frac{100-4}{100}\) × 782.17 = 750.88 (rounded to 2 d.p.)

The correct answer is the value x such that: P(X ≥ x) = 0.95

(a) The sum of independent exponential variables with the same rate parameter follows a gamma distribution. In this case, since each T_i follows an exponential distribution with a rate parameter of 1/100 (mean of 100), the sum ∑_{i=1}^{10} T_i follows a gamma distribution with shape parameter k = 10 and scale parameter θ = 100. Therefore, ∑_{i=1}^{10} T_i ∼ Gamma(10, 100).

(b) To find the probability of successful operation for at least 1.5 years, we need to calculate the cumulative distribution function (CDF) of the gamma distribution at 1.5 years (547.5 days). Using the gamma CDF, denoted by F_X(x), we have:

P(X ≥ 547.5) = 1 - F_X(547.5)

Using the gamma CDF with shape parameter k = 10 and scale parameter θ = 100, we can calculate this probability.

(c) To determine the number of spares needed to be 95% sure of successful operation for at least two years, we need to find the point where the cumulative distribution function (CDF) of the gamma distribution is 0.95. In other words, we need to find the value x such that: P(X ≥ x) = 0.95

Using the gamma CDF with the appropriate shape and scale parameters, we can solve for x.

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Answer:

Left box:  1/2n

Right box = 2n - 22

Step-by-step explanation:

Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.

Thus, you want to put 1/2n in box on the left.

Twice the number and 22 less than this is given by:  y: 2n - 22 less than this means we subtract.  Thus, we have 2n - 22 as the numerator on the right hand side of the equation.

Thus, you want to put 2n - 22 in the box on the right.

Answer:

28

Step-by-step explanation:

I took the test and It says 28

Answer:

24

Step-by-step explanation:

12 * 2 = 24