Use linear combination to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]2x+4y=6\\x-4y=-21[/tex]

Answer:

(secΘ+tanΘ-1)(secΘ-tanΘ+1)

=sec²Θ-secΘtanΘ+secΘ+secΘtan-tan²Θ+tanΘ-secΘ+tanΘ-1

=2tanΘ+(sec²Θ-tan²Θ)-1

=2tanΘ+1-1

=2tanΘ

The cοrrect answer is d. 11.5°, This is because the equatiοn 4x = 46 can be rearranged tο x = 46/4 = 11.5.

An equatiοn is a mathematical statement that describes the relatiοnship between twο values using an equal sign. It cοnsists οf twο expressiοns οn either side οf the equal sign, and the expressiοns must be equal in οrder fοr the equatiοn tο be true. Equatiοns are used tο sοlve prοblems and tο understand hοw different variables interact with each οther.

Fοr example, the equatiοn "2 + 2 = 4" is true because twο plus twο dοes in fact equal fοur. Equatiοns can alsο be used tο represent physical phenοmena, such as the equatiοn F = ma, which describes the relatiοnship between fοrce and mass. Equatiοns can be used tο sοlve many prοblems in mathematics, science, engineering, ecοnοmics, and οther fields.

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A line is breaking a segment into two making two angles, one of the angle is 46° which 4 times the other angle x. Solve for x

a. 4°

b. 4. 5°

c. 6°

d. 11. 5°

The greatest possible difference between David's result and Armen's result is 5.

Let's first consider the maximum number of odd shirts Armen can count. Since there are only 5 odd numbers between 1 and 9, the maximum number of odd shirts Armen can count is 1+3+5+7+9 = 25.

Now, let's consider the maximum number of even shirts David can count. Since there are only 4 even numbers between 1 and 9, the maximum number of even shirts David can count is 2+4+6+8 = 20.

Therefore, the greatest possible difference between David's result and Armen's result is

= 25 - 20

Subtract the numbers

= 5

The maximum difference occurs when Armen counts all 5 odd shirts and David counts all 4 even shirts.

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Answer:

Below

Step-by-step explanation:

You want to divide 81 into (2+1 = 3) parts

   81 / 3 = 27   for each part

    2 parts would be  2 * 27 = 54    

          so 2:1    would be   54:27

All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:

ax² + bx + c = 0.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation.

The functions in standard form are:

3x² + 6x - 12 = 0

3x² + 2x + 10 = 0

5x² - 10x + 5 = 0

2x² - 4x + 6 = 0

All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are constants and a ≠ 0.

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According the question given above  the value of n is 21.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.

Calculations and problem-solving techniques simplify the issue. The act of substituting a complex mathematical expression with a simpler counterpart is known as simplification (usually shorter).

Here, we have

Given : 7 = n/3

we have to find the value οf n.

We apply simplification here and we get

7 = n/3

n = 7×3

n = 21.

Hence, the value οf n is 21.

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Answer:

800

Step-by-step explanation:

the answer is 800 as 1 rounds down

Answer:

9(5)-/y

9(5)-15/3

45-15/3

45-5

40

Well, I do agree that if k is a real number, then the compound inequality xk's solution set contains only real numbers.

A sentence with two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The word "and" indicates that both claims in the compound sentence are true at the same time. It occurs when the multiple statement's solution sets overlap or intersect. Compound inequalities are those that have the conjunctions "and" or "or" between them. It should be understood that plimb[/[/ofs (Ors Or/ Orss ultras "is larger than -2 and less than or equal to 5" should be translated as 2 x 5. x is greater than or equal to 3 or equal to -4, or "x 3." You'll observe that each of these differences has two inequality signals. Inequality that is compounded by two or more factors.

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We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878. The number of turkeys, y, in the population at the end of t years is obtained by substituting this value into the exponential decay formula and getting the following result: y = 250(0.878)t.

The equation y = 250(1 - 0.022)t, where t is the number of years, may be used to calculate the number of turkeys, y, in this population at the end of t years.

Using the exponential decay formula, A = P(1 - r)t, where A is the final amount, P is the beginning amount, r is the rate of decay in decimal notation, and t is the duration in years, we may arrive at this function.

If we substitute the values provided, we get: 209 = 250(1 - 0.022)^8

We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878.

This value may be substituted into the exponential decay formula to obtain the number of turkeys, y, in the population at the end of t years: y = 250(0.878)t.

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Answer:

(5,1)

(7, -5)

Step-by-step explanation:

y = mx + b

The b is the y intercept.  This is where the graph crosses the y axis.  Graph this first.  The m is the slope.  It is the rise over the run.  You can make any number a fraction by putting it over 1.  From the y-intercept you use the slope (rise/run) to graph the second point.  

For example, if the slope is 1. then 1/1 would show your rise and run. Start when the y-intercept is and go up 1 and then 1 right.  Connect the two points that you have graphed.

If the slope is 2/7, then from the y-intercept go up 2 and right 7.  Graph that point and draw a line connecting that point to the point on the y-intercept.

Helping in the name of Jesus.

ANSWER OF THE FIRST TWO EQUATIONS

y = x -4

y= -x+6

both the equations represent a straight line with y intercept as -4 and 6 respectively

x-y-4 = 0. ........(equation 1)

x+y-6 = 0. .........(equation 2)

adding equation 1 and 2

2x - 10 = 0

x = 5

subtracting equation 2 from 1

-2y -2 = 0

y = 1

FINAL ANS : (5,1)

The baker can decorate 1.4 or 1 1/3 of cupcakes in a minute.Step-by-step explanation: 42 cupcakes in 30 minutes so if you divide 42 cupcakes in 30 groups you get 1 in each group and 12 left so if make 30 in 3 it makes 4 in each group but it is 30 so you make the four in to a 0.4 or 1/3 which is 1.4.You can also multiply if you make 1.4 into 14 x 3 = 42 same as 1.4 x 30 = 42 so the answer is 1.4.

Answer:

The outcomes when rolling a fair six-sided die are: 1, 2, 3, 4, 5, and 6.

a. The probability of getting a 1, 3, or a 6 is 3/6 or 1/2.

b. The probability of getting a number less than 5 is 4/6 or 2/3.

The probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.

To find the probability of a task taking more than 25 days to complete, given that the mean and standard deviation of the normal distribution are 20 and 3 days, respectively, one can use the Z-score formula.Z = (X - μ)/σwhere Z is the standard score, X is the observed value, μ is the mean, and σ is the standard deviation. Therefore,Z = (25 - 20)/3 = 5/3 ≈ 1.67The area to the right of Z = 1.67 on a standard normal distribution table represents the probability that the task will take more than 25 days to complete. Using a standard normal distribution table or calculator, we can find that P(Z > 1.67) = 0.0475 or approximately 4.75%.Therefore, the probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.

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If the company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by P(x)=−3(x−5) ^2+12, the maximum profit is $87 million.

The given profit function is in the form of a quadratic equation with a negative coefficient of the squared term. This means that the graph of the function is a downward-facing parabola, and the vertex of this parabola represents the maximum value of the function.

To find the vertex, we need to convert the given function into vertex form:

P(x) = -3(x - 5)^2 + 12

= -3(x^2 - 10x + 25) + 12

= -3x^2 + 30x - 63

Completing the square, we get:

P(x) = -3(x - 5)^2 + 12 + 75

= -3(x - 5)^2 + 87

The vertex of this parabola is at the point (5, 87), which represents the maximum profit the company can earn.

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The birthday supper cost $94.73 and also the tax rate is $72.72 and was paid by Mr. Shoaf's mother.

A flat charge called valuation tax (VAT) is imposed on a purchase. It resembles a sales tax in the some ways, but unlike with a state taxes, the consumer pays the entire amount due to the government at the moment of sale.

Value added tax is levied by the Dutch government on all products and services. VAT is added by businesses to the sales price to determine the final amount that customers pay. Businesses must pay taxes to the Customs and Tax Administration when goods are sold.

Cost of the meal [tex]= 76.55 -[/tex] (5% of 76.55)

Cost of the meal [tex]= 76.55 - 3.83[/tex]

Cost of the meal [tex]= 72.72[/tex]

calculate tip,

Tip = 25% of the cost of the meal

Tip [tex]= 0.25 *72.72[/tex]

Tip [tex]= 18.18[/tex]

calculate the total amount paid

Total amount paid = cost of the meal + sales tax + tip

Total amount paid [tex]= 72.72 + 3.83 + 18.18[/tex]

Total amount paid [tex]= 94.73[/tex]

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The only true statement in the following equation are B and D.

A. When the bacteria population reaches 900, 12 hours have passed since the colony was placed on the petri dish.

To check this statement, we can use the formula for exponential growth:

P(t) = P0 * [tex]3^{(t/6)[/tex]

Where P(t) is the population at time t, P0 is the initial population, and t is the time in hours.

If P(t) = 900, we can solve for t:

900 = [tex]100 * 3^{(t/6)[/tex]

9 = [tex]3^{(t/6)[/tex]

ln(9) = (t/6) * ln(3)

t = 6 * ln(9) / ln(3) ≈ 12.68

So, it takes approximately 12.68 hours for the population to reach 900. Therefore, statement A is false.

B. Three hours after the colony is placed on the petri dish, there are 200 bacteria.

Using the formula above with t=3:

P(3) = [tex]100 * 3^{(3/6) = 200[/tex]

So, statement B is true.

C. Three hours after the colony is placed on the petri dish, there are about 173 bacteria in the colony.

Using the formula above with t=3:

P(3) = [tex]100 * 3^{(3/6) = 200[/tex]

So, statement C is false.

D. In the first hour the colony is placed on the petri dish, the population grows by a factor of [tex]$3^{\frac{1}{6}}$[/tex]

Using the formula above with t=1:

P(1) = [tex]100 * 3^(1/6)[/tex]

So, the population after 1 hour is 100 times the sixth root of 3. We can write this as:

P(1) = [tex]100 * (3^(1/6)) = 100 * 3^{\frac{1}{6}}[/tex]

Therefore, statement D is true.

E. Between 8 a.m. and 9 a.m., the population grows by a factor of [tex]$3^{\frac{2}{3}}$[/tex]

Between 7 a.m. and 8 a.m., the population grows by a factor of 3. Then, between 8 a.m. and 9 a.m., it grows by another factor of 3. So, between 7 a.m. and 9 a.m., the population grows by a factor of [tex]3^2[/tex] = 9. Taking the sixth root of 9 gives:

[tex](3^2)^(1/6) = 3^(1/3) = 3^{\frac{2}{6}} = 3^{\frac{1}{3}}[/tex]

So, the population between 8 a.m. and 9 a.m. grows by a factor of [tex]3^(1/3)[/tex]. Therefore, statement E is false.

In summary, the true statements are B and D.

We can employ the AC approach to factor the quadratic expression seen in the image. To achieve -6 * -15 = 90, we first multiply the coefficients of the first and last terms. The middle term's coefficient, which is -9, is then shown to be two factors of 90. Since -6 * -15 = 90 and -6 + (-15) = -21, which is the same as -9 when we factor out the GCF of 3, these factors are -6 and -15:

[tex]x^2 - 9x - 90 = (x - 15)(x + 6)[/tex]

As a result, the quadratic expression's factored form is (x - 15)(x + 6).

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Answer: A geometric figure which touches only the sides (or interior) of another figure.

Step-by-step explanation:

its inside but does not go past the innner edges

Answer:25 percent​ means ​one fourth​. To calculate 25 percent of a number, simply divide it by 4. For example, 25 percent of 12 is 12 divided by 4, or 3

Answer:

If the model is 5cm and 1cm is equal to 2m, it means the actual rocket is 10 meters.

Step-by-step explanation:

1cm = 2m

5cm is 5 times the amount of 1cm.

10m is 5 times the amount of 2m

Answer : 10 Meters

Explanation : 2 × 5 = 10

Stockton lake lost the least amount of water.

What is Denominator?

In mathematics, the denominator is the bottom number in a fraction that indicates the number of equal parts into which a whole is divided.

To compare the amount of water lost by each lake, we need to express the amounts lost in the same units. One way to do this is to find a common denominator for the fractions and percentages involved.

Lake Jensen lost 5/6 of its water, which can be expressed as a fraction with a common denominator of 300:

5/6 = 250/300

Lake Parlow lost 85% of its water, which can be expressed as a fraction with a denominator of 100:

85% = 85/100 = 255/300

Lake Stockton lost 246/300 of its water, which is already in terms of a common denominator of 300.

Now we can compare the amounts lost directly:

Lake Jensen lost 250/300 of its water

Lake Parlow lost 255/300 of its water

Lake Stockton lost 246/300 of its water

To determine which lake lost the least amount of water, we need to find the smallest fraction among these three.

We can see that Lake Stockton lost the least amount of water, since 246/300 is smaller than both 250/300 and 255/300. Therefore, Lake Stockton lost the least amount of water.

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The Pythagorean triple created by the steps are (3, 4, 5) where the hypotenuse is 5

The numbers x and y

Let's choose 3 and 4 as our x and y, respectively.

How we chose x and y

We can choose any numbers for x and y.

However, we usually choose numbers such that x > y to avoid duplicates.

Finding the triple

To find the Pythagorean triple, we substitute x = 3 and y = 4 in the Pythagorean identity:

(x²- y²)² + (2xy)² = (x² + y²)²

(3² - 4²)² + (2(3)(4))² = (3² + 4²)²

(-7)² + (24)² = (9)² + (16)²

49 + 576 = 81 + 256

625 = 625

We can see that this equation is true, which means that (3, 4, 5) is a Pythagorean triple.

Why at least one leg must be even

At least one leg of the triangle represented by the Pythagorean triple must have an even-numbered length because if one of the legs is odd, then the other leg and the hypotenuse must be odd too.

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Hence, in response to the provided question, we can say that As a result,  function the discus takes approximately 0.03125 seconds to strike the ground.

Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.

The supplied function for discus height is as follows:

[tex]h(t) = -16t^2 + 38t + 5\\h(0) = -16(0)^2 + 38(0) + 5 = 5[/tex]

As a result, the discus's starting height is 5 feet.

[tex]-16t^2 + 38t + 5 = 0\\[/tex]

To find t, we can apply the quadratic formula:

t = (-b \sqrt(b2 - 4ac)) (2a)

where a=-16, b=38, and c=5.

[tex]t = (-38 + \sqrt(38^2 - 4(-16)(5))) / (2(-16))\\t = (-38 + \sqrt(1524)) / (-32) (-32)\\t = (-38 + 39) / (-32) (-32)\\[/tex]

As a result, [tex]t = (-38 + 39) / (32) or t = (-38 - 39) / (32) (-32)[/tex]

t = 1/32 or t = 77/32

As the negative value doesn't make sense in this situation, we chose the positive value:

t = 1/32

As a result, the discus takes approximately 0.03125 seconds to strike the ground.

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If the bottle can only hold 13 ounces, then the probability the bottle will overflow is approximately 0.0032 or 0.32%.

First, we need to calculate the z-score, which is the number of standard deviations that the mean value of 12.2 ounces is away from the bottle's capacity of 13 ounces. We can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the bottle capacity (13 ounces), μ is the mean value of soda dispensed by the machine (12.2 ounces), and σ is the standard deviation (0.3 ounces).

Substituting the values, we get:

z = (13 - 12.2) / 0.3 = 2.67

The z-score of 2.67 means that the bottle capacity of 13 ounces is 2.67 standard deviations away from the mean value of soda dispensed by the machine.

Substituting the values, we get:

P(Z > 2.67) = 1 - P(Z ≤ 2.67) = 1 - 0.9968 = 0.0032

Therefore, the probability of the soda bottle overflowing is approximately 0.0032 or 0.32%.

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The probability that at least 29% of the sample are from poverty-level households is 0.17% and we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that at least 29% of the sample are from poverty-level households.

To answer part (a) of the question, we can use the normal approximation to the binomial distribution. The mean of the distribution is np = 300 * 0.22 = 66 and the standard deviation is sqrt(np(1-p)) = sqrt(66 * 0.78) = 7.09. We can use the normalcdf function to find the probability that at least 29% of the sample are from poverty-level households:

normalcdf(87.5, 300, 66, 7.09) = 0.0017

So the probability is 0.17%.

For part (b) of the question, we need to determine if there is convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

Since the probability that at least 29% of the sample are from poverty-level households is 0.17%, which is very small, we can conclude that there is not convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

The small probability suggests that the observed sample result is unlikely to occur by chance if the true population proportion is 22%, so we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.

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The two plans will cost the same if Kira drives 90 miles over the weekend.

The two plans cost the same when Kira drives 90 miles, and the cost of each plan is $72.

To find the mileage for which the two plans cost the same and the cost at that mileage, you should set the cost expressions for both plans equal to each other. After that, you will solve for the mileage (x).

The steps to do this are as follows:Let the mileage be x

The cost of plan 1 (C1) is given by:

C1 = 45 + 0.30x

The cost of plan 2 (C2) is given by:

C2 = 0.80 x

To find the mileage at which both plans cost the same, set C1 equal to C2 and solve for x:

45 + 0.30 x = 0.80 x x (0.30 - 0.80) = - 45- 0.50 x = -45 x = -45/-0.50 x = 90

To find the cost when the two plans cost the same,

substitute x = 90 into one of the expressions for cost.

C1 = 45 + 0.30x = 45 + 0.30(90) = 45 + 27 = $72C2 = 0.80x = 0.80(90) = $72

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Answer:

A

Step-by-step explanation:

The answer is 2x+2y+2 which is A

Answer: I think its B but I'm not quite sure

Step-by-step explanation:

If the angle of elevation from the spot where a basketball player is standing up to the top of a 10ft high hoop is 25 degrees, the player is approximately 21.45 feet away from the base of the hoop.

To solve this problem, we can use the trigonometric function tangent, which relates the opposite side of a right triangle to its adjacent side, using the angle of elevation:

tan(25 degrees) = opposite / adjacent

where the opposite side is the height of the hoop (10 feet), and we need to find the adjacent side, which is the distance from the player to the base of the hoop.

To isolate the adjacent side, we can rearrange the equation:

adjacent = opposite / tan(25 degrees)

adjacent = 10 / tan(25 degrees)

Using a calculator, we can find that tan(25 degrees) is approximately 0.4663:

adjacent = 10 / 0.4663

adjacent ≈ 21.45 feet

We round to the nearest hundredth of a foot, which gives us the final answer of 21.45 feet.

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The monthly periodic rate with APR 20.3% is 1.69%

APR is also known as Annual Payment Rate. And it is the cost of your mortgage credit as a yearly rate.

Annual Percentage Rate is typically higher than your interest rate because it includes your interest rate plus certain fees, such as lender and mortgage broker fees, based on the specific characteristics of your loan.

Monthly Interest Payment means the amount of interest paid on a Payment Date for the preceding Interest Period based on interest calculated for such preceding Interest Period at the Monthly Interest Rate.

If the Annual Percentage Rate is 20.3% and there are 12 months on a year , the monthly interest = 20.3/12 = 1.69 %

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