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Laura and Luis are hosting a FIFA World Cup Finals party and have purchased dinnerware to represent their favorite teams. Lara, a fan of team Germany, bought 25cups and 40plates with the German flag printed on them. Luis, who is rooting for Argentina, bought20cups and 35plates with the Argentinian Flag printed on them. Laura spent a total of $445.00and Luis spent a total of $380.00.

Which of the following systems could represent the situation? Select all that apply.
25c+40p=445
25c+25c=445
20+35=380
35+40=380
45+75=825

______________________________

 - Quadratic polynomial can be factored using the transformation \(ax^2+bx+c=a(x-x_{1})(x-x_{2})\), where \(x_{1}\) and \(x_{2}\) are the solutions of the quadratic equation \(ax^2+bx+c=0\).

 - This steps basically means change you current equation using the formula \(ax^2+bx+c=0\).

 - All equations of the form \(ax^2+bx+c=0\) can be solved using the quadratic formula: \(\sqrt{\frac{-b\frac{+}{}\sqrt{b^2-4ac}}{2a} }\).

 - The quadratic equation formula gives two solutions, one when \(\frac{+}{}\) is addition and one when it is subtraction.

Equation at the end of Step 3:

Equation at the end of Step 4:

Equation at the end of Step 5:

Equation at the end of Step 6:

Equation at the end of Step 7:

Equation at the end of Step 8:

Equation at the end of Step 9:

Now solve the equation \(x=\frac{15\frac{+}{}17}8}\) when \(\frac{+}{}\) is plus.

Add 15 to 17:

Divide 32 by 8:

Now solve the equation \(x=\frac{15\frac{+}{}17}8}\) when \(\frac{+}{}\) is minus.

Subtract 15 by 17:

Reduce the fraction to lowest terms by extracting and canceling out 2:

Factor the original expression using \(ax^2+bx+c=a(x-x_{1})(x-x_{2})\). Substitute 4 for \(x_{1}\) and \(-\frac{1}{4}\) for \(x_{2}\):

Simplify all the expressions of the form \(p-(-q)\) to \(p+q\):

Add \(\frac{1}{4}\) to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible:

Cancel out 4, the greatest common factor in 4 and 4:

______________________________

Answer: \(x+3\)

Step-by-step explanation:

Given

\((x+5)\) is a factor of \(x^2+8x+15\) , that is

If \(x^2+8x+15\) is divided by \((x+5)\), it yields 0 remainder

Solve the quadratic equation

\(\Rightarrow x^2+8x+15=0\\\Rightarrow x^2+3x+5x+15=0\\\Rightarrow (x+3)(x+5)=0\\\Rightarrow x=-3,-5\)

Therefore, \(x+3\) is another factor of the quadratic equation.

Answer:

x+3

Step-by-step explanation:

its A or first option or (x+3)

The solution Jada seeks does not require any algebra but can be solved to give; x = 22.

When solving the given equation;

The solution of the equation can be obtained by subtracting 6 from both sides of the equation so that we have;

Therefore, the value of x is; 22

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Answer:

(7 + 3√5)/(3 + √5) + (7 - 3√5)/(3 - √5) =

(7 + 3√5)(3 - √5)/4 + (7 - 3√5)(3 + √5)/4 =

(21 + 2√5 - 15)/4 + (21 - 2√5 - 15)/4

6/4 + 6/4 = 3

a = 0, b = 3

Answer:

-1,458

Step-by-step explanation:

The table for given situation is:

pages read by Elena  |     pages read by Jada

             4                                       5

             1                                        1.25

             9                                       11.25

             s                                        1.25

             12                                      15

            0.8                                       j

And an equation for this relationship: e = 0.8j

In this question, we have been given Elena and Jada both read at constant rate.

For every 4 pages that Elena can read, Jada read 5 pages.

We need to complete the given table.

First we find the rate of reading.

To find so we take the ratio,

5/4 = 1.25

this means when Elena reads 1 page, Jada would read 1.25 pages.

Let x be the number of pages read by Elena and y be the number of pages read by the Jada.

so we get an equation for this situation as:

y = 1.25x

for y = 11.25,

x = 11.25/1.25

x = 9

for x = 12

y = 1.25 * 12

y = 15

if Jada reads j pages and Elena reads e pages

consider ratio 4/5 = 0.8

so, we get an equation e = 0.8j

This means, when Jada reads 1 page, Elena  would read 0.8 page.

Therefore, the table for given situation is:

pages read by Elena  |     pages read by Jada

             4                                       5

             1                                        1.25

             9                                       11.25

             s                                        1.25

             12                                      15

            0.8                                       j

And an equation for this relationship: e = 0.8j

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Answer:

The right answer is:

Option OB: f(1) = -9

Common difference: 7

Step-by-step explanation:

Given sequence is:

-9, -2, 5, 12,...

Here the first number is f(1)

Common Difference:

Common difference is the difference between consecutive terms of an arithmetic sequence. It is denoted by d.

In the given sequence,

f(1) = -9

f(2) = -2

f(3) = 5

\(d=f(2)-f(1) = -2-(-9) = -2+9 = 7\\d = f(3)-f(2) = 5-(-2) = 5+2 = 7\)

Hence,

The right answer is:

Option OB: f(1) = -9

Common difference: 7

Answer:

Answer:

The right answer is:

Option OB: f(1) = -9

Common difference: 7

Step-by-step explanation:

Given sequence is:

-9, -2, 5, 12,...

Here the first number is f(1)

Common Difference:

Common difference is the difference between consecutive terms of an arithmetic sequence. It is denoted by d.

In the given sequence,

f(1) = -9

f(2) = -2

f(3) = 5

\(\begin{gathered}d=f(2)-f(1) = -2-(-9) = -2+9 = 7\\d = f(3)-f(2) = 5-(-2) = 5+2 = 7\end{gathered} \)

d=f(2)−f(1)=−2−(−9)=−2+9=7

d=f(3)−f(2)=5−(−2)=5+2=7

Hence,

The right answer is:

Option OB: f(1) = -9

Common difference: 7

Answer:

Step-by-step explanation:

5

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

Since, Triangle ACD

ΔACD is a right angle triangle.

Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

Hence,

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

Triangle ABC

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

Hence,

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

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Answer:

i wil tell you

Step-by-step explanation:

if you will work hard and you can earn double money

so you can double the money in 6 years

Answer:

1/3 or 0.3

Step-by-step explanation:

5/8 x 4/5 x 2/3 =

1/3 or 0.3

Answer:

1/3 in^3

Step-by-step explanation:

In order to find the volume, you must multiply the length, by the width, by the height. This would mean you need to do 2/3x5/8x4/5=40/120

40/120 simplified will give you 1/3

Answer: 21

Step-by-step explanation:

To find the missing number you set the two equations as a proportion:

\(\frac{7}{9} = \frac{x}{27}\)

To solve for x we cross multiply:

27 × 7 = 189

9 × x = 9x

Set up an equation:

9x = 189

Divide both sides by 9:

x = 21

Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.

The annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense=  $400, Accumulated Depreciation = $400

The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

1. Straight-Line Depreciation:

The straight-line depreciation method allocates an equal amount of depreciation expense each year over the useful life of the equipment. In this case, the annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense         $400

  Accumulated Depreciation    $400

2. Units-of-Production Depreciation:

The units-of-production method bases depreciation on the actual units produced. The depreciation per unit is calculated as ($4,800 - $800) / 2,000 = $2 per unit. The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

3. Double-Declining-Balance Depreciation:

The double-declining-balance method accelerates depreciation in the early years of the asset's life. The depreciation rate is twice the straight-line rate. The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

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The value of each measure, rounded to the nearest degree, is \(\boxed{115^\circ}\).

The measure of an angle between a tangent and a chord drawn from the point of contact is equal to half the measure of the intercepted arc.

Determine the value of each measure, rounding your answer to the nearest degree.

Two lines tangent to a circle are presented in the figure below:

\(\text{AB}\) and \(\text{CD}\).

In the first step, it is necessary to connect the points where the tangents intersect to form a chord.

\(\text{AC}\) and \(\text{BD}\) are both chords that pass through the circle.

Let \(\text{m}\widehat{\text{C}}=\text{x}\) and

\(\text{m}\widehat{\text{D}}=\text{y}\).

In accordance with the theorem, the following can be written:

\(\text{m}\widehat{\text{A}} =\frac{1}{2}(\text{x}+\text{y})\)

\(\text{m}\widehat{\text{B}} =\frac{1}{2}(\text{x}+\text{y})\)

Therefore, \(\text{m}\widehat{\text{A}}=\text{m}\widehat{\text{B}}\)

There are a few other results as well. Therefore, we have

\(\text{m}\widehat{\text{ACB}}=\text{m}\widehat{\text{A}}+\text{m}\widehat{\text{B}}[/tex

\(\text{m}\widehat{\text{ACB}}=2\times\frac{1}{2}(\text{x}+\text{y})\)\(\text{m}\widehat

{\text{ACB}}=\text{x}+\text{y}\)

Accordingly, the value of each measure is

\(\text{m}\widehat{\text{ACB}}=\text{x}+\text{y}=45^{\circ}+70^{\circ}=115^{\circ}\).

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The slope of the secant line joining (1, f(1)) and (7, f(7)) is 3.

To find the slope of the secant line joining (1, f(1)) and (7, f(7)), we'll use the formula:

Slope = (f(7) - f(1)) / (7 - 1)

First, let's find the values of f(1) and f(7) using the given function

f(x) = x^2 - 5x:
f(1) = (1)^2 - 5(1) = 1 - 5 = -4
f(7) = (7)^2 - 5(7) = 49 - 35 = 14

Now, substitute these values into the slope formula:

Slope = (14 - (-4)) / (7 - 1) = (14 + 4) / 6 = 18 / 6 = 3

So, the slope of the secant line joining (1, f(1)) and (7, f(7)) is 3.

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Matrix-vector multiplication is a linear operation because it satisfies the properties of scalar multiplication and vector addition, which are a(u+v) = au + av and a(cu) = cau, where a is a scalar and u and v are vectors.

Matrix-vector multiplication is a fundamental operation in linear algebra, where a matrix is multiplied by a vector to produce another vector. This operation is considered linear because it adheres to certain properties.

The first property is scalar multiplication, which states that multiplying a vector u by a scalar a and adding it to another vector v (a(u+v)) is equivalent to multiplying u by a (au) and v by a (av) separately and then adding the results (au + av). In other words, the operation distributes over vector addition.

The second property is the distributive property of scalar multiplication, which states that multiplying a vector u by a scalar c and then multiplying the resulting vector (cu) by another scalar a is equivalent to multiplying u by the product of the two scalars (cau). This property allows the scalar multiplication to be distributed over scalar multiplication.

These properties ensure that matrix-vector multiplication preserves the linearity of the underlying vector space. They enable the manipulation and analysis of systems of linear equations, transformations, and other mathematical operations involving matrices and vectors.

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Using the properties of percentages we can calculate that there are 200 kids in the archery camp that summer.

Long before the decimal numeral system, Ancient Rome routinely computed in fractions as multiples of 1/100.

A percentage is a dimensionless (pure) number; it has no unit of measurement.

The % value is determined by multiplying the numerical value of the ratio by 100. To calculate 50 apples as a percentage of 1250 apples, first compute 50/1250 = 0.04, then multiply by 100 to get 4%.

Let the total number of kids in the camp be x.

The number of kids who took archery = 25%

But 50 students took archery.

hence 25% of x = 50

Solving we infer:

x = 200

Therefore there are 200 kids in the camp.

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It is a hot summer day, and Jade is trying to save money to buy a new shoe. She has 32 dollars, and she plans to sell smoothies at her neighborhood for four dollars a cup. At the end of the day, she is left with a total of 164 dollars in her wallet. How many smoothies did Jade sell?

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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The correct answer is (b) divide the sum of the cross-products of Z scores by the sample size.

When calculating the correlation coefficient, also known as Pearson's correlation coefficient, the last step involves dividing the sum of the cross-products of Z scores by the sample size. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

To calculate the correlation coefficient, we follow these steps:

Standardize the variables: Convert the raw scores of each variable into Z-scores. The Z-score represents the number of standard deviations a particular score is from the mean. This step is done to put both variables on the same scale and make them comparable.

Calculate the cross-products: Multiply the Z-scores of the corresponding pairs of observations. This step gives us the cross-products of Z-scores for each pair of observations.

Sum the cross-products: Add up all the cross-products of Z-scores.

Divide by the sample size: Divide the sum of the cross-products of Z-scores by the sample size. The sample size represents the number of paired observations used in the analysis.

By dividing the sum of the cross-products by the sample size, we obtain the covariance of the variables. The covariance measures the extent to which the variables vary together. However, the covariance itself is not sufficient to determine the strength and direction of the relationship.

The final step involves dividing the covariance by the product of the standard deviations of the variables. This step normalizes the covariance and results in the correlation coefficient, which is a value between -1 and 1. The correlation coefficient indicates the strength and direction of the linear relationship between the variables. A positive correlation coefficient indicates a positive linear relationship, a negative correlation coefficient indicates a negative linear relationship, and a correlation coefficient close to zero indicates a weak or no linear relationship.

Therefore, the last step in calculating the correlation coefficient is to divide the sum of the cross-products of Z-scores by the sample size.

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If Sergio draws a rectangle with a length of 27 centimeters, the width of the rectangle must be 9 centimeters to maintain the same proportional relationship as Catlynn's rectangle.

The proportional situation represents (indirect, direct) variation: Direct variation.

In direct variation, two variables are related in such a way that an increase in one variable leads to a proportional increase in the other variable. In this case, the length and width of the rectangle are directly related to its area. As the length increases, the width also increases proportionally to maintain the same area.

If Sergio draws a rectangle with a length of 27 centimeters, the width of the rectangle must be (9, 6, 4) centimeters: 9 centimeters.

Since we know that the constant of variation, k, is 3, we can use it to find the width when the length is 27 centimeters. By rearranging the formula for direct variation, we have width = length / k. Substituting the values, we get width = 27 / 3 = 9 centimeters.

Therefore, if Sergio draws a rectangle with a length of 27 centimeters, the width of the rectangle must be 9 centimeters to maintain the same proportional relationship as Catlynn's rectangle.

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Answer:

u gotta find the variable

Step-by-step explanation:

the letter is x find it by subject

At the 90% confidence level, we can conclude that mean 1 is significantly greater than mean 2.

A confidence interval for the difference of means (mean 1 - mean 2) containing all positive values implies that mean 1 is consistently higher than mean 2.

In this scenario, the lower limit of the confidence interval is above zero, indicating that there is a 90% probability that the true difference between the means falls within this interval. Therefore, at the 90% confidence level, we can conclude that there is a significant difference between the two means, and mean 1 is greater than mean 2.

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