Solve using substitution.

Slope of PR = Slope of SU = rise / run = -3/2

The slope of a line is the ratio of the rise over the run, which is m = change in y / change in x.

To prove that the slope of line segment PR and the slope of line segment SU are equal, find the slope of each of the line given that are similar triangles:

Slope of PR = rise / run = PQ/QR = -3/2

Slope of SU = rise / run = ST/TU = -6/4 = - 3/2

Therefore, both line segments have the same slope of -3/2.

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Answer:

Step-by-step explanation:

4.  16 players enter the tournament.  f(0) = 16(1/2)° = 16

This is the value of y when x=0

5.  After 4 rounds, 1 player is left.  f(4) = 16(1/2)⁴ = 1

6.  Rate of change = Δy/Δx = (4-8) / (2-1) = -4

f(1) = 16(1/2)¹ = 8

f(2) = 16(1/2)² = 4

The average rate of change between rounds 1 and 2 is 4, meaning 4 players are eliminated.

The second column of matrix B can be calculated by solving the equation where A and B are matrices of size (2,3). The second column of B is
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]

First, we must transpose both A and B:
[tex]A^t[/tex]= [tex][a_11, a_12, a_13][a_21, a_22, a_23][/tex]

[tex]B^t[/tex] = [tex][b_11, b_21][b_12, b_22][b_13, b_23][/tex]
The second column of B.

[tex]B^tA^t[/tex] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
[1, -2] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]


Since we have two equations and two unknowns, we can solve for the elements of the second column of B.
Solving for [tex]b_21[/tex]:
[tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Solving for [tex]b_22[/tex]:
[tex]-2 = a_11b_12 + a_12b_22 + a_13b_32b_22 = (-2 - a_11b_12 - a_13b_32)/a_12[/tex]

Therefore, the second column of B is:
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]

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Based on the properties of rectangles, the angles and the side lengths are KN = 11 and NLK = 32

From the question, we have the following parameters that can be used in our computation:

JN = 2x + 7, LN = 6x - 1

NKJ = 58 degrees

The diagonals or a rectangle are equal

So, we have

2x + 7 = 6x - 1

Evaluate the like terms

4x = 8

Divide

x = 2

So, we have

KN = 2 * 2 + 7

KN = 11

Adjacent angles in this case add up to 90 degrees

This gives

NLK = 90 - 58

Evaluate

NLK = 32

Hence, the measure of the angle is 32 degrees

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Answer:

Tamara has $31.01 left

Step-by-step explanation:

Tamara has $70

Dress - $10

Drink - $4.99

Necklace - $20

Snack - $4

Add all of these costs up then subtract them by 70

10 + 4.99 + 20 + 4 = 38.99

70 - 38.99 = 31.01

[tex]70 - (10+4.99+4+20) = 70 - 38.99 = \$ \ 31.01[/tex]

Answer:

  x=4.3m

Step-by-step explanation:

It is made up by six graphics.

Two triangles=1/2*x*5.6*2=5.6x

Base rectangular: 11.3x

Back rectangular: 11.3*5.6=63.28

Front rectangular:11.3*7.1=80.23

Add together: 5.6x+11.3x+63.28+80.23=216.18

                      16.9x=72.67

                            x=4.3m

The vector in the form \( \langle a, b\rangle \) is simply the given vector with the values of a and b identified and simplified as necessary.

To write the vector in the form \( \langle a, b\rangle \), we need to identify the values of a and b from the given vector. The value of a corresponds to the x-component of the vector, and the value of b corresponds to the y-component of the vector.

If the given vector is \( \langle 3, -4\rangle \), then the value of a is 3 and the value of b is -4.

If the given vector is \( \langle \frac{5}{2}, \sqrt{3}\rangle \), then the value of a is \(\frac{5}{2}\) and the value of b is \(\sqrt{3}\).

If the given vector is \( \langle -2\sqrt{2}, 7\sqrt{3}\rangle \), then the value of a is \(-2\sqrt{2}\) and the value of b is \(7\sqrt{3}\).

In all of these cases, the values of a and b are either integers or fractions, and any radicals are simplified as much as possible.

So, the vector in the form \( \langle a, b\rangle \) is simply the given vector with the values of a and b identified and simplified as necessary.

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Using the subtraction, the result of (29v)−(−13v+59) is 42v - 59

The distributive property is a fundamental property of arithmetic and algebra that involves the distribution of a factor across a sum or difference of two or more terms. The property states that when you multiply a number or term by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses and then simplify.

To subtract (29v)−(−13v+59), we first need to distribute the negative sign in front of the parentheses, which will change the signs of each term inside. So, we have

= 29v + 13v - 59

Then, we can combine the like terms, which in this case are the two terms with the variable v. We add the coefficients (numbers in front of v) to get

= 42v - 59

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If the length of the rectangle is represented by x, then the height and width can be represented by the factors a and b, respectively. Therefore, the expression for the height and width in terms of the length can be written as:

Height = a * x

Width = b * x

These expressions can be used to find the height and width of the rectangle if the length and the factors are known.

For example, if the length is 10 and the factors are 2 and 3, then the height would be 2 * 10 = 20 and the width would be 3 * 10 = 30.

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let's convert all mixed fractions to improper fractions, let's add all berries and then see how many times 1/2 go into that sum or namely division.

[tex]\stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} ~\hfill \stackrel{mixed}{4\frac{1}{2}} \implies \cfrac{4\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ strawberries }{\cfrac{13}{4}}~~ + ~~\stackrel{ blueberries }{\cfrac{9}{2}}\implies \cfrac{(1)13~~ + ~~(2)9}{\underset{\textit{using this LCD}}{4}}\implies \cfrac{13+18}{4}\implies \cfrac{31}{4} \\\\\\ \stackrel{\textit{now let's divide that sum by }\frac{1}{2}}{\cfrac{31}{4}\div \cfrac{1}{2}}\implies \cfrac{31}{4}\cdot \cfrac{2}{1}\implies \cfrac{31}{2}\implies {\Large \begin{array}{llll} 15\frac{1}{2} \end{array}}[/tex]

Answer:

Step-by-step explanation: your hot

Answer:

Step-by-step explanation: first if you do x/32.5 ≤ 117 = 3802.5 and also we know that 1 mile= 32.5, so if you take 32.5 * 117 it also equals 3802.5

so it will take him a minimum of 3802.5 gallons to drive 117 miles

Dakota would need at least 3.6 gallons of gasoline to drive 117 miles to his brother's house.

A statement that compares two numbers or expressions using an inequality symbol, such as (less than), > (greater than), (less than or equal to), or, is known as an inequality in mathematics (greater than or equal to).

Let x be the volume of gasoline required for Dakota to travel 117 miles to his brother's home. The minimum value of x can be calculated using the inequality shown below:

x ≥ 117 / 32.5

Here, we calculate the bare minimum amount of gasoline Dakota would require to travel 117 miles by dividing the whole distance (117 miles) by the miles per gallon (32.5 miles/gallon).

The inequality is reduced to: x ≥ 3.6

Dakota would therefore require 3.6 gallons of fuel to travel 117 miles to his brother's house.

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The average number of fruit flavored pieces you get in a bowl is 18.

To find the number of fruit flavored pieces you get in a bowl, you can calculate the average of the fruit flavored pieces in the five bowls you poured.

Here's how:

1: Add the number of fruit flavored pieces in each bowl: 3 + 23 + 20 + 23 + 21 = 90

2: Divide the total number of fruit flavored pieces by the number of bowls: 90 / 5 = 18

Therefore, the average number of fruit flavored pieces you get in a bowl is 18.

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So it will take 20 years for High School R and High School T to have the same enrollment.

Enrollment is the process of registering for classes at a college or university. The process usually involves submitting an application and providing transcripts and other documents to the school.

The enrollment at High School R is increasing by 15 students per year while High School T is decreasing by 10 students per year. To figure out how many years it will take for both schools to have the same enrollment, we need to calculate the difference between the two schools.
High School R currently has 200 students and High School T has 400 students. The difference between the two schools is 200 students (400-200 = 200).
Since High School R is increasing by 15 students per year and High School T is decreasing by 10 students per year, it will take 20 years for the two schools to have the same enrollment.
To calculate this, we divide the difference between the two schools (200 students) by the difference between the two schools' enrollment growth (15 students - 10 students = 5 students). This gives us 200/5 = 40. Since 40 years is too long, we divide 40 by 2 and get 20, which is the answer. So it will take 20 years for High School R and High School T to have the same enrollment.

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This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

To find the total displacement vector for this walk, we can use the Pythagorean Theorem to find the magnitude of the displacement vector and the direction of the displacement vector.

First, let's find the magnitude of the displacement vector:

d = √((Δx)² + (Δy)²)

Where Δx is the change in the x-direction and Δy is the change in the y-direction.

Δx = 5 + 4cos(45°) + 0 + 3cos(225°) + 4 = 9.83 miles
Δy = 0 + 4sin(45°) + 6 + 3sin(225°) + 0 = 2.17 miles

d = √((9.83)² + (2.17)²) = √(96.58 + 4.71) = √(101.29) = 10.06 miles

So, the magnitude of the displacement vector is 10.06 miles.

Next, let's find the direction of the displacement vector:

θ = tan⁻¹(Δy/Δx) = tan⁻¹(2.17/9.83) = 12.58°

So, the direction of the displacement vector is 12.58°.

Therefore, the total displacement vector for this walk is 10.06 miles at an angle of 12.58°.

If this person walked straight home, they'd have to walk 10.06 miles.

This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

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The probability that a person from the survey who has a tablet also has a laptop is 5.8%.

To calculate this, we can use conditional probability. We know that 62% of respondents have a tablet, and 12% of the respondents who have a laptop also have a tablet. So, the probability that a respondent has a laptop given that they have a tablet can be calculated as follows:

We know that P(laptop and tablet) = 0.12 (since 12% of laptop owners also have a tablet), and P(table) = 0.62 (since 62% of respondents have a tablet). So, plugging these values into the formula gives:

However, this is the probability that a person who has a tablet also has a laptop. The question asks for the probability that a person from the survey who has a tablet also has a laptop, which means we need to consider the overall probability of having a laptop, regardless of whether or not they have a tablet. This can be calculated as follows:

P(laptop) = 0.3

So, the probability that a person from the survey who has a tablet also has a laptop, given that they have a laptop, is:

P(laptop|tablet and laptop) = P(laptop and tablet) / P(laptop) = 0.12 / 0.3 = 0.4 or 5.8%

Therefore, the correct answer is 5.8%.

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1.3567% is the average percent change in population in California from 2000-2009.

The term "population" is frequently used to describe the total number of people living in a particular location. To estimate the number of the residents within a certain territory, governments conduct censuses.

Population is referred to a group of people who share some established characteristics, such as region, race, culture, nationality, or religion, in sociology or population geography. The social science of demography involves the statistical analysis of populations.

average percent change in population =1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9

= 1.3567%

Therefore, 1.3567% is the average percent change in population in California from 2000-2009.

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If today it was sunny in the morning and raining in the afternoon, and Laura traveled a total of 24 km in 40 minutes, then she is calculated to have rode the electric scooter for  24 minutes in the afternoon.

Let's assume that Laura rode her scooter for x minutes in the morning and for (40 - x) minutes in the afternoon.

In the morning, she traveled a distance of 45 × (x/60) km.

In the afternoon, she traveled a distance of 30 × ((40-x)/60) km.

The total distance traveled is 24 km, so we can set up the equation:

45 × (x/60) + 30 × ((40-x)/60) = 24

Multiplying both sides by 60, we get:

45x + 30(40-x) = 1440

Simplifying and solving for x, we get:

15x + 1200 = 1440

15x = 240

x = 16

Therefore, Laura rode her scooter for (40-16) = 24 minutes in the afternoon.

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The question is :

Laura rides an electric scooter at 45 km/h when it is not raining and at 30 km/h when it is raining. Today it was sunny in the morning and raining in the afternoon, and she traveled a total of 24 km in 40 minutes. How many minutes did she ride in the afternoon?

The values of the variables are y =50 and x = 130

From the question, we have the following parameters that can be used in our computation:

The isosceles trapezoid

An isosceles trapezoid is a quadrilateral with two parallel sides of equal length and two non-parallel sides of unequal length.

This means that the base angles are congruent

Using the above as a guide, we have the following for the variable y

y = 50

Solving further, we have the following equation for variable x

x + 50 = 180

Evaluate the equation

x = 130

Hence, the value of x is 130

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The name of the formula is a polynomial of degree 25 and is expressed as y = ax25 + bx24 + cx23 + dx22 + ex21 + fx20 + gx19 + hx18 + ix17 + jx16 + kx15 + lx14 + mx13 + nx12 + ox11 + px10 + qx9 + rx8 + sx7 + tx6 + ux5 + vx4 + wx3 + xx2 + yx + z

The formula you have provided is called a polynomial equation. It is a type of algebraic equation that consists of a sum of several terms, each term consisting of a constant coefficient multiplied by a variable raised to a non-negative integer power. In this case, the variable is x and the coefficients are a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z. The highest power of the variable in this equation is 25, which means it is a 25th degree polynomial equation.

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Other roots of the given trinomial equation apart from (x -1) will be:

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given a trinomial equation x³ + x²-6x +4 that has a root (x + 1)

Let P(x) = x³ + x²-6x +4

It is given that ( x - 1 ) is one of the factor of p(x)

On dividing p(x) by (x - 1), we get:

P(x) = (x- 1) (x² +2x -1)

For the quotient of the factor we will use the quadratic formula

(x² +2x -1) = 0

From quadratic formula,

x = 1/2a(-b ± √(b² - 4ac))

x = 1/2(-2 ±√(4 +4)

x = -1 ± √2

Thus,

Other roots of the given trinomial equation apart from (x -1) will be:

x = -1 -√2

x = -1 + √2

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Complete question:

if (x - 1) is a factor of x³ + x²-6x +4· find the other two factors​

The slope-intercept form of the equation of the line that has a slope of -1/6 and passes through the point (8,0) is y = -1/6x + 4/3.

To find the slope-intercept form of the equation of the line that has the given slope m and passes through the given point, we can use the point-slope form of a linear equation and then rearrange it to the slope-intercept form.

The point-slope form of a linear equation is given by:

y - y₁ = m(x - x₁)

Where m is the slope and (x₁, y₁) is the point that the line passes through.

In this case, m = -1/6 and the point is (8, 0).

Plugging these values into the point-slope form, we get:

y - 0 = -1/6(x - 8)

Simplifying and rearranging to the slope-intercept form, we get:

y = -1/6x + 8/6

y = -1/6x + 4/3

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To find all zeros for the function f(x) = x3 - 12x? - 13x + 24.

To find all zeros for the function f(x) = x3 - 12x? - 13x + 24, we can use the Rational Root Theorem to find the list of possible rational zeros.

The Rational Root Theorem states that if a polynomial f(x) = anxn + an-1xn-1 + ... + a1x + a0 has integer coefficients, then any rational zero of f(x) must be of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an.

In this case, the constant term is 24 and the leading coefficient is 1. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 1 are 1. Therefore, the possible rational zeros are:

±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±8/1, ±12/1, ±24/1

Simplifying these fractions gives us the list of possible rational zeros:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Now, we can use synthetic division to test each of these possible zeros until we find one that gives us a remainder of 0. Once we find a zero, we can factor it out of the polynomial and continue the process with the remaining polynomial until we have found all the zeros.

For example, if we test the possible zero 2, we get:

2 | 1 -12 -13 24
| 2 -20 -66
-----------------
1 -10 -33 -42

Since the remainder is not 0, 2 is not a zero of the function. We can continue testing the other possible zeros until we find all the zeros of the function.

Once we have found all the zeros, we can write them as a list. For example, if the zeros are 3, -2, and 4, we would write:

The zeros of the function are 3, -2, and 4.

Therefore, to find all zeros for the function f(x) = x3 - 12x? - 13x + 24, we can use the Rational Root Theorem to find the list of possible rational zeros, and then use synthetic division to test each possible zero until we find all the zeros of the function.

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Answer:

To predict the number of people whose favorite snack is brownies, we need to use the proportion of people in the sample who said brownies were their favorite and apply it to the total number of people attending the reception.

The total number of people in the sample is:

27 + 19 + 74 + 60 = 180

The proportion of people in the sample who said brownies were their favorite is:

27/180 = 0.15

To predict the number of people at the reception whose favorite snack will be brownies, we can multiply the total number of people attending the reception by the proportion of people in the sample who said brownies were their favorite:

3200 x 0.15 = 480

Therefore, we can predict that approximately 480 people at the reception will have brownies as their favorite snack.

The product of 2/3 and 3/5 is 2/5    

To represent a fraction on a grid, we need to divide the grid into equal parts based on the denominator of the fraction, and then shade in a number of those parts based on the numerator of the fraction.

Here we have

=> 2/3 × 3/5

To solve 2/3 × 3/5, we multiply the numerators together and the denominators together

=> [ 2/3 × 3/5 ] = 6/15

=> [ 2/3 × 3/5 ] = 2/5        

This multiplication can be represented as given in the picture

Therefore,

The product of 2/3 and 3/5 is 2/5    

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Answer: You have to simplify divide by x

Step-by-step explanation:

The null hypothesis (H0) is the hypothesis that is assumed to be true until there is evidence to suggest otherwise. In this case, the null hypothesis is that the percentage of car crashes that occur within 2 miles of the motorist's home is less than or equal to 47%. The alternative hypothesis (Ha) is the hypothesis that is being tested and is the opposite of the null hypothesis. In this case, the alternative hypothesis is that the percentage of car crashes that occur within 2 miles of the motorist's home is greater than 47%.

To express the null and alternative hypotheses in symbolic form, we can use the following symbols:

H0: p <= 47% (The percentage of car crashes that occur within 2 miles of the motorist's home is less than or equal to 47%)
Ha: p > 47% (The percentage of car crashes that occur within 2 miles of the motorist's home is greater than 47%)

Note that we are using the symbol <= for less than or equal to, and > for greater than. These symbols are used in hypothesis testing to express the null and alternative hypotheses in symbolic form.

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Answer:

Aquí hay tres situaciones en las que se hace necesario el uso de números negativos:

Temperaturas: Las temperaturas pueden ser positivas o negativas, dependiendo de si estamos midiendo la temperatura por encima o por debajo del punto de congelación del agua. Por ejemplo, si la temperatura es de -10°C, significa que hace 10 grados bajo cero.

Deudas: Cuando una persona toma un préstamo o usa una tarjeta de crédito, puede acumular una deuda que debe ser pagada en el futuro. Esta deuda se representa con un número negativo, ya que representa el dinero que se debe.

Altitud: Cuando se mide la altitud de un lugar, puede ser por encima o por debajo del nivel del mar. Si la altitud es por debajo del nivel del mar, se representa con un número negativo. Por ejemplo, la altitud del Mar Muerto es de aproximadamente -430 metros.

we can reject the null hypothesis

Null Hypothesis (H₀): μ ≥ 50

Alternative Hypothesis (H₁): μ < 50

Assumptions:
- A normal distribution for the population of LCBO stores
- A random sample of 20 stores
- A significance level of 0.05

Critical-value approach:

First, calculate the test statistic using the formula:

Test statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

= (41.3 - 50) / (12.2 / √20)

= -2.6

Then, compare this test statistic to the critical-value.

The critical-value is the value that divides the acceptance and rejection regions of the distribution. The critical-value for a two-tailed test with a significance level of 0.05 is ±1.96.

Since -2.6 is less than -1.96, the test statistic falls into the rejection region and we reject the null hypothesis.

p-value approach:

Calculate the p-value using the formula:

p-value = 1 - CDF(test statistic)

Where CDF is the cumulative distribution function.

= 1 - CDF(-2.6)

= 0.004

Since 0.004 is less than 0.05, we reject the null hypothesis.

In conclusion, based on the critical-value approach and the p-value approach, we can reject the null hypothesis and conclude that the population mean sales increase is less than 50 cases.

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Answer:

A. 5 cm

Step-by-step explanation:

AB = BC

x + 3 = 3x - 1

x - 3x = -1 - 3

-2x = -4

x = -4/-2

x = 2

BC = 3x - 1 = 3(2) - 1 = 6 - 1 = 5