An Isosceles triangle and a square have the same perimeter. Find the side lengths of the triangle.
triangle base: 3x
triangle height: 2x+1
square height: 4
Answer: 5, 5, 6
How you get this answer?

On solving the equation " [tex]2y + 3 = 13[/tex] " for y , we get the value of y is 5  .

What is an Equation ?

An Equation is defined as the mathematical statement which shows that the two mathematical expressions are equal .

the equation is given as : [tex]2y + 3 = 13[/tex] ;

In the given equation , we have to solve for y ;

Subtracting 3 from both sides ,

we get ;

⇒ [tex]2y+ 3 - 3 = 13 -3[/tex] ;

⇒ [tex]2y = 10[/tex] ;

dividing both sides by 2 ,

we get ;

⇒ [tex]y = \frac{10}{2}[/tex] ;

On simplifying ,

we get y = 5 .

Therefore , After solving for y , the value of y = 5 .

The given question is incomplete , the complete question is

How do you solve the problem 2y + 3 = 13 for y ?

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The longest portion is 18 inches longer than the shortest portion.

What is algebraic equation ?

An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.

We know that the ratio of the portions is 1:2:4, so we can use this ratio to find the length of each portion by dividing 42 inches by the sum of the ratio, 1+2+4 = 7.

So each portion is 42 inches / 7 = 6 inches.

The longest portion is 4 times the length of the shortest portion, which is 6 inches. So the longest portion is 4 * 6 inches = 24 inches.

24 - 6 = 18 inches ,

Therefore, the longest portion is 18 inches longer than the shortest portion.

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The solution of the trigonometric equation is θ = π/6 radian

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

2cosθ = √3

Divide both sides by 2:

cosθ = (√3)/2

θ = cos⁻¹[(√3)/2]

θ = 30°

Convert 30° to radian by multiplying it with π/180. That is:

θ = 30 × π/180

θ = π/6 radian

Thus, the solution is θ = π/6 radian

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Answer:

Impossible: Pigs can fly. It will rain in the Sahara Desert for a week.

Probability is the likelihood that an event will happen.

Unlikely: It will snow today. Dying in a shark attack.

Likely: If you are underwater for more than 2 minutes, you drown. A cat chases a mouse.

Certain: The year is 2023.

The data set would list each day in February with a temperature measurement, measured on an interval scale.

The data set in question would list the temperatures in Albany, NY each day in the month of February. This data set would be classified as interval data, as it would measure temperatures on a numerical scale. Interval data is composed of numerical values that are measured on an interval scale, meaning that the difference between any two values is the same, regardless of their position on the scale. Temperature is an example of an interval data type, as it is measured numerically and the difference between two temperatures is the same regardless of where they are on the scale (e.g. the difference between 50°F and 55°F is the same as the difference between 90°F and 95°F). This data set would be useful for tracking temperature trends over a period of time, and for making predictions about future temperatures in a certain area.

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The price of the carpet per square meter is $32.13. It will cost $1,556.86 to carpet an area of 1475 square feet.

1. To find the price of the carpet per square meter, first convert $28.99 per square yard to meters.

1 yard = 0.9144 meters

$28.99 per yard x (1 meter/ 0.9144 meters) = $32.13 per square meter

2. To find the cost of carpeting an area of 1475 square feet, first convert 1475 square feet to square yards.

1 square foot = 0.11111 square yards

1475 square feet x (1 square yard/ 0.11111 square yards) = 13,333.33 square yards

3. Multiply the cost per square yard by the number of square yards needed to carpet the area.

$28.99 per square yard x 13,333.33 square yards = $1,556.86

The complete question is:

a carpet sells for $28.99 a square yard. what is the price of the carpet per square meter? how much will it cost to carpet an area of 1475 square feet? 1 yard is equal to 0.9144 meters

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Answer:

Untuk mencari nilai x dari persamaan 4x+7x+141+85+x+27=360, pertama-tama kita harus menyederhanakan persamaan tersebut dengan menambahkan semua x yang ada di sisi kiri persamaan.

4x+7x+x = 12x

Selanjutnya, kita harus mengurangi semua bilangan yang ada di sisi kiri persamaan dari kedua sisi persamaan:

360 = 12x + 141 + 85 + 27

Setelah itu, kita harus mengurangi semua bilangan yang ada di sisi kanan persamaan dari kedua sisi persamaan:

360 - 253 = 12x

107 = 12x

Akhirnya, kita harus membagi 107 dengan 12 untuk mencari nilai x:

x = 8.9167

Jadi, nilai x dari persamaan tersebut adalah 8.9167.

It's worth noting that some steps are not needed to be done and the equation can be simplified by doing some operations at once like : (4x+7x+x+141+85+27=360) => (12x+253=360) => (12x=107) => (x=8.9167)

Answer: The slope is equal to "-3".

Explanation: You can obtain the slope of a linear graph if you know two points on it. In this case, these points are (-2,3) and (0, -3).

If you know these points, you can use the formula below:

Slope = (Difference between y values) / (Difference between x values)

Here => 3 - (-3) / (-2) - (0) = -3, this gives the slope.

In addition, we can conclude that the formula of the graph is (y = -3x - 3), by using a specific point with the known slope value on a linear equation (mx + n).

The value that represents the smiley face is given as follows:

402.

The first three equations compose a system of equations, and then the three solutions to this system are used to obtain the value of the smiley face.

The variables and shapes are attributed as follows:

From the third equation, the square has the value obtained as follows:

8x - 6x + 3x = 60

5x = 60

x = 60/5

x = 12.

From the second equation, the value of the star is obtained as follows:

12(12) + 5y = 234

5y = 90

y = 90/5

y = 18.

From the first equation, the value of the triangle is given as follows:

12 + 3z + 18 = 57

3z = 27

z = 9.

Considering these values, the value of the smiley face is given as follows:

Smiley = 18(9 + 18 - 12) + 12(18/9 + 9)

Smiley = 18(15) + 12(2 + 9)

Smiley = 18 x 15 + 12 x 11

Smiley = 402.

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Answer: 4xy²(5-y)

Step-by-step explanation:

To factorize, we must take out common multiples in both parts of the equation. Think of 20xy² and -4xy³ as two completely separate parts. Now, we need to see which parts of the equation are found in both. For instance, 4 can go into both, an x can go into both, and y² can go into both. Now, we simply factor.

Bring the similarities out to the front: 4xy²()

Now, use division to find what would be inside the parenthesis: 5 - y

Now, combine these two parts: 4xy²(5-y)

To check your work, you can simply multiply the outside of the parenthesis by the inside, and you should get the same as what you started with. Hope this helps!

The expression that represents the magazine sale of  Graham's is 2a - 6.

Profit & Loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

The sentence "Graham sold 6 magazines less than double what Adrianne sold" can be represented by the expression 2a - 6, where a is the number of magazines Adrianne sold.

So, the expression that represents Graham's sales is 2a - 6.

Graham's magazine sales are represented by the expression 2a - 6.

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The vertex is (-5 , 5) , y-intercept is (0 , -20) and reflection of y-intercept across symmetry is (-10 , -20).  

What is parabola ?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

a curve made when a cone's surface collides with a plane that is perpendicular to a straight line: a curve created when a point moves in such a way that its separation from a fixed point equals its separation from a fixed line something with a bowl-like form.

Parabola, also known as an open curve or conic section, is formed when a right circular cone and a plane perpendicular to one of the cone's elements cross.

In the equation you provided, the corresponding values are:

a = -1

b = -10

c = -20

Plugging in the values to find the vertex yields:

- (-10)/(2*-1)

= 10/-2

= -5

This is the x-coordinate of the vertex

-x²-10x - 20

= -(-5)² - 10×(-5) - 20

= -25 +  50 - 20

= 5

∴The vertex is located at the point (-5 , 5)

The y-intercept when x = 0

-x² - 10x - 20

= -20

The y-intercept of the vertex at the point (0 , -20)

Since you have 2 points, look at the y-intercept and imagine a point reflected across the line of symmetry.

That point will be your last point, and is located at: (-10 , -20)

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Answer:

  see attached for a graph

  a. BA≅BC (the compass told me so)

  c. AD≅CD

Step-by-step explanation:

You want a graph of ∆ABC, with A(4, 7), B(0, 0), and C(8, 1). You want to identify the congruent sides, construct an angle bisector, and comment on how it divides the opposite side.

The graph of the points, and the construction of the angle bisector are shown in the attachment.

Since you have your compass available for construction, you can use set it to the measure of one side and compare that to the other two sides. It does not take long to identify AB ≅ BC. (A compass setting shows they are the same length.)

As you know, an angle bisector is constructed by first identifying two points on the sides of the angle that are the same distance from the vertex of the angle. Then two intersecting arcs are drawn with the same radius using those points as their centers. The vertex and the intersection of the arcs defines the ray that is the angle bisector. This is shown in the attachment.

You can count grid squares (or use the compass) to determine that AD and CD are the same length: D is the midpoint of AC.

This reinforces your knowledge that the angle bisector of the a.pex angle of an isosceles triangle is also an altitude and a median.

The break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

What is average ?

The average is a measure of central tendency that is calculated by adding a set of values together and dividing the sum by the number of values. It is also known as the arithmetic mean. It is a way to represent a typical value of a dataset.

The break-even point is the point at which the cost of the products equals the revenue from the sales of the products. To find the break-even point, we need to set the cost function (C(x) = 550 + 3.00x) equal to the revenue function (R(x) = 5.50x) and solve for x.

C(x) = 550 + 3.00x = R(x) = 5.50x

3.00x = 5.50x - 550

0.50x = 550

x = 1100

So the break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

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The value of the given function f(x) and g(x) is [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere and are crucial for constructing physical relationships.

The given functions are:

[tex]f(x) = 5x^2 - 3 \\\\g(x) = x^2 -4x-8[/tex]

(f - g)(x) is equivalent to the following:

(f - g)(x) = f(x) - g(x)

[tex]f(x) - g(x) = 5x^2 - 3 - x^2 +4x+8\\\\f(x) - g(x) = 4x^2 +4x+5[/tex]

Hence, the value of [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

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Answer:

the answer is 46% which is option d.

Step-by-step explanation:

To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.

His total monthly debt payments are:

$2,500 (mortgage payment)

$250 (lease payment)

$500 (credit card payments)

$425 (speed boat payment)

Total Monthly Debt Payments = $2,500 + $250 + $500 + $425 = $3,675

His gross monthly income is his annual salary of $96,000 divided by 12 months which is $8,000

DTI = Total Monthly Debt Payments / Gross Monthly Income = $3,675 / $8,000 = 0.46 or 46%.

The value of Jim's DTI (debt-to-income) ratio is 40%.

Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.

Given that,

Annual salary = $96,000

Monthly income = 96000/12 = $8000

Total income per month = $8000 + $1,200 = $9,200

Monthly expenses = $2,500 + $250 + $500 +  $425

                               = $3675

DTI = 3675 / 9,200 = 0.399 = 39.9% ≈ 40%

Hence the DTI of Jim is 40%.

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Now your friend would also like to determine the most likely continent of origin for each coin. Logistic regression model best suited to predict the continent of origin. So the option b is correct.

A variable's value can be estimated using linear regression analysis depending on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Based on a given dataset of independent variables, logistic regression calculates the likelihood that an event will occur, such as voting or not voting. Given that the result is a probability, the dependent variable's range is 0 to 1.

The log chances of the outcomes are modelled as a linear combination of the predictor variables in multinomial logistic regression, which is used to model nominal outcome variables.

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The complete question is:

Now your friend would also like to determine the most likely continent of origin for each coin. Which model best suited to predict the continent of origin?

(1) Linear regression

(2) Logistic regression

(3) Multinomial logistic regression

Answer:

17/20

Step-by-step explanation:

The ratio 8.5 to 10 as a fraction in simplest form is 17/20. 8.5/10 = 85/100 = 17/20

(8.5:10 = 85:100 = 85/100 = 17/20)

Answer:

30 feet

Step-by-step explanation:

The scale factor is 1 inch = 3 feet

So 10 inches = 10 x 3 feet= 30 feet

Height of the lighthouse is 30 feet

1. The  triangles, which are similar to ΔAED  are ΔAFE, ΔEFD, ΔECD, ΔABE

2.  The length of segment FA is, 32/3 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

A rectangle ABCD having triangles in it,

1.  ΔAED is a right angle triangle,

all the triangle which are right angle triangle will be similar to  ΔAED

So,  ΔAFE, ΔEFD, ΔECD, ΔABE are similar triangles

2. Now, consider ΔEFD

EF = 8 unit

ED = 10 unit

∠CEB = 53°

∠CEF = 90°

∠DEF = 37°

∠AED = 90°

∠AEF = 53°

tan53° = FA/FE

4/3 = FA/8

FA = 32/3

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High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

We have to find from the given options which data outcome of the number of customers in line would best support opening another cash register.

The number of customer in the line having high mean with small standard deviation means deviation in data small and data cluster around mean. High mean I'm play high number of customer in line. This help to opening another cash register.

Hence, High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

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The requried, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

Null Hypothesis (H0): The mean height of five-year-old children in the city is not greater than 42.5 inches.

Alternative Hypothesis (Ha): The mean height of five-year-old children in the city is greater than 42.5 inches.

We will conduct a one-sample t-test since we have the sample mean and standard deviation.

Let's calculate the t-statistic and find the corresponding p-value.

The formula for the t-statistic is:

[tex]t=\dfrac{x-\mu}{s/\sqrt n}[/tex]

Where:

x  is the sample mean (44.1 inches),

μ is the population mean under the null hypothesis (42.5 inches),

s is the sample standard deviation (3.5 inches),

n is the sample size (40).

Let's calculate the t-statistic:

[tex]t=\dfrac{44.1-42.5}{3.5/\sqrt n}\\t=2.89[/tex]

Now, we need to locate the p-value associated with this t-statistic. The p-value is the probability of observing a t-statistic as extreme as the one calculated (or even more extreme) under the assumption that the null hypothesis is true.

The p-value can be looked up using a t-distribution table or calculated with statistical software. In this matter, since the t-statistic is quite large, the p-value will be very small.

Suppose the p-value is less than the significance level (α) chosen for the test (commonly 0.05). In that case, we reject the null hypothesis in favor of the alternative hypothesis. This means there is convincing evidence that the mean height of five-year-old children in this city is greater than 42.5 inches.

Conversely, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

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Considering the expression of a line, the slope intercept form is y= -x+2.

A linear equation o line can be expressed in the form y = mx + b

where

This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).

In this case, the line is x+y=2. Expressed in the form y = mx + b, you get:

y= 2 -x     or     y= -x +2

Finally,  x+y=2 in slope intercept form is y= -x+2.

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The kind of triangle in the image above is a scalene triangle.

A scalene triangle is a type of triangle that has three sides with different lengths. It is one of the three main types of triangles, the other two being isosceles and equilateral triangles. They also have three different angles.

Scalene triangles do not have any congruent sides or angles, making them the most diverse and versatile type of triangle. They can be used to construct many different shapes and figures, and have many unique properties and characteristics that make them useful in a variety of fields, including mathematics, physics, and engineering.

In the image given, the three sides of the triangle appears to be of different sizes.

Therefore, we can conclude that the triangle is a scalene triangle.

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The original expression [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex] was rationalized by multiplying both numerator and denominator by [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex], and then dividing numerator and denominator by [tex]$\sqrt[3]{4}$[/tex].

[tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}} = \frac{\sqrt[3]{8}}{4}$[/tex]

Minimum possible value of [tex]$ab = 32$[/tex]

[tex]= \frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{4}$[/tex]

We start with the given expression, [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex], which is in the form [tex]$\frac{p}{qr}$[/tex]. To rationalize the denominator, we need to multiply both numerator and denominator by qr (which is [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex] in this case). This gives us[tex]$\frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$[/tex]. We can simplify this expression further by dividing both numerator and denominator by [tex]$\sqrt[3]{4}$[/tex], giving us [tex]$\frac{\sqrt[3]{8}}{\sqrt[3]{2} \sqrt[3]{4}}$[/tex]. Finally, we can simplify the denominator further by multiplying both numerator and denominator by [tex]$\sqrt[3]{2}$[/tex], giving us the final result of [tex]$\frac{\sqrt[3]{8}}{4}$[/tex]. The minimum possible value of ab is 32.

The original expression [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex] was rationalized by multiplying both numerator and denominator by [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex], and then dividing numerator and denominator by [tex]$\sqrt[3]{4}$[/tex]. The final result was[tex]$\frac{\sqrt[3]{8}}{4}$[/tex], and the minimum possible value of ab was 32.

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As a result, the solution is shaped like a circle ( -5 , 7 ). The second half of the text has a 6 mm diameter. Three and four are FALSE. There are ten miles between points A and B.

The construction of a circle is the outcome of following a thinking object in a plane and keeping a fixed distance from a particular location. A Greek word kirkos, which means hoop or ring, is the source of the English word circle.

Here,

Typically, a circle's equation is,

( x - h )² + ( y - k ) ( y - k )

x² = r²

( y - k ) ( y - k ) = r²

6² = r²

where the radius of the ring is and the center's coordinates are (h, k).

Part 1.

We arrive to using the formula for the common circle.

The circumference of a circle's coordinate is ( -5 , 7 )

As a result, the second choice is the best.

Part 2.

We arrive to using the formula for the common circle.

The circle's diameter is six.

The initial choice is therefore the best.

Part 3.

We arrive to using the equation again for common circle.

Circle circumference coordinate: ( 2 , 3 )

False as a result.

The axis coordinates of the circle are: ( 2 , 3 )

False, then.

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When you divide a number by 1/2, it is the same as multiplying the number by 2. Therefore, the result of the division is two times the original number.

Let's say we have a number, X.

When you divide X by 1/2, you can rewrite the equation as:

X ÷ 1/2 = X × 2

Thus, the result of the division is two times the original number, X.

Let's say we have a number, X. When you divide X by 1/2, you are essentially multiplying X by 2. This means that the result of the division is two times the original number. In other words, if you divide X by 1/2, the answer will be 2X. To put it another way, if you take any number, X, and divide it by 1/2, the result will be two times the original number. This is because 1/2 is the same as multiplying the number by 2. For example, if you divide 10 by 1/2, the result will be 20, since 10 multiplied by 2 is 20. Similarly, if you divide 25 by 1/2, the result will be 50, since 25 multiplied by 2 is 50. In conclusion, when you divide any number, X, by 1/2, the result will always be two times the original number.

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The coordinates of its midpoint M are (0,6)

A line is an infinitely long object with no width, depth, or curvature.

Given that a line segment has the endpoints B(0, 2) and C(0, 10).

We need to find the  coordinates of its midpoint M.

Midpoint=(0+0/2, 2+10/2)

Midpoint=(0, 12/2)

Midpoint=(0, 6)

The coordinates of its midpoint M are (0,6)

Hence, the coordinates of its midpoint M are (0,6)

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