3-1 The roof area of a fable roof is made up of two rectangles. (True or False)

Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

The midpoint between [tex]-3,5 and 1,6 is (-1,5.5)[/tex]

The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between [tex]-3,5 and 1,6[/tex].

The coordinates of the two points are:

Point 1: ([tex]-3,5[/tex])

Point 2: ([tex]1,6[/tex])

To find the midpoint, we can average the x-coordinates and y-coordinates separately.

Midpoint's x-coordinate = (x-coordinate of Point [tex]1[/tex] + x-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]

Midpoint's y-coordinate = (y-coordinate of Point [tex]1[/tex] + y-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]

According to the problem

Midpoint's x-coordinate = [tex](-3+1)/2= -2/2= -1[/tex]

Midpoint's y-coordinate = [tex](5+6)/2= 11/2 = 5.5[/tex]

So, the midpoint between [tex]-3,5[/tex] and [tex]1,6[/tex] is [tex](-1,5.5)[/tex].

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The angles formed by the bisector are equal in measure, adjacent, supplementary, form a linear pair, and are congruent.

When a line bisects an angle, it divides the angle into two equal parts. The resulting angles have several properties

They have equal measures: The two angles formed by the bisector have the same degree measurement.

They are adjacent: The two angles share a common side and vertex.

They are supplementary: The sum of the two angles formed by the bisector is 180 degrees.

They form a linear pair: The two angles, together with the adjacent angle on the other side of the bisector, form a straight line or a linear pair.

They are congruent: The two angles formed by the bisector are congruent to each other.

These properties are useful in solving problems involving angle bisectors in geometry.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What are some properties of the angles formed by the bisector?

Therefore , the solution of the given problem of inequality comes out to be  x< 3, which denotes that x can be any real number below 3.

The distinction in algebra can be expressed by an amalgamation or set of two numbers since there is no indicator for it. Equity usually comes after equilibrium. The persistent gap in standards is what causes inequality. Disparity and equality are not the same thing. As was the least favourite symbol, despite the fact that its components are typically neither connected nor adjacent to one another.

Here,

We can use the procedures listed below to solve the inequality 4x - 1 11:

To isolate the term with x on one side of the inequality, add 1 to both sides of the inequality in step 1:

=> 4x - 1 + 1 < 11 + 1 4x < 12

Step 2: To find x, multiply both sides of the inequality by 4.

=> 4x/4 < 12/4 x < 3

The answer to the inequality 4x - 1 11 is therefore x< 3, which denotes that x can be any real number below 3.

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The new cost after the discount and tax are applied is $872.10, which is option (d).

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

First, let's calculate the amount of discount Angel will receive using the coupon code:

Discount = 15% of $950 = 0.15 x $950 = $142.50

Next, let's calculate the new price of the jacket after the discount is applied:

New price = $950 - $142.50 = $807.50

Now, let's calculate the amount of tax that will be applied to the new price:

Tax = 8% of $807.50 = 0.08 x $807.50 = $64.60

Finally, let's add the tax to the new price to get the total cost:

Total cost = $807.50 + $64.60 = $872.10

Therefore, the new cost after the discount and tax are applied is $872.10, which is option (d).

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Answer: 49/60 of corn

Step-by-step explanation:

How I got this answer was I basically paid attention to the wording. 1/6 as much meaning x 1/6. So, I converted 4 9/10 to a fraction and got 49/10. Then, I multiplied 49/10 by 1/6 and got 49/60. The fraction can't be simplified any lower, so it is supposed to be left as is. Hope this helped!

The protein requirement may be slightly higher, around 1.0 to 1.2 g/kg, this would put his daily protein needs between 72.6 and 87.1 grams.

As a healthy 20-year-old college student who jogs at a moderate pace 3 days per week for 20 minutes, John has an active lifestyle that requires a certain amount of protein to maintain his body.

Protein is an essential nutrient that is needed for the growth and repair of muscles, bones, and other tissues in the body.
According to the Dietary Reference Intake (DRI), the recommended daily allowance of protein for an adult male is 56 grams per day.

However, this amount can vary depending on a person's body weight, activity level, and other factors.
In John's case, he weighs 160 lbs and exercises moderately 3 days per week. Based on this information, he would need approximately 72-80 grams of protein per day.

This is because athletes and people who exercise regularly need more protein to repair and build muscle tissue.
To meet his daily protein requirements, John can include protein-rich foods in his diet such as lean meats, fish, eggs, dairy products, nuts, and beans.

It is also important for him to spread out his protein intake throughout the day rather than consuming all of it in one meal.
John needs approximately 72-80 grams of protein per day to support his active lifestyle and maintain his overall health.

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Answer:

y=5x-6

Step-by-step explanation:

The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:

P(X > $429.35) = 0.011

Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:

-2.33 = ($429.35 - $395) / σ

Solving for σ, we get:

σ = ($429.35 - $395) / (-2.33) = $14.57

Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

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The ladder should she placed 12 feet from the base of her house

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

Using the above as a guide, we have the following:

We make use of the pythagoras theorem to calculate how far the ladder should be placed

Represent this with x

So we have

x^2 = 20^2 - 16^2

Evaluate

x^2 = 144

So, we have

x = 12

Hence. the ladder should she placed 12 feet from the base of her house

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The critical z-value for a 98% confidence level is 2.33.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

Statistics plays a significant role in various fields, including business, economics, social sciences, medicine, engineering, and many others.

To find the critical z value for a 98% confidence level, we need to look up the z-value associated with an area of 0.01 in the upper tail of the standard normal distribution table (since 98% of the area lies within the confidence interval, leaving 2% in the tails).

Using a standard normal distribution table, we can find that the z-value that corresponds to an area of 0.01 in the upper tail is approximately 2.33.

Therefore, the critical z-value for a 98% confidence level is 2.33.

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Answer:

$14.80

Step-by-step explanation:

First you need to subtract .50 from 2.35, which is 1.85.

Next you need to multiply 1.85 times 8.

1.85 x 8 = 14.80

Therefore, she has made $14.80 since the new price.

The percent increase for the dinner is 25%

The first step is to calculate the increase

The price rose from $7 to $8.75

Increase= 8.75-7

= 1.75

Therefore the percent increase can be calculated as follows

1.75/7 × 100

= 0.25 × 100

= 25

Hence the percent increase is 25%

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Therefore, the solution to the equation 10ˣ = 23 is: x = log(23) that is option B.

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be solved to find the value(s) of the variable(s) that make the equation true.

Here,

Taking the logarithm of both sides of the equation 10ˣ = 23:

log(10ˣ) = log(23)

Using the power rule of logarithms, the left-hand side simplifies to:

x log(10) = x

Since log(10) = 1, we have:

x = log(23)

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The chord length is approximately 1.397 centimeters where 0.7 centimeters is the separation from the center of the circle to the chord.

We can use the properties of circles to find the angle formed by the chord at the center of the circle to evaluate the length of the chord.

0.7 centimeters is the separation from the center of the circle to the chord. This remove is additionally the stature of the isosceles triangle shaped by the chord and the two radii of the circle. 

Let θ be the angle between the chord and the center of the circle. You can use trigonometry to find θ.

sin(θ/2) = 0.7/2.5

[tex]θ/2 = sin⁻¹(0.7/2.5)[/tex]

θ/2 = 0.2793

θ=2×0.2793

θ ≈ 0.5586 radians

Now that we know θ, we can use the formula for the chord length of a circle.

chord length = 2 × radius × sin(θ/2)

Chord Length = 2 × 2.5 × sin(0.2793)

String length ≈ 1.397 cm

Therefore, the chord length is approximately 1.397 centimeters.

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The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

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a. The length of one side of the cube  shape x ≈ 3.633 ft

b. The length of one side of the cube  shape is roughly 3.633 feet.

c. The case has a more noteworthy surface region than the block by roughly 10.325 square feet.

Let x be the length of one side of the cube. Since the cube has equal length, width, and height, its volume is  = x^3.

The volume of the box  = (4 feet 5 in) * (3 feet 2 in) * (4 feet 3 in),

which can be converted to feet as Volume of box =

(4 + 5/12) * (3 + 2/12) * (4 + 3/12) = 4.3135 * 3.1667 * 4.25 =

55.0448 cubic feet.

Since the cube has the same volume as the box, we can set Volume of cube = Volume of box and

solve for x:

[tex]x^3 = 55.0448\\x = (55.0448)^{1/3}\\[/tex]

x ≈ 3.633 ft

b. The length of one side of the cube is approximately 3.633 feet.

c. We must determine the surface area of each to compare the cube's and box's surfaces. A cube with side length x has the surface area given by

Surface area of cube = [tex]6x^2[/tex], and

Surface area of a box = 2lw + 2lh + 2wh is the formula for the surface area of a box with the dimensions l, w, and h. Based on the box's dimensions, we have:

Surface area of cube = [tex]6(3.633)^2[/tex] ≈ 79.342 sq. feet

Surface area of box = 2(4.4167 * 3.25) + 2(4.4167 * 4.25) + 2(3.25 * 4.25) ≈ 89.667 sq. feet

By about 10.325 square feet, the surface area of the box is greater than that of the cube.

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The new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

To rotate a triangle 270 degrees clockwise with the origin as the centre of rotation, you can follow these steps:

Draw the coordinates of the vertices of the triangle. Let's assume that the coordinates of vertex A are (x₁, y₁), the coordinates of vertex B are (x₂, y₂), and the coordinates of vertex C are (x₃, y₃).

To rotate the triangle 270 degrees clockwise, you need to reflect it first over the x-axis, and then over the y-axis.

To reflect the triangle over the x-axis, you need to change the sign of the y-coordinates of each vertex. So the new coordinates of vertex A would be (x₁, -y₁), the new coordinates of vertex B would be (x₂, -y₂), and the new coordinates of vertex C would be (x₃, -y₃).

To reflect the triangle over the y-axis, you need to change the sign of the x-coordinates of each vertex. So the final coordinates of vertex A would be (-y₁, x₁), the final coordinates of vertex B would be (-y₂, x₂), and the final coordinates of vertex C would be (-y₃, x₃).

These final coordinates represent the vertices of the rotated triangle.

So, the new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

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The percentage price of the item has decreased by 45%.

What is the definition of percentage?

A percentage is a quantity or ratio that is stated as a fraction of 100.

"%" is the symbol for percentage.

For example, if 25 of 100 students in a class received a "A," we may represent this as a percentage by dividing the number of "A" students by the total number of students and multiplying by 100:

(25/100) x 100% = 25%

This signifies that 25% of the students in the class received a "A".

Now,

To obtain the % drop, subtract the difference between the original and new prices, divide by the original price, then multiply by 100 to get the percentage decrease.

The difference between the original and updated prices is equal to

140 - 77 = 63

So the percentage decrease is:

(63/140) x 100% = 45%

Therefore, the price of the item has decreased by 45%.

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The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.

Here is a detailed explanation:

a = 1 (coefficient of x²),

b = -7 (co - efficient of x), and

c = 12 are the trinomial's coefficients and constant (constant term).

Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).

The two numbers are -3 and -4.

Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers

Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).

Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).

Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).

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Answer:

[tex] \sf \: x = 25[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 11x - 24 = 7x + 76

Then the value of x will be,

→ 11x - 24 = 7x + 76

→ 11x - 7x = 76 + 24

→ 4x = 100

→ x = 100 ÷ 4

→ [ x = 25 ]

Hence, the value of x is 25.

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It is an exercise of linear equations with one variable is a fundamental topic in the study of algebra. These types of equations are characterized by being first-degree polynomials in one variable, and can be found in various contexts, such as physics, economics, engineering, among others. Therefore, the ability to solve these equations is essential in the training of any mathematics student and in the development of their ability to solve problems in real life situations.

A linear equation with a variable can be solved by means of a series of algebraic operations that allow us to simplify the expression and clear the variable to be solved. These operations include adding, subtracting, multiplying, and dividing, always maintaining equality between both sides of the equation. The ultimate goal is to find the numerical value that satisfies the equation, that is, the value that makes the equality true.

Solving linear equations with one variable is an important skill not only for mathematics students, but also for professionals in various fields. For example, in engineering, linear equations are used to model physical systems and phenomena, and their resolution is necessary to perform calculations and make informed decisions. In the economy, they are used to analyze the behavior of financial variables and make projections for the future.

To solve the equation 11x - 24 = 7x + 76 we need to isolate the variable x on one side of the equation.

First, we can simplify both sides of the equation by combining like terms:

      11x - 7x = 76 + 24

Which gives us

       4x = 100

Next, we can solve for x by dividing both sides of the equation by 4:

       4x/4 = 100/4

       x = 25

Therefore, the solution to the equation is x = 25.

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The expression for the area of the triangle is given as follows:

A = 1.5x^4 + x³ - 0.5x².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5(3x² - x)(x² + x)

A = 0.5(3x^4 + 3x³ - x³ - x²)

A = 0.5(3x^4 + 2x³ - x²)

A = 1.5x^4 + x³ - 0.5x².

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Answer:

The number series 2, 4, 6, 8, 10, 12, . . . . , 80. Therefore, 1640 is the sum of first 40 even numbers.......Sep 23, 2018

PLS MARK BRAINLIEST

Step-by-step explanation:

Answer: D

Step-by-step explanation:

lines a and b are perlendicularr and the equation of line a is y=x+3.Therefore, after calculation, the equation of line b is y = -x + 3.

Perpendicular refers to a line, ray, or segment that intersects another line or segment at a right angle, or 90-degree angle. The point of intersection is called the point of perpendicularity and is equidistant from the endpoints of the segment.

An equation of a line is a mathematical representation of a straight line. It can be written in various forms, including slope-intercept form, point-slope form, and standard form, and relates the variables x and y.

According to the given information:

If line a has the equation y = x + 3 and line a is perpendicular to line b, then the slope of line b is the negative reciprocal of the slope of line a.

The slope of line a is 1, so the slope of line b is -1/1, which simplifies to -1.

To find the equation of line b, we need to find the y-intercept (b) using the point-slope form of a linear equation. We can choose any point on line b, but since we don't have any specific point given, we can use the y-intercept of line a, which is 3.

So, the equation of line b is y = -x + 3.

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Answer:

  a) '34'

Step-by-step explanation:

You want the result of executing the Python expression "3" +"4".

The tokens "3" and "4" are both strings. In this context, the "+" operator does concatenation of the strings, so the result is the string "34". The Python interpreter outputs this as '34'.

The graph that represents f(x) =3x-2 is the graph (b)

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

The equation: f(x) = 3x - 2

From the above equation, we have

f(x) = 3x - 2

The above equation is a linear function with the following features

Slope = 3

y-intercept = -2

This means that the graph intersects with the y axis at y = -2

Using the above as a guide, we have the following:

The graph intersects with the y axis at y = -2 and has a slope of 2 is graph (b)

Hence, the graph that represents f(x) =3x-2 is graph (b)

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An inequality that correctly models the situation is:

4x² + 50x + 154 ≤ 320

The correct answer is an option (D)

Let us assume that l represents the length (height) and w represents the width of the poster and frame together.

Here, the original poster is 11 inches wide and 14 inches tall and the frame will be x inches thick on each side.

So, the height l would be,

l = (14 + 2x) inches

and the width w would be,

w = (11 + 2x) inches

We know that the formula for the area of rectangle.

A = l × w

So, the expression for the area of the poster and frame together would be,

A = (14 + 2x) × (11 + 2x)

A = 154 + 22x + 28x + 4x²

A = 4x² + 50x + 154

The total area of the poster and frame together to be no more than 320 square inches.

So, we get an inequality

A ≤ 320 in²

4x² + 50x + 154 ≤ 320 in²

Thus, the correct answer is an option (D)

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Find the complete question below.

Quadrilateral ABCD can be dilated by a scale factor 1.25 to create a smaller image and by a scale factor 1.5 to create a bigger image.

To calculate the scale factor of a given shape for its dilation or reduction, the formula that should be used is given as follows:

Scale factor = bigger dimension/smaller dimension.

To create a smaller image;

bigger dimension length AB = 22in

smaller dimension length AB = 17.6in

Scale factor = 22/17.6 = 1.25

To create a bigger image:

Bigger dimension length = 33in

Smaller dimension length = 22in

scale factor = 33/22 = 1.5

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