safety information about a ladder indicates that a ladder should not be set up at an angle less than 45 degrees or at an angle greater than 75 degrees. What range of height can a 20-foot ladder reach?

Lauren assumed that the Roof Truss Diagram is an accurate representation of the actual roof design that will be used on the shed. She used the given measurements, such as the length of the bottom chord, and the angles in the diagram to calculate the pitch of the roof. If the diagram was not accurate, her calculations would not have been useful in determining the pitch of the actual roof. Therefore, Lauren had to make the assumption that the diagram was a reliable representation of the shed's roof design.

The logical assumption that Darin make about the Roof Truss Diagram is that the rise is 4.6 ft and the run is 9 feet.

A logical assumption is simply an idea that can be inferred, or identified, in a text without the writer stating it in an obvious way. One simple example may be the logical assumption that if you do not turn in your homework, your teacher will be disappointed in you.

Here, we have,

Based on the information provided, it appears that Darin assumed that the Roof Truss Diagram is symmetrical, meaning that both sides of the roof have the same dimensions and angles. This assumption is supported by his calculation that the pitch of both sides of the roof is close to 1/2.

Rise will be:

= 9 × tan 27°

= 9 × 0.5095

= 4.6 feet.

Run will be 9ft

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So, the inverse function of f(x) = -x + 3 is g(x) = 3 - x, and it is in slope-intercept form. The slope of g(x) is -1 and the y-intercept is 3.

An inverse function is a function that reverses the operation of another function. More specifically, if f is a function that maps inputs from a set A to labors in a set B, also an inverse function g is a function that maps labors from B back to inputs in A, similar that for any input x in A, applying f and also g (or g and also f) results in the same value. In other words, if f(a) = b, also g(b) = a

by the question.

To find the inverse function of f(x) = -x + 3 in slope-intercept form, we need to solve for x in terms of y.

Start by replacing f(x) with y:

[tex]y=-x+3[/tex]

Now, isolate x on one side of the equation. To do this, we can add x to both sides:

[tex]y+x=3[/tex]

Finally, solve for x by subtracting y from both sides:

[tex]x=3-x[/tex]

So, the inverse function of f(x) = -x + 3 is given by:

[tex]f^{-1}(x)=3-x[/tex]

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Using a calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:

y = 6.5x - 279.1.

To find the equation, we need to insert the points (x,y) in the calculator. The same is true for any regression equation such as quadratic or exponential. However, as the problem states, a line of best fit is calculated in this problem.

From the table presented in the problem, the points are given as follows:

(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).

Inserting these points into the calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:

y = 6.5x - 279.1.

Here

x is the daily temperature, in F.

y is the sales, in dollars.

The complete question is-

The table compares the average daily temperature and ice cream sales each day

Temperature ("F) Ice Cream Sales

$112

$135

$138

$146

$166

$180

$188

$199

$220

$280

58.2

642-

64.3

66.8

684

71.6

72.7

76.2

77.8

82.8

Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth

09=38x-1092

09=-38xx-1092

Oý=65x-279.1

O ý= -65x-279.1

and also attached an image of the question.

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Answer:

The mean, median and mode are exactly the same.

Step-by-step explanation:

I ( g o o g l e d ) ur answer and gave u it

The characteristics of a normal distribution are  Symmetric, Unimodal,  Bell-Shaped,  Mean and Median are equal.

A. Symmetric: True. A normal distribution is symmetric, meaning the left and right halves of the distribution are mirror images of each other.

B. Unimodal: True. A normal distribution is unimodal, meaning it has a single peak.

C. Bimodal: False. A normal distribution is not bimodal; it has only one mode (peak).

D. Bell-Shaped: True. A normal distribution is bell-shaped, meaning it forms a symmetric, bell-like curve.

E. Mean and Median are equal: True. In a normal distribution, the mean and median are equal, and they both coincide with the highest point of the curve.

F. The Peak is on the left: False. The peak of a normal distribution is at the center; it is not necessarily on the left.

G. 64% of the data falls within 1 standard deviation of the mean: False. In a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, not 64%.

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When Sarah and Gavyn win money, they divide it in a 5:3 ratio.If  Sarah gets £14 more than Gavyn, Gavyn gets £21.

Let's call the amount of money that Sarah and Gavyn win "x".

According to the problem, they share the money in the ratio 5:3, which means that Sarah gets 5 parts and Gavyn gets 3 parts.

Let's call the amount of money that Gavyn gets "y". Then, we know that:

Sarah gets £14 more than Gavyn, which means that Sarah's share is y + £14.

We can set up an equation to represent the fact that the ratio of their shares is 5:3:

5/3 = (y + £14)/y

To solve for y, we can cross-multiply:

5y = 3(y + £14)

5y = 3y + £42

2y = £42

y = £21

Therefore, Gavyn gets £21.

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For the right-angled triangle, the value for x is obtained as √2/4.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right angle triangle is given.

It has angles 90°, 45° and 45°.

The hypotenuse measures 4√2.

The perpendicular measures x.

In a 45°-45°-90° right triangle, the legs are congruent and the hypotenuse is √2 times the length of a leg.

Therefore, in this triangle, each of the legs has length -

(4√2)/√2 = 4

So x is equal to one of the legs, which is 4.

To fill in the blanks -

x : 4√2 = 1 : 4

4x = 4√2

x = (√2)/4

Therefore, the value for x is obtained as √2/4.

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bearing in mind that the sum of all interior angles in a polygon is

180(n - 2)    n = number of sides in the polygon

a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.

[tex]\bold{120+140+160+130+125+140+165+160+140+v=1440}[/tex]

[tex]\bold{1275+v=1440 \implies v=1440-1275 \implies v=165}[/tex]

Answer:h<13

Because h has to be less than 13, so h<13 is the correct answer

Step-by-step explanation:

Answer:

it could either be h<13 or 13-h depending on what you're studying

Answer:

g(x) = -5tan(x) - 3

Step-by-step explanation:

the parent tangent function would be g(x) = tan(x)

- reflection over the x-axis is going to make it negative

- horizontal stretch by a factor of 5 is going to multiply it by 5

- vertical shift down 3 units will subtract 3

so together, this would be the equation g(x) = -5tan(x) - 3.

Answer:

These angles are complementary and congruent, so x = 15.

Step-by-step explanation:

[tex]3x + 45 = 90[/tex]

[tex]3x = 45[/tex]

[tex]x = 15[/tex]

Answer:

C.

Step-by-step explanation:

The vertex and the point of intersection is just one point identifiied by its x and y vlaues

.........................

So the acute angle of the rhombus is 90 degrees, and the obtuse angle is twice as large, or 180 degrees.

The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's start by finding the length of one half of the longer diagonal. We can use the shorter diagonal (which we know is 10 cm) and the side length (which we know is 13 cm) to form a right triangle. The hypotenuse of this triangle is half of the longer diagonal, so we can solve for it using the Pythagorean theorem:

[tex]a^2+b^2 = c^2 \\(13/2)^2 + 10^2 = c^2\\169/4+100 =c^2 \\ 269/4= c^2 \\c = \sqrt{(269)}/2\\[/tex]

Therefore, the length of one half of the longer diagonal is sqrt(269)/2 cm. To find the full length of the longer diagonal, we just need to double this value:

longer diagonal = [tex]2 \times \sqrt{(269)}/2 = \sqrt{(269)}cm[/tex]

Now, we can use the fact that the sum of the angles in a rhombus is 360 degrees to solve for x:

2x + 2x = 360

4x = 360

x = 90

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Warren Braxton paid $2,700.30 for his homeowner insurance policy.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Given that, Warren Braxton purchased homeowner insurance for 70%.

Thus,

0.7 x $495,000 = $346,500.

Now, the premium is:

Premium = ($346,500 / 100) x $0.78 = $2,700.30

Hence, Warren Braxton paid $2,700.30 for his homeowner insurance policy.

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Answer:

The inequality that describes the problem is given as follows:

x ≤ 75.

How to obtain the inequality?

To describe the inequality in this problem, we need to obtain the upper bound of the total amount that Ted and his friends are expected to spend.

To obtain the upper bound of the total amount, the relevant information is given as follows:

Ted and his friends decided to split the bill evenly among the 5 of them.

Ted figured that each person will pay no more than $15.

Hence the upper bound of the total amount is calculated as follows:

5 x $15 = $75.

The upper bound of $75 means that in total, they are expected to pay at most $75, hence the inequality that describes this problem is given as follows:

x ≤ 75.

Hello and greetings ririleyyyii

The discriminant of 6y² - 9y + 1 = 0 equals 57.

6y² - 9y + 1 = 0

We identify the coefficients a, b and c of the quadratic equation.

The coefficients of a quadratic equation are the numbers that multiply the variables together with the independent term.

ax² + bx + c = 0

So the coefficients are: a = 6, b = -9, c = 1.

We evaluate the discriminant by substituting a, b and c inside the expression b² - 4ac.

The exercise remains: (-9)² - 4 × 6 × 1

                                      (-9)² - 4 × 6

                                      81 - 4 × 6 = 24, so 81 - 24 = 57

The discriminant of 6y² - 9y + 1 = 0 equals 57.

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Answer:

NO

Step-by-step explanation:

It is a parabola, you can tell cuz of the x^2

:)

Answer:

11 adults

Step-by-step explanation:

First, set up a system of equations:

Let x = number of children and y = number of adults

There is a total of 16 people, so x+y = 16. This is your first equation.

Each child ticket costs $6, so 6x = cost of children's tickets based on the number of children present (x)

Each adult ticket costs $9, so 9y = cost of adult's tickets based on the number of adults present (y)

The total cost of tickets is $129, so 6x+9y = 129. This is your second equation.

Your system of equations is now this:

x +   y = 16

6x + 9y = 129

You can solve this system using the method of elimination, where we will eliminate the variable x (number of children), since we are focused on y (number of adults).

Multiply the top equation by -6. This will give the following equation:

-6x - 6y = -96

You can now solve the system of equations by placing the new equation under the second equation like this:

6x + 9y = 129

-6x - 6y = -96

Now, add the two equations together.

6x + (-6x) = 0

9y + (-6y) = 3y

129 + (-96) = 33

After doing this, you get the following equation:

3y = 33

As you can see, the variable x has been eliminated, and you are left with y.

Solve the equation for y:

3y = 33

y = 33/3 = 11

y = 11 adults

Value of angle C in the cyclic quadrilateral is 62°

A cyclic quadrilateral is a quadrilateral that can be circumscribed by a circle such that all four vertices of the quadrilateral lie on the circle.

Some properties of cyclic quadrilaterals include:

In the given diagram

∠B=3x°

∠D=x+20°

For cyclic quadrilateral opposite angle sum is 180°

∠B+∠D=180°

3x°+x°+20°=180°

4x+20=180°

x=160/4

x=40°

∠A+∠C=180°

C=180-2x+38

C=180-2*40-38

C=62°

Hence, Value of angle C in the cyclic quadrilateral is 62°

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The probability of drawing a lettered card from a deck of shuffled 52 cards is 50%.

There are 52 cards in a deck, and 26 of them are lettered cards (A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2) while the other 26 cards are suited cards (clubs, spades, hearts, diamonds).

If the deck is well shuffled, each card is equally likely to be drawn.

Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is simply the number of lettered cards divided by the total number of cards:

P(Drawing a lettered card) = Number of lettered cards / Total number of cards

= 26 / 52

= 1/2

= 0.5

Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is 0.5 or 50%.

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The probability of selecting a green marble from a jar containing 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles is 0.1875 or 18.75%.

To find p(g), we need to first determine the total number of marbles in the jar, and then determine the number of green marbles in the jar.

Total number of marbles = 4 blue marbles + 3 green marbles + 7 red marbles + 2 white marbles = 16 marbles.

Number of green marbles = 3.

So p(g) = number of green marbles / total number of marbles = 3 / 16.

Therefore, p(g) = 0.1875 or 18.75%.

Therefore, Choosing a green marble from a container holding 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles has a probability of 0.1875 or 18.75%.

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Answer: [tex]\frac{1}{3}[/tex] yds²

Step-by-step explanation:

    To find the area, we will multiply 2/3 by 2/4. When multiplying fractions, you multiply straight across.

[tex]\displaystyle \frac{2}{4} *\frac{2}{3} =\frac{2*2}{4*3} =\frac{4}{12} =\frac{1}{3}[/tex]

    We can also use the model, see attached.

Step-by-step explanation:

The three angles of the triangles are equal ...use  A-A-A theorem

The point on the image of figure 2 corresponds to point I from Figure 1 is Q, as figure 2 is the image of the figure one after reflection about its origin.

When a figure is constructed around a single point known as the figure's centre, or point of reflection, the result is a point reflection.

From the two given figures: the figure 2 is the image of the figure one after reflection about its origin.

Thus, the point on the image of figure 2 corresponds to point I from Figure 1 is Q.

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Complete question :

Figure 1 and figure 2 below are congruent. Which points corresponds to point I.

The figure is attached.

In the trapezoid , C) Area = 22.5 [tex]mi^2[/tex] , Perimeter = 22.5 mi.

What is area and perimeter?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape.

Here Base a = 3.5 mi , Base b = 5.5 mi and Height h = 5 mi.

Then Area of the Trapezoid = [tex]\frac{1}{2}[/tex] ( a + b ) h square unit

=> A = [tex]\frac{1}{2}(5.5+3.5)\times5[/tex]

=> A = [tex]\frac{1}{2}\times9\times5[/tex]

=> A = 22.5 [tex]mi^2[/tex]

Now perimeter is sum of all sides of the trapezoid. Then,

=> 3.5+5.5+7.5+6

=> 22.5 mi

Hence the area is 22.5 [tex]mi^2[/tex] and perimeter is 22.5 mi.

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Answer: Square

Step-by-step explanation:

A square has 4 parallel sides and has 4 90 degree angles

According to the given figure, the area of the shaded region in the shape is 49.5mm2.

The total area of every one of the shapes which cover an object's surface is known as its surface area. The length and width of this type of rectangle are multiplied to determine its area.

To solve the following question we first need to separate the single shape into two according to the shapes given

Therefore we have two shapes with us, i.e., rectangle and triangle.

First of all, we need to calculate the area of both the shares separately:

Firstly, area of the rectangle, formula is:

Area = length x width

By entering the length and width values,

Area of rectangle= 7 x6

Area of rectangle= 42 mm2

Now, we need to calculate the area of the second shape, that is, triangle,

Triangle area is equal to height x base / 2.

Now, by putting values in the formula:

Area of triangle=3 x 5 / 2

Area of triangle= 15/2

Area of triangle= 7.5 mm2

Therefore, the area of the shaded region:

Area = (rectangular area + triangular area)

Area = 42 + 7.5

Area = 49.5 mm2

Therefore, the area of the shaded region of the shape given is 49.5 mm2.

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There are 27 students in the class who walk to school.

Word problem refers to problem expressed entirely in words typically used as an educational tool.

Given that:

Total number of students in the class: 80

Number of girls in the class: 44

Number of girls who walk to school: 17

Number of boys who cycle to school: 14

Number of boys who take the bus to school: 12

We have to subtract the students who take the bus or cycle from the total number of students first. The number of boys who walk to school will be:

= Total number of boys - Boys who cycle - Boys who take the bus

= (Total number of boys) - 14 - 12

= (80 - 44) - 14 - 12

= 36 - 14 - 12

= 10

To get total number of students who walk to school, we compute as follow. The number of students who walk to school:

= Number of girls who walk to school + Number of boys who walk to school

= 17 + 10

= 27.

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Answer:

Step-by-step explanation:

The quadratic function in vertex form is  f(x) = -(x + 5)^2 - 23

To find the quadratic function in standard form, we first need to determine the factors of the quadratic equation that corresponds to the given x-intercepts. Since the x-intercepts are at x = -12 and x = 2, we can write the quadratic equation in factored form as:

f(x) = a(x + 12)(x - 2)

where a is a constant that we need to determine.

To find the value of a, we can use the given minimum y-value of -49. Since the vertex of a quadratic function occurs at the axis of symmetry, which is the midpoint of the x-intercepts, we can find the x-coordinate of the vertex by taking the average of the x-intercepts:

x-coordinate of vertex = (-12 + 2)/2 = -5

Substituting this value of x into the factored form of the quadratic function, we get:

f(-5) = a(-5 + 12)(-5 - 2) = 49a

Since the minimum y-value is -49, we have:

f(-5) = 49a = -49

Solving for a, we get:

a = -1

Substituting this value of a into the factored form of the quadratic equation, we get:

f(x) = -(x + 12)(x - 2)

Expanding this equation, we get the quadratic function in standard form:

f(x) = -x^2 - 10x - 24

To find the quadratic function in vertex form, we can complete the square on the standard form of the equation:

f(x) = -x^2 - 10x - 24

f(x) = -(x^2 + 10x) - 24

f(x) = -(x^2 + 10x + 25) + 1 - 24

f(x) = -(x + 5)^2 - 23

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