Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
ABC is scalene

The Answer:

Width = 6

Step-by-step explanation:

Let width be w

(3w + 8) x w = 156

3 \(w^{2}\) x 8n - 156 = 0

(w + 8 x 6) (w-6) = 0

w = 6

Applying the tangent ratio, the length of n in simplest form is: n = 3.

One of the ratios of the trigonometric ratios that is used to solve a right triangle is the tangent ratio, which is:

tan ∅ = opposite side length/adjacent side length, where ∅ is the reference angle.

Given the following:

Substitute

tan 60 = 3√3 / n

Multiply both sides by n

n(tan 60) = (3√3/n)(n)

n(tan 60) = 3√3

Divide both sides by tan 60

n(tan 60)/tan 60 = 3√3/tan 60

n = 3√3/tan 60

n = 3√3 / √3 [Note: tan 60 = √3]

n = 3

Therefore, applying the tangent ratio, the length of n in simplest form is: n = 3.

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1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment

2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive

3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism

4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle.  Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion

According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.

Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.

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Answer:

The price for 4 people is 52 dollars.

4 × (5.75 + 7.25) = 52

The total cost including drink and popcorn is $52 according to a given condition.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Cost of movie ticket =  $7.25/person

Cost of popcorn and drink =  $5.75/person

Total cost per person = 5.75 + 7.25 = $13

Now,

Number of people = 4

So,

4(5.75 + 7.25) = 4(13) = $52

Hence "The total cost including drink and popcorn is $52 according to a given condition".

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The value of X is 3.25

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Step-by-step explanation:

Let the cost of paint set is s.

cost of sketch book = s/2

cost of brush = s/3

Money spent = $ 28 - $ 3 = $ 25

So,

s +  s/2 + s/3 = 25

6 s + 3 s + 2 s = 150

11 s = 150

s = $ 13.64

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Answer:

x > -5, so the correct answer is C.

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

5,379.80

Step-by-step explanation:

you multiply $3,635 times .06, and you'll get $218.10. then you multiply $218.10 times 8. you will get $1,744.80. you then add your original amount of $3,635 and the final answer is $5,379.80

Answer:

20.1 feet

Step-by-step explanation:

sin = opp/hyp

sin85 = 20/x

xsin85 = 20

x = 20/sin85 ≈ 20.07

If you have a volume of 894,195 cm³, then the volume in cubic feet will be 31.6 cubic feet.

Conversion means to convert the same thing into different units.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

1 cm = 0.0328084 ft

If you have a volume of 894,195 cm³. Then the volume in cubic feet is calculated as,

⇒ 894,195 x 3.53 x 10⁵

⇒ 31.6 cubic feet

If you have a volume of 894,195 cm³, then the volume in cubic feet will be 31.6 cubic feet.

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Answer:

18 is less then 23

Step-by-step explanation:

Answer:

right out the equation solve

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

Circumference of a circle = 2πr

where

r is the radius

From the question

r = 8 yd

π = 3.14

Substitute the values into the above formula and solve

Circumference = 2(8)(3.14)

We have the final answer as

Hope this helps you

Answer:

100 inches Over 1 minute times × 1 foot Over 12 inches

Step by Step explanation

Remember that

1ft=12in

The expression converts 100 inches per minute to feet per minute is

100 inch / min x 1 ft/ 12 inch.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. Time can be expressed in minutes rather than hours, and distance can be expressed in miles, kilometres, feet, or any other measurement unit.

We know

1 feet = 12 inch

We have to convert 100 inches per minute to feet per minute.

So, 100 inches

= 100 inch / min x 1 ft/ 12 inch

= 8.33 ft per minute

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Answer: 80

Step-by-step explanation:

⇒  −(8 − 12) + 60 + (−4)²

⇒ -(-4) + 60 + 16

⇒ 4 + 60 + 16

⇒ 80

Answer:

9m ×5m

Step-by-step explanation:

Area of a rectangle= length ×width

Let the width be W meters and the length be L meters.

2 equations can be written from the given information:

45= WL -----(1)

L= W +4 -----(2)

Substitute (2) into (1):

45= W(W +4)

Expand:

45= W² +4W

-45 on both sides:

W² +4W -45= 0

Factorise:

(W +9)(W -5)= 0

W+9=0 or W-5=0

W= -9 or W= 5

(reject)

Substitute W= 5 into (2):

L= 5 +4

L= 9

∴ The dimensions of the garden is 9m ×5m.

Since 100 cm = 1 m (100 centimeter equals 1 meter), when we divide 100 cm by 1 m we get 1 as a result. Then, we can multiply a measure by this fraction (equivalent to one) without changing the measure, but converting the units.

So, let's multiply 9 m by the fraction 100cm/(1m):

The criterion that she should use to prove that triangles RST and XYZ are congruent are:

i. Hypotenuse Leg (HL)

ii. Side-Angle-Side (SAS)

When the corresponding properties i.e. length of sides and measure of internal angles of two or more triangles are equal, then the triangles are said to be congruent. The relations can be shown using some theorems.

From the given triangles RST and XYX, it can be observed that;

TR ≅ XZ

RS ≅ XY

<R ≅ <X   (given)

<T ≅ <Z   (given)

Angles R and X are included angle of the triangles. Thus, the criterion that can be used to show that triangles RST and XYZ are congruent at;

i. Hypotenuse Leg (HL)

ii. Side-Angle-Side (SAS)

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Answer:

20

21.75

27.85

29.5

Step-by-step explanation:

Arranging the values in ascending order we get

16 21 24 24 27 28 30 35

n = Number of values = 8

Rank is given by

\(\dfrac{\text{Percentile}}{100}\times (n+1)\)

\(=\dfrac{20}{100}(8+1)=1.8\)

Taking the fraction of the rank i.e., 0.8 and work out the weighted mean

\(0.8\times (21-16)+16=20\)

The 20th percentile is 20

\(\dfrac{25}{100}(8+1)=2.25\)

\(0.25(24-21)+21=21.75\)

The 25th percentile is 21.75

\(\dfrac{65}{100}(8+1)=5.85\)

\(0.85(28-27)+27=27.85\)

The 65th percentile is 27.85

\(\dfrac{75}{100}(8+1)=6.75\)

\(0.75(30-28)+28=29.5\)

The 75th percentile is 29.5

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Step-by-step explanation:

Howdy there :)

To describe the transformation of the parent logarithmic function, you just need to follow these rules

1. A +  on the outside of the parentheses will mean a vertical shift upwards. As such, the transformation is moved 5 units up. If it was -, it would move 5 units down.

2. The inside of the parentheses will result in a horizontal shift right 4 units. The rule to remember is that these kinds of functions follow x(a - b) rules, meaning that when the 4 is subtracted, we are really talking about a positive four, unlike in standard arithmetic. Vice versa, a + 4 will mean a -4 four, since a - -4 is the same as a + 4. As such, we will move in the positive direction (right) on the y axis.

3. Since x is now -2x, we are reflecting about the y axis, meaning the function will switch from left to right or right to left.

4. The 2 in front of it represents a vertical dilation by a factor of 2. This is because our constant, 2, is greater than 1. If the number were in between 0 and 1, it would represent a vertical compression by the constant number.

Answer:2,576

Step-by-step explanation:

A vertical line can be written in the form x = a, where a is the x-coordinate of any point on the line.

In mathematics, an equation is a statement that asserts the equality of two expressions. It contains an equals sign (=) and one or more variables, which represent unknown values. Equations are often used to solve problems and find the values of the variables that make the equation true. There are many types of equations, including linear equations, quadratic equations, and systems of equations, among others.

Here,

1. To find the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope of the line and b is the y-intercept. We are given the x-intercept and y-intercept of the line, so we can use them to find the slope and y-intercept:

x-intercept = -2, y-intercept = -10

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1), where (x1, y1) = (-2, 0) and (x2, y2) = (0, -10)

m = (-10 - 0)/(0 - (-2)) = -10/2 = -5

So the slope of the line is -5.

Now we can use the slope-intercept form equation to find the equation of the line:

y = mx + b

Substituting the values of m and b, we get:

y = -5x - 10

Therefore, the equation of the line in slope-intercept form that passes through the x-intercept = -2 and y-intercept = -10 is y = -5x - 10.

2. We are given a point (0, -6) and the slope m = 8. We can use the slope-intercept form equation to find the equation of the line:

y = mx + b

Substituting the values of m and the point (0, -6), we get:

-6 = 8(0) + b

b = -6

Therefore, the equation of the line in slope-intercept form that passes through the point (0, -6) and has a slope of m = 8 is y = 8x - 6.

3. We are given that the line is parallel to y = 5 and passes through the point (4, 9). Since the line is parallel to y = 5, it has the same slope as y = 5, which is 0. We can use the point-slope form equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values of m, x1, and y1, we get:

y - 9 = 0(x - 4)

y - 9 = 0

y = 9

Therefore, the equation of the line in slope-intercept form that is parallel to y = 5 and passes through the point (4, 9) is y = 9.

4. We are given that the line is perpendicular to x = -4 and passes through the point (3, 7). Since the line is perpendicular to x = -4, it is a vertical line and its slope is undefined. We can use the equation x = 3 to represent the line.

5. To find the slope of a line, we can use the formula:

m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

6. If the slope of a line is undefined, it means that the line is vertical. This happens when the change in the x-coordinates between any two points on the line is zero, which makes the denominator in the slope formula zero. In this case, the line does not have a slope, since the slope is defined as the ratio of the change in y-coordinates to the change in x-coordinates.

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Answer:

The distance from John's house to Bill's house is 5 units

Step-by-step explanation:

John's house is located at the point (-5,7) and Bill's house is located at (-2,3) in a map of the town of Springville.

We need to find the distance from John's house to Bill's house. We use the formula of the distance between two points:

Given two points A(x,y) and B(w,z), the distance between them is:

\(d=\sqrt{(w-x)^2+(z-y)^2}\)

Applying the formula:

\(d=\sqrt{(-2+5)^2+(3-7)^2}\)

\(d=\sqrt{3^2+4^2}\)

\(d=\sqrt{9+16}=\sqrt{25}\)

d=5

The distance from John's house to Bill's house is 5 units

Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

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The percentage of the rent to the total rent, utilities, and food budget is 60%.

Answer:

a ) See Annex

b) P₁  =  0,0464       or    P₁  =  4,64 %

c) P₄  = 0,92   or   P₄  = 92 %

Step-by-step explanation:

b) P₁ [ X being defective ]  =  P₂   +   P₃

Where P₂  is the probability of X rays machine detects a weld defective and the weld is really defective

And  P₃  is the probability of X rays machine detects a weld defective and the weld is not defective

Then

P₂  =  0,04 *  0,92  =  0,0368

P₃  =  0,96 * 0,01  = 0,0096

Then  P₁  =  0,0368  +  0,0096

P₁  =  0,0464       or    P₁  =  4,64 %

c) P₄ = 0,04 *0,92

P₄  = 0,92   or   P₄  = 92 %

The transformation required to obtain the graph of the function f(x) from the graph of the function g(x) is by stretching the function g(x) horizontally by 3.

When a function is transformed, the curve that represents the graph either "moves to the left/right/up/down," "it expands or compresses," or "it reflects." By moving, extending, compressing, or reflecting the curve rather than directly graphing the function from scratch, function transformations are particularly useful for graphing the functions.

Given:

\(f(x) =\) \(cos(\frac{x}{3} )\)

\(g(x) = cos x\)

As g(x) is the parent function of f(x)

⇒ \(f(x) = g( \frac{x}{3})\)

given function \(g(x) = cos x\)

Substituting the value of x as \(\frac{x}{3}\)

we get,

⇒ \(g(\frac{x}{3} ) = cos (\frac{x}{3} )\)

Therefore, the transformation required to obtain the graph of the function f(x) from the graph of the function g(x) is by stretching the function g(x) horizontally by 3.

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Answer: umm it k

Step-by-step explanation: k+g-g=k

g-g=0

k=k