Name:
Date:
2.
5.
Directions: Solve for x
This is a 2-page document
Directions identify the similar triangles in the diagram, then sketch them so the coresponding
sides and angles have the same orientation
1.
52
48
Per
20
9.24 and 32
طلال سلال
kl ma jkk
Jkm-kim
Unit 7: Right Triangles & Trigonometry
Homework 3: Similar Right Triangles
& Geometric Mean
X=4.8
6.
22.4
13.2
26
Directions: Find the geometric mean of each pair of numbers.
7.16 and 27
8. 5 and 36
10.8 and 48

Answer:

x = 50

Step-by-step explanation:

2x = 60+40

simply 60 + 40 to 100

so 2x = 100

and then divide 2 to get it to the other side.

like this = x = 100/2

then divide 100 by 2 and get 50

so x=50

Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Student 1 correctly started the proof.

To complete the proof using the law of sines, student 1 should use the fact that the sum of angles in a triangle is 180 degrees to obtain an expression for angle C, and then use the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side to obtain an expression for side c in terms of sin(A) and sin(B).

Here's the complete proof:

Starting with Student 1's work:

bsin(A) = h

asin(B) = h

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180 - A - B

Using the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting in the expressions for c and sin(C) in terms of sin(A) and sin(B):

a/sin(A) = b/sin(B) = 2h/(sin(A)+sin(B))

Simplifying:

a = 2hsin(A)/(sin(A)+sin(B))

b = 2hsin(B)/(sin(A)+sin(B))

c = 2hsin(C)/(sin(A)+sin(B)) = 2hsin(180-A-B)/(sin(A)+sin(B)) = 2h*sin(A+B)/(sin(A)+sin(B))

Therefore, the law of sines is:

a/sin(A) = b/sin(B) = c/sin(C) = 2h/(sin(A)+sin(B))

1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.

2. The range of the function is given as follows: The set of real numbers less than -5.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:

y = a(1/3)^x - 2.

When x = 0, y = -1, hence the parameter a is obtained as follows:

-1 = a - 2

a = 1.

Thus the function is:

g(x) = (1/3)^x - 2.

For item 2, we have that the function is:

Hence the range of the function is given as follows:

The set of real numbers less than -5.

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Answer:

[tex]\huge\boxed{\sf Yes.}[/tex]

Step-by-step explanation:

In a right angled triangle, the longest side is called hypotenuse.

So,

Hypotenuse = 13 m

The rest are:

Base = 5 m

Perpendicular = 12 m

Using Pythagoras Theorem to verify:

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

Put the given data

(13)² = (12)² + (5)²

169 = 144 + 25

Since, both left hand side and right hand side are equal, this means the triangle is a right-angled triangle.

[tex]\rule[225]{225}{2}[/tex]

Answer: no answer

Step-by-step explanation:

The quantity of ounce for each kind of food that will be used would be given as follows;

Food A= 2.18oz

For food A;

The calories in an Oz = 100 cal

Total calories in the whole food = 1100cal

The equivalent of cal that should be in 2400;

= X

That is;

100= 1100

X = 2400

Make X the subject of formula;

x= 100×2400/1100

X = 240000/1100

X = 218

if 1 Oz = 100 cal

X Oz = 218

X Oz = 218/100

= 2.18oz

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Answer:

[tex] \frac{468}{14.4} = \frac{d}{16.8} [/tex]

[tex]32.5 = \frac{d}{16.8} [/tex]

[tex]d = 546[/tex]

Wyatt can drive 546 miles on a full tank (16.8 gallons) of gas.

The depreciation schedule for this truck using the declining-balance method at twice the straight-line rate are $24,000, $33,600, $39.744, $43,502 and $45,248

To create the depreciation schedule, we'll start with the cost of the asset and subtract the depreciation for each year. The depreciation for each year is calculated by multiplying the declining-balance rate by the book value of the asset at the beginning of the year.

The book value is simply the cost of the asset minus the accumulated depreciation. So in year 1, the book value is $30,000, and the depreciation is $8,000 (the declining-balance rate) times $30,000, which is $24,000. This means that the accumulated depreciation at the end of year 1 is $24,000.

To calculate the book value at the end of year 1, we simply subtract the accumulated depreciation ($24,000) from the cost of the asset ($30,000), which gives us $6,000.

=> $30000 - $6000 = $24000

This process is continued for the next five years that can be illustrated through the table.

Year Cost Depreciation Accumulated Depreciation Book Value

1        30,000 24,000                     24,000                      6,000

2           6,000 9,600                      33,600                       -3,600

3         -3,600 6,144                       39,744                      -9,744

4         -9,744 3,758                       43,502                      -13,502

5          -13,502 1,746                       45,248                       -15,248

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Answer:

A- 304.8 cm²

Step-by-step explanation:

Find the area for the 4 sides (excluding both the top and base).

(2(12×7.5))+(2(12×5.2)) = 302.8

Answer:

A.  304.8 cm²

Step-by-step explanation:

The rectangular prism has a total of 6 rectangular sides

~   two at the bottom and top both of equal dimensions 5.2 x 7.5

~   two at the front and back both of equal dimensions 12 x 7.5

~    two one on the left side and the other on the right side both of equal dimensions 12 x 5.2

The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces

For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle

Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)

We multiply by 2 since there are 2 of each rectangular surface

2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm²   ANSWER

3. The value of the function (f+g)(x) is option A: 3x+5. 4. The value of: (f·g)(x) is Option C: 2x² + 10x.

The function that results from summing the results of the two functions for a specific input value x is known as the sum of two functions (f+g)(x). To put it another way, we just add the function values at each x-axis point. The function that results from multiplying the outputs of the two functions for an input value x is known as the product of two functions (fg)(x). In other words, we multiply the values of the function at each x-axis position. Two functions can be combined or multiplied to create new functions, each of which has a unique set of attributes.

Given that, f(x)=x+5 and g(x)=2x.

3. The value of (f+g)(x) is:

f(x + g) (x)= f(x) + g(x) = (x+5) + 2x = 3x+5

4. The value of:

(f·g)(x) = f(x) · g(x) = (x+5) · 2x = 2x² + 10x

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The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.

In this context, the value -5 represents the temperature outside in Celsius degrees.

The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.

Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.

The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.

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The equation of the line in slope-intercept form is:

y = 4x + 9

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, we know that the line passes through the point (-4, -7) and has a slope of 4. So, we can plug in the values of x, y, and m into the slope-intercept form and solve for b:

-7 = 4(-4) + b

Simplifying the right side:

-7 = -16 + b

Adding 16 to both sides:

9 = b

So the y-intercept is 9. Therefore, the equation of the line in slope-intercept form is:

y = 4x + 9

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To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

We know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.

Arrange in ascending order:

229 234 248 255 263

When, odd terms are there then the middle term is the median:

Median: 248

New Median:

229 234 248 255 263 597

When there are even terms we will add the middle two terms and divide it by 2 as follows:

248+255/2

Median: 251.5

Median change: 251.5 - 248 = 3.5

Therefore, we know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.

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The ceiling function, denoted by ⌈x⌉, gives the smallest integer that is greater than or equal to x. Therefore, ⌈-0.75⌉ is the smallest integer that is greater than or equal to -0.75.

Since -1 is the smallest integer that is greater than or equal to -0.75, we have:

⌈-0.75⌉ = -1

Therefore, the functional value for the ceiling function at -0.75 is -1.

The answer is option A.

The height of the rectangular prism is 8 inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that:

Volume V = 241.92 in³

Length l = 5.6 in

Width w = 5.4 in

Height h = ?

Plug the given values into the above formula and solve for h

V = w × h × l

h = V / ( w × l )

h = 241.92 in³ / ( 5.4 in × 5.6 in )

h = 8 in

Therefore, the height is 8 inches.

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A

Step-by-step explanation:

There is 1 number that is a multiple of both 3 and 4.

9 numbers are a multiple of 4 and not 3.

9 numbers are a multiple of 3 and not 4.

1 number is not a multiple of 3 or 4.

Hope this helps!

Answer:

The party opposed to expanding slavery in the United States was the Republican Party. It was actually formed to go against slavery.  

Answer:

Step-by-step explanation:

7.3 is the anwser

Answer:

Part a 6 and 9

Step-by-step explanation:

Part B is 7.3 because u just find the sq root of 54 which can't go down the easiest is finding the decimal form

As per the question of trigonometry the another equation that describes the given graph is

y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.

The sine and cosine function graphs' main characteristics are:  

a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.

b. We can simplify the following equation and compare it with  [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.

We obtain this by applying the same trigonometric identity as before.

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The ratio of the width to the length of the cell phone is 23/65.

Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

To find the ratio of the width to the length of the cell phone, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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(a) The vertex is (6, 144),(b) When the fireworks are launched at time x = 0 and return to the earth at time x = 12 seconds, respectively, these times are denoted by zeros in the function,.(c) this is the quadratic function that represents the situation f(x) = -4 + 144.

a. To find the zeros and vertex of the quadratic function, we need to first write it in the standard form:

[tex]f(x) = ax^2 + bx + c[/tex]

where a, b, and c are constants.

The vertex of the function is given by:

x = -b/2a

Since the quadratic function is symmetrical around the vertex, we know that the time it takes to reach the maximum height is halfway between the launch time and the time it hits the ground again. So, the time to reach maximum height is (4 + 8)/2 = 6 seconds.

Therefore, we can set up a system of equations using the information given:

f(4) = 0 (the firework is launched from the ground)

f(6) = 256 (the firework reaches its maximum height)

f(12) = 0 (the firework hits the ground again)

Plugging in the values of x and f(x), we get:

16a + 4b + c = 0

36a + 6b + c = 256

144a + 12b + c = 0

Solving this system of equations, we get:

a = -4

b = 48

c = 0

Therefore, the quadratic function that represents the situation is:

[tex]f(x) = -x^2 + 48x[/tex]

The zeros of the function can be found by setting f(x) = 0:

[tex]f(x) = -4x^2 + 48x[/tex]

0 = x(-4x + 48)

x = 0 (the firework is launched from the ground)

x = 12 (the firework hits the ground again)

The vertex can be found using the formula:

x = -b/2a = -48/(-8) = 6

So the vertex is (6, 144).

b. Using the zeros and vertex, we can sketch a graph of f(x):

The quadratic function's graph

Considering the function's primary characteristics in light of the circumstances:

The peak height of the fireworks, which occurs at x = 6 seconds and f(6) = 256 feet, is represented by the function's vertex.

The firework is at ground level at x = 0 (launch time) and x = 12 seconds (when it reaches the ground again), which are represented by zeros in the function.

The graph's form suggests that the firework rises before falling again, which is consistent with the scenario given.

c. The quadratic function that represents the situation is:

[tex]f(x) = -4x^2 + 48x[/tex]

This function can be simplified by factoring out -4:

[tex]f(x) = -4( x^2- 12x)[/tex]

Completing the square:

[tex]f(x) = -4( x^2- 12x + 36 - 36)[/tex]

[tex]f(x) = -4( (x^2-6)- 36)[/tex]

[tex]f(x) = -4(x^2-6) + 144[/tex]

This form of the function shows that the vertex is (6, 144), and that the maximum height is 144 feet.

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Therefore , the solution of the given problem of expressions comes out to be points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).

Instead of using random estimates, shifting variable numbers should be employed instead, which can be growing, diminishing, or blocking. They could only help one another by transferring items like tools, knowledge, or solutions to issues. The explanations, components, or mathematical justifications for strategies like expanded argumentation, debunking, and blending may be included in the explanation of the reality equation.

Here,

Figure XYZ will be scaled down by 1/4, with the centres being X(-2,4), Y(-4,4), and Z(4,2)

=>  Old_x - Center_x - Scale_factor * New_x + Center_x

=>  Scale factor * (Old y - Centre y) + Centre y = New y

Regarding X:

=>  New_x = 1/4 * (-2 - (-2)) + (-2) = -2

=>  New_y = 1/4 * (4 - 4) + 4 = 4

Therefore, X'(-2,4) is the image of point X after dilation.

Regarding Y:

=>  New_x = 1/4 * (-4 - (-2)) + (-2) = -3

=>  New_y = 1/4 * (-4 - 4) + 4 = -1

Therefore, Y'(-3,-1) is the image of point Y following dilation.

Regarding Z:

=> New_x = 1/4 * (4 - (-2)) + (-2) = 0

=> New_y = 1/4 * (2 - 4) + 4 = 3

Therefore, Z'(0,3) is the image of point Z after dilation.

As a result, the image points for the dilated figure XYZ with the centre points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).

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Answer:

24.6 degrees.

Step-by-step explanation:

To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.

sin(θ) = opposite/hypotenuse

sin(θ) = 3/7

Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.

θ = sin^-1(3/7)

θ ≈ 0.429 radians

To find the degree measure, we must convert radians to degrees by multiplying by 180/π.

θ ≈ 0.429 x 180/π

θ ≈ 24.6 degrees

Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.

The equation to calculate the cost of her shoes without shipping included is: x = 55.25

Let x be the cost of Carly's shoes.

The problem states that the total cost of her purchase (including shoes and shipping) is $60.75, so we can set up the equation:

x + 5.50 = 60.75

To find the cost of her shoes without shipping, we need to isolate x. We can do this by subtracting 5.50 from both sides:

x + 5.50 - 5.50 = 60.75 - 5.50

Simplifying:

x = 55.25

Therefore, the equation to calculate the cost of her shoes without shipping included is: x = 55.25

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The model predicts that the population of the inner-city area will be 107,079 people in 7 years

The number of inhabitants in a given region is characterized as the quantity of individuals normally living around there, estimated on 1 January in a given year.

The given model for the number of inhabitants in the rough part of town region is:

P(t) = 108,000 - 0.011t

where t is the number of years from the present and P(t) is the estimated population at time t.

To find the predicted population in 7 years, we can substitute t=7 into the given model and evaluate:

P(7) = 108,000 - 0.011(7)

P(7) = 108,000 - 0.077

P(7) = 107,923

As a result, the model projects that the inner-city area will have a population of 107,079 people in seven years, rounded to the nearest person.

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Answer:

just 2 outcomes

Step-by-step explanation:

no matter how often you throw it, there are only two sides available

Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

Net income, considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

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The solid displayed in the image is a trapezoidal prism.

A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.

To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.

Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.

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