The second angle of the triangle is 25 degrees larger than the first, while the third angle of the triangle is 3 times the second. How big is the first angle? Remember, the sum of the angles in any triangle is 180 degrees.

MaryAnn can order a total of 213 prints for cost $35, including shipping.

Each print costs $0.15, so MaryAnn can order $35/$0.15 = 233.33 prints, but since she can only order whole prints, she can order a maximum of 233 prints.

The shipping charge is a flat fee of $3.00 per order, regardless of how many prints MaryAnn orders.

Let's say MaryAnn orders x prints, then her total cost would be:

Cost = $0.15 x + $3.00

Since her total cost can't exceed her budget of $35, we can set up the following inequality:

$0.15 x + $3.00 ≤ $35.00

Subtracting $3.00 from both sides, we get:

$0.15 x ≤ $32.00

Dividing both sides by $0.15, we get:

x ≤ 213.33

Since MaryAnn can only order whole prints, she can order a maximum of 213 prints.

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A geometric progression is the sum of the terms of a geometric progression. The nth partial sum of a geometric sequence can be calculated from the first term a1 and the common quotient r as: Sn=a1(1−rn)1−r.

A geometric progression is a sequence of numbers formed by multiplying the common quotient 'r' by each of the preceding numbers. The first term in this series is a1. And the nth partial sum of the series, Sn is calculated by multiplying the first term a1 by the magnitude (1-rn) divided by (1-r).

This equation gives us the sum of the first n terms of a geometric progression. For example, if a1 = 2 and r = 2, then partial sum S3 of the first three terms in the series is 2*(1-2^3)/(1-2)= 2/1 = 2. In other words is the sum of the first three terms of series '2.' The subsumed equation is very useful tool for computing sum of any number of terms in a geometric series.

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Answer:

Domain = {2, -5, 5, -7 }

Range = { 0, 1 , 3 , 8 }

Reflection across x=3 is a transformation that involves reflecting a figure across a vertical line of symmetry at x=3.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.


This transformation produces a mirror image of the original figure. Reflection across x=3 can be represented in the form of a matrix equation,

A= [[-1, 0],
   [ 0, 1]]

This matrix equation demonstrates that the x coordinates of a point will be multiplied by -1, while the y coordinates will remain unchanged. This transformation is also known as a reflection over the y-axis.

Reflection across x=3 can be used to change the orientation of a figure in a 2-dimensional coordinate plane. For example, if a triangle is located at the position (2,4) and the coordinates need to be changed so the triangle is reflected across x=3, the coordinates would be transformed to (-2,4).

Reflection across x=3 can also be used to solve various types of mathematical problems. For example, if a problem asks for the coordinates of a point that is the reflection of a point across x=3, the coordinates of the reflected point can be calculated by multiplying the original x coordinate by -1 and leaving the y coordinate unchanged.

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n = 10

Her sister is 7 years old subtract that from 31 gets you 24, then double 7 is 14 so subtract 14 from 24, and that gets you the value of 10 which equals 10

12 adults can go with the 9 kids, while ratio changes 3kids to 4 adults.

A ratio is a comparison between two or more quantities. It is usually expressed as two numbers separated by a colon.

For example, 2:3 is a ratio indicating two parts of a whole compared to three parts of the same whole. Ratios can also be used to compare different units, such as 5 miles to 8 kilometers. Ratios can provide a useful tool for comparing and contrasting different values.They can be used to compare sizes, proportions, costs, and more.

3 kids : 4 adults

9 kids : x adults

9x = 12*4

x = 12

Therefore, 12 adults can go with the 9 kids.

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The equivalent of 1/4 acre in square feet according to the relation between the two is 10,890.

Square feet and acre are the units which are representative of area covered by a land. The conversion of square feet and acre is simple and can be performed through simple formula -

1 acre is equal to 43, 560 square foot

So, using this relationship to find the square feet equivalent of 1/4 acre.

Area covered by 1/4 acre = amount of area covered in acre × equivalent of one acre in square foot

Area covered by 1/4 acre = 1/4 × 43, 560

Performing multiplication on Right Hand Side of the equation

Area covered by 1/4 acre = 10, 890 square feet

Hence, 10, 890 square feet is occupied by 1/4 acre.

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Answer:

1 pin = 473.17 ml

Step-by-step explanation:

1 pin = 473.17 ml

To convert pin to ml, you need to take the number of pin times 473.17.

The number of ways the adults and the kids can be served is 831600

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

Volume = 1 gallon 3 pints

By conversion

1 gallon = 8 pints

So, we have

Volume = 8 pints +  3 pints

Volume = 11 pints

Also, we have

Adult = 2 cups

Kid = 1 cup

Convert to pints

Volume = 11 pints

Adult = 4 pints

Kid = 2 pints

The number of ways is then calculated as

Ways = 11!/(4! * 2!)

Evaluate

Ways = 831600

Hence, the number of ways is 831600

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Answer:

I hope u understand my handwriting

Answer:

9 Paper Clips

Step-by-step explanation:

See picture below :)

Answer:

9(x + 17) ≥ -23

Step-by-step explanation:

Let's start by breaking down the sentence:

"A number": We can represent this as a variable, say "x".

"The sum of a number and 17": This is x + 17.

"Nine times the sum of a number and 17": This is 9(x + 17).

"Is at least -23": This means the expression on the left-hand side of the inequality is greater than or equal to -23.

Putting it all together, we get the inequality:

9(x + 17) ≥ -23

The transformed parent cube root function's equation is,

y = ∛(x-4) - 1.

The equation of the function is satisfied by all (and only those) points that lie on the graph of the function.

Hence, if a point fits on a function's graph, it must also fit the function.

The parent cube root function is transformed in the shown graph

The Parent cube root function is

y = ∛(x -h) - k

where the value of h  and k is equal to 0

h=0, k=0 in parent function

At (0,0) in the parent function, the graph changes orientation.

We can observe from the above graph that it changes direction at (4,-1) meaning it is moved 4 units to the right and 1 unit down.

So, the value of h=4  and value of k=1

The equation of the transformed function is,

y = ∛(x-4) - 1

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Answer:

it will have one real solution

Step-by-step explanation:

The value of x if lines m and n are parallel is 64 degrees

The missing information to answer this complete question is added as an attachment

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

Lines m and n are parallel lines

This means that

2x - 8 + 60 = 180 ---- by angles on a straight line theorem

Collect the like terms

2x = 180 - 60 + 8

Evaluate the like terms

2x = 128

Divide by 2

x = 64

Hence, the value of x is 64 degrees

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The system of equations has no solution. Option A is the correct optio.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations is

3x - 9y =0 .....(i)

-x + 3y = -3 .....(ii)

Multiply -3 with equation (ii)

3x - 9y = 9 .....(iii)

Subtract equation (i) from (iii):

3x - 9y = 9

3x - 9y =0

________

        0 = 9

Which is a false statement.

Thus the system of equations has no solution.

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Answer:

the answer is A. 0

domain is x

range is y

domain is time

range is distance

domain is between 0 & 170 seconds

range is 0 & 60 meters

meters per seconds is like

miles per hour so

this graph is about SPEED !

speed is usually indicated by the graph's

SLOPE !

The average height for a 15-year-old male in the United States is roughly 5 feet, 7 inches, according to the Centers for Disease Control and Prevention (CDC) growth charts (170 cm). Some 15-year-old guys may be shorter or taller than usual.

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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Answer:

35xΔ2-67x-22

Step-by-step explanation:

a) matrix is 4 x5 , null space is 3 dimensional then rank = 2. b) A is 6x7 matrix :  the column vectors with leading 1's of the row vectors forms a basis for column space. Maximum possible dimension for Col(A) = 6.

A matrix's rank is defined as the largest number of its characteristic equation columns (or rows). A matrix's rank is limited to a handful of its rows and columns.

A square matrix has columns (rows) that are only linearly independent if the matrix is not unique. To put it another way, any nonsingular matrix of order m has rank m. The symbol for a matrix A's rank is (A).

A null matrix has 0 rank. No non-zero rows or columns exist in a null matrix. There are no distinct rows or columns as a result. Hence, a null matrix has a rank of 0.

a) matrix is 4 x5 , null space is 3 dimensional then rank = 2

b) A is 6x7 matrix :  the column vectors with leading 1's of the row vectors forms a basis for column space.

Maximum possible dimension for Col(A) = 6

c) If null space = {0,0,0,0,0}, then

The for Ax= B, column vector B is the solution for the system.

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No,Sarah would have 16 small stones and 14 large stones on the sixth day, since it's +4 small stones and +3 large stones per day. You must show your working if you want the marks. Best of luck!

The height of cliff is 62.50 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, the angle of elevation from point A to the top of a cliff is 38°, the point A is 80 feet from the base of the cliff,

Refer to figure attached,

The scene is making a right triangle, with an acute angle 38°, and base (distance from point to base of the cliff) 80 ft, we need to find the length of perpendicular line which is the height of the cliff,

Therefore,

We know that,

tan β = ratio of the perpendicular side to base of a triangle,

Therefore,

tan 38° = AB / 80

AB = 62.50

Hence, the height of cliff is 62.50 ft

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Answer:

484ft

Step-by-step explanation:

Split the shape into different shapes like triangles and squares.

area of a triangle: [tex]A=\frac{ab}{2}[/tex]

Area of a square: A = l x w

The correct statement about position of 2 is the 2 in 142 represents 10 times the value of the 2 in 124.

We know about the place value of digits. It states that the first digit on the Right Hand Side is the units place. Moving to the left, the next digit holds the value of tens. Moving further left the value increases 10 times.

Based on this, 142 has 2 at the leftmost place. Thus, it's value is 2. But, in the number 124, the two is at second position. It makes it value 20 (as 2 × 10 = 20). Therefore, the number in 124 is ten times of the number is 142.

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The correlation coefficient for the data shown in the scatter plot is- 0.9.

The correlation coefficient is a measure of the strength of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. The correlation coefficient can be used to measure the strength of the linear correlation between two variables, as well as identify whether a relationship between two variables is positive or negative. It can also be used to compare the strength of different relationships between multiple variables.

The scatter plot shows a strong negative linear relationship between the two variables, indicating that as one variable increases, the other variable decreases. Therefore, the correlation coefficient is likely to be close to -1, making -0.9 the best estimate.

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Answer:

Total surface area of the prism = 333 cm².

Step-by-step explanation:

The total surface area of the prism is A = 420 cm²

The surface area of the prism is calculated as

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

Given data ,

The length of the prism L = 15 cm

Now , cross section of the prism is the trapezium ABCD

And , ∠DAB = ∠CDA = 90°

The measure of sides of the prism are

AB = 9 cm

DC = 6 cm

And , AD = 4 cm

Now , total surface area of prism is A = 2B + ph

On simplifying , we get

S₁ = ( 1/2 ) ( 6 + 9 ) ( 4 x 2 ) + ( 6 x 15 ) + ( 4 x 15 ) + ( 9 x 15 )

S₁ = 345 cm²

Now , the perpendicular CE to AB is drawn and

DC = AE = 6 cm

And , BE = AB - AE = 3 cm

BC² = CE² + BE²

On simplifying , we get

BC = 5 cm

S₂ = 5 x 15 = 75 cm²

So , the total surface area S = S₁ + S₂ = 420 cm²

Hence , the surface area of prism is S = 420 cm²

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The complete question is attached below :

The diagram shows a solid prism of length 15 cm. The cross section of the prism is the trapezium ABCD. Angle DAB = angle CDA = 90°. AB = 9 cm, DC = 6 cm and AD = 4 cm. Calculate the total surface area of the prism.​

Answer:

Step-by-step explanation:

(90 +100) / 2 = 190/2 = 95

Suppose that a certain population obeys the logistic equation dy/dx= ry[1-(y/k)]

a) So if y0= K/3, then

dy/dx=  ry[1-(y/k)]

The above statement is equation 1.

Equation 2 is in the form of

dy/dx + P(t)y = yⁿQ(t)

which is a Bernoulli's differential equation with n=2. So 1- 2= -1

To solve it we put

Then dz/dx= -y⁻²(dy/dx)

This above statement is equation 3.

P(t)= -r, Q(t)= -(r/K)

and integrating factor is given by

IF= e ∫(1-n)P(t)dt= e ∫(-1)(-r)dt= ert

Then the solution is given by

z(IF)= ∫(1-n)Q(t)(IF)dt+C

If given y0= K/3, then

3/K= 1/K+C

Thus the solution to this part is

y⁻1ert= ert/K+2/K= 1/K(2+ert)

To find the time at which the initial population doubled that is 2K/3

Thus

2K/3= Kert/(2+ert)

For r=0.025, then r= 55.452

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We would substitute the expression for g(x), which is 4x, into the expression for f(g(x)), giving f(g(x)) = 3(4x) + 2 = 12x + 2.

What is function ?

Function can be defined in which it relates an input to output.

To simplify f(x) + g(x) where f(x) = 3x + 2 and g(x) = 4x, we can simply add the two functions by adding their corresponding terms. Therefore, f(x) + g(x) = 3x + 2 + 4x = 7x + 2.

To simplify the function f(g(x)), we would first substitute g(x) into the expression for f(x) wherever x appears, giving f(g(x)) = 3(g(x)) + 2

Then, we would substitute the expression for g(x), which is 4x, into the expression for f(g(x)), giving f(g(x)) = 3(4x) + 2 = 12x + 2.

Combining functions can be useful in many situations, such as in physics or engineering where multiple variables or parameters are involved in a single equation. It can also be useful in finance or economics where the behavior of multiple factors needs to be modeled in a single function.

Therefore, we would substitute the expression for g(x), which is 4x, into the expression for f(g(x)), giving f(g(x)) = 3(4x) + 2 = 12x + 2.

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The coordinates of triangle A'B'C' after a translation of triangle ABC based on the transformation rule (x, y) → (x - 4, y + 3) are A' (-2, 7), B' (-2, 0), and C' (3, 0).

The coordinates of quadrilateral Q'R'S'T' after a translation based on the transformation rule are Q' (-2, 0), R' (4, 0), S' (-2, -8), and T' (-2, -8).

In Mathematics, the translation of a geometric figure to the right simply means subtracting a digit to the value on the x-coordinate (x-axis) of the pre-image of a function.

By translating the coordinate of triangle ABC to the left by 4 units and vertically upward by 3 units, the coordinates include the following:

(x, y)                               →                          (x - 4, y + 3)

Coordinate A = (2, 4)   →    Coordinate A' (2 - 4, 4 + 3) = (-2, 7).

Coordinate B = (2, -3)   →    Coordinate B' (2 - 4, -3 + 3) = (-2, 0).

Coordinate C = (7, -3)   →    Coordinate C' (7 - 4, -3 + 3) = (3, 0).

By translating the coordinate of quadrilateral QRST vertically downward by 4 units, the coordinates include the following:

(x, y)                               →                          (x, y - 4)

Coordinate Q = (-2, 4)   →    Coordinate Q' (-2, 4 - 4) = (-2, 0).

Coordinate R = (4, 4)   →    Coordinate R' (4, 4 - 4) = (4, 0).

Coordinate S = (-4, -4)   →    Coordinate S' (-4, -4 - 4) = (-2, -8).

Coordinate T = (-2, -4)   →    Coordinate T' (-2, -4 - 4) = (-2, -8).

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sinθ = -0.9798 (rounded to two decimal places).

What is the Trigonometry ?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

We can use the identity sin²θ + cos²θ = 1 to find sinθ, since we know cosθ:

sin²θ + cos²θ = 1

sin²θ + 0.2² = 1 (substituting cosθ = 0.2)

sin²θ = 0.96

Taking the square root of both sides, we get:

sinθ = ± 0.9798

Since θ is in the second quadrant, sinθ is negative.

Hence, sinθ = -0.9798 (rounded to two decimal places).

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