what is the solution to this equation?
[tex](\frac{1}{4})x^+{1}=32[/tex]

Answer:

make the x and y variables to each other variables by addition or subtraction

173x-7x +4y-4y=5

166x + 0y=5

166x =5

x= 166/5

x=33.2

Answer: 4 strawberries

Step-by-step explanation:

First, we can change the total number of strawberries into a fraction, that way it makes the division process easier. 12 is really equivalent to 12/1 since it is a whole number. Now, we can set up an equation: (12/1) * (1/3) will solve to give us the number of strawberries the brother has. Since there is a one in both the numerator and the denominator, they will cancel, leaving us with (12/3). This is now just division, which gives us 4. Therefore, the brother will receive 4 strawberries. Hope this helps!

The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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The angles are 36,118,62

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.

Given: m and n are parallel lines with 3 transversals

We can observe that a=36 (vertically opposite angles)

and b =180-(36+26)     ∵  They all lie on a line .

          =118

and c= 180-118               ∵They all lie on a line.

         =62

Hence, The angles are 36,118,62

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1. The completion of the mathematical expression to represent the change in Estella's account balance due to guitar lessons after 2 years is 52 - 35x, where x is the number of years.

2. After two years, the account balance will be $-18, without reflecting interest.

A mathematical expression is a combination of variables, constants, numbers, and mathematical operands (addition, subtraction, division, and multiplication).

A mathematical expression may not convey any meaning since it sounds like a phrase in the English language that does not make complete sense.

The unit rate (cost per lesson) for guitar lessons = $35

Estella's account balance = $52

Let the number of years = x

Lesson period, x = 2 years

Mathematical Expression: 52 - 35x

Solution: 52 = 35(2)

= $-18

Thus, after 2 years of guitar lessons, Estella will be indebted to the bank by $18 if she does not deposit an additional amount in her account.

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Expression: 52 - 35

Answer:

  x = 18.3

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle given the side opposite the 41° angle is 12 units.

The sine relation is ...

  Sin = Opposite/Hypotenuse

This can be rearranged to ...

  Hypotenuse = Opposite/Sin

  x = 12/sin(41°) ≈ 18.3 . . . . units

The value of x is about 18.3.

__

Additional comment

This is the SOH relation from the mnemonic SOH CAH TOA, which is intended to remind you of the relation between trig functions and sides of a right triangle. The others tell you ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

In the attached, note the calculator mode is set to DEG (degrees) so the argument of the Sin( ) function will be interpreted properly.

Answer:

To find f(2), we substitute 2 for x in the equation of the parabola F(x) = x^2 - 2x - 3:

F(2) = 2^2 - 2(2) - 3 = 4 - 4 - 3 = -3

So f(2) = -3

To find g(-3), we substitute -3 for x in the equation of the line g(x) = x - 2:

g(-3) = -3 - 2 = -5

So g(-3) = -5

The correct solution to this question is as follows:

f(2)= -3   &  g(-3)=-5

Step-by-step explanation:

[tex]f(x)=x^{2} -2x-3[/tex]

[tex]f(2)=2^{2} -2(2)-3[/tex]

[tex]f(2)=4 -4-3[/tex]

[tex]f(2)=-3[/tex]

[tex]g(x)=x-2[/tex]

[tex]g(-3)=-3-2[/tex]

[tex]g(-3)=-5[/tex]

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Therefore , the solution of purchased so that the consumer has an equal amount of each LCM if hot dogs are packaged with 10 dogs per pack .

"Sandwich rolls or hot dog buns are typically sold in packs of eight because the buns are baked in clusters of four in pans designed to hold eight rolls." Because hot dogs are sold by the pound and store-bought standard-sized hot dogs weigh 1.6 ounces,

Here,

purchased so that the consumer has an equal amount of

each if hot dogs are packaged with 10 dogs per pack and hot dog buns are packaged with 8 buns per pack  LCM is 40.

hot dog buns are packaged with 8 buns per pack  LCM is 40. 4 packages of hot dogs and 5 packages of buns are required.

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Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.

What are the domain and range?

The domain and range of a function are the set of all the inputs and outputs a function can give respectively. The domain and range are important aspects of a function. The domain takes all the possible input values from the set of real numbers and the range takes all the output values of the function.

We have the functions, f(x) = eˣ and g(x) = x+6

So, their composition will be g(f(x)).

Then, g(f(x)) = g(eˣ) = eˣ+6

Thus, g(f(x)) = eˣ+6.

Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.

Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.

Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.

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Answer:

2,260.80 cubic millimeters

Step-by-step explanation:

The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters

Answer:

1/3

Step-by-step explanation:

Everytime x increases by 3 units, y increases by 1 unit.

Hence, when Δx=3, Δy=1  (Δx = change in x)

m=Δx/Δy

m=1/3

Answer:

-------------------------------------

We know that the area of a rectangle with same dimensions is twice the area of a triangle.

The shaded area is half the area of the rectangle:

You already divided it to rectangle and triangle.

Area of rectangle:

The triangle have same base, 12 units. It height is 16 - 10 = 6 units.

Its area is:

Area of the small rectangle in the middle:

The shaded area is the difference of the total area and the small rectangle:

The number of terms (n) in the sequence = 10.

We know that,

                      S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}

Where,

            S = Sum of A. P. series

            n = number of terms in A. P. series

            a = first term of the series

            d = common difference

According to the question,

           Sum of the series, S = 340

                         First term,  a = 7

         Common difference, d = 6

                  S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}

                  340 =  [tex]\frac{n}{2}[/tex] {2*7 + (n-1)6}

                  340 =  [tex]\frac{n}{2}[/tex] {14 + 6n - 6}

                  340*2 = n( 6n + 8)

                   680   = 6n^2 + 8n

        6n^2 + 8n - 680 = 0

        2 (3n^2 +4n - 340) = 0

            3n^2 +4n - 340 = 0

        3n^2 + 34n - 30n - 340 = 0

        n (3n+ 34) - 10 (3n + 34) = 0

        (3n + 34) (n - 10) = 0

   if we take, 3n + 34 = 0

                         3n = - 34

                           n = -34/3

which is not possible, as the number of terms can not be negative

   if we take, n- 10 = 0

                       n = 10

Hence, the number of terms in the given A. P. series is 10.

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Answer:

Hope This Helps <3

Step-by-step explanation:

Printer cost 265

Computer cost 795

Answer:

below

Step-by-step explanation:

1/2  = e^(-.0372t)        ln   both sides to get :

-.693147 = - .0372t      then t = 18.6 yrs

The statement 4, 6 and 7 is enough to prove that 45° + m∠AOW = 90°.

A harmonious relationship, agreement, or correspondence are all concepts that are denoted by the mathematical term "congruence," which is used in a variety of contexts.

The two geometric figures are said to be congruent, or to be in the relation of congruence, if they can be superimposed on one another so that their entire surfaces match. If two triangles have the same two sides and included angle, they are said to be congruent.

The idea of a "rigid body," which can be moved from one place to another without changing the internal relationships between its parts, appears to be the foundation for congruence.

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Answer:

y - 9

Step-by-step explanation:

(y-9)²/4÷(4y-36)/16

is a fraction divided by a fraction.

When you have one or two fractions with a division, use Keep-Change-Flip.

Keep the first term:

(y-9)²/4

then Change the ÷ to a times.

(Y-9)²/4•

then Flip the second term.

(y-9)²/4 • 16/(4y-36)

You can factor the term (y-9)² into

(y-9)(y-9).

The other term (4y-36) can also be factored into

4(y-9).

see image.

The 4's and the y-9 terms can be "cancelled".

see image. The only term left is y-9.

The perimeter of the fencing in terms of 'x' will be 13x + 3.

The complete stretch of a shape's border is referred to as the perimeter in geometry. A shape's periphery is calculated by summing the lengths of all of its sides and borders. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

The perimeter of the fencing in terms of 'x' is given as,

P = x + x + x + x + (3x + 1) + (3x + 1) + (3x + 1)

Simplify the equation, then we have

P = x + x + x + x + (3x + 1) + (3x + 1) + (3x + 1)

P = x + x + x + x + 3x + 1 + 3x + 1 + 3x + 1

P = 13x + 3

The perimeter of the fencing in terms of 'x' will be 13x + 3.

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If Joshua drove at a constant rate, he drove 24 miles in one hour since he could drive 22 miles in 55 minutes or 0.4 miles per minute (driving speed).

Joshua's driving speed is the quotient of the total distance and the time.

The quotient is the result of a division operation, where a numerator (distance) is divided by the denominator (time) to obtain the unit rate or constant rate.

This constant rate (speed) is multiplied by the time (one hour), according to the distance, time, and speed formula, to obtain the distance to be covered.

The distance covered in 55 minutes = 22 miles

Constant driving speed or rate = 0.4 miles per minute (22/55)

1 hour = 60 minutes

For one hour, the distance Joshua could cover = 24 miles (60 x 0.4)

Thus, we can assert that in one hour, Joshua traveled 24 miles, given his constant driving rate.

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The reason that completes the proof for step 6 is given as follows:

D. Definition of midpoint.

The midpoint between two points is the halfway point between them, hence it is found obtaining the mean of the coordinates of each endpoint.

Thus the coordinates of P' are obtained as follows:

(applying the mean of the coordinates of x and y for the endpoints of the segment P').

The coordinates of R' are obtained as follows:

The coordinates of Q' are obtained as follows:

Meaning that the correct option is given by option D.

The problem is given by the image presented at the end of the answer.

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The number of pounds needed for 6045 square​ feet will be 45.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If 3 pounds of grass seed cover 403 square​ feet.

The ratio of the number of pounds of seed to the area that covers the seed.

Let 'x' be the pounds needed of seed. Then the equation is given as,

x / 6045 = 3 / 403

x = 6045 × 3 / 403

x = 15 · 3

x = 45

The number of pounds needed for 6045 square​ feet will be 45.

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Answer:

a) The population of interest in this situation is individuals who are following a weight loss diet plan.

b) There are several sources of bias in this study:

Self-report bias: Town A relies on self-reported weight loss, which may not be accurate as participants may not accurately report their weight loss or may exaggerate their progress.

Measurement bias: Town B uses a different method of measuring weight loss than Town A, which could introduce a bias in the results.

Selection bias: Participants in this study are self-selected, which means that individuals who are more motivated or more likely to succeed in the diet may be more likely to sign up for the study. This can lead to a bias in the results as the sample may not be representative of the population of interest.

Hawthorne effect: Participants in Town B may have changed their behaviors simply because they knew they were being weighed, which could lead to a bias in the results.

Placebo effect: Participants in Town A may have lost weight due to the mere act of participating in a study and receiving attention, which could lead to a bias in the results.

Answer:

50%

Step-by-step explanation:

25%+25%

The composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.

Given that, c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost of shoes after the markdown.

Here, the composition function is

c(s(x))= 0.75x-25

Therefore, the composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.

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Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

The constant of proportionality will be $0.79

It is defined as the rate or the ratio of two proportional values which are known to be at the same value.

The two variable values are said to have a proportional association if or when either of their ratio or their product are known to bring about a constant.

Hence, the proportionality constant's value is known by the proportion between the two said quantities.

Jason bought 4 pounds of bananas for $3.16.

k = $3.16/4

k = $0.79

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The correct brackets for the equations are added as follows:

a) (42 - 8) x 3 - 22 = 80

b) 75+ (5 x 4) -70 = 25

c) (160 ÷ 4) x (3 + 2) = 200

d) 120 ÷ (2 x 3) + 5 = 25.

Equations are mathematical statements that equate or show that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to show the equality of the algebraic expressions.

Using parentheses in equations enable the use of the distributive property to solve the equation.

Thus, the correct parentheses have been added to the equations to prove them correct when solved.

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In November 2018, the frequency tree shows us that 35 students aged 15 years old had part-time work.

That number 35 drops to 23 a year later in 2019. There are two reasons for this:

Case (2) mentioned above only works if the student's birthday is before April 2019.

Therefore, the three consecutive odd integers that add up to 93 are 33, 35, and 37.

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Answer:

C. 43

A. 40

C. 37

E. Other

A rectangle with sides of length 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon

Ans:

The perimeter of a rectangle is given by 2length + 2width. In this case, the perimeter of the rectangle is 284 + 245 = 258.

Since the perimeter of the hexagon is the same as the rectangle, and the sides of the hexagon are all the same length, we can find the length of a side of the hexagon by dividing the perimeter by the number of sides.

A hexagon has 6 sides, so the length of a side of the hexagon is 258/6 = 43.

So the answer is (C) 43.

A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure.

Ans:

The perimeter of the new figure would be 40. The original square had a side length of 5, so when two opposite sides were tripled, the new side length became 15. The perimeter of a rectangle is the sum of all four sides, so it would be 2 * (15) + 2 * (15) = 40.

(A).40

A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q.

Ans:

The probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 can be found by comparing the areas of the two triangular regions formed by the point and the two sides. The area of the triangular region formed by the point and the side of length 25 is (1/2) * 6 * (distance from point to side of length 25) while the area of the triangular region formed by the point and the side of length 6 is (1/2) * 25 * (distance from point to side of length 6).

For the point to be closer to the side of length 25, the area of the triangular region formed by the point and the side of length 25 must be greater than the area of the triangular region formed by the point and the side of length 6. This means (1/2) * 6 * (distance from point to side of length 25) > (1/2) * 25 * (distance from point to side of length 6). Therefore, the probability that the point is closer to the side of length 25 is (1/2) * (6/25) = 3/25. The sum of p and q is 3 + 25 = 28.

Therefore, the answer is (C) 37.

The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence.

Ans:

It is not possible to determine the sum of the possible values of the common ratio of the geometric sequence without more information about the values of m and n in the equation X^3 + mx = 37x^2 +n. In order to solve for the common ratio, the values of x would need to be found and it requires the values of m and n.