trish is breaking ground for a rose garden inher backyard. the garden will be a square with a side length of 7 meters. what will be the area of the rose garden?

Answer: The first choice.

Step-by-step explanation:

As you can see in the diagram, the line passes through the points[tex](x, y) = (4, -4)[/tex] and [tex](x, y) = (-4, 8)[/tex] . Thus, the slope of the line is [tex]\frac{8-(-4)}{-4-(4)} = \frac{12}{-8} = -\frac{3}{2}.[/tex] Thus, the correct answer is the first choice, as that line has a slope of [tex]-\frac64=-\frac32.[/tex]

The answer of the given question based on the Rectangular prism is , the surface area of the given triangular prism is 3360 cm².

A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as rectangular parallelepiped or cuboid. A rectangular prism has a length (l), width (w), and height (h) and the formula for the volume of a rectangular prism is given as V = l * w * h.

To find the surface area of a triangular prism, we need to add up the areas of all of its faces. A triangular prism has two identical triangular bases and three rectangular faces.

First, let's find the area of the triangular base. We know that it is an isosceles triangle with a perpendicular height of 35 cm and base of 24 cm, and the length of the two equal sides is 37 cm. We can use the formula for the area of a triangle:

Area of base = (1/2) * base * height

Area of base = (1/2) * 24 cm * 35 cm

Area of base = 420 cm²

Since there are two identical bases, we can multiply this by 2 to get the total area of the triangular bases:

Total area of bases = 2 * 420 cm²

Total area of bases = 840 cm²

Now, let's find the area of the three rectangular faces. We know that the height of the prism is 35 cm, and the length of each rectangular face is equal to the base of the triangular base, which is 24 cm. To find the width of each rectangular face, we need to use the Pythagorean theorem to find the length of the altitude of the triangular base:

a² + b² = c²

where a and b are the two equal sides of the triangular base, and c is the base.

Substituting the given values, we get:

a² + b² = c²

37² + 12² = c²

1369 + 144 = c²

c² = 1513

c = √1513

c = 38.95 cm

Therefore, the altitude of the triangular base is approximately 35 cm, and we can use this value as the width of each rectangular face. So, area of each rectangular face is given:

Area of each rectangular face = length*width

Area of each rectangular face = 24 cm * 35 cm

Area of each rectangular face = 840 cm²

Since there are three identical rectangular faces, we can multiply this by 3 to get the total area of the rectangular faces:

Total area of rectangular faces = 3 * 840 cm²

Total area of rectangular faces = 2520 cm²

Finally, we can find the total surface area of the prism by adding the areas of the two triangular bases and the three rectangular faces:

Total surface area = Total area of bases + Total area of rectangular faces

Total surface area = 840 cm² + 2520 cm²

Total surface area = 3360 cm²

Therefore, the surface area of the given triangular prism is 3360 cm².

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Answer:

Circumference/Diameter = π

If the diameter is 2, then the circumference is 2π.

If the diameter is 6, then the circumference is 6π.

The equivalent value of the fraction is A = 11/4

Given data ,

Let the fraction be represented as A

Now , let the first fraction be p = 2 1/5

Let the second fraction be q = 4/5

Now , A = p/q

On simplifying the equation , we get

A = ( 2 1/5 ) / 4/5

A = ( 11/5 ) / ( 4/5 )

On further simplification , we get

A = ( 11/5 ) x ( 5 / 4 )

A = 11/4

Therefore , the value of A is 11/4

Hence , the fraction is A = 11/4

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The correct option is A, the inequality is:

2.75x + 1.95y ≤ 750

Let's define the variables we will be using:

x = number of chicken sandwiches

y = number of hamburgers.

We know that the budget is $750, and the chicken sandwich costs $2.75 to make and the hamburger costs $1.95 to make, then we can write the inequality:

"Total cost equal to or smaller than 750"

2.75x + 1.95y ≤ 750

That is what we can see in option A, so that is the correct one.

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Answer: 28.27m^2

Step-by-step explanation:

Area of a circle: [tex]A = \pi r^{2} \\[/tex]

Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.

6/2 = 3m

[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]

a. On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

b. On a 33 rpm record (12-inch diameter), the fly would travel 1,245.6 inches in 1 minute.

c. On a 78 rpm record (10-inch diameter), the fly would travel 2,430 inches in 1 minute.

Radius of 45 rpm record = 3.5 inches (7/2)

Circumference = 2 * π * r = 2 * π * 3.5 ≈ 22 inches

Distance in 1 minute = Circumference * rpm = 22 * 45 = 990 inches

Thus, it can be seen that On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

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Answer:-by-step explanation:

the function has the x-intercept of (-2, 0)

the function has the y-intercept of (0, -8)

the function has the x-intercept of (4, 0)

A rigid transformation and the three types of rigid transformations are: B. Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.

Generally speaking, there are three (3) main types of rigid transformation and these include the following:

In conclusion, rigid transformation are movement of geometric figures where the size and shape does not change because they have congruent preimages and images.

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g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

what is function ?

In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.

In the given question,

To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

Step 1: Apply f to -3

f(x) = 3x + 7

f(-3) = 3(-3) + 7 = -2

Step 2: Apply g to the result of f(-3)

g(x) = 2x - 5

g(-2) = 2(-2) - 5 = -9

Therefore, g°f = -9.

So, the correct answer is (B) -9.

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The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.

Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.

From the first sentence, we know that:

S + P + Ph = 308.0 million

From the second sentence, we know that:

P = Ph + 49.4 million

And from the third sentence, we know that:

P + Ph = S + 24.4 million

Now we can substitute the second equation into the third equation:

(Ph + 49.4 million) + Ph = S + 24.4 million

Simplifying:

2Ph + 49.4 million = S + 24.4 million

2Ph = S - 25 million

Substituting this into the first equation:

S + P + Ph = 308.0 million

S + (Ph + 49.4 million) + Ph = 308.0 million

2Ph + S = 258.6 million

Now we can substitute the equation we derived earlier:

S + 2Ph - 49.4 million = 258.6 million

S + 2Ph = 308.0 million

Substituting 2Ph = S - 25 million:

S + S - 25 million = 308.0 million

2S = 333.0 million

S = 166.5 million

Now we can use this value to find P and Ph:

P = Ph + 49.4 million

P + Ph = S + 24.4 million

Substituting S = 166.5 million in both equations:

P + Ph = 190.9 million

P = Ph + 49.4 million

Solving these two equations simultaneously:

Ph = 57.6 million

P = 107.0 million

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The expressions are solved to give;

1.n = 1

2. h = 1

3. x = -5

4. n = 1/4

5. x = 7/2

6. p = 2/3

7. x = -12

8. n = 3

9. c = -1

10. x = 6

These are expressions that are made up of term, variables, constants, factors and coefficients.

They are also made up of mathematical operations.

From the information given, we have;

1. 5n + n = 2n + 4

collect and add the like terms

4n = 4

Make n subject

n = 1

2. 5h + 2 = h - 2

collect and add the like terms

4h = 4

h = 1

3. 2x - 1 = 3x + 4

collect and add or subtract the like terms

-x = 5

x = -5

4. n = n + 1/5

cross multiply

4n = 1, n = 1/4

5. x + 5 = 3x - 2

collect like terms

-2x = -7

x = 7/2

6. p = p + 2/4

cross multiply

3p = 2

p = 2/3

7. 4(2 + x) = 3x - 4

expand the bracket

8 + 4x = 3x - 4

collect like term

x = -12

8. 5n + 2 = 3n + 4

collect like terms

n = 3

9. 3c - 2 = -3c - 8

collect like terms

6c = - 6

c = -1

10. 3x + 1 = 2x - 5

collect the like terms

x = 6

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Answer: 6,450 words per minute

Step-by-step explanation:

Each hour is 60minutes long, making your total number of minutes 150.

The last step would be to multiply 150 by the wpm (43) and making the total number typed 6,450

Answer:

Her rate of mowing lawns per hour is 4 lawns to one hour

Step-by-step explanation:so on a table you divide 4÷4=1 then you do the same thing for the 16÷4=4. So Oliva can mow 4 lawns per hour

Answer:

I would say probability.

Answer:

no

Step-by-step explanation:

-5/3x+10=5

-5/3x=5-10=-5

3x=-5/-5=1

=>x=1/3

Answer:

When we have a set of points, we can find the distance between them using the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.

OB:

Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]

Thus, the first part/step in the equation is your subtraction expression to find the length of OB.

AB:

For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]

The first part/step is your subtraction expression for the length of AB.

The equation that represents a quadratic function is option b: [tex]y=3x^2-5x+9[/tex]

What is a quadratic function ?

A quadratic function is a function that can be written in the form of f(x) = [tex]ax^2 + bx + c[/tex] , where a, b, and c are constants, and a is not equal to 0. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the coefficient a.

In option b, we can see that the equation is in the form of [tex]f(x) = 3x^2 - 5x + 9[/tex] , which is a quadratic function. The coefficient of [tex]x^2[/tex] is a non-zero constant (a=3), which means that the graph of this function is a parabola.

Option a is not a quadratic function, as it is in the form of [tex]x=y^2-2y+4[/tex], which is a quadratic equation in terms of y, but not in terms of x.

Option c is a little more complicated, as it contains a radical term. However, if we simplify it, we can see that it is also a quadratic function, in terms of x.

Option d is a linear equation, not a quadratic function, because it does not have an [tex]x^2[/tex] term.

Therefore, the quadratic function is [tex]y=3x^2-5x+9[/tex], option b.

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Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Answer:

Billy has £20, Liam has £40, and Nicola has £120. The total amount of money they have is £180, as given in the problem.

Step-by-step explanation:

Let's start by defining the variables:

Billy's money: x pounds

Liam's money: 2x pounds (twice as much as Billy)

Nicola's money: 3(2x) = 6x pounds (three times as much as Liam)

The total amount of money they have is £180, so we can write an equation:

x + 2x + 6x = 180

Simplifying the left side of the equation:

9x = 180

Solving for x:

x = 20

Now we can find out how much money each person has:

Billy: x = 20 pounds

Liam: 2x = 2(20) = 40 pounds

Nicola: 6x = 6(20) = 120 pounds

Maxwell's filing status can be described as: b. Married filing jointly.

A filing status is a category that defines your tax-filing status based on your marital status and family situation. The filing status determines tax rate and standard deduction, as well as the eligibility for certain credits, deductions, and exemptions.

Maxwell can be described as married filing jointly because he and his spouse combined their income, deductions, and credits on one tax return. This status generally results in lower tax rates and a larger standard deduction compared to filing separately.

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The value of (a) in given triangle is approximately 7.44 cm.

A triangle is a three-sided polygon consisting of three sides and three vertices. The most important property of a triangle is that the sum of its interior angles  is  180 degrees.

Let ΔABC is a triangle

Given ∠ B = 75°

∠ C = 31.8°

AB = 12cm

AC = 22cm

find BC = ?

We can use the law of cosines to solve for BC:

BC² = AB² + AC² – 2(AB)(AC)cos(B)

We know that angle B = 75 degrees, so we can substitute:

BC² = 12² + 22² - 2(12)(22)cos(75)

Evaluating cos(75) with a calculator, we get:

BC² ≈ 144 + 484 - 572.59

BC² ≈ 55.41

Taking the square root of both sides gives us:

BC ≈ 7.44

Therefore, BC is approximately 7.44 cm.

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The factors in this algebraic expression are:

14 And (18 - 3x)

An algebraic expression can also be written as a list of its constituent parts. Variables, constants, and operators are the components of an algebraic expression. Terms are separated from one another in an algebraic equation by the addition operation.

Algebraic Expressions can be factorized using many methods. The most common methods used for factorization of algebraic expressions are:

Factorization using common factors

Factorization by regrouping terms

Factorization using identities

The algebraic expression written by Aaron to represent the product of 14 and the difference of 18 and 3x is:

14 * (18 - 3x)

The factors in this expression are:

14

(18 - 3x)

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Programme 2 in Los Angeles will be well received by 22 out of 25 people.

Given that the chances of a positive response from Los Angeles residents to two government programmes are 78.4% for Programme 1 and 88.1% for Programme 2, the likelihood of a positive response for Programme 2 given that the person is from Los Angeles must be calculated as follows:

88.1 / 100 = X 44.05 / 50 = X 22,025 / 25 = X

Therefore, Programme 2 will be well-received by 22 out of 25 people in Los Angeles.

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For the functions, f(x) = −x+2, and g(x)=5x²,

a) f∘g(x) =  5x² + 2

b) g(f(x)) = 5x² -20x + 20

c) f∘(g(x))² = 25x⁴

d) g(x - 1)    = 5x² - 10x + 5

Here, the functions are: f(x) = −x+2, and g(x)=5x²

a) f∘g(x)

We know that composite function f∘g(x) means f(g(x))

For function f(x) substitute x = g(x)

i.e., f(g(x)) = -(g(x)) + 2

                = -(5x²)  +2

                = 5x² + 2

b) g(f(x))

For function g(x) substitute x = f(x)

i.e., g(f(x)) = 5x²

                = 5(-x + 2)²

                = 5(x² -4x + 4)

                 = 5x² -20x + 20

c) f∘(g(x))²

First we find the (g(x))²= (5x²)²

                                     = 25x⁴

Now the composite function  f∘(g(x))² would be,

 f∘(g(x))² = f((g(x))²)

              = -(g(x))²+ 2

              = -(g(x))² + 2

d) g(x - 1)

Substitute x = x -1 in function g(x)

g(x - 1) = 5(x - 1)²

           = 5(x² - 2x + 1)

           = 5x² - 10x + 5

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Answer:

We can use trigonometry to find AB.

First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:

A + B + C = 180°

A + 90° + 30° = 180°

A = 60°

Now, we can use the sine function to find AB:

sin A = opposite/hypotenuse

sin 60° = AB/96

AB = 96 * sin 60°

AB = 96 * √3/2

AB = 48√3

Therefore, AB is approximately 83.14 cm (rounded to two decimal places).