Tara will draw a scale model of the garden she wants to plant. Her scale will be 1 cm=2.5 ft. What will be the actual dimensions of Tara's garden?

Answer:

radius: 9

center: (-6, -8)

Step-by-step explanation:

First, you may wan to rearrange the equation so it is easier to sole, like:

x^2 + 12x + y^2 + 16y + 19 =0

Next, we need to complete the square. x^2 + 12x is the start of the square of x + 6, which ends in 36, and y^2 + 16y is the start of the square of x + 8, which ends in 64. We can start to write in the squares like:

x^2 + 12x + 36 - 36 + y^2 + 16y + 64 - 64 + 19 = 0

(36 & 64 are subtracted so the equation stays the same)

You can factor getting:

(x + 6)^2 - 36 + (y + 8)^2 - 64 + 19 = 0

You can combine the constants to get -36 - 64 + 19 = -81 and we can add 81 to both sides to get:

(x + 6)^2 + (y + 8)^2 = 81

The standard form of a circle equation is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center and r is the radius.

In this case, by substituting, we get the center is (-6, -8) and the radius is 9.

Answer:

You are correct. The answer is the blue point marked

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Ben uses clay to make the rectangular prism to the left. Naomi uses cardboard to make the triangular prism to the right. Therefore, Naomi's prism has a greater volume.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

Ben uses clay to make the rectangular prism to the left.

Volume of rectangular prism = (length x width x height)

= 11 x 5 x 2

= 110 cubic in

Naomi uses cardboard to make the triangular prism to the right.

The volume of a right triangular prism = ( height× Base Area)

= 4 x 18 x 4

= 288 cubic in

Therefore, Naomi's prism has a greater volume.

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Answer:

Diameter = 14 yd

Step-by-step explanation:

Given:

Area of semicircle = 76.97 yd²

Required:

Diameter of semicircle

Solution:

Area of a semicircle = ½(πr²)

Area = 76.97 yd²

Plug in the values

Thus:

½(π*r²) = 76.97

Multiply both sides by 2

πr² = 2*76.97

πr² = 153.94

Divide both sides by π

r² = 153.94/π

r² = 49.0

Take the square root of both sides

r = √49.0

r = 7 yd

Diameter = 2(r)

Diameter = 2(7) = 14 yd

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..

Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.

Here,

Angle of elevation to the balloon's peak: = 28°

When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.

Aside from the hypotenuse

l = The leg next to the provided reference angle

,h = The leg perpendicular to the specified angle,

Trigonometric ratios give us;

Cosx is equal to the product of the hypotenuse and adjacent lengths.

where we obtain;

Cos x equals l/d

=>Cos 28 = 30 m /d

=> d = 30m/Cos 28 ≈ 33.977

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.

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Answer:

A) I’m 100% sure it’s correct!

Step-by-step explanation:

Answer:

A. 7

Step-by-step explanation:

[tex]82 - 75 \\ = 7[/tex]

Answer:

Mode

Step-by-step explanation:

If you have an outlier, the best way to measure a set of data is the mode, or the number that occurs the most.

Answer:

d

Step-by-step explanation:

61-1/2=30

30-4=26

The dimensions of the rectangle are 40 and 18 units respectively

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The length of a rectangle is 4 feet more than twice the width.

Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116

                       3x+4      = 58

                             3x    = 54

                               x     = 18

Hence, the dimensions of the rectangle are 40 and 18 units respectively.

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Answer:

7(x+5)=49

Step-by-step explanation:

7 times means multiplication, so 7 times the sum of x and five is 7(x+5). When they say is 49, that means 7(x+5)=49

Answer:

34.84

Step-by-step explanation:

5.2 times 6.7= 34.84

Answer:

Using the Quadratic Formula

x=-b ± √b²-4ac/[2a]

x= -(-5) ± √5² - 4(1)(5)/(2)

x= 5 ± √25-20 /(2)

x= 5 ± √5 /(2)

x= 5 + √5/(2) and 5 - √5/(2)

Answer

B and C

Answer:

Step-by-step explanation:

Of the twenty times in this experiment the following are prime (3,5,2,7,3,7,2,2,7,3,3,5) or 12 of the twenty

12/20 = 6/10  = 60%

So 60% is the experimental probabilty.

The theoretical probability given that there are four prime numbers (2,3,5,7) out of 8 on the dice should be 50%  because 1/2 of the numbers are prime.

The experimental probability is 10% more than the theoretical probability

60% - 50% = 10%

Answer:

60%,  10%

Step-by-step explanation:

Plato/Edmentum

Answer:

Step-by-step explanation:

1. If there are 4 apples, each apple has 4 fourths x 4 apples =16 fourths

2. Something is missing???

3. 6/4 x 5/5=30/20, 15/10 x 2/2=30/20 so both are same length

Answer:

Five hours after the museum opens, there are 36 visitors.

Step-by-step explanation:

V(5)=36 means that when h is 5, V is 36. Assuming this is a function from what information this gives.

Step-by-step explanation:

f(x) = 2x²+8x+10

vertex point :

x = -8/2(2)= -8/4

=> x = -2 <= this is a symetry axis

f(-2)= 2(-2)²+8(-2)+10=8-16+10=2

the vertex point : (-2, 2)

intercept with y-axis :

f(0) = 0+0+10 = 10

the point : (0, 10)

the drawing as attached

X coordinate of vertex

y coordinate

Vertex is at (-2,2)

Put x=0

Graph attached

Answer: The formula for the interest charged on a credit card debt is:

Interest = (Principal * Annual Interest Rate) / 12

We know that the interest charged last month is $55, and the principal (the credit card debt) is $6000, so we can substitute these values into the formula and solve for the annual interest rate:

55 = (6000 * r) / 12

To find the annual interest rate, we will solve for r.

r = (55 * 12) / 6000

r = 0.09 which is a 9% annual interest rate.

So, the annual interest rate on the credit card is 9%.

Step-by-step explanation:

Answer:

the answer is B.450 +15x

Answer:

B

Step-by-step explanation:

Answer:

  8.4

Step-by-step explanation:

You want to know the value of x that satisfies 1.2/4 = x/28.

The equation ...

  x/28 = 1.2/4

can be solved in one step by multiplying by 28.

  x = 28(1.2/4) = 8.4

The value of x is 8.4.

__

Additional comment

The fraction involving x can be cleared by multiplying by its denominator, effectively the inverse of the coefficient of x. This is the same way you solve any similar one-step equation.

Often, you are told to "cross-multiply" a proportion. Doing that gives you ...

  4·x = 28·1.2

Then you have to divide by 4 (multiply by the inverse of the coefficient of x) to find the value of x:

  x = 28·1.2/4 . . . . same as above.

That is, there is no need to multiply by 4, and then divide by 4. You can simply multiply by 28 and be done.

Answer:

8.4

Step-by-step explanation:

[tex]\frac{1.2}{4}[/tex] = [tex]\frac{x}{28}[/tex]

cross multiply to solve for x:

(1.2)(28) = 4x

4x = 33.6

x = 33.6/4 = 8.4

Answer:

The length is 15 inches squared

Step-by-step explanation:

total area / height = length

120 / 8 = 15

957÷3=319 this divide answer i hope help you

It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet

An equation is an expression that shows the relationship between two or more numbers.

The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:

Speed = distance / time

Distance = Speed * time

The spaceships are moving at 110000 km/h

The distance covered by each in x hours is:

Distance = 110000 * x = 110000x

Since they are 7100 km apart, hence:

110000x + 110000x = 7100

220000x = 7100

x = 0.03227 hours = 116.18 seconds

It would take 116.18 seconds for the spaceships to meet.

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Answer:

y = 3x + 9

Step-by-step explanation:

The initial equation would be y = mx + b where m is the slope and b is the y-intercept. Then you would use the equation y^2 - y^1 / x^2 - x^1 to get the slope. Substituting the factors in it would be, 15 - 12 / 2 - 1 having a slope of 3. Then seeing as x is 0 y is 9, 9 must be the y-intercept.

An area surrounding a measurement that indicates how accurate it is called a confidence interval.

Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.

Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:

p ± Zα/2[√{P(1 –p)/n}] ……(1)

where

Zα/2 is the upper (α/2)% point of N(0, 1),

pcap = sample proportion, and

n = sample size.

One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)

Now to work out the solution,

The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)

for Part (a)

equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.

for Part (b)

equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.

For Part (c)

Margin of error is: Zα/2[√{P(1 –P)/n}]

If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be

[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]

= √(n1/n2)

= 1/√6 [given the second sample size is 6 times the first sample size]

= 0.4082

= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082

= 0.05 x 0.4082

= 0.020.

Thus, the margin of error when the sample size if 6-fold is 0.020.

For Part (d)

The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.

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Answer:

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Step-by-step explanation:

Step-by-step explanation:

1. you must first find the value of y

[tex]6y + 12 = 30 \\ 6y = 30 - 12 \\ 6y = 18 \\ y = 3 \\ 23 + 7 - 5y \\ 23 + 7 - 5(3) = 15[/tex]

Option A) In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

A function f is said to be injective if it maps different items in its domain to other elements; for example, f = f implies x1 = x2. Alternatively, every element of the function's codomain is at most one of its domain's elements.

If some function output value corresponds to more than one input value, the function is said to be many-to-one (sometimes written as "many-one"). If the domain of f contains two different values a and b such that f(a)=f, the function f is many-to-one in symbols (b).

In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

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Answer:

its 9 only

Step-by-step explanation:

cuz the formula of area of square is side²

Answer:

Yeah it's 9. Bcs the area of the square is *side × side*

Answer: A) solution is 1

Step-by-step explanation: