If the length (l) of a rectangular garden is x metres, express the breadth (b) in terms of x

Answer:

Isosceles

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

6.   \(-3x^2+9=-3\)

           \(-3x^2 =-12\)

               \(x^2=4\)

                \(x=\) ±\(2\)

Solution: \(x=2, x=-2\)

Points of intersection:  (2, -3) and (-2, -3)

7.         \((x-2)^2-10\leq (x-6)^2-2\)

     \(x^2-4x+4-10\leq x^2-12x+36-2\)

                   \(-4x-6\leq -12x+34\)

                            \(8x\leq 40\)

                              \(x\leq 5\)

Solution:  \(x\leq 5\)

Point of intersection is (5, -1)

The length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

In the given kite ABCD, we know that sides AB and BC are congruent, and the length of AB is 14 units. Additionally, sides CD and AD are congruent, and the length of CD is 22 units.

To find the length of BC, we can use the properties of a kite. Since AB and BC are congruent, we can conclude that BC is also 14 units long.

This is because a kite has two pairs of congruent adjacent sides. Therefore, the length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

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Answer:

The length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

Step-by-step explanation:

just took test

The probability that 2 students chosen at random from a class of 25 are both on the track team is 0.02 or 2%.

To calculate the probability that 2 students chosen at random from a class of 25 are both on the track team, we need to consider the total number of possible combinations and the number of favorable outcomes.

The total number of possible combinations of choosing 2 students from a class of 25 can be calculated using the combination formula:  

nCr = n! / (r!(n-r)!), where n is the total number of students in the class (25) and r is the number of students we want to choose (2).

Using the formula, we have:

25C2 = 25! / (2!(25-2)!) = (25 \(\times\) 24) / (2 \(\times\) 1) = 300.

So, there are 300 possible combinations of choosing any 2 students from the class of 25.

Now, let's consider the favorable outcomes, which are the combinations where both chosen students are on the track team.

Since there are 4 students on the track team, the number of combinations of choosing 2 students from this group can be calculated as:

4C2 = 4! / (2!(4-2)!) = (4 \(\times\) 3) / (2 \(\times\) 1) = 6.

Therefore, there are 6 favorable outcomes where both chosen students are on the track team.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = favorable outcomes / total outcomes = 6 / 300 = 0.02.

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The solution set of the given equation is x = 8.39 or x = -12.39

\( \frac{1}{4} {{(x + 2} )}^{2} = 27\)

cross product

\( {1} {{(x + 2}^{} )}^{2} = 27 \times 4\)

(x + 2²) = 108

find the square root of both sides

\( \sqrt{ ({x + 2)}^{2} } = ± \sqrt{108}\)

x + 2 = ± 10.39

So,

x = 10.39 - 2 or x = -10.39 - 2

x = 8.39 or x = -12.39

Therefore, the equation has a solution set of x = 8.39 or x = -12.39

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Answer:

C) 157 \(cm^3\)

Step-by-step explanation:

\((3.14)5^2*6/3= 157\)\(cm^3\)

Hope this helped! :)

Answer:

I think the answer is A if my math is wriye

Step-by-step explanation:

The area of the region common to the interiors of the cardioids r = 1 + cosθ and r = 1 - cosθ is (π + 2)/4.

We can find the area of the region common to the interiors of the cardioids by setting the two equations equal to each other and solving for θ. This will give us the values of θ that define the boundaries of the region. We can then integrate the area enclosed between the two curves over those boundaries.

1 + cosθ = 1 - cosθ

2cosθ = 0

cosθ = 0

θ = π/2, 3π/2

So the boundaries of the region are θ = π/2 and θ = 3π/2.

To find the area of the region, we can integrate the area enclosed between the two curves over these boundaries:

A = 2 ∫[0, π/2] (1 + cosθ) / 2 × dθ

Note that we multiply by 2 to account for the area in the other half of the region, between θ = 3π/2 and θ = 2π, which is symmetric.

Simplifying the integrand:

A = ∫[0, π/2] (1 + cosθ) / 2 × dθ

= (1/2) ∫[0, π/2] (1 + cosθ) dθ

= (1/2) (∫[0, π/2] dθ + ∫[0, π/2] cosθ dθ)

Evaluating the integrals:

A = (1/2) (θ ∣[0, π/2] + sinθ ∣[0, π/2])

= (1/2) (π/2 + sin(π/2) - 0 - sin(0))

= (1/2) (π/2 + 1)

= (π + 2) / 4

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the center of the sphere is (1, 0, -4) and the radius is sqrt(17.5) ≈ 4.183.

To write the equation of the sphere in standard form, we want to express it as

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

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

First, we'll complete the square for the x and z terms by moving the constants to the right side:

\(2x^2 + 2y^2 + 2z^2 - 4x + 16z = 1\)

Next, we'll factor out the coefficients of the x and z terms:

\(2(x^2 - 2x) + 2y^2 + 2(z^2 + 8z) = 1\)

To complete the square for the x and z terms, we'll add and subtract the square of half the coefficient of each term:

\(2(x^2 - 2x + 1) - 2 + 2y^2 + 2(z^2 + 8z + 16) - 32 = 1\)

Simplifying, we get:

\(2(x - 1)^2 + 2y^2 + 2(z + 4)^2 = 35\)

Dividing by 35 on both sides, we get the standard form of the equation of the sphere:

\((x - 1)^2/17.5 + y^2/17.5 + (z + 4)^2/17.5 = 1\)

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Answer:

D

Step-by-step explanation:

Y=1/2x because the line is going straight up diagnolly and the 1 makes it higher

The option that summarizes a t-test that was significant and associated with a large effect size is: d. t(12) = 2.95, p < .05, d = .82

In this option, the t-value is 2.95, indicating a significant result. The p-value is less than .05, indicating that the result is statistically significant at the chosen significance level. Furthermore, the effect size is large, with a Cohen's d value of .82. A large effect size suggests a substantial difference between the groups being compared.

The summary presented in option d is as follows:

t(12) = 2.95, p < .05, d = .82

- t(12) represents the t-value and the degrees of freedom (df) associated with the t-test. In this case, the t-value is 2.95, indicating the magnitude of the difference between the groups being compared. The degrees of freedom is 12, which is determined by the sample size and the design of the study.

- p < .05 indicates the p-value, which is a measure of the probability of obtaining the observed results by chance alone. In this case, the p-value is less than .05, indicating that the difference observed is statistically significant at the .05 significance level.

- d = .82 represents the effect size, specifically Cohen's d. Effect size measures the magnitude of the difference between groups or the strength of the relationship between variables.

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17) its equivalence is 3(x + 2y + 1) (option A)

To determine its equivalence, we will factorize the expression:

Hence, its equivalence is 3(x + 2y + 1) (option A)

Step-by-step explanation:

u= 4

...................

Answer:

x= 2\(\sqrt{6}\)

Step-by-step explanation:

To solve this problem we first observe the Pythagoras equation. If a=x and b = 7 are the lengths of the legs of a right triangle and c= \(\sqrt{73}\) is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

a*a + b*b = c*c

\(x^{2}\) + \(7^{2}\) = \((\sqrt{73} )^2\)

=> x= \(2\sqrt{6}\)

Step-by-step explanation:

1.

use equation 1

vf = vi + a×t = 5.2 + 2.3×7 = 21.3 m/s

deltax (displacement) not needed

vi = 5.2 m/s

vf = 21.3 m/s

a = 2.3 m/s²

t = 7 s

2.

use equation 4.

vf² = vi² + 2×a×deltax

47² = vi² + 2×4.7×150

2209 = vi² + 1410

vi² = 799

vi = 28.26658805... m/s

deltax = 150 m

vi = 28.26658805... m/s

vf = 47 m/s

a = 4.7 m/s²

t not needed

3.

use equation 2.

deltax = (vf + vi)×t/2

228 = (3.15 + 3.15)×t/2

456 = 6.3×t

t = 456/6.3 = 72.38095238... s

deltax = 228 m

vf = 3.15 m/s

vi = 3.15 m/s

a not needed

t = 72.38095238... s

4.

use equation 5.

deltax = vf×t - 1/2 × a×t²

897 = 0×15.5 - 1/2 × a×15.5² = -1/2 ×a×240.25 = a×-120.125

a = 897/-120.125 = -7.467221644... m/s²

deltax = 897 m

vi not needed

vf = 0 m/s

a = -7.467221644... m/s²

t = 15.5 s

Gazelle vs. Lion.

use equation 2.

deltax = (vf + vi)×t/2

deltax = (18.4 + 0)×3.09/2 = 18.4×3.09/2 =

= 9.2×3.09 = 28.428 m

deltax = 28.428 m

vi = 0 m/s

vf = 18.4 m/s

a not needed

t = 3.09 s

Answer:

864 km

Step-by-step explanation:

Hope this helps! (I would appreciate brainliest, if not that's okay!!)

Answer:

2+9 is 11

so write any expression that equals 11  like...

1+10=11

2+9=11

3+8=11

4+7=11

5+6=11

and those above are all example of expression that is equivalent to 2+9

Answer: C ON EDGE 2021

Step-by-step explanation:

Step-by-step explanation:

1 hour she travels = 19 km

60 min = 1 hr

53 min = 1/60 * 53 hr = 53/60 hr

Now,

1 hr = 19 km

4 + 53/60 hrs = 19 * ( 4 + 53/60) km

She travels 92.78 km in 4 hrs and 53 minutes.

Answer:

x²^41

Step-by-step explanation:

x²^41 combine the factors only

Answer:

5

Step-by-step explanation:

this is in slope intercept form or y=mx+b

m represents slope and m is 5

Answer: \(m = 5\)

The slope of the line in this equation is 5.

y = mx + b

the m multiplied with x is the slope.

Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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Answer:  Choice B

Writing k ≤ 1 means "either k = 1, or k < 1"

The closed filled in endpoint at 1 shows us that it is part of the solution set. You would use an open hole if you had k < 1 without the "or equal to".

The area of the rectangle is 128 square feet.

To find the area of a rectangle, you multiply the length by the width. In this case, the rectangle is 16 feet long and 8 feet wide.

Area = Length * Width

Substituting the given values:

Area = 16 feet * 8 feet

To perform the calculation, multiply the numbers:

Area = 128 square feet

Therefore, the area of the rectangle is 128 square feet.

The area of a rectangle represents the total amount of space enclosed within its boundaries. In this case, the rectangle measures 16 feet in length and 8 feet in width, so the area is calculated as 16 feet multiplied by 8 feet, resulting in 128 square feet.

The concept of area is fundamental in geometry and is used to measure the size of two-dimensional shapes. In the case of a rectangle, the area represents the product of its length and width, as every point within the rectangle contributes to its overall size.

Knowing the area of a rectangle can be useful in various situations. For example, if you want to determine how much flooring material is required to cover a rectangular room, you would need to know the area of the floor.

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Answer:

8.5

Step-by-step explanation:

The predicted value of y when x = 3, based on the least-squares regression line equation y = 50 - 15x, is y = 50 - 15(3) = 5.

The given least-squares regression line equation y = 50 - 15x represents a linear relationship between the variables x and y. In this equation, the coefficient of x (-15) represents the slope of the line, and the constant term (50) represents the y-intercept.

To find the predicted value of y when x = 3, we substitute x = 3 into the equation and solve for y. Plugging in x = 3, we have y = 50 - 15(3). Simplifying this expression, we get y = 50 - 45 = 5.

Therefore, when x = 3, the predicted value of y based on the least-squares regression line is 5. This means that according to the regression line, when x is 3, the expected or estimated value of y is 5.

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Poppy's sister used approximately 3.14 inches more wire per wall hanging than Poppy.

To find the amount of wire used by both Poppy and her sister, we'll calculate the circumference of their respective wall hangings using the formula:

C = 2πr

Since the diameter is twice the radius, we can find her sister's radius as follows:

Poppy's radius = 6.25 inches

Poppy's diameter = 2 * 6.25 = 12.5 inches

Sister's diameter = Poppy's diameter + 1 = 12.5 + 1 = 13.5 inches

Sister's radius = 13.5 / 2 = 6.75 inches

Now, we'll calculate the circumferences using the given value for π:

Poppy's circumference = 2 x 3.14 x 6.25 ≈ 39.25 inches

Sister's circumference = 2 x 3.14 x 6.75 ≈ 42.39 inches

Difference = Sister's circumference - Poppy's circumference

Difference = 42.39 - 39.25 = 3.14 inches

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The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.

In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.

Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.

The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.

To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.

The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.

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In the given relation, 1 is not a domain.

The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.

All the values that go into a function. The output values are called the range.

The domain of a function is the set of all possible inputs for the function.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.

Given that, a function,

{(5, 1), (4, -3), (3, -1)}

We know, a domain is the set of all "x" values.

Therefore, domain of the function are, 5, 4 and 3

But, if we see, 1 is one of the values of y.

Hence, 1 is not a domain.

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