Square ABCD is reflected about side BC. Which of the following statements are true? Select three that apply.

Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.

From the question, we have

Area = A = xy

A = xsqr(9-x^2)

Taking the derivative and set = 0

A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0

A' = -x^2 + 9 -x^2 = 0

-2x^2 =-9

x^2 = 9/2

x = 3/sqr2 = (3/2)sqr2 = 4.242

y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121

Dimensions of the rectangle are 4.242 and 2.121 respectively

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

Complete question:

A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?

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Answer:

y = 300x + 100

Step-by-step explanation:

y = mx + c

the line intersects the y axis at 100, so c = 100

m = difference between y-coordinates / difference between x-coordinates

m = (400-100)/(1-0) = 300/1 = 300

y = 300x + 100

Given that the hoop makes one complete oscillation in 2s, this implies that the period of oscillation is 2s

Then,

T = 2s

Let the Mass of the thin hoop be M

Let the Radius of the hoop be R

The moment of inertial of a hoop is

I = MR²

The period of a physical pendulum of small amplitude is given by

T = 2π √(I / Mgd)

Where,

T is the period in seconds

I is the moment of inertia in kgm²

M is the mass of the hoop

g is the acceleration due to gravity

g = 9.8m/s²

d is the distance from the rotational axis to the center of gravity

Therefore, d = R

Then, applying the formula

T = 2π √ (I / MgR)

So, we know that

I = MR²

Then,

T = 2π √( MR² / MgR)

T = 2π √(R/g)

Make R the subject of the formula

Square both sides

T² = 4π²(R/g)

T²g = 4π²R

Then, R = T²g / 4 π²

Since g = 9.8m/s² and T= 2s

R = 2² × 9.8 / 4π²

R = 0.993m

Then, the radius of the hoop is 0.993m

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The rules SSS SAS ASA and AAS are the rule that is used to prove the congruence of the triangle

The rules  SSS SAS ASA and AAS are used to prove the congruence of the triangles .

The congruence  means if shape and size of the one shape is same as the shape and size of the another shape, then we can say that both the shapes are congruent

If you consider the case of triangle, two triangle can be prove as congruent if the specifics sides and angles of the triangle is equal to the other triangles.

The rules that used to prove the congruence of the triangles are

SSS - side-side-side rule of congruence

SAS = side-angle-side rule of congruence

ASA = angle-side-angle rule of congruence

AAS = angle-angle-side rule of congruence

Therefore, these rules are used to prove the congruence of the triangle

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y - 9 = -14(x + 2) is the point-slope form of the line with slope − 14 that passes through the point − 2 9 )

Given a line with slope -14 that passes through the point (-2, 9).

To determine the point-slope form of the line, we need to use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values into the formula, we get:

y - 9 = -14(x + 2)

Therefore, the point-slope form of the line is y - 9 = -14(x + 2).

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Answer:

To turn the given statement into an inequality, we can write it in the form "m - s >= 8", which means that the amount of money you have (m) minus the amount you spend on snacks (s) must be greater than or equal to 8. This inequality represents the constraint that your mom has placed on your spending, requiring you to spend at least $8 on the pizza. In mathematical notation, the inequality would be written as:

m - s >= 8

This inequality states that the amount of money you have, minus the amount you spend on snacks, must be greater than or equal to 8 in order for you to be able to buy the pizza.

Step-by-step explanation:

The equations that could be used to determine the number of small boxes sent and the number of large boxes sent is 85b = 440.

From the information, each small box can hold 20 books and each large box can hold 45 books.

There was also twice as many large boxes sent as small boxes, which altogether can hold 440 books.

This will be:

2(20b) + 45b = 440

where b = number of books

40b + 45b = 440

85b = 440

The equation is 85b = 440

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AC bisects angle BAD and AC bisects angle BCD is proved using CPCT rule.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, ΔABC≅ΔADC.

We know that, corresponding parts of congruent triangle are equal.

So, ∠BAC=∠DAC (∵CPCT)

∠BCA=∠DCA (∵CPCT)

∠BAD=∠BAC+∠DAC

⇒ ∠BAD=2∠BAC

⇒ ∠BAC=∠BAD/2

So, AC bisects ∠BAD

∠BCD=∠BCA+∠DCA

⇒ ∠BCD=2∠BCA

⇒ ∠BCD/2=∠BCA

So, AC bisects ∠BCD

Hence, proved AC bisects ∠BAD and AC bisects ∠BCD.

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Answer:

No

Step-by-step explanation:

if you divide 8:3 you get 4:1.5 which is not equivalent. In order for them to be equivalent it would need to be 4:1 and 8:2

Answer: No

Step-by-step explanation:

Let's start with what we know. Ratios can also be written as fractions:

4/1 and 8/3

These fractions do not simplify to the same thing, therefore they are not equal.

Answer:

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

Linear function is:

Given points:

The first point represents the y-intercept, b = - 4.

Find the slope:

The function is:

Answer: 5/4, -7/11, 1/2

Step-by-step explanation:

Slope of ordered pairs (y2-y1/x2-x1): -5/4

Y intercept (b in y=mx+b): (0, -7/11)

Slope of graph (rise over run) : 1/2

The number of peanuts that Alex had initially will compute to a total of 108 in the observations of the situation provided above.

The computation of the peanuts in the hands of Alex can easily be ascertained using the given information, and input of values from the same into the generalized formula, as shown below,

Let p be the number of peanuts. Thus, it can be stated that

3p = 444 – 9 – 25 – 5

3p = 409

p = 409/3 = 135.3

Now, it can also be stated that

p+9=144

[tex]\[\dfrac{144}{k} + 144 + k \cdot 144 = 444 \\\\ \\\dfrac{144}{k} + k \cdot 144 = 300\\\\ \\ \dfrac{12}{k} + k \cdot 12 = 25\\\\\\k= \dfrac{4}{3} \\\\\\\\ \dfrac {144\cdot 3}{4} =108}\][/tex]

Therefore, Alex has a total of 108 peanuts initially.

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Complete question

Initially, Alex, Betty, and Charlie had a total of 444 peanuts. Charlie had the most peanuts, and Alex had the least. The three numbers of peanuts that each person had formed a geometric progression. Alex eats 5 of his peanuts, Betty eats 9 of her peanuts, and Charlie eats 25 of his peanuts. Now, the three numbers of peanuts each person has forms an arithmetic progression. Find the number of peanuts Alex had initially.

Answer:

x = 4.5

Step-by-step explanation:

The height of the top section of the tower is 32 feet.

The radio station tower is built in two sections. The tower is 87 feet from the viewing point. The angle of elevation of the bottom section is 25 degrees. The angle of elevation from the top of tower (both sections) is 40 degrees. Let the height of the bottom section be y and height of the bottom and top section be z.

Considering a right-angled triangle, tangent formula states that:

Tan ɵ = opposite side/ adjacent side where ɵ is the angle of elevation.

Hence, when ɵ = 25, opposite side = y, and adjacent side = 87

Tan 25 = y/ 87

y = 40.57 feet

Hence, when ɵ = 40, opposite side = z, and adjacent side = 87

Tan 40 = z/87

y = 73 feet

Let the height of the top section of the tower be x.

Hence, x = 73 - 40.57 = 32.4 ≈ 32 feet

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The number of pens the store manager purchase, if A store manager purchased a total of 15 pens and markers, is 7.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75, the manager spent a total of $38.50,

Write the equation of the statement as shown below,

x + y = 15  and 3.5x + 1.75y = 38.5

Here, x is the number of pens and y is the number of markers,

Solve the equations by using the elimination method,

x = 7, y = 15 - 7 = 5

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The two-column proof shows that LP = LQ

LP = √(LM² + PM²)

LQ² = √(LM² + PM²)

LP = LQ

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Point M is the midpoint of PQ.

This means,

PM = QM ______(A)

LM is the perpendicular bisector of PQ .

           L

      /    |    \

   /       |       \

/          |         \

P         M         Q

Applying the Pythagorean theorem.

Triangle LMP is a right triangle.

LP = LM² + PM² _____(1)

Triangle LMQ is a right triangle.

LQ² = LM² + QM² _____(2)

Thus,

From (A), (1), and (2) we get,

LP = √(LM² + PM²)

LQ² = √(LM² + PM²)

LP = LQ

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Answer:

Step-by-step explanation:

180=28+73+x

180-28-73=79

79=x

The side JE is equal to side IE because all the sides of the square are congruent.

It is a polygon with four sides. The total interior angle is 360 degrees. In a square, all the sides of the square are equal and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

JH is opposite to JE and Hello is opposite to IE. Also, JH is congruent with HE.

Let 'm' be the side of the square.

HI = JE         (Congruent)

HJ = IE         (Congruent)

∠H = ∠J = ∠I = ∠E = 90°

Then the shape that is defined will be a square.

The side JE is equal to side IE because all the sides of the square are congruent.

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The radius of a circle with equation is x² + y² + 8x - 6y + 21 = 0 is 2  units .

In the question ,

it is given that ,

the equation of circle is ⇒ x² + y² + 8x - 6y + 21 = 0 ,

we know that the general equation of the circle is x²+y²+2fx+2gy+c=0

so , the radius of the circle is calculated using the formula ,

radius = √(f² + g² - c)

On comparing the given equation with general equation

we get , the values of f as 4 and g as -3 .

So after substituting the values of f , g and c in the radius formula ,

we get ,

radius = √(16 + 9 - 21)

= √(16 + 9 - 21)

= √(25 - 21)

= √(4) = 2 .

Therefore , the radius of given circle is 2 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0  ?

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By entering the values of m and b into the slope-intercept form of a line (y = mx + b), you may obtain the equation for the line.

Given,

Equation of a line;

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

We have to find the equation of a line with 2 points;

Here,

Slope, m = (y₂ - y₁) / (x₂ - x₁)

The x and y of your equation y = mx + b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.

Therefore,

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx + b).

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0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

According to collect from the data

Let us assume that the data as followed by

How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.

Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.

2,3,3,4,4,4

now then:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .

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Answer:

width = 6 cm

Step-by-step explanation:

Area = width x length

let x = length

width = x - 6

A = 72 cm² = x(x-6) =  x² - 2x

rewrite the equation:

x² - 2x - 72 = 0

solve for x by factoring or the quadratic equation:

(x-12)(x+6) = 0

x = 12, -6

therefore x = length = 12

Width = 12 - 6 = 6

The p-value is 0.15 which is greater than the significance value 0.10 so null hypothesis cannot be rejected at 10% significance level , we do not have enough evidences to state that no- show rate is less than 6%.

As given in the question,

Null hypothesis : No show rate for passengers booked on given flight is 6%

Alternative hypothesis: No show rate  for passengers booked on given flight  is less than the 6%

P = 6%

  = 0.06

1 -  P = 1 - 0.06

       = 0.94

random sample size 'n' = 380

no shows = 18

Sample proportion 'p' = 18/ 380

                                    = 0.047

Now , z test statistic value :

z = (p - P)/ √P (1- P)/n

 = (0.047 - 0.06)/√0.06( 0.94)/380

 = -0.013 /0.012

 = -1.083

p-value = 0.2788 ( using table)

0.2788 > 0.10

p-value is greater than significance value 0.10

Do not reject null hypothesis at 10% level of significance.

Therefore, as p-value is greater than significance value do not have enough evidences to state that no- show rate is less than 6%.

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The scalar equation of the plane that contains given points and lines can be written as: (-4)(x-1) + 4(y-2) + (-10)(z-3) = 0.

What is equation of plane?

A given point p(x, y, z) that is located on the plane and a normal vector n define the equation of a plane. A plane's vector and scalar components can be used to formulate the equation for the plane.

The parametric form of line equation,

[tex]p = p_0 + t. \vec v[/tex]

On comparing with the given equation in question, we can say that,

p = {x, y, z}, p₀ = {0, 6, 1,},  vec(v) = {3, -2, -2}

The scalar equation can be given by,

[tex][ \vec \omega, p - p_1] = 0[/tex]

Here, p₁ = {1, 2, 3} and ω is perpendicular to v and to the segment p₁ - p₀ So,

[tex]\vec \omega = \vec v \times (p_1 - p_0) = ( 3, -2, -2 ) \times (1, -4, -2)[/tex]

then,

[tex]\vec \omega = (-4, 4, -10)[/tex]

Therefore, the scalar equation can be written as:

(-4)(x-1) + 4(y-2) + (-10)(z-3) = 0

It can also be written as:

26 - 4x + 4y - 10z = 0

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Complete Question

Find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t) = [3t, 6 - 2t, 1 -2t] ?

Answer:

a. shen's car

8 gallons

b. 400 miles

shen's car

The equation that best represents this scenario is x/(3x-4) =20/80. So, the correct option is B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of bats be x.

The number of baseballs is four less than three times the number of bats.

The, the number of baseballs are 3x-4

The equipment is 80% baseballs. Then, the equipment is 20% bats.

So, the ratio from number of bats to number of baseballs is

x/(3x-4) =20%/80%

⇒ x/(3x-4) =20/80

Therefore, the option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

The sporting equipment has been sorted into baseballs and bats. The number of baseballs is four less than three times the number of bats. The equipment is 80% baseballs. Choose the equation that best represents this scenario

x/(3x-4) =80/20

x/(3x-4) =20/80

x/(3x-4) =80/100

x/(3x-4) =20/100

Answer:

12%

Step-by-step explanation:

Christy Peterson's total income last year was $77,340. Of that amount, she spent $7,240 on transportation costs and $2,100 on clothing. What percent of Christy's total income did she spend on transportation and clothing combined? Round your answer to the nearest percent.

7,240 + 2,100 = $9,340

9,340 / 77,340 = 0.120765

0.120765 * 100 = 12.0765%

rounded = 12%

The method used by Horace to select his sample is Systematic Sampling.

A form of probability sampling technique called systematic sampling selects sample members from a broader population using a predetermined, periodic interval in addition to a random beginning point. The population size is divided by the intended sample size to arrive at this range, which is known as the sampling interval.

Horace desires to select every 1000th person to enter the park, starting with the 364th person. So he selects the 364th person, 1364th person, 2364th person, and so on. This is a perfect situation for Systematic Sampling.

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