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The diameter of a regulation soccer ball is about 8 3/5 inches. This number was graphed on a number line. (Ill show the number line below) With point could be the point representing the graph of the diameter of the ball?

Both slope-intercept form and point-slope form are equally important and useful, and easy to use. The advantages and disadvantages of both forms of linear equations are shown below.

Advantages: One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form.

This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.

Disadvantages: Since vertical lines have arbitrary slopes, one limitation of the point-slope form is that it cannot be used to describe the equation of a vertical line.

Standard form and slope-intercept form are two additional frequently used forms.

Slope-intercept:

Advantages: The slope of the line and the y-intercept are both clearly displayed in slope-intercept form.

The slope of the line and the single point the line passes through are both plainly displayed in point-slope form.

When working with equation systems, the standard form is more convenient. (specifically, to locate the intersection with matrices).

Disadvantages: Slope-intercept form has the same drawbacks as a point-slope form in that vertical lines cannot be represented since the slope of a vertical line is ill-defined.

Therefore, both slope-intercept form and point-slope form are equally important and useful, and easy to use. The advantages and disadvantages of both forms of linear equations are shown below.

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To prove △BDA ≅ △BDC, SSS congruence theorem should be used.

What is the Side-Side-Side congruence theorem of triangles?

If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by the SSS rule.

Given that ΔBDA is similar to ΔBDC and:

AD ≡ DC

AB ≡ BC

BD ≡ BD (shared side)

△BDA ≅ △BDC

The best postulate to use is the side-side-side (SSS) postulate.

Hence, to prove △BDA ≅ △BDC, the SSS congruence theorem should be used.

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Answer:

Given,

Let's assume the maximum safe height of wall = h

angle formed between ladder and ground = 70°

length of ladder = 16 ft

From the given data, it can be seen that ladder will form a right angle triangle structure with the wall

So,from the concept of trigonometry,

Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70

o

=

length of ladder

maximum safe height of wall

= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70

o

=

16 ft

h

= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70

o

=> h = 16 x 0.9396

=> h = 15.03 ft

So, the maximum safe height that can be reached by the ladder will be 15.03 ft.

Sorry I put the wrong answer.

The pH of the cleaning compound is 2.51.

pH, quantitative measure of the acidity or basicity of aqueous or other liquid solutions.

Given that, The hydrogen ion​ concentration, ​[H​+], in a certain cleaning compound is [H+]=3.3x10^-12.

[OH-] = 1.0*10^-14/3.3*10^-12 = 0.303*10^-12

pH = -log0.303*10^-12 = 2.51

Hence, The pH of the cleaning compound is 2.51.

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The given algebraic equation 2(x-3)= 2x+5 has no solution. Option C is correct.

Given that,
To determine the solution to the equation 2(x-3)= 2x+5.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
Given equation,
2(x-3)= 2x+5
2x - 6 = 2x + 5
-6 ≠ 5

Thus, The given algebraic equation 2(x-3)= 2x+5 has no solution. Option C is correct.

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To represent outside games, playground equipment, and paint for all three classrooms, multiply the polynomial expressions by 3x2, xy3, 2x3y, and 4xy, accordingly.

This polynomial's formula is 12x^5y^3 + 24x^4y^3 + 18x^3y^3

Numerous branches of mathematics and science use polynomials. used to approximate other functions in calculus and numerical analysis to approximate other functions in calculus and numerical analysis. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics.Algebraic varieties and polynomial rings, two core concepts in algebra and algebraic geometry, are constructed using polynomials in higher mathematics.

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Answer:

= 16x - 8

Step-by-step explanation:

3(2x - 1) + 5(2x - 1)

8(2x - 1)

16x - 8

Answer:

16x - 8

Step-by-step explanation:

Given expression,

→ 3(2x - 1) + 5(2x - 1)

Simplifying the expression,

→ 3(2x - 1) + 5(2x - 1)

→ 6x - 3 + 10x - 5

→ (6x + 10x) + (-3 - 5)

→ 16x +(-8)

→ 16x - 8

Hence, solution is 16x - 8.

The correct measure of the third angle in the triangle as we can see is 40 degrees.

We know that a right angle triangle is one in which one of the angles of the triangle is 90 degrees. If we know that one of the angles of the triangle has been given as 90 degrees, it then follows that the other two angles would have to be complementary.

Let us remind ourselves here and now that the angles that we say that they are complementary are the angles that do add up to about an angle of ninety degrees.

Having said this, we can see that the third angle is the angle A measures 90 degrees and angle B measures 50 degrees, it then follows that the third angle must have to measure 40 degrees. This would now give the correct balance of all the angles in the triangle.

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Missing parts;

Which statement can be concluded using the true statements shown? If two angles in a triangle measure 90° and x degrees, then the third angle In triangle ABC, angle A measures 90 degrees and angle B measures 50°. A.Angle C must measure 50 degrees B.Angle C must measure 40 degrees C.Angle C must measure (90 - 40) degrees D.Angle C must measure (90 - 30) degrees

Answer:

Angle C must measure 40 degrees.

Step-by-step explanation:

took it

the length and breadth of the rectangle is L = 4, B =16

Let L and B stand for length and width, respectively.

a rectangle is 4 times a long as it is wide

L=4B …….(1) (1)

L1 and B1 should represent the revised length and width.

L1=(L+4)

B1=(B-1)

Area = L1 + B1 + 60.

=> (L+4)×(B-1)=60 …….(2) (2)

Using (1)-

=> (4B+4)×(B-1) =60

=> 4×(B^2–1) = 60

=> B^2–1 = 15

=> B^2 = 16

=> B = +4 or -4

B=4 inches because breadth is always positive.

L = 4 B = 16 inches.

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Using Pythagoras theorem, the numbers are from a right angled triangle

Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

In this question, to find out if the numbers are a Pythagorean triple, we can use pythagoras theorem while assuming the longer side is the hypothenuse.

13² = 12² + 5²

169 = 144 + 25

169 = 169

The numbers are Pythagorean triple because the sum of square of the two sides is equal to the square of the hypothenuse.

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Answer:

x=0,4,6

Step-by-step explanation:

Answer: The first option

Step-by-step explanation: Once you multiply all the denominators to make them the same, the numerators (in the original order they are given in) become 63, 16, and 44.

16<44<63, which is the first option.

Part a: Height of tree;  15 feet.

Part b: distance of tree from person; 14.25 feet.

Part a: Height of the tree;

We get the following mathematical formula (equation) since the ratio of a corresponding sides of similar triangles is equal in magnitude:

22.5/8.25 = x/5.5

In which

x is the height of the tree.

Then,

22.5/8.25 = x/5.5

Further simplifying;

8.25x = 22.5 × 5.5

8.25x = 123.75

x = 123.75/8.25

x = 15 feet. (height of the tree)

Part b: distance of tree from person;

These calculations can be used to determine how far away from the tree this individual is:

Distance equals the product of a person's shadow and a tree's shadow

Distance = 22.5 - 8.25

Distance = 14.25 feet.

Thus,  distance of tree from person is 14.25 ft.

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Answer:

length of base = 9 feet

Step-by-step explanation:

b= base   A= area   h= height

[tex]b=2*\frac{A}{h} = 2*\frac{29.25}{6.5} = 9[/tex]

The correct option e. Statements (1) and (2) TOGETHER are NOT sufficient.

For the stated question-

1. R is less than 20: insufficient since s is unknown.

2. Because there is no date for r, statement 2 is insufficient because S is bigger than 65.

We now have two conditions when combined. s>0 and s>65, r 20 and r>0.

Using the maximum possible value of r as an example and the least possible value of s as an example, the value is greater than 1/3.

Therefore, every values for r would only decrease, while s will rise.

Therefore, simply stating that it won't be below 1/3 will do.

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The complete question is-

If r and s are positive integers, is r/s less than 1/3 ?

(1) r is less than 20.

(2) s is greater than 65.

a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

d. EACH statement ALONE is sufficient.

e. Statements (1) and (2) TOGETHER are NOT sufficient.

Solving the equation a(c + b) = d for variable c, the variable c = (d/a) – b. (Option A)

Equation refers to a statement that represents an equality of values of two mathematical expressions and is indicated by the sign =.

In the given equation a(c + b) = d, in order to solve for the variable c, we must isolate the c variable at one side and collect other variables on the other side of the equation.

Given equation is:

a(c + b) = d

Divide both sides by a:

(1/a)*a(c + b) = d/a

c + b = d/a

Subtract b from both sides:

c + b – b = (d/a) - b

c = (d/a) – b

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The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 3750, hence:

Area = length * width = x * y

3750 = xy

y = 3750/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x

To minimize the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 1800/x²

2 - 1800/x² = 0

2 = 1800/x²

2x² = 1800

x² = 900

x = 30 feet

y = 600/x = 600/30 = 20 feet

Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

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Answer:

It will take the pool 1,960.5 days for the pool to become empty.

Step-by-step explanation:

We can find this answer by simply dividing the two numbers together:

15,684 ÷ 8 = 1,960.5 days.

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Answer:

1960.5 days

Step-by-step explanation:

[tex]\boxed{\textsf{Rate (gallons per day)} = \sf \dfrac{Volume\;(gallons)}{Number\; of\; days}}[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies 8=\dfrac{15684}{\sf Number\;of\;days}[/tex]

[tex]\implies \sf Number\;of\;days=\dfrac{15684}{8}[/tex]

[tex]\implies \sf Number\;of\;days=1960.5[/tex]

Therefore, if the pool is leaking at a rate of 8 gallons per day, the pool will be empty after 1960.5 days.

The dimensions of the garden would be length = 28 meters and width = 9.5 meters.

What are quadratic equations?

A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, and b, are the coefficients, c is the constant term, and x is the variable. Since the variable x is of the second degree, there are two roots or answers for this quadratic equation.

Let the width be = w

Let the length be = L

enclose three side ( 2w+L) = 47 meter

L = 47-2w

Area of field = w*L

Area = w(47 - 2w)

266  = 47w - 2w²

2w² - 47w + 266 = 0

Solving this, we get

w = 14 or w = 9.5

The width should be less than the length so w = 9.5
Length = 47 - 2(9.5)

            = 47 - 19

            = 28 meters.

Hence, the dimensions of the garden would be length = 28 meters and width = 9.5 meters.

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Answer:

Answer: 3 or 2 1/2 ethier is right

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer:

PR

Step-by-step explanation:

The longest side is opposite the largest angle.

Answer: There are two equal sides

Step-by-step explanation:

Considering P and R are both 48 degrees and the only different angle is Q that would mean there are two equal sides.

What grade is that?

Step-by-step explanation:

The percentage of racers that  did not complete the marathon is 12.9 %

What is arithmetic?

Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots

Main Body:

Total racers = 240

racers that completed race = 209

so racers that did not complete the marathon = 240 - 209

 = 31

percentage of racers that  did not complete the marathon = (31/240)*100

                                                                           = 12.9 %

Hence percentage of racers that  did not complete the marathon is 12.9%

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Answer:

v > -1

Step-by-step explanation:

v + 6 > 5

We want to work backwards to solve this, therefore we must subtract 6 on both sides to isolate v.

v + 6 > 5

  (- 6)  (-6)

v > -1

Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and  brianna received 21 stickers.

The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.

Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4

The number of stickers Briana received is 21

Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are

Avea = xBriana = 3x

Carson = 4x

As we know 3x = 21 x

 = 21/3

= 7

then,4x

= 4×7

= 28

The number of stickers that Avea received is 28. Hence, the answer is 28

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The converse, inverse and contrapositive statements for the given conditional statement are :

Converse: if I sleep well, then I go to be early

Inverse: if I don't go to be early, then I don't sleep well

Contrapositive: if I don't sleep well, then I don't go to be early.

A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.

Given is a conditional statement, "If I go to be early, then I sleep well", we need to form its converse, inverse and contrapositive statements,

The rules for the given conditional statement are ;

Let p and q be the parts of the statement,

1) Converse statement = if p then q, converse = if q then p.

Therefore,

Converse: if I sleep well, then I go to be early.

2) Inverse statement = if p then q, inverse = if not p then not q.

Therefore,

Inverse: if I don't go to be early, then I don't sleep well.

3) Contrapositive statement = if p then q, Contrapositive = if not q then not p.

Therefore,

Contrapositive: if I don't sleep well, then I don't go to be early.

Hence, the converse, inverse and contrapositive statements for the given conditional statement are :

Converse: if I sleep well, then I go to be early

Inverse: if I don't go to be early, then I don't sleep well

Contrapositive: if I don't sleep well, then I don't go to be early.

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The expected variance of red balls chosen is 2/3 from the urn.

Six red balls and four green balls are in an urn.

Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.

The, the variance is found as-

Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)

E(XY)  = 25×(6/10)(4/9)

E(X) = 5×(6/10)

E(Y) = 5×(4/10)

Thus,

Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)

Variance(X,Y) = 2/3

Thus, the variance for choosing red balls is 2/3.

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