What is an equation of the line that passes through the point (1,7)(1,7) and is perpendicular to the line x+6y=42x+6y=42?

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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A researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.

Inferential statistics use data from the experiment's sample of subjects to compare the different treatments and draw conclusions about the subject population as a whole.

Thus, a researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.

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Answer:

x=0,4,6

Step-by-step explanation:

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.

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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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:

7/10

Step-by-step explanation:

30 : 5 = 6 to Sali

10 : 100 = x : 30

x = 30 * 10 / 100

x = 3 * 1 = 3 to Jane

30 - (6+3) = 30 - 9 = 21

21/30

(21 : 3)/(30:3)

7/10

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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Answer: Yes

Step-by-step explanation:

If you were to be given the numbers for the corresponding coefficient you can solve this question just like as if they were real numbers. Even if you weren't given values, The coefficients unknown value is usually presumed as 1.

if a= 10 b=5 c=6 d=50 e=100 f=1

ab= 10:5

ac= 10:6

de= 50:100

ef= 100:1

if they were all one then they would just be 1:1

The mystery number by Sonya is 55

From the question, we have the following equation that can be used in our computation:

m = 4f + 7

Where

f = favorite number = 12

So, we have

m = 4 * 12 + 7

Evaluate the products

This gives

m = 48 + 7

Evaluate the sum

m = 55

Hence, the number is 55

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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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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

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.

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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Answer:A

Step-by-step explanation:

Inequality could the theme park use to determine the Total number of tickets that must be sold in a day to make a profit is 159.50a + 109c ≥5,490,000.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Given, Tickets for an amusement park are available for adults (a) for $159.50 and for kids (c) for $109.00. The theme park requires daily revenue of at least $5.49 million to turn a profit.

total earning per day = 159.50a + 109c

this should be greater than (>) or at least equal to 5.49 million.

Therefore, The total number of tickets that must be sold in a day to generate a profit is 159.50a + 109c ≥ 5,490,000. Inequality might be used by the theme park to calculate this amount.

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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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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.

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:

Answer: 3 or 2 1/2 ethier is right

Step-by-step explanation:

Answer: A. yes, closed and lines are straight B. No, curved lines C. no, curved lines D. yes, closed have lines are straight E. yes, closed have lines are straight  E. yes, closed and lines are straight F. No, curved lines G. yes, closed and lines are straight H. yes, closed and lines are straight

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.

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

Answer:

Step-by-step explanation:

This impact shows the Eleanor and Billie will have some leftover brownies.

Lets see.

752/9

752=720+27+5

720/9=80, 27/9=3, and 5/9 has a Remainder of 5.

80+3=83 R 5

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:98.3333333333 (98)

The number 590 is called the numerator or dividend, and the number 6 is called the denominator or divisor.

The quotient of 590 and 6, the ratio of 590 and 6, as well as the fraction of 590 and 6 all mean (almost) the same:

590 divided by 6, often written as 590/6. The answer is actually 98 but if I am wrong sorry.

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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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 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.