11. Write four solutions for each of the following equation: (i)7x + 2y = 9 (ii) 2x = -5y​

The given statements:

1) ΔQRS ≅ ΔSTU (according to the ASA axiom)

2) The congruent ∠S: ∠RSQ ≅ ∠UST (Vertical angles)

The ASA axiom states that "two triangles are said to be congruent if two pairs of corresponding angles and the sides between these angles are equal".

It is given that,

S is the midpoint of QT.

So, SQ ≅ ST <S>

Since ∠S is at the intersection of two transversal lines, ∠RSQ ≅ ∠UST <A>.  This is beacuse they are vertically opposite.

And QT is the transverse line for the parallel lines, QR║UT. So, the alternate angles(interior) are congruent. I.e., ∠SQR ≅ ∠UTS <A>.

From this, the given triangles have two equal corresponding angles and congruent sides in between them.

So, ΔQRS ≅ ΔSTU according to ASA axiom.

Therefore, ΔQRS ≅ ΔSTU and ∠RSQ ≅ ∠UST.

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Answer:

D

Step-by-step explanation:

simplified is 1 1/2, 1.5 or 3/2

Answer: 113.1 ft^3

Step-by-step explanation:

We know the radius is 3 so substitute it in the formula like this...

V = 4/3 π (3)^3

Solve for (3)^3 which is 27.

Next multiply 4/3 by π. Which equals 4.1887....

Then multiply that answer by 27.

And your answer is 113.1 ft^3.

Answer:

[tex]V=108ft^{3}[/tex]

Step-by-step explanation:

[tex]V=\frac{4}{3}(3)(3)^{3}[/tex]

[tex]V=\frac{4}{3}(3)(27)[/tex]

[tex]V=\frac{4}{3} (81)=\frac{324}{3}[/tex]

[tex]V=108[/tex]

Hope this helps

Considering the given functions in the graph, we have that:

We look at the graph, and find f(3) and g(3), then add them. Hence:

Then the addition is:

(f + g)(3) = f(3) + g(3) = 0 + 4 = 4.

Same logic, at the graph we have that:

Hence:

(f - g)(1) = f(1) - g(1) = -1 - 1 = -2.

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Answer:

y = 33.6

Step-by-step explanation:

1/2 y + 3.2 = 20     subtract 3.2 from both sides of the equation

1/2y = 16.8              multiply both sides by 2

y = 33.6

The width of his patio is 19.5 feet based on the information about the area given.

Area = Length × Width

175.5 = 19.5 × w

Width = 175.5/19.5

Width = 9 feet

The width of his patio is 19.5 feet.

The number of blocks that were used will be:

= 175.5/(1.5 × 1.5)

= 175.5/2.25

= 78 blocks

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Complete question

Gavin made the patio area out of square block that are 1.5 by 1.5 feet. The area of the patio is 175.5 ft² and the length is 19.5ft.

a. Determine the width of his patio.

b. Determine the number of blocks Gavin used to make his patio.

The polynomial function in standard form that has the zeros listed. i and -i is  x² +1 = 0.

A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.

The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Calculation for the polynomial function-

The general two degree/quadratic equation is given by-

ax² + bx + c = 0

Where a ≠ 0

If the two roots of the equation are x1 and x2.

Then the relation between roots and coefficients of the polynomial are -

         x1 + x2 = (-b)/a

        x1.x2 = c/a

From the above two relation the general equation can be written as-

x² -(x1 - x2)x + x1.x2 = 0

Lets say x1 = i and x2 = -i

Substitute the values of x1 and x2 in the general equation

x² -(i - i)x + (i).(-i) = 0

x² - i ² = 0

x² + 1 = 0

Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.

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Using the combination formula, the probability that a person with one combination of five numbers will win is:

[tex]\frac{1}{1,221,759}[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For this problem, 5 numbers are taken from a set of 45, hence the number of combinations is:

[tex]C_{45,5} = \frac{45!}{5!40!} = 1,221,759[/tex]

Hence the probability is:

[tex]\frac{1}{1,221,759}[/tex]

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The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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The service area of the cylinder is 42[tex]\pi[/tex] square fts.

Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.

Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.

The uses of cylinder are-

Total surface area of the cylinder formula:

It is the sum of the base surface area and the lateral surface area;

Total area = base area + lateral area , or

Total area = 2 π r² + (2 π r) h , or

Total area = 2 π r (r + h)

Calculation for the total area of the cylinder;

Base diameter is 6 ft

Radius is 6/2 = 3 ft

Height is 4 ft

Total area = 2[tex]\pi[/tex]3(3 + 4)

                 = 6[tex]\pi[/tex]×7

                 = 42[tex]\pi[/tex]

Therefore, the total surface area of the cylinder is 42[tex]\pi[/tex] square fts.

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Answer:

D

Step-by-step explanation:

You are looking for what you would need to cancel the yards in 800 yards.

800 yards (1 mile/ 1760 yards).  You have yards in the numerator of your original measurement.  You will cross cancel out the yard on the the top and the yards on the bottom.

Answer:

21+21+7+7+7+7+8+8+8+8+9+9

Step-by-step explanation:

amswer is 120

Answer:

Step-by-step explanation:

21+2=42.There are four sevens-which is  7x4=28.There are four eights meaning it is 8x4=32+28=60+42=102+(9+9)=102+18=120

Answer:

d. 90

Step-by-step explanation:

z = (x - mean)/SD = (15 - 18)/5.4 = - 3/5.4 = -0.55555555... ≈

≈ -0.56

remember the z-table represents the rounded values.

the z-table at -0.56 gives us the p-value of 0.28774.

that is the probability to the left of 15 pounds, so, the probability to have lost 15 pounds or less.

to have lost at least 15 pounds, we have to get the right side of 15 pounds in the bell curve.

and that is 1 - 0.28774 = 0.71226

so, the probability to have lost at least 15 pounds is therefore 0.71226.

how many people are that ?

well, there were in total 128 people (with the total probability of 1 representing everything).

the number of people that lost at least 15 pounds are the proportionate share of 0.71226 of 1 (the whole) :

128 × 0.71226 = 91.16928...

so, the closest answer option is d. 90

Answer:

Step-by-step explanation:

Formula

Area = 1/2 b* h

Givens

b = 25

h = 9

Solution

Area = 1/2 * 25 *  9     Substitute givens into formula

Area = 1/2 * 225         Combine

Answer

Area = 112.5 ft^2

The expression has been dragged the correct location on the table.

It should be noted that an exponential expression simply means a way to write Lowe's in short form.

In this case, the expression has been dragged the correct location on the table.

This is attached below.

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Answer:

Step-by-step explanation:

20% of a number is 17 . find the number

divide 17 by 20 and you find 1%, multiply by 100 and you get 100%

x = 17 : 20 * 100

x = 0.85 * 100

x = 85

The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;

a. A'(4, 6), B'(10, 8), C'(6, 12)

b. A'(-2, -2), B'(4, 0), C'(0, 4)

c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)

d. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1

The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;

[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]

Where;

(a, b) = The center of dilation

k = The scale factor of dilation

(x, y) = The coordinate of the pre-image

The given points are;

A(2, 3), B(5, 4), C(3, 6)

a. The scale factor of dilation = 2

The center of dilation = The origin (0, 0)

Therefore;

[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]

Therefore dilation about the origin, with a scale factor of 2 gives;

Similarly

b. With the center of dilation at (6, 8), we have;

[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]

[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]

[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]

c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places

Using notation, we have;

The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.

d. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;

Given that the side lengths are the same, by AAA congruency postulate, we have;

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Answer:

The angle measures are the same.

Step-by-step explanation:

The statement which is true about the translation is; The asymptote of g(x) is the asymptote of f(x) shifted six units down.

Since it follows from the task content that the function g(x) represents a 6 units vertical shift downward, it can then be concluded in the same regard that The asymptote of g(x) is the asymptote of f(x) shifted six units down.

Therefore, the true statement is; the asymptote of g(x) is the asymptote of f(x) shifted six units down.

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Using the binomial distribution, there is a 0.265 = 26.5% probability that at least two of them have the same number.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

p = 1/65 = 0.0154, n = 65.

The probability that at least two of them have the same number is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

P(X < 2) = P(X = 0) + P(X = 1)

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{65,0}.(0.0154)^{0}.(0.9846)^{65} = 0.3647[/tex]

[tex]P(X = 1) = C_{65,1}.(0.0154)^{1}.(0.9846)^{64} = 0.3703[/tex]

So:

P(X < 2) = P(X = 0) + P(X = 1) = 0.3647 + 0.3703 = 0.735.

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.735 = 0.265[/tex]

0.265 = 26.5% probability that at least two of them have the same number.

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Answer:

t = 3/2

Step-by-step explanation:

Instead of randomly guessing values of "t" that will satisfy the equation, you can easily find the correct value by solving the equation in terms of "t". In other words, you can set the equation equal to "t" to find the final answer.

(-2/3)t - 2 = -3                             <----- Original equation

(-2/3)t = -1                                   <----- Add 2 to both sides

t = 3/2                                        <----- Divide both sides by -2/3

You can check this value by plugging it into "t" and determining whether both sides of the equations will be equal.

(-2/3)t - 2 = -3                            <----- Original equation

(-2/3)(3/2) - 2 = -3                      <----- Plug 3/2 into "t"

-6/6 - 2 = -3                               <----- Multiply -2/3 and 3/2

-1 - 2 = -3                                    <----- Simplify -6/6

-3 = -3                                        <----- Subtract

Helen needs a replacement ball bearing whose radius is 5.99mm

A sphere is a perfectly round geometrical 3-dimensional object. It can be characterized as the set of all points located distance r (radius) away from a given point (center). It is perfectly symmetrical, and has no edges or vertices.

The formula of surface area of the sphere is [tex]4\pi r^{2}[/tex] where r represents radius

Given:  Surface area of ball  = 452.16[tex]mm^{2}[/tex]

Using formula we get,

[tex]4\pi r^{2}[/tex] = 452.16[tex]mm^{2}[/tex]

r^2 = 452.16/4[tex]\pi[/tex]

r = 5.99 mm

Thus Helen needs a replacement ball bearing whose radius is 5.99mm

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The given equation is equivalent to (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3). And the zero of the function are: [tex]\pm \frac{3}{2}[/tex] and [tex]\pm \frac{3}{2}i[/tex].

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm\sqrt{D} }{2a}[/tex].

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

The question gives: [tex]16x^4-81=0[/tex], you can factor this equation. See below.

(4x²+9)*(4x²-9)

(4x²+9)*(2x-3)*(2x+3)

Therefore, you should choose one of options: (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3).

Next step is to solve the given equation. Solving for  (4x²+9)*(2x-3)*(2x+3)=0, then:

For 2x-3=0

      x=3/2

For 2x+3=0

      x= -3/2

For 4x²+9=0

      4x²=-9

       x²= -9/4

      x = [tex]\pm \sqrt{\frac{-9}{4} }[/tex]

      x   =[tex]\pm \frac{3}{2}*\sqrt{-1 }\\ \\ \pm \frac{3}{2}*i[/tex]

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Answer:

Step-by-step explanation:

John has $1.25

James has $1.75

i think

Answer:

$1.00

Step-by-step explanation:

James has $0.50 more than John.

When they put their money together, they have a combined total of $2.50.

[tex]2.50-0.50=2.00[/tex]
[tex]2.00\div2=1.00[/tex]
[tex]1.00+1.50=2.50[/tex]
[tex]=2.50[/tex]

John has one dollar.

Hope this helps.

Answer:

Step-by-step explanation:

You have 2 x's.  I think the first one is for multiplication and the second one is a variable.

2x2 -1 = 7x  

4-1 = 7x (first multiple 2x2)

3=7x  (second 4-1)

0.428571429 = x (Divide both sides by 7.  On the left side, 3/7 is 0.428571429 and 7x/7 is just x because the 7s cancel out.

Since the answer needs to be to two decimal places, I have to decide if 0.428571429 is closer to 0.42 or 0.43 Since the digit after the 2 in the answer is 8, that makes the number closer to 0.43 than 0.42.  So, the final answer is 0.43

Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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Answer:

See below

Step-by-step explanation:

Slope, m of given line = - 1/2

perpendicular slope is = -1/m = -1 / (-1/2) = +2

Point (6,9)  slope form of line

y -9 = 2(x-6)    expand and simplify

y - 9 = 2x -12

y = 2x -3

Answer:

7.6

Step-by-step explanation:

mean = [weights] / amount of weights

m = 10 + 7 + 6 + 10 + 13 + 10 / 6

m = 46 / 6

m = 7.66666666 (recurring)

m = 7.6

By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.

Herein we must find the difference bewteen the two temperatures, defined as the subtraction of the minimum temperature from the maximum temperature:

x = 21.85 °C - (- 4.7 °C)

x = 26.55 °C

By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.

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In order to avoid double counting, statisticians just count the final goods and services.

According to the statement

we have to find the procedure which is used by statisticians to avoid the double counting.

final goods and services are the type of way which is used to avoid the double counting.

In other words, statisticians count only the final results rather than the efforts.

So, In order to avoid double counting, statisticians just count the final goods and services.

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Answer:

Step-by-step explanation:

144,72

Answer:

If you cut the rectangle in half, you have two squares of area 144 ft², or side length 12 ft.

The length of the rectangle is 24 ft; its width is 12 ft.