Which equation represents a circle with a diameter of 10 units that is centered at (3,-7)

1. [tex]\overline{AD}[/tex] bisects [tex]\angle A[/tex] (given)

2. [tex]\angle CAD \cong \angle DAB[/tex] (definition of angle bisector)

3. [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

4. [tex] \angle ADC[/tex] is a right angle (given)

5. [tex]\angle ADC[/tex] and [tex]\angle ADB[/tex] are supplementary (angles that form a linear pair are supplementary)

6. [tex]\angle ADB[/tex] is a right angle (an angle supplementary to a right angle is a right angle)

7. [tex]\angle ADC \cong \angle ADB[/tex] (all right angles are congruent)

8. [tex]\triangle ADB \cong \triangle ADC[/tex] (ASA)

ΔADB ≅ ΔADC by ASA congruence rule as they have angle- side- angle ratio are same.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved. "≅" is the congruence symbol.

When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent.

Given: AD bisect Angle A          

That means ∠BAD = ∠CAD

Proof:   In ΔADB and ΔADC              

∠ADB = ∠ADC (each right angle)

AD = AD (Common)

∠BAD = ∠CAD (Given)              

By ASA Congruence Rule  

ΔADB and ΔADC are Congruent  

Hence Proved.

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60% of Julio's number was Bill"s number

percentage, a relative value indicating hundredth parts of any quantity.

Given,

bill and julio each thought of a whole number between 1 and 20.

Bill"s number was 15

Julio's number was 6

We need to find what percent of Julio's number was Bill"s number

Original number minus new number by original number

(15-61)/15

9/15

0.6

Now we have multiply with 100 as it is a hundredth part.

0.6×100=60

Hence, 60% of Julio's number was Bill"s number

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The value of [tex]f_{x}[/tex](3,2)≈12.2, [tex]f_{x}[/tex](3,2.2)≈16.8, [tex]f_{x}[/tex](3,2)≈23.25

This problem aims to find the values of a function having alternate independent variables.

A-

[tex]f_{x}(3,2) f_{x} (x,y)=lim_{h-0} \frac{(3+0.5,2)-f(3,2)}{0.5}[/tex]    considering h =±0.5

Solving for h=0.5

⇒[tex]\frac{f(3.5,2)-f(3,2)}{0.5}[/tex]

Using the table to plug in the values of the function: 22.4-17.5/0.5=9.8

Now, solving for h=-0.5

⇒[tex]\frac{f(3.5,2)-f(3,2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 22.4-17.5/(-0.5)=14.6

Taking the average of both ±0.5 answers for the final answer of f(3,2)

[tex]f_{x}(3,2)=\frac{9.8+14.6}{2} \\or, f_{x}(3,2)=12.2[/tex]

B-

[tex]f_{x}(3,2.2)=lim_{h-0} \frac{(3+0.5,2.2)-f(3,2.2)}{0.5}[/tex]    considering h =±0.5

Solving for h=0.5

⇒[tex]\frac{f(3.5,2.2)-f(3,2.2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 26.1-15.9/0.5=20.4

Now, solving for h=-0.5

⇒[tex]\frac{f(2.5,2.2)-f(3,2.2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 9.3-15.9/(-0.5)=13.2

Taking the average of both ±0.5 answers for the final answer of f(3,2.2)

[tex]f_{x}(3,2.2)=\frac{20.4+13.2}{2} \\or, f_{x}(3,2.2)=16.8[/tex]

C-

[tex]f_{xy} (3,2)=lim_{h-0} \frac{f_{x}(3,2+h)-f_{x} (3,2) }{h} \\[/tex]     considering h =±0.2

Solving for h=0.2

⇒[tex]\frac{f_{x} (3,2.2)-f_{x} (3,2)}{0.2}[/tex]

Plugging in the answers from A and B: 16.8-12.2/0.2= 23

Now solving for h= -0.2

⇒[tex]\frac{f_{x} (3,1.8)-f_{x} (3,2)}{-0.2}[/tex]

Plugging in the values: 7.5-12.2/-0.2= 23.5

Taking an average of h=±0.2 answers to find the final answer:

[tex]f_{x}(3,2)=\frac{23+23.5}{2} \\or, f_{x}(3,2)=23.25[/tex]

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The result in the form of a mixed number if we multiply the numerator of the complex fraction in part D by the reciprocal that you found in part E is  8[tex]\frac{1}{4}[/tex].

A whole number and a legal fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it. An integer (whole number) plus a correct fraction together make up a mixed number, also known as a mixed fraction (a fraction whose numerator is less than its denominator).

Pretzels, peanuts, Cheerios, and of course rice and corn Chex are all included in this mix, which is why it is called a mix. It is possible for a number to contain both an integer and a fraction. As a result of combining these two sorts of numbers, they are known as "mixed numbers."

PART D:

(33/8)/(11/4)

Reciprocal of PART E is:

11/4

Therefore, multiplying it with PART D, we get:

=((33/8)/(11/4))×(11/4)

=(33/8)×(4/11)×(11/4)

=33/8

=8[tex]\frac{1}{4}[/tex]

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1. The Millers pay $675 monthly to repay their mortgage loan.

2. The average monthly expenditure for the telephone for Millers is $41.00.

3. The Millers' average monthly expenditure for transportation costs is $592.46.

4. The information is not available for determining the amount the Millers' monthly savings.

The average cost is the mean, which represents the quotient of the total costs and the number of months.

We compute the average cost using the division operation.

July $37.85

August $47.29

September $37.85

Total costs = $122.99

Average cost = $41.00 ($122.99 ÷ 3)

                         July           August       September

Gasoline        $118.60       $123.36        $96.74          $338.70

Car loan         278.50         278.50        278.50           835.50

Car repair       126.36         278.50         198.31            603.17

Total costs  $523.46      $680.36      $573.55       $1,777.37

Average monthly transportation cost = $592.46 ($1,777.37 ÷ 3)

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For the parabola y = 2x² + 3x + 1,

a. i.  The x-intercepts are x = -1/2 and x = -1

a. ii. The y-intercept is y = 1

b. i. The line of symmetry is at x = -3/4

b. ii. The equation of the line of symmetry is x = -3/4

c.  The vertex is at (-3/4, -1/8)

A parabola is part of a conic section which is a curve.

Given the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.

So, y = 2x² + 3x + 1

2x² + 3x + 1 = 0

2x² + 2x + x + 1 = 0

Factorizing, we have

2x(x + 1) + (x + 1) = 0

(2x + 1)(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

2x = -1 or x = -1

x = -1/2 or x = -1

So, the x-intercepts are x = -1/2 and x = -1

Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.

So, y = 2x² + 3x + 1

So, y = 2(0)² + 3(0) + 1

y = 0 + 0 + 1

y = 1

So, the y-intercept is y = 1

The line of symmetry passes through the vertex of the parabola where dy/dx = 0.

So, y = 2x² + 3x + 1

dy/dx = d(2x² + 3x + 1)/dx

= d(2x²)/dx + d3x/dx + d1/dx

= 4x + 3 + 0

= 4x + 3

So, when dy/dx = 0,we have

4x + 3 = 0

4x = -3

x = -3/4

So, the line of symmetry is at x = -3/4

The equation of the line of symmetry is x = -3/4

Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have

y = 2x² + 3x + 1

y = 2(-3/4)² + 3(-3/4) + 1

y = 2(9/16) - 9/4 + 1

y = 9/8 - 9/4 + 1

y = (9 - 18 + 8)/8

y = (17 - 18)/8

y = -1/8

So, the vertex is at (-3/4, -1/8)

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Answer: 37, 15, 12, 0, -6, -8, -23

Step-by-step explanation:

So, the higher the negative number, the lower the value is. Hope this helps!

Answer: x=2

Step-by-step explanation:

Area of square = s^2

So we know that (2x+3)^2 = 49

We get rid of the square root first

2x + 3 = 7

2x = 4

x = 2

The value of the angle x in the triangle is; x = 70°

Looking at the given image, it is clear that both triangles are similar triangles. This is because we see that after the duplicate, 2 sides apiece are equal.

Thus, the third angle bordering the center of the triangle with one angle as 15° is;

y = 180 - (15 + 20)

Since sum of angles in a triangle equals 180 degrees.

y = 180 - 35

y = 145°

Similarly,

z = 180 - (20 + 15)

z = 180 - 35

z = 145°

Now, sum of angles at a point is 360 degrees. Thus;

x = 360 - (145 - 145)

x = 70°

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Answer:

There is around 30 meter in 100 feet

Step-by-step explantion I did it mentally.

The required lines are parallel to x-axis and they are horizontal lines.So option (B) is correct.

Given two points  on a line, we can compose a condition for that line by finding the slant between those places, then, at that point, settling for the y-intercept in the slope-intercept equation y=mx+b.

a) y =9

It is equation of line parallel to x-axis.

b) A line passing through the points (0, 1) and (1, 1).

Using two point formula,

(y - 1) = [tex]\frac{1-1}{1-0}[/tex](x - 0)

y = 1

So, it is also a line parallel to x-axis.

Thus, both the lines are parallel to x- axis or can say horizontal lines.

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Answer:

x = 1 1/2

Step-by-step explanation:

1/3 x + 1/4 = 3/4

Solving for x

Subtract 1/4 from each side

1/3 x + 1/4 -1/4 = 3/4-1/4

1/3 x = 2/4

Simplify

1/3x = 1/2

Multiply each side by 3

1/3 x * 3 = 1/2 * 3

x = 3/2

Changing to a mixed number

x = 1 1/2

Answer:

[tex]\sf \frac{3}{2} = 1 \frac{1}{2} \\ [/tex]

Step-by-step explanation:

[tex] \sf \frac{1x}{3} + \frac{1}{4} = \frac{3}{4} \\ [/tex]

To solve easily, multiply the whole equation by it's LCM ( LCM of 3 & 4 is 12 ).

[tex] \sf12 \times ( \sf \frac{1x}{3} + \frac{1}{4} = \frac{3}{4} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \\ \\ \sf \frac{1x}{3} \times 12 + \frac{1}{4} \times 12= \frac{3}{4} \times 12\\ \\ \sf \sf \frac{12x}{3} + \frac{12}{4} = \frac{36}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf4x + 3 = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

And now solve for x.

First, subtract 3 from both sides.

[tex] \sf4x = 9 - 3 \\ \sf4x = 6[/tex]

Divide both sides by 4.

[tex] \sf \: x = \frac{6}{4} \\ [/tex]

To write the fraction in its simplest form, divide both the numerator and denominator by 2.

[tex] \sf \frac{3}{2} = 1 \frac{1}{2} \\ [/tex]

The percentage decrease from the first number to the second of 150 to 100 is 33.33% and for 300 to 250 is 16.67%.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

Initial number  = 150

Final number = 100

Calculate the percentage decrease by the formula given below,

[tex]Percentage\ decrease = (Initial \ number -Final\ number )Initial\ number \times 100[/tex]

Percentage decrease = (150 - 100) / 150 × 100

Percentage decrease = 50 / 150 × 100

Percentage decrease = 33.33%

Similarly, for 300 to 250

Percentage decrease = (300 - 250) / 300 × 100

Percentage decrease = 50 / 300 × 100 = 16.67%

Therefore, the percentage decrease from the first number to the second of 150 to 100 is 33.33% and for 300 to 250 is 16.67%.

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Answer:

B $3.00

Step-by-step explanation:

We need to estimate a little.  We are trying to find the slope.  We need two points.  The one point that is clear is (4,15)  I would estimate the other points to be (0,3)  The slope is the change in y over the change in x

the y values from the two points are 15 and 3.  The x values are 4 and 0

[tex]\frac{15-3}{4-0}[/tex] = [tex]\frac{12}{4}[/tex] = 3

If Inez has 8/3 cup of raisings and each batch takes 2/3 cup of raisins, she may create 4 batches of raisin granola bars.

In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator. A common fraction is a numeric representation of a rational integer. The same number can be expressed as a decimal, a percentage, or with a negative exponent. Fractions indicate pieces of a whole or group of items. A fraction is made up of two components. The number at the top of the line is referred to as the numerator. It specifies the number of equal sections of the whole or collection that are taken. The figure below the line is denominator.

Here,

8/3÷2/3=4

2/3 • 4 = 8/3

2/3 + 2/3 + 2/3 + 2/3 = 8/3

2/3 = 0.67

0.67 • 4 = 2.67

8/3 = 2.67

4 batches of raisin granola bars can inez make if she has 8/3 cups of raisings and each batch requires 2/3 cup of raisins.

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The true statement about exponential smoothing forecasting model is option (d) The exponential smoothing technique is most useful when short-term forecasts are needed.

Exponent:

In math, exponent tells a number says how many times to use that number in a multiplication.

Given,

Here we need to find the statements about exponential smoothing forecasting model is true.

In order to find the true statement we have to know the definition of exponential smoothing forecasting model.

Exponential smoothing forecasting model also known as ETS model is a family of forecasting models.

And it is used as weighted averages of past observations to forecast new values.

And the idea is to give more importance to recent values in the series. Therefore, as observations get older in time, the importance of these values get exponentially smaller.

Based on these explanation we have identified that option (d) is correct.

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The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

In Geometry, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:

m∠5 + m∠6 =180°.

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

Additionally, the sum of all the angles that are formed by a triangle is equal to 180º and this is given by:

m∠2 + m∠3 + m∠5 = 180°,

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The solutions of system of equation are x = 1 and y =-4.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given that the system of equation;

-5x-4y = -17 , (equation 1)

-3x-y =  1, (equation 2)

First step is to write both equation in the standard form, both of these above equations are in standard form.

Now we will make the coefficients of variable y opposite, for that we multiply -4 to the equation 2.

12x+4y = -4

Now, in equation 2 coefficients of variable y are opposite.

Next step is combining the both of the equation;

-5x + 12x = -17 -4

7x = -21

x = -3

Substitute the value of x into equation 2,

-3x-y = 1

-3 (-3) -y = 1

-y = 1-9

y = 8

Therefore, the solutions of system of equation, x = -3 and y = 8.

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1. The function [tex]g(x)=x^2+6[/tex] is related to the parent function[tex]f(x) = x^2[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply add 6 to the expression for

[tex]f: g(x) = f(x) + 6\\ = x^2 + 6[/tex]

2. The function [tex]g(x) = x^2 - 3[/tex]  is related to the parent function [tex]f(x) = x^2[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply subtract 3 from the expression for

[tex]f: g(x) = f(x) -3 \\ = x^2 -3[/tex]

3.The function [tex]g(x) = -(x -2)^3[/tex]  is related to the parent function [tex]f(x) = (x - 2)^3[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply negate the expression for f:

[tex]g(x) = -f(x)\\= -(x - 2)^3[/tex]

4. The function  [tex]g(x) = |x -1| + 5[/tex]  is related to the parent function [tex]f(x) = |x - 1|[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply add 5 to the expression for f:

[tex]g(x) = f(x) + 5\\= |x - 1| + 5[/tex]

5. The function [tex]g(x) = 2 \sqrt{x}[/tex]  is related to the parent function [tex]f(x) = \sqrt{x}[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply multiply the expression for f by 2:

[tex]g(x) = 2[/tex] × [tex]f(x)[/tex]

[tex]= 2 \sqrt{x}[/tex]

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Cost of one sandwich is $7 and cost of milkshake $5.

What is an equation?

In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

According to question:

let cost of one sandwich be x and cost of milkshake be y .

7x + 5y = $79           -------(1)

2x + 5y = $44          -------(2)

subtracting equation 2 from 1 , we get

5x = 35

x = $7

so cost of one sandwich is $7.

now substituting value of x in equation 1 , we get

7(7) + 5y = 79

49 +5y = 79

5 y = 20

y = 4

so cost of one milkshake is $5.

Hence cost of one sandwich is $7 and cost of milkshake $5.

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(-∞, ∞) is the domain of y=-0.25x² and (−∞,0] is range.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is y=-0.25x²

y equal to minus zero point two five times of x square.

We need to find the domain and range of the function.

Let us find few points of x and y.

x    0    1            2           3              4

y    0    -0.25    -1        -0.5625     -4

In the given attachment the graph is given.

The domain is:

{x∣x is R} or (-∞, ∞)

The range is {x∣x≤0} or (−∞,0]

Hence, the domain of y=-0.25x² is (-∞, ∞) and range is (−∞,0].

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Answer:

77

Step-by-step explanation:

60+128+95+x=360

283+x=360

x=77

Answer:

(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab)

Which of the following shows the sum of the polynomials rewritten with like terms grouped together?

[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)

[3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab)

[3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2)

[3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)

The answer is A.

Step-by-step explanation:

Answer:

63 =  EHF

Step-by-step explanation:

We know that EHG is a right angle which is 90 degrees

FHG is 27 degrees

EHG = FHG + EHF

90 = 27+  EHF

90-27 = EHF

63 =  EHF

yes yes yes yes yes yes yes yes yes yes yes yes yes yes

A matched-subjects study and an independent-measures study both included 17 participants.

In statistics, the number of degrees of freedom is the number of values in the final computation of a statistic that are free to change. Estimates of statistical parameters might be based upon differing quantities of information or data. Degrees of freedom refer to the maximum number of logically independent values in a data sample, which are values with the freedom to vary. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.

Here,

Sample size=degree of freedom(df)+1

=16+1

=17

17 individuals participated in each study of a matched-subjects study and an independent-measures study both.

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The slope of the equation is m that is derivative of the given function if you take the graph of ln (K) and 1/T. I t makes intercept at ln[A] and the slope is given by m= -Ea/R that means option D is correct.

For many physical and chemical reactions, the relationship between reaction rate and temperature is described by the Arrhenius equation.

Based on hydrolysis S2 peak data measured at multiple heating rates and burial histories occurring over geological time scales, Arrhenius-equation first-order reactions are useful for modelling the timing and temperatures of petroleum generation from organic-rich shakes and oestrogens at laboratory scales.

The slope of the equation is m that is derivative of the given function if you take the graph of ln (K) and 1/T. I t makes intercept at ln[A] and the slope is given by m= -Ea/R that means option D is correct.

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Answer:

12 and 24 gcf = 4

so the only choice left is

(H) 4x²y

(I) 4xy

12x²y³ + 20x³y = lowest of x is x² and y is y

then its

(H) 4x²y