Line AB contains point A(−4, 1) and point B (−1, 3). Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.

The value of the angle is 120°.

The corresponding angle of a given angle refers to the angle in a congruent position in another figure. For example, if two lines intersect, the angle formed at one vertex of the intersection is called a vertex angle. The corresponding angle in the other figure is the angle in a congruent position, meaning that it has the same measure.

We are given two lines to be parallel

Hence the angle adjacent to x is 40°

Now Sum of All three angle is 180° (Angles in linear pair)

Hence we have

40 + x + 20 = 180°

x = 120°

Hence the measure of angle x is 120°

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1/(x+1)(x-2) is the simplified form of the expression

Given the expression below

x+2/4x²+5x+1 · 4x+1/x²-4

Factorise the quadratic expressions

4x²+5x+1 = 4x²+4x + x+1

4x²+5x+1 = 4x(x+1)+1(x+1)

4x²+5x+1 = (4x+1)(x+1)

For the expression x²-4

x²-4 = (x+2)(x-2)

Substitute

x+2/4x²+5x+1 · 4x+1/x²-4 = x+2/(4x+1)(x+1) · 4x+1/(x+2)(x-2)

x+2/4x²+5x+1 · 4x+1/x²-4 = 1/x+1 · 1/x-2

x+2/4x²+5x+1 · 4x+1/x²-4  = 1/(x+1)(x-2)

Hence the simplified form of the expression is 1/(x+1)(x-2)

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The two integers are 1 and 2.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so they are positive integer.

A number is negative if it is less than zero, so they are negative integer.

A number line is a visual representation of numbers on a straight line. This line is used for comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

x be a positive number

x + 1 = y

The sum of reciprocal of the smaller and twice the reciprocal of the larger number

Substitute

[tex]\frac{1}{x} + \frac{2}{y} = 2[/tex]

[tex]\frac{1}{x} + \frac{2}{x + 1} = 2[/tex]

[tex]\frac{x+ 1 + 2x}{x(x +1)} = 2[/tex]

[tex]x + 1 + 2x = 2x^2 + 2x[/tex]

Subtracting 2x on both sides, we get

x + 1 + 2x - 2x = 2x² + 2x - 2x

x + 1 = 2x²

2x² - x - 1 = 0

2x² - 2x + x - 1 = 0

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

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

x = -1/2 and x = 1

But x = -1/2 is not possible. Becuase x is a positive number.

So, x = 1

y = x + 1

y = 2

The two integers are 1 and 2.

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The requried teacher needs $59.5 more to buy cups and napkins, as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To find out how much more money the teachers will need to buy cups and napkins, we can first calculate the cost of each item and then add those costs together.

Each package of cups costs $3.50

The teachers need to buy 12 cups

So the total cost of cups is = 12 cups × ($3.50 per package) = $42

Now let's do the same thing for the napkins:

Each package of napkins costs $4.25

The teachers need to buy 10 napkins

So the total cost of napkins is = 10 napkins × ($4.25 per package) = $42.50

To find out how much more money the teachers will need to buy cups and napkins,

= $42 + $42.50 - $25
= $59.50 - $25 = $59.5

Therefore, the teachers will need $59.5 more to buy cups and napkins.

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The completed two-column table that is used to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution. The correct option is option B

B. Substitution

Congruent angles are angles that have the same measurement,

The two-column table is presented as follows;

[tex]{}[/tex]  Statements                                                           Reasons

1. ABCD is a parallelogram with diagonal [tex]\overline{AC}[/tex]  [tex]{}[/tex]     Given

2. [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{AD}[/tex]║[tex]\overline{BC}[/tex]  [tex]{}[/tex]                                Definition of a parallelogram

3. ∠2≅∠3, ∠1≅∠4   [tex]{}[/tex]                                           Alt. int. ∠s are ≅

4. m∠2 = m∠3 and m∠1 = m∠4 [tex]{}[/tex]                        Measures of ≅ ∠s are =

5. m∠1 + m∠2 = m∠4 + m∠2 [tex]{}[/tex]                             Addition prop. of equality

6. m∠1 + m∠2 = m∠4 + m∠3[tex]{}[/tex]                              Substitution

7. m∠1 + m∠2 = m∠BAD [tex]{}[/tex]                                    Angle addition property

m∠3 + m∠4 = m∠DCB

8. m∠BAD = m∠DCB [tex]{}[/tex]                                         Substitution

9. ∠BAD ≅ ∠DCB [tex]{}[/tex]                                             Angles are congruent if [tex]{}[/tex]    

[tex]{}[/tex]                                                                          their measures are the same

The missing reason in the partial proof is therefore;  B. Substitution

The abbreviations in the table are expanded as follows;

Alt. int. ∠s are ≅; Alternate interior angles are congruent

Measures of ≅ ∠s are =; Measures of congruent angles are equivalent

Addition prop. of equality; Addition property of equality

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The percent of two inches to the length of a ruler is 16.7 percent.

The length of a standard ruler is 12 inches. Therefore, the percent of two inches to the length of a ruler can be calculated as follows:

percent length = 2 / 12 × 100

Hence,

percent length = 200 / 12

percent length = 16.6666666667

percent length = 16. 7 %

Therefore, the percent length of 2 inches to the length of a ruler(12 inches) is 16.7 percent.

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The exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

What is meant by tangent?

A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.

Given function is f(x)=4-2secx

We can write it as

y=4-2secx

The slope of the tangent to this curve is:

[tex]\frac{dy}{dx} =-2secx*tanx[/tex]

Given that the tangent is horizontal, which means that the slope is zero.

-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].

So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].

When x=0 ⇒ y=4-2sec0

⇒y=2

When x=π ⇒ y=4-2secπ

y=6

When x=-π⇒ y=4-2sec(-π)

y=6

Therefore the exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

The graph is attached below.

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Answer:

The surface area of a cylinder can be calculated using the formula:

Surface area = 2πr^2 + 2πrh

Where r is the radius and h is the height of the cylinder.

Plugging in the values we have:

Surface area = 2π(8^2) + 2π(8)(8) = 2π(64) + 2π(64) = 128π

Rounding to the nearest thousandth, we have:

Surface area = 128π = 403.23 in^2 (rounded to the nearest thousandth)

So the surface area of the cylinder with height 8 in and radius 8 in is 403.23 in^2.

Step-by-step explanation:

On solving the provided question, we can say that The pace at which the y-values change relative to the x-values is the average rate of change for a function, average rate = m = 81-9/6 = 72/6 = 12

Mathematics is the study of quantities and their variations, equations and related structures, shapes and their locations, and the locations where they can be found. The term "function" refers to the relationship between a set of inputs, each with its own output. A function is a connection between inputs and outputs in which each input leads to a single, distinct result. Each function is assigned a domain and a codomain, also known as a scope. f is commonly used to denote functions (x). The input is an x. Based on the following factors, there are four main types of functions available: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

f(x) =

x1, x2 = 3,9

average rate = f(x2) - f(x1) / 6

average rate = m = 81-9/6 = 72/6 = 12

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The average rate of change of the function between x = a and x = a + h is -6

The slope is -6

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

g(x) = -6x + 1

The interval is given as

x = a and x = a + h

So, we have

g(a) = -6a + 1

g(a + h) = -6(a + h) + 1

This gives

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

Subtract the functions

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

g(a) - g(a + h) = -6h

The average rate is then calcualated as

Average = [g(a) - g(a + h)]/(a - a - h)

This gives

Average = (-6h)/-h

Evaluate

Average = -6

This also represents the slope

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Answer:(4,-1)

Step-by-step explanation: The vertex is the highest point of the parabola (curved line). The vertex is the point where the parabola crosses its axis of symmetry.

The volume of the composite figure is 2592 cubic feet.

The area that any composite shape covers is known as the area of composite shapes. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These shapes or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.

The volume of the figure = Volume of the mounted object + Volume of the base object.

The volume of the mounted object is:

V = (l)(b)(h)

V = (9)(12)(6)

V = 648 cubic feet.

The volume of the base object is:

V = (l)(b)(h)

V = (27)(12)(6)

V = 1944 cubic feet.

The total volume of the composite figure is:

V = 648 + 1944

V = 2592 cubic feet

Hence, the volume of the composite figure is 2592 cubic feet.

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Angle b is equal to 35°, angle a and angle e are each equal to 145°

An angle is formed when two lines intersect at a point. Types of angles are acute angle, obtuse angle and right angle. Vertical opposite angles are always congruent to each other. The sum of angles along a straight line is supplementary (add up to 180 degrees)

From the diagram:

b = 35° (vertical opposite angles are congruent)

a + b = 180° (sum of angles along a straight line)

a + 35 = 180

a = 145°

a = e = 145° (vertical opposite angles are congruent)

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Answer:(4x^2 + y^2)(2x + y)(2x - y)

Step-by-step explanation:

16x^4 - y^4

= (4x2)^2 - (y^2)^2

= (4x^2 +y^2)(4x^2 - y^2)

=(4x^2 + y^2)( (2x)^2 -y^2)

= (4x^2 + y^2)(2x + y)(2x - y).

"Communist infiltration in the entertainment industry" was the first target of the HUAC hearings among the following choices given in the question.

HUAC was created in 1938 to investigate alleged disloyalty and rebel activities on the part of private citizens, public employees and organizations suspected of having Communist ties.

Originally organized as a minor congressional committee investigating domestic subversion, HUAC (also known as the House Un-American Activities Committee) rose to such power in the late 1940's and early 1950's that the mere threat of investigation by it could ruin a person's career. By the time it was abolished in 1975, HUAC had widened its scope of investigation to include almost every aspect of American society.

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Answer:

Step-by-step explanation: The expression for f(x) is not a valid mathematical equation. It should specify the relationship between x and the output value of f(x). If the correct equation for f(x) is given, we can then find the expression for (f + g)(x) and g(x).

Assuming that the equation for f(x) is as follows:

f(x) = 12 + x

Then, the expression for (f + g)(x) can be found by adding f(x) and g(x):

(f + g)(x) = f(x) + g(x) = 12 + x + (5 - x) = 17

So, (f + g)(x) is a constant function with a value of 17 for all values of x.

And the expression for g(x) was already given:

g(x) = 5 - x

Step-by-step explanation:

please review the attachment. That's the answer.

The antiderivative of the given expression can be found using the substitution method. We'll make the substitution u = 4 - 9x^2, so du/dx = -18x.

Substituting these into the original expression, we get:

∫{√(4-9x²)/x}dx = ∫{√u/x}du = 2√u * ln|x| + C, where C is an arbitrary constant of integration.

Substituting back for u, we get:

∫{√(4-9x²)/x}dx = 2√(4 - 9x^2) * ln|x| + C.

To verify this result, we can differentiate the antiderivative and see if it matches the original expression. Taking the derivative of the antiderivative with respect to x, we get:

d/dx [2√(4 - 9x^2) * ln|x| + C] = -18x√(4 - 9x^2)/x + 2 * (-9x) / (2√(4 - 9x^2)) = (√(4-9x²)/x)

Thus, the antiderivative found is indeed correct.

The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°

Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°

W =25.0277

Now,
Area of the triangle is given as
= 1/2 UW sinv

= 1/2× (25.027)×(6.7)×(sin156°)

= 34.1 square inch

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Answer:

Graph D is Greg's graph

From the resting point it goes up and then it straightens out and then increases again

Answer:

(-4,-2)

Step-by-step explanation:

Answer: (-4,-4)

Step-by-step explanation: the y- coordinate stays the same you would have to move the x-coordinate only which would give you -4. Because you are adding 2 to -6.

Answer:

a.  2p + 2d + 1c + 1p + 1c + 2p + 1d

b. 5p + 3d + 2c

c. In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

Step-by-step explanation:

a.
From the cute diagram we see that the family bought

2 pizzas + 2 drinks + 1 cone + 1 pizza + 1 cone + 2 pizzas + 1 drink

Using the variables provided, this becomes

2p + 2d + 1c + 1p + 1c + 2p + 1d

b.
Combining like terms the total purchase is:
(2p + 1p + 2p) + (2d + 1d) + (1c + 1c)

Adding the coefficients of each grouped term we get

(5p) + (3d) + (2c)

Opening the brackets, this becomes
5p + 3d + 2c

c.
In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

The value of the quadratic like equation is given as y = 1 and y = 81.

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be favoured over the cross-multiplication method and the elimination method for straightforward equations without a lot of complicated calculations.

The equation is:

[tex]y^{\frac{1}{2} } - 4y^{\frac{1}{4} } + 3 = 0[/tex]

Using the exponent property we can write the equation as follows:

[tex](y^{\frac{1}{2} })^{\frac{4}{4} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{\frac{4}{2} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{2} - 4y^{\frac{1}{4} } + 3 = 0[/tex]

Now suppose the value of [tex]y^{\frac{1}{4} } = x[/tex].

x² - 4x + 3 = 0

x² - 3x - x + 3 = 0

x(x - 3) -1 (x - 3) = 0

(x - 1)(x - 3) = 0

x = 1

x = 3

Now, back substituting the value of [tex]y^{\frac{1}{4} } = x[/tex].

[tex]y^{\frac{1}{4} } = 1\\\\y^{\frac{1}{4} } = 3\\[/tex]

Raise to four on both sides of the equation we have:

y = 1

y = (3)⁴

y = 81

Hence, the value of the quadratic like equation is given as y = 1 and y = 81.

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Step-by-step explanation:

an arithmetic progression or arithmetic sequence is a sequence of terms, where the difference bergen neighboring terms is a constant d for the whole sequence.

a1 = 29

a2 = 29 + d

a3 = a2 + d = a1 + d + d = 29 + 2d

...

an = 29 + (n-1)d

a7 = -13 = 29 + 6d

-42 = 6d

d = -42/6 = -7

therefore,

a10 = 29 + 9×-7 = 29 - 63 = -34

The value of x in the given equation using laws of exponents is; x = -9

We want to solve the problem correctly expressed as;

3^(4x) = 27^(x - 3)

Now, some of the laws of exponents are;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

Now, 27^(x - 3) can also be expressed as;

3^(3(x - 3))

Now, according to power of power rule, if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same. Thus;

3^(3(x - 3)) = 3^(3x - 9)

Thus, we now have;

3^(4x) = 3^(3x - 9)

4x = 3x - 9

3x - 4x = 9

-x = 9

x = -9

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Answer:

= 9x - 1

Step-by-step explanation:

[tex] \frac{(5x - 1)}{x} + 4 \\ = x \times \frac{5x - 1}{x} + 4(x) \\ = 5x - 1 + 4x \\ = 5x + 4x - 1 \\ = 9x - 1[/tex]

The solution is, the Factor out the greatest common factor from the expression is 5(5p+6).

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.

here, we have,

given expression is,

16p+5+9p+25

=25p+30

=5(5p+6)

Hence, The solution is, the Factor out the greatest common factor from the expression is 5(5p+6).

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The value of 4(3/2) times 1 is 6.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

Given:

4(3/2) times 1

Simplifying 4 (3/2) we get

= 4(3/2)

= 12/2

= 6

Now, we have to find 6 times of 1.

= 6 x 1

= 6

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75

Step-by-step explanation:

I think this is the answer I'm not sure I hope this helps