4. Triangle XYZ with vertices X(-6, 4), Y(0, 6), and Z(-4, 2):
a) 180° counterclockwise rotation about the origin
b) dilation with scale factor of 3/2 centered at the origin
X')
Y')
Z'

Kelly pours 1/3 litre of fruit punch into each glass at a party for her chess team.

What does the division do?

divides left-hand operands into right-hand operands while performing a division operation in mathematics.

For instance, 4/2 = 2.

She combined the prescribed amounts of 1 2/5 litres of cranberry juice and 1 3/5 litres of pineapple juice.

The appropriate response to the aforementioned situation would be

⇒ 1 2/5 + 1 3/5

fractionalizing mixed numbers

⇒ 7/5 + 8/5

Consider the LCM in the previous equation.

⇒ (7 + 8)/5

⇒ 15/5

⇒ 3

She then divided the fruit punch equally among the nine cups.

3 litres of fruit punch must now be divided among 9 glasses.

3/9, therefore, equals 1/3 litres of fruit punch.

She, therefore, fills each glass with a third of a litre of fruit punch.

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The values of the three basic trigonometric ratios are Sine, Cosine, tangent.

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trig ratios, cosec, sec, and cot.

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So,  the y-intercept of the equation 3x + y = -1 is the point (0, -1).

The y-intercept of a linear equation in the form of y = mx + b is the point at which the line crosses the y-axis, which is the point (0, b). In the equation 3x + y = -1, the y-intercept is the point at which y = -1 and x = 0, which can be found by solving for y when x = 0:

3(0) + y = -1

y = -1

So the y-intercept of the equation 3x + y = -1 is the point (0, -1). This means that the equation of the line passes through the point (0, -1) on the Cartesian plane.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Using Pythagoras theorem, The height of the television is 56.65 inches.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

d² = (ax)² + (bx)²

= x² (a² + b²)

⇒ x = √(d²/a²+b²)

length = a . √(d²/a²+b²)

width = b. √(d²/a²+b²)

with an aspect of 16:9,

has an advertised size of 65 inches,

a = 16, b = 9, d = 65

length = 56.65 inches

width = 31.87 inches

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The equation of the directrix for the parabola y = 18 · x² - 4 · x + 41 is y = 2935 / 72.

In this question we find the case of the equation of a parabola in standard form:

y = a · x² + b · x + c

Where:

This equation must be changed into vertex form:

y - k = C · (x - h)²

Where:

Where the vertex constant is:

C = 1 / (4 · p)

Where p is the distance between focus and vertex.

And the equation of directrix is:

y = k - 1 / (4 · C)

First, write the quadratic equation in standard form:

y = 18 · x² - 4 · x + 41

Second, use algebra properties until vertex form is obtained:

y = 18 · [x² - (2 / 9) · x + 41 / 18]

y = 18 · [x² - (2 / 9) · x + 1 / 81] + 18 · (367 / 162)

y = 18 · (x - 1 / 9)² + 367 / 9

y - 367 / 9 = 18 · (x - 1 / 9)²

Third, find the equation of the directrix:

y = 367 / 9 - 1 / (4 · 18)

y = 2935 / 72

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For the given equation, the value of x = -21.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

For the given equation,

x ≠ ±3

On taking LHS,

⇒ [tex]\frac{5}{x+3} - \frac{2}{x-3}[/tex]

Taking LCM,

⇒ [tex]\frac{5(x-3) - 2(x+3)}{(x+3)(x-3)}[/tex]

⇒ [tex]\frac{5x - 15 - 2x - 6}{x^2 - 9}[/tex]

⇒ [tex]\frac{3x - 21}{x^2 - 9}[/tex]

On Comparing both sides,

⇒ [tex]\frac{3x - 21}{x^2 - 9} = \frac{4x}{x^2 - 9}[/tex]

⇒ 3x - 21 = 4x

⇒ x = -21

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Answer:

[tex]6\frac{3}{4}[/tex] and [tex]3\frac{1}{8}[/tex]

Step-by-step explanation:

I don't know what benchmark fractions are but here's what I did

[tex]4\frac{7}{8} + 1 \frac{7}{8} = 5 \frac{14}{8} = 6 \frac{6}{8} or 6\frac{3}{4}\\5\frac{3}{8} - 2\frac{1}{4} = 5\frac{3}{8} - 2\frac{2}{8} = 3\frac{1}{8}[/tex]

The first question is straight forwards since the fractions have the same denominator, so its simply adding and simplification.

The second questions needs you to find a common denominator (8) and swap the fraction to that of 8 before subtracting

Step-by-step explanation:

what happen if a body is projected at an angle of 75 to the horizontal then it is a projector Once More with the same initial speed as an angle of 15 so he wants me to calculate the horizontal Range and I don't know have

Answer:

y > -14

Step-by-step explanation:

4y < 5y + 14

Subtract 5y from both sides of the < sign:

4y - 5y < 5y - 5y + 14

-y < 14

Divide both sides by -1:

y > -14 is the answer.

Note, in the last step, the sign flips because we are dividing by a negative

The graph of the inequality x - 6y > 18 is plotted and attached

Inequality are graphed considering the table of values formed by assigning several values for x

x - 6y > 18

rearranging the equation will result to

x - 18 > 6y

y < x/6 - 3

for x = -6, y < -6 / 6 - 3 = -4

for x = 0, y < 0 / 6 - 3 = -3

for x = 6, y < 6 / 6 - 3 = -2

Table of value

x      y

-6    -4

0      -3

6      -2

the equation: y < x/6 - 3 will have a dashed line and shading is below the line because it has a less than sign

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When the discriminant b² - 4ac is greater than zero and also a perfect square, the nature of roots of the quadratic equation ax² + bx + c = 0 will be real and distinct.

A perfect square means that the discriminant can be written as a product of two equal factors, for example (x+y)^2 = x^2 + 2xy + y^2. In this case the roots can be easily calculated by using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this scenario, the square root of the discriminant will be a real number and not a complex number, and the equation will have two distinct solutions for x. This means that the graph of the equation will cross the x-axis twice.

It's important to notice that the values of a,b and c also play an important role in the nature of the roots.

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Answer:

25

Step-by-step explanation:

(-4 + 9) x (8 - 3)

= (5) x ( 5)

= 25

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(-4 + 9) \times (8 - 3)}\\\\\mathsf{-4 + 9 = \boxed{\frak 5}}\\\mathsf{8 - 3 = \boxed{\frak 5}}\\\\\mathsf{= (-4 + 9) \times (8 - 3)}\\\mathsf{= 5\times5}\\\mathsf{= 25}[/tex]

[tex]\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{25}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The seven types of symmetry are Euclidean, Reflectional, Point reflection, Rotational, Translational, Glide reflection, Helical and Double rotation symmetry.

In math the term symmetry is defined as one shape is exactly like the other shape when it is moved, rotated, or flipped.

Here we need to identify the seven types of symmetry.

As per the definition of symmetry here we have identified the types of symmetry as are possible for a geometric object depend on the set of geometric transforms available and on what object properties should remain unchanged after a transformation.

They are listed as follows, Euclidean symmetries, Reflectional symmetry, Point reflection and other involutivity isometries, Rotational symmetry, Translational symmetry, Glide reflection symmetry, Helical symmetry and Double rotation symmetry.

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Step-by-step explanation:

always remember :

the sum of all angles in a triangle is always 180°.

so, in triangle EFD

180 = E + F + D = 37 + 105 + D

D = 38°

since we know that the combination (sum) of B and D is 90° (right angle),

B + D = 90

B + 38 = 90

B = 52°

and now we look at the triangle ABC and its angles to get A, which then in turn gets us I of the triangle A(BD)I.

180 = A + B + C = A + 52 + 83

A = 45°

and that means for A(BD)I

180 = A + (B + D) + I = 45 + 90 + I

I = 45°

FYI : that means that the total triangle is an isoceles triangle (both legs are equally long : AB = DI).

Answer:

Step-by-step explanation:

Emani will be able to purchase the subscription for a maximum of 5 months if she wants to spend $210 or less from her summer job.

The subscription has a one-time fee of $30 plus $9 per month, so the total cost per month is $9 + $30 = $39.

Emani plans to spend $210 or less from her summer job on this subscription, so we can write an inequality to represent this situation:

$39x <= $210

Where x is the number of months Emani will be able to purchase the subscription.

To solve for x, we need to divide both sides of the inequality by $39:

x <= (210/39)

x <= 5.38

So Emani will be able to purchase the subscription for a maximum of 5 months, if she wants to spend $210 or less from her summer job.

Note: This is an approximation, since x can't be a decimal. And if you round down to 5 months she will be able to spend $195.

Therefore, Emani will be able to purchase the subscription for a maximum of 5 months if she wants to spend $210 or less from her summer job.

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The subscription has a one-time charge of $30 and a monthly fee of $9, making the monthly cost total $9 + $30 = $39 for the subscription.

We can create an inequality to symbolize this circumstance since Emani intends to spend no more than $210 from her summer job on this subscription:

$39x <= $210

Emani will have the option to buy the subscription for x months.

Divide both parts of the inequality by $39 to find the value of x:

x <= (210/39)

x <= 5.38

Answer: y = -2/3x+4

Step-by-step explanation:

negative slope

y intercept (0,4)

4th answer choice.

Answer:

D.  

Step-by-step explanation:

It's really blurry but here's what I did

Pick two random points:

(0, 4) and (6,0) is what I picked personally.

Calculate slope: rise/run = [tex]\frac{0 - 4}{6 - 0} = \frac{-4}{6} = \frac{-2}{3}[/tex]

b is the y-int at 4 therefore your equation is [tex]y = \frac{-2}{3}x + 4[/tex]

a. You replace each card before selecting the next card.

The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is also 13/52 or 1/4. And the probability of drawing a heart on the third draw is also 13/52 or 1/4.

Since the events are independent, we can multiply the probability of each event to find the probability that all three cards are hearts: (1/4) * (1/4) * (1/4) = 1/64.

b. You do not replace each card before selecting the next card.

The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is 12/51 since we already drew a heart before, the total number of cards left in the deck is 51. The probability of drawing a heart on the third draw is 11/50 since we already drew 2 hearts before, the total number of cards left in the deck is 50.

The probability that all three cards are hearts is (1/4) * (12/51) * (11/50) = 0.0217 or approximately 2.17%.

It's important to note that in the first case the probability of drawing a heart on the second and third draw is still 1/4 because we are replacing the cards back before drawing the next one, so all 52 cards are available again. While on the second case, we don't replace the cards back and that's why the probability of drawing a heart on the second and third draw is different.Answer:

Step-by-step explanation:

Answer:

31.875 m

Step-by-step explanation:

We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.

The volume of the well is given by the formula for the volume of a cylinder:

V = πr^2h

where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).

V = π(1.5)^2(21) = 42.5π m^3

The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:

V = 1/3 πr^2h

where r is the radius of the base of the cone (4 m) and h is the height of the embankment.

V = 1/3π(4)^2h = 4/3πh m^3

Now we know that the volume of the embankment is equal to the volume of the well:

V = 42.5π m^3 = 4/3πh m^3

Then we can solve for h by dividing both sides by 4/3π:

h = 42.5π m^3 * 3/4π = 31.875 m

So the height of the embankment is 31.875 m.

The degree measure is which is equivalent to [tex]\frac{7 \pi}{11}[/tex] is 114.54°.

The size of an angle is measured in terms of a unit of measurement. 1 degree is equivalent in magnitude to 1/360 of a whole rotation.

A rotational angle is said to have a measure of one degree, denoted by the symbol 1°, if it is (1/360)th of a revolution from the initial side to the terminal side. Radian scale. A unit circle's unit arc's centrally subtended angle is said to have a measure of 1 radian.

The radius of an arc divided by its length is known as the radian measure (r). Radian measure is a pure number that doesn't require a unit symbol because it is the ratio of one length to another.

Convert radians to degrees, multiply by 180/π, since a full circle is 360° or 2π radians.

= [tex]$ \frac{7 \pi}{11} \times \frac{180}{\pi}[/tex]

= [tex]$ \frac{7 }{11} \times 180[/tex]

=[tex]$ \frac{1260}{11}[/tex]

= 114.54°

Therefore, the correct answer is 114.54°.

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Full question:

According to the given statement, 3x^3y^4 represents the length of the room.

Its length w is calculated using the formula h = A/w if you have an area A and a width w. Its length can be determined using the formula h = P/2w if you know its perimeter (P) and width (W). The length is given by h = (d2w2) if the diagonal d and width w are present.

Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.

The area of a square box is length x width, so that we can set up the calculation:

length x (2x³y²) = 6x6y8

To find the length of the court, we can divide both sides by 2x³y²:

length = (6x6y8) / (2x³y²)

so the length of a room is represented by 3x^3y^4

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The complete question is -

Oscar's rectangular room has an area of 6x^6y^8 square units. If the width of Oscar's room can be represented by 2x^3y^2, which of the following represents the length of the room?​

(a)3x^2y^4

(b)3x^3y^4

(c)12x^9y^10

(d)12x^18y^16

On the Richter scale is 1258.93 times as intense as a standard earthquake.

The Richter scale is a base-10 logarithmic scale, which means that each order of magnitude is 10 times more intensive than the last one. We have,

the an earthquake measuring 3. 1 on the Richter scale.

On Richter Scale, A = log(I/Iₛ)

here, A ---> amplitude

I --> intensity of earthquake

Iₛ ---> standard intensity of earthquake

As, A = 3.1

=> 3.1 = log(I/Iₔ)

Taking anti-logarithm both sides

=> 10³·¹ = I/Iₛ

=> 1258.93 = I/Iₛ

=> I = 1258.93 Iₛ

Therefore, the earthquake with measuring 3.1 on Richter scale is 1258.93 times as intense as a standard earthquake.

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The solutions of the equation x⁴ - 5x² - 36 = 0 are: x = -3, x = 3, x = 2i and x = -2i

Consider given equation x⁴ - 5x² - 36 = 0

Let us assume that x² = p

so, we get an equation,

p² - 5p - 36 = 0

Now we solve above quadratic equation.

p² - 5p - 36 = 0

using the Quadratic Formula where

a = 1, b = -5, and c = -36

[tex]\Rightarrow p=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow p = \frac{5\pm \sqrt{25+144} }{2}\\\\\\\Rightarrow p = \frac{5\pm \sqrt{169} }{2}\\\\\\ \Rightarrow p=\frac{5\pm 13 }{2}[/tex]

So, p = 9 and p = -4

But p = x²

So, x² = 9 OR x² = -4

For x² = 9, by taking square-root we get x = 3, x = -3

an equation x² = -4 has complex roots, x = 2i and -2i

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Answer:

B

Step-by-step explanation:

2 ÷ 0.4 = 5

----------------

Based on the unit rate, Brand X costs $0.10 per fluid ounce less than Brand Y.

The unit rate refers to the ratio of one value to the whole.

The unit rate is the average of the values of the data set.

We can compute the unit rate by dividing the total value by the number of units.

The total cost of Brand X for 5 fluid ounces = $3.25

The unit cost of Brand X per fluid ounce = $0.65 ($3.25/5)

The total cost of Brand Y for 8 fluid ounces = $6.00

The unit cost of Brand Y per fluid ounce = $0.75 ($6.00/8)

The difference in the unit cost of Brand X and Brand Y = $0.10 ($0.75 - $0.65)

Thus, we can state that Brand Y costs more than Brand X per unit.

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Inequality 5 > 6 is an example of an inequality whose solution is an empty set.

What is inequality?

An inequality is a statement that compares two expressions using one of the following mathematical symbols: <, >, ≤, ≥, ≠. It shows the relationship between the values of the expressions, but unlike an equation, it does not show that the expressions are equal.

For example, the inequality 3x + 4 > 7 compares the value of the expression 3x + 4 to the value of 7. It shows that 3x + 4 is greater than 7 for all values of x.

An inequality that has an empty set as its solution is one that has no solutions. For example, inequality 5 > 6 is an example of an inequality whose solution is an empty set because it is impossible for any value of x to satisfy the inequality. Any value of x will be less than 6 so it is impossible for x to be greater than 6.

Hence, Inequality 5 > 6 is an example of an inequality whose solution is an empty set.

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1. On simplifying the radical expression √28 the result is 2√7.

2. On simplifying the radical expression √40 the result is 2√10.

3. On simplifying the radical expression √72 the result is 6√3.

4. On simplifying the radical expression √99 the result is 3√11.

What is a radical expression?

Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.

The first radical expression is -

√28

Take the LCM of 28.

The LCM is obtained as - 2 × 2 × 7.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 2√7.

Therefore, the expression is 2√7.

The second radical expression is -

√40

Take the LCM of 40.

The LCM is obtained as - 2 × 2 × 2 × 5.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 2√10.

Therefore, the expression is 2√10.

The third radical expression is -

√72

Take the LCM of 72.

The LCM is obtained as - 2 × 2 × 2 × 3× 3.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 6√3.

Therefore, the expression is 6√3.

The fourth radical expression is -

√99

Take the LCM of 99.

The LCM is obtained as - 3 × 3 × 11.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 3√11.

Therefore, the expression is 3√11.

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Answer:[-11, ∞]

The range of the function f(x) = 3x2 + 6x - 8 is [-11, ∞].

Step-by-step explanation: