There are two types of packages that are available for hotel stay

- you can use the hotel unlimited for $500 a month

- Or you can spend $50 a day per visit.

Enter an equation that can be used to find the number of visits per month needed for the two packages to cost the same amount

Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

Answer:

A Circle

Step-by-step explanation:

Answer:

Question 1

This is a special triangle as the angles are 30-60-90

This means that the sides have a special ratio of
1 : √3 : 2 = short leg : long leg : hypotenuse

So the hypotenuse is twice the length of the short leg,
and the long leg is √3 times the length of the short leg.

Given:

⇒ x = 30 ÷ 2 = 15

⇒ y = 15 × √3 = 15√3

Question 2

The sum of the interior angles of a triangle is 180°.  Therefore the unknown angle of the triangle is 60°.

So again, this is a special 30-60-90 triangle, and we can use the same method as question 1 above.

Given:

⇒ x = 5 × √3 = 5√3

⇒ y = 5 × 2 = 10

Question 3

Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

To find x:

Given:

⇒ 8² + 6² = x²

⇒ x² = 100

⇒ x = √100

⇒ x = 10

To find y:

Given:

⇒ 5² + 10² = y²

⇒ y² = 125

⇒ y = √125

⇒ y = 5√5

Question 4

Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

To find x:

Given:

⇒ 5² + 12² = x²

⇒ x² = 169

⇒ x = √169

⇒ x = 13

To find y:

Given:

⇒ y² + 13² = 14²

⇒ y² + 169 = 196

⇒ y² = 27

⇒ y = √27

⇒ y = 3√3

Answer:

i can barely see it sorry

Step-by-step explanation:

A line passes through (3, 7) and (-4, 9). Find the value for x if (x, 1) is on the line.​

step 1

find the slope of the line

m=(9-7)/(-4-3)

m=2/-7

m=-2/7

step 2

find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=-2/7

(x1,y1)=(3,7)

substitute

y-7=(-2/7)(x-3)

step 3

substitute the point (x,1)

1-7=(-2/7)(x-3)

-6=-(-2/7)(x-3

solve for x

multiply by -7 both sides

42=2(x-3)

divide by 2 both sides

21=x-3

x=21+3

x=24)

Suppose that an item regularly costs $100.00 and is discounted 15%. If it is then marked up 15%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.​

1) 100%-15%=85%=85/100=0.85

If is discounted 15%

the new price is

100,000*0.85=$85,000.00

2) f it is then marked up 15%

100%+15%=115%=115/100=1.15

the new price is

1.15*85,000=$97,750.00

therefore

the resulting price is not $100,000

the resulting price is $97,750.00

Answer:

675 devided bye 9 = 75

Step-by-step explanation:

Answer: 75 words per minute

Step-by-step explanation:

We can set this problem up similar to a ratio
675:9
Knowing that this is for 9 minutes, dividing by 9 will give you the amount per one minute
675/9   9/9
75:1 or 75 words per minute

Answer:

12

Step-by-step explanation:

TB= TA

6= TA

TA+TB= AB

6+6=12

Answer:

Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.

Step-by-step explanation:

For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.

For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.

Answer:

Step-by-step explanation:

Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.

The segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.

When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.

"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.

Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.

__

Additional comment

The rigid motions include ...

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The Inequality which ensure triangle exists is A. 7/4 < x < 11/2

Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Theorem used In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

Substitute the value in the inequality to ensure triangle exists we get 7/4 < x < 11/2. The correct option is A.

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Answer:

The answer is A

Step-by-step explanation:

You can use a graphing calculator (geogebra) It works

Answer: 117 tickets left

Step-by-step explanation:

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer:

X-intercept: (6, 0)

Y-intercept: (0, -9)

Step-by-step explanation:

Required: Find the X and Y intercept of the standard from equation:

-3x + 2y = -18.

We shall write equation in the form \(\frac{x}{a} +\frac{y}{b} =1\) and find the intercepts on X and Y axis:

-3x + 2y = -18

∴ -3x + 2y = -18

∴ -3x/-18 + 2y/-18 = 1

∴ x/6 + y/-9 = 1

Comparing this equation with \(\frac{x}{a} +\frac{y}{b} =1\), we get:

intercept of X-axis = a = 6

intercept of Y-axis = b = -9

Thanks.

Answer:

The y-intercept for the line is ( 0, -9 ).

Hope this helps!

Step-by-step explanation:

The y-intercept is where the graph intercepts the y-axis and is the y-value of the point, ( x, y ).

Answer:

Domain: X<5

Range: f(x)∈ R

Step-by-step explanation:

The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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Answer:

Step-by-step explanation:

5

The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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Answer: The number is 14

Step-by-step explanation:

A number is increased by 20:  (X + 20)

Then doubled: 2(X + 20)

5 times the number: 5X

2 less than 5 times the number: 5X - 2

Setting the bold statements equal: 2(X+20) = 5X - 2

Distribute left side: 2X + 40 = 5X - 2

Move X's: 40 = 3X - 2

Move numbers: 42 = 3X

Divide both sides by 3: X = 14

Answer:

x=9, y=-9

Step-by-step explanation:

pic attached with step by steps

Answer:

\(m_{perpendicular}\) = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

Answer:

The pattern that we know is:

D₁ = 4 night eyes

D₂ = 8 night eyes

D₃ = 16 night eyes

Ok, with these 3 elements we can see that this seems like a geometric sequence.

How we test it? well, the quotient between any pair of consecutive terms must be constant.

D₂/D₁ = 8/4 = 2

D₃/D₂ = 16/8 = 2

Then we can write the n-th term as:

Dₙ = D₁*2^(n-1) = 4*2^(n-1)

Then in day 25, we have n = 25.

Then the term is:

D₂₅ = 4*2^(24) = 67,108,864 night eyes

Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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As the sum of the interior angles of a triangle equals 180°, we can build the following relation:

Replacing the expressions given:

Simplifying the equation we get:

Then, to get the value of each angle we have to substitute this value in each expression given.

• m∠K

• m∠L

• m∠M

Answer:

• Equation

• m∠K = 28°

• m∠L = 89°

• m∠M = 63°

The only  polynomial that can be factored using the binomial theorem is; D: 625x⁴ + 7500x³ + 33750x² + 67500x + 50,625

1) 25x² + 75x + 225

Let us factorize 25 out to get;

25(x² + 3x + 9)

This cannot be factored further to a perfect square.

2) 25x² + 300x + 225

Let us factorize 25 out to get;

25(x² + 12x + 9)

This cannot be factored further to a perfect square.

3)  625x⁴ + 1,875x³ + 5,625x² + 16,875x + 50,625

Let us factorize 25 out to get;

625(x⁴ + 3x³ + 9x² + 27x + 81)

This can be factored into a perfect square as;

625(x + 3)⁴

Using Pascals triangle in binomial theorem gives;

625(1(x⁴ * 3⁰) + 4(x³ * 3¹) + 6(x² * 3²) + 4(x¹ * 3³) + 1(3⁴))

= 625(x⁴ + 12x³ + 54x² + 108x + 81)

This does not tally with the given expression

4) 625x⁴ + 7500x³ + 33750x² + 67500x + 50,625

Let us factorize 25 out to get;

625(x⁴ + 12x³ + 54x² + 108x + 81)

This can be factored into a perfect square as;

625(x + 3)⁴

Using Pascals triangle in binomial theorem gives;

625(1(x⁴ * 3⁰) + 4(x³ * 3¹) + 6(x² * 3²) + 4(x¹ * 3³) + 1(3⁴))

= 625(x⁴ + 12x³ + 54x² + 108x + 81)

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Julia have to pay to buy 2 pounds of cherries is $11.50. The cost to buy  p pounds of cherries is 7.50p.

To find price of 2 pound of cherries we have to calculate:

The price per pound pound of cherries = $7.50

The price of 2 pound of cherries = $15.00

when the coupon value of $3.50 has been deducted from purchase cost then the final price

= $15.00 - $3.50

= $11.50.

cost of p pounds of cherries=(p x $7.5)

cost of p pounds of cherries=7.50p

Julia have to pay to buy 2 pounds of cherries is $11.50. The cost to buy  p pounds of cherries is 7.50p.

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