On a coordinate graph, your house is located at the origin (0,0) You leave your house and walk 6 blocks north. Then you turn and walk 22 blocks west. Since it is getting late, you decide to walk straight back home. How many blocks is it to walk straight back to your house? Round your answer to the nearest tenth​

Answers

Answer 1

Answer:

22.8 blocks

Step-by-step explanation:

We can think of your path as traveling on a coordinate plane. You start by walking 6 units in the positive y direction, then 22 units in the negative x direction, then walking from this point (-22, 6) back to (0, 0)

This path draws a right triangle. The shorter leg is 6 units long, and the longer end is 22 units long. You want to find the hypotenuse of this triangle.

The hypotenuse is found using the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

A and B represent the sides of the triangle, and c represents the hypotenuse!

Before plugging in the functions, isolate c, since that's the answer we're looking for:

[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]

Now, plug in the side lengths of the triangle:

[tex]c=\sqrt{6^2+22^2}[/tex]

Now simplify!

[tex]c=\sqrt{36+484} \\x=\sqrt{520} x=22.8[/tex]

It is 22.8 blocks back to your house! Hope this helps!

 


Related Questions

33 is 22% of what
number?

Answers

Answer:

150

Step-by-step explanation:

[tex]33 = 0.22(x)\\\\\\frac{33}{0.22} =\frac{0.22(x)}{0.22} \\\\\large\boxed{x=150}[/tex]

which multiplication expression is equal to 2/3 ÷ 1/2?​

Answers

Answer:

2/3*2/1

this is the answer

Answer:

2/3 × 2/1

Hope this helps :)

Explanation below.

Step-by-step explanation:

To find the multiplication expression, use the Keep, Change, Flip (KCF) method.


How far apart are the foci of an ellipse with a major axis of 32ft and minor axis of 14ft ?

Answers

The foci are placed 4 feet apart from the ellipse's center. Then the distance between the foci of the ellipse will be separated by 8 feet.

What is an ellipse?

Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.

A major axis of 32 ft and a minor axis of 14 ft.

The major axis 2a of the ellipse will be

2a = 10 feet

a = 5 feet

The minor axis 2b of the ellipse will be

2b = 14

b = 7 feet

We must utilize the following connection to get the foci's coordinate:

b² = a² - c²

3² = 5² - c²

c² = 25 - 9

c² = 16

c = ± 4

As a result, the foci are placed 4 feet apart from the ellipse's center. As a result, the foci are separated by 4 + 4 = 8 feet.

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Find the 17 th term of each sequence. a₁₆=18, d=5

Answers

The 17 th term of the Arithmetic Progression (AP) is found to be a₁₇ = 26.

What is the AP sequence for arithmetic progression?

In Arithmetic Progression (AP), the difference between the two numerical orders is a constant value. Arithmetic Sequence is another name for it.

We'd come across a few important words in AP, denoted as:

The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)

The AP may also be characterized in concepts of common distinctions, as shown below.

The following is the formula for determining an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ......      = an - an-1.

Now, as per the given data in the question;

16th term; a₁₆ = 18

Common difference; d = 5

Then, the 17th term would be calculated as;

Use the common difference formula;

d = a₁₇ - a₁₆

a₁₇ = a₁₆ + d

a₁₇ = 21 + 5

a₁₇ = 26

Therefore, the value of the 17th term of a AP is found as 26.

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Write each number as a percent.
1.23

.

Answers

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100.

The number 1.23 as a percentage is 123 %.

What is a percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The percent sign, %, is frequently used to indicate it. There is no unit of measurement for a percentage. It is a dimensionless number (pure number).

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Let the number be 1.23

To find percentage multiply it by 100, we get

So, 1.23 × 100 = 123 %

Therefore, the number 1.23 as a percentage is 123 %.

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Find the missing term of each arithmetic sequence.... 5, .. , 21,...

Answers

The missing terms of an arithmetic progression (AP) are -3, 5, 13, 21, 29.

What is meant by arithmetic progression (AP)?

An arithmetic progression (AP) is a pattern in which each successive term has the same distinctions.

Each term in an arithmetic progression (except the first) is deduced by adding a specific range to the term preceding the first.The following arithmetic progression concepts are most often used to solve various AP problems for the initial term 'a' of an AP together with the common difference 'd.'The most common difference AP is 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1. nth term of an AP: an = a + (n - 1) dThe sum of an AP's n terms is; Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the final term of the AP.

The arithmetic sequence.... 5, .. , 21,...

There are total 5 terms in the series.

Let the initial term be 'a₁'.

Let the second term be 'a₂' = 5.

Let the third term be 'a₃'.

Let the fourth term is be 'a₄' = 21.

And final, the fifth term be 'a₅'.

The common difference of the AP are same. so,

d = a₃ - a₂      ........(equation 1)

d = a₄ - a₃  .......(equation 2)

Thus, equate the two formed equation;

a₃ - a₂ = a₄ - a₃

Substituting the values;

a₃ - 5 = 21 - a₃

Simplify the above equation;

a₃ = 26/2

a₃ = 13.

Put the value in equation 1 and find the common difference.

d = a₃ - a₂

d = 13 - 5 = 8

So, the first term will be;

d = a₂ - a₁

a₁ =  a₂ - d

a₁ = 5 - 8

a₁ = -3

Now, the fifth term will be;

a₅ = a₄ + d

a₅ = 21 + 8

a₅ = 29.

Therefore, the arithmetic sequence of the AP formed as -3, 5, 13, 21, 29.

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round 0.6666 to 3 sf

Answers

0.6666 contains 4 sigificant figures and 4 decimals. 0.6666 rounded to 3 sig figs is 0.667, to 2 sig figs is 0.67, and to 1 sig figs is 0.7.

Answer:

0.66 with a bar

Step-by-step explanation:

An elevator was on floor number 27 of a hotel building when a guest on a different floor pushed the button to call the elevator. Over the next few minutes the elevator traveled up 6 floors, down 11 floors, up 3 floors, up 5 floors, and then down 14 floors. Write and evaluate an expression that models the situation. On what floor did the elevator finally stop?​

Answers

The elevator finally stopped on the 16th floor.

What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one mathematical operation. This math operation can be addition, subtraction, multiplication, or division. An expression has the following structure: (Number/variable, Math Operator, Number/variable)

So, the expression would be:

6x - 11x + 3x + 5x - 14x = 2714x - 25x = 27-11x = 27

Now,

27 - 11 = 16

Therefore, the elevator finally stopped on the 16th floor.

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Can you help me in identifying m?

Answers

The length of the side m are obtained using the theorem of Pythagoras and proportional triangles to give;

a) m ≈ 28.4

b) m ≈ 12.09

c) m ≈ 9.38

Which theorem can be applied to find the value of m?

a) The given triangle, is a right triangle.

The length of the legs of the triangle are; 33 and 56.

According to Pythagorean theorem, the length of the hypotenuse side, l, is therefore;

l = √(33² + 56²) = 65

From the formula for the area of a triangle, we have;

Area of a triangle, A, equals half the base length multiplied by the height.

A = 0.5 × Base length × Height

For the right triangle, we have;

A = 0.5 × Leg 1 × Leg 2

Which gives;

A = 0.5 × 33 × 56 = 924

However;

A = 0.5 × l × m

Where;

l = The hypotenuse = The base length = 65

m = The height of the triangle

Which gives;

A = 0.5 × 65 × m = 924

m = 924/(0.5 × 65) ≈ 28.4

m ≈ 28.4

b) The side m is parallel the 14 units long side.

The proportion the side m divides a side of the triangle = 3 and 19

Given that the triangle formed by m is proportional to the larger triangle, we have;

m/14 = 19/(19+3)

m = 14 × 19/(19+3) ≈ 12.09

c) From the proportionality of similar triangles, we have;

m/16 = 17/(14+15)

m = 16×17/(14+15) ≈ 9.38

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What is the sum of the 9th square number and the 1st square number?

Answers

Answer:

sum is 82

Step-by-step explanation:

[tex]\sf \textsf{The 9th square number is }9^2 = 81[/tex]

[tex]\sf \textsf{The 1st square number is }1^2 = 1.[/tex]

In order to find the sum of these two square numbers, simply add them together:

[tex]\sf Sum = 81 + 1 = 82[/tex]

The sum of the 9th square number and the 1st square number is 82.


Find the distance between each pair of parallel lines with the given equations.
y=x-11 y=x-7

Answers

The distance between each pair of parallel lines with the given equations y = x-11 and y = x-7 is 4 units.

We can find the points passing through the lines

Hence,

The points passing through the line y = x - 11  are:-

Let x = 11

y = 11 - 11 = 0

(11,0)

and;

Let x = 12

y = 12 -11 = 1

(12,1)

The points passing through the line y = x - 7 are:-

Let x = 7

y = 7 - 7 = 0

(7,0)

and;

Let x = 8

y = 8 -7 = 1

(8,1)

Hence, using distance formula, the distance between the parallel lines will be:-

[tex]\sqrt{(1-1)^2+(12-8)^2} =\sqrt{0+16}=\sqrt{16} =4 units[/tex]

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Draw a tessellation using the following shape(s).
octagon and square

Answers

The network of equilateral triangles, squares, and hexagons is used in just three regular tessellations.

What does tessellation of a form mean?

A flat surface is tessellated when one or more geometric forms, known as tiles, are used to tile the surface without any gaps or overlaps.Tessellations in mathematics can be expanded to greater dimensions and a wide range of geometries.A tiling is referred to as "non-periodic" if it doesn't have a repeating pattern.

Only regular triangles, squares, and hexagons can tessellate on their own.

If you use more than one sort of form, you can create additional tessellations of regular shapes.

The network of equilateral triangles, squares, and hexagons is used in just three regular tessellations.

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Solve the equation.
100 t=70 /240

Answers

The solution of t in 100 t=70 /240 is t= 7/2400

How to solve the equation?

The equation is given as

100 t=70 /240

Divide both sides of the equation by 100

So, we have

t=70 /240 * 1/100

Evaluate

t= 7/2400

Hence, the solution of t in 100 t=70 /240 is t= 7/2400

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Ariane feeds her kitten kkk grams of food 222 times in the morning and 222 times in the evening. She feeds her dog ddd grams of food 111 time in the morning and 111 time in the evening.
Which expressions can we use to describe how many grams of food Ariane feeds her animals per day?

Answers

Step-by-step explanation:

in the morning, 222k + 111d

in the evening, 222k + 111d

grams, g = 444k + 222d

Worth 60 POINTTSS!!! PLEASE HELPP MEEE i need explanation on how u got it tho ​

Answers

Answer:

1.-150 250-400 is -150

2. 6570 6288+282=6570

3.123 because 102+21 is 123

Step-by-step explanation:

can i have the brainlieast award?

6+2(2+3)divided by 2

Answers

6 + 2(2 + 3) ÷ 2= 11

Answer:

11

Step-by-step explanation:

[tex]6+2(2+3)/2[/tex]

[tex]6 + \frac{2 * (2+3) }2}[/tex]   Cancel out 2* and the bottom 2

[tex]6+2+3[/tex]     6+2=8

 ⬇️

   8 + 3

    = 11

Given parallelogram LMNO with diagonals intersecting at point P. If MP = 2x + 5 and OP = 3x − 4, find OP.


−9

9

23

31

Answers

Given parallelogram LMNO with diagonals intersecting at point P, OP is equal to 23.

A parallelogram is a two-dimensional figure with two pairs of parallel sides. A parallelogram's pair of opposite sides are of equal length and its opposite angles are of equal measure.

The diagonals of a parallelogram bisect each other, divides each other into two equal lengths.

If the diagonals of parallelogram LMNO intersects at point P, then MP is equal to OP. If MP = 2x + 5 and OP = 3x − 4, solve for x.

MP = OP

2x + 5 = 3x − 4

5 + 4 = 3x - 2x

x = 9

Substitute the value of x to solve for OP.

OP = 3x − 4

OP = 3(9) - 4

OP = 27 - 4

OP = 23

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This graph shows the amount of medicine in a patient after receiving an injection.

How much medicine was in the patient after `4` hours?
729 mg
144 mg
2/3 mg
4 mg

Answers

Answer:

144 mg

Step-by-step explanation:

At a football game half time show, the marching band was in 3 sections, each with 8 rows of 8 players. The dancers were in 2 sections each with 6 rows of 7 dancers. What is the total number of band members and dancers in the halftime show?

Answers

The total number of band members and dancers in the halftime show in all rows were 276.

What is a row?

A row is an arrangement of things in a straight line next to each other.

if there are n rows and each row has m members then total number of members = m* n

Given that marching band was in 3 sections and each section has 8 rows of  8 players , then players in each section of marching band  = 8 *8 = 64

As, there are 3 such sections then total number of marching band players =3*(players in each section) = 3* 64 = 192

Given that there are 2 sections of dancers and each section has 6 rows of 7 dancers.

Then, dancers in each section of  dancers = 6*7 =42

As there are two such sections, then the total dancers = 2* 42 = 84

total no of band members and dancers = 192+84 = 276

Therefore, The total number of band members and dancers in the halftime show were 276.

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Find a₁ for each arithmetic series. S₈ =440 and d=6

Answers

An arithmetic sequence (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the passage/progression is constant.

Therefore, the expression for the nth term is,

an = a₁ + (n − 1) d

and in general

an = am + (n - m) d.

where d is the difference.

For an arithmetic series with initial term a₁ and difference between terms of d

an = a₁ + (n − 1) d

We are given some of the values,

d = 6 and

S8 = 440

So, we will put the values in the formula and calculate the desired value,

a1 = 440 = a1 + ( 8 - 1 ) * 6 = a1 + 42

a1 = 440 - 42 = 398.

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Which expressions are equivalent to-2y-8+4y?

Answers

Answer:

The expression that is equivalent to -2y-8+4y is 2y-8.


The length of an animal's stride is the distance between two consecutive tracks. The average stride length of a duck is about 5 inches. Write a glide reflection that can be used to predict the location of the next track for the following animal tracks.
duck

Answers

The glide reflection  ( x + 2.5 , y ) is  that is reflected in the line that separates the left prints from the right prints.

A glide translation is what?

A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.

Now, let's assume that the initial position is (x , y) .

Since, the average stride length of a turkey is about 11 inches; also since the turkey has two legs, therefore, the average stride length between the two legs is as shown below:

average = 5/2  = 2.5

Thus, the glide reflection is ( x + 2.5 , y )

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If a voltage of 110 V is applied across a
load and the resulting current flow is 2.2 A,
what is the resistance of the load in Ohms

Answers

Answer:

50 ohms.

Step-by-step explanation:

Volts = current * resistance

110 = 2.2 * r

R = 110 / 2.2

  = 50 ohms.

She bought 0.85 pounds of ground beef for $5.60 per pound and 1 can of tomatoes for $1.79. if she had a coupon for $1.50 off, how much did she spend all together on the ingredients?

Answers

Answer:

$5.05

Step-by-step explanation:

.85($5.60) + $1.79 - $1.50

$4.76 + $1.79 - $1.50 = $5.05


A tea bag is shaped like a regular square pyramid. Each edge of the base is 4 centimeters, and the slant height is 5 centimeters. What is the surface, area of the tea bag in square centimeters? Round to the nearest tenth if necessary.

Answers

Therefore, the surface area of the tea bag is 56 cm².

The slant height of the tea bag is l.

l = 5 cm

Each edge of the base of the tea bag = 4 cm

The lateral surface area of tea is L.

The Surface area of the tea bag is S.

The perimeter of the tea bag is p.

The lateral surface of the tea bag is,

[tex]Lateral \: Surface \: Area = \frac{1}{2} \times Perimeter × Slant \: height [/tex]

[tex]L = \frac{1}{2} \times p \times l[/tex]

[tex] = \frac{1}{2} \times 16 \times 5[/tex]

= 40 cm²

The lateral surface area of the tea bag is 40 cm².

Base Area = (4) ²

= 16 cm²

The surface area of the tea bag is,

Surface Area = Lateral surface area + Base area

S= 40 + 16

= 56 cm²

Therefore, the surface area of the tea bag is 56 cm².

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Um yea anyone want to answer this for me

Answers

Final answer —-> 10 tutors
Let’s solve this by identifying the unit rate. We can mark out what we know so far:

• 6 tutors are needed for every 72 students

• The part about the teachers is inserted to throw us off; we can disregard it

Given that information, we can set up equations:

6 tutors / 6 tutors = 1 tutor

72 students / 6 = 12 students

Our unit rate is 12; there is one tutor required for every 12 students.

Now that we have the unit rate, let’s multiply:

1 • 10 = 10

12 • 10 = 120

The academy needs 10 tutors for if it has 120 students.


What is the value of r when s=-1 , t=4 and u = (1/5) ?
r=3s² + 5(t-2u)
A 7
B 15
C 21
D 22(1/5)

Answers

The value of r is 21 when s = -1 , t = 4 and  u = 1/5 for the equation r = 3s² + 5 (t - 2u).

Quadratic Equation:

Quadratic equations are the polynomial equations of degree 2 in one variable of type.

The general form of a quadratic equation is,

f(x) = ax² + bx + c = 0

where a, b, c, ∈ R and a ≠ 0.

‘a’ is called the leading coefficient and

‘c’ is called the absolute term of f (x).

Given,

Equation is,

r = 3s² + 5 (t - 2u).

Here we need to find the value of r when the values of s = -1 , t = 4 and  u = 1/5.

Apply the values on the given equation then we get,

=> r = 3 (-1)² + 5 ( 4 - 2(1/5))

Expand the values,

=> r = 3 (-1)² + 5( [20 -2] /5)

Here the value 5 is getting cancelled then we get,

=> r = 3(-1)² + 18

We know that the value of (-1)² = 1

So,

=> r = 3(1) + 18

=> r = 3 + 18

=> r = 21

Therefore, the value of r is 21.

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Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. (Lesson 5-3)
measures less than m∠5

Answers

The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

Exterior Angle Inequality Theorem

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .

Therefore, the correct answer is ∠ 7 and ∠ 8.

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Someone please help I’ll give brainles u gotta put the steps

Answers

Answer:

All answers in explanation

Step-by-step explanation:

Step 1: Unknown
Unknown is the number of refills purchased

Step 2 Key Information
Cost of souvenir cup, price per refill and total money spent

Step 3: Strategy (equation)
Define a variable x that represents the number of refills bought

The souvenir cup cost $14.25

Each refill costs $1.25

So x refills will cost 1.25x

Total cost = 14.25 + 1.25x

We are told she spent $23

So the equation is
14.25 + 1.25x = 23

Step 4: Solution
Equation is
14.25 + 1.25x = 23

a) Isolate the x term by subtracting 14.25 on both sides

14.25 - 14.25 + 1.25x = 23 - 14.25

1.25x = 8.75


b) Divide both sides by 1.25:
1.25x/1.25 = 8.75/1.25

x = 7

Solution is 7 refills

Step 5: Check your answer
Plug x = 7 back into the left side of the equation and check if it works out to 23
14.25 + 1.25 (7) = 14.25 + 8.75 = 23

So our answer is correct

Use synthetic division to divide the polynomials.

Answers

Answer:

                           11

8z² + 9z + 12 + -------

                         z  - 1

Step-by-step explanation:

x - c = x - 1

change the sign of -1 to +1

8z³ + z² + 3z -1

1 |  8     1    3   -1

     ↓     8   9   12

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

     8     9   12   11

8z² + 9z + 12 remainder of 11

I hope this helps!

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