Multiply −14y(7y − 5).

−98y2 + 70y
−98y2 + 70
−98y2 − 5
98y2 − 70y

Given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j

In this question, we have been given a vector whose initial point is (-2, -1) and the final point is (8, -5)

We need to write vector v as a linear combination of the standard unit vectors i and j.

Let (x1, y1) = (-2, -1) and (x2, y2) = (8, -5)

We know that for vector A having initial point (x1, y1) and terminal point (x2, y2), a linear combination of the standard unit vectors i and j is:

vec A = (x2 - x1)i + (y2 - y1)j

So, for given vector it would be,

vec v = (x2 - x1) i + (y2 - y1) j

vec v = (8 - (-2)) i + (-5 - (-1)) j

vec v = (8 + 2) i + (-5 + 1) j

vec v = 10 i -4 j

Therefore, given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j

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Answer:

Step-by-step explanation:

The integer is 5 and the next consecutive odd integer will be 7.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

let the integer be x

then, next consecutive odd integer will be x + 2

Now, according to the question :

integer is subtracted from 2 times the next consecutive odd integeb the difference is 9 means :

2(x+2) - x = 9

2x+ 4-x = 9

x + 4 = 9

x = 5

Therefore, The integer is 5 and the next consecutive odd integer will be 7.

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There are 29 nickels and 12 dimes in the piggy bank.

In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes.

We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.

Let x be the number of nickels and y be the number of dimes.

We know that, 1 dollar = 20 nickels

and 1 dollar = 10 dimes

So, we get an equation

0.05x + 0.1y = 2.65                   ...........(1)

Also the number of nickels is 7 less than three times the number of dimes.

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

Substitute above value of x in equation (1)

0.05(3y - 7) + (0.1)y = 2.65

0.15y - 0.35 + 0.1y = 2.65

0.25y = 2.65 + 0.35

0.25 y = 3

y = 12

Substitute above value of y in equation  (2)

x = 3(12) - 7

x = 29

Therefore, there are 29 nickels and 12 dimes in the piggy bank.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{5}{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Slope (m) of a line can be calculated by using this formulae :

[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]

Considering two points [ (60 , 0) and (80 , 50) ]

[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{50 - 0}{80 - 60} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{50}{20} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{5}{2} [/tex]

So, slope of given line is 5/2

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

TheThe number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48,135 miles.

Distance from Station 1 to satellite:

tan8.7 = length of longest leg / length of longest leg

tan8.7 =  3963/length of shortest leg

Length of longest leg=3963/tan8.7°

Length of longest leg=3963/0.15302150298

Length of longest leg =25,898 miles

Distance from Station 2 to satellite:

sin 8.7 = length of longest leg / length of hypotenuse

sin  8.7 =  3963/length of hypotenuse

Length of hypotenuse =3963/ sin 8.7

Length of hypotenuse =3963/0.1526082024

Length of hypotenuse=26, 200 miles

Hence,

26, 200 miles  - 3,963 =22,237 miles

Total distance:

Total distance = 25,898 miles  + 22,237 miles

Total distance = 48,135 miles

Therefore the distance is 48,135 miles.

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The complete question is:

A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.

How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?

The function which represents the relation between the perimeter and the length of the square is; y = 4x.

For the given question;

Let x be the side of the square.

Let y be the perimeter of the square.

Perimeter is 4 times the side of the square.

Then,

Perimeter = 4×side

y = 4x.

Thus, the function which describes the relation between the perimeter and the side of square is y = 4x.

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From the tape diagram, your allowance and your friends' allowance is $48 and $32 respectively.

What is tape diagram?

A tape diagram is a visual representation that looks like a piece of tape and is used to help with ratio calculations, addition, subtraction, and most frequently multiplication. A divided bar model, fraction strip, length model, or strip diagram are other names for it. It is employed in mathematics education to help elementary school-aged children solve word problems. Students can use a tape diagram as a pictorial model to represent a mathematical relationship or to better understand a mathematical concept. Although they are frequently used with word problems, tape diagrams are helpful for solving many different kinds of math problems.

Let the ratio is given by 3:2 and total is 5
hence, 5 parts represent $80, so each part represents= 80/5= 16
hence, your allowance is 3×16 =48 and your friend allowance is 2×16= 32

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Answer:

I believe it's 9 people

Step-by-step explanation:

The hiking trail that has the least change in elevation, related to sea level, is:

Southern Moon.

The change in altitude of each trail is calculated as the subtraction of the highest altitude by the lowest altitude, that is:

Change in elevation = highest altitude - lowest altitude.

For Eastern Point, the change is given as follows:

Change = 78 - (-85) = 78 + 85 = 163 feet.

(subtracting by a negative is the same as adding to the positive of the number).

For Northern Star, the change is given as follows:

Change = 34 - (-150) = 34 + 150 = 184 feet.

For Southern Moon, the change is calculated as follows:

Change = 48 - (-62) = 48 + 62 = 110 feet.

The smallest amount is of 110, hence Southern Moon has the least change in elevation relative to sea level.

The table is shown by the image at the end of the answer.

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Answer:

read below

Step-by-step explanation:

1. $4, five granola bars cost $20. $20/5 = $4

2. 40 miles per hour, travels 100 miles at a constant speed for 40 miles. 100/2.5 = 40 miles

3. 12.5 situps per minute, 50 situps in 4 minutes. 50/4 = 12.5

4. $1.43 per one ounce, 3 ounces cost $4.29. 4.29/3 = $1.43

Z is Odd.

Eg :- The Association between Height and Age

This is a relation since you would get various heights if you entered a specific age and checked all the persons of that age. Nevertheless, if you were to look at a person's height over time, it would depend on their age.

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Answer:

10

Step-by-step explanation:

To find the value of the smaller integer, start by letting a variable be that integer. This helps us to refer to the integer with greater ease in our working.

Let the smaller integer be x.

Consecutive numbers refers to numbers coming after one another, such as 1, 2 and 3.

The next integer coming after the integer x would thus be (x +1). Three times the next consecutive integer would then be 3(x +1).

Subtract refers to a minus sign, thus the equation would be:

3(x +1) -x= 23

Expand:

3x +3 -x= 23

Simplify:

2x= 23 -3

2x= 20

Divide both sides by 2:

x= 20 ÷2

x= 10

Thus, the smaller integer is 10.

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*Note that when b is subtracted from a, the expression would be a -b.

Answer:2 to the 5, 8 to the 2, and 4 to the third

Step-by-step explanation:

2x2x2x2x2=64

8x8=64

4x4x4=64

Answer:

x = 40

Step-by-step explanation:

We just have to manipulate the terms, putting each term that has the variable "x" on one side of the equation like this:

5x + 8 = 7x - 72​

5x - 7x = - 72 - 8​

-2x = -80

x = -80/--2

x = 40

Answer:

x = 40

Step-by-step explanation:

Given equation:

[tex]5x+8=7x-72[/tex]

Add 72 to both sides:

[tex]\implies 5x+8+72=7x-72+72[/tex]

[tex]\implies 5x+80=7x[/tex]

Subtract 5x from both sides:

[tex]\implies 5x+80-5x=7x-5x[/tex]

[tex]\implies 80=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{80}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies 40=x[/tex]

Therefore, the solution to the given equation is x = 40.

The coordinates of the vertices of triangle A'B'C' after a reflection over the y-axis to triangle ABC are: C. A' = (3, -3), B' = (6, -3), C' = (5, -6), D' = (0, -6).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (x, y).

By applying a reflection over the y-axis to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:

(x, y)                    →            (x, y)

Point A = (3, -3)   →  Point A' = (3, -3)

Point B = (6, -3)   →    Point B' = (6, -3)

Point C = (5, -6)   →     Point C' = (5, -6)

Point D = (0, -6)   →     Point D' = (0, -6)

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The scale factor of figure A to figure B is 5/2

A scale factor can be defined as the ratio of the scale difference between  a given original shape and a new shape.

It is seen as a number from which the size of a dimensional shape or figure can be transformed with respect to its original size or magnitude.

It is also described as the ratio between corresponding measurements of an object and a representation of that object.

The formula for scale factor is expressed as;

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

This is so for the downgrading of a shape

Now, we have;

Scale factor = Adjacent of the triangle A/adjacent of triangle B

Scale factor = 10/ 4

Reduce to simply forms

Scale factor = 5/ 2

Hence, the scale factor is 5/2

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Answer:

2.4x10^6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

assuming everyone takes their own car, 9.75+17.75 * 7 = 192 I don’t know the state tax, because each state is different but 192 gives about $3 worth of room for tax. If the tax is higher in your state maybe I’d answer with 6 people. Hope this helped!

Answer: 18>=S>=-9

Explanation:

The total surface area of the pyramid (a) is  624.32 cm² , and of pyramid (b) is 265.6 m²  .

The Total Surface Area of the Pyramid with pentagon base can be calculated using the formula

TSA = 5/2*b(a+s) ,

where b is the base length (side of pentagon)

s is the slant height ,

a is the apothem

and the Total Surface Area of the Pyramid with square base can be calculated using the formula .

TSA = b² + 2bs

where , b is the base and

s is the slant height .

Pyramid (a)

we can see from the figure that ,the pyramid has a pentagon base ,

So, the TSA will be 5/2*b(a+s) ,

in the figure , given that height =12 cm , apothem = 7.8cm

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 7.8²

(slant height) = √(12² + 7.8²)

(slant height) = √(144+60.84)

(slant height) = 14.3 cm

Substituting in TSA formula , TSA = 5/2*b(a+s)

we get ,

TSA = 5/2*11.3(7.8+14.3)

= 2.5*11.3(22.1)

= 28.25*22.1

=624.32 cm²

Pyramid (b)

we can see from the figure that ,the pyramid has a square base ,

So, the TSA will be b² + 2bs,

in the figure , given that height =12 m , apothem = 4 m

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 4²

(slant height) = √(12² + 4²)

(slant height) = √(144+16)

(slant height) = 12.6 m

Substituting in TSA formula , TSA = b² + 2bs

we get ,

TSA = 8² + 2*8*12.6

= 64 + 16*12.6

= 64 + 201.6

= 265.6 m²

Therefore , the total surface area of the pyramid (a) is 624.32 cm²  , and of pyramid (b) is 265.6 m² .

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The values of the radical expressions are [tex]\frac{5x^4z^3}{7y}[/tex] and [tex]2x^2y\sqrt{5z}[/tex]

Expressions are mathematical statements that are represented by variables, coefficients and operators

Expression 1

Here, we have

[tex]\sqrt{\frac{25x^8z^6}{49y^2}}[/tex]

Take the square roots of 25 and 49

So, we have

[tex]\frac{5}{7}\sqrt{\frac{x^8z^6}{y^2}}[/tex]

Next, we apply the law of indices in simplifying the radical expressions

This gives

[tex]\frac{5}{7}\frac{x^{(8/2)}z^{(6/2)}}{y^{(2/2)}}[/tex]

Evaluate

[tex]\frac{5}{7}\frac{x^4z^3}{y}[/tex]

Rewrite as

[tex]\frac{5x^4z^3}{7y}[/tex]

Expression 2

Here, we have

[tex]\frac{\sqrt{100x^4y^2z}}{\sqrt 5}}[/tex]

Take the square roots of 100

So, we have

[tex]10\frac{\sqrt{x^4y^2z}}{\sqrt 5}}[/tex]

Rationalize

[tex]10\frac{\sqrt{5x^4y^2z}}{5}[/tex]

Next, we apply the law of indices in simplifying the radical expressions

This gives

[tex]10\frac{\sqrt{5z}x^{4/2}y^{2/2}}{5}[/tex]

Evaluate

[tex]2\sqrt{5z}x^2y[/tex]

Rewrite as

[tex]2x^2y\sqrt{5z}[/tex]

Hence, the solution is  [tex]2x^2y\sqrt{5z}[/tex]

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Answer:

-2(-10x^2 + 3x -5)

Step-by-step explanation:

Combine like terms

Then find the common factor

Answer:

[tex]-20x^{2} -6x+10[/tex]

Step-by-step explanation:

[tex]=-23x^{2} +x^{2} +2x^{2} -6x+10[/tex]

[tex]=-23x^{2} +3x^{2} -6x+10[/tex]

[tex]=-20x^{2} -6x+10[/tex]

Hope this helps

To convert Celsius to Fahrenheit, we take the given Celsius measurement, multiply it by 1.8, and add 32, and vice versa.

To convert Celsius to Kelvin, we add 273 into the given Celsius measurement, and vice versa.

1) 18oC to F and to K

18oC = 18 x 1.8 + 32 = 64.4oF = 18 + 273 = 291oK

2) 95oF to C to K

95oF = (95-32) : 9/5 = 35oC = 35 + 273 = 308oK

Triangle A is right angled triangle

Triangle B is right angled triangle

Triangle C is obtuse angled triangle

Triangle D is acute angled triangle

In right angled triangle one of the three angles in the triangle is 90 degrees

In acute angled triangle all the angels in the triangle is less than 90 degrees

In obtuse angled triangle one of the three angles in the triangle is greater than 90 degrees

In triangle A one of the angle is 90 degrees, then the triangles is right angled triangle

In triangle B one of the angle is 90 degrees, then the triangles is right angled triangle

In triangle C one of the angle is greater than 90 degrees, then the triangle is obtuse angled triangle

In triangle D all the angles are less than 90 degrees, then the triangle is acute angled triangle

Hence, Triangle A is right angled triangle

Triangle B is right angled triangle

Triangle C is obtuse angled triangle

Triangle D is acute angled triangle

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The temperature when the pressure is 450 is 225°.

Given:

The pressure of a gas varies directly with the temperature.

So, P ∝ T

P = kT , here k is the constant of proportionality

Pressure(P) = 800psi

Temperature(T) = 400°

Putting the values to get the value of k,

P = kT

800 = 400k

k = 2

We need to find the temperature when the pressure is 450.

​P = kT

450 = 2T

T = 450/2

T = 225°

Therefore, the required temperature is 225°.

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The items matched in the left column to the items in the right column are

Ratio is the number representing a comparison between two named things or quantities.

1. total to fish

= 8 : 3

2. starfish to fish

= 5 : 3

3. starfish to total

= 5 : 8

4. fish to starfish

3 : 5

In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5

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