solve for x: -3x-7=-8x-57

The expression written in terms of sinx and cosx is

sinx· cos7π/4 - cosx ·sin7π/4

What is an algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given expression is sin(x - 7π/4).

Use the formula for sin(A-B) to rewrite the expression:

sin(x - 7π/4)

= sinx· cos7π/4 - cosx ·sin7π/4

Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4

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By using Unitary method, it can be calculated that

a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g

   Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g

b) 900 g of oats is required to make 16 flapjacks

What is Unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here Unitary method will be required

a) Let Trevor use x g Syrup, 2x g butter and 3x g oats

Trevor uses 200 g syrup

So x = 200

i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g

ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g

b) To make 8 flapjacks 150 g of syrup is used

   To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used

   To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used

   To make 16 flapjacks 300g of syrup is used

   To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used

   To make 16 flapjacks 900 g of oats is used

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By solving a linear inequation, it can be concluded that

The sweater can be worn comfortably

What is a linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥

A one degree inequation is known as linear inequation.

Here, the given linear inequation is

[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]

As 53° F lies between 50 and 62, the sweater can be worn comfortably

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Answer:

27

Step-by-step explanation:

first you multiply 6x4 which is 24 the you divive 15 by 5 you'll get 3 then you add 24 + 3 and your answer is 27

The rules of proof is that every statement should be justified and never assume things when proofing in contradiction

The basic rules of proofs are as followings:

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Answer:

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

Step-by-step explanation:

Information—especially that which is slanted or deceptive—used to advance or publicize a specific political cause or point of view.

Glitzy Generalizations

Use expressions or words that sound appealing and are widely accepted.

Card Arranging

Using only those ideas and facts that support your argument.

Plain people

Tell voters that you are a normal person with same needs and beliefs as theirs.

Testimonial

Persuades people to do something by leveraging their popularity as a celebrity or athlete.

Bandwagon

Encourages a tendency to follow the crowd

Using names

Put a bad name on your opponent.

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

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It is important to make a ten in lower grades to make students understand the subtraction.

According to the question,

We have the following information:

Making a ten

Now, we know that in making a ten method we take 1 from the next left digit of the number from which we are subtracting any other number.  Now, this number 1 is treated as 10 instead of 1 and then 10 is added to the digit to ease subtraction in lower grades.

Now, the subtraction can be easily performed by subtracting the smaller number from the larger number.

Hence, it is important to make tens in lower grades to make students understand the subtraction.

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Answer:

[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]

[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]

Step-by-step explanation:

A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.

Linear functions are not symmetric with respect to the y-axis.

Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.

Cubic functions are not symmetric about the y-axis.

Square root functions are not symmetric about the y-axis.

There are two quadratic functions with x² in the given answer options.

Test to see if they are symmetric with respect to the y-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

Given function:

[tex]y=-6x^2[/tex]

Replace x with (-x):

[tex]\implies y=-6(-x)^2[/tex]

[tex]\implies y=-6x^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

Given function:

[tex]y=4x^2-2[/tex]

Replace y with (-y) and x with (-x):

[tex]\implies y=4(-x)^2-2[/tex]

[tex]\implies y=4x^2-2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.

Linear functions are not symmetric with respect to the x-axis.

Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.

Cubic functions are not symmetric about the x-axis.

Square root functions are not symmetric about the x-axis.

There is one quadratic functions with y² in the given answer options.

Test to see if it is symmetric with respect to the x-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

Given function:

[tex]x=\dfrac{1}{4}y^2[/tex]

Replace y with (-y):

[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]

[tex]\implies x=\dfrac{1}{4}y^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.

Answer:0.5

Step-by-step explanation:

here you go

The solution to the inequality expression is x ≥ - 5

what is inequality expressions ?

Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.

solution:

The given expression - 4(x + 3) ≤ –2 – 2x

                                     - 4x - 12  ≤ -2 - 2x

                                      -4x + 2x  ≤ -2 + 12

                                              -2x  ≤  10

                                               -x  ≤ 5

Multiply  both sides by - 1

Then x ≥ - 5

Hence the solution to the inequality expression is x ≥ - 5

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The value of x in the Algebraic expressions is x = w / (56+r).

What is Algebra?

Algebra is a branch of mathematics focused on the study of mathematical symbols and the rules for manipulating those symbols. In algebra, letters and other symbols represent numbers, which can be manipulated and combined to solve equations and other mathematical problems. Algebra is used in a variety of different fields, from engineering to economics, and is essential for anyone studying mathematics. Algebra can be used to solve problems involving linear equations, quadratic equations, polynomials, and more. Algebra also provides an important foundation for more advanced fields of mathematics, such as calculus. By learning the basics of algebra, students can gain an understanding of key mathematical concepts and gain the skills necessary to solve complex problems.

The solution is,

given:        19x + rx  = -37x + w

            ( 19x + 37x) = w - rx

                56x + rx  = w

                 x(56+r )  = w

                             x = w / (56+r)

Therefore the value of x in the algebraic expression is  x = w / (56+r).

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The equation that can be used to find x is

3x + 6 = 2x + 9

Option E is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Lydia started with 6 charms and bought 3 more packs.

Claudia started with 9 charms and bought 2 more packs.

If each pack had x charms.

This can be written as,

Lydia:

Number of charms = 6 + 3x

Claudia:

Number of charms = 9 + 2x

Now,

Lydia and Claudia have the same number of charms in their collections.

This can be written as,

6 + 3x = 9 + 2x

3x + 6 = 2x + 9

Thus,

The equation that can be used to find x is

3x + 6 = 2x + 9

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Answer:

Subtract 5

Step-by-step explanation:

72 , 67, 62, 57,..

    Each term is obtained by subtracting 5 from the previous term.

72 - 5 = 67

67 - 5 = 62

62 - 5 = 57

The sixth chapter's Brother 0.66 pages were read.

According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.

Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.

Assumed the question is how many pages are in each chapter.

Let it be x:

6x + 8 = 12

6x = 4

x = 4 /6

x = 0.66.

The sixth chapter's Brother 0.66 pages were read.

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Answer:

25 people

Step-by-step explanation:

10 people will be vaccinated for 2hrs

10 = 2

y people will be vaccinated for 5hrs

y = 5

(To find y we need to cross multiply)

10 = 2

y = 5

2y= 50

y=50/2

y=25

:- 25 people will be vaccinated in 5hrs.

Lets check if our answer is correct let us make 5 hrs our unknown x

10 = 2

25 = x

(cross multiply)

25×2=10x

50=10x

x=5hrs

so our answer is correct.

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Answer:

6.40

Step-by-step explanation:

For this we will divide,

look below for a explanation

Purchase Price:

$64

Discount:

(64 x 90)/100 = $57.60

Final Price:

64 - 57.60 = $6.40

The number of distinguishable permutations in the given letters are:

a.) Bigger= 720

b.) Hollywood = 362,880

C.) possess = 5040

Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.

The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720

For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880

For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.

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Answer: 2 and 2/3

Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.

You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.

So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.

This gives us 17/3 ÷ 17/8.

When we divide fractions, we just change the division sign

to multiplication and take the reciprocal (flip) the second fraction.

So we have 17/3 · 8/17.

before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.

So we have 1/3 · 8/1 which is 8/3.

Now since 3 goes into 8 twice, our we have 2 as our whole fraction.

Since there is 2/3 left over, we have a fraction of 2/3.

So our final answer is 2 and 2/3.

The equations are matched as below and the graph is plotted and attached

A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.

The exponential graph is the opposite of logarithmic graph

In the given functions

log (x) is logarithmic function

10× is exponential function

Similarly, the natural exponent graph is the opposite of natural logarithm graph

in the given functions

e× is the natural exponential

ln (x) is the natural logarithm

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The probability for each event are

[A] -  36/1320

[B] -  36/1320

[C] -  36/1320

[D] -  The probability doesn’t change in any order.

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.

[A] -

{3/12} x {3/11} x {4/10} =

36/1320

[B] -

{3/12} x {4/11} x {3/10}

36/1320

{C} -

{4/12} x {3/11} x {3/10}

36/1320

D) The probability doesn’t change in any order.

Therefore, the probability for each event are -

[A] -  36/1320

[B] -  36/1320

[C] -  36/1320

[D] -  The probability doesn’t change in any order.

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Answer:

75%

Step-by-step explanation:

First, you subtract 200 from 350 to get the difference, which is 150.

Then, you do 150 divided by 200 since 200 is the starting number and it is increasing by 150.

150/200 = 0.75

To convert the decimal into a fraction multiply by 100.

0.75*100 = 75

The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters

An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.

The year André planted the cedar hedge tree = 15 years ago

The present height of the hedge = 3 meters = 300 cm

The average rate at which the cedars grew = 12 cm per year

The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;

The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d

Where;

a₁ = The initial height of the tree

d = The amount the tree grows each year = 12 cm

n = The number of years ago, the tree was planted

When n = 15, we get;

a₁₅ = 3 meters = 300 cm

Therefore;

300 = a₁ + (15 - 1) × 12

a₁ = 300 - (15 - 1) × 12 = 132

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The 12 kinds of polygons are:

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Hendecagon

Dodecagon

Tridecagon

Tetradecagon

Polygons:

A polygon is a closed shape figure that has a minimum of three sides and three vertices.

Poly → many

gon → angle

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The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440

From the question, we have

⁸C₇ and ¹¹P₅

The combination expression: ⁸C₇

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 7

Substitute the known values in the above equation

Total = ⁸C₇

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

⁸C₇ = 8!/7!1!

Evaluate

⁸C₇ = 8

(b) The permutation expression: ¹¹P₅

The number of ways of selection could be drawn is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 11 and r = 5

Substitute the known values in the above equation

Total = ¹¹P₅

Apply the permutation formula

ⁿPᵣ = n!/(n - r)

So, we have

¹¹P₅ = 11!/6!

Evaluate

¹¹P₅ = 55440

Hence, the values are 8 and 55440

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Answer:

835786543225644323567

We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.

An discriminant value definition ?

The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

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Answer:

D. The longest side is twice as long as the shortest side.

Step-by-step explanation:

Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.

By using a linear combination, we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:

2,857 = a*100 + b*1

There are multiple solutions for this, we can use b to cover the ones and the tens, so:

57 = b*1

57 = b

And we can use a to cover the hundreds and thousands, so:

2,800 = a*100

2,800/100 = a

28 = a

Then we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

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The Linear equation that represents the above situation is given by

x + 3x + 15 = 63

A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.    

Here given that

Luke and Cade have started running

Luke runs 15 more miles than thrice of that of number of miles Cade runs

Since we don't know the number of miles run by Cade

Let us assume that Cade runs x miles

=> Number of miles run by Cade = x miles

From the given data,

The number of miles run by Luke will be = 3x + 15

=> Number of miles run by Luke and Cade = x + 3x + 15

Given that the total mile run by Luke and Cade =  63 miles  

=> x + 3x + 15 = 63

Therefore,

The Linear equation that represents the above situation is given by  

x + 3x + 15 = 63

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