Identify the variable expression for “Two times the difference of x and the square of 7”

The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8) thus option (A),(B) and (D) are correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

3x - y = 1

Substitute, x = -2

3(-2) - y = 1

y = -7 thus  (-2,-7) satisfied.

Similarly (-1,-4) and (3,8) are also satisfied.

Hence "The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8)".

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Answer:

Step-by-step explanation:

You need a take a picture so I know what question your talking about

To know if the equation of this line k(x) = 3x - 6 is true, you should determine its slope and then write the equation in slope-intercept form.

In Mathematics, the y-intercept of any graph generally occur at the point where the value of "x" is equal to zero (x = 0), which is -6 in this scenario.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Making slope (m) the subject of formula, we have the following:

Slope, m = (y - c)/x

Slope, m = (0 - (-6))/2

Slope, m = (0 + 6)/2

Slope, m = 6/2

Slope, m = 3.

For the equation of this line, we have the following:

y = mx + c

y = k(x) = 3x - 6 (True)

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Answer:

c, d, f

Step-by-step explanation:

acute angles are small and less then 90 degrees so we know if it’s wide it’s not acute it’s an obtuse angle

Angle a is a right angle because of the box it has which is 90 degrees

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Answer:

f, e, c, d

Step-by-step explanation:

Angles that are acute are less than 90 degrees only. Not over, not exactly 90, but only below.

F is an acute angle.

A is a right angle.

B is an obtuse angle.

C is an acute angle.

D is an acute angle.

E is an acute angle.

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Answer:

f(x)

Step-by-step explanation:

the function g(x) has y-interception in point (0;0), the function f(x) has y-interception in point (0; 1/3). For more details see the attachment.

The student who can write more words per minute is Marcus because he writes at a speed of 1.3 words per second, that is, in one minute he writes 79.8 words while Rhys writes at a speed of 1.1 words per second and in one minute he writes 66.66 words.

To identify the speed at which students write we must divide the number of words the student writes in time (seconds) as shown below.

Marcus

Rhys

Using the information above, we need to multiply the number of words each student types per second by the number of seconds that equals one minute.

Rhys

Marcus

According to the information above, Marcus has a faster typing speed than Rhys because he types 79.8 words in one minute, while Rhys types 66.6 words in the same time.

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Using the substitution the system of equations y + 4 = x and 10x + 2y + 16 is solved to be

Substitution involves replacing a value with it's equal

The given equation include

y + 4 = x

10x + 2y + 16

substituting x = y + 4 into 10x + 2y + 16

10x + 2y + 16

= 10(y + 4) + 2y + 16

= 10y + 40 + 2y + 16

collecting like terms

= 12y + 16

12y = -16

y = -16/12

y = -4/3

substituting y = -4/3 into x = y + 4

x = -4/3 + 4

x = 8/3

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Answer:

Approximately 51.21 cm

Step-by-step explanation:

to find circumference we multiply the diameter by pi

16.3pi

51.21 cm

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Answer:

C = 51.182 cm

Step-by-step explanation:

The circumference is given by

C = pi * d  where d is the diameter

C = pi * 16.3

C = 16.3 pi

We can approximate pi by 3.14

C = 16.3 * 3.14

C = 51.182 cm

Answer:

y= -x+1

Step-by-step explanation:

The slope of a line that is perpendicular to a graph is equal to the negative reciprocal of the graph's slope.

slope = 1  negative reciprocal = - (1/1) = -1

Now, you have to find the y-intercept by using the given points (3,-2) and the slope that was found (-x)

y= -x+b

-2=-3+b

1=b

y= -x+1

The given graph of the function f (x) = 4x² will be facing up , has a minimum and it's horizontally compressed.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The graph of the function f(x) = 4x² compares to its parent function

f(x) = x².

Now,

By graph we have;

Function f (x) = 4x² is facing up because it is positive function.

And, It has a minimum because any quadratic function that faces up will have a minimum.

Since, In the figure below, f(x)=4x² (red) has more slope, So it's condensed toward the y-axis.

Hence, if the coefficient is bigger than 1, then the function will be horizontally compressed.

Thus, It's horizontally compressed.

Therefore, The given graph of the function f (x) = 4x² will be facing up , has a minimum and it's horizontally compressed.

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Step-by-step explanation:

Solve the inequality for x.

10x > 9(2x - 5) - 11

10x > 18x - 45 - 11

10x > 18x - 56

subtract 18x from both sides:

10x - 18x > 18x - 56 - 18x

-8x > - 56

divide both sides by -8 and remember to flip the sign:

-8x/-8 < - 56/-8

x < 7

This means that x can be any number below 7.

In set builder notation: (-∞ , 7).

Answer:

A.  56

Step-by-step explanation:

Let the three consecutive integers be:

Given:

Create an equation with the given information and solve for x:

[tex]\implies x+(x+1)+(x+2)=2x+30[/tex]

[tex]\implies 3x+3=2x+30[/tex]

[tex]\implies 3x+3-2x=2x+30-2x[/tex]

[tex]\implies x+3=30[/tex]

[tex]\implies x+3-3=30-3[/tex]

[tex]\implies x=27[/tex]

Therefore, the three consecutive integers are:

So the sum of the first and last integer is:

[tex]\implies 27+29=56[/tex]

Answer:

a) 56 --- (27, 28, 29)

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) + (x + 2) = 2x + 30

Now the value of x will be,

→ x + (x + 1) + (x + 2) = 2x + 30

→ x + x + 1 + x + 2 = 2x + 30

→ 3x - 2x = 30 - 3

→ [ x = 27 ]

The last integer will be,

→ x + 2

→ 27 + 2 = 29

Sum of first and last integer is,

→ x + (x + 2)

→ 27 + (27 + 2)

→ 27 + 29 = 56

Hence, required answer is 56.

Answer:

7650 rupees

Step-by-step explanation:

Use I = Pnr

Here P = Principal = 20000 rupees

n = time = 4.5 years

r = rate of interest = 8.5% = 8.5/100

Answer:

Number 2

Step-by-step explanation:

The given term of the arithmetic sequence is -18. The correct option is (A).

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

The given arithmetic sequence is as below,

27, 22, 17, 12, 7, 2,...

Since the nth term of an arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

Where d is the common difference.

The common difference for the given sequence is,

d = 22 - 27

  = -5

Substitute d = -5 and n = 10 in the general form of nth term to obtain,

a₁₀ = a₁ + (n - 1)d

     = 27 + -5(10 - 1)

     = 27 - 45

     = -18

Hence, the value of the 10th term of the given sequence is -18.

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The length of the rectangular garage will be 13 while the width will be 10.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

The perimeter of the rectangle = 2( length + width).

It is known that,

Area of rectangle = length × width.

130 = L× W

L = 130/W

The perimeter of the rectangle = 2( length + width).

46= 2( L+ W)

L + W = 23

130/W + W = 23

130 + W² = 23W

W² - 23W + 130 = 0

W² -13W - 10W + 130 = 0

W(W - 13) -10(W - 13) = 0

(W - 13)(W - 10) = 0

W = 13,10

For W = 13

L = 23 - 13 = 10

For W = 10

L = 23 - 10 = 13

Let's say the bigger dimension is the length and the smaller is the width.

Length = 13 and Width = 10

Hence "The length of the rectangular garage will be 13 while the width will be 10".

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Answer:

m = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac = 0 then the roots are real and equal

• if b² - 4ac < 0 then roots are not real

For

(m + 1)t² + 5 = - 6t ( add 6t to both sides )

(m + 1)t² + 6t + 5 = 0 ← in standard form

with a = m + 1 , b = 6 , c = 5

for the equation to have only one solution then

b² - 4ac = 0

6² - 4 × (m + 1) × 5 = 0

36 - 20(m + 1) = 0 ( subtract 36 from both sides )

- 20(m + 1) = - 36 ( divide both sides by - 20 )

m + 1 = [tex]\frac{-36}{-20}[/tex] = [tex]\frac{9}{5}[/tex] ( subtract 1 from both sides )

m = [tex]\frac{4}{5}[/tex]

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

What is a transformation of a shape?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

If the geometry is rotated, then there is no change in angles.

The translation does not change the shape and size of the geometry. But changes the location.

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

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Disclaimer

The question given by you is incomplete, so a similar question have been solved here and the image is attached.

Determine a series of transformations that would map Figure M onto Figure N.

Answer: 105 words

Step-by-step explanation:

15x7=105

Answer:

focusing is your key to get this

Step-by-step explanation:

The cosine and sine functions are presented as follows;

(a) cosine function is; f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) f(x) = -5·sin((4/3)·x - 530/3) + 2.5

A sine function is a periodic function used bases on the sine of an angle.

(a) The cosine function is f(x) = a·cos(b·x - c) + k

Where;

a = The amplitude

The amplitude = (Max - Min)/2

Therefore;

a = (7.5 - (-2.5))/2 = 5

f = b/(2·π)

c = The phase shift

k = The vertical shift

The minimum is at x = 200° = (200/360)·(2·π) = 10·π/9

The period = 270° = 3·π/2

Frequency, f = 2/(3·π)

b = 2·π·f = 2·π×2/(3·π) = 4/3

When the function is at the minimum point, θ = π

Therefore;

(4/3)×(10·π)/9 - c = π

c = 13·π/27

k = The minimum value + a

Therefore, k = -2.5 + 5 = 2.5

The cosine function is therefore;

f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) The negative sine function is found as follows;

f(x) = a·sin(b·x - c) + k

b = 4/3

k = 2.5

Minimum point sin((4/3)200 - c) = 180

((4/3)200 - c) = 180

c = 260/3

Using a negative sign function, we get;

((4/3)200 - c) = 90

c = 530/3

The equation is therefore;

f(x) = -5·sin((4/3)·x -530/3) + 2.5

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Answer:

answer is 3.2

Step-by-step explanation:

Simplifying

8[4 + -1a] = 2a

[4 * 8 + -1a * 8] = 2a

[32 + -8a] = 2a

Solving

32 + -8a = 2a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2a' to each side of the equation.

32 + -8a + -2a = 2a + -2a

Combine like terms: -8a + -2a = -10a

32 + -10a = 2a + -2a

Combine like terms: 2a + -2a = 0

32 + -10a = 0

Add '-32' to each side of the equation.

32 + -32 + -10a = 0 + -32

Combine like terms: 32 + -32 = 0

0 + -10a = 0 + -32

-10a = 0 + -32

Combine like terms: 0 + -32 = -32

-10a = -32

Divide each side by '-10'.

a = 3.2

Simplifying

a = 3.2

Answer:

a = 3.2

Step-by-step explanation:

if the linear equation is: 8 (4-a)=2a the value of a would be 3.2 because

a = 16/5 which equals to 3 1/5 which is the same as 3.2

Answer:

simplify 8/6, and you get 4/3.

This is a coincidence, because this is a Pythagorean triple,

which means: opp = 4, adj = 3, hyp = 5

now, we can solve the rest easily

sin(0) = 4/5

cos(0) = 3/5

sec = 5/3 (opposite of cos)

The measure of angle VUT is ∠VUT = 70°.

What are angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

In the given figure, ∠RVU and ∠UVT are in linear pair, so by using the property of angles in a linear pair, we can write

                ∠RVU + ∠UVT = 180°

                  120° + ∠UVT = 180°

                         ∠UVT = 60°

Now as we know the sum of all angles of a triangle is equal to 180°,

               ∠UVT + ∠VTU + ∠VUT = 180°.

                   60° + 50° + ∠VUT =180°

                       110° + ∠VUT = 180°

                        ∠VUT = 180° - 110°

                        ∠VUT = 70°

Hence, the measure of angle VUT is ∠VUT = 70°.

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y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3, 19)

What is a gradient?

A straight line's steepness can be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative. A line's gradient can either be uphill (positive value) or downward (negative value).

Here, we have

Equation of line

y = mx  + c

m = Slope of line = Gradient  = 6

= y = 6x + c

a line passes through (3, 19)

so, we find the value of c

= 19 = 6(3)  + c

= c = 1

Now, we put the value of c in the equation and we get

= y = 6x  + 1

Hence,y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3  19)

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Answer:

-33

Step-by-step explanation:

just fill in the values

3-6^2

3-36

-33

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Answer:

-33

Step-by-step explanation:

a = 3; b = -6

a - b² = 3 - (-6)² = 3 - 36 = -33

The Vertical opposite angles are ∠1 = 141° ; ∠2 = 39° ; ∠3 = 141° ; ∠4 =39°

The given angle cover the whole circle which will have 360°

∠1 + ∠2 +∠3 + ∠4 = 360°

∠1 + 39° +∠3 + ∠4 = 360°

Vertically Opposite angle:

Hence, ∠1  = ∠3 and ∠2 = ∠4. So  ∠4 = 39°

∠1 + 39° +∠3 + 39° = 360°

Let x be the ∠1 and ∠3;

x + 39° +x + 39° = 360°

2x = 360° - 78°

2x = 282°

x = 141°

Now, we know all the angles with respect to Vertical opposite Angles  .

∠1 = 141°

∠2 = 39°

∠3 = 141°

∠4 =39°

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Using the ratio of 2:5 to make the shade, we need 5.7L of red paint and 28.6L of yellow paint.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

This is basically a fraction that represents the number of times a quantity is greater or less than another.

To make the orange shade, we simply need to add them in ratio of 2:5. This has to be solved using the fraction and ratio.

2 + 5 = 7

(2/7) * 20 = 5.7 L

(5 / 7) * 40 = 28.6L

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Answer:

A) [tex]\frac{484}{7}[/tex]cm

B)[tex]44[/tex]in

C)[tex]\frac{880}{7}[/tex]mi

D)[tex]\frac{660}{7}[/tex]yd

Step-by-step explanation:

The formula for the circumference of a circle is:

[tex]C=2\pi r[/tex]

Within the problem it is stated to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex] so our equation will be:

[tex]C=2\frac{22}{7}r[/tex] which simplifies to  [tex]C=\frac{44r}{7}[/tex]

The variable [tex]r[/tex] in the equation for the circumference represents 'radius' which is half the diameter, for circle's A and C we are given a diameter. We can divide these numbers in half to get a radius. From there we plug in each radius to get circumference of each circle!

A)

[tex]\text{Diameter}=22\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{22}{2}=11\\\text{Circumference}=\frac{44(11)}{7}=\frac{484}{7}[/tex]

B)

[tex]\text{Radius {\it (r)}}=7\\\text{Circumference}=\frac{44(7)}{7}=\frac{308}{7}=44[/tex]

C)

[tex]\text{Diameter}=40\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{40}{2}=20\\\text{Circumference}=\frac{44(20)}{7}=\frac{880}{7}[/tex]

D)

[tex]\text{Radius {\it (r)}}=15\\\text{Circumference}=\frac{44(15)}{7}=\frac{660}{7}[/tex]

Remember to include units of measurement in your answers.