1) Solve for a
a+6=6 a-5= -8 a x -10= 100 (5+2a) ÷ 17 = 3

2) A rectangular field has an area of 49m. If its not a square field and the dimension is a whole number then
a) What are the dimensions of the field?
b) What is the perimeter of the field?
c) Make an equation that shows how you could find the answer to A



3) The following are the first 5 terms in a patterns: 3,5,7,9,11...
a) Make a T chart of term
b) Come up with a pattern rule relating T and V

Answer:

x = - 144

Step-by-step explanation:

Given

\(\frac{x}{6}\) + 12 = - 12 ( subtract 12 from both sides )

\(\frac{x}{6}\) = - 24 ( multiply both sides by 6 )

x = - 144

Answer:

11 1/2 miles per hour is the answer I believe

Answer:

I have no clue but good luck

Step-by-step explanation:

The error in writing the rule for the nth term of the geometric sequence is in the step where the value of a₁ is determined. The correct value for a₁ is √(147/49) or √3, not √√21.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio (r). The general formula for the nth term (aₙ) of a geometric sequence is given by aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.
Given that a₃ = 147 and r = 7, we can find the value of a₁ by substituting these values into the formula. Let's correct the error in the calculation step:
a₃ = a₁ * r^(3-1)
147 = a₁ * 7²
147 = a₁ * 49
To isolate a₁, we divide both sides of the equation by 49:
a₁ = 147 / 49
a₁ = 3
Therefore, the correct value for a₁ in the geometric sequence is 3, not √√21 as stated in the error.

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Given

Find

derivatives using increment method.

Explanation

Given

replace x and y by

so ,

now divide by

so ,

now taking limit

Final Answer

Therefore , the derivative of the function using increment method is 12x + 10

The answer is C (x = 91.2)

Step-by-step explanation:

x - 15.2 = 76

x = 76 + 15.2

x = 91.2

After divide, the solution of the expression is,

⇒ x (x + 2y) / 5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (x² - 4y²) ÷ (5x - 10y) / x

Now, We an simplify as;

⇒ (x² - 4y²) ÷ (5x - 10y) / x

⇒ (x² - (2y)²) ÷ (5x - 10y) / x

⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x

⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)

⇒ x (x + 2y) / 5

Thus, The solution of the expression is,

⇒ x (x + 2y) / 5

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If a storage facility charges $1 per cubic yard and the storage space is 32 ft. The storage charge is $1999.97.

What is mathematical conversions?

Mathematical conversions refer to the process of changing one unit of measurement to another unit of measurement that is equivalent in value.

First, we need to convert the dimensions from feet to yards, since the rate is given per cubic yard.

32 feet = 10.6667 yards (dividing by 3)

160 feet = 53.3333 yards (dividing by 3)

10 feet = 3.3333 yards (dividing by 3)

Next, we can calculate the volume of the storage space in cubic yards by multiplying the three dimensions:

Volume = 10.6667 yards x 53.3333 yards x 3.3333 yards

Volume = 1999.97 cubic yards (rounded to two decimal places)

Finally, we can calculate the storage charge by multiplying the volume by the rate:

Charge = 1999.97 cubic yards x $1/cubic yard

Charge = $1999.97

Therefore, the storage charge is $1999.97.

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Answer:

B is the correct chose

Step-by-step explanation:

In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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Answer:

x=10

Step-by-step explanation:

3x+10=6x-20 Set the angles equal to each other b/c they are alt. int. angles.

-3x       -3x Subtract by 3x on both sides to get x by itself

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

+10    =3x-20

+20         +20 Add 20 to both sides to get x by itself

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

30    =3x

/3        /3 Divide both sides by 3 to get x by itself

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

10    =x

x=10 Write x first.

To verify that the vector xp is a particular solution of the given nonhomogeneous linear system, we need to substitute xp into the system and check if it satisfies the equation.

The given nonhomogeneous linear system can be written in the form x' = Ax + f, where A is the coefficient matrix (2 1 1 -1) and f is the constant vector (-5 2). The vector xp = (1 3) is a particular solution if it satisfies the equation x' = Ax + f.

Substituting xp into the equation, we get:

x' = (2 1 1 -1) (1 3) + (-5 2)
  = (1 -1 2 -8)

Therefore, the left-hand side of the equation is:

x' = (1 -1 2 -8)

And the right-hand side is:

Ax + f = (2 1 1 -1) (1 3) + (-5 2)
       = (1 -1 2 -8)

Since the left-hand side is equal to the right-hand side, we can conclude that the vector xp = (1 3) is indeed a particular solution of the given nonhomogeneous linear system.

We have verified that the vector xp = (1 3) is a particular solution of the given nonhomogeneous linear system by substituting it into the equation and checking if it satisfies the equation.

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Answer:

372

Step-by-step explanation:

Since we know the total weight which is 714 and we know the weight of one garden which is 342, all we need to do now is subtract:

714 - 342 = 372

Answer:

The second and third choices are true

Step-by-step explanation:

In mathematics, a translation is a type of transformation where the object is moved horizontally and/or vertically, but it is not resized, reshaped, or rotated. To create R'T', the segment RT can be moved up, down, left, right, or diagonally. However, the length will be the same.

The first choice is incorrect because R'T' is the same length as RT, so it is definitely not shorter. That being said, the second statement must be correct because the length is the same.

The third choice is also correct. R'T' will be in a different position because it will have been translated, but the orientation will be the same (orientation typically refers to rotation, and the line is not rotated in a translation).

The fourth choice is incorrect because R'T' is not a rotation (so it is not turned). The fifth statement is incorrect because the only ways to switch the positions of R and T would be rotation or reflection (two other types of transformations). Finally, the last choice is incorrect because the line is moved, so there is a position change involved.

Therefore, the second and third choices are true

The length of the rectangle is 23 km and the width of the rectangle is 15 km.

A rectangle is 8 km longer than it is wide.

Its area is 345 sq-km.

Let the width of the rectangle is x.

The length is 8 km longer than the width.

So the width of the rectangle is x + 8 km.

The formula of the area of rectangle is:

A = length × width

We know A = 345 sq-km.

Now putting the value

x × (x + 8) = 345

Now simplifying

x^2 + 8x = 345

Subtract 345 on both side, we get

x^2 + 8x - 345 = 0

Now factor the equation

x^2 + (23 - 15)x - 345 = 0

x^2 + 23x - 15x - 345 = 0

x(x + 23) - 15(x + 23) = 0

(x - 15)(x + 23) = 0

Now equation the factor equal to zero.

x - 15 = 0           or             x + 23 = 0

x = 15                or              x = -23

Since the dimension of the rectangle can't be negative. So

The width of the rectangle is 15 km.

Now we determine the value of length

x + 8 = 15 + 8 = 23

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

volume of a pyramid is Length×Base×Height/3 (divided by 3)

Answer:

The volume of the pyramid is easy

Step-by-step explanation:

Answer:

Given:

To Find:

Solution:

First, we have to find the Circumference of the Wheel:

As, we know:

\( \bigstar \:{\boxed{ \rm{Circumference_{(Circle)} = 2 \pi r }}} \: \bigstar\)

where,

So, the Circumference of wheel will be:

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = 2 \times \frac{22}{7} \times 1.75 }}}} \)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{2 \times 22}{7} \times 1.75}}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44}{7} \times 1.75 }}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44 \times 1.75}{7} }}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{77}{7} }}}}\)

\({\large{\rm{\dashrightarrow{Circumference_{(Wheel)} ={ \boxed{ \rm{ \red{11m}}}}}}}}\)

Hence, the circumference of the wheel is 11m.

Now, we have to convert distance covered km into m:

\({\leadsto{\large{\rm{ \: Distance \: Covered = 22km}}}}\)

\({\leadsto{\large{\rm{ \: Distance \: Covered =(22 \times 1000)m }}}}\)

\({\leadsto{\large{\rm{ \: Distance \: Covered = {\boxed{\rm{\red{22000m}}}}}}}}\)

Hence, the distance covered is 22000m.

Now, we have to find the number of revolution:

Given:

According to the question by using the formula, we get:

\( \bigstar \: { \boxed{ \large{ \rm{Number \: of \: Revolution \: = \: \frac{Distance \: Covered}{Circumference }}}}}\)

\({ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = \frac{22000}{11} }}}}\)

\({ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = { \boxed{\red{2000}}}}}}}\)

Answer: 1 1/2

Step-by-step explanation:

First subtract 1 1/3 from 3 1/3 to find what is left over from her first batch of browns, 2. Then subtract 1 1/3 from 2 and get 2/3. 2/3 is 1/2 of 1 1/3, so she can make 1 1/2 more batches of brownies.

Answer:

C

Step-by-step explanation:

Report if wrong

-Stylez-

Answer: look at the picture

Step-by-step explanation: Hope this help :D

Answer:

x=30.2

Step-by-step explanation:

30.2-20.7=9.5 So therefore x=30.2

The equation for the set of points equidistant from the point P(-9, 2) and the line l: x = -3 is\((x + 3)^2 + (y - 2)^2 = 121.\)

To find the equation for the set of points equidistant from a point and a line, we first consider the distance formula. The distance between a point (x, y) and the point P(-9, 2) is given by the distance formula as sqrt(\((x - (-9))^2 + (y - 2)^2).\)

Next, we consider the distance between a point (x, y) and the line l: x = -3. Since the line is vertical and parallel to the y-axis, the distance between any point on the line and a point (x, y) is simply the horizontal distance, which is given by |x - (-3)| = |x + 3|.

For the set of points equidistant from P and the line l, the distances to P and the line l are equal. Therefore, we equate the two distance expressions and solve for x and y:

sqrt(\((x - (-9))^2 + (y - 2)^2) = |x + 3|\)

Squaring both sides to eliminate the square root and simplifying, we get:

\((x + 3)^2 + (y - 2)^2 = (x + 3)^2\)

Further simplification leads to:

(y - 2)^2 = 0

Hence, the equation for the set of points equidistant from P and the line l is \((x + 3)^2 + (y - 2)^2 = 121.\)

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Answer:

yehshjdjejrdjjej3u Rudd ixjje

Answer:

-2,7

Step-by-step explanation:

\(\huge\bold\red{Answer:-}\)

Step by step solution :

STEP 1 : Trying to factor by splitting the middle term

1.1 Factoring x2+5x-14

The first term is, x2 its coefficient is 1 .

The middle term is, +5x its coefficient is 5 .

The last term, "the constant", is -14

Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14

Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is 5 .

-14 + 1 = -13

-7 + 2 = -5

-2 + 7 = 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 7

x2 - 2x + 7x - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-2)

Add up the last 2 terms, pulling out common factors :

7 • (x-2)

Step-5 : Add up the four terms of step 4 :

(x+7) • (x-2)

Which is the desired factorization.

Equation at the end of step 1 :

(x + 7) • (x - 2) = 0

STEP 2 : Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x+7 = 0

Subtract 7 from both sides of the equation :

x = -7

Solving a Single Variable Equation:

2.3 Solve : x-2 = 0

Add 2 to both sides of the equation :

x = 2

Supplement : Solving Quadratic Equation Directly

Solving x2+5x-14 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2+5x-14

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000

Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :

y = 1.0 * -2.50 * -2.50 + 5.0 * -2.50 - 14.0

or y = -20.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2+5x-14

Axis of Symmetry (dashed) {x}={-2.50}

Vertex at {x,y} = {-2.50,-20.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = {-7.00, 0.00}

Root 2 at {x,y} = { 2.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2+5x-14 = 0 by Completing The Square .

Add 14 to both side of the equation :

x2+5x = 14

Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4

Add 25/4 to both sides of the equation :

On the right hand side we have :

14 + 25/4 or, (14/1)+(25/4)

The common denominator of the two fractions is 4 Adding (56/4)+(25/4) gives 81/4

So adding to both sides we finally get :

x2+5x+(25/4) = 81/4

Adding 25/4 has completed the left hand side into a perfect square :

= x2+5x+(25/4)

= (x+(5/2)) • (x+(5/2))

= (x+(5/2))2

Things which are equal to the same thing are also equal to one another. Since

x2+5x+(25/4) = 81/4 and

x2+5x+(25/4) = (x+(5/2))2

then, according to the law of transitivity,

(x+(5/2))2 = 81/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

= (x+(5/2))2 is

= (x+(5/2))2/2

= (x+(5/2))1

=x+(5/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x+(5/2) = √ 81/4

Subtract 5/2 from both sides to obtain:

x = -5/2 + √ 81/4

Since a square root has two values, one positive and the other negative

x2 + 5x - 14 = 0

has two solutions:

x = -5/2 + √ 81/4

or

x = -5/2 - √ 81/4

Note that √ 81/4 can be written as

√ 81 / √ 4 which is 9 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2+5x-14 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = 5

C = -14

Accordingly, = B2 - 4AC

=25 - (-56)

= 81

Applying the quadratic formula :

-5 ± √ 81

x = —————

2

Can √ 81 be simplified ?

Yes! The prime factorization of 81 is

3•3•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 81 = √ 3•3•3•3 =3•3•√ 1

= ± 9 • √ 1

= ± 9

So now we are looking at:

x = ( -5 ± 9) / 2

Two real solutions:

x =(-5+√81)/2=(-5+9)/2= 2.000

or:

x =(-5-√81)/2=(-5-9)/2= -7.000

Two solutions were found :

The fraction computed shows that 9/32 of the shapes are circles.

Find the equivalent ratio for the total shapes:

Total Black Shapes : Total White Shapes = 5 : 11

Multiply by 2:

Total Black Shapes: Total White Shapes = 10 : 22

Find the ratio for the white shapes:

White circles : White squares = 3 : 7

Sum of the units = 3 + 7

Sum of the units = 10

Find the equivalent ratio for the total shapes:

Black circles : Black squares = 3 : 8

Multiply by 2:

Black circles : Black squares = 6 : 16

Sum of the units = 6 + 16

Sum of the units = 22

Combine the ratios:

white circles : white squares : black circles : black square = 3 : 7 : 6 : 16

Circles = 3 + 6

Circles = 9 units

Total = 3 + 7 + 6 + 16

Total = 32 units

Find the fraction of all the shapes that are circles:

Fraction = 9/32

Therefore, 9/32 of the shapes are circles

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Find the biggest common factor between the ratio's two terms to write the ratio in its simplest form. The largest number that equally divides both numbers is known as the greatest common factor of two numbers.

1 : 1/2 = 2 : 1

Add whole numbers to the values.

Create a fraction with the full number 1 as the denominator.

Next, we have:

1 : 1/2 = 1/1 : 1/2

Remove the denominators from fractions to convert them to integers.

We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.

1 1/3 : 4 4/7 = 7 : 24

There are now:

1 1/3 : 4 4/7 = 4/3 : 32/7

Remove the denominators from fractions to convert them to integers.

We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.

0.360 : 0.153 = 40 : 17

Add whole numbers to the values.

By multiplying both sides by 103 = 1000 to remove all three decimal places, you can convert any decimal values to integers.

Next, we have:

0.360 : 0.153 = 360 : 153

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Answer:

90 degrees counterclockwise

Step-by-step explanation:

Answer:

jfmfmhhcmcmfnf. cbimvncnvnj

The answer is 39 degrees