PLEASE HELP REALLY IMPORTANT The price of a container of laundry detergent (in dollars)
varies with the size (x) of the container (in pounds). The
variables have a strong linear correlation and the equation
for the least squares regression line is y^= 0.86x + 0.52
Based on the regression equation, which is the best
prediction for the price of a 70-pound container of detergent?
$70
$86
$65
$60

The average rate of change for the function f(x)= 3^x + 25 using the intervals of x=2 to x=6 is 6.75

The function is given as:

f(x) = 3^x + 25

The interval is given as:

x = 2 to 6

Start by calculating f(2) and f(6)

f(2) = 3^2 + 25 = 34

f(6) = 6^2 + 25 = 61

The average rate of change is then calculated as:

\(m = \frac{f(6) - f(2)}{6 -2}\)

This gives

\(m = \frac{61 - 34}{6 -2}\)

\(m = \frac{27}{4}\)

m = 6.75

Hence, the average rate of change is 6.75

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The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

6turns

Step-by-step explanation:

Circumference= 1turn

Circumference=πd

22/7 × 49

=154cm

1turn =154cm

?=924cm

924÷154=6turns

Step-by-step explanation:

Here, two angles i.e, (x + 13)° and (4x + 2)° are forming a straight line, thus the sum of these two angles will be 180° because they are forming a linear pair.

\(\longrightarrow\) (x + 13) + (4x + 2) = 180°

\(\longrightarrow\) x + 13 + 4x + 2 = 180°

\(\longrightarrow\) 5x + 15 = 180°

\(\longrightarrow\) 5x = 180° ― 15

\(\longrightarrow\) 5x = 165°

\(\longrightarrow\) x = 165° ÷ 5

\(\longrightarrow\) x = 33°

Therefore, the value of x is 33°.

Quick Check!

\(\longrightarrow\) x + 13

\(\longrightarrow\) (33 + 13)°

\(\longrightarrow\) 46°

And, another angle :

\(\longrightarrow\) (4x + 2)°

\(\longrightarrow\) {4(33) + 2}°

\(\longrightarrow\) (132 + 2)°

\(\longrightarrow\) 134°

★ Sum of the angles should be 180° :

\(\longrightarrow\) (x + 13) + (4x + 2) = 180°

\(\longrightarrow\) 46° + 134° = 180°

\(\longrightarrow\) 180° = 180°

L.H.S = R.H.S, hence verified!

The value of x is 33

"It is  a mathematical statement which consists of equal symbol between two algebraic expressions."

"Two angles are supplementary angles if the sum of the angles is 180° "

For given question,

angle (x + 13) and angle (4x + 2) form linear pair of angles.

So, these angles are supplementary angles.

⇒ (x + 13)° + (4x + 2)° = 180°

We solve above equation to find the value of x

⇒ x + 4x + 13 + 2 = 180

⇒ 5x + 15 = 180

⇒ 5x = 165

⇒ x = 33

Therefore, the value of x is 33

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x > - 1

x ∈ ( - 1 ; + oo)

Hi there !

x + 5 > 4

x > 4 - 5

x > - 1

x ∈ ( - 1 ; + oo)

Good luck !

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

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Answer:

The correct snswer is

There are three basic methods for solving quadratic equations:factoring, using the quadratic formula, completing the square.

Step-by-step explanation:

hope this works out!!!

10√2

Step-by-step explanation:

i thin so it will be ans

Answer:

\( y = \frac{2}{3}x - 6 \)

Step-by-step explanation:

Recall that the the equation of a line in slope-intercept form is given as \( y = mx + b \).

m = the slope of the line

b = the y-intercept. This is the point at which the line intercepts the y-axis.

We are given:

slope (m) = ⅖

y-intercept (b) = -6

All you need to do to get an equation of the line is to simply substitute m = ⅔ and b = -6 into \( y = mx + b \).

\( y = \frac{2}{3}x + (-6) \)

\( y = \frac{2}{3}x - 6 \)

The equation for the line is .\( y = \frac{2}{3}x - 6 \)

Answer:

18 degrees

Step-by-step explanation:

If <ABC and <DEF are complementary, m<ABC + m<DEF = 90 degrees. So M<DEF = 90 - 72 = 18 degrees.

Answer: 18

Step-by-step explanation: Complementary angles sum up to 90. (90 - 72 = 18)

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 0.0074

n = number of samples = 27

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 27 - 1 = 26

Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.9 = 0.1

α/2 = 0.1/2 = 0.05

the area to the right of z0.05 is 0.05 and the area to the left of z0.05 is 1 - 0.05 = 0.95

Looking at the t distribution table,

z = 1.706

The critical value is 1.706

Margin of error = 1.706 × 0.0074√27

= 0.0024

The 90% confidence interval is

0.097 ± 0.0024

Answer:

Step-by-step explanation:

30

Answer : -3

Since, the elevattor is going down the floor

This means its decreasing from the its original height

An elevetor goes down 3 floors = -3

The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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Answer: -1 3/5

Step-by-step explanation:

If doing it as a fraction is to confusing, you can change it to a decimal by diving the numerator by the denominator(e.g. 1/4 = 4 divided by 1=0.25) then change it back to a fraction using a converter. Good luck!

The equation of line that passes through the given point is y = 4.

Given line : y = 7​

So, the slope (m₁ = 0 )

Let's consider the slope of the line perpendicular to the given line as m₂,

m₁ * m₂ = -1

m₂ = 0

Now,

The equation of the line perpendicular to the given line and passing through the point (−8,4) will be

y−y₁ = m(x−x₁)

y−4 =  0(x−(−8)

y-4 = (0)(x+8)

y -4 = 0

y = 4

Thus, the equation of the required line is y = 4.

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The measure of angle c is 37 degrees and the measure of angle b is 53 degrees

Angles are formed when two or more lines intersect.

This in other words means that angles is the measure of space between the intersection of rays or lines

The measure of angle c

The given triangles are similar triangles

This means that the corresponding angles of the triangles are congruent

By comparing the corresponding angles of the given triangles, we have the following congruent equation

Angle c = 37

Hence, the measure of angle c is 37 degrees

The measure of angle b

As mentioned in part (a)

This means that the corresponding angles of the triangles are congruent

By comparing the corresponding angles of the three triangles, we have the following congruent equation

Angle b = 53

Hence, the measure of angle b is 53 degrees

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Answer:

One solution, there is only one set of values for x and y. (9,23)

Step-by-step explanation:

Y=3x-4

y=2x+5

replacing for y, put them equal to each other.

3x-4=2x+5

x=9

solve for y by putting x value in either equation.

y=3x-4

y=3(9)-4

y=27-4

y=23

or

y=2x+5

y=2(9)+5

y=18+5

y=23

The coordinates of image point is (15, 20)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

The transformation is given as

T<0, 1>D5

Mathematically, this

(x, y) = 5(x, y + 1)

So the image point is

(x, y) = 5(3, 3 + 1)

(x, y) = (15, 20)

So the image point of is (15, 20)

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

\(\frac{-2}{3}\)

Step-by-step explanation:

to find the slope of linear line, you need two points.  It does not matter which pints you use.  I am going to use (0,5) and (3,3)  The slope is the change in y over the change is x.  Our y values are 3 and 5.  Our x values are 3 and 0

\(\frac{3-5}{3-0}\) = \(\frac{-2}{3}\)

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".

A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.

An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.

The quotient of a number"x" and 4 can be written as x/4.

So, one more than the quotient of a number x and 4 can be represented by the expression:

⇒ x/4 + 1,

Therefore, required mathematical expression is "x/4 + 1".

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The given question is incomplete, the complete question is

Write an expression to represent : One more than the quotient of a number x and 4.

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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Principal = $3000

Rate = 5%

time = 2

Amount after 2 years =

= $3307.5

Option D is the correct answer

Answer:

4 L 600 mL

Step-by-step explanation:

1 L = 1000 mL

so 27 L 600 mL = 27000 + 600 = 27600 mL

27600/6 = 4600 mL

4 L 600 mL.

The exact value of sin(5π/12) is (√6 + √2)/4

From the question, we have the following parameters that can be used in our computation:

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

Step-by-step explanation:

this is very complicated and i suggest you to go to einstin