Solving for the area.

The graph is shown in the attached image.

Answer:

v=-7

Step-by-step explanation:

13v-5v=-27-29

8v=-56

v=-56/8=-7

Answer:

it matches with equation c

The total number of servings Stephen can achieve with 1/10 kilograms of tofu at 2/25 kilograms per serving is 5/4 servings

Number of servings = Total tofu Stephen has ÷ Tofu per serving

= 1/10 ÷ 2/25

= 1/10 × 25/2

= (1×25) / (10 × 2)

= 25/20

= 5/4 servings

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Step-by-step explanation:

there are several formulas that could play a role.

but in our case, where we have velocities and the deceleration, we are going to use

fV = iV + at

fV = final velocity (0 on our case)

iV = initial velocity (40 m/s in our case)

a = acceleration (-15 m/s² in our case)

t is the time it takes to reach fV.

0 = 40 + (-15)t = 40 - 15t

15t = 40

3t = 8

t = 8/3 = 2.666666666... seconds

so, it takes 2.6666666... or 2 2/3 seconds to bring the vehicle to a standstill.

Answer:

[tex]f(x) = 20x - 4 \\ substitute \: y \: for \: f(x) \\ y = 20x - 4 \\ interchange \: x \: and \: y \\ x = 20y - 4 \\ swap \: the \: sides \: of \: the \: equation \\ 20y - 4 = x \\ move \: the \: constant \: to \: the \: right \: hand \\ 20y = x + 4 \\ divide \: both \: sides \: by \: 20 \\ y = \frac{1}{20} x + \frac{1}{5} \\ substitute \: f {}^{ - 1} (x) \: for \: y \\ f {}^{ - 1} (x) = \frac{1}{20} x + \frac{1}{5} [/tex]

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.

Thus, domain of f(x): x∈R = range of f¯¹(x)

and range of f(x): x∈R =domain of f¯¹(x)

The tires can be arranged in 24 ways. Computed using permutation.

The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.

For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:

nPr = n!/(n - r)!.

In the question, we are asked the number of ways in which the four tires can be arranged on a car.

As we need to select 4 tires, from 4 tires, with any order, we will use permutation.

Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.

Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.

Thus, the tires can be arranged in 24 ways. Computed using permutation.

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Answer:

B is correct

Answer: -2 and 4

Step-by-step explanation:

Let [tex]t=x/2[/tex].

[tex]f(t)=0 \longrightarrow t=-1, 2\\\\\therefore x=-2, 4[/tex]

The type of motion which transforms the letter “p” into a “b” is; Reflection.

It follows that the task content demands that the type of motion which maps p to b be identified. On this note, it follows that the type of motion in discuss is Reflection. More particularly, a reflection over the horizontal axis most definitely causes this transformation.

Therefore, the motion which transforms the letter “p” into a “b” is; Reflection.

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Answer:

13/8

Step-by-step explanation:

4 2/8 - 2 5/8

34/8 - 21/8 = 13/8

1 5/8 as a mixed fraction

The values of x after the statement are:

This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.

Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false

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Using it's concept, the standard deviation of the data is of 3.742.

For this data-set, the mean is:

M = (1 + 4 + 4 + 4 + 4 + 6 + 5)/7 = 4.

Hence the standard deviation is:

[tex]S = \sqrt{\frac{(1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (5 - 4)^2}{7}} = 3.742[/tex]

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The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)

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(a) The particle's distance from O when it first started to move is 24 m.

(b) The time when the particle first reaches O is 15 mins.

(c) The particle's speed when it has been moving for 3 minutes is 0.2 m/s.

D = 24 + 15 - t²/2

when the time, t  = 0

D = 24 m

When the object reaches O, its final velocity, v = 0

v = dD/dt

v = 15 - t

0 = 15 - t

t = 15 mins

v = 15 - t

v = 15 - 3

v = 12 m/min

v = 12 m/min x 1min/60s = 0.2 m/s

Thus, the particle's distance from O when it first started to move is 24 m.

The time when the particle first reaches O is 15 mins.

The particle's speed when it has been moving for 3 minutes is 0.2 m/s.

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Answer: False

Step-by-step explanation:

G(x) is not a one-to-one function (since it fails the horizontal line test). Therefore, it doesn't have an inverse.

The line PQ is altitude of the triangle. This can be obtained by understanding what an altitude is.

Properties of altitude of a triangle:

In the given triangle,

it is clear that angle Q is 90° and therefore PQ is a perpendicular line from the point P.

Since the perpendicular line, which is PQ, is drawn from the vertex, which is P  of the triangle to the opposite side, which is SR.

Thus PQ is the altitude of the triangle.

Hence in the given figure, the line PQ is the altitude of the triangle.

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The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

The expression is given as:

1/2 * 1/2 *1/2

Apply the product law of indices

1/2 * 1/2 *1/2 = (1/2)^3

Apply the power law of indices

1/2 * 1/2 *1/2 = (2^-1)^3

This gives

1/2 * 1/2 *1/2 = 2^-3

Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

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Answer:

80

Step-by-step explanation:

DAB =DAC...........

The real engine is 65.25 feet long

The scale is given as:

Scale = 87 feet to 1 foot

The scale length is given as

Scale length = 9 inches

Convert inches to feet

Scale length = 9/12 feet

The actual length is then calculated as:

Actual = 87 * 9/12 feet

Evaluate

Actual = 65.25 feet

Hence, the real engine is 65.25 feet long

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Answer:

[tex]\sqrt{65}[/tex], so [?] = [65]

Step-by-step explanation:

This is a classic Pythagorean Theorem problem :)

We are given a right triangle with 2 sides, so all we have to do is plug it into the formula a² + b² = c², or in simple terms: the square of one side plus the square of the other equals the square of the hypotenuse.

line h is going to bisect the diameter of the circle (8) so one side will be 4. We're given 9 as our hypotenuse, so:

(4)² + (h)² = (9)².

16 + h² = 81

h² = 81 - 16, h² = 65, h = [tex]\sqrt{65}[/tex].

Answer:

67 years old. (you only gave 4 people and missed out one person)

Step-by-step explanation:

take all the ages first and put the unknown (age of the person who entered the room) as x.

14, 16, 16, 13, x

all of these numbers added to together would be:

59 + x

Because the question is talking about the mean age, to find mean:

add all the values in the data (ages) and divide by the total number of values on the list. (in your case would be 6 people (following your question) but you gave only 5 people including the x).

then (59 + x) / 6 = 21

21 x 6 = 126

126 = 59 + x

x = 67

Answer:

D

Step-by-step explanation:

As the function approaches a certain x-value, it makes a very sharp turn and doesn't touch the axis as you can see in the graph. It does that because if the x-value is applied to the function, it would make it undefined. In this case, the graph is approaching x = -3 and x = +7 since at those points, the lines for the graph change suddenly. You would look for a function that if x is -3 or 7, it makes the y-value undefined.

Another way to easily do this would be to substitute values that are in front of the value that the graph is avoiding like 6 or 8 for 7 and -2 and -4 for -3. You can see if the y-values that would output from substituting those numbers are correct.

The perimeter of the rectangle based on the factors given is 46.

The area of the rectangle is given as (x² + 13x - 90). This will be:

= (x² + 13x - 90)

= x² + 18x - 5x - 90

= x(x + 18) - 5(x + 18)

= (x - 5)(x + 18)

The sides of the rectangle are 5 and 18. The perimeter will be:

= 2(l + w)

= 2(5 + 18)

= 46

The area of the rectangle is given as (x² + 24x - 81.

= (x² + 24x - 81)

= x² + 27x - 3x - 81

= x(x + 27) - 3(x + 27)

= (x - 3)(x + 27)

The sides are 3 and 27. The perimeter will be:

= 2(l + w)

= 2(27 + 3)

= 60

= (x + 1)² + 3(x + 1) + 2

= (x + 1)(x + 1) + 3x + 3 + 2

= x² + x + x + 1 + 3x + 5

= x² + 5x + 6

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hi

monthly interest rate is :     [tex]\sqrt[12]{1.05}[/tex]

So in forty month there will be  :  10 000 * ( [tex]\sqrt[12]{1.05}[/tex] )^40  ≈11 776,06

Answer:

{-5,-2,0,2,5,-1,1,8}

Step-by-step explanation:

The union of two sets contains all elements that are in set A or in set B (possibly both).

{-5,-2,0,2,5} ∪ {-5,-1,1,5,8} = {-5,-2,0,2,5,-1,1,8}

[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]

Answer:

Step-by-step explanation:

d = 13.416408

For:

(X1, Y1) = (-4, -5)

(X2, Y2) = (8, 1)

Answer:

L = 9.49 units

Step-by-step explanation:

From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6.  These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:

12^2 = 144 and 6^2 = 36.

Combining these results in the length of the diagonal:

L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem

Rounding off, we get L = 9.49 units

The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.

According to the statement

we have given that the percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. And

The traditional method was 78% effective.

we have to show that the success rate for PN is greater than the historical success rate then

we use the percentage formula to find the success rate of the new method. So,

(a) Total patients = 350

Success rate in number of patient = 289

Percentage of success rate = (289/350)*100

Then after calculating

Percentage of success rate = 82.57%

It is clear that the outcome success rate is 82.57% which is greater than traditional method.

(b) we have a 95% confidence that the success rate of new method is higher than the older method from a confidence interval of 2.262 and 3.67

So, The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.

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