radical equals 2x plu

A suitable delta (δ) for ε = 0.01 is any positive value smaller than √6.

To find a suitable delta (δ) for the given limit, we need to consider the epsilon-delta definition of a limit.

The definition states that for a given epsilon (ε) greater than zero, there exists a delta (δ) greater than zero such that if the distance between x and the limit point (2, in this case) is less than delta (|x - 2| < δ), then the distance between the function (√x + 7) and the limit (3) is less than epsilon (|√x + 7 - 3| < ε).

Let's solve the inequality |√x + 7 - 3| < ε:

|√x + 7 - 3| < ε

|√x + 4| < ε

-ε < √x + 4 < ε

To remove the square root, we square both sides:

(-ε)^2 < (√x + 4)^2 < ε^2

ε^2 > x + 4 > -ε^2

Since we're interested in the interval around x = 2, we substitute x = 2 into the inequality:

ε^2 > 2 + 4 > -ε^2

ε^2 > 6 > -ε^2

Since ε > 0, we can drop the negative term and solve for ε:

ε^2 > 6

ε > √6

Please note that this solution assumes the function √x + 7 approaches the limit 3 as x approaches 2. To verify the solution, you can substitute different values of δ and check if the conditions of the epsilon-delta definition are satisfied.

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Answer:

D. 2.19

Step-by-step explanation:

ok so the formula for the surface area of a sphere is 4\(\pi\)\(r^2\)

We see that 4\(\pi\)\(r^2\)=60.

To find the radius we must isolate r on one side of the equations.

\(r^2\)=60/4\(\pi\)

\(r^2\) = 4.77464829276

r = \(\sqrt{4.77464829276}\)

That is approximately equal to 2.19

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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9514 1404 393

Answer:

  (4, -1)

Step-by-step explanation:

The orthocenter is the intersection of altitudes. Each altitude is the line through a vertex and perpendicular to the opposite side of the triangle.

It is useful to plot the points on a graph. This shows you segment KM is a horizontal line, so one altitude line is x=4, the vertical line through point L.

The graph also shows you segment KL has a rise of 8 for a run of 2, so a slope of rise/run = 8/2 = 4. Then the altitude perpendicular to that side will have slope -1/4 (the opposite reciprocal of 4), and will go through point M(8, -2). In point-slope form, the equation of the altitude through M can be written ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y +2 = -1/4(x -8)

We want to find the y-coordinate of the point of intersection of this line with the line x=4. We can substitute x=4 and solve for y.

  y +2 = -1/4(4 -8) . . . . . . substitute x=4

  y = 1 -2 . . . . . . . . . . simplify and subtract 2

  y = -1

The orthocenter for the given triangle has coordinates (4, -1).

The property illustrated ca be classified as the transitive property of equality

Equation are expressions separated by an equal sign. For transitive property, if two system of equation are equal, and the first is equal to the second, then they 2nd is equal to the third, they are transitive.

According to the transitive property of equality, two quantities that are equal to the same thing are equal to each other. For instance If x = 10 and 10 = y, then x = y.

Given that g = 3h and 3h = 16, then g = 16, then the property illustrated ca be classified as the transitive property of equality

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Answer:

the answer to this question is 1/755

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

4 chairs

Step-by-step explanation:

Start with 2/3 can of paint: (2/3)

He used 1/6 of the can to paint each chair: (divided by 1/6)

Now use the 'keep, change, flip' method to get the expression: (2/3x6/1)

Then simplify your answer: (12/3)

Lastly simplify again: (4)

Thus, he painted 4 chairs.

Answer:

False

Step-by-step explanation:

3x4=12

12 divided by 3=4

4x8=32

32=34

Hence, this equation is false.

is simply changing from percentage form to a decimal form usually, but the fractional form works the same.  Check the picture below.

Answer and Step-by-step explanation:

Solution:

Given:

Let A is the event of a person over 50 diagnosed by health service.

B1 is the event that an adult over 50 actually has diabetes.

B2 is the event that an adult over 50 does not have diabetes.

P (B1) = 8% = 0.08

And P (B2) = 1 – P (B1)

                  = 1 – 0.08

                  = 0.92

Correctly diagnose of all persons with diabetes= 95%

P (A/B1) = 0.95

Incorrectly diagnose of all persons without diabetes=   2%

P (A/B2) = 0.02

(a) ) the community health service will diagnose an adult over 50 as having diabetes.

P (B1) P (A/B1) = (0.08) (0.95) = 0.076

P (B2) p (A/B2) = (0.92) (0.02) =0.0184

P (B1) P (A/B1) + P (B2) p (A/B2) =  0.076 + 0.0184

                                                     = 0.0944

(b)  A person over 50 diagnosed by the health service as having diabetes actually has the disease.

By using formula:

P (B1/A) = P (B1) P (A/B1) / P (B1) P(A/B1) + P (B2) P (A/B2)

Put all the given values:

= (0.08) (0.95) / (0.08) (0.95) + (0.92) (0.02)

=0.076 / 0.076 + 0.0184

=0.076 / 0.0944

= 0.8050

Using conditional probability, it is found that there is a:

a) 0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.

b) 0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

Item a:

The percentages of a positive test is:

Hence:

\(P(A) = 0.95(0.08) + 0.02(0.92) = 0.0944\)

0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.

Item b:

From item a, \(P(A) = 0.0944\).

The probability of both a positive test and having the disease is:

\(P(A \cap B) = 0.95(0.08)\)

Hence, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.08)}{0.0944} = 0.8051\)

0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.

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Answer:

108

Step-by-step explanation:

Because the area formula is a*b and 12*9 is 180

So the answer is 180 which is A

I hope this helps :)

The area of kite is 54 units square.

The  correct option is (C)

The area of a kite is half the product of the lengths of its diagonals.

The formula to determine the area of a kite is: Area = ½ × (d)1 × (d)2.

Diagonals of a kite intersect each other at right angles. The longer diagonal is the perpendicular bisector of the shorter diagonal. A kite is symmetrical about its main diagonal. The shorter diagonal divides the kite into two isosceles triangles.

Here d1 and d2 are diagonals.

Given:

d =12

d2= 9

Now, area of kite is

= ½ × (d)1 × (d)2.

=1/2*12*9

=1*2*108

=108/2

=54

Hence, the area of kite is 54 units square.

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Answer:

24.012

Step-by-step explanation:

y=kx^2

54=81k

k=54/81

k=0.667

y=kx^2

y=0.667×36

y=24.012

its false ik this because im one of the boyzz

The simplified expression is: -2x - 4x^2 + 2.

simplify the given expression, 3(x-2x^2) + (x-2)(2x-1).

First, let's distribute the 3 into the first set of parentheses: 3x - 6x^2. Now, let's apply the distributive property to the second set of parentheses: (x-2)(2x-1) becomes 2x^2 - x - 4x + 2, which simplifies to 2x^2 - 5x + 2.

Now, combine the simplified expressions: (3x - 6x^2) + (2x^2 - 5x + 2). Add the corresponding terms: (3x - 5x) + (-6x^2 + 2x^2) + 2. This results in -2x - 4x^2 + 2.
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Answer:

11-)B, x = 10.5,

8-)B

Step-by-step explanation:

11-)

12X = 14 x 9

X = 10.4

.

8-) (a + b)/2 x (h) = (10 + 6)/2 x X

.

The equivalent fraction for the given fraction is 1/5.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

The given fraction is 3/15.

The equivalent fraction is 3/15 =1/5

Therefore, the equivalent fraction for the given fraction is 1/5.

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The value of secant XY is 37.5 units.

The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

VZ * VW = VX * VY

30 * 45 = 22.5 * VY

22.5VY = 1350

VY = 1350/22.5

VY = 60 units

Since VY = VX + XY. We have:

60 = 22.5 + XY

XY = 60 - 22.5

XY = 37.5 units

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The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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9514 1404 393

Answer:

  61/27

Step-by-step explanation:

Perhaps you want to evaluate (12a +2d +8)/(2ad). The result is shown below.

The probability of selecting an elm or oak tree is 0.38.

The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:

P(elm or oak) = P(elm) + P(oak)

P(elm) = 0.04

P(Oak) =0.34

Plug in these values

= 0.04 + 0.34

= 0.38

Therefore, the probability of selecting an elm or oak tree is 0.38.

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If it takes 15 minutes to preheat your oven to 325 degrees.

a.  The formula to express the total time T, in minutes, needed to preheat the oven and then bake a turkey weighing p pounds is: T = 15 minutes  +  p × 14 minutes/pound.

b. The approximate time required to prepare a turkey weighing 15 pounds is  284 minutes.

a. Total time

Preheat time = 15 minutes

Turkey time = p × 14 minutes/pound

Total time = T = 15 minutes  +  p × 14 minutes/pound

b. Approximate time required to prepare a turkey

p = 19 pounds

T = 15 minutes + 19 pounds× 14 min/pound

T = 15 minutes + 266 minutes

T = 284 minutes (4 hrs 44 min)

Therefore the formula to express the total time T  is: T = 15 minutes  +  p × 14 minutes/pound and the approximate time required to prepare a turkey weighing 15 pounds is  284 minutes.

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(-2,-6) and (2,-3) are points on the graph

Here, we want to select the ordered pairs that are on the graph

What we have to do here is to substitute the coordinates of the points into the equation

If we substitute say for example the x value, and we are able to get the y value, then the point is on the graph

We look at each of the points as follows;

a) (-9,-6)

This is not on the equation

b) (-2,-6)

This is a point on the graph

c) (0,6)

This is not on the graph

d) (2,-3)

This is a point on the graph

e) (3,10)

This is not a point on the graph

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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Answer:

488

Step-by-step explanation:

You divide 28453 by 58.3053278689 and get 488.

Answer:

B i believe

Step-by-step explanation:

Answer:

25 + 12.5v ≤ 170

Step-by-step explanation:

namely, what is "t" when f(t) = 2000

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t\)

Answer:

Standard Form:

2√ 73

Decimal form:

17.08800749...

Step-by-step explanation:

Answer:

6.09 * 10 ^-3

Step-by-step explanation:

We want one non zero digit to the left of the decimal

Move the decimal 3 places to the right

6.09

The exponent is 3 and it is negative since we move to the right

6.09 * 10 ^-3

Answer:

6.09(10⁻³)

Step-by-step explanation:

Step 1: Put number into proper scientific decimal form

6.09

Step 2: Figure out how many decimals places it moves

Since it moves to the left 3, our exponent would be -3