Determine where the function f(x) is continuous. f(x)= 3√2-x
The function is continuous on the interval (Simplify your answer. Type your answer in interval notation.)

Answer:

Explanation:

Given the expression:

First, open the brackets:

Next, rearrange to bring like terms together:

Finally, combine the powers of 10 using the addition law of indices:

Answer:

The 4th one. Math class grade decreases if the number of days absence increases.

Step-by-step explanation:

With more days absent, lower math grade is shown.

Given:

The expressions are:

\((5x-3y)\) and \((8x+8y)\)

To find:

The difference of \((5x-3y)\) and \((8x+8y)\).

Solution:

Difference of \((5x-3y)\) and \((8x+8y)\) is written as:

\(Difference=(5x-3y)-(8x+8y)\)

On simplification, we get

\(Difference=5x-3y-8x-8y\)

\(Difference=(5x-8x)+(-3y-8y)\)

\(Difference=-3x-11y\)

Therefore, the difference of \((5x-3y)\) and \((8x+8y)\) is \(-3x-11y\).

The 100th number of the sequence 1, 4, 7, 10..., is 298.

The given series 1, 4, 7, 10..., is an AP.

Arithmetic Progression (AP) is a sequence of numerals in order, in which the difference between any two consecutive digits is a constant value. A progression is a type of sequence for which it is possible to get a formula for the nth term.  

The Arithmetic Progression is the most generally used sequence in maths with easy-to-understand formulas. The nth-term formula of the AP (arithmetic progression) is

aₙ = a₁+ d(n-1)

Where

n = number of terms

a = first term

d = common difference

Here, n = 100, d = 3 and a₁ = 1

\(a_{100}\) = 1 + 3(100-1)

\(a_{100}\) = 1 + 3(99)

\(a_{100}\) = 1 + 297

\(a_{100}\) = 298

--The given question is incorrect, the correct question is

''If we count by 3's starting with 1, the following sequence is obtained: 1, 4, 7, 10..., what is the 100th number in this sequence?"--

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Answer:

\(x=(b-a)^{3}\)

Step-by-step explanation:

Answer:

x = b³ - 3b²a + 3a²b - a³

Step-by-step explanation:

Given:

\(\sqrt[3]{x} + a = b\)

To determine the value of "x", we need to isolate it. Start out by subtracting "a" both sides. Then, we can cube both sides to remove the cube root. Finally, we can simplify both sides to obtain the value of x.

Subtract "a" both sides to isolate ∛x:

\(\implies \sqrt[3]{x} + a - a = b - a\)

\(\implies \sqrt[3]{x} = b - a\)

Cube both sides to remove the cube root on the L.H.S:

\(\implies (\sqrt[3]{x})^{3} = (b - a)^{3}\)

\(\implies x= (b - a)^{3}\)

Use the formula (a - b)³ = a³ - 3a²b + 3ab² - b³

\(\implies x = b^{3} - 3(b)^{2}(a) + 3(b)(a)^{2} - a^{3}\)

\(\implies \boxed{x = b^{3} - 3b^{2}a + 3a^{2}b - a^{3}}\)

Thus, the value of x is b³ - 3b²a + 3a²b - a³.

SOLUTION

From the diagram, the total outcome is 4

Probability of spinning A is

Probability of spinning B is

So probability of spinning A or B becomes

Hence the answer is

The length of the fencing is 12 feet and the width of the fencing is 24 feet.

What is length and width?

The dimensions of length and width are crucial in the study of geometry because they help define the models.

Given in the question,

The width must be twice the length,

So, Let the length as L and and the width will be equal to 2L.

Total fencing = 72 feet.

Assuming the flower bed to be rectangular.

The total perimeter = 2(Length + width)

72 = 2(L + 2L)

72 = 6L

L = 12,

So length will be 12 feet,

And, width will be 2L = 24 feet.

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Answer:

The proportional relationship is same

Step-by-step explanation:

Generally, we can get the unit rate by dividing the y-value by the x-value

This will be;

9/2 or 18/4 or 27/6 = 4.5

from what we have y = 4.5x

Now, as we can see, the proportional relationship is same

Answer:

Answer below

Step-by-step explanation:

The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size.

Answer:exactly equal shape and size

Step-by-step explanation:

Answer:

0.35

Step-by-step explanation:

if you divide them together you get 0.35

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The displacement function r(t) is given by r(t) = 2i - ti - j - t^2 j + k + t^3 k. The integration of the acceleration function twice with respect to time.

To find the displacement function r(t), we need to integrate the acceleration function a(t) twice with respect to time.

Given that a(t) = i + 2tj - 3t^2k, we can integrate each component separately.

Integrating the x-component of a(t) with respect to t, we get:

∫(i) dt = t i + C1,

where C1 is a constant of integration.

Integrating the y-component of a(t) with respect to t, we get:

∫(2t j) dt = t^2 j + C2,

where C2 is a constant of integration.

Integrating the z-component of a(t) with respect to t, we get:

∫(-3t^2 k) dt = -t^3 k + C3,

where C3 is a constant of integration.

Now, let's determine the constants of integration using the given initial conditions.

Given that r(0) = 2i - j + k, we can equate the components of r(t) and r(0) to find the constants.

Comparing the x-components, we have:

t i + C1 = 2i.

This implies C1 = 2i - ti.

Comparing the y-components, we have:

t^2 j + C2 = -j.

This implies C2 = -j - t^2 j.

Comparing the z-components, we have:

-t^3 k + C3 = k.

This implies C3 = k + t^3 k.

Now that we have determined the constants of integration, we can write the displacement function r(t):

r(t) = (2i - ti) + (-j - t^2 j) + (k + t^3 k).

Simplifying, we have:

r(t) = 2i - ti - j - t^2 j + k + t^3 k.

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Answer:

One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

a + b + 10 = 24

a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

\(a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0\)

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

Perimeter of triangle = Sum of all sides.

One side of triangle = 10 cm

Measure of other two sides will be → 24-10

Other two sides sum will be = 14 cm

Let's assume one side as x and other as 14-x

Now hypotenuse is of 10 cm

According to Pythagorean theoram

Hypotenuse² = Perpendicular ² + base²

→ 10² = (x)² + (14-x)²

→ 100 = x² + (14-x)²

(a-b)² = a²+b² -2ab

→ 100 = x² + 196 + x² -28 x

→ 100 = 2x² + 196 - 28x

Taking 2 commen both sides

→ 50 = x² -14x + 98

→ 0 = x² -14x +98-50

→ x² -14 x +48 = 0

Factorising :-

→ x² - 6x - 8x + 48 = 0

→ x( x -6) -8(x -6) = 0

→ (x-6)(x-8) = 0

→ x = 6 or x = 8

So x is 6 or 8

Other two sides of triangle are 6 cm and 8 cm

Answer:

a is the area of the largest rectangle

The value of a that makes ∠2 and ∠3 perpendicular is 20.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

From the image, HL is perpendicular to HJ, hence:

m∠2 + m∠3 = 90° (Definition of perpendicular)

Substituting gives:

(a + 15) + (a + 35) = 90

2a + 50 = 90

a = 20

value of a = 20

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Answer:

To create a dog ramp for stairs, you’ll want to first find a pallet or a sturdy support frame that can be used as a platform. Next, you’ll want to make a cross-section of the support frame and the pallet. Ayers that form the ramp. Using a saw or hacksaw, cut out the shape of the cross-section pieces and then use a wooden pallet as support. Finally, nail the cross-section pieces together using nails driven into the ground. 

Next, you’ll want to nail the cross-section pieces together using nails driven into the ground. The length of the ramp will depend on the space you have available. It should be long enough to walk a dog and provide some support. You can build your outdoor dog ramp frame out of stone, over-stairs, concrete, or other materials that are weather-resistant. If you’re using a wooden pallet, use caution when installing the frame because it can easily crack or break.

In triangle $abc$, let angle bisectors $bd$ and $ce$ intersect at $i$. the line through $i$ parallel prove that  $AB < AM < AN < AC$.

To solve this problem,  use the angle bisector theorem and some geometric properties of triangles. Let's begin.

Given: Triangle $ABC$ with angle bisectors $BD$ and $CE$ intersecting at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. Also, $AB < AC$.

to prove: $AB < AM < AN < AC$.

Proof:

Angle Bisector Theorem:

According to the angle bisector theorem,

$frac{BD}{DC} = frac{AB}{AC} quad$ (1)

Parallel Lines:

Since line $MI$ is parallel to $BC$,

$angle MIB = angle IBC quad$ (2)

Angle Bisector Property:

From the angle bisector property,

$frac{AB}{BD} = frac{AC}{DC}quad$ (3)

Combining Equations (2) and (3):

$frac{AB}{BD} = frac{AC}{DC} =frac{AB}{MI} quad$ (4)

Using Equations (1) and (4):

$frac{BD}{DC} = frac{AB}{MI}$

From Equation (5):

$frac{AB}{MI} + 1 = frac{AB}{BD} + 1$

Simplifying Equation (6):

$frac{AB + MI}{MI} = frac{AB + BD}{BD}$

Using Equation (7):

$frac{AM}{MI} = frac{AB}{BD} quad$ (8)

Comparing Equations (1) and (8):

$frac{AB}{AC} = frac{AB}{BD} = frac{AM}{MI}$

Since $AB < AC$, it follows that $frac{AB}{AC} < 1$. Thus, $frac{AM}{MI} < 1$.

From Equation (10),  $AM < MI$.

Using the same logic,  prove $MI < AN$.

Finally, since $AM < MI < AN$, it follows that $AB < AM < AN < AC$, as required.

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The function that represents the profit p for selling b bracelets is p = 3.5b - 84

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

This means that

Cost of b brackets = 3.5b

So, we have

Profit = Cost of b brackets - Cost price

substitute the known values in the above equation, so, we have the following representation

p = 3.5b - 84

Hence, the function that represents the profit p for selling b bracelets is p = 3.5b - 84

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Answer:

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

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{14 - - 4}{12 - - 15} = \frac{14 + 4}{12 + 15} = \frac{18}{27} = \frac{2}{3} \\ \)

We have the final answer as

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

Hope this helps you

Answer:

the answer is one cup of oil for each cup of water. hope this helps!

Answer:

a) x is less than or equal to −2/3

b) x=1

 Step-by-step explanation:

Answer:

43

Step-by-step explanation:

Answer:

sorry but all i got from this is the first one should be -3

Step-by-step explanation:

sorry that i couldn't answer all :)

Answer:

Step-by-step explanation:

The solution of the system with two lines is the x-coordinate of their intersection point.

a. there is only a solution if the lines are identical

b. both the x–coordinate and the y–coordinate of the intersection point,

c. the y–coordinate of the intersection point

d. the x–coordinate of the intersection point

the next number in the sequence is -2, therefore the complete sequence would look like: 1, 1, 2, -1, 1, -2, -1, -2

The given sequence seems to be alternating between three values: 1, -1, and 2. Looking at the pattern, we can see that the first two numbers in the sequence are both 1. Then, the next number is 2, which is obtained by adding the two previous numbers together. After that, the sequence alternates between -1 and 1, which are obtained by subtracting the previous number from the one before it. Finally, we have two negative numbers in a row: -2 and -1. These are obtained by subtracting the previous number from the sum of the two numbers before that.

Using this pattern, we can find the next number in the sequence:

To get the next number in the sequence, we need to subtract the previous number (which was -1) from the sum of the two numbers before that (which were 1 and -2).

So the next number in the sequence should be:

1 + (-2) - 1 = -2

Therefore, the next number in the sequence is -2.

So the complete sequence is: 1, 1, 2, -1, 1, -2, -1, -2

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Answer:

About 5.5, but it is technically closer to 5.6 so I am not entirely sure

Step-by-step explanation:

Since EB and DC are parallel, triangles ABE and ACD are similar by AA. Therefore:

\(\dfrac{x}{10}=\dfrac{10}{18} \\\\\\x=10\cdot \dfrac{10}{18}\approx 5.5\)

Hope this helps!

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer:

x-intercepts- (4,0) and (3,0)

Y-intercepts-(0,12)

Step-by-step explanation: