Which values of x will make the absolute value equation true?

|x – 4| = 7

A.
{–3, 3}
B.
{–3, 11}
C.
{–11, 11}
D.
no solution

Answer:

Another word for mean is the "average", your goal is to find the average of the following data set, it's pretty easy, you just have to add up all the numbers in the data set and divide it with the total numbers in the data set.

For example:

Find the mean of the following data set:

4, 1, 8, 5, 7, 3

Mean: 4 + 1 + 8 + 5 + 7 + 3 = 28

then we divide 28 with 6 since there are 6 numbers in the following data set.

Mean: 4 + 1 + 8 + 5 + 7 3 = 28/6 = 4.6

We get the final answer of 4.6!

-8,-6,-4

-10,-6,0

these are the possible test points for your three intervals

The given inequality is, x² + 12 x+35≥0

→ x²+7 x +5 x+5×7≥0

→ x (x+7) +5(x+7)≥0

→ (x+5)(x+7)≥0

→ x+5=0  ∧ x+7=0 gives x= -7 ∧ x= -5

Now drawing the number line and marking point ,-5 and -7 on it.

Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).

The solution set of inequality (x+5)(x+7)≥0 is  (-∞ , -7] and [-5,∞).

The set of possible test points for

⇒ (-∞ , -7] → -8,  -10

⇒ [-7,-5] → -6

⇒ [-5,∞) → -4, 0

Option (1) -8,-6,-4 and Option (2) -10,-6,0 satisfies the given condition.

Answer:

Option A, C, D, are the correct options.

Step-by-step explanation:

To check the exponential functions which have been simplified correctly we will take option one by one.

A). [tex]f(x)=5(\sqrt[3]{16})^{x}=5(\sqrt[3]{2^{4}})^{x}=5(2\sqrt[3]{2})^{x}[/tex]

B). [tex]f(x)=2.3(8^{\frac{1}{2}})^{x}=2.3(2.\sqrt{2})^{x}\neq 2.3(4^{x})[/tex]

C). [tex]f(x)=81^{\frac{x}{4}}=(3^{4})^{\frac{x}{4}}=(3^{\frac{4}{4}})^{x}=3^{x}[/tex]

D). [tex]f(x)=\frac{3}{4}(\sqrt{27})^{x}=\frac{3}{4}(\sqrt{3^{3}})^{x}=\frac{3}{4}.(3\sqrt{3})^{x}[/tex]

[tex]f(x)=(24)^{\frac{1}{3}x}=(2^{3}.3)^{\frac{1}{3}x}=(2.3^{\frac{1}{3}})^{x}\neq 2(\sqrt[3]{3})^{x}[/tex]

Exponential functions and their inverses like the natural logarithm are inverse functions, meaning they can undo each other. Simplifications like ln(e^x) result in x, and e^(ln x) simplifies to x. This property is integral to correctly simplifying exponential functions.

The exponential functions and their inverses, like the natural logarithm (ln), have specific properties where they can "undo" each other. This relationship allows us to simplify expressions involving exponentials and logarithms. For example, when you have ln(ex), this simplifies to x because the natural logarithm and the exponential function are inverse functions.

Similarly, when applying the exponential function to a natural logarithm, like eln(x), the result is just x. Furthermore, when taking square roots of exponentials, you can adjust the exponent to be evenly divisible by 2 and then take the square root of the base number, followed by dividing the exponent by 2. Also, while dividing exponentials, you subtract the exponents when the bases are the same.

Here is an example of this simplification: to compute the square root of e4, we can write it as e4/2, which simplifies to e2.

Answer:

introducing customer retention strategies

Step-by-step explanation:

Answer:

42 125 becuase i got um right bozzzzzzzz

Step-by-step explanation:

Answer:

SAS Postulate

Step-by-step explanation:

Answer:

false 9.13 is greater

Step-by-step explanation:

103 thousanths are smaller then 13 hundreths

with decimals the farther you go the lower you get bc its half a number

1/2 to 1/4 to  1/8 it gets smaller

Final answer:

The dimensions of the rectangular plot of land, where the length is 10 yards more than its width and the area is 600 square yards, are 20 yards by 30 yards. We arrived at this by setting up a quadratic equation and solving for the width.

Explanation:

To find the dimensions of a rectangular plot of land where the length is 10 yards more than its width and the area is 600 square yards, we can set up an equation. Let w be the width of the plot. Then the length is w + 10 yards. The area of a rectangle is given by the formula length × width, which in our case is (w + 10) × w = 600.

Setting up the equation, we get:

w(w + 10) = 600

w^2 + 10w - 600 = 0

To solve the quadratic equation, we can factor it, use the quadratic formula, or complete the square. Factoring the equation, we find that:

(w - 20)(w + 30) = 0

Thus, the width w can be either 20 yards or -30 yards. Since a width cannot be negative, we take w = 20 yards. Then, the length is:

w + 10 = 20 + 10 = 30 yards

The dimensions of the rectangular plot of land are 20 yards by 30 yards.

Notice that the above sequence is arithmetic because the common difference: d is constant.

d = second term - first term.

= 15 - 9

= 6

The general term of an arithmetic sequence is,

a_{n} =a_{1} +(n-1)d

Where , nth term = [tex] a_{n} [/tex]

[tex] a_{1} [/tex] = First term

and d = common difference.

The given sequence is: 9, 15, 21, ...

Here a_{1} = 9,

d = 6

We need to find the 31st term. So, n = 31.

Next step is to plug in these values in the above formula. Therefore,

[tex] a_{31} =9 +(31-1)*6 [/tex]

= 9 + 30* 6

= 9 + 180

= 189

So, 31st term of this sequence is 189.

Hope this helps you.

Answer:

189

Step-by-step explanation:

To find f(a) for the given function, substitute a for x in the function and simplify the expression.

Given the function f(x) = 5x0 + 4x-3, we need to find f(a). To find f(a), we substitute a for x in the function. Plugging in a, we get f(a) = 5a0 + 4a-3. Since any number raised to the power of 0 is equal to 1, we have f(a) = 5(1) + 4a-3. Simplifying further, we get f(a) = 5 + 4/a3.

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Answer:

option B  

Step-by-step explanation:

Given in the question are ∠x ≅ ∠y and ∠zwx ≅ ∠ ywz and wz is common in both.

These angles are adjacent angles of triangles.

We know theorem for congruence is Angle - Angle - Side

Therefore, for the congruence of these two triangles option B, AAS congruence theorem is the answer.

The postulate that proves that △JHG and △EFG are congruent is;

Option B; ​ ASA Congruence Postulate ​

From the given image, we can see two triangles namely;

△JHG and △EFG

Now, we can see that;

FG = GH

That is given because we see that G has divided FH into 2 equal parts.

Also, we see the right angle sign at ∠F and ∠H of both triangles.

Thus, since they are both right angles, then we can say that;

∠EFG = ∠JHG

Also, at point G, we have two vertically opposite angles which are;

∠EGF and ∠JGH

Now, from vertically opposite angle theorem, vertically opposite angles are always equal;

Thus; ∠EGF = ∠JGH

So far, we have;

FG = GH

∠EFG = ∠JHG

∠EGF = ∠JGH

This is 2 corresponding equal angles and 1 corresponding equal side. The side is included between the two angles and as such the proof that  △JHG and △EFG are congruent is the ASA Congruence Postulate.

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Final answer:

To find two consecutive even integers, we can set up and solve an equation. The equation in this case is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions.

Explanation:

To find two consecutive even integers, let's represent the first integer as x and the second integer as x + 2. Now, according to the given information, twice the lesser of the two integers is 4 less than two times the greater integer. We can write this as:

2x = 2(x + 2) - 4

Simplifying the equation:

2x = 2x + 4 - 4

2x = 2x

This equation is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions. In this case, there are infinitely many pairs of consecutive even integers that satisfy the given conditions.

465 / 3 = 155

so -153 + -155 + -157 = -465