Question 11 of 20
What is the solution to the equation below? (Round your answer to two
decimal places.)
log₂ x = 5.6

Answer:

x- intercept = - 1 , y- intercept = 2

Step-by-step explanation:

the x- intercept is the value of the x- coordinate where the curve crosses the x- axis , that is

x- intercept = - 1

the y- intercept is the value of the y- coordinate where the curve crosses the y- axis , that is

y- intercept = 2

An equation is formed when two equal expressions. The value of k that makes the equation true is 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of k that will make the equation true is,

[tex]5a^2b^3(6a^kb)=30a^6b^4\\\\30\ a^{(2+k)}\ b^{(3+1)} = 30\ a^6\ b^4\\\\30\ a^{(2+k)} \ b^4 = 30\ a^6\ b^4\\\\a^{(2+k)} =a^6\\\\2+k = 6 \\\\ k = 4[/tex]

Hence, The value of k that makes the equation true is 4.

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3) [tex]3(2x-6)=\boxed{6x-18}[/tex]

4) [tex]2x(5x+11)=10x^{2}+22x[/tex]

Answer:

t = 2

Step-by-step explanation:

Look at the fraction on the left, 1/3.

Notice that the denominator is 3 times the numerator.

Since the fractions are equal, for the second fraction, you also need the denominator to be 3 times the numerator. Since the denominator is 6, the numerator must be 2 since 6 is 3 times 2.

Answer: t = 2

Of course, since you have two fractions that are equal, and fractions are also ratios, you have a proportion.

You can solve the problem as a proportion.

1/3 = t/6

Cross multiply:

3t = 1 × 6

3t = 6

t = 6/3

t = 2

Either way, you get t = 2.

The expression 1/7 – 3(3/7n – 2/7) is equivalent to the expression 1 – 9/7n.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ 1/7 – 3(3/7n – 2/7)

On simplifying the expression, we have

⇒ 1/7 – 9/7n + 6/7)

⇒ 1 – 9/7n

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Answer:

-9/7 n + 1

Step-by-step explanation:

On khan

The Correct Question is ......

Question :

Choose the simplified form of  the fifth term of  ⁶C₄ (2x)² (-y²)⁴

Answer: D. 60x²y⁸ is the simplified form of the fifth term of the

expansion ⁶C₄ (2x)² (-y²)⁴.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

According to the Given Expression,

⁶C₄ (2x)² (-y²)⁴

The value of the combination can be written as,

[tex]= [\frac{6!}{4!(6-4)!} ] (2x)^{2} (-y^{2})^{4}[/tex]

= 15 (4x²)  (-y²)⁴

The value of y can be written as,

= 15 (4x²)  y⁸

= 60 x²y⁸

Therefore,

The value of the expression ⁶C₄ (2x)² (-y²)⁴ is 60x²y⁸.

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An isosceles triangle is one with two equal-length sides. The value of l is 8 ft.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

In the given image it can be observed except 140° angle, the other two angles are congruent to each other which means the triangle is an isosceles triangle.

As per the base angle theorem in an isosceles triangle the sides opposite to the congruent triangle are equal therefore, the length of side l will be 8 ft as well.

Hence, the value of l is 8 ft.

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The greatest common factor for the numerical part will be 2.

The greatest common factor, as the name implies, is the greatest among all common factors among the quantities given.

We can factorize the quantities in the smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could.

Those will together compose GCF(The greatest common factor).

Given;

[tex]6x^2-8+22[/tex]

Since the expression contains both numbers and a variable part.

For numerical parts 6, -8, 22

The factors are

6 = -6, -3. -2, -1,1, 2, 3 , 6

8 = -8, -4, -2, -1,1, 2, 4, 8

22 = -22, -11, -2, -1,1, 2, 11, 22

The greatest common factor for the numerical part will be 2.

The number part does not contain any common variable factor.

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Answer:

A

Step-by-step explanation:

she worked a total of 34 hours , then

x + y = 34

earnings are $10 per hour babysitting , that is 10x for x hours

$15 per hour for yardwork, that is 15y for y hours

she made a total of $410 , then

10x + 15y = 410

system of equations is

x + y = 34

10x + 15y = 410

Answer:

x=10

Step-by-step explanation:

Answer:

Each student ticket costs $10, and each adult ticket costs $17.

Step-by-step explanation:

Let s represent the cost of a student ticket and a represent the cost of an adult ticket.

31s + 32a = 854

31s + 31a = 837

----------------------

a = 17

31s + 31(17) = 837

31s + 527 = 837

31s = 310, so s = 10

The domain of the linear function is a real number, and the range of the linear function is also a real number.

The domain means all the possible values of x and the range means all the possible values of y.

The table is given below.

  x               y

 -4              5

 -2              3

  0              1

  2             -1

  4             -3

Then the linear function will be

y – 1 = [(5 – 1) / (- 4 – 0)] (x – 0)

y – 1 = -x

x + y = 1

Then the domain of the linear function is a real number and the range of the linear function is also a real number.

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The correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.

The given inequality is -3(2x-5)<5(2-x).

Inequality is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

At first simplify each side

LHS of inequality -3(2x - 5) = -3(2x) + -3(-5) [∵(-)(-) = (+)]

⇒ -3(2x - 5) = - 6x + 15

Now, RHS of the inequality 5(2 - x) = 5(2) + 5(-x) [∵(+)(-) = (-)]

⇒ 5(2 - x) = 10 - 5x

Now, - 6x + 15 < 10 - 5x

Subtract 15 from both sides

That is, - 6x < -5 - 5x

Add 5x to both sides

That is, - x < - 5

Remember the coefficient of x is negative, and then when you divide both sides by it you must reverse the sign of inequality.

Now, the coefficient of x is -1

So, divide both sides by -1

Then, x > 5.

Hence, the correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.

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The slope- intercept is y> (1-4x) / 5 and y< 2x + 6

A  statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

4x – 5y < 1  and 1/2y – x < 3

Solving

4x – 5y < 1

-5y < 1- 4x

-y < (1-4x) / 5

y> (1-4x) / 5

Now, the second inequality,

1/2y – x < 3

1/2y< 3+x

y< 2x + 6

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Answer:

Answer:

(3*6) - (6/2) = 15

Step-by-step explanation:

3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.

The answer of the equation is 15.

The correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given functions are:-

When we plot the graph of the two functions given in the question we will see that the graph of the function F(x) = x²-16 is compressed by the factor 7 and the vertex of the graph shifted to the 16 points down.

Therefore the correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.

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Using proportions, it is found that the value of the total sum that was shared was of $45.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:

The difference is of $15, hence:

[tex]A - K = 15[/tex]

[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]

[tex]\frac{4N}{12} = 15[/tex]

[tex]\frac{N}{3} = 15[/tex]

N = 15 x 3 = 45

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Answer:

23

Step-by-step explanation:

area of a trapezoid = 1/2 × (a + b) × h

so, we have

96 = 1/2 × ((4x - 1) + (x + 3)) × 6 = (5x + 2) × 3

32 = 5x + 2

30 = 5x

x = 6

a = 4x - 1 = 4×6 - 1 = 24 - 1 = 23

Answer:

B

Step-by-step explanation:

There is 2 options, win and lose, no tie so 3 and 4 get cancelled. there are only 2 roots so 1 gets cancelled leaving 2 (B)

Therefore, the incorrect statement is option B, which states that 28 pounds is equal to 44 dollars. The correct value should be 42 dollars.

To determine which statement is incorrect, we can use the given conversion rate of 2 pounds being equal to 3 dollars and evaluate each option accordingly:

A. 11 pounds is 16.50 dollars:

To check this, we can multiply 11 pounds by the conversion rate:

11 pounds * (3 dollars / 2 pounds) = 16.50 dollars

This statement is correct.

B. 28 pounds is 44 dollars:

Using the same calculation:

28 pounds * (3 dollars / 2 pounds) = 42 dollars

This statement is incorrect because 28 pounds would actually be equal to 42 dollars, not 44 dollars.

C. 10 pounds is 15 dollars:

Again, applying the conversion rate:

10 pounds * (3 dollars / 2 pounds) = 15 dollars

This statement is correct.

D. 23 pounds is 34.50 dollars:

Using the conversion rate:

23 pounds * (3 dollars / 2 pounds) = 34.50 dollars

This statement is correct.

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Answer:

374795-57770

Step-by-step explanation:

Abby uses

To find the zeros of a rational function, we must identify values of x that make the numerator equal to 0. We can do this by factoring and by keeping in mind the zero-product property.

The zero-product property states that if the product of two terms is 0, then one of the terms must be equal to 0.

We're given:

[tex]f(x)=\dfrac{4x^2-36x}{x-9}[/tex]

First, factor 4x out of the numerator:

[tex]f(x)=\dfrac{4x(x-9)}{x-9}[/tex]

Let f(x) = 0:

[tex]0=\dfrac{4x(x-9)}{x-9}[/tex]

In this case, either x or (x-9) is equal to zero, as they are the two terms being multiplied in the numerator to get 0 as a product.

This makes the x-intercepts of this function 0 and 9.

However, the denominator in this function is x - 9. If x = 9, then it would make the denominator 0, which is not allowed. Therefore, x cannot equal 9, and the only x-intercept is 0.

x = 0

Let that angle be x

Linear pairs are supplementary

So

Answer:

(9, 3 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 9, 3 ) → (9, 3 )

Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

Helpful fact:  Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

Option 1.  m∠R > 90°

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

Option 2.  m∠S + m∠T < 90°

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) >  m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

Option 3.  m∠S = m∠T

Not necessarily.  While m∠S could equal m∠T, it doesn't have to.  

Example 1:  m∠S = m∠T = 10°;  By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2:  m∠S = 15°, and m∠T = 10°;  By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

Option 4.  m∠R > m∠T

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

Option 5.  m∠R > m∠S

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

Option 6.  m∠S > m∠T

Not necessarily.  While m∠S could be greater than m∠T, it doesn't have to be.  (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

Answer: Option 1, 2, 4, & 5  or  

A. m∠R > 90°;  B. m∠S + m∠T < 90°;  D. m∠R > m∠T;  & E. m∠R > m∠S

Step-by-step explanation:   Trust Me!  

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.

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Answer:

Con qué necesitas ayuda?

Step-by-step explanation:

Graphically, we will see that the solutions of the system are (−4,2) and (2,−1)

To solve the system of equations graphically, we need to graph both of the equations and see in which points the graphs intercept.

The graph of the system can be seen below, there you can see that the intercepts are at:

(-4, 2) and (2, -1)

So these are the two solutions of the system of equations.

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