solve x for (2x+15)8-3y=x

Answer:

60 and -60

Hope this helps! :)

The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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Answer:

True.

Step-by-step explanation:

It explains itself right

Answer:

Step-by-step explanation:

#1 is 24k^15

just add the #

#2 4096

4x4x4=64^2

64x64

=4096

Answer:

Step-by-step explanation:

Given equation:

Now, let's solve the equation:

Their rate was 85 toys per day.

Answer:

Han has the strongest orange juice.

Step-by-step explanation:

she has way less water ans barely any less juice concentrate.

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

f(x) is discontinuous.

Since LHS ≠ RHS ≠ f(x).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Now,

A x = 1

LHS of f(x) = \(\lim_{x\to1^-}\) f((h - 1)) = \(\lim_{h \to 0}\) (h - 1 - 1) = 0 -2 = -2

RHS of f(x) = \(\lim_{x\to1^+}\) f(h + 1) = \(\lim_{h \to 0}\) (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1

f(1) = x + 1 = 1 + 1 = 2

We see that,

LHS ≠ RHS ≠ f(x)

So,

f(x) is not continuous, it is discontinuous.

Thus,

f(x) is discontinuous.

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The complete question.

Show that the following functions are continuous or discontinuous at x = 1.

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Answer:

Step-by-step explanation:

Ok well first you need to put 9,000

       4 years-                           207.26

        5% interest rate-

Now add all those together and the 4 years how many days are in 4 years?

Find that out and add all together.

                                                                 Signed,

                                                                              Emily Blevins

The graph for the inequality -12x-4y<5 is option C.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

The given inequality expression is -12x-4y<5.

First plot the graph for 12x-4y=5.

The expression has a < symbol which means the graph will have dotted lines.

Now, check does the origin (0,0) satisfy -12x-4y<5.

Substituting the values of x and y -

-12(0) - 4(0) < 5

0 - 0 < 5

0 < 5

Since, the condition is satisfied the region including the origin (0,0) is shaded.

Therefore, the graph is plotted for the expression.

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Answer:

Javon is incorrect

Step-by-step explanation:

You have to subtract 5 both sides to move it to the other side:

5 -2x -1/3 = 4

5 - 5 - 2x - 1/3 = 4 -5

-2x - 1/3 = -1

Answer:

Javon is incorrect because he didnt subtract 5 from both sides, or add -5

Step-by-step explanation:

I had this question

Answer: 60

Given,

Ratio of Girls:Boys (G:B) = 7:5

Also, number of girls = 10 + number of boys

G = 10 + B

G/B = 7/5

(10+B)/B = 7/5

50 + 5 B = 7B

2B = 50

B = 25

G = 10 + B = 35..

A. Number of girls = 35

B. Number of boys = 25

C. Total students = 60

OR

Given G:B = 7:5

Difference between number of girls and boys = 10

Ratio difference = 2 parts (7-5=2)

2 parts===10

1 part ===5

7 parts(gilrs) == 7*5 = 35

5 parts (boys) == 5*5 =25

12 parts(total) = 5*12 = 60.

The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

72

Step By Step Explanation:

Answer:

\(\text{27}\)

Step-by-step explanation:

Given that :

\(\text{Dimension of poster board} = 1 \ \text{yd} \ \text{by} \ 1 \ \text{yd}\)

\(\text{Dimension of each poster board} = \dfrac{1}{3} \ \text{yd} \ \text{by} \ \dfrac{1}{9} \ \text{yd}\)

Number of poster signs that can be cut :

\(\text{Area of poster sign} = \dfrac{1}{3} \times \dfrac{1}{9} = \dfrac{1}{27} \ \text{yard}^2\)

\(\text{Area of poster board} = 1 \ \text{yard}^2\)

Number of poster signs that can be cut :

\(\dfrac{\text{Area of poster board}}{\text{Area of poster sign}}\)

\(1 \ \text{yard}^2\div (\dfrac{1}{27} ) \ \text{yard}^2\)

\(1 \div \dfrac{1}{27}\)

\(1 \times \dfrac{27}{1}\)

\(\bold{= 27 \ poster \ signs}\)

Levi pays $3.99 for her ride as per the values given in the problem.

A percentage is a value that indicates 100th part of any quantity. A percentage can be converted into a fraction or a decimal by dividing it by 100. In the same manner a fraction being multiplied by 100 becomes percent.

The charge for the uber ride is given as $19.95.

And, the percent value of the tip is 20%.

Now, the amount of tip can be calculated by taking the percent value of the total charge as follows,

20% × Uber charge for ride  

⇒ 20% × 19.95

⇒ 20/100 × 19.95

⇒ 3.99

Hence, the required money to be paid by Levi is given as $3.99.

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Answer: G

Step-by-step explanation:

when professional service worker, farmer and government worker are added up the percentage is equal to 50% which is half of the chart.

The polynomial -6x⁵ - 1/8 - x³ in standard form is -6x⁵ - x³ - 1/8

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

-6x⁵ - 1/8 - x³

To rewrite polynomial in standard form, we order the powers in decreasing order

Using the above as a guide, we have the following:

-6x⁵ - x³ - 1/8

Hence, the polynomial in standard form is -6x⁵ - x³ - 1/8

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Answer:

1 lemon = 2 cups of lemonade

Step-by-step explanation:

Answer:

x= 4.33333333

Step-by-step explanation:

First, you need to get the constants to the other side. That would equal 13. You do this by using the opposite sign to get it to the other side. In this instance you would first add 6 to -6 and 0:

-6 = 0

+6 +6

You do this with all the other constants until you have this

3x = 13

You then divide each side by 3 because the whole point of solving the equation is to get x by itself. After you divide 3x by 3 you cancel out the 3 there. And when you divide 13 by 3 you get 4.33333333

So x = 4.33333333

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

..

...the second one .......

The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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The integral test compares an infinite sum to an improper integral and is the test that can only be applied when we are considering a series whose terms are all positive.

1) For a series ∑n=1∞aₙ to converge, the nth term an must satisfy aₙ→0

 as n→∞.

Therefore, from the algebraic limit properties of sequences,

lim k→∞a k = lim k→∞(S k−S k−1)=limk→∞S k−lim k→∞S k−1 = S−S = 0.

Therefore, if  ∑n=1∞aₙ converges, the nth term an→0 as  n→∞. An important consequence of this fact is the following statement:

If aₙ↛0 as n→∞,∑n=1∞aₙ diverges

The integral test compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

2) The sum of the areas of the rectangles is less than the sum of the area of the first rectangle and the area between the curve f(x)=1/x2 and the x -axis for x≥1

Since the area bounded by the curve is finite, the sum of the areas of the rectangles is also finite.

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The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Answer:

\((4f)^3 = 64*f^3\)

\((-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4\)

Step-by-step explanation:

Solving (a):

\((4f)^3\)

Apply law of indices:

\(x^3 = x * x * x\)

So, we have:

\((4f)^3 = 4f * 4f * 4f\)

Rewrite as:

\((4f)^3 = 4 * 4 * 4*f*f*f\)

\((4f)^3 = 64*f^3\)

Solving (b):

\((-\frac{3}{2}t^2)^2\)

Apply law of indices:

\(x * x = x^2\)

So, we have:

\((-\frac{3}{2}t^2)^2 = (-\frac{3}{2}t^2) * (-\frac{3}{2}t^2)\)

Remove brackets

\((-\frac{3}{2}t^2)^2 = -\frac{3}{2}t^2 * -\frac{3}{2}t^2\)

Rewrite as:

\((-\frac{3}{2}t^2)^2 = -\frac{3}{2}*-\frac{3}{2}*t^2 * *t^2\)

\((-\frac{3}{2}t^2)^2 = \frac{3}{2}*\frac{3}{2}*t^4\)

\((-\frac{3}{2}t^2)^2 = \frac{9}{4}*t^4\)

\((-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4\)