ASAP Select the statement that correctly describes the expression below.

(2x+5)^2
a) the sum of the square of 2 times x and 5

b)the square of the sum of 2 times x and 5

c)the square of 2 times the addition of x and 5

d)the sum of 2 times x and the square of 5

Answer:

Measure of ∠A is 106°

Step-by-step explanation:

We are given that, 'Quadrilateral ABCD is inscribed in the circle'.

So, we get that,

'ABCD is a cyclic quadrilateral' i.e. The sum of the opposite interior angles is 180°.

Thus, we have,

∠A +∠C = 180°

i.e. ∠A + 74° = 180°

i.e. ∠A = 180° - 74°

i.e. ∠A = 106°

Thus, the measure of ∠A is 106°.

By forming an algebraic equation based on the given information, we find that Elga's age is 29 years.

This question belongs to the category of Algebraic equations. We know that Alvin's age is two times Elga's, so we could represent Alvin's age as 2E, where E represents Elga's age.

The problem also tells us that the sum of their ages equals 87. That means we can form this equation: E + 2E = 87.

Combining like terms, we get 3E = 87. Finally, dividing each side by 3, we find the value of E (Elga's age).

So, Elga's age is 87 / 3, which equals 29 years.

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Final answer:

The area of a rectangle with dimensions of 1/3 yards by 2/3 yards is calculated using the formula length × width, resulting in an area of 2/9 square yards. This value is already in simplest form.

Explanation:

The question asks us to find the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to calculate the area of a rectangle is length × width. Therefore, to find the area, we multiply 1/3 yards by 2/3 yards.

Area = (1/3) yd × (2/3) yd = 2/9 yd²

This calculation shows that the area of the rectangle is 2/9 square yards. It is important to express the answer in simplest form, as the question requests, and 2/9 is already in its simplest form.

Answer:

the answer is 2 and 2/3 if that doesn't pop up then 8/3 also works.

Step-by-step explanation:

Final answer:

The patient should be given 0.25 mls of the medication.

Explanation:

To calculate the volume of medication a patient should be given, we can use a basic formula that relates the ordered dose, the concentration of the medication available, and the volume required to deliver the ordered dose. In this case, the student has been asked to determine how many milliliters (mls) of medication to administer when 0.5 mg is ordered and the medication concentration available is 2 mg/ml.

The formula to use is:

Dose ordered (mg) / Concentration of medication (mg/ml) = Volume to administer (ml)

So for this problem:

0.5 mg / 2 mg/ml = 0.25 ml

Therefore, the patient should be given 0.25 mls of the medication.

Let us denote the total land area of Tennessee by [tex] T [/tex].

Now, It has been given to us that the total land area of Tennessee is about 53927 square miles.

Therefore, [tex] T=53927 [/tex]

It has also been given to us that the total land area of the United States is about 3483511 square miles more than the total land area of Tennessee.

Let us denote the total land area of the United States by [tex] U [/tex].

Now, if the total land area of the United States (denoted by [tex] U [/tex]) is 3483511 square miles more than the total land area of Tennessee (which is 53927 square miles and is denoted by [tex] T [/tex]), then that means that we have to add 3483511 square miles to the total land area of Tennessee to get the total land area of the United States. This can be written in the equation form as:

[tex] U=3483511+T=3483511+53927=3537438 [/tex]

Thus the total area of the United States is 3537438 square miles.

Final answer:

The total land area of the United States is calculated by adding the land area of Tennessee to the difference given in the question. The equation is US Area = 53,927 + 3,483,511. Solving this equation, the total land area of the United States is approximately 3,537,438 square miles.

Explanation:

To find the total land area of the United States, we can use the given information and set up an equation. The total land area of Tennessee is about 53,927 square miles. The question states that the total land area of the United States is about 3,483,511 square miles more than Tennessee's land area. We can express this relationship with the following equation:

Total land area of the United States = Land area of Tennessee + 3,483,511 square miles

US Area = 53,927 + 3,483,511

Solving for the total land area of the United States:

US Area = 3,537,438 square miles

Therefore, the total land area of the United States is approximately 3,537,438 square miles.

Using factorization, the factors of the given equation are; ±√5 and ±10i.

In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.

we have been given the equation:

x⁴ + 95x² – 500 = 0

Factorizing the above equation,

x⁴ + 100x² - 5x² - 500 = 0

x²(x² + 100) - 5(x² + 100) = 0

(x² - 5)(x² + 100) = 0

Solving further:

x² = 5

x² = -100

x = ±√5

x = √-100

Factors : ±√5 and ±10i

Therefore, we know that the factors of the given equation are; ±√5 and ±10i.

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I will have to pay $4500 interest for the loan I have taken to start a small business.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = $10,000, r = 9% and t = 5.

∴ SI = (10000×9×5)/100.

SI = 100×45.

SI = 4500.

So, I need to pay $4500 for the loan.

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Answers:

She made __50__ grams of __20__% solution

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Work Shown:

There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.

We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.

By using a rule of 3, we will see that:

In the first case, we want to know by what percent of the first number is the second larger.

Then the 100% will be taken as the first number, so we have the relation:

100% = 15

And the other number will represent a percentage X, so we write:

X = 20

By taking the quotient of these two equations, we get:

X/(100%) = 20/15

Solving this for X, we get:

X = (20/15)*100% = 133.33%

We can conclude that the second number is 33.33% larger than the first number.

For the second part, we take 20 as our 100%, and we do the same thing:

X = (15/20)*100% = 75%

Then 15 is (100% - 75% = 25%) 25% smaller than 20.

As you can see the percentages are different. Why does this happen? because in each case the 100% represents a different number.

Finally, we can conclude that:

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Answer:

The given rectangle is not possible.

Step-by-step explanation:

The minimum perimeter of such a rectangle is 4√30 meters, about 21.9 meters. That is about 71.9 feet. The largest rectangle with a perimeter of 26 feet will have an area of about 3.93 square meters.

The rectangle described cannot exist.

Answer:

A. [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]

Step-by-step explanation:    

Let x be the measure of arc BD.

Since we know that an angle formed by two intersecting tangents equals one-half the difference of the measures of the intercepted  arcs (the major arc-minus the minor arc).  

[tex]\text{ Measure of tangent-tangent angle}=\frac{1}{2} (\text{measure of major arc-measure of minor arc})[/tex]

We can see from our given graph that the tangent-tangent angle's measure is 53 degree. The measure of its intercepting major arc equals 233 degrees and minor arc equals x.

Upon substituting our given values in above formula we will get,

[tex]53^{o}=\frac{1}{2} (233^{o}-x)[/tex]

[tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]

Therefore, the equation that can be solved to find x (the measure of arc BD) will be [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex] and option A is the correct choice.

Answer:

The statement "They are parallel" is true.

Step-by-step explanation:

The general form of the equation of a straight line is:

[tex]Ax+By+C=0[/tex]

where A, B, and C are three real numbers.

A line parallel to the x-axis has this form [tex]y=C[/tex] where C is a real number.

A line parallel to the y-axis has this form [tex]x=C[/tex] where C is a real number.

From the lines given none of these have the form of a line parallel to the x-axis or the y-axis. Therefore the statements "They are parallel to the x-axis" and "They are parallel to the y-axis" are false.

Two non-vertical lines in a plane are parallel if they have both:

Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.

To check if the lines are parallel of perpendicular you must transform these lines into the slope/intercept form

[tex]y=mx+b[/tex]

where m represents the slope and b represents the y-intercept.

The slope/intercept form for the first line is:

[tex]3y+2x-9=0\\\\3y+2x-9-2x=0-2x\\\\3y-9=-2x\\\\3y-9+9=-2x+9\\\\3y=-2x+9\\\\y=\frac{-2x+9}{3}\\\\y=\frac{-2}{3}x+3[/tex]

The slope/intercept form for the second line is:

[tex]12y+8x-5=0\\\\12y+8x-5-8x=0-8x\\\\12y-5=-8x\\\\12y-5+5=-8x+5\\\\12y=-8x+5\\\\y=\frac{-8x+5}{12}\\\\y=\frac{-2}{3}x+\frac{5}{12}[/tex]

We can see that the lines have the same slope and different y-intercepts. Therefore the statement "They are parallel" is true.

We can check our work with the graph of the lines.

Final answer:

To find the actual length represented by YX, we set up a proportion using the given scale length and solve for the unknown length x. Using one of the provided scale ratios, such as 0.5 inches representing 2000 miles, we perform cross-multiplication to solve for x and determine the accurate length after calculations.

Explanation:

The student is asked to find the actual length represented by the segment YX on a map or a diagram when given a scale length. To solve the problem, we set up a proportion based on the scale provided and solve for the unknown length x. There are different given scales in the prompts such as 0.5 inches representing 2000 miles, 8 inches representing an unknown number of miles, and 3 inches also representing an unknown number of miles.

Example with a Scale Ratio of 0.5 inches to 2000 miles

To solve for x when the scale is 0.5 inches on the map corresponds to 2000 miles in reality, we use a proportion: 1 inch/2000 miles = 0.5 inches/x miles. After cross-multiplication, we get x = 0.5 inches * 2000 miles, which after calculation will give us the value of x rounded to the nearest hundredth.

Example with a Scale Ratio of 0.25 inches to 2000 miles

Similar steps are taken if the scale is 0.25 inches. We set up the proportion 1 inch/2000 miles = 0.25 inches/x miles and solve for x after cross-multiplication.

The length of the diagonal of this monitor, to the nearest tenth of an inch, would be 14.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall.

[tex]a^2 + b^2 = c^2\\12^2 + 7^2 = c^2\\144 + 49 =c^2\\193 = c^2\\c= 13.89 14[/tex]

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