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The equations that gives true value for x = -2 and x = 2 are option A: x² - 4 = 0 and option D: 4x² = 16.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equations that are true for x = -2 and x = 2 are -

x² - 4 = 0 (when x = -2, this becomes 4 - 4 = 0; when x = 2, this becomes 4 - 4 = 0)

4x² = 16 (when x = -2, this becomes 4(4) = 16; when x = 2, this becomes 4(4) = 16)

The other options are not true for x = -2 and x = 2.

Specifically -

x² = -4 is not true for any real value of x, since the square of any real number is always non-negative.

3x² + 12 = 0 is not true for x = -2 or x = 2, since plugging in these values gives 12 ≠ 0.

2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since plugging in x = -2 gives 2(16) ≠ 0.

Therefore, the options x² - 4 = 0 and 4x² = 16 are the correct ones.

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Answer:

Below

Step-by-step explanation:

15 point average for 6 games = 90 points total

   for the final 6 games she can score a total of 90 points to maintain her average of 15 points per game

  there are a LOT of possibilities....here is one

   Pts:   16    14    16   14   16  14    = 90 points (with no 15 point games)

The inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is 202.5 + 36.39x ≤ 480.

What is an inequality?

An inequality is a comparison between two or more mathematical expressions. It can be of the form ≤, ≥, < or >.

We are given per day charges as $36.39 and the charges per mile as $0.90.

Also, it is given that in total 225 miles have been driven.

So, the charges of 225 miles are:

⇒225 x 0.90

⇒$202.5

It is given that he can spend maximum $480.

So, for the maximum number of x days, we get the inequality as

202.5 + 36.39x ≤ 480

Hence, the inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is

202.5 + 36.39x ≤ 480.

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Answer:

To find the percent increase in price, we need to calculate the difference between the original price and the new price, and then express that difference as a percentage of the original price.

The original price of the sweatshirt was $40, and the new price is $65, so the difference is:

$65 - $40 = $25

To express this as a percentage of the original price, we divide the difference by the original price and multiply by 100:

($25 / $40) x 100% = 62.5%

Therefore, the percent increase in the price of the sweatshirt is 62.5%.

Lim initially had $5145, and he withdrew an additional $1040 from his bank account, so he had a total of:

$5145 + $1040 = $6185

Lim divided this total amount equally among his 5 sons, so each son would receive:

$6185 ÷ 5 = $1237

Therefore, each son would receive $1237.

Answer:

Step-by-step explanation:

to write the proportion is a number of the girl in intramural sport is [tex]\frac{x}{y} 2/3=230[/tex]

and find the number a girl in intramural sport is 90

The base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.

Exponential growth is a mathematical concept that describes a process where a quantity grows at an increasing rate proportional to its current value. In other words, the larger the quantity, the faster it grows. This leads to a graph that is characterized by a rapid upward curve that becomes steeper and steeper over time.

Exponential growth is often represented by the equation y = abˣ, where y is the final amount, a is the initial amount, b is the growth factor or base, and x is the time or number of periods.

The function f(x) = a(1+r)ˣ represents exponential growth, where "a" is the initial value, "r" is the growth rate as a decimal, and "x" is the time variable.

In this case, the initial value is 50, and the growth rate is 75%, or 0.75 as a decimal. Therefore, the equation for the function becomes:

f(x) = 50(1+0.75)ˣ

Simplifying this expression, we have:

f(x) = 50(1.75)ˣ

Since the base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.

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Answer: If we let "the number of snakes" be represented by the variable "s", we can write the equation as:

s - 24 = 35

This can be simplified by adding 24 to both sides:

s = 59

Therefore, the number of snakes is 59.

Step-by-step explanation:

Step-by-step explanation:

Please when you come across any questions including two equations of two variables, please solve that question by using the simultaneous method.

To go about that, since you would be given two equations, name one equation as "equation one" (eq 1) and the other, "equation two" (eq 2).

Right after that, make any of the variables a subject ( make it stand alone or be on one side of the equal to sign). Now, substitute that variable you've made the subject into the other equation which you didn't make any variable the subject. Solve for that, by grouping all like terms and you would realize that the final result would be the answer of one of the variables.

After getting that value, substitute that value in place of its variable. (For instance, x = 1, substitute the value which is 1 in place of x in the equation you made a variable the subject at the beginning). Solve for that equation too, and finally you would arrive at an answer or a value.

To verify that your answers are right, substitute the values in their respective variables. ( For instance, if x = 1 and y = 2, put 1 in place of x and 2 in place of y in the first equation then do same for the second equation as well). The answer would be the same as the number it has been equated to.

The cardinality of (B ⋃ C) will be n(B ⋃ C)=3.

In mathematics, cardinality refers to the size or number of elements in a set. It is a concept used to compare the sizes of sets, regardless of their specific elements. For instance, the cardinality of the set {1, 2, 3} is 3, while the cardinality of the set {2, 4, 6, 8, 10} is 5. Cardinality is typically denoted using vertical bars, such that |S| represents the cardinality of set S.

Now,

The symbol "n(S)" represents the cardinality

To find the cardinality of the sets:

We have to see how many elements are there in (B ⋃ C) and

As we can see from Venn diagram there are 23 elements in (B ⋃ C) i.e.

5+3+1+2+4+8

Hence,

           The cardinality of n(B ⋃ C) will be 23.

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1) The volume of the first rectangular prism is 175 ft³

2) The volume of the second rectangular prism is 60ft³

3) The volume of the third rectangular prism 140ft³

4) The volume of the Fourth rectangular prism 216ft³

Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.

Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:

a)

Length = 7ft

Height = 2ft

width = 2ft

Volume = Volume = 7ft x 2ft x 2ft

Volume = 28  ft³

b)

Length = 7ft

Height = 3ft

width = 7ft

Volume = 147 ft³

Total Volume = 28  ft³ + 147 ft³

Volume for Shape 1 = 175 ft³

In shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 3ft

Height = 2ft

width = 1ft

Volume = 6 ft³

b) Length = 6ft

Height = 3ft

width = 3ft

Volume = 54 ft³

Thus, total volume for shape 2 is:

Volume = 6 + 54

Volume = 40 ft³

Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 7ft

Height = 1ft

width = 2ft

Volume = 14ft³

b)

Length = 7ft

Height = 3ft

width = 6ft

Volume = 126ft³

Thus, the total volume for shape 3, =

Volume = 14ft³ + 126ft³

Volume = 140ft³

Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 4ft

Height = 3ft

width = 2ft

Volume = 24 ft³

b) Length = 4ft

Height = 12ft

width = 4ft

Volume = 192 ft³

Thus, the total volume for Shape 4:

Volume =  24 ft³+ 192 ft³

Volume = 216ft³

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Answer:

look in the comments have a good day

The measures of the angles, obtained using circle theorems are;

a = 90°, b = 12°, c = 64°, d = 54°, e = 54°, f = 48°, g = 66°, h = 32°, i = 36°, and j = 20°

Circle theorems are theorems that specify the relationships between the chords, tangents, sectors, and angles in a circle.

The linear pair angles ∠a indicates;

a + a = 2·a = 180°

a = 180°/2 = 90°

The 78° angle in the inscribed right triangle indicates;

∠b = 90° - 78° = 12°

The 32° angle at the circumference of one of the circles indicates;

Angle at the center, which nis a base angle of the large triangle = 2 × 32° = 64°

A base angle of the large triangle = 64°

∠C = A base angle of the large triangle = 64°

2·c + d = 180° (Properties of a cyclic quadrilateral)

Therefore;

2 × 64° + d = 180°

d = 180° - 2 × 64° = 54°

d = 54°

Angle ∠e = Angle ∠d = 54°

The vertex angle of the inscribed isosceles triangle in the circle with angle ∠f is; 4·b

Therefore;

The vertex angle = 4 × 12° = 48°

An angle formed between a chord and a circle is equivalent to the angle in the segment that is in the alternate side or area, therefore;

Circle theorem indicates; ∠f = The vertex angle = 48°

The base angles of the isosceles triangle = (180° - 48°)/2 = 66°

Angle ∠g = 66°

The  chord which is the base of the isosceles triangle in the circle with the angle h forms an isosceles triangle with the sides of the large triangle, such that the base angles are also ∠c = 64°

Circle theorem indicates that the vertex angle of the triangle with angle h is also 64°

Therefore, according to circle theorem; 2·h = 64°

h = 64°/2 = 32°

The vertex angle of the quadrilateral with angle 2·f is; 180° - 2·f

The vertex angle is therefore; 180° - 2 × 48° = 84°

The angle at the center is therefore; 2 × 84° = 168°

Angle ∠i is therefore;

i = 360° - 5·b - 2·f - 168°

i = 360° - 5 × 12° - 2 × 48° - 168° = 36°

5·b + 2·h + i + j = 180°

Therefore; j = 180° - (5·b + 2·h + i)

j = 180° - (5 × 12° + 2 × 32° + 36°) = 20°

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Answer: 5/7 of the kids chose New York or L.A.

Step-by-step explanation:

All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:

4/7 + 1/7 = 5/7

There are only one solution  x= 1/2 in the expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.\

Given that;

The expression is,

⇒ 8x - 4 = 3 - 6x

Now, We can simplify the expression as;

⇒ 8x - 4 = 3 - 6x

Add 6x both side,

⇒ 8x + 6x - 4 = 3 - 6x + 6x

⇒ 14x - 4 = 3

Add 4 both side,

⇒ 14x - 4 + 4 = 3 + 4

⇒ 14x = 7

Divide by 14;

⇒ x = 7/14

⇒ x = 1/2

Thus, There are only one solution  x= 1/2 in the expression.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{22\% of 72}}{\left( \cfrac{22}{100} \right)72}\implies 15.84~\hfill \underset{ new~price }{\stackrel{ 72~~ + ~~15.84 }{\text{\LARGE 97.84}}}[/tex]

The number of different ways will be 108000.

Permutations are various ways to arrange things in a specific order. It can also be stated as the linear reordering of items in an already ordered set.

A first guess for the number of ways to select a committee consisting of 3 engineers, 2 physicists, and 2 computer scientists from 10 engineers, 5 physicists, and 6 computer scientists could be to simply multiply the number of ways to select each group separately:

10 choose 3 x 5 choose 2 x 6 choose 2

This would give us the number of ways to select 3 engineers out of 10, 2 physicists out of 5, and 2 computer scientists out of 6.

The number of ways can be,

N = ¹⁰C₃ x ⁵C₂ x ⁶C₂

N = 10 x 9 x 8 x 5 x 6 x 5

N = 108000

Therefore, the number of different ways will be 108000.

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The values of f(-10) = 20101 , f(2) = 17 , f(3) = 142.

An expression consisting of variables, coefficients, and non-negative integer exponents is known as polynomial. For example, 2x² + 3x - 5 is a polynomial with three terms. The highest exponent of the variable is the degree of a polynomial. Polynomials can be used to represent many mathematical and scientific concepts, such as curves and functions.

To find f(-10), we need to substitute -10 for x in the given polynomial:

F(-10) = 2(-10)⁴ + (-10)²-10(-10) + 1

= 20000+100+100+1

= 20101

To find f(2), we again substitute 2 for x in the polynomial:

F(2) = 2(2)⁴ + (2)² -10(2) + 1

= 32+4-20+1

= 17

To find f(3), we can use synthetic division with 3 as the divisor. The coefficients of the polynomial are 2, 0, 1, -10, and 1.

F(3) = 142

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After simplificatiοn οf the given expressiοn the factοr is 11. Thus, οptiοn b is cοrrect.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

When we replace these in the statement, we get:

=[tex]\dfrac{(2^{10} \times 3^{10})(5^3 \times 11^3)(3^2 \times 5^2) }{(2^{10} \times 5^5)(3^{12})(11^{20})}[/tex]

= [tex]\dfrac{(11 \times 15^2) } {15^2}[/tex]

= 11

After simplificatiοn of the given expressiοn the factor is 11. Thus, οption b is correct.

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The value of the function g(x + a) - g(x) is a(-2x - a + 5).

To find the value of function g(x + a) - g(x), we first need to substitute g(x + a) and g(x) into the expression and simplify:

g(x + a) - g(x) = [- (x + a)^2 + 5(x + a)] - [-x^2 + 5x]

= [-x^2 - 2ax - a^2 + 5x + 5a] - [-x^2 + 5x]

= -x^2 - 2ax - a^2 + 5x + 5a + x^2 - 5x

= -2ax - a^2 + 5a

= a(-2x - a + 5)

Therefore, the value of g(x + a) - g(x) is a(-2x - a + 5).

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Proportionately, if Lexi uses 360 g of flour, the quantity of blueberries she must use is 150 g of blueberries.

Proportion describes the two ratios equated to each other.

Proportions are fractional values between zero and one.

Recipe for making Blueberry Muffins

Ingredient  Quantity

Egg              1

Flour           120 g

Sugar         120 g

Butter          60 g

Blueberries 50 g

120 g of flour = 50 g of blueberries

The Ratio of flour to blueberries = 2.4:1

360 g of flour = 360/120 x 50

= 150 g of blueberries (360/2.4)

Thus, if Lexi uses 360 g of flour, based on the given recipe, she must use 150 g of blueberries.

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Answer:

A. (1,2), (2,4), (3,6), (4,8)

Step-by-step explanation:

The 1st number in parenthesis is the number of boxes of popcorn. The 2nd number is the cost.

The correct equation is P = (a x b) ÷ 43, 560

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, an agricultural research assistant, you often need to calculate the amount of pesticide needed for test fields.

For each acre, b pounds of pesticide are required.

1 acre = 43,560 ft²

Pesticide needed for each acre = b / 43,560

Pesticide needed for the given area = 43,560 (a x b)

Therefore,

P = 43,560 (a x b)

Hence, the correct equation is P = (a x b) ÷ 43, 560

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Therefore, the types of transformation and the value of k for each equation are: Horizontal compression by a factor of 1/2, k = 0. Vertical stretch by a factor of 2, k = 0. Horizontal stretch by a factor of 2, k remains the same as in f(x). Vertical compression by a factor of 1/2, k = 0.

Given by the question.

We can use the given table of values for f(x) and the transformed function g(x) to determine the type of transformation and the value of k for each equation.

g(x) = f(2x):

This is a horizontal compression by a factor of 1/2. The value of k is not affected by this transformation, so k remains the same as in f(x).

g(x) = 2f(x):

This is a vertical stretch by a factor of 2. The value of k is also multiplied by 2, so k = 2(0) = 0.

g(x) = f(1/2x):

This is a horizontal stretch by a factor of 2. The value of k is not affected by this transformation, so k remains the same as in f(x).

g(x) = 1/2 f(x):

This is a vertical compression by a factor of 1/2. The value of k is also divided by 1/2, so k = (0)/(1/2) = 0.

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Answer:

C:  constant of proportionality is 5

Step-by-step explanation:

x       k       y

3       5        15

5       5        25

8       5        40

10      5        50

12      5        60

constant of proportionality (k) is 5.  All the rows check out.

y = kx = 5x

Therefore , the solution of the given problem of equation comes out to be w + x + y + z = 35 optian A is correct.

The same letter is frequently used in mathematical formulas to attempt to enforce uniformity among two variable assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.

Here,

In order to remove variables and obtain an expression for w + x + y + z, we can begin by adding the four equations. As a result, we get:

=> (5w + 3y + 7x -2z) + (3z - w + y -3x) + (-2x -2y + 3z - 2w) + (3x + 3y + z + 3w)

=>  17 - 4 + 9 + 13

By condensing both parts, we obtain:

=> 4x + 4y + 4z + 5w = 35

By separating it on one side, we can finally find the solution for

=> w + x + y + z:

=> w + x + y + z = 35

As a result, w + x + y + z = 35

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To solve the equation 3/4x + 3 - 2x = -1/4 + 1/2x + 5, we first need to simplify both sides by combining like terms:

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

Next, we can simplify the fractions on the right side by finding a common denominator of 4:

3/4x - 2x + 3 = -1/4 + 2/4x + 20/4

Simplifying the right side further, we get:

3/4x - 2x + 3 = 19/4 + 1/2x

Now we can isolate the variable x by moving all the terms containing x to one side of the equation and all the constants to the other side:

3/4x - 2x - 1/2x = 19/4 - 3

Combining like terms:

-5/4x = 5/4

Finally, we can solve for x by multiplying both sides by the reciprocal of -5/4:

x = -1

Therefore, the solution to the equation is x = -1.

The height of the skyscraper is 201.49 meters.

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Sadie is seeing a skyscraper making an angle of the elevation of 36°, she is 275 meters away from the skyscraper, we need to find the height of the skyscraper,

Using the concept of height and distance and trigonometric ratios,

Tan 36° = x / 275 [please refer to the figure attached]

x = 275 × Tan 36°

x = 199.80 meters

Therefore, the height of the skyscraper is x+1.69 = 199.80+1.69 = 201.45 m

Hence, the height of the skyscraper is 201.49 meters.

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The complete question is :-

From her eye, which stands 1.69 meters above the ground, Sadie measures the angle of elevation to the top of a prominent skyscraper to be 36. If she is standing at a horizontal distance of 275 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.