Consider 4x + 12 ≤ 28. Which value of x makes the given inequality TRUE?

Responses

A 1010

B 77

C 33

D 6

The expression that is equivalent to 38(251m − 45) is

The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.

This property also holds of subtraction

In the problem, applying distributive property gives

38(251m − 45)

= 38 * 251 m - 38 * 45

this is equivalent to option A and hence the answer

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Answer:

52

Step-by-step explanation:

14+13= 27+2=29+23=52

The value of the numerical expression 12 ⋅ (14 + 13)² + 23 will be 8771.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The expression is given below.

⇒ 12 ⋅ (14 + 13)² + 23

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.

⇒ 12 ⋅ (14 + 13)² + 23

⇒ 12 ⋅ (27)² + 23

⇒ 12 ⋅ 729 + 23

⇒ 8748 + 23

⇒ 8771

The value of the numerical expression 12 ⋅ (14 + 13)² + 23 will be 8771.

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The sum of the Polynomial as required to be used to verify the additive property is; 5x² + 5x +9.

Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x).

Hence, to justify the associative property; we must sum up the polynomials given in two ways as follows;

Method 1;

(3x + 4) + ( (5x² - 1) + (2x + 6) )

3x + 4 + ( 5x² + 2x + 5 )

3x + 4 + 5x² + 2x + 5.

Therefore, the sum is; 5x² + 5x + 9

Method 2;

(3x + 4) + ( (5x² - 1) + (2x + 6) )

= ( 3x + 4 + 5x² - 1 ) + ( ( 2x + 6 ) )

= 5x² + 3x + 3 + ( (2x + 6) )

5x² + 3x + 2x + 3 + 6

5x² + 5x +9

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Answer:

c= 5 yards.

Step-by-step explanation:

4*1.5=6

30/6= 5

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

4, 2, 9, 3, 6

Step-by-step explanation:

756/4= 189

756/2= 378

756/9= 84

756/25= 30.24

756/5= 151.2

756/8= 94.5

756/10= 75.6

756/3= 252

756/6= 126

The arc cossecant of the given value is of 30º.

The cosecant of an angle is given by the ratio between 1 and the sine of the angle, as follows:

cos(x) = 1/sin(x)

The arc cossecant of an angle is represented by the expression arc csc(x), and represents the inverse of the cossecant, that is, it is the angle which has a cosecant of x.

In this problem, the arc cossecant that is asked is:

\(\arccsc{\left(\frac{2}{3\sqrt{3}}\right)}\)

Basically, it asks for the angle which has a cossecant value of 2/(3sqrt(3)). This angle is found using a calculator, and it is of 30º.

Hence the numeric value of the expression is presented as follows:

\(\arccsc{\left(\frac{2}{3\sqrt{3}}\right)} = 30^\circ\)

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To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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Answer:

lim as x---->0 of (x²-5) = -5 which is D

Answer:

The answer is

(f.g)(x)= x^5-2x^3+2x^2-8x+4

Step-by-step explanation:

Hope this helps:)

In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.

If we substitute the points from option A, we get

for (1,8), we have

then, option A is false.

Now, if we substitute the points in option B, for point (2,5), we have

which is correct. Now, for point (-1.8) we obtain

Since all the points fulfil the equation, then option B is an answer.

Lets continue with option C and D.

If we substitute point (1,8) from option C, we have

then, option C is false.

If we substite point (4,11) from option D, we get

then, option D is false.

Therefore, the answer is option B.

1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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Answer:

z = 3/31

Step-by-step explanation:

5z + 3 = 36z

subtract 5z on both sides

3 = 31z

divide by 31 on both sides

z = 3/31

Answer: the number of sides of a regular polygon is the same as the number of lines of reflection that can map the polygon into itself. The number of lines of symmetry is the same as the number of lines of reflection for mapping. (this is word for word so i suggest rewording)

Step-by-step explanation:

Answer:

The number of sides of a regular polygon is the same as the number of lines of reflection that can map the polygon onto itself. The number of lines of symmetry is the same as the number of lines of reflection for mapping.

Step-by-step explanation:

PLATO

La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.

En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.

Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:

I = (1 + r / 36500)ⁿ

Donde:

La situación es descrita por la siguiente expresión matemática:

1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵

Donde R es la tasa efectiva de interés anual.

Finalmente, despejamos la variable correspondiente:

R = 21,375

La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.

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Answer:

well its -3

Step-by-step explanation:

i did the work

Answer:

Either, (9+√69)/6 or (9-√69)/6

Step wise:

3x²-9x+1=0-------------------(i)

comparing equation onw with (ax²+bx+c=0), we get,

a=3, b=-9, c=1

now,

using Quadratic Formula,

(-b±√b²-4ac)/2a=x

{-(-9)±√(-9)²-4.3.1}/2.3=x

(9±√81-12)/6=x

(9±√69)/6=x

Taking +(ve) sign                   Taking -(ve) sign

(9+√69)/6=0                           (9-√69)/6=0

∴(9+√69)/6=0                         ∴(9-√69)/6=0

[∵They cannot be further solved]

The solutions to the given quadratic equation are x = 2.884 and

x = 0.116.

The equation of the form ax² + bx +c is known as a quadratic equation.

The given equation is 3x² - 9x + 1 =0.

Solve the equation as follows:

3x² - 9x + 1 =0

Use the quadratic formula to solve the equation:

\(x = \frac{-(-9)\pm\sqrt{(-9)^2-4(3)(1)}}{2(3)}\\\\x= \frac{9\pm\sqrt{81-12}}{6}\\\\x=\frac{9\pm\sqrt{69}}{6}\\\\x = \frac{9\pm8.306}{6}\\\\x=\frac{9+8.306}{6}\quad\text{ or }x=\frac{9-8.306}{6}\\\\x=2.884\quad\text{ or }x=0.116\)

Hence, the solutions to the given quadratic equation are x = 2.884 and

x = 0.116.

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The surface area of the wooden structure is approximately 1012 cm².

To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.

Surface Area of the Cone:

The surface area of a cone is given by the formula:

A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.

The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:

\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)

Using the given measurements:

\(s_{cone\) = √(7² + 24²) cm

\(s_{cone\) ≈ √(49 + 576) cm

\(s_{cone\) ≈ √625 cm

\(s_{cone\) ≈ 25 cm

Now, we can calculate the surface area of the cone:

\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)

\(A_{cone\) = (22/7) × 7 cm × 32 cm

\(A_{cone\) = 704 cm²

Surface Area of the Hemispherical Base:

The surface area of a hemisphere is given by the formula:

\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.

Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:

\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²

\(A_{hemisphere\) = (22/7) × 2 × 49 cm²

\(A_{hemisphere\) = 308 cm²

Total Surface Area:

To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:

Total Surface Area = \(A_{cone} + A_{hemisphere}\)

Total Surface Area = 704 cm² + 308 cm²

Total Surface Area = 1012 cm²

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Correct Option is No matter what number you choose to substitute for the variable, the result will be a true statement.

The number of solutions of an equation based on the total number of variables contained in it. As a result, the equation system consists of two or more equations with two or more variables.

It can be any combination such as

There are three different forms of equation solutions, depending on the quantity of variables and equations. They are

The term “infinite” represents limitless or unboundedness.

For the infinite number of solution of the equation No matter what number you choose to substitute for the variable, the result will be a true statement.

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Answer:

The equation of the line in slope-intercept form is:

\(\:y=-\frac{1}{6}x\:+\:4\)

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where  

Given the points on the line graph  

Determining the slope between (0, 4) and (3, 3.5)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{3.5-4}{3-0}\)

\(m=\frac{\frac{7}{2}-4}{3-0}\)

\(m=-\frac{1}{6}\)

Thus, the slope of the line = m = -1/6

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 4

Thus, the y-intercept b = 4

now substituting b = 4 and m = -1/6 in the slope-intercept form

\(y = mx + b\)

\(\:y=-\frac{1}{6}x\:+\:4\)

Therefore, the equation of the line in slope-intercept form is:

\(\:y=-\frac{1}{6}x\:+\:4\)

Answer:

y=5x-11 is the equation of the required line

The interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.

Suppose that the function is y = f(x)

If for an interval I, when x increases meanwhile staying in the interval I, the function's output decreases (or can stay same), then we say that the function is decreasing in the interval I.

This interval I was of values that x can take for this function, which is the domain of the considered function, so we say:

y = f(x) is decreasing function in an interval I if:

\(f(x+\delta) \leq f(x) \: \forall x \in I : x+\delta \in I\)

If we have:

\(f(x+\delta) < f(x) \: \forall x \in I : x+\delta \in I\), then the function is called strictly decreasing in the interval I.

Similarly, there increasing( \(f(x+\delta) \geq f(x) \: \forall x \in I : x+\delta \in I\) ) and strictly increasing(\(f(x+\delta) > f(x) \: \forall x \in I : x+\delta \in I\) ) functions.

For this case, the function is:

\(h(x) = \left \{ {{2^x, x < 1} \atop \: \atop {\sqrt{x+3}, x \geq 1}} \right.\)

The function is differentiable in either side of 1.

Sign of rate of function at a point tells whether its increasing or decreasing.

\(h'(x)= 2^x ln(2)\)
We know that:

\(2^x > 0 \: \rm \forlall x \in \mathbb R\)

And \(ln(2) \approx 0.69 > 0\)

Thus, \(h'(x)= 2^x ln(2) > 0 \: \forall x \in \mathbb R\)

So, rate is positive, the function is strictly increasing for this case.

\(h'(x) = \dfrac{1}{2\sqrt{(x+3)}}\)

For all x > 1, \(\sqrt{x+3} > 0\), and so as h'(x)

So rate is positive and therefore strictly increasing for this case too.

\(h(1+\delta) - h(1)= \sqrt{1+\delta + 3} - \sqrt{1+3} = \sqrt{4+\delta} - \sqrt{4} > 0 \forall \delta > 0\)

So rate of the considered function is positive,so function is strictly increasing all over the domain.

Thus, the interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.

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The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28

From the given information, we are to determine the expression that is equivalent to the given expression

The given expression is

(ab⁷)⁴

To determine the expression that is equivalent to this expression, we will expand the given expression

Expanding the expression

(ab⁷)⁴

Applying the distributive exponent law of indices,

(a)⁴ × (b⁷)⁴

Simplifying

a⁴ × b²⁸

= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸

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Answer:

I think it's a4b28

Step-by-step explanation:

Answer:(7/3)x - 8/3.

Step-by-step explanation:

To simplify this expression, you need to distribute the 1/3 to the expression inside the parenthesis. This gives:

1/3(5x-8) = (1/3)*5x - (1/3)*8 = (5/3)x - (8/3)

Now, you can distribute the 2/3 to the x-term:

2/3x = (2/3)x

Putting the two terms together, you get:

(5/3)x - (8/3) + (2/3)x = (5/3 + 2/3)x - 8/3 = (7/3)x - 8/3

So, the simplified expression is (7/3)x - 8/3.

Answer:

Step-by-step explanation:

1/3(5x-8)+2/3x

multiply everything by the LCM of the denomenators

LCM of the denomenators=3

1/3 x 3=0

(5x-8)x3=15x-24

2/3x x3=2x

15x+2x-24

=17x-24

Answer: C

Step-by-step explanation:

Hello! :)

\(\large\boxed{\text{m = -8, b = 22}}\)

Find the slope and y-intercept by rearranging the equation into the following format:

y = mx + b

We are given the equation:

16x + 2y = 44

Rearrange by subtracting 16x from both sides:

2y = -16x + 44

Divide all terms by 2:

y = -8x + 22

In this equation, the m-value is -8 and the b value is 22.

Therefore, m = -8, and b = 22.