Which expression is equivalent to 1/2b -15?

A. -1/2 (b + 30)

B. -1/2 (b - 30)

C. 1/2 (b - 30)

D. 1/2 (b + 30)

Answer:

A

Step-by-step explanation:

Your answer was correct.

The account balance after 9 years is $528.28. The result is obtained by adding the interest to the initial deposit.

The simple interest of an amount of money can be counted by the following formula.

I = P₁ - P

I = P × r × t

Where

We have

Find the final account balance!

After 9 years, the simple interest of the savings is

I = P × r × t

I = $425.00 × 2.7% × 9 years

I = $3,825.00 × 0.027

I = $103.28

The final account balance would be

I = P₁ - P

$103.28 = P₁ - $425.00

P₁ = $425.00 + $103.28

P₁ = $528.28

Hence, after 9 years, the account balance would be $528.28.

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2 exponent is also known as the "square" of a number. When a number is raised to the power of 2, it means that the number is multiplied by itself.

For example, 2^2 means 2 multiplied by 2, which is equal to 4. The term "square" is used because the result of raising a number to the power of 2 is the same as finding the area of a square with that number as the length of each side.

This notation is widely used in mathematics, particularly in algebra and geometry. When we see a number with exponent 2, we can understand it as the number is multiplied by itself, which is the square of the number.

The term "square" is widely used in mathematics, particularly in algebra and geometry. Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.

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We solved using elimination method, For the given set of equations, no solution exists.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given,

two equations as

60x-42y=0                                                          ........... (1)

-100x + 70y=0                                                     ............(2)

Now, multiplying the equation (1) by 10 and (2) with 6

we get the equation as

⇒ (60x-42y=0) × 10

⇒ 600x - 420y = 0                                         ............(3)

⇒ (-100x + 70y=0 ) × 6

⇒ -600x + 420 = 0

Solving equation 2 and 3 simultaneously

⇒ 600x - 420y = 0

⇒ -600x + 420 = 0

⇒ x = y = 0

∴ No Solution exists for this problem

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Step-by-step explanation:

f(x) = 2x² - 7x - 7

f(6) = 2(6)² - 7(6) - 7

f(6) = 72 - 42 - 7

f(6) = 23

Answer:

A

Step-by-step explanation:

using BODMAS

3×7=21+2=23

The percentage and the z-scores for specific heights of the given normal distributions are as detailed below.

The first step is to draw the Normal curve with 8 regions, and then we now label the 7 vertical dividing lines with the mean plus/minus one/two/three standard deviations:

By adding the percentage values in the areas indicated in the question, we will arrive at;

The percentage of Ixxians that are;

i) Over 30 inches tall = 100% - (2.35% + 0.15%) = 97.5%

ii) Over 45 inches tall =  13.5% + 2.35% + 0.15% = 16%

iii) Under 50 inches tall = 100% - (2.35% + 0.15%) = 97.5%

iv) under 40 inches tall = 34% + 13.5% + 2.35% + 0.15% =  50%

v) between 35 and 55 inches tall = 34% + 34% +  13.5% + 2.35% = 83.85%

vi) between 25 and 35 inches tall = 13.5% + 2.35% 15.85%

The z-score is defined as the number of standard deviations above the mean corresponding to the given value. Thus;

i. For a height of 32 inches, the z-score is;

z = [32-40]/5

z = -1.6

ii. For a height of 47 inches, the z-score is;

z = [47 - 40]/5

z = 1.4

iii. For a height of 51 inches, the z-score is;

z = [51 - 40]/5

z = 2.2

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Complete question is;

The hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]

a) What percentage of Ixxians are

i over 30 inches tall?

ii over 45 inches tall?

iii under 50 inches tall?

iv under 40 inches tall?

v between 35 and 55 inches tall?

vi between 25 and 35 inches tall?

b) What is the z-score for an Ixxian of height?

i. 32 inches?

ii. 47 inches

iii. 51 inches

Answer 50 for the bottom and 48 for the sides

The exponent 3 is called the power or index. It is the number that indicates how many times the base number (in this case 3) is multiplied by itself.

To determine this

For example, 3³ means 3 multiplied by itself 3 times, or 3 x 3 x 3 = 27. So 3 is the base number and 3 is the exponent or power.

In mathematical notation, the exponent is written as a small number or variable above and to the right of the base number, with a caret symbol (^) separating them. For example, 3³ is written as 3³, and x² is written as x².

Additionally, in mathematics, exponents are also used to represent the number of times a number is multiplied by itself, the exponent number represents how many times the number is being multiplied.

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Answer: D

Step-by-step explanation:

The amount needs to be saved 8 times, and the phrase "at least" means the value can be greater than or equal to. So, the answer's the 4th option.

In an ordered pair (x,y), the x-coordinate comes first, followed by the y-coordinate. The x-coordinate represents the horizontal position of the point on a coordinate plane and the y-coordinate represents the vertical position of the point on a coordinate plane.

For example, in the ordered pair (4,3), 4 is the x-coordinate, and it represents the horizontal position, and 3 is the y-coordinate, and it represents the vertical position of the point (4,3) on a coordinate plane.

[tex]3 (2x - 4) = 3 (2x + 4)[/tex]

Distribute:

[tex](3)(2x)+(3)(-4)=(3)(2x)+(3)(4)[/tex]

[tex]6x-12=6x+12[/tex]

Subtract 6x from both sides:

[tex]6x-12-6x=6x+12-6x[/tex]

[tex]-12=12[/tex]

Add 12 to both sides:

[tex]-12+12=12+12[/tex]

[tex]0=24[/tex] (false)

[tex]\fbox{No solution}[/tex]

Answer:

False Expresion, Wrong , Error

Step-by-step explanation:

if solving for x

3 (2x - 4) = 3 (2x + 4) insert the 3 into the parenthesis [remember to imput for each element])

6x - 12 = 6x +12 False expression

if we decide to go further we would get

0x = 24

On solving the provided question, we can say that volume of cylinder  =  [tex]\pi r^2h[/tex] = 13564.8

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

volume of cylinder  =  [tex]\pi r^2h[/tex]

[tex]\pi[/tex] = 3.14

r = 15 cm\

h = 18 cm

V = [tex]3.14*15*16*18[/tex] = 13564.8

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When the object's acceleration reaches 6.67 m/s2, the force is 20 N.

The mass of an object determines the acceleration it experiences.

The force is 6 N if the object's acceleration increases to 3 m/s2.

Reason:

The parameters listed are;

The occupying force the object's acceleration.

The acceleration produced by a force, F, of 18 N is equal to 6 m/s2.

Newton's Second Law of Motion states that;

F = M × A

Where;

m = The object's mass

In light of the parameters, F = 18 N and a = 6 m/s2, we may determine the mass of the

the following is the provided object;

Weight = F/A

Therefore, the force acting when the acceleration is an is;

20 = 3 kg, where a = a = 6.67 m/s2.

When the object's acceleration reaches 6.67 m/s2, the force is 20 N.

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The inequality d > 3 has infinitely many solutions because 4 and any number to the right of 3 on the number line can be substituted for d to make this inequality true.

In Mathematics, an equation or an inequality is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.

This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.

The given inequality d > 3 simply means that the variable d is greater than three (3). Therefore, d represents the set of all possible real numbers that are greater than 3 and from the right of 4 on the number line for d > 3 because it has infinitely many solutions.

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Complete Question:

Use the drop-down menus to complete the statement about the inequality d > 3.

The inequality d > 3 has _____ solutions because ______ can be substituted for d to make this inequality true.

Options: for the first one 0 1 2 8 9 Infinitely many

For the second one: No numbers only 1 number 4 and any number to the right of 3 on the number line

The rule for the linear function in the table include the following: y = 2x.

In order to write a rule for the linear function, we would have to use the point-slope form formula. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the linear function representing the relationship between the x-value and y-value in the given table as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (4 - (-4))/(2 - (-2))(x - (-2))

y + 4 = 8/4(x + 2)

y + 4 = 2(x + 2)

y = 2x + 4 - 4

y = 2x

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Answer:

A, B, C, and G

Step-by-step explanation:

f(0)=75 is true because that's the y-intercept

f(30)=100 is true

f(20)=175 is true

f(0)=0 is not true because we already identified f(0) as 75

f(x)=100 when x=20 is not true because we already identified f(20) as 175

f(10)<f(5) is not true because looking at the graph, f(10)>f(5)

f(10)=f(15) is true because the graph is constant between the two points

Answer:

134 + 48 = 182

182 + x = 335

x = 153

Answer:

153

Step-by-step explanation:

335-134=201

201-48=153

Answer:

Step-by-step explanation:

-2x-3=-7

+3 +3
-2x=-4

/-2 /-2

x=2

Y=5(2)-9

Y=10-9

Y=1

Answer:

Step-by-step explanation:

y = 5x - 9 (eq'n 1)

-2x - 3 = -7 (eq'n 2)

Solve for x in (eq'n 2)

-2x -3 = -7 (add 3 to both side of the eq'n)

(-2x - 3) + 3 = -7 + 3

-2x = -4 (divide both side by -2)

x = 2

Therefore the value of y is:

From  (eq'n 1), Substitute the value of x

y = 5x - 9

y = 5(2) - 9

y = 1

To graph the inequality 2y - 4x < 8, we can start by isolating the y variable on one side of the inequality. To do this, we add 4x to both sides:

An explanation graph is what?

A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.

2y - 4x < 8

2y < 4x + 8

Next, we divide both sides by 2 to get y by itself:

y < 2x + 4

To graph this inequality, we can start by plotting the y-intercept, which is the point where x = 0. In this case, y = 2(0) + 4 = 4, so the y-intercept is (0, 4). Next, we can find the slope of the line, which is -2.

To graph the inequality -4y > -x + 12, we can start by isolating the y variable on one side of the inequality. To do this, we add x to both sides:

-4y > 12 - x

Next, we divide both sides by -4 to get y by itself:

y < -3 + (1/4)x

To graph this inequality, we can start by plotting the y-intercept, which is the point where x = 0. In this case, y = -3 + (1/4)(0) = -3, so the y-intercept is (0, -3). Next, we can find the slope of the line, which is (1/4).

The equation | x + 3 |= y represent a vertical line with x = -3

The equation |2x – 6| + 2 = y represent a V shape with the vertex at (-3,2)

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Answer:

200/3

Step-by-step explanation:

4+5=9

5\9*120=200/3

=

Answer:

The volume of a balloon is directly proportional to the cube of its radius, so we can use the formula:

V1/V2 = (R1/R2)^3

Where V1 is the initial volume, V2 is the final volume, R1 is the initial radius, and R2 is the final radius. We know that when the radius is 4 inches, the volume is 192 cubic inches, so we can use this information to find the final volume when the radius is 3 inches.

V1 = 192 cubic inches

R1 = 4 inches

R2 = 3 inches

V1/V2 = (R1/R2)^3

V2 = V1 / (R1/R2)^3

V2 = 192 / (4/3)^3 = 192/ (4/27) = 192 * 27/4 = 192 * 6.75 = 1296 cubic inches

So, 1296 cubic inches of gas must be released to reduce the radius down to 3 inches.

Answer: The expression (st)(6) means to substitute the value of 6 into the function (st) which is the composition of two functions s and t. The order of applying the functions is crucial, so the first function s will be applied to the result of the second function t after being applied to the 6. So the correct equivalent of (st)(6) is s(t(6))

Step-by-step explanation:

Discriminant of the eqaution √2x²-5x+√2 is 17

The discriminant of a polynomial in mathematics is a number that relies on the coefficients and allows inference of some root features without computing them. It is basically a polynomial function of the original polynomial's coefficients.

To calculate the Discriminant of a quadratic equation which   is generally expressed as

ax² + bx + c = 0

The quadratic equation's discriminant, indicated by the letter D, is defined as

D = b² - 4ac

So D= 5*5 -4 * √ 2 *√ 2

=> 25 -4 *2

=> 25-8

=> 17

so discriminant of the eqaution √2x²-5x+√2 is 17

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Complete question :

For √2x²-5x+√2=0 find the value of discriminant​

Answer:

X = 10

Step-by-step explanation:

Because it has a variable and that variable is raised to a certain power, the expression 3x2+2x is a polynomial.

A polynomial is a mathematical formula that involves only the operations addition, subtraction, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

A polynomial term, a series term, or an expression's multiplicative factor is known as a coefficient in mathematics. In addition to being any statement, it is frequently a number. If the coefficients are variables in and of themselves, they may also be known as parameters.

The fact that the above phrase 3x2+2x contains a variable makes it a polynomial. The power of that variable is likewise increased. The mathematical expression that results becomes a polynomial.

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Clare's account balance is $40

Clare has $150 in her bank account

She withdraws $110 from this money to purchase a bike

The amount of money left in her account after purchasing the bike can be calculated as follows

150-110

= 40

Hence Clare has $40 in her account after purchasing the bike

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Answer: y=−2.8x + 11.4

Answer:

-4 and -4

Step-by-step explanation:

The end behavior of the graphs of polynomial functions is determined by the highest degree of the polynomial.

For example, a polynomial with degree n will eventually approach infinity as x increases or decreases without bound. This can be expressed mathematically as:

f(x) = axn -> lim x->∞ f(x) = ∞

and

f(x) = axn -> lim x->-∞ f(x) = ∞

where a is a constant.

For a polynomial of degree n, the graph will have n-1 turning points. As the degree increases, the graph approaches a smooth curve. Additionally, the graph will have either one up-turn or one down-turn depending on the sign of the leading coefficient. If the leading coefficient is positive, the graph will have an up-turn; if the leading coefficient is negative, the graph will have a down-turn.

For example, the end behavior of the graphs of the polynomial f(x) = 2x3 + 2x2 - 2x - 1 has degree 3, so it will have 2 turning points and will have an up-turn as the leading coefficient is positive.

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