The ordered pairs (0, 5) and (1, 15) satisfy an exponential growth function. Write an
equation of the form f(x) = ab* for the function.

Answer:

  D.  y = 2 1/16

Step-by-step explanation:

You want to know the value of f(x) when x = 1/4 and f(x) = x²+2.

The domain of a function is the set of values for which it is defined. The given function f(x) is defined for all values of x. However, the problem statement tells you the only domain value of interest is x = 1/4.

The range is the set of function values corresponding to the domain values. Here, the only range value of interest is the value of f(1/4).

Put the value of the variable where the variable is in the function definition and do the arithmetic.

  y = f(1/4) = (1/4)² +2 = 1/16 +2

  y = 2 1/16

__

Additional comment

A calculator can help you evaluate an expression.

Answer: D

Step-by-step explanation:

Answer:

M=49

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees

Angle M is 49 degrees

The measure of angle "1" would be m∠1 = 123°.

What is an exterior angle theorem?

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

In the given figure, the measure of the exterior angle ∠1 is equal to the sum of the measures of the two non-adjacent interior angles 65° and 58°, therefore:

      ∠1 = 65° + 58°

      ∠1 = 123°

Hence, the measure of angle "1" would be m∠1 = 123°.

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Answer:

what triangle

Step-by-step explanation:

Answer: x = 9500

Step-by-step explanation:

Ok, so we know the bank loaned part of the $17,500 at a 4% interest rate.  Lets call this loan amount x.  Then the rest of the 17,500 was loaned at a 9% interest rate.  Whatever this amount was, we can define it as 17,500 - x.  We also know that the total interest earned was $1,100.  With this information, we can form the following equation:

.04(x) + .09(17500 - x) = 1100

Multiply the .09 times the inside of the parentheses:

.04x + 1575 - .09x = 1100

Simplify:

-.05x + 1575 = 1100

-.05x = -475

x = 9500

Since x is originally the amount loaned at the 4% interest rate, we know that $9,500 was loaned at a 4% interest rate.

To figure out the other amount loaned at 9%, simply subtract 9,500 from 17,500 -- this gets us 8,000.  So $8,000 was loaned at a 9% interest rate.

Answer:

Step-by-step explanation:

if 2^4x = 16, then x = ?

2^4x = 16

2^4x - 16 = 0

(16) ⋅ x + (−16) = 0

x = [- (- 16)] : 16

x = 1

Answer: The value of x is 1.

Step-by-step explanation: solution :

Here,

       2^4x = 16

    or, 2^4x = 2^4    (we should factor 16 by 2)

    or, 4x = 4            (Here coefficient 2 is same. so, we shouldn't write it)

     or, x = 4 ÷ 4

     or, x = 1

Therefore, the value of x is 1.

The length of 'Added metal bar' will be;

⇒ Approximately 5.4 m

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

The sides of box are;

⇒ a = 4 meters

⇒ b = 2 meters

⇒ c = 3 meters

Now,

Let the length of Added metal bar = d

By the formula of 3D Pythagoras theorem, we get;

⇒ d² = a² + b² + c²

⇒ d² = 4² + 2² + 3²

⇒ d² = 16 + 4 + 9

⇒ d² = 29

⇒ d = √29

⇒ d = 5.38

⇒ d = 5.4 meters

Thus, The length of ''Added metal bar'' is ''Approximately 5.4 m''.

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The y intercept of the linear equation is 4

The y intercept is identified by first finding the equation of the line and substituting x = 0 in to the equation

The slope, m of the linear function is calculated using the points (-2, 5) and  (8, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (5 - 0) / (-2 - 8)

m = (5) / (-10)

m = -1/2

equation passing through point (8, 0)

(y - y₁) = m (x - x₁)

y - 0 = -1/2 (x - 8)

y = -1/2 x + 4

the y intercept is calculated at x = 0

y = -1/2 x + 4

y = -1/2 (0) + 4

y = 4

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The simplified expression would be [tex]\frac{1}{x^2y^4}[/tex].

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and operators. Expressions can be simplified, evaluated or manipulated to solve problems or explore mathematical concepts. Expressions can be represented using algebraic notation, where variables are represented by letters and numbers, and operators are represented by symbols such as +, -, *, and /.

For example, 2x+3, 5y-7z, and 7+2x+3y/4 are all examples of expressions.

[tex]\frac{x^{-2}}{y^4}[/tex] can be simplified as [tex]x^{-2} * y^{-4}[/tex].

Then the resulting expression is

[tex]=x^{-2} * y^{-4} \\\\= \frac{1}{x^2} * \frac{1}{y^4} \\\\= \frac{1}{x^2y^4}[/tex]

Hence, the simplified expression would be [tex]\frac{1}{x^2y^4}[/tex].

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Answer:

You need 130ft² of net to cover the surface area of the rectangular prism.

Step-by-step explanation:

1. find smallest sides surface:

S1=ab

S1=5*1=5ft²

There are two sides so 2*5=10ft²

2. find middle sized sides surface:

S2=cb

S2=10*1=10ft²

There are two sides so 2*10=20ft²

3. find biggest sides surface:

S3=ca

S3=5*10=50ft²

There are two sides so 2*50=100ft²

4. Sum up all the sides:

S=2ab+2cb+2ac

S=10+20+100=130ft²

Answer:r:

Surface Area: 130ft

Step-by-Step explanation:

Width: 5  ft

Height: 1  ft

Length: 10  ft

Formula: 2(wl+hl+hw)

2(1·10+5·10+5·1)=130

C. I'm not sure.....

Answer:

m=1/3

Step-by-step explanation:

slope is rise over run

go up 1 over 3

The percentage change in the population from 1400 to 1500 will be 7.14%

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The percentage change in the population from 1400 to 1500 will be:

= (1500 - 1400) / 1400 × 100

= 100/1400 × 100.

= 7.14%

Therefore, it can be seen that based on the calculation above, the percentage change will be 7.14%.

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Answer:

1/4 is the slope of the line that passes through these points

Step-by-step explanation:

120 - 80 = 40
30 - 20 = 10
10/40
10/40 as a fraction simplified is 1/4 so y = 1/4x

The number of pounds of macaroni in the order is 4 pounds and the number of pounds of chickpeas is 5 pounds.

Let x be the number of pounds of macaroni and y be the number of pounds of chickpeas. Then, we can write the following system of equations:

x + y = 9 (the total weight of macaroni and chickpeas is 9 pounds)

1.5x + 3y = 21 (the total cost of macaroni and chickpeas is $21)

To solve for x and y, we can use the first equation to eliminate one of the variables.

If we substitute y = 9 - x into the second equation, we get:

1.5x + 3(9 - x) = 21

Expanding and simplifying:

1.5x + 27 - 3x = 21

-1.5x = -6

x = 4

So, there are 4 pounds of macaroni in the order. We can use the first equation to find out that there are 9 - 4 = 5 pounds of chickpeas in the order.

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F60.

246 in hexadecimal is F6. When multiplied by 10, the result is F60.

The correct order of steps to match the work shown is Add 4x to the 10x, Subtract 5 from the 47, and Divide 42 by 14, and the value of x is 3.

In other terms, an Equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

10 x + 5 = -4 x + 47

Firstly, Add 4x to the 10x as shown below,

10 x + 4 x + 5 =  47

14x + 5 = 47

Subtract 5 from the 47,

14x = 47 - 5

14x = 42

Divide 42 by 14,

x = 42 / 14

x = 3

Thus, the value of x is 3.

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Answer:

x is 40.

Step-by-step explanation:

The triangle with all sides equal is an equilateral triangle, one you shouldn't be bothered about. This is because the angle of 100 has already been given. If you look at the diagram closely, you can see that the triangle in which angle x is present is an isosceles triangle. Since the top angle is already given, there is a formula to calculate the bottom angle, i.e., x.

The formula is : (180- the top angle, in this case 100) / 2

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The number of people who felt that traffic improved in there area will be 1800.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, 2/5 felt that traffic improved in there area. If 4,500 people were surveyed, the number of people who felt that traffic improved in there area will be:

= 2/5 × 4500

= 1800

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In an area, 2/5 felt that traffic improved in there area. If 4,500 people were surveyed, how many people felt that traffic improved in there area.

22 x 47,389 = 1,042,558

please give brainliest

Answer:

I = $ 11.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 11%/100 = 0.11 per year,

then, solving our equation

I = 100 × 0.11 × 1 = 11

I = $ 11.00

The simple interest accumulated

on a principal of $ 100.00

at a rate of 11% per year

for 1 years is $ 11.00.

$22

Using the initial loan amount, interest rate, and term we can find the amount of simple interest paid.

Simple Interest

First, let's define simple interest. Simple interest is the simplest to calculate.  Simple interest is calculated based on the initial loan, aka the principle (P). Compound interest, on the other hand, is calculated based on the principle and any accumulated interest.

Solving for Interest

We are given every value we need, so we can just plug them into the given formula. The principle is the initial $100 loan, so P = 100. The interest rate is 11%, but for the formula, we should use this in decimal form. This way r = 0.11. Then, we are told the total time is 2 years, so t = 2.

The statement which is true is that: B. the y-value of Function A when x = -4 is less than the y-value of Function B when x = -4.

First of all, we would determine a linear equation that represents Function B by determining its slope using the point-slope form as follows;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Substituting the given parameters into the point-slope formula, we have the following;

y - 11 = (23 - 11)/(9 - 3)(x - 3)

y - 11 = 12/6(x - 3)

y - 11 = 2(x - 3)

y - 11 = 2x - 6

y = 2x - 6 + 11

y = 2x + 5

Next, we would evaluate both Function A and Function B as follows:

y = x - 4

y = -4 - 4

y = -8.

y = 2x + 5

y = 2(-4) + 5

y = -8 + 5

y = -3.

Therefore, the output value (y-value or range) of Function A is lesser than that Function B.

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Adding an additional independent variable to a multiple regression model does not guarantee that the original independent variable will remain significant

Adding an additional independent variable to a multiple regression model does not guarantee that the original independent variable will remain significant. This is because the effect of the original variable may be partially or completely outweighed by the effects of the new variable. For example, if the original variable is correlated with the new variable, the significance of the original variable may be reduced, as the new variable may capture the majority of the variance in the data. Additionally, if the new variable is correlated with the outcome variable, then it may have a stronger effect on the outcome than the original variable, thus reducing its significance. Therefore, it is important to always re-run the regression model once a new variable has been added to ensure that the original variable still has a significant effect.

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The z-score, also known as the standard score, tells us how many standard deviations an individual data point is from the mean of the data set.

What is an illustration of statistics ?

A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.

For Class 1, where the mean is 70 and the standard deviation is 10, the z-score for your midterm score of X = 70 is (70-70)/10 = 0. This means that your score is exactly at the mean and the same as other students in the class.

For Class 2, where the mean is 50 and the standard deviation is 20, the z-score for your midterm score of X = 70 is (70-50)/20 = 1. This means that your score is one standard deviation above the mean and better than most of the students in the class.

For Class 3, where the mean is 80 and the standard deviation is 5, the z-score for your midterm score of X = 70 is (70-80)/5 = -2. This means that your score is two standard deviations below the mean and worse than most of the students in the class.

For Class 4, where the mean is 80 and the standard deviation is 20, the z-score for your midterm score of X = 70 is (70-80)/20 = -0.5. This means that your score is half a standard deviation below the mean and worse than some of the students in the class but better than others.

Overall, from the z-scores, in class 1 and class 4, you have scored at the mean, in class 2 you have scored better than most of the students in the class and in class 3 you have scored worse than most of the students in the class.

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The equation of the straight line joining A to B and the equation of the straight line joining B to C is  y = 1/2x +3

a ) The point A = [tex](x_1, y_1)[/tex] = (-8, -1)

   The point  B = [tex](x_2, y_2)[/tex]  = (-4, 1)

           [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m=\frac{2}{4} \\\\m= \frac{1}{2}[/tex]

        y = mx +b  --- (1)

       -1 = 1/2 (-8) +b

        b = 4- 1

        b = 3

        So, the y- intercept  , b is 3.

        y = 1/2x +3

The equation of the straight line joining A to B is  y = 1/2x +3

b) The point B = [tex](x_1, y_1)[/tex] = (-4, 1)

   The point  C = [tex](x_2, y_2)[/tex]  = (12, 9)

           [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m=\frac{8}{16} \\\\m= \frac{1}{2}[/tex]

        y = mx +b  --- (1)

        1 = 1/2 (-4) +b

        b = 2 + 1

        b = 3

        So, the y- intercept , b is 3.

        y = 1/2x +3

The equation of the straight line joining B to C is  y = 1/2x +3

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On solving the provided question, we can say that Area of the triangle is = 1/2 X B X H = 1/2 X 10 X 25 = 125sq units

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in triangle ABC and CDE

base = 25

height = 10

Area of the triangle is = 1/2 X B X H = 1/2 X 10 X 25 = 125sq units

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A linear graph represents a proportional relationship include the following: C. A graph of a straight line that passes through the points 0 comma negative 4 and 1 comma negative 4.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

In this scenario, a graph of a straight line that passes through the data points (0, -4) and (1, -4) represents a proportional relationship because it would go through the origin (0, 0).

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A linear graph represents a proportional relationship include the following: C. A graph of a straight line that passes through the points 0 comma negative 4 and 1 comma negative 4.

What is a graph?

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

In this scenario, a graph of a straight line that passes through the data points (0, -4) and (1, -4) represents a proportional relationship because it would go through the origin (0, 0).

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Santa ran [tex]2\frac{1}{8}[/tex] miles on Friday to meet his goal of 20 miles a week.

A fraction is a part of a whole. The number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

The expression will be;

[tex]4\frac{1}{2} + 3\frac{7}{8} + 5\frac{1}{4} + 0 + x + 4\frac{1}{4} = 20[/tex]

[tex]\frac{9}{2} + \frac{31}{8} + \frac{21}{4} + 0 + x + \frac{17}{4} = 20[/tex]

Multiplying through by 8

36 + 31 + 42 + 8x + 34 = 120

143 + 8x = 160

8x = 160 - 143

8x = 17

x = 17/8

x = [tex]2\frac{1}{8}[/tex] miles

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