Write an algebraic expression that models the following statement:

Four times the sum of 'x' and '7'.

Answer:

B) 5, 20, 80, 320

Step-by-step explanation:

Complete question

Given the recursive formula shown, what are the first 4 terms of the sequence?

f(1) = 5 if n=1

f(n) = 4f(n-1) if n> 1

A) 5. 25, 100, 400

B) 5, 20, 80, 320

C) 5, 25, 125, 625

D) 5. 14, 60, 236

Get f(2)

f(2) = 4f(2-1)

f(2) = 4f(1)

f(2) = 4(5)

f(2) = 20

Get f(3)

f(3) = 4f(3-1)

f(3) = 4f(2)

f(3) = 4(20)

f(3) = 80

Get f(4)

f(4) = 4f(4-1)

f(4) = 4f(3)

f(4) = 4(80)

f(4) = 320

Hence the first 4 terms of the sequence are 5, 20, 80 and 320

Answer:

B) 5, 20, 80, 320

Step-by-step explanation:

Answer:

Step-by-step explanation:

24 : 30 = 4 : 5

44 : 99 = 4 : 9

108 : 36 = 3 : 1

33 : 9 = 11 : 3

49 : 14 = 7 : 2

Answer: 12

Step-by-step explanation:

Convert fraction (ratio) 3 / 25 Answer: 12%

The value of z in the given arrangement is 2 m.

Similar triangles are the triangles that look similar to each other, but their sizes might not be exactly the same.

Also,

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given that, an engineer needs to find the length of a beam to support the beam holding the wall, the two beams are perpendicular to one another, and a=4 m and b=1 m, we need to find z.

So, here we will use the concept of similar triangles,

According to the definition the corresponding sides are in proportion.

So, we get,

z/a = b/z

z² = 4

z = 2

Hence, the value of z in the given arrangement is 2 m.

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Answer:

30 ft²

Step-by-step explanation:

The formula to find the area of a rectangle is:

Length x Width

Assuming everything else stays the same, an increase in the price of smartphones will decrease the quantity supplied of smartphones. Option c is the correct answer.

This is because the quantity supplied is the number of smartphones that suppliers are willing and able to sell at a given price, while supply refers to the entire range of quantities that suppliers are willing and able to sell at different prices.

When the price of smartphones increases, the cost of production and supply also increases. This leads to a decrease in the profitability of supplying smartphones at the current market price, and hence suppliers reduce the quantity supplied.

As a result, the quantity supplied of smartphones decreases, causing a leftward shift in the supply curve.

However, it is important to note that a decrease in the quantity supplied does not mean that there is a decrease in demand for smartphones. The demand for smartphones could remain the same, or even increase, leading to a shortage of smartphones in the market.

Therefore, the correct option is c.

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Answer is : Step-by-step explanation:

Given Find the smallest non-zero whole number which can be multiplied by 112 to give a square number and a cube number.

So cube root of 21,952 will be 28.

Reference link will be.

brainly.in/question/4396403.

hope it helps

Answer:

176.

Step-by-step explanation:

112 = 2*2*2*2*7

For a cube number there must be 3 or a multiple of 3 of each factor.

So we multiply  by 2*2 and 7 * 7 to give 2^6 * 7^3 which is 21952.

The answer is 4*49

= 176.

Checking that 21952 is a cube:

- the cube root is 28,

Answer:

8 and 2

Step-by-step explanation:

Answer:

the numbers that lie between is 11 and 12

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

correct

Step-by-step explanation:

Answer:

{-4,-2,4}

Step-by-step explanation:

range are y values so we just look at the y values of the coordinates plotted on the graph

Hopes this helps

The range of the relation that is graphed above is: {-4, -2, 4}.

All values of x that are plotted on a graph of a relation is the domain, while the corresponding y-values on the graph is the range of the relation.

Given the graph of the relation above, the x-values of each of the points make up the domain of the relation, while the corresponding y-values of each point make up the range of the relation.

The y-values of each of the points are: -4, -2, and 4

Therefore, the range is: {-4, -2, 4}.

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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Answer:

Step-by-step explanation:

We can defined the amplitude of a wave as the height of it, because it's the distance from the maxium point to the minimum point. In other words, it's the longest vertical displacement along the wave.

Additionally, amplitude represents power, when we apply waves to real phenomenons like the sound. So, greater grade of amplitude would represent louder sounds.

Therefore, the increase of amplitude would increase distance between the maximum and minimun point of the wave.

The direction of increasing t is indicated by an arrow along the curve,

To sketch the curve described by the vector equation r(t) = (6 sin(t), 4 cos(t)), we can observe that it represents a parametric equation in terms of the variable t. The x-coordinate of the curve is given by 6 sin(t), while the y-coordinate is given by 4 cos(t).

As t increases, the curve moves in a counterclockwise direction around the origin (0,0). The curve is periodic with a period of 2π, as both sin(t) and cos(t) have a period of 2π.

To visualize the curve, plot points for various values of t, starting from t = 0 and incrementing it gradually.

Connect these points smoothly, and you will obtain a smooth curve. The direction of increasing t is indicated by an arrow along the curve, representing the counterclockwise movement around the origin.

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Answer:

Denote the two numbers: a and b

Two numbers are in the ratio 7:5

=> a/b = 7/5

=> a = (7/5) x b     (1)

When 10 is subtracted from each term , the ratio becomes 3:2

=> (a - 10)/(b - 10) = 3/2

=> 2 x (a - 10) = 3 x ( b - 10)

=> 3 x b - 2 x a = 10

From (1) => 3 x b - 2 x (7/5) x b = 10

             => (1/5) x b = 10

             => b = 50

             => a = (7/5) x b = (7/5) x 50 = 70

Hope this helps!

:)

Answer:

Positive Correlation

Step-by-step explanation:

The graph shown as a positive correlation.

Two variables move in the same direction in a positive correlation.

You can also tell that the graph has a correlation that is positive because of the line moving in a upward direction from left to right.

Hope this helps.  

Answer:

the second one the positive correlation

Step-by-step explanation:

the x and y are both positive

The graph shown as a positive correlation.

Two variables move in the same direction in a positive correlation.

You can also tell that the graph has a correlation that is positive because of the line moving in a upward direction from left to right.

Hope this helps.  

Answer:

The y-intercept is 22 spaces higher.

Step-by-step explanation:

a. The price elasticity of blue jeans on the weekend is approximately -2.14, indicating that a 1% decrease in price will result in a 2.14% increase in quantity demanded.

b. The quantity demanded of blue jeans will increase by approximately 10.7%.

a. The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Given:

Price = $40

Price of khakis = $50

Advertising = $2

Weekend (dummy variable) = 1 (indicating it is the weekend)

To calculate the price elasticity of blue jeans on the weekend, we need to use the coefficient for the "Price" variable from the regression results.

Price elasticity of demand = (Coefficient for Price * Price) / Quantity demanded

Coefficient for Price = -4.5 (from regression results)

Price = $40 (given)

Quantity demanded can be calculated using the regression equation:

Quantity demanded = Intercept + (Coefficient for Price * Price) + (Coefficient for Price Khakis * Price of khakis) + (Coefficient for Advertising * Advertising) + (Coefficient for Weekend * Weekend)

Intercept = 200 (from regression results)

Coefficient for Price Khakis = 2.2 (from regression results)

Coefficient for Advertising = 6.5 (from regression results)

Coefficient for Weekend = 10.0 (from regression results)

Quantity demanded = 200 + (-4.5 * 40) + (2.2 * 50) + (6.5 * 2) + (10.0 * 1)

Quantity demanded = 200 - 180 + 110 + 13 + 10

Quantity demanded = 153

Now we can calculate the price elasticity of demand:

Percentage change in quantity demanded = (Quantity demanded - Quantity demanded with a 5% price decrease) / Quantity demanded

Percentage change in quantity demanded = (153 - Quantity demanded with a 5% price decrease) / 153

Percentage change in price = 5% (given)

Price elasticity of demand = (Percentage change in quantity demanded / Percentage change in price) * (Price / Quantity demanded)

Price elasticity of demand = ((153 - Quantity demanded with a 5% price decrease) / 153) / 0.05 * (40 / 153)

To find the quantity demanded with a 5% price decrease, we calculate:

New price = $40 - (5% of $40) = $40 - ($2) = $38

New quantity demanded = 200 + (-4.5 * 38) + (2.2 * 50) + (6.5 * 2) + (10.0 * 1)

New quantity demanded = 200 - 171 + 110 + 13 + 10

New quantity demanded = 162

Substituting the values into the formula:

Price elasticity of demand = ((153 - 162) / 153) / 0.05 * (40 / 153)

Price elasticity of demand = (-0.059 / 0.05) * (40 / 153)

Price elasticity of demand ≈ -2.14

The price elasticity of blue jeans on the weekend is approximately -2.14, indicating that a 1% decrease in price will result in a 2.14% increase in quantity demanded.

b. We already calculated the price elasticity of demand (-2.14). Now, we can use this elasticity to determine the percentage change in quantity demanded when the price is reduced by 5%.

Percentage change in price = -5% (given)

Percentage change in quantity demanded = Price elasticity of demand * Percentage change in price

Percentage change in quantity demanded = -2.14 * (-5%)

Percentage change in quantity demanded = 10.7%

Therefore, if the price of blue jeans is reduced by 5%, the quantity demanded will increase by approximately 10.7%.

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Let's take the subspace (X,T) of (Y,T*), where (Y,T*) is a subspace of (Z,T**). Here, we are required to show that (X,T) is also a subspace of (Z,T**). Let's start our proof.

To show that (X,T) is a subspace of (Z,T**), we must show that (X,T) satisfies the subspace axioms. The subspace axioms that must be satisfied are:

1. The zero vector, 0, is in (X,T).

2. If u and v are in (X,T), then u + v is also in (X,T).

3. If u is in (X,T) and a is a scalar, then au is also in (X,T).

So, let's prove each axiom for (X,T) to be a subspace of (Z,T**):

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Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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Answer:c Thursday

Step-by-step explanation:

If on Monday, the temperature was 43°F. On Tuesday, the temperature increased by 6°F the overall change in temperature from Monday to Wednesday will be  24°F.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

It is given that on Monday, the temperature was 43°F. On Tuesday, the temperature increased by 6°F. On Wednesday, the temperature decreased by 13°F.

The overall change in temperature from Monday to Wednesday is found as,

=  43°F  + 6°F  - 13°F

= 24 °F

Thus, if on Monday, the temperature was 43°F. On Tuesday, the temperature increased by 6°F the overall change in temperature from Monday to Wednesday will be  24°F.

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The length of the shortest leg of T is approximately 18.33 units. We are given that the length of the altitude drawn to the hypotenuse (h) is 8, and the length of the hypotenuse (c) is 20.

We can start by using the area formula for a triangle:

Area = 1/2 * base * height

In this case, the base is the length of the hypotenuse (c), and the height is the length of the altitude (h). So we have:

Area = 1/2 * c * h

Substituting the given values, we get:

Area = 1/2 * 20 * 8 = 80

We also know that T is a right triangle, so we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Substituting the given values, we get:

a^2 + b^2 = 20^2

a^2 + b^2 = 400

We can now solve for b by substituting a in terms of h (using the formula for the area of a triangle) and simplifying:

Area = 1/2 * base * height

80 = 1/2 * 20 * h

h = 8

a = (2 * Area) / c

a = (2 * 80) / 20

a = 8

Substituting a and h in the Pythagorean theorem equation, we get:

8^2 + b^2 = 20^2

64 + b^2 = 400

b^2 = 336

b = sqrt(336)

b ≈ 18.33

Therefore, the length of the shortest leg of T is approximately 18.33 units.

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Answer: 20 over 4     or      4/20

Step-by-step explanation:             I belive this is you answer for number 2.

The non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.

The simplified expression that represents the total number of members after the third year is 4.5(53 + x).

Let's call the number of members from the other club "x".

After the first year, the total number of members is 20 + x, and it doubles to 2(20 + x) = 40 + 2x.

After the second year, half of the members from the other club leave, so there are 0.5x members left from the other club. And another 40 members join, so the total number of members is (40 + 2x - 0.5x) + 40 = 80 + 1.5x.

After the third year, the total number of members triples, so we have 3(80 + 1.5x) = 240 + 4.5x.

Therefore, the non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.

To simplify, we can factor out 4.5 from the expression to get 4.5(53 + x). So the simplified expression that represents the total number of members after the third year is 4.5(53 + x).

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The distance between Kim and Louise is 340.75 feet.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

The distance of Kim from the ground level, who is standing on the deck at point K  = 140.75 feet.

Also, the distance of  Louise at point L, who is standing below Kim's position, = 200 feet.

The distance between point K and L,

= 200 + 140.75

= 340.75 feet

The required distance between K and L is 340.75 feet.

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Answer:

EG = 26

Step-by-step explanation:

We use the angle-bisector theorem here

The theorem is that given an angle that is bisected in a triangle, it splits the opposite side into two parts, with the ratio of the sides facing the angle and the adjoining leg equal for the two bisections

So, we have this as;

EF/ED = GD/FG

x/24 = x+10/54

54(x) = 24)x + 10)

54x = 24x + 240

54x-24x = 240

30x = 240

x = 240/30

x = 8

But;

EG = EF + FG

EG = x + x + 10 = 2x + 10

EG = 2(8) + 10

EG = 16 + 10 = 26

Answer:

Brenton's annual earnings are $39,240.

The percent decrease in Val's fund from last quarter to this quarter is 14.4%

To calculate the percent decrease in Val's mutual fund from last quarter to this quarter, we can use the following formula:

Percent Decrease = (Change in Value / Initial Value) * 100

Given that last quarter her fund was worth $37,500 and this quarter it is worth $32,100, we can calculate the change in value:

Change in Value = Initial Value - Final Value

= $37,500 - $32,100

= $5,400

Now we can plug these values into the formula for percent decrease:

Percent Decrease = (5,400 / 37,500) * 100

= 0.144 * 100

= 14.4%

Therefore, the percent decrease in Val's fund from last quarter to this quarter is 14.4%.

This means that the value of Val's mutual fund decreased by 14.4% over the given time period. It is important to note that this calculation assumes a simple percentage decrease based on the initial and final values and does not take into account any additional factors such as fees or dividends.

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Answer:

B.97

Step-by-step explanation:

Heyy so angle ADC and DAB are supp to one another, thus

83 + DAB = 180 --> subtracting

DAB =97. B

Hope that made sense :)