If a₁ = 2 and aₙ = aₙ₋₁ - 4, then find the value of a4.

Answer:

Context? You need to have some information or a picture.

Step-by-step explanation:

The numbers of + and - signs tikes in the expressions given in the question are:

a) two - , and zero +

b) two - , and one +

c) one + , and one -

What is expression?

A finite collection of symbols that are correctly created in line with context-dependent requirements is referred to as an expression or a mathematical expression. Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. They may also be used to denote the operation order or other aspects of the logical grammar.

a) Given expression, (-2) + (-6)

When + and - signs comes together we can consider it as - sign only.

Therefore, there are two -, and zero +.

The the result of this expression is -8.

b) Given expression, (-2) + 4 + (-2)

When + and - signs comes together we can consider it as - sign only.

Therefore, there are two -, and one +.

the the result of this expression is -4.

c) Given expression, 5 + (-8)

When + and - signs comes together we can consider it as - sign only.

Therefore, there are one +, and one -.

the the result of this expression is -3.

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Answer:

b)

Step-by-step explanation:

2x+y=7

2x=7-y

x=(7-y)/2

Answer: B

Step-by-step explanation:

n

The total yield for an acre, T, in pounds as a function of the number of walnut tree per acre, x is given by T = -1.5x² + 95x.

In order to solve this word problem, we would assign variables to the number of walnut tree per acre and total yield for an acre, and then translate the word problem into algebraic equation as follows:

Mathematically, the total yield for an acre can be calculated by using this mathematical expression:

Total yield for an acre (T) = yield of each tree × number of trees per acre

Substituting the given parameters into the mathematical expression, we have the following;

Total yield for an acre (T) = [50 - 1.5(x - 30)] × x

Opening the bracket, we have:

Total yield for an acre (T) = [50 - 1.5x + 45] × x

Total yield for an acre (T) = 50x - 1.5x² + 45x

Next, we would rearrange the function by collecting like terms and simplifying as follows:

Total yield for an acre (T) = -1.5x² + (50x + 45x)

Total yield for an acre (T) = -1.5x² + 95x

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The equation of straight line of the points is given as y = -x - 2

To solve this problem, we simply need to find the equation of straight line which can be done by finding the slope of the line and then intercept of the line.

In the given points;

The formula of slope of a line is given as

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the values into the equation;

[tex]m = \frac{3 - (-6)}{-5 - 4} \\m = \frac{9}{-9} \\m = -1[/tex]

The slope of the line is equal to 1.

Let's find the intercept of the line

[tex]y = mx + c[/tex]

Taking point A;

[tex]y = mx + c\\-6 = -1(4) + c\\-6 = -4 + c\\c = -2[/tex]

The equation of the line is y = -x - 2

Translation: Find the equation of a straight line from two point A(4, -6) and B(-5, 3).

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The value of g(-4) from the function is 1

A function can be defined as a law, rule or theorem that asserts or explains the relationship between two variables in an equation or expression.

These variables are called;

Given the functions as;

To determine g(-4), we can see that the first function of g(x) would be used.

We have;

g(-4) = [tex]\sqrt[3]{x + 5}[/tex]

Substitute the value of x as - 4, we have;

g(-4 = [tex]\sqrt[3]{-4 + 5}[/tex]

g(-4) = ∛1

Find the cube root

g(-4) = 1

Hence, the value is 1

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The equivalent expression to 3x - [tex]\frac{1}{2}[/tex]y + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{5}{6}[/tex]x is C. 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{1}{6}[/tex]y

An expression is simply used to show the relationship between the variables that are given in the data.

The fractions given will be illustrated as:

3x - [tex]\frac{1}{2}[/tex]y + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{5}{6}[/tex]x

Collect like terms

= 3x - x + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{1}{2}[/tex]y

= 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{4}{6}[/tex]y - [tex]\frac{3}{6}[/tex]y

= 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{1}{6}[/tex]y

In conclusion, the correct option is C.

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The length of the fence (including the gates) that was built around the park is (4w + 50) feet.

Here, we are given that a rectangular park is w ft wide and the park is 25 ft longer than its wide.

Thus, the length of the park = (w + 25) ft

Now, the park has to be fenced along all of its sides. Thus, we need to find the perimeter of the rectangular park.

The perimeter of a rectangle is given as-

2( length + breadth)

Thus, here, the perimeter will be-

2( w + 25 + w )

= 2( 2w + 25 )

= 4w + 50

Thus, the length of the fence (including the gates) that was built around the park is (4w + 50) feet.

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Answer:

-17 would be three tick marks to the right of  -20

-11 would be 9 tick marks to the right of -20 or 6 right of the tick mark for -17

-2 would be 18 tick marks to the right of -20 or 15 tick marks to the right of -17 or 9 tick marks to the right of -11

Step-by-step explanation:

-20, -19, -18,-17      This is what -17 is three tick marks to the right of -20  

-20 -19 -18 -17 -16  -15 -14 -13 -12 -11      

-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2

Answer:

6 students have their own cell phone and 3 of them can use social media.

Step-by-step explanation:

One fifth of 30 is 6. One half of six is 3.

Answer: 5 feet

Step-by-step explanation:

The kangaroo added 2 feet of length to the shadow, therefore adding 2 feet of length of the 5 foot tree.

7-2=5

( sorry if it's confusing ^^ )

Answer: 0.25$ or a quarter

Step-by-step explanation:

Katlin bought 14 pencils, which cost her $3.50. So all you have to do is divide the amount ($) by the number of pencils.

3.50/14 = 0.25$

3.50 divided by 14

Each pencil cost a quarter

According to the given data we have the following proportion:

8hours/10 workers = Xhours/15 workers

A) The above proportion is not appropiate for solving the problem.

Since, the relationship between the number of workers and the time taken for sewing is an inverse relation:

The above proportion is just a direcly proportional relation.

B). As I stated above the relationship between the number of workers and the time taken for sewing is an inverse relation, hence, if the number of workers doubles then the number of time taken reduces to half.

So, since 15=10*15/10

therefore, time taken for 15 workers to sew pants is:

8/ 15/10 = 8* 10/15

=5 1/3 hours.

The time taken for 15 workers to sew pants is 5 1/3 hours.

Step-by-step explanation:

ab + 3c = 2x

Subtract 3c from both sides

ab = 2x - 3c

Isolate b by dividing by a

b = (2x -3c)/a

Answer:

3. ∠A = 110°

4. ∠H = 70°

5. ∠D = 70°

6. ∠F = 70°

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary (sum to 180°).

⇒ ∠A + ∠B = 180°

⇒ ∠A + 70° = 180°

⇒ ∠A = 110°

In a parallelogram, opposite angles are congruent.

⇒ ∠C = ∠A = 110°

⇒ ∠D = ∠B = 70°

If two parallelograms are similar, their corresponding interior angles are congruent.

⇒ ∠A = ∠E = 110°

⇒ ∠B = ∠F = 70°

⇒ ∠C = ∠G = 110°

⇒ ∠D = ∠H = 70°

The provided expression is equivalent to the expression mentioned in option (C) is correct.

It is defined as the combination of constants and variables with mathematical operators.

The number expression is:

[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} }[/tex]

After applying the integer exponent property:

[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} } \times\dfrac{\sqrt[3]{2^2} }{\sqrt[3]{2^2} }[/tex]   (rationalization)

[tex]= \dfrac{\sqrt[4]{6} \times\sqrt[3]{2}}{2 }[/tex]

= [tex]\rm \dfrac{\sqrt[12]{55296} }{2}[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Thus, the provided expression is equivalent to the expression mentioned in option (C) is correct.

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Given:

The length of the parallel sides,

a=17.4 m

b=44.1 m

The height, h=23.5 m

The measurements of the other two sides are,

c=27.5m and d=26.6m.

To find the area of the trapezium:

Using the formula,

Hence, the area of the figure is 722.6 sq. m (rounded to the nearest tenth).

To find the perimeter of the trapezium:

Hence, the perimeter of the figure is 115.6 m.

3. The slope of the line through the  points (0, 10) & (24, 6) is  [tex]\frac{1}{4}[/tex]

4. The slope of the line through the points (0, 6) & (20, 14) is  [tex]\frac{2}{5}[/tex]

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope of a line, or a section of a line connecting two points, is a measure of its steepness.

Or. A line's slope is the ratio of how much y increases as x increases by some amount. The slope-intercept form of an equation is when the equation of a line is written in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b).

How are the slopes calculated?

3. We know that , slope = m

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

[tex](x_{1}, y_{1})=(0, 10)\\\\(x_{2}, y_{2})=(24, 16)[/tex]

[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{16- 10}{24 -0}\\\\m= \frac{6}{24}\\\\m=\frac{1}{4}[/tex]

4. We know that , slope = m

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

[tex](x_{1}, y_{1})=(0, 6)\\\\(x_{2}, y_{2})=(20, 14)[/tex]

[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{14- 6}{20 -0}\\\\m= \frac{8}{20}\\\\m=\frac{2}{5}[/tex]

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The number of ounces of oats and dried fruit are needed for different numbers of servings are as follows:

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, we know that the ratio of the number of ounces of oats (O) in one serving to the number of ounces of dried fruit (D) in one serving is equal to 4 to 7.

For 2 servings, the ratio would be given by:

O:D = 2 × 4 : 2 × 7 = 8:14

Therefore, we have 8 ounces of oats and 14 ounces of dried fruit.

For 6 servings, the ratio would be given by:

O:D = 6 × 4 : 6 × 7 = 24:48

Therefore, we have 24 ounces of oats and 48 ounces of dried fruit.

For 7 servings, the ratio would be given by:

O:D = 7 × 4 : 7 × 7 = 28:49

Therefore, we have 28 ounces of oats and 49 ounces of dried fruit.

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( 5,0 ) and ( 0,4 ) are the x and y-intercept of the function 4x + 5y = 20 respectively.

The intercept of a line on a graph is simply the point at which it intersects either the x-axis or y-axis.

Given the data in the question;

Now, we find the intercepts of the equation of line, plug in y = 0 and solve for x

4x + 5y = 20

4x + 5(0) = 20

4x = 20

x = 20/4

x = 5

Hence, the x-intercept is ( 5,0 )

For the y-intercept, plug in x = 0 and solve for y

4(0) + 5y = 20

5y = 20

y = 20/5

y = 4

Hence, the y-intercept is ( 0,4 ).

Therefore the x and y-intercept are ( 5,0 ) and ( 0,4 ).

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The ordered pair of the solution of the equations -5x-4y=3 and 3x+10y=-17 is (1,-2).

The provided equations are,

Equation 1,

-5x-4y=3

Equation 2,

3x+10y=-17

Both the equations are linear equations is two variables,

We can use substitution method to solve these two equations,

From equation 1 we get,

-5x-4y=3

y = (-5x-3)/4

Now, substituting the value of y in equation 2,

we get,

3x+10( (-5x-3)/4)=-17

Solving and simplifying,

12x-50x-30 = -68

-38x = -38

x = 1,

Now, substituting x = 1 in equation 2,

we get,

3(1)+10y=-17

10y = -20

y = -2.

So, the ordered pair is (1,-2).

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The equation that represents the relationship between the weight and number of oranges is [tex]w[/tex]·[tex]g=24.5[/tex]

What is an equation?

An equation is a formula which represents the equality between two expression.

We are given each orange weight the same.

Let the weight of one orange be [tex]w[/tex].

Also we are given that there are [tex]g[/tex] oranges in the crate

Also the weight of the crate is 24.5 pounds

Now the equation representing the relationship between weight and number can be given by

[tex]w[/tex]·[tex]g=24.5[/tex]

Hence the equation representing the relationship between weight and number can be given by [tex]w[/tex]·[tex]g=24.5[/tex]

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Answer:

10+15x=?

Step-by-step explanation:

x=every week

Answer: y=15x+10

Step-by-step explanation: the y is the amount of money he has, the x is the number of weeks, and the 15 shows he gets 15 dollars a week and the 10 shows he starts with 10$

Answer:

(-1,2),(-1,-3),(3,-3)

Step-by-step explanation:

You times the coordinate by 1/3

The sale price of the backpack is $25.50.

The original price of the sweatshirt is $40.

From the information, the sale price of every item in a store is 85% of its usual price and the usual price of a backpack is $30.

The sale price will be:

= Percentage × Original price

= 85% × $30

= $25.50

The sale price of a sweatshirt is $34, its original price will be:

= 85% × x = $34

0.85x = $34

x = $34 / 0.85

x = $40

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The distance between the Earth and the Sun is 1.5 extend eight kilometers, and the distance between Mars and the Sun is 2.2 8 X 10 eight kilometers. The scientific notation for the distance between Earth and Mars is 3.78 x 10^8 km.

The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.

Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.

Given,

The distance between Earth and Sun = 1.5 x 10^8 km

The distance between Sun and Mars = 2.28 x 10^8 km

Therefore the distance between Earth and Mars =

(1.5 x 10^8 + 2.28 x 10^8) km

= (1.5 + 2.28) x 10^8 km

= 3.78 x 10^8 km (Ans)

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Answer:

17

Step-by-step explanation:

So, you start with division. 15/3=5, so you have 5+4x3

Then, you have to multiply. 4x3=12, so you have 5+12

Finally, you do 5+12, which is 17.

So, the simplified expression is 17.

Answer:

Step-by-step explanation:

Simplify the expression

15 ÷ 3 + 4 x 3​                (Remember PEMDAS)

5 + 12 =

17

Answer:

p = 5 ; q = -11

Step-by-step explanation:

      [tex]\sf (a - b)^2 = a^2 + b^2 - 2ab\\\\(\sqrt{5}-3)^2 = (\sqrt{5})^2+3^2-2*\sqrt{5}*3[/tex]

                       [tex]\sf = 5 + 9 -6\sqrt{5}\\\\= 14 - 6\sqrt{5}[/tex]

[tex]\sf \dfrac{(\sqrt{5}-3)^2}{\sqrt{5}+1}=\dfrac{14-6\sqrt{5}}{\sqrt{5}+1}[/tex]

 Multiply the denominator and the numerator by (√5 - 1).

                 [tex]\sf= \dfrac{(14-6\sqrt{5})(\sqrt{5}-1)}{(\sqrt{5}+1)(\sqrt{5}-1)}\\\\\\= \dfrac{14*\sqrt{5}-14*1-6\sqrt{5}*\sqrt{5}+6\sqrt{5}*1}{(\sqrt{5})^2-1^2}\\\\\\=\dfrac{14\sqrt{5}-14-6*5+6\sqrt{5}}{5-1}\\\\\\=\dfrac{14\sqrt{5}+6\sqrt{5}-14-30}{4}[/tex]

                 [tex]\sf = \dfrac{(14+6)\sqrt{5}-44}{4}\\\\\\= \dfrac{20\sqrt{5}-44}{4}\\\\=\dfrac{20\sqrt{5}}{4}-\dfrac{44}{4}\\\\\\=5\sqrt{5}-11[/tex]

p = 5

q = -11

We got the factors which is prime numbers = 2 × 2 × 2 × 3

The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. That can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.

For e.g, let's take number of 24 and factor it,

24/2 = 12

12/2 = 6

6/2 = 3

3/3 = 1

We got the factors which is prime numbers = 2 × 2 × 2 × 3

which is equal to given number i.e, 24.

See another example in image.

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