Translate the following statements into algebraic expressions.
One-half of the sum of 8 and x.

The values of k and r are given by 5 and 3 respectively.

Here in this problem it is given that,

General formula for the sequence is given by,

[tex]U_{n+1}=kU_n+r[/tex]

First term of the sequence, [tex]U_1=37[/tex]

Second term,

[tex]U_2=188[/tex]

[tex]U_{1+1}=188[/tex], rearranging

[tex]kU_1+r=188[/tex], applying general formula

[tex]37k+r=188[/tex]..........(1)

Third term,

[tex]U_3=943[/tex]

[tex]U_{2+1}=943[/tex], rearranging

[tex]kU_2+r=943[/tex], applying general formula

[tex]188k+r=943[/tex]..........(2)

Now (2) - (1) we get,

188k+r-37k-r = 943-188

151k = 755

k = 755/151 = 5

Hence the value of k is 5.

Substituting the value of k in (1) we get,

37*5+r = 188

185+r = 188

r = 188-185 = 3

Thus the value of r is 3.

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Answer:

==============

Imagine the height of the triangle is h, which is perpendicular to 15 m side.

The area is:

Use this formula and given values and find the value of h:

Since h is opposite to 30° angle and x is the hypotenuse of the formed right triangle, we'll use the property of 30°x60°x90° triangle.

In our case h is opposite to 30° angle, therefore we have:

Answer:

x = 16

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] absinC

where a, b are 2 sides of the triangle and C the angle between them

here a = 15, b = x, C = 30° and A = 60 , then

[tex]\frac{1}{2}[/tex] × 15 × x × sin30° = 60

7.5x × [tex]\frac{1}{2}[/tex] = 60 ( multiply both sides by 2 to clear the fraction )

7.5x = 120 ( divide both sides by 7.5 )

x = 16

Answer: This represents a linear function.

Step-by-step explanation:

I used Desmos to plot them on a graph. You can see that this is linear because each point is in a line. I hope this helps!!

Answer:

400 calories

Step-by-step explanation:

A bran muffin has around 380 calories, when rounded off it is 400 calories.

Hope I helped

Answer:

A. 400 Calories.

Step-by-step explanation:

Look it up on the net.

If this is wrong, it is because there wasn't enough information given.

Hope this helps!

If not, I am sorry.

The rotation is 180 degrees in clockwise direction.

What is rotation?

The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.

The complete question is:

Angie’s rotation maps triangle XYZ to triangle X’Y’Z’.

X(3, –6) maps to X’(–3, 6)

Y(1, –2) maps to Y’(–1, 2)

Z(–1, –5) maps to Z’(1, 5)

Which describes the rotation?

If we look at the coordinates carefully then we can see that the sign of the coordinates have been changed.

As, (x,y) to (-x, -y)

Hence, the rotation is  180 degrees rotation (x,y) to (-x, -y) in clockwise rotation.

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Answer:

2. All reals

Step-by-step explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

Answer:

you have jbjhgbjhih7g6ginyfygino

Step-by-step explanation:

area of rectangle= 12×6

=72ft^2

A2=9ft^2 whereby the base of the hole is 3ft

height is 6ft

therefore the square is 18 ft

Answer:

The expression that represents the PS is 7x – 7 .

if I am right mark the answer as brainliest

The correct answer is option C which is the given expression is cubic.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given expression

5x³ + 2x − 3

The cubic expression is one in which the highest power of the variable is three or we can say that the degree of the expression is three so the expression will have three solutions.

Therefore the correct answer is option C which is the given expression is cubic.

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Standard form of quadratic equation: ax² + bx + c

Here given equation: f(x) = -(x - 4)²  + 2

Simplify the equation:

⇒ f(x) = -(x - 4)² + 2

Use perfect square formula: (a + b)² = a² + 2ab + b²

⇒ f(x) = -(x² + 2(x)(-4) + (-4)²) + 2

⇒ f(x) = -(x² - 8x + 16) + 2

⇒ f(x) = -x² + 8x - 16 + 2

⇒ f(x) = -x² + 8x - 14

[tex]\hrulefill[/tex]

Here given equation: f(x) = (x - 4)²  + 2

Simplify the equation:

⇒ f(x) = (x - 4)² + 2​

⇒ f(x) = x² + 2(x)(-4) + (-4)² + 2

⇒ f(x) = x² - 8x + 16 + 2

⇒ f(x) = x² - 8x + 18

Answer:

f(x)=x²-8x+18

Step-by-step explanation:

f(x) = (x-4)² + 2​

To find the answer for the first part (x-4)², you need to use the formula.

This is the formula: (a-b)²=a²-2ab+b²

Plug in x for a and -4 for b.

(x-4)²=x²-8x+16

Now, put x²-8x+16 for (x-4)².

f(x)=x²-8x+16+2

Add like terms.

f(x)=x²-8x+18

Our answer is already in standard form because it is from greatest to least.

Hope this helps!

If not, I am sorry.

Answer:

the original population was 425

Step-by-step explanation:

Answer:

425

Step-by-step explanation:

Let the original population of blackbirds be x.

Original population              decreases by                   New population

          100                                     24                                       76

            x                                        24                                     323

Now we can make an expression like this.

100  ⇒  76

x     ⇒   323

And now let us use cross multiplication and solve for x.

Let us solve it now.

323 × 100 = 76x

32300 = 76x

425=  x

Answer:

first blank: 3

second blank: 4

Step-by-step explanation:

The completed equation should say:

y = -3x + 4

This is slope-intercept form of the equation. It's a fill-in-the-blank equation. You put the slope in the first blank and the y-intercept in the second blank. Your math program put the negative sign in and it does need to be there. To find the slope, look at the points on the line. To get from one point to the next you go DOWN3 and over 1. DOWN3 and OVER1 is the slope -3/1, which is -3. This number goes beside (in front of) the x. The line crosses the y-axis at 4, fill that in at the end of the equation (the second blank).

The equation for the line is

y = -3x + 4

i

Step-by-step explanation:

i

Answer:

D

Step-by-step explanation:

(f • g)(x)

= f(x) × g(x)

= (x + 4)(3x² - 7)

each term in the second factor is multiplied by each term in the first factor , that is

x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis

= 3x³ - 7x + 12x² - 28

= 3x³ + 12x² - 7x - 28 ← in standard form

Answer:

[tex]\fbox {See below} \downarrow[/tex]

Step-by-step explanation:

Question 1

Part (a) :

⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ

⇒ 6⁷ = 6ˣ

⇒ x = 7

Part (b) :

⇒ y² = 169

⇒ √y² = √169

⇒ y = ± 13

⇒ y = 13, y = -13

Question 2

Part (a) :

⇒ (√5)² × (√3)²

⇒ 5 × 3

⇒ 15

Part (b) :

⇒ (∛9)³ × (√30)²

⇒ 9 × 30

⇒ 270

Answer:

15/7 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

15/21

Step-by-step explanation:

First do 5 times 3, which is 15 (5+5+5). Then do 7 times 3, which is 21 (7+7+7). Since the denominator is 7 and there is 3 models with 7 parts each, there are 21 total parts. Out of each model, only 5 parts are highlighted/colored out of the 7. Add all the parts that are colored together to get 15. To put it simpler, 15 out of 21 parts are colored. This cannot be further simplified, giving you 15/21

Answer:

[39/(15-2)]-(2×9) = -15

Step-by-step explanation:

[39/(15-2)]-(2×9)

Let’s start with this part : 39/(15-2)

According to the order of operations parentheses comes before division

then

39/(15-2) = 39/(13) = 39/13 = 3

We get [39/(15-2)]-(2×9) = 3 - (2 × 9)

…………………………………………

Calculating 3 - (2 × 9)

According to the order of operations parentheses and multiplication comes before division

Then

3 - (18) = 3 - 18 = -15

Thus

[39/(15-2)]-(2×9) = -15

Answer:

- 15

Step-by-step explanation:

1) Simplify 15 - 2 to 13.

39/13  - 2 × 9

2) Simplify 39/13 to 3.

3 - 2 × 9

3) Simplify 2 × 9 to 18.

3 - 18

4) Simplify.

- 15

Answer:

(x - y)(x² + xy + y²)

Step-by-step explanation:

Since both are cubed (³),

we can apply the Difference of Cubes Formula:

A binomial that is of the form (something)³ – (something else)³

To factor any difference of cubes,

the formula a³ – b³ = (a – b)(a² + ab + b²).

hence, x³ - y³ = (x - y)(x² + xy + y²)

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Answer:

6

Step-by-step explanation:

The equation becomes 9 *4 * 1/6. Then you simplify and get 6.

Please mark me as Brainliest if it is correct, thx.

Answer:

(3^2(-2)^6)/5^4

Step-by-step explanation:

See attached image.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The value of the given series is 240.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

aₙ = a₁ + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

The value of [tex]\log_{a^{\frac12}}(a)[/tex] will be equal to 2. Therefore, the series will become,

series = 2 + 4 + 6 + 8 + 10 + 12 + .... + 30

Now, as it can be observed that the given series is an arithmetic series, therefore, the number of terms in the series are,

30 = 2 + (n-1)1

28 = (n - 1)2

n - 1 = 14

n = 15

Further, the sum of the of the series will be,

sum = (15/2)[2(2) + (15-1)2]

sum = (15/2) [4 + 28]

sum = 240

Hence, the value of the given series is 240.

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Answer:

%50 1÷2

if there is missing information. if there is 10 total marbels 5 would be red, 5would be blue.

Answer: 15 goats

Step-by-step explanation:

h = hens - they have 2 legs

g = goats - they have 4 legs

The equations would be:

h + g = 19

2h + 4g = 68

To solve this, I personally prefer substitution, we're isolating h since we need to find g:

h + g = 19

h = 19 - g

Now that we have h, we can plug this into the second equation:

2h + 4g = 68

2(19 - g) + 4g = 68

38 - 2g + 4g = 68

2g = 30

g = 15

There are 15 goats.

Adding onto this, 19 - 15 = 4, so there are 4 hens.

If Bruce can deduct 40% from other interest then the total interest deducted is $2927.

Given Adjusted gross income=$36500, mortgage interest =$2787 and other interest $350.

It is said that 40% of other interest can be deducted by Bruce but it is not said that nothing will be deducted by Bruce from Mortgage interest so we will deduct full of mortgage interest and 40% of other interest. So,

Mortgage interest =$2787

Other interest=$350

Other interest deductable=40%*350

=$140

So the total will be 2787+140 =$2927.

Hence the interest deducted by Bruce is $2927if only 40% of  other interest is deductable.

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Answer:

4

Step-by-step explanation:

2L=w

32=LxW

so you put the 2L as the w

which is 32=Lx2L

32=2L^2

16=L^2

4=L

*To find the width you input 4 as L*

So 8=W

The shortest side would be 4

Answer:

182

Step-by-step explanation:

Sum = a(r^n -1) ÷ r - 1

1(-3^6 - 1) ÷ -3 -1

= 182

r = t2 ÷ t1 * since they stated that it is geometric

Answer: x = 44

Step-by-step explanation:

The exterior angles of a polygon add to 360 degrees so: