A rectangle is 29 feet long and 7 feet long. What is the area of this rectangle?

The results of factoring are presented below for each algebraic expression.

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: y²-y= y(y-1), where y is a common term.

You should apply the factor out a common term for solving the question.

       x(x+2) + y (x + 2) - 5(x + 2)

       x²+2x+xy+2y-5x-10

      x²-3x+xy+2y-10

      x(x-3)+y(x+2)-10

        [tex]5y^2 - 10y^3[/tex]

        5y²(1-2y)

        ax+ay+az

        a(x+y+z)

        yx(y+1) + 4x(y + 1) - 5(y + 1)

       xy²+xy+4xy+4-5y-5

       xy²+5xy-1-5y

       y(xy +5x-5)-1

        [tex]6p^2 - 3p^3[/tex]

       3p²(2-p)

        [tex]4x^4 + 2x[/tex]

        [tex]2x(2x^3+1)[/tex]

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assuming is simple interest

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]

Step-by-step explanation:

y + 1 = 2(x + 5) = 2x + 10

y - 9 = 2x

2x - y = -9

Answer:

See below

Step-by-step explanation:

Sine function would be easiest

  in a right triangle   sin = opposite leg / hypotenuse

sin 57 =   10.8 / x    

then   x = 10.8 / sin 57               then x = 12.88 units

Any time we have a single positive tile pair up with a single negative tile, those two tiles cancel out.

Three positive tiles and three negative tiles will pair up and cancel out. We're left with two positive tiles only. This represents the number 2.

In other words, 5 + (-3) = 5 - 3 = 2

Answer:

[tex](f+g)(x) = -8x-6[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle f(x) = -5x - 4 \text{ and } g(x) = -3x - 2[/tex]

And we want to find:

[tex](f+g)(x)[/tex]

Recall that this is equivalent to:

[tex]\displaystyle (f+g)(x) = f(x) + g(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned} (f+g)(x) &= (-5x-4)+(-3x-2) \\ \\ &= -8x-6 \end{aligned}[/tex]

In conclusion:

[tex](f+g)(x) = -8x-6[/tex]

The set of ordered pair that has point symmetry in respect to origin is (5, 4), (-5, -4).

This is a term that is used to refer to the points that are on the same distance from the origin but are on opposite sides.

The line that connects the points are known to move through the origin such that when measured on the graph, the distances between these points but they are opposite because they are in negatives and positives on the two sides.

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Answer:

the answer is (5,4),(-5,4)

Step-by-step explanation:

The value of x of the cubic equation e³ˣ + eˣ - 6 = 0 will be 0.49

The cubic equation is given as ax³ + bx² + cx + d = 0. Then degree of the equation will be 3. Then we have

The cubic equation will be

e³ˣ + eˣ - 6 = 0

Let eˣ = u, then the equation will be

u³ + u - 6 = 0

Then the root of the equation is calculated by the calculator, then we have

u = 1.634, -0.817, -0.817

eˣ = 1.634, -0.817, -0.817

Take log on both sides, then we have

x = ln 1.634, ln(-0.817), ln(-0.817)

x = 0.49, not defined, not defined

Then the value of x will be 0.49.

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Answer:

a, b, d, e

maybe c

Step-by-step explanation:

Answer:

(y - 6)(y + 8)

Step-by-step explanation:

Find two numbers that add to 2 and multiply to -48. Then put them in the form above. Afterwards, use FOIL (First, Outside, Inside, Last) to check the factoring and you get: y² + 2y - 48

Have a great day! :)

Answer:

−8, 6

Step-by-step explanation:

Write the factored form using these integers. (y−8) (y+6)

Answer:

do u still need help with this

Answer: pi/4 and -1

Step-by-step explanation:

After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have:

If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.

We know the exponential decay can be given as:

D = a(1 - r)ⁿ

a is the starting value and n is the number of hours.

D = 75(1 - 0.20)⁶

D = 19.66 milligrams

Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

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Answer:

[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]

Answer:

Total area = 187.65 cm^2

Step-by-step explanation:

AREA of a triangle = 1/2 base * height

THREE sides    3     * 1/2 *9 *  11.3  = 152.55 cm^2

Bottom                       1/2 * 9 * 7.8  = 35.1 cm^2

  total = 187.65  cm^2

The linear function that has a graph perpendicular to y = 2x – 4 is given by:

D. 2x + 4y = 1

A linear function is modeled by:

y = mx + b

In which:

If two lines are perpendicular, the multiplication of their slopes is of -1. The line y = 2x + 4 as a slope of 2, hence the slope of the perpendicular line will be given by m as such:

[tex]2m = -1[/tex]

[tex]m = -\frac{1}{2} = -0.5[/tex]

Hence option D is correct, as:

2x + 4y = 1

4y = -2x + 1

y = -0.5x + 0.25

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The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

The equation is given as:

x = 7 - 4√3

So, we have:

[tex](x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2[/tex]

Take the LCM

[tex](x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2[/tex]

Rationalize

[tex](x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2[/tex]

Evaluate the difference

[tex](x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2[/tex]

Expand

[tex](x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2[/tex]

Expand

[tex](x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3[/tex]

[tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

Hence, the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

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Using translation concepts, considering S(2,-1), the x-coordinate of S' is given by 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the rule is given by:

(x, y) -> (x+4, y-2).

Considering S(2,-1), 4 is added to the x-coordinate in the translation, hence:

2 + 4 = 6.

The x-coordinate of S' is given by 6.

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Answer:

  B; (-4, -8)

Step-by-step explanation:

The given forms of the equation are standard form, vertex form, and intercept form.

__

It is not surprising that the vertex form yields the vertex most quickly.

  B) m(x) = 2(x +4)² -8

Compare this to the generic vertex form ...

  f(x) = a(x -h)² +k . . . . . . . . . vertex (h, k)

We see that the vertex is (h, k) = (-4, -8).

The attached graph shows that the system of equation has no solution since there is no point of intersection

Inequalities are expressions not separated by an equal sign

Given the following inequalities

2y < -12x + 4

y <- 6x +4

_________________

2y < -6x + 4

y <- 6x +4.

Find the y-intercept. When x = 0

y < -6(0) + 4

y < 4

Plot the graphs and determine the point of intersection

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Answer: (0, 1), (-1, -3)

Given two equation's:

Solve them simultaneously:

[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]

[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]

[tex]\sf 6x^2 + 6x = 0[/tex]

[tex]\sf 6x(x + 1) = 0[/tex]

[tex]\sf 6x = 0, \ x + 1 = 0[/tex]

[tex]\sf x = 0, \ x = -1[/tex]

(a) When x = 0,     y = −4(0)² + 1 = 1

(b) When x = -1,    y = -4(-1)² + 1 = -3

Solution: (x, y) → (0, 1), (-1, -3)

Answer:

System of equations

[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]

To solve the given system of equations, use the substitution method:

[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]

Therefore the x-values of the solutions are:

        [tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]

Substitute the found values of x into the second equation to find the y-values:

[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]

Therefore, the solutions of the system of equations are:

(-1, -3) and (0, 1)

Answer:

x= 67, y= 113 , z= 67........... ...........

AND means multiply, so if probability is dependent on two things happening, then we will multiply the individual probabilities together.

1. P(A and 1) = 1/4 x 1/6 = 1/24

2. P(C and 2) = 1/4 x 2/6 = 2/24 = 1/12

3. P(B and 3) = 2/4 x 1/6 = 2/24 = 1/12

4. P(A and 4) = 1/4 x 2/6 = 2/24 = 1/12

5. P(C and 3) = 1/4 x 1/6 = 1/24

6. P(B and 2) = 2/4 x 2/6 = 4/24 = 1/6

7. P(a consonant and an odd #) = 3/4 x 2/6 = 6/24 = 1/4

8. P(a consonant and a prime #) = 3/4 x 3/6 = 9/24 = 3/8

9. P(a vowel and a 5) = 1/4 x 0/6 = 0

10. P(a vowel and a number less than 3) = 1/4 x 3/6 = 3/24 = 1/8

11. P(B and 1) = 2/4 x 1/6 = 2/24 = 1/12

Experimental probability is based on something that has already happened, or data that has already been collected.

12. P(1) = 3/30 = 1/10

13. P(2) = 8/30 = 4/15

14. P(3) = 7/30

15. P(4) = 5/30 = 1/6

16. P(5) = 3/30 = 1/10

17. P(6) = 4/30 = 2/15

Hope this helps!

Answer:

5 times bigger

Step-by-step explanation:

(6-4) = 2

(6-4) x 5 = 10

Answer:B

Step-by-step explanation:

The amoeba splits 24 times, meaning that the number of amoebas will be

2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24

An equation that can be used to determine how much each cookie cost originally is ($13.32 + $7) / 16.

A coupon reduces the price of an item. Thus, the amount paid by Louis would be lower than the original price.

Original price = coupon + price paid

($13.32 + $7)

The cost per cookie, can be determined by dividing the original price by the total number of cookies bought.

($13.32 + $7) / 16

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Answer:

Step-by-step explanation:

Givens

Number of cookies = 16

Deduction =  7

Final Cost = 13.31

Equation

16c - 7 = 13.31

Solution

You are not asked for a solution but I'll put it here anyway.

16c - 7 = 13.32                      Add 7 to both sides

16c -7+7 = 13.32+ 7              Combine

16c = 20.32                          Divide by 16

16c/16 =  20.32/16                

c = 1.27

The given sum for n = 1 to n = 15 is equal to 255, so the correct option is B.

We want to find the sum of the series whose elements are of the form:

(2n + 1)

From n = 1 to n = 15.

Then our sum will be:

(2*1 + 1) + (2*2 + 1) + ... + (2*15 + 1).

3 + 5 + ... + 31

This is the sum of all odd numbers in the interval [3, 31]

Which gives:

[tex]S = 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 = 255[/tex]

So the correct option is B.

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Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.