Elijah put 2x+3
2
x
+
3
dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

−3x−9=−15

Step 1: Add 9 to both sides.

−3x−9+9=−15+9

−3x=−6

Step 2: Divide both sides by -3.

−3x/−3 = −6/−3

x=2

The hypotenuse of a right triangle = 19.31cm

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Let the measure be,

Perpendicular = 18cm

Base = 7cm

Hypotenuse = ?

To find the Hypotenuse we can Pythagoras Theorem:

Hypotenuse² = Perpendicular²+ Base²

H² = (18)² + (7)²

H² = 324 + 49

H² = 373

H = [tex]\sqrt{373}[/tex]

H = 19.31cm

Hence, The measure of the other leg is²

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The equation of the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

The given parameters are

Leading coefficient = 1

Zeros =  − 2 , − 4 , 3 , and 3 .

Polynomial equations have their multiplicities to add up to their degree.

This means that the multiplicity of the zeros is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

From the question, the polynomial is to be factored

This means that we represent it as

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

Hence, the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

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Polynomial is an expression consisting of indeterminates and coefficients the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3)

Polynomial is an expression consisting of indeterminates and coefficients, which involves  the operations like addition, subtraction, multiplication, and positive-integer powers of variables

Factors are the numbers which divide the expression or number with a remainder zero.

We need to write the factored form of the polynomial functions with real; coefficients and zeros minus two comma  minus four comma three and 3.

The leading coefficient of the polynomial is 1. Leading coefficient means coefficient of leading term.

Zeros =  − 2 , − 4 , 3 , and 3 .

Let the polynomial is of variable x.

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

(x-(-2))=x+2

(x-(-4))=x+4

(x-3)=x-3

So the factored form is (x+2)(x+4)(x-3)(x-3)

the polynomial is P(x)=(x+2)(x+4)(x-3)(x-3)

Hence the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3).

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From the figure, draw from D parallel to AB.

Calculate angle D from triangle DWC = 180 - (90+60) = 180 - 150 = 30

Angle D = 30

Angle W = 90 + 30 = 120

Final answer W = 120

The cost for a year is cheaper in Gym A.

The value of k for the cheaper membership is $10.

An equation in the form y = kx is known as a linear equation. A linear equation is an equation that increases at a constant rate.

In the equation : y = kx

k = y/x

Cost per month at Gym A = $50 / 5 = $10

Cost per month at Gym B = $40 / 3 = $13.33

Membership cost at Gym A for a year = $10 x 12 = $120

Membership cost at Gym B for a year = $13.33 x 12 = $160

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The decimal figure that would be added to 1/5 to give 3/6 = 0.3

A decimal form is defined as the expression of figures that are more than a whole number with the use of decimal point.

Examples of figures that are in decimal form include the following: 0.2, 0.3, 0.4, 0.5, 1.2, 2.2,3.3 and 4.4.

To represent the given fractions in decimal form;

1/5 = 0.2

3/6 = 0.5

Therefore, X + 0.2 = 0.5

make X the subject of formula,

X = 0.5 - 0.2

X= 0.3

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The area of the region within the square and without the circle is equal to 13.7 square inches.

In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:

A = L² - 0.25π · D²

Where:

If we know that D = L = 8 in, then the area of the region is:

A = (8 in)² - 0.25π · (8 in)²

A = 64 in² - 50.265 in²

A = 13.735 in²

The area of the region is equal to 13.7 square inches.

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Answer:

See below

Step-by-step explanation:

The  equation is

y = [tex]x^{2}[/tex] + x

x equals the step

We see steps: 1, 2,3 and 4

y equals the number of squares that you see in each step.

If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2

Step 2: [tex]2^{2}[/tex] + 2 = 6

Step 3: [tex]3^{2}[/tex] + 3 = 12

Step 4: [tex]4^{2}[/tex] + 4 = 20

Can you see at each step there is a square of the number and then a little extra?  That little extra equals the number of the stop.

In the equation

y = 4x -2

Step 1

y = 4(1) -2

y = 2  It works!

Step 2:

y = 4x -2

y = 4(2)  - 2

y = 8 - 2

y = 6  It works!

Step 3:

y = 4x -2

y = 4(3) - 2

y = 12 - 2

y = 10  It does not work!

Step 4:

y = 4x -2

y  = 4(4) - 2

y = 16 - 2

y = 14  It does not work!

The equation y= 4x -2  only worked for the first 2 steps.

Answer:

27

Step-by-step explanation:

Divide 270 by 10

EXPLANATION

Let's see the facts:

The increasing rate is:

The increasing rate is 1.67

In percentage this is:

The percentage of increasing is of 60%.

Answer:

2

Step-by-step explanation:

512÷2=256

256÷2=128

128÷2=64

64÷2=32

32÷2=16

16÷2=8

8÷2=4

4÷2=2

2÷2=1

=(2^2)+(2^2)+(2^2)+(2^2)+2

When 2 is multiplied it will make it a perfect square.

512×2=1024

√1024

=32

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma([tex]\alpha ,\beta[/tex])

E(X)= [tex]\alpha \beta[/tex]                 [tex]\beta[/tex]= [tex]12^{2}/24[/tex]=6 weeks

V(x)= [tex]\alpha \beta ^{2}[/tex]                [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, [tex]\alpha[/tex], [tex]\beta[/tex], False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6\leq G\leq 24/6[/tex])

P([tex]2\leq G\leq 4[/tex])

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer: is 72 people to 27 animals

Step-by-step explanation:

I can find the ratio by cross multiplying

40/15 to x/27

15x = 1080

x = 72

you can also divide 40/15 for a ratio percent = 8/3

multiply 27 animals x 8/3 = 72

two ways to solve for ratios

Answer:Given : f(x)=x

4

−3x

2

+4

f(2)=(2)

4

−3(2)

2

+4

=16−12+4=8

This can also be verified by the actual divison

Answer:

23

Step-by-step explanation:

4h = 92

Divide both sides by 4 to get h by itself

h = 23

Answer:

No, it is not.

Step-by-step explanation:

A function only has exactly one output for each input. In other words, for each X input, there is only one Y output. In the given set of coordinates, 3 is repeated as an input, which makes this set of coordinates not a function.

The shows the expression below simplified 0.0042 - (1.2 x 10-6) as D. 4.1988 x 10^-3.

The concept that is been used is subtraction of the first expression from second expression.

The given expression is 0.0042 - (1.2 x 10-6) and this can be expressed in standard form as ( 4.2 *10^-3) - (1.2 x 10-6)

Then then the subtraction can be done as [ ( 4.2 *10^-3) ] - [ (1.2 x 10^-6) ] = 4.1988 x 10^-3

In conclusion, iif we go through the options., then we can see that the forth option is the best option that match the expression.

Therefore, option D is correct.

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2, 4, 5, 10 and 20 cast members were possible attendees at the celebration.

The acting teacher provided 20 biscuits and 40 carrot sticks as refreshments in light of this.

What are the factors?

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

2, 4, 5, 10, and 20 make up the factors of 20 and 40.

Additionally, the number of cast members must be greater than one and a divisor of 20 and 40.

Therefore, there could be 2, 4, 5, 10, or 20 cast members.

Therefore, 2, 4, 5, 10 and 20 cast members may have attended the celebration.

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The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.

Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,

13 · x + 7 · x = 180°

Now we clear the variable x:

20 · x = 180°

x = 9

And the missing angles are:

13 · 9 = 117°

7 · 9 = 63°

The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.

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No, the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

In the question ,

an equation y=(1/2)x-3 is given ,

if the ordered pair (-8,1) is a solution of the equation , then it should satisfy the equation .

Substituting x=-8 and y=1 in the equation y=(1/2)x-3 , we get

y=(1/2)x-3

1 = (1/2)(-8) -3

1 = -8/2 -3

1 = -4-3

1 ≠ -7

Since 1≠7 , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3 .

Therefore , No , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

The given question is incomplete , the complete question is

Is the ordered pair (-8,1) a solution to the equation y=1/2x-3  ?

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Answer:

92 over 100

Step-by-step explanation:

Answer:

Since all triangle angles sum to 180 then we can say

2x + 3x + 7x = 180

12x = 180

x = 15

There fore the angles are

2 * 15 3 * 15 and 7 * 15 or

30 45 and 105

Those 3 total 180 degrees

Step-by-step explanation:

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

1. x - 3 is not a factor

2. The remainder is 32.

Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.

So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then

p(3) = 0

So, substituting x = 3 into the equation, we have

p(3) = 2x³ - 4x² - 6

= 2(3)³ - 4(2)² - 6

= 2(27) - 4(4) - 6

= 54 - 16 - 6

= 54 - 22

= 32

Since p(3) ≠ 0.

x - 3 is not a factor

Since p(3) = 32,

The remainder is 32.

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The lines aren't parallel since they intersect at point B.

Parallel lines never intersect.

I WILL USE THE LAWS OF EXPONENTS

[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]

AND

[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]

[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]

ATTACHED IS THE SOLUTION.

Answer:

i hope this one is good for you

Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.

Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).

Here the ΔCED and ΔPOR,

∠CED=∠POR

Side PR=CD

Side ED=PO

by using SAS rule,

ΔCED≅ΔPOR

Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.

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