You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The first bend is made 6 inches from one end. Describe two ways you could complete the triangle.

Step-by-step explanation:

[tex]y = \sin {}^{4} (3x) [/tex]

Using the chain rule

[tex] \frac{d( \sin(3x)) {}^{4} }{dx} = 12 \sin {}^{3} (3x) \cos(3x) [/tex]

( 3,7 ) will be point when its moved 5 units down on coordinate plane .

What is the short definition of a coordinate plane?

( 3,2) is the point .

when the point is moved 5 units down

then the point will be  = ( 3, 7 )

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The angles of the given figure are:

∠1 = 128°

∠2 = 52°

∠3 = 47°

∠4 = ∠5  = 81°

What are corresponding angles?

The angle is supplementary(∠5)

52° + ∠5 + 47° = 180°

∠5 + 99° = 180°°

∠5  = 180° - 99°

∠5  = 81°

Then the  ∠1 and 52° are supplementary (Interior adjacent angles)

∠1 + 52° = 180°

∠1 = 180° - 52°

∠1 = 128°

Now,  ∠2

∠2 +  ∠5  + 47° = 180°

∠2 + 81° + 47° = 180°

∠2 = 180° - 128°

∠2 = 52°

Based on interior opposite angles are equal. Then

∠5 =  ∠4 and ∠3 = 47°

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The correct ascending order is 33000 cm, 0.34 km, 430 m.

to find the ascending order we firstly have to convert the  all values into a same unit system.

we will convert all the values into cm units.

so, 0.34 km = 0.34*100000 cm,

0.34 km = 34000 cm.

similarly 430 m = 430* 100 cm,

430 m = 43000 cm.

and lastly we have 33000 cm.

so in all the values 33000 cm is smallest and 43000 cm is largest and the correct ascending order will be 33000 cm, 0.34 km, 430 m.

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Dividing both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore,  the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right

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The two functions f and g such that h(x) = (fog) (x) , are f(x) = 7x + 5  and g(x) = √x  .

In the question ,

it is given that

the two functions f(x) and g(x) , form a composite function h(x) such that

h(x) = (f o g)(x) , and h(x) = √(7x + 5)

the composite function (f o g)(x) means f(g(x)) which means g(x) is within h(x) .

By this we get that

the function g(x) is (7x + 5)

and function f(x) is √x  .

Therefore , The two functions f and g such that h(x) = (fog) (x) , are f(x) = 7x + 5  and g(x) = √x  .

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5.5% compounded monthly will be the best investment.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Now the formula for compound interest compounded monthly is,

A = P(1 + r/100)¹²ⁿ as a year has 12 months.

The formula for compound interest compounded semiannually is,

A = P(1 + r/100)²ⁿ as there are two semi-annuals in a year.

The formula for compound interest compounded continuously is,

[tex]A = P(1 + r/100)^{5.5n}[/tex] as the rate of interest is 5.5%.

Now from all these A = P(1 + r/100)¹²ⁿ which is compounded monthly has the highest power hence it will be the best investment.

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Answer:

  3 -n/2 ≤ 5

Step-by-step explanation:

You want a math expression that means "half a number less than 3 is at most 5."

We can let "n" represent "a number." Then "half a number" is (1/2)n or n/2.

That amount "less than 3" means it is subtracted from 3:

  3 -n/2 . . . . . . half a number less than 3

The wording "is at most" means "is less than or equal to." In symbols, the words mean ...

  3 -n/2 ≤ 5

__

Additional comment

Often 'x' is used to represent an unknown quantity. We like 'n' for "a number" because it is mnemonic, and because the numbers of interest are often integers or natural numbers from the set represented by ℕ.

English expressions of math relations are often ambiguous. In this case, we're not completely sure that the intention is not "half (a number less than 3)", which would be (3 -n)/2. Usually, we fall back on the Order of Operations, which requires that multiplication be done before addition. That is "half a number" must be computed before "less than 3" is evaluated, hence 3 -n/2.

Using proportions here, the solution must contain 42 mL of HCL

Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.

We can write the ratio as this

49 / 91 = x / 78

cross multiply both sides and solve for x

x = 42 milliliters

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Answer:

Step-by-step explanation:

You want the complete factorization of x³ +4x² -4x -16.

Pairing terms of the given polynomial, we have ...

  (x³ +4x²) -(4x +16)

Factoring each pair gives ...

  x²(x +4) -4(x +4)

  = (x² -4)(x +4)

The factorization of x² -4 is found using the form for factoring the difference of squares:

  a² -b² = (a +b)(a -b)

  x² -4 = (x +2)(x -2)

Note that x+2 is a factor here.

The complete factorization of the given polynomial is ...

  x³ +4x² -4x -16 = (x +4)(x +2)(x -2)

This is confirmed by the graph, which shows zeros at x = -4, -2, 2.

Answer: p = -2/3, sum = 0

Step-by-step explanation:

Additive inverse has the name numerical value as the given number but has the opposite sign so when they are added together they equal zero. The sum of any number and its additive inverse equal 0.

EX: 1 and -1      

1+ (-1) = 0

EX: -4.5 and 4.5

-4.5 + 4.5 = 0

Answer:

x = 15

Step-by-step explanation:

To solve this question and find value of x, we need to use Euclidean relation.

According this relation:

[tex] {x}^{2} = 9 \times 25[/tex]

[tex] {x}^{2} = 225[/tex]

Find the root of both expressions,

x = 15

Answer:23000

Step-by-step explanation:

The principal amount​ is ₹20000.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Let the money at beginning of the year 2005, a person invests in a bank be x.

At the beginning of 2010, the accumulated interest was ₹10000.

Now, x(1+r/100)⁵=x+10000 ------(I)

Let x(1+r/100)⁵=A

At the beginning of 2015, the accumulated interest became ₹25000.

So, x(1+r/100)¹⁰=x+25000 ------(II)

From the equation (I),

x(A-1)=10000 ------(III)

From equation (II), we get

x×A²=x+25000

x(A²-1)=25000 ------(IV)

From equation (III) and (IV), we get

10000(A+1)=25000

A=1.5

Put A=1.5 in equation (III), we get

0.5x=10000

x=10000/0.5

x=₹20000

Therefore, the principal amount​ is ₹20000.

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Answer:

t = (x - μ) / SE. where x is the sample mean, μ is the hypothesized population mean in the null hypothesis, and SE is the standard error. P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic.

Step-by-step explanation:

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The mean in hypothesis testing is the parent population from which the samples are drawn.

In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population parameter. The analyst's methodology is determined by the nature of the data and the purpose of the analysis. Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis.

Hypothesis testing is a type of statistical inference that employs sample data to draw conclusions about a population parameter or probability distribution. First, an educated guess is made about the parameter or distribution.

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Answer:

The number is 5

Step-by-step explanation:

Let us use an equation ( X is the unknown number)

2(x-3)=4

2x-6=4

2x-6+6=4+6

2x/2=10/2

x=5

Answer:

Here we need to find the value of y

In the given figure, 2y and 110 are adjacent to each other.

Hence the value of y = 110.

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Answer:

11.0 cm

Step-by-step explanation:

Answer:

11.8 cm

Step-by-step explanation:

2.5 + 5 + 2.5√3 = 7.5 + 2.5√3 = 11.8 cm

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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For given polynomial function f(x)=−2/9x^9(x−9)^2(x−8),

the leading term ( -2/9x^12 ) is negative with even exponent (12).  The curve decreases as x approaches both negative infinity and positive infinity.

In this question, we have been given a polynomial f(x)=−2/9x^9(x−9)^2(x−8)

We need to determine the end behavior of the following polynomial function.

We write given polynomial functions as,

f(x) = -2/9x^12 + 52/9 x^11  -50x^10 + 144x^9

The leading term of the polynomial is:  -2/9x^12

The degree of f(x) is : 12

The leading coefficient is: -2/9

We can see that the leading term is negative with even exponent.  The curve decreases as x approaches both negative infinity and positive infinity.

Therefore, for given polynomial function f(x)=−2/9x^9(x−9)^2(x−8),

the leading term ( -2/9x^12 ) is negative with even exponent (12).  The curve decreases as x approaches both negative infinity and positive infinity.

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Answer:

x ≥ 1

Step-by-step explanation:

Solving inequalities are essentially like solving equations where the main focus is getting the variable, x in this case, on one side and a constant on the other using inverse operations.

10x+16 ≥ 6x+20

==> subtract 16 from both sides

10x ≥ 6x + 4

==> subtract 6x from both sides

4x ≥ 4

==> divide both sides by 4

x ≥ 1

So the answer would be A

Also an important note for future references is when you divide one of the sides by a negative number you must flip the inequality sign.

E.g. -4x>8

We would divide both sides by -4 and because we divide by a negative number we must flip the inequality signs

This would result to x<-2

E and M are shown as congruent. This could be an Isosceles Triangle, so let's check. In an isosceles triangle, there are two congruent angles adjacent to the non-congruent side, and two congruent sides to the non-congruent angle. This angle is the apex. The apex of this triangle is adjacent to two congruent sides, however it is congruent to angle M, and thus this cannot be an isosceles triangle. That means this is an equilateral triangle, so all sides are congruent. So: LM = 16

If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.

What is division in mathematics?

In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 means dividing 15 into three equal groups of five. The symbol " or sometimes '/' represents division.

Sumalee won a total of 40 super bouncy balls.

then she gave two balls to each of her friends.

So she can distribute the balls to = 40/2

                                                       = 20 friends.

But after the distribution, she remained with 8 balls.

Now the number of balls will be = 40 - 8 = 32 balls.

and she can distribute 32 balls to = 32/2

                                                        = 16 friends.

Hence, If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.

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The second graph represents that the function has two complex roots.

What are Complex Numbers?

Complex numbers are made up of two parts: a real number and an imaginary number. Complex numbers serve as the foundation for more complex arithmetic, such as algebra.

Solution:

Since, the graph in the second option is not making any contact with thew point on x-axis it can be very well said that the solutions/roots/zeros of the quadratic equation are complex numbers.

Which is not the case for option one and option two because, the curves are making intercepts on x-axis thus, giving real roots.

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Answer:

I'm doing the same exact test, it's B.

Answer:

yes, The result is the same

Step-by-step explanation:

-3(5)=-15

5(-3)=-15

Answer:

They are same (equal)

Step-by-step explanation:

-3 multiplied with 5 is equal to -15.

5 multiplied with -3 is also equal to -15

so these two expressions are same when multiplied because the products are equal to one another.

Answer:

11/56 i think

Step-by-step explanation:

The slope of the line is m = - 11/7

And the y-intercept is b = 8

Find the slope and the y-intercept.

Step 1 – Transform the equation.

-11x - 7y = -56

To get a slope-intercept form, we need to isolate the variable y on the left-hand side of the equation.

First, we need to eliminate variable x from the left-hand side.

To eliminate the term with x, we'll add it to both sides of the equation. Remember to always perform the same operation on both sides to keep the equality true!

-11x – 7y + 11x = -56 + 11x

Now, let's add terms on the left-hand side. Keep in mind that two opposites add up to zero, so we can just remove it.

-7y = -56 + 11x

Since the variable x should be the firs on the righ-hand side in slope-intercept form, let's make it that way. Use the commutative property to reorder the terms.

-7y = 11x – 56

We're almost there! We just have to eliminate -7 from the left-hand side. To do that, let's divide both sides of the equation by -7.

(-7y)/(-7) = (11x - 56)/(-7)

Simplify the left-hand side. Each number divided by itself equals 1, so we are left with y.

y = (11x - 56)/(-7)

Next, separate the fraction on the righ-hand side into two fractions.

y = 11x/(-7) - 56/(-7)

Simplify the fraction on the right-hand side of the equation.

y = - 11x/7 + 56/7

y = - 11x/7 + 8

Finally, write the expression with x as a product.

y = - 11/7 x + 8

That's it! We've got the slope-intercept form of the equation.

Step 2 – Identify the slope.

Since the equation is written in slope-intercept form, y = m x + b, identify the slope of the lines as the coefficient next to the variable x.

y = - 11/7 x + 8

m = - 11/7

Step 3 – Identify the y-intercept.

Identify the y-intercept of the line as the constant term.

y = - 11/7 x + 8

m = - 11/7

b = 8

The slope of the line is m = - 11/7

And the y-intercept is b = 8

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The function rule for the line is f(x) = [tex]\frac{2}{3}x[/tex] - 2

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

The line cuts the x and y axis at (3,0) and (0, -2)

standard form of equation of line: y = mx + c

when x =3, y = 0

substitute these values into the equation

0 = 3m + c

c = -3m----------------1

when x = 0, y = -2

substitute these values into the equation, we have

-2 = 0(m) + c

c = -2

substitute the value of c in equation 1 to find m

-2 = -3m

m = 2/3

Substitute the values of m and c into the standard equation,

y =  [tex]\frac{2}{3}x[/tex] - 2

In conclusion, the function rule for the given line is y =  [tex]\frac{2}{3}x[/tex] - 2

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By using the concept of ratio, it is obtained that

AB : BC : CD = 4 : 3 : 13

What is ratio?

Ratio between two number signifies how much one number is larger than as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent

Here, the concept of ratio has been used

Here, AB : BD = 1 : 4

AC : CD = 7 : 13

AC  + CD = 7 + 13 = 20

[tex]AB = \frac{1}{1 + 4} \times 20 = 4[/tex]

[tex]BD = \frac{4}{1+4} \times 20 = 16[/tex]

[tex]CD = 13[/tex]

BC = BD - CD = 16 - 13 = 3
AB : BC : CD = 4 : 3 : 13

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1) Saleena worked for 20 hours in total.

2) She earned $220 during the week.

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Given,

Saleena has a part time job.

a) On Monday

Start time = 4: 30 pm

End time = 9:00 pm

Hours worked = 4 : 30 hours

b) On Tuesday

Start time = 3: 00 pm

End time = 9 : 00 pm

Hours worked = 6 hours

c) On Thursday

Start time = 4: 30 pm

End time = 9: 00 pm

Hours worked = 4 hours 30 minutes

d) On Saturday

Start time = 10:30 pm

End time = 3 : 30 pm

Hours worked = 5 hours

Total hours worked = 4:30 + 6 + 4: 30 + 5

1) Saleena worked for 20 hours in total.

2) She earns $11/h

Saleena worked for 20 hours in total.

Multiplying by $11 for per hour

20 × 11

220

2) She earned $220 during the week.

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