If two expressions have the same factor and base , what happens to the exponents when the expressions are multiplied

The required possible values of x is 1. Hence the option A. is correct.

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°.

Since. in the question we have two known sides of the right angle triangle. The number of possible values of x will be 1. because with the help of other two side third side can be calculate.

Thus, the required possible value of x will be 1.

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The volume of the modified globe would be 523.3 cubic inches (Option 3)

What is the volume of the globe with modified dimensions?

Information Given

The current diameter of the globe = 20 inches

We know that the radius of a sphere (globe) is half its diameter.

⇒ The radius of the globe = 10 inches

If the dimensions of the globe were reduced by half, the new diameter would be, [tex]\frac{20}{2} = 10[/tex] inches.

⇒ New radius of the globe, [tex]r = 10[/tex] inches

Calculating the Volume of the Modified Globe

The volume of a sphere (globe) is given by,

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

Here, [tex]r[/tex] is the new radius of the globe.

∴ The volume of the new globe would be,

[tex]V = \frac{4}{3} \pi (5)^{3}[/tex]

Use [tex]\pi =3.14[/tex]

⇒ [tex]V = \frac{4}{3} (3.14) (5)^{3}[/tex]

⇒ [tex]V = 523.333..[/tex] cubic inches

Rounding off the result to the nearest tenth, we get,

[tex]V = 523.3[/tex] cubic inches

Thus, if the dimensions of the globe were reduced by half, its volume would be 523.3 cubic inches.

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Answer:

1. to c.

2. to d.

3. to a.

4. to b.

Step-by-step explanation:

These answers should be right.

Hope this helps!

The matching of the polynomials to their correct names are:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

A polynomial is an expression having more than one algebraic terms.

1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.

2) A cubic monomial is defined as a a monomial that has a degree of 3.

3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.

4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4

Thus:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

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Hello !

[tex]\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}[/tex]

[tex]\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}[/tex]

[tex]\Leftrightarrow AX = B [/tex]

With

[tex]A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] [/tex]

[tex]X=\left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]

[tex]B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]

The solution is given by [tex]X=A^{-1}B[/tex].

[tex]X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^{ - 1} \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]

[tex]X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right] [/tex]

The point of intersection between the lines is (4;5).

Have a nice day

Answer:

Point of intersection (4,5)

Step-by-step explanation:

5x + 3y - 35 = 0

3x - 4y = -8

 ⇒ 5x + 3y = 35

     3x - 4y = -8

  Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.

[tex]\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right][/tex]

[tex]\sf B = \left[\begin{array}{c}35&-8\end{array}\right][/tex]

AX = B

 [tex]\sf X =A^{-1}B[/tex]

[tex]Now ,\ we \ have \ to \ find \ A^{-1}[/tex],

Find the workout in the document attached.

Answer:

I am not sure how that works but from the way it look and adding it up it comes to 66.6 but I was thinking around 75 - 85

Step-by-step explanation:

The volume of the ring-shaped remaining solid is 1797 cm³.

The volume is the total space occupied by an object.

The volume of a sphere of radius r units is given as (4/3)πr³.

The volume of a cylinder with radius r units and height h units is given as πr²h.

In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.

The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.

Therefore, the volume of the ring-shaped remaining solid is given as,

= (4/3)π(9)³ - π(5)²(18) cm³,

= π{972 - 400} cm³,

= 572π cm³,

= 1796.99 cm³ ≈ 1797 cm³.

Therefore, the volume of the ring-shaped remaining solid is 1797 cm³.

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Answer:

the answer is C, I got it too from the website, I got the answer from it

If the function is f(x)=35.5x+6 and snowfall in inches are 53,42,55,63,58,47 then the income received will be $1887.5,$1497,$1958.5,$2242.5,$2065$1674.5.

Given Snowfall received during the years:53,42,55,63,58,47 and f(x)=35.5x+6

We have to find the income in dollars received if f(x) shows the income.

Function is a relationship between variables and it have each value of y for each value of x.

To find the income we have to just put the values of x=53,42,55,63,58,47one by one and we will get income.

f(53)=35.5*53+6=1887.5

f(42)=35.5*42+6=1497

f(55)=35.5*55+6=1958.5

f(63)=35.5*63+6=2242.5

f(58)=35.5*58+6=2065

f(47)=35.5847+6=1674.5

Hence the income for snowfall 53,42,55,63,58,47 inches are 1887.5,1497,1958.5,2242.5,2065,2674.5.

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The graph that corresponds to the proportional relationship M = 3n is graph vs.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the relationship is:

M = 3n.

Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, the vertical axis is triple the horizontal axis, having points (100, 300), (200, 600) and so on, the graph is graph vs.

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The expected value of x is 10.

It is given that the number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).

The expected value of this random variable is n*p = 4*1/2 = 2.

The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable.

Thus E(X) = 5*2 = 10.

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The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

An equation is an expression that shows the relationship between two or more variables and numbers.

Let w represent the width, hence:

length = w + 33, height = w - 13

Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w

V(w) = w³ + 20w² - 429w

Rate of change = dV/dw = 3w² + 40w - 429

When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423

When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118

Rate = 10118 - 5423 = 4695 in³/in

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

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The value of n is calculated as n = 2 times 10 superscript 16.

The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12.

Simplification, in mathematics, is to solve the equation through mathematical operations

1.3 x 10^-4 x n = 2.3 x  10^12
n = 2 x 10^ 16

Thus the value of n is calculated as n = 2 times 10 superscript 16.

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The inequality shows that the number of texts will be 205.

The carriers charged $59 and 20 cents after. Therefore, the inequality to illustrate the information will be:

Let t be the number of texts.

59 + 0.2t = 100

0.2t = 100 - 59

0.2t = 41

t = 205

The number of texts will be 205.

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[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)

[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)

Answer:

(2x - 5)(3x + 1)

Step-by-step explanation:

6x² - 13x - 5

ax² + bx + c

ac = 6 × (-5) = -30

-30 = -15 × 2

-13 = -15 + 2

6x² - 13x - 5 =

= 6x² - 15x + 2x - 5

= 3x(2x - 5) + 1(2x - 5)

= (2x - 5)(3x + 1)

Answer: its a.) (2x-5)(3x+1)

Step-by-step explanation:

6x² - 13x - 5ax² + bx + cac = 6 × (-5) = -30-30 = -15 × 2-13 = -15 + 26x² - 13x - 5 == 6x² - 15x + 2x - 5= 3x(2x - 5) + 1(2x - 5)= (2x - 5)(3x + 1)

and got it right on the test review.

Answer:

E. Isosceles Triangle

Step-by-step explanation:

It is because it has 2 equal sides and 2 equal angles.

Answer:

d - the minimum value of d is 5 more than the maximum value of c

Step-by-step explanation:

we can see from the graph that d has a minimum value

that value is at (-1, 2) and the minimum is 2

for c the vertex is where the graph reflects itself

that point is (-4, -3) and the maximum is -3

that means that the minimum value of d is 5 more than the maximum value of c because 2 - (-3) = 5

Answer:

D

Step-by-step explanation:

This result is true by De Moivre's theorem.

Given f(x)=2−∣x−5∣

Domain of f(x) is defined for all real values of x.

Since, ∣x−5∣≥0⟹−∣x−5∣≤0

⟹2−∣x−5∣≤2⟹f(x)≤2

Hence, range of f(x) is (−∞,2].

The domain of the function  y= 2√x-6 is [6, ∞).

A relation is a function if it has only One y-value for each x-value.

In the given function, we have a square root of x-6 which means that the value inside the square root must be non-negative, otherwise the function will not be real.

Therefore, we have x - 6 ≥ 0

Adding 6 to both sides, we get:

x ≥ 6

So, the domain of the function y = 2√(x-6) is all real numbers greater than or equal to 6.

In interval notation, we can write the domain as:

Domain: [6, ∞)

Hence, the domain of the function  y= 2√x-6 is [6, ∞).

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1. Lines a and b are parallel by the converse of alternate interior angles theorem

2. l║m by the converse of consecutive interior angles theorem.

Given that the interior angles, ∠3 ≅ ∠7, according to the converse of alternate interior angles theorem, the lines they are found on, lines a and b would be parallel.

1. Lines a and b are parallel.

Given that the interior angles, m∠5 + m∠12 = 180, according to the converse of consecutive interior angles theorem, the lines they are found on, lines l and m would be parallel.

2. Lines l and m are parallel.

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Answer:

12ft

Step-by-step explanation:

length of one side of the square now

32ft / 4 = 8ft

length of one side of the square before decreasing the length

(original lenght)

8ft +4ft = 12ft

[tex]A_{ij}[/tex] refers to the entry of [tex]A[/tex] in row [tex]i[/tex] and column [tex]j[/tex].

When [tex]i=j[/tex], the entry in question lies on the diagonal. In this case, [tex]A_{ij}=0[/tex] so

[tex]A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}[/tex]

When [tex]i<j[/tex], the row number is smaller than the column number, which happens for each [tex]A_{ij}[/tex] in the upper half of [tex]A[/tex].

[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}[/tex]

When [tex]i>j[/tex], the row number is larger, which happens everywhere else in the matrix.

[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}[/tex]

Using the z-distribution, the 99% confidence interval of the population mean number of days it takes to find a job is (35.38, 44.62).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are:

[tex]\overline{x} = 40, \sigma = 10, n = 31[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 40 - 2.575\frac{10}{\sqrt{31}} = 35.38[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 40 + 2.575\frac{10}{\sqrt{31}} = 44.62[/tex]

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The statement which best describes the translation from the graph y= 6x² to the graph of y = 6(x+1)² is; The translation represents a unit shift rightward.

The translation involved in the transformation of the graph as given in the task content represents a rightward shift of the graph y = 6x² by 1 unit.

On this note, it follows that the translation involved between the two graphs is; a unit shift to the right.

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Answer:

Step-by-step explanation:

one unit to the right

Hence, the function increases at a constant multiplicative rate..

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.

We know,

the answer is (B) the function increases at a constant multiplicative rate.

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Answer:

(a) 7 + 3( n - 1 )

(b) 1006

Step-by-step explanation:

ARITHMETIC SEQUENCE.

The number of term of an Arithmetic progression has the formular :

nth term = a + ( n - 1 ) d

a = 7

d = 10 - 7 = 3

nth term = 7 + ( n - 1 ) 3

= 7 + 3n - 3

= 7 + 3( n - 1 )

Therefore,

the nth term of the sequence

= 7 + 3( n - 1 )

(b) For the 1000th term

= 7 + 3 ( 1000-1 )

= 7 + ( 999 )

7 + 999 = 1006

Therefore,

the 1000th term = 1006

Answer:

[tex]y = \dfrac{1}{2}x-4[/tex]

Step-by-step explanation:

       [tex]\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}[/tex]

         [tex]\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\[/tex]

                [tex]\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4[/tex]

Yolanda’s error during the calculation of the volume is that A. Yolanda should have found the volume by multiplying 8 by Two-thirds.

It should be noted that the volume of a sphere is simply 4/3πr³.

In this case, the sphere and a cylinder have the same radius and height and the volume of the cylinder is 8 meters cubed.

Based on the information given, Yolanda’s error during the calculation of the volume is that she should have found the volume by multiplying 8 by two-thirds.

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