Select the correct answer. What are the solutions to this equation? 16x2 + 9 = 25

The expression which is equivalent to the given expression in the task content is; 1/x²⁴.

It follows from the task content that the given expression is; ((x)^-6/x²)³.

Hence, it follows from the laws of indices that the expression can be evaluated as follows;

= (x^-8)³

= x^-²⁴

= (1/x²⁴).

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Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

Indirect variation is expressed as;

y ∝ 1/x

Given that;

y ∝ 1/x²

y = k/x²

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

y = k/x²

8 = k/4²

8 = k/16

k = 128

Now, we find y when x = 8

y = k/x²

y = 128 / 8²

y = 128 / 64

y = 2

Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

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Answer:

min = a_1

for i:= 2 to n:

      if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]

return min

Step-by-step explanation:

We call the algorithm "minimum" and a list of natural numbers [tex]a_1, a_2, \cdot\cdot\cdot, a_n.[/tex]

So lets first set the minimum to [tex]a_1[/tex]

min = a_1

now we want to check all the other numbers.

We can use a simple for loop, to find the minimum

min = a_1

for i:= 2 to n:

      if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]

return min

Answer:

The sequence of natural numbers is a_1, a_2, a_3, ..., a_n.

Use min as the variable that will contain the minimum value.

Set min = a_1

In a loop, compare min to each number from a_2 to an.

If min > a_i, then let min = a_i

min = a_1

for i = 2 to n

  if min > a_i, then min = a_i

Answer:  Point B

Reason:

This point is the highest point in the neighborhood or interval. Yes point D is higher up, but points immediately adjacent to point D are higher. This means D is not a relative max. We need a hill shape like where B is located.  In contrast, point C is a relative minimum since it is at the bottom of the valley.

Answer:

100 pi = about 314.16

Step-by-step explanation:

the surface area of a cylinder: SA = 2πrh+2πr^2

we plug in the values of r and h, and get

SA = 50pi + 50pi = 100 pi, which is approximately 314.16

Answer: H. Parallel lines may intersect.

Step-by-step explanation:

By definition, parallel lines never intersect.

The simple interest rate is 4.7%

The given parameters are:

Principal = $2100

Interest = $1,559.46

Time = 15.8 years

The simple interest is calculated as:

I = PRT

Make R the subject

R = I/(PT)

So, we have:

R = 1559.46/(2100 * 15.8)

Evaluate

R = 0.047

Express as percentage

R = 4.7%

Hence, the simple interest rate is 4.7%

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The recursive function o f the given sequence will be an = an-1 + 4

The formula for calculating the recursive function of n arithmetic sequence is expressed as
an = an-1 + d

Determine the common difference

d = 19 - 15 = 23 -19

d = 4

The recursive function o f the given sequence will be an = an-1 + 4

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Answer:

13

Step-by-step explanation:

7+2x=3x-6

knowing this then you solve it

Step-by-step explanation:

7 more = + 7

twice a number = 2*x = 2x

6 less = -6

3 times the same number = 3 * x = 3x

Putting this together we get:

2x + 7 = 3x - 6

subtract two from both sides to isolate x

(-2x) + 2x + 7 = 3x - 6 (-2x)

7 = x - 6

add 6 to both sides to get your answer

7 (+6) = x - 6 (+6)

13 = x

or

x = 13

The value of x in the trapezoid given, to the nearest tenth, is: 10.5.

A trapezoid is a quadrilateral that has two sides only that are parallel to each other.

To find the area of a trapezoid, the formula used is expressed as: 1/2(a + b) × h, where:

Given the following:

Area of trapezoid = 174 units²

AP = 6

PB = x + 3

CD = 2x + 6

AC = 10

Using the formula, we variables in the formula are:

a = AP + PB = 6 + x + 3 = x + 9

b = CD = 2x + 3

h = PC = √(AC² - AP²)

h = √(10² - 6²) = 8

Plug in the values into 1/2(a + b) × h:

174 = 1/2(x + 9 + 2x + 3) × 8

174 = 1/2(3x + 12) × 8

174 = (3x + 12) × 4

174 = 12x + 48

174 - 48 = 12x

126 = 12x

126/12 = x

10.5 = x

x = 10.5

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The length of side PS according to the quadrilateral descriptions is; 21.

Since, it follows from the task content that the two quadrilaterals given are congruent, hence, the corresponding sides are congruent and are in proportion to each other.

On this note, we have;

x/35 = 15/25

x = (35×15)/25

x = 21.

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The dot product of the D⋅n is 32.

According to the statement

We have given the value of n vector and d matrix and we have to find the dot product of these.

So, For this purpose,

The given values:

n = {-2,-1} and D = [−4423].

The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers, and returns a single number.

So, The d matrix become

[tex]D = \left[\begin{array}{cc}-4&4&\\2&3&\\\end{array}\right][/tex]

Now solve it with the help of multiplication then the matrix become

D = (-12, -8)

and n = {-2,-1}

Now multiply both terms with the dot product.

So, the dot product of the both terms will become

D.n = 24 +8

Then

The output of the dot product of both terms is 32.

So, The dot product of the D⋅n is 32.

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Answer:

11

Step-by-step explanation:

try it and see, .........

Answer: 17 inches by 7 inches

Step-by-step explanation:

119 = 1 x 119 & 7 x 17

7 x 17 is the more likely answer, so let's test it

7 x 2 + 3 = 17

Therefore, the dimensions are 17 by 7.

Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation: 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

Possible Dimensions of one prism are; 2cm, 3 cm and 4cm

Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm

We are told that volume of both rectangular prisms is; V = 24 cm³

Now, formula for Volume of a rectangular prism is;

V = lwh

where;

l is length

w is width

h is height

Thus, to solve this, we have to look for multiples of 24 which are;

1, 2, 3, 4, 6, 8, 12, 24.

Now, we must pick 3 numbers from the above in which their products will be equal to 24.

Thus;

Possible Dimensions of one prism are; 2cm, 3 cm and 4cm

Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm

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The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:

[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex]     (1)

Where each element of the resulting matrix is equal to the following expression:

[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex]     (2)

Where the operator "[tex]\bullet[/tex]" represents a dot product.

Now we proceed to calculate each element of the matrix:

[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

5 · 1 + 7 · 5 + 3 · (- 1)

37

[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

5 · 7 + 7 · 2 + 3 · 2

55

[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

5 · (- 3) + 7 · 1 + 3 · (- 4)

- 20

[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

(- 3) · 1 + 7 · 5 + 9 · (- 1)

23

[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

(- 3) · 7 + 7 · 2 + 9 · 2

11

[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

(- 3) · (- 3) + 7 · 1 + 9 · (- 4)

- 20

[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

2 · 1 + 5 · 5 + 2 · (- 1)

25

[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

2 · 7 + 5 · 2 + 2 · 2

28

[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

2 · (- 3) + 5 · 1 + 2 · (- 4)

- 9

The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

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The equation of the perpendicular line is y = -2x + 4

The line equation is given as:

2x = 4y - 8

Make y the subject

4y = 2x +8

Divide by 4

y = 0.5x + 2

The slope of the above equation is

m = 0.5

The slopes of perpendicular lines are opposite reciprocals.

This means that, the slope of the perpendicular line is:

n = -1/m

This gives

n = -1/0.5

n = -2

The equation is then calculated as:

y = n(x - x1) + y1

This gives

y = -2(x - 1) + 2

Expand

y = -2x + 2 + 2

Evaluate

y = -2x + 4

Hence, the equation of the perpendicular line is y = -2x + 4

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Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. The number of pennies will be in the last roll is 30.

To find out the number of pennies will be in the last roll.

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given that:

Cara has saved 1, 430 pennies.

Each penny roll holds 50 pennies.

1430 divides by 50 = 143/5≈29 roles and in last roll it will be 30 pennies.

So, the number of pennies will be in the last roll is 30.

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The surface area of the trapezoidal prism is: 4,190 in.².

Surface area = (b1+b2)h + PH, where:

Plug in the values

Surface area = (b1+b2)h + PH = (20 + 60)15 + (130)(23)

Surface area = 4,190 in.²

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Using equivalent angles, we have that the measures are given as follows:

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

120º is in the second quadrant, hence the equivalent on the first quadrant is:

180º - 120º = 60º.

The sine on the second quadrant is positive, hence:

[tex]\sin{120^\circ} = \sin{60^{\circ}} = \frac{\sqrt{3}}{2}[/tex]

The cosine on the second quadrant is negative, hence:

[tex]\cos{120^\circ} = \cos{60^{\circ}} = -\frac{1}{2}[/tex]

The tangent is given by the sine divided by the cosine, hence:

[tex]\tan{120^\circ} = \frac{\sin{120^\circ}}{\cos{120^\circ}} = -\sqrt{3}[/tex]

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The equation for a circle is:

[tex](x-a)^{2} + (y-b)^{2} + = r^{2}[/tex]

Where (a,b) is the circle's center and r is the circle's radius.

First, we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.

The formula to find the mid-point of a line segment giving the two endpoints is:

M = [tex](\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{y} )[/tex]

Where M is the midpoint and the given points are:

[tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} , y_{2})[/tex]

Substituting the values from the two points in the problem gives:

[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{-2+4}{2} )[/tex]

[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{2-4}{2})[/tex]

[tex]M = (\frac{20}{2} , \frac{2}{2})[/tex]

[tex]M = (10,1)[/tex]

Answer:

81

Step-by-step explanation:

The measure of dispersion that measures how much the data differ from the mean is called the standard deviation.

Standard deviation is a statistical measure of dispersion as opposed to the measure of central tendency like mean, median and mode.

The standard deviation is a measure of how spread out data values are around the mean.

It is defined as the square root of the variance and represented with the Greek letter σ.

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Answer:

7.26

Step-by-step explanation:

Here

Diameter=2m

Length =2.6m

Breadth=4m

Now

Area of circle=(22*2*2*4)/7

=22/7

=3.14m^2

again

Area of rectangle= lb

=2.6m*4m

=10.4m^2

So

Area of the shaded region is 10.4m^2-3.14m^2

=7.26m^2

The answer is 7.26 m².

To find the shaded area, subtract the area of the circle from the area of the rectangle.

Answer:

Step-by-step explanation:

will give brainiest wrrwrwvrwvr

Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Answer:

U-A empty

Step-by-step explanation:

all in a is in u in u is in a therfore empty is found on u but not in a

The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

From the given table, we see that the x-intercepts are;

(-3, 0), (1, 0) and (2, 0)

Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;

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

Then, the polynomial will be;

h(x) = (x + 3) * (x - 1) * (x - 2)

h(x) = (x + 3)(x² - 3x + 2)

h(x) = x³ + 3x² - 3x² - 9x + 2x + 6

h(x) = x³ - 7x + 6

Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

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