Please help me
Slope=
Y- intercept=
Equation=

By algebra properties, the resulting expression of the power 2⁴⁰ is (2⁸)⁵.

In this problem we must rewrite a power expression in terms of the power 2⁸, which is the base of the resulting expression. This can be done by applying algebra properties:

Step 1 - Write the original expression presented in the statement.

2⁴⁰

Step 2 - By definition of multiplication between real numbers.

2⁽⁸⁾⁽⁵⁾

Step 3 - By the definition of the power of a power.

(2⁸)⁵

The resulting expression is (2⁸)⁵.

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Step-by-step explanation:

To find the Area of a Trapezium, we use 1/2(a+b)*h

where a=2.8 and b=4.4, Height=3.5

1/2(2.8+4.4) *3.5

1/2(7.2)*3.5

3.6*3.5

12.6cm2

Answer:

Step-by-step explanation:

Area of a trapezium = 1/2(a + b) x h

1/2 (2.8 + 4.4) x 3.5

1/2 x 7.2 x 3.5

12.6

Answer:

B

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

Slope: 5

y-intercept: (0,-10)

Answer:

Step-by-step explanation:

The slope is 5

The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.

What is a perpendicular line?

Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.

Here,

The slope of ax + by = c is given by m = -a/b

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

m = 4/3 for this line.  

A perpendicular line will have a slope -1/m = -3/4

The line through (6, 8) with slope -3/4

y = (-3/4)x + b

8 = (-3/4)(6) + b

b = 8 + 9/2 = 25/2

y = (-3/4)x + 25/2

4y = -3x + 50

3x + 4y = 50

Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.

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The probability of the experiment is = 0.375, 0.665.

acc  to our question-

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Answer:

z = 52°

Step-by-step explanation:

Formula we use,

→ A + B + C = 180°

Then the value of z will be,

→ 81° + 47 ° + z = 180°

→ 128° + z = 180°

→ z = 180° - 128°

→ [ z = 52° ]

Hence, the value of z is 52°.

The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:

In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;

For ordered pair (3, 9), we have:

-5x + 3y > 12

-5(3) + 3(9) > 12

-15 + 27 > 12

12 > 12 (False).

For ordered pair (-5, 5), we have:

-5x + 3y > 12

-5(-5) + 3(5) > 12

25 + 15 > 12

40 > 12 (True).

For ordered pair (3, -6), we have:

-5x + 3y > 12

-5(3) + 3(-6) > 12

-15 - 18 > 12

-33 > 12 (False).

For ordered pair (-2, -5), we have:

-5x + 3y > 12

-5(-2) + 3(-5) > 12

10 - 15 > 12

-5 > 12 (False).

For ordered pair (2, 8), we have:

-5x + 3y > 12

-5(2) + 3(8) > 12

-10 + 24 > 12

14 > 12 (True).

For ordered pair (-6, 0), we have:

-5x + 3y > 12

-5(-6) + 3(0) > 12

30 + 0 > 12

30-5 > 12 (True).

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Step-by-step explanation:

x + y = 17

x = 17 - y

xy = 20

(17 - y)y = 20

-y² + 17y = 20

-y² + 17y - 20 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =

= (-17 ± sqrt(289 - 80))/-2 =

= (-17 ± sqrt(209))/-2

y1 = (-17 + sqrt(209))/-2 = 1.271583853...

y2 = (-17 - sqrt(209))/-2 = 15.72841615...

the 2 numbers are

1.271583853...

15.72841615...

Answer:A is 7 B is -1 C is -9 D is -13

Step-by-step explanation: I hoped i  have helped u! Have a wonderful day!

We are 90% certain that the average number of  hamsters per litter is between 7.1077 and 8.3323.

A confidence interval is a range of values that includes a population value with a high degree of certainty. When a population mean falls between an upper and lower interval, it is frequently expressed as a percentage. The confidence level is the long-run proportion of corresponding CIs that contain the parameter's true value. For example, 95% of all intervals computed at the 95% level should contain the true value of the parameter.

Given, n=47

[tex]\bar{x}[/tex]=7.72

s=2.5

c=90%=0.90

To find the t-value, look in the row that starts with degrees of freedom.

df=n-1

df=47-1

df=46>45 and in the column with c=90% in the table

=1.679

Now, the margin of error is then:

E=[tex]t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}=1.679\times \dfrac{2.5}{\sqrt{47}}\approx 0.6123[/tex]

The confidence interval's boundaries are thus:

[tex]\overline{x}-E[/tex]=7.72-0.6123=7.1077

[tex]\overline{x}+E[/tex]=7.72+0.6123= 8.3323

The average number of hamsters per litter is between 7.1077 and 8.3323, and we are 90% certain of this.

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Answer: 600$

Step-by-step explanation:

2/5 of 600 is 240

Answer:

Step-by-step explanation:

The average length of two raven eggs is about 0.1 m.

Since the average length of a robin egg is about 0.02 m, 5 eggs laid end to end would measure about 0.1 m.

Answer: 13

Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.

Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.

The ceiling of the ballroom is rectangular in structure.

The dimensions of the rectangle are 12 by 5 meters.

So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.

We will use Pythagoras theorem to calculate the length of the diagonal.

12² +5 ² = D²

or, D² = 144 + 25

or, D =√169

or, D = 13

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.

Hence Tony will need 13 meters of garland.

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A graph of the given equation (x - y = 6) is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Next, we would rewrite the given equation in standard form as follows:

x - y = 6

Adding y to both sides of the equation, we have the following:

x - y + y = 6 + y

x = 6 + y

Rearranging the equation, we have the following:

y = x - 6

By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.

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The equations y=3+2 and y=2x+1 both will meet at x=3

Acc to our question-

Hence,The lines y=3x−2 and y=2x+1 both will intersect at x=3

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The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2

The curve opens downward.

from, the graph, the roots of the equation are -4 and 0

so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y = [tex]x^{2}[/tex] + 4x

the x coordinate of the vertex = -b/2a = axis of symmetry

where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

substitute x = -2 into y =  [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex

y = [tex](-2)^{2}[/tex] + 4(-2)

y = 4 -8

y = -4

vertex  = (-2, -4)

The axis of symmetry is -b/2a which is -2

The curve opens downward as the vertex is at -4

In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward

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3√2x is the simplified form of the given expression by rationalizing the denominator.

In the form p q, where p and q are integers and q0, rational numbers can be expressed. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.

A common factor is a whole number that is a factor of at least two other numbers. The greatest common factor is the biggest factor that may be divided into two or more integers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).

Make the denominator simpler.

12/2√2x

Reject the 12/2 common factor.

6/√2x

Multiply the numerator and denominator by √2x

(6√2x⋅√2x/√2x)

Combine and make the denominator simpler.

6√2x/2x

= 3√2x

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The coordinates of the image of the point (-7, 5) are (7, -5).

We are given point P. The coordinates of the point P are (-7, 5). We perform a transformation on the given point. We rotate the given point about the origin counter-clockwise. The angle of rotation is 180°. We need to find the coordinates of the image of the point after rotation.

Let the new coordinates of the image of the point after rotation be denoted by (X, Y). If the coordinates of the original point are (x, y), then the relations between the coordinates of the point and the image are given below.

X = x*cosθ - y*sinθ

X = (-7)*cos(180°) - (5)*sin(180°)

X = (-7)*(-1) - (5)*(0)

X = 7

Y = x*sinθ + y*cosθ

Y = (-7)*sin(180°) + (5)*cos(180°)

Y = (-7)*(0) + (5)*(-1)

Y = -5

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The fraction that is equivalent to the fraction expression given as 5/8 is 40/64

From the question, we have the following fraction expression that can be used in our computation:

Fraction = 5/8

The above expression is a fraction and at the same time it is a rational number

The denominator of the fraction is 8

So, we start by rationalizing the expression by the fraction

This is represented as

5/8 = 5/8 * 8/8

Evaluate the products of the numerator

So, we have the following representation

5/8 = 40/8 * 1/8

Evaluate the products of the denominator

So, we have the following representation

5/8 = 40/64

The above expression cannot be further simplified

Hence, the equivalent expression of the fraction is 40/64

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Possible question

Which of the following is equal to the fraction below? (5/8)

40/64

0.556

2/5

Answer:The equation 8.9+(6.4 +7.2) is correctly applying the Associative Property of Addition.

Step-by-step explanation:

The Associative Property of Addition states that when adding three or more numbers, the order in which the numbers are added does not affect the sum.

The height of the electric pole is 12 m

When an electric wire falls, its one end touches the ground at P, 5 m away from the base of the pole,

base = 5

length of the wire from the top of the pole to the ground is 13 m

Height of the plant can be calculated by pythagoras theorem

h² = p² + b²

13² = p² + 5²

p² = 169 - 25

p = √144

p = 12m

Therefore, the height of the electric pole is 12 m

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The slope of the line is 0.393.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

Given,

A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.

We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:

m = 8ₓ/8ₐ

where m is the slope of the best-fit line.

8ₓ = Standard deviation of the x-coordinates is 5.591,

8ₐ =  the standard deviation of the y-coordinates is 2.772.

Slope is:

m = 8ₐ/8ₓ

m = (0.793)(2.772)/5.591

m = 0.393

The slope of the line is 0.393.

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The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).

We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.

E = x³ - 6x² + 3x + 10

One of the factors in the expression is already given. The given factor is (x + 1).

Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.

E = (x + 1)(x² - 7x + 10)

Now we will factorise the quadratic expression.

E = (x + 1)[x² - 2x - 5x + 10]

E = (x + 1)[x(x - 2) - 5(x - 2)]

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

We cannot simplify and factorise the expression any further.

Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).

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Answer:

Step-by-step explanation:

To find Mr.Santos's age subtract morgan's age from their combined age

44-15=29

Therefore Mr. Santos age is 29 years

Hope that helps

In this problem 0.7 is the standard deviation of the contents.

It is a statistic that gauges a dataset's dispersion from its mean, and it is calculated as the variance's square root. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean. A dataset's dispersion from its mean is measured by standard deviation. It is determined as the variance's square root. In the financial industry, standard deviation is frequently employed as a gauge of an asset's relative riskiness.

Given,

A random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces.

In this problem 0.7 is the standard deviation of the contents.

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The two triangles are congruent and they are congruent by ASA.

Triangles are congruent when they have exactly the same three sides and exactly the same three angles. This simply implies the corresponding sides and angles of the triangles are congruent.

Let's check if the triangles are congruent.

One of the congruent angles in the triangles are vertically opposite angle.

Recall vertically opposite angles are congruent.

In these two triangles, we have a congruent angle pair and a congruent side pair.

Therefore, we can say the triangles are congruent by ASA.

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Answer:

120,000

Step-by-step explanation:

To estimate the product of 283 × 416, first round each number so that each number contains only 1 non zero digit.

In this case, we will round 283 to the nearest hundred and we will also round 416 to the nearest hundred. To round 283 to the nearest hundred, the number next to two is higher than 5 so we round up. 283 rounds to 300.

416 rounded to the nearest hundred is 400 because the digit to the right of 4 is less than 5 which means we round down. 416 rounds down to 400.

Now we have 300 × 400 which equals 120,000

This means that 283 x 416 is approximately 120,000.