Find the area of each figure. Round to the nearest hundredth where necessary.

A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line. The slope of the line y = 2/7x - 8 is 2/7. To find the slope of the line that is perpendicular to it, we take the negative reciprocal of 2/7 which is -7/2.

We know that the line we're trying to find passes through the point (-4, 2), so we can use this point and the slope to write the equation of the line in point-slope form:

y - y1 = m (x - x1)

where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.

So the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is:

y - 2 = -7/2 (x + 4)

Simplifying this, we get

y = -7/2 x - 8

Therefore the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is y = -7/2 x - 8

The area of the triangle having sides 3 cm 4 cm and 5 cm is calculated to be 6 cm².

Given that,

The sides of the triangle are said to be 3 cm, 4 cm and 5 cm.

By looking at the lengths of the sides of the triangle, it is clear that they are the sides of a right angled triangle. The Pythagorean theorem can be used to verify this.

5² = 3² + 4²

25 = 25

So, 5 is said to be the hypotenuse side of the right triangle and 3, 4 are said to be the base and height of the right triangle.

The formula to find out the area of the triangle is given by,

Area A = 1/2 × Base b × Height h

A = 1/2 × b × h

From the above conclusion, b and h are found to be 3, 4.

So, A = 1/2 × b × h = 1/2 × 3 × 4 = 6 cm²

Thus, the area of the required triangle is calculated to be 6 cm².

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The maximum value of p = x + 3y for the feasible region is 11.

The minimum value of p = x + 3y for the feasible region is 2.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

x > 2 ____(1)

y > 0 ____(2)

x + 2y < 8 _____(3)

When all the inequalities (1), (2), and (3) are graphed we get the graph given below.

The points on the graph given below (2, 0), (8, 0), and (2, 3) are in the feasible region.

Objective function is p = x + 3y

Substitute the points on p = x + 3y.

So,

For (2, 0),

p = 2 + 3 x 0 = 2 + 0 = 2

For (8, 0),

p = 8 + 3 x 0 = 8 + 0 = 8

For (2, 3),

p = 2 + 3 x 3 = 2 + 9 = 11

We see that,

The maximum value is 11 at (2, 3).

The minimum value is 2 at (2, 0).

Thus,

The maximum value is 11.

The minimum value is 2.

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The intersection of x = -1 and x = 1 is where f(x) = g(x) has its solution.

Therefore,

The intersection of the two lines, or the point at which they are equal, is the answer to the equation f(x) = g(x). According to the table provided, only the values 9 and 12 are shared by both f(x) and g(x).

Consequently, the intersection of x = -1 and x = 1 is where f(x) = g(x) has its solution.

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the volume of the rectangular prism is 1/2 x³.

What is rectangular prism?

The normal's length from the prism's base to its top base serves as a gauge for the structure's height. At their base, certain prisms have an angle. Prism's top end is referred to as the "base" since the word "base" can refer to either end of a prism. The area (A) of the base of a prism's base times its height (H) equals the prism's volume (V). Since A is the base area and H is the prism's height, the volume of the prism is therefore A H cubic units.

The base area is A = x*x =x²

The height is 1/2 x

The volume of the rectangular prism is A*H = 1/2 x³.

Hence the volume of the rectangular prism is 1/2 x³.

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The area occupying a three-dimensional shape's exterior is known as its surface area.

The quantity of space enclosing the exterior of a three-dimensional shape is its surface area. The surface area of a three-dimensional shape refers to how much open space it occupies outside of itself.

The entire area of all the faces makes up the surface area of a three-dimensional form. We calculate the area of each face and put them together to determine the shape's surface area.

The total area that all of a 3D object's faces cover is the surface area.

Add up every region. SA=2B+2πrh. Find the base's area, multiply it by 2, and then add those areas to the rectangle's areas, which are equal to the rectangle's diameter times its height.

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Answer:

The result can be shown in multiple forms.

Exact Form:

− 3/2

Decimal Form:

− 1.5

Mixed Number Form:

−1 1/2

Step-by-step explanation:

Answer:

[tex]\displaystyle -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \biggr(\frac{7}{4}-\frac{8}{3}\biggr)-\biggr|\frac{1}{6}-\frac{3}{4}\biggr|\\ \\=\biggr(\frac{7*3}{4*3}-\frac{8*4}{3*4}\biggr)-\biggr|\frac{1*2}{6*2}-\frac{3*3}{4*3}\biggr|\\ \\=\biggr(\frac{21}{12}-\frac{32}{12}\biggr)-\biggr|\frac{2}{12}-\frac{9}{12}\biggr|\\ \\=-\frac{11}{12}-\biggr|-\frac{7}{12}\biggr|\\\\=-\frac{11}{12}-\frac{7}{12}\\\\=-\frac{18}{12}\\ \\=-\frac{3}{2}[/tex]

The percentage of vertebrates that are reptiles is approximately 13.8%

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to express rates, ratios, and proportions. A percentage is represented by the symbol "%" and is calculated by multiplying a number by 100 and dividing the result by the total number of items being considered.

In this problem, we need to determine the percentage of vertebrate that are reptiles.

This can be represented mathematically as;

Percentage of reptiles = [number of reptiles / total number of vertebrates] * 100

Percentage = [8240 / 59811] * 100

Percentage = 13.8%

The percentage of reptiles is 13.8%

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After using the triangle inequality theorem, the possible values of the unknown side of the triangle is 15 < n < 25.

In this case, we are given that:

The lengths of the sides of a triangle are 20, 5, and n centimeters.

The theorem of triangle inequality stated that the lengths of any two of a triangle's sides added together must be bigger than the length of the third side. Given two sides, x and y, we can use the triangle inequality theorem to predict that the length of the third side will be between x + y and x - y.

Therefore,

x - y < n < x + y

20 - 5 < n < 20 + 5

15 < n < 25

As the result, the possible value of the unknow side of the triangle would be 15 < n < 25.

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Answer:

x = 149 degree

Step-by-step explanation:

First, we have to find the missing angle of the triangle

1 triangle = 180 degree

We know 2 angles, one is 63 degrees and one is 86 degrees.

63 + 86 = 149 degree

180 - 149 = 31 degree

So, the angle of the triangle is 31 degrees. Now we know that angle add with the x to get 180 degrees, so

180 - 31 = 149 degree

So, x = 149 degree

The slope, and the y-intercepts are

A linear equation can be represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the above as a guide, we have the following:

See attachment for the graph

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Answer: By 40J

Step-by-step explanation:

pls mark it as brainliest

The wideness of the actual balcony would be = 5.2 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

The actual size = scale factor × blueprint

where actual length = 9 inches

blueprint = 11.7 = 140.4 inches

scale factor = actual size/blue print

= 140.4/9 = 15.6

If the blue print width size = 4

the actual size = 4× 15.6 = 62.4 inches = 5.2 feet

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There are both numbers and letters in algebra. Numbers are constant, i.e. e. The unknown quantities in the algebraic formula are represented by letters or alphabets. The 9 formulas of algebra are explained further.

Algebra is a mathematical tool that we use to calculate distances, volumes, and perimeters of spaces as well as to calculate costs, rent things out, and understand time relationships.

The 9 formulas of algebra are explained as:

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Answer:

in decimal it is 36.72, in fraction it is 918/25

Step-by-step explanation:

The amount of shovels that can be produced in h hours is 960 shovels

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

In the given equation,

The number of shovels produced are

C(x)=26*20+400

=520+400

=920 shovels

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The number of balls that Eve has will be 25 balls.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this situation, Eve had some balls she tried to share them evenly first in 2 bags ,then in 3bags,and finally in 4 bags and each time ,she had one ball left over.

The number of balls that Eve has will be:

= (2 × 3 × 4) + 1

= 24 + 1

= 25 balls

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Answer:

2x^3 -9x^2 +11x-6 divided by x-3

Step-by-step explanation:

     2x^2  - 3x  + 2

                 ------------------------------

x - 3             2x^3 - 9x^2 + 11x - 6

                  2x^3 - 6x^2

               --------------------------------------subtract

                           -3x^2    + 11x

                           -3x^2    + 9 x

               ----------------------------------------subtract

                                         2x    - 6

                                         2x    - 6

                                -----------------------------subtract

                                         0

- 2x^2 - 3x + 2

:/

Answer:

x=8

Step-by-step explanation:

11x+2=90

11x=88

x=8

Answer:

19. X=8

20. x=7

When there are two factors—a fixed element and a variable factor—the law of variable proportions is created. According to the law of variable proportions, the marginal product of a factor will gradually decrease when its quantity is raised while the other elements remain constant.

We are aware that the relationship between the number of units of a variable factor and the entire physical product is shown by the law of variable proportions.

Additionally, the TPP increases initially at a rising pace, then at a falling rate, and finally declines if we maintain other parameters constant and increase the units of the variable factor.

According to the law of variable proportions, if a producer raises the units of a variable factor while keeping other elements constant, the total product will initially increase at an increasing pace, then it will increase at a diminishing rate, and finally it will begin to decline.

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The system of equations is:

-2 = a + b + c

7 = 4a - 2b +c

-2 = 25a + 5b + c

The polynomial is:

y = (1/3)*x^2 - 6x - 1/3

The general polynomial of degree 2 can be written as:

y = a*x^2 + b*x +c

If we use the fact that it passes through the 3 given points, then we can write the 3 equations:

-2 = a*1^2+ b*1 + c

7 = a*(-2)^2 + b*-2 + c

-2 = a*5^2 + b*5 + c

We can simplify these to get the system of equations:

-2 = a + b + c

7 = 4a - 2b +c

-2 = 25a + 5b + c

First, isolate c on the first equation to get:

c = -2 - a- b

Replace it on the other two:

7 = 4a - 2b + (-2 - a - b)

-2 = 25a + 5b + (-2 - a - b)

9 = 3a - 3b

0 = 24a + 4b

Using the second equation we can rewrite:

-24a = 4b

-24a/4 = b

-6a = b

Ande replace that in the other equation:

9 = 3a - 3*(-6a)

9 = 3a + 18a

9/21 = a

1/3 = a

And the value of b is:

-6*(1/3) = b

-2 = b

And the value of c is:

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

c = -1/3

The polynomial is:

y = (1/3)*x^2 - 6x - 1/3

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Answer:  resultant

Step-by-step explanation:

Answer:

She's thinking of 19 and -7.

Step-by-step explanation:

x+y=12

x-y=26

-----------

2x=38

x=38/2

x=19

19+y=12

y=12-19=-7

Answer:

B，8.8cm

Step-by-step explanation:

I don't know if you have learned about the relations between the three sides of a 30,60,90 right-angled triangle. It shows one angle is 29, we will estimate it for 30.

Relations： 30 angled face side DF is 1, 60 face side EF is √3=1.732， 90 face side DE is 2

And we knew EF=7.7

So, 1.732/7.7=2:DE

1.732DE=15.4

       DE=8.89

Sorry, I hope someone can help you in a simpler way.

For all samples of 5, there is a 0.05 probability that the sample mean would be higher than 22 pounds.

The selection of bags weights, on average, 19.7 pounds.

The standard variation is 3.1 pounds.

Both the normal probability density function and the sampling distribution theorem were used.

When dealing with issues involving samples of data that are regularly distributed, the z-score algorithm is applied.

The z-score of a measure X is calculated as follows:

z = (x - μ) ÷ σ

The number of standard deviations is calculated using the Z-score. The average is the metric employed.

We examine the p-value linked with the Z-score in the z-score table after computing the Z-score.

The chance that the measure's value is less than X, or what proportion of X, is represented by this p-value.

We may calculate the likelihood that the metric exceeds X by subtracting 1.

The Central Limitation Theorem also holds for skewed variables when n is at least 30.

The sample mean will remain constant regardless of sample size.

The standard error, though, will alter.

The probability that the sample means will be higher than 22 is shown by P(a > 22).

For all samples of size 5, the possibility that they will weigh more than 22 pounds is about 0.05.

Your question is incomplete but most probably your full question was

at a certain high school, the distribution of backpack weight is approximately normal with a mean of 19.7 pounds and a standard deviation of 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. what is the probability that my next five samples will average 22 pounds?

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The original linear function is:

y = 2*x + 4   with the point (1, 6)

The translated function is:

y = 2x + 7

And the translated point is (-3, 1)

First, we want to write a random linear function, I will use:

y = 2*x + 4

To find a point on that line, we can just evaluate the function in x = 1, we will get:

y = 2*1 + 4

y = 2 + 4

y = 6

So we have the point (1, 6)

Now we want to translate it 4 units to the left and 5 units down.

To translate it 4 units to the left, we need to add 4 to the argument.

y = 2*(x + 4) + 4

And to translate it  5 units down, we just need to subtract 5, we will get:

y = 2*(x + 4) + 4 - 5

Now we can simplify this to get:

y = 2*x + 2*4 + 4 - 5

y = 2x + 8 + 4 - 5

y = 2x + 7

The new coordinates of the point are the same as the last ones, but we subtract 4 to the x-value and 5 to the y-value:

(1 - 4, 6 - 5) = (-3, 1)

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The values of x and  y are 24 and 25 when the sum of two numbers is 49 and the difference between the numbers is 1

What is Linear equation ?

linear equation can be defined as the equation in which the highest degree is one.

Given ,

the sum of two numbers is 49 and

the difference between the numbers is 1

Let the two numbers be x and y .

so x+y = 49

x-y = 1

x = 1+y

from two equations ,

Substitute x = 1+y in x+y = 49

we get,

1+y+y = 49

2y = 49 - 1

2y = 48

y = 24

substitute y =24 in x=1+y ,

we get

x = 24+1

x = 25

Hence , the values of x and  y are 24 and 25 .

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Answer:

c. $350.00

Step-by-step explanation

im sorry if this didn't help i wrote everything down on paper

Point G is two, which divides the directed line segment from D to F into a 5:4 ratio at that place.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

From negative five to positive ten is a number line.

Points D and F are at -2 and +7, respectively.

The distance between point D and F is,

=9

If Point G divides the directed line segment from D to F into a 5: 4 ratio, then,

=2

Hence, The directed line segment from D to F is divided into a 5:4 ratio at point G by the number 2.

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