Mathematics High School

hello can someone help me pls

Answers

Answer 1

The size of the angle x = 54 degrees

The regular pentagon is given

Number of sides of the pentagon = 5

O is the center of the pentagon

The sum of all the angle around a point is 360 degrees

From the figure we can see that the it equally divided by 5 parts

The measure of each angle = 360/5

= 72 degrees

Consider the corresponding triangle

Sum of all the interior angles of the triangle is 180 degrees and the two sides of the triangle is equal, therefore it is an isosceles triangle

Then,

x + x+ 72 = 180

2x + 72 = 180

2x = 180- 72

2x = 108
x = 108/2

x = 54 degrees

Hence, the size of the angle x = 54 degrees

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Related Questions

Match the following definitions with the correct term.

Answers

Answer:

that's biology but

Step-by-step explanation:

autotrophs make their owner food

heterotrophs can't make their own food

photosynthesis is the 3rd one

photosynthesis happens in the chloroplast

photosynthesis makes glucose

I can go in depth about any of these, ask me if needed

Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?

Answers

Answer:

0.86 pounds of fruit is left.

Step-by-step explanation:

If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86

Someone help

Given the function f(x) = 1 + 1/2x³, find the value of f(-4) in simplest form.

Answers

Answer: -62.5

PLEASE GIVE BRAINLIEST THANK YOU!!!

Step-by-step explanation:

What is a counterexample for the conjecture?
If the area of a rectangle is 80 square units, the perimeter must be greater than 35.9 units.
A) A rectangle with length 39.5 units and width 0.5 unit has a perimeter of 80 units and an area of 19.75 square units.
B) A rectangle with length 8 units and width 10 units has a perimeter of 36 units and an area of 80 square units.
C) A rectangle with length 8 units and width 9 units has a perimeter of 34 units and an area of 72 square units.
D) A square with a side length of √80 units has a perimeter of approximately 35.8 units and an area of 80 square units.

Answers

The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.

What is counterexample?An instance or example that refutes the proposition is referred to as a counterexample. To determine if a statement is true or not, logic uses this. Counterexamples typically offer strong arguments in opposition to the assertion under discussion.The goal of the inquiry is to demonstrate any possible relationship between the area and perimeter of a rectangle.

acc to our question-

The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.

The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.

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Triangles UVW and VUX are congruent identifier common sides are angles.

Answers

Answer:

Common side: UV

Step-by-step explanation:

Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
Question 20 options:

f(–5) = 10, f(0) = 0

f(–5) = 12, f(0) = 5

f(–5) = –20, f(0) = –2

f(–5) = 20, f(0) = 10

Answers

Answer:

Step-by-step explanation:

f(-5) = 2|-5-5|

f(-5) = 2|-10|

f(-5) = 2 * 10

f(-5) = 20

f(0) = 2|0-5|

f(0) = 2|-5|

f(0) = 2 * 5

f(0) = 10

2. The lengths of a certain species of fish was
found to be normally distributed. The mean
length is 78 cm with a standard deviation
of 14 cm. In a school of 370 of these fish,
how many would be longer than than
92 cm

Answers

So, approximately 59 fish in the school would be longer than 92 cm.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.

Here,

We can solve this problem using the normal distribution formula, which states:

z = (x - mu) / sigma

where z is the standard score, x is the raw score, mu is the mean, and sigma is the standard deviation.

To find the number of fish longer than 92 cm, we need to find the proportion of fish in the population with lengths greater than 92 cm. We can then multiply this proportion by the total number of fish in the school to get the number of fish longer than 92 cm.

First, we calculate the standard score for 92 cm:

z = (92 - 78) / 14

z = 1

Next, we look up the proportion of the standard normal distribution that corresponds to a z-score of 1. We can use a standard normal distribution table or calculator to find this value. The proportion of the distribution that is greater than z = 1 is approximately 0.1587.

Therefore, the proportion of fish in the population with lengths greater than 92 cm is 0.1587. To find the number of fish longer than 92 cm, we multiply this proportion by the total number of fish in the school:

370 * 0.1587 = 58.8

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in order to estimate the proportion of all credit card holders who pay their credit card bills in full each month a credit counseling bureau took a random sample of 450 credit card holders and found that 127 pay all their credit card bills in full each month. a 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is:

Answers

A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.

Define confidence interval.

Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Given,

Number of credit card holders

n = 450

x = 127

p = 127/450

Proportion:

p = 0.2822

99% confidence interval:

C I = 0.2822 ± 2.576 × 0.2122

CI = 0.2822 ± 0.05465

CI = 0.282 + 0.055

A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.

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The sum of the squares of two consecutive positive numbers is 1,105. Find the numbers.

Answers

Answer:

23 and 24

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1 , then

n² + (n + 1)² = 1105

n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )

2n² + 2n - 1104 = 0 ( divide through by 2 )

n² + n - 552 = 0 ← in standard form

(n + 24)(n - 23) = 0 ← in factored form

equate each factor to zero and solve for n

n + 24 = 0 ⇒ n = - 24

n - 23 = 0 ⇒ n = 23

However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24

the numbers are 23 and 24

Write an equation of the line in slope-intercept form.
Ay
4
y =
(0, 2)
2
(3, 3)
4
AX

Answers

Equation of line in slope-intercept form is [tex]y = (\frac{1}{3})x + 2[/tex].

Given in graph,

A(0,2) and B(3,3)

Slope-intercept form => y = mx + c

Slope, m = [tex]\frac{y2-y1}{x2-x1}[/tex]

= [tex]\frac{3-2}{3-0}[/tex]

= [tex]\frac{1}{3}[/tex]

Therefore, y = (1/3)x + c

Put A(0,2) in above equation

2 = (1/3)*0 + c

2 = c

Hence, y = (1/3)x + 2.

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Given the following function, find the vertex, y=5x^2-8x+6

Answers

Answer:

The vertex is (0.8, 2.8)

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

GivenFunction y = 5x² - 8x + 6

Find the x-coordinate of the vertexx = - b/(2a)x = - (-8)/(2*5) = 8/10 = 0.8

Find the y-coordinate of the vertexy = 5(0.8²) - 8(0.8) + 6 = 2.8

find the slope through(0,10) and (24, 6)

Answers

Answer:

slope = - [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )

m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]

help me please
Ayuda pro favor

Answers

The values of x after applying congruency to solve the complete shape is 3.5.

What are congruent shapes?

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.

To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.

Comparing ΔQHG and ΔQFE, we can deduce that

ΔQHG ≅ ΔQFE

Therefore,

x+8 = 3x+13x-x = 8-12x = 7x = 7/2x = 3.5

Hence, the values of x in is 3.5.

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What is the value of x?
1.9x+0.1x=0.6
Enter your answer as a decimal in the box.
x = ???

Answers

1.9x+0.1x=2x
2x = 0.6
divide by 2 on both sides
x=0.3

Answer:

x = 0.3

Step-by-step explanation:

[tex] \sf1.9x + 0.1x = 0.6[/tex]

Combine like terms.

[tex] \sf2x = 0.6[/tex]

Divide both sides by 2.

[tex] \sf \: x = 0.3[/tex]

Example of a slope intercept form equation with a negative slope and y-intercept of 0

Answers

Answer:

An example would be y = -x.

Step-by-step explanation:

Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.

Hope this helps.

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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64

Answers

Answer:

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{12}[/tex]

= [tex]\sqrt{4(3)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

= 2[tex]\sqrt{3}[/tex]

Then

[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]

= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)

= 12 + 36[tex]\sqrt{3}[/tex] - 40

= - 28 + 36[tex]\sqrt{3}[/tex]

write the inverse: if the 2 smallest sides sum to be larger than the 3rd side, then it is a triangle.

Answers

Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."

The statement is given as if the sum of two sides is greater than the third side then it is a triangle.

Now for the inverse we have to convert the given line into double negative.

Hence we get:

If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle

Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.

the various types of conditional statements are:

When the conditional statement's hypothesis and conclusion are both untrue, it is referred to as an inversion of the statement.If both a hypothesis and a conclusion are false at the same time, the statement is contrapositive.A statement is said to be biconditional when it is both conditional and converse at the same time, satisfying both conditions as true.

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What is the product of (4i-5)(4i+5)

Answers

The product of (4i-5)(4i+5) is -41.

What are complex numbers?

Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.

Here, we have

Given function

= (4i-5) (4i+5)

After applying the product rule, we get

= 16i² + 20i - 20i - 25

= 16i² - 25

after putting i² value, we get

= 16(-1) - 25

= -41

Hence, the product of (4i-5)(4i+5) is -41.

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according to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?

Answers

There should be 12 emails total.

7.200 and 2.683 are the variance and standard deviation, respectively.

What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.

Calculation of expected number of emails, variance and standard deviation:

Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683

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What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?

Answers

Answer:

-15, 9

Step-by-step explanation:

Substituting into the distance formula,

[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]

The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 side touching. What is the total number of white cubes that were used to build the prism?

Answers

Answer:34?

Step-by-step explanation: not too sure but yeah

This rectangular design is made from 6 squares. there are 2 small squares surrounded by 4 larger squares. the area of each small square of 1sq.cmwhat is the total area of the design?

Answers

The total Area the design is 8 square cm.

Area of rectangular design is product of length and breadth of rectangular design.

In the given question we have,

Rectangular design is made up from 6 squares .

there is 2 small squares surrounded by 4 large squares.

Area of each small square = 1 sq.cm

let the length of rectangular design be l cm

and breadth is b cm.

Area of rectangular design= l×b sq.cm

from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .

Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.

so, length of rectangular design= 4 cm

breadth of rectangular design= 2cm

Area of rectangular design= 4×2 = 8sq. cm

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x³+10<9 help pls pls pls pls pls pls

Answers

Answer:

x< -1

Step-by-step explanation:

x^3 < 9 - 10

x^3 < -1

x< -1

Answer:

x < -1

Step-by-step explanation:

x³<9-10

x³<-1

x < -1

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What is the
y-intercept of the function f(x)=-2/9x+1/3?

Answers

Answer:

1/3

Step-by-step explanation

We can immediately tell the y-intercept is 1/3.

Slope intercept form:

y = mx + b

m = slope

b = y-intercept.

Answer: the y - intercept is 1/3

Step-by-step explanation: trust

Which statement is true about 67?

A. its a prime number

B. its a composite number

C. its neither prime or composite

Answers

Answer:

a. its a prime number cuz as far as ik 67 has one factor 67x1

Answer:

Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself

Bloomington University charges $53,730 for tuition. If they raise their tuition by 8% each
year, how much will tuition be in 2 years?
If necessary, round your answer to the nearest cent.
$
E

Answers

The tuition in 2 years will be $62,670.67

GHLJ and GSTU are both parallelograms. Why is
∠L ≅ ∠T?

Parallelogram G S T U is inside of larger parallelogram G H L J. Side G S in on side G H, and side G U is on side G J.

Answers

The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that opposite angles of a parallelogram are congruent.

How to identify congruent angles?

We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.

Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.

Thus, angle G is congruent to angle T and angle L .

Therefore, ∠L ≅ ∠T

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Answer:

By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation:

got it right on edge2

Write the equation of a line in point slope form that has a slope of 1/3 and passes through the point (6,-2)

Answers

The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].

What is point-slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point-slope form is used to determine the equation of a line whose slope is "m" and passes through the point ([tex]x_{1}, y_{1}[/tex]). The equation of a straight line can be expressed in various ways, Point slope shape is one of them. The point slope form's equation is as follows:[tex]y-y_{1} =m(x-x_{1} )[/tex]where (x, y) is a chance point on the line that should be treated as a variable when using the formula.A fixed point on the line is ([tex]x_{1}, y_{1}[/tex]).The slope of the line is m.

Calculation

[tex]y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]

[tex]y+2 =\frac{1}{3} (x-6 )[/tex]

Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]

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Calculate (8.42 x 109) − (2.35 x 108).

Answers

Answer:

Step-by-step explanation:

663.98

Answer: 663.98

Step-by-step explanation:

(8.42*109)=917.78

(2.35*108)=253.8

917.78-253.8=663.98

Write an equation for the transformation of y=x; vertical by a factor of 1/10

Answers

The equation the function after the transformation is g(x) = x/10

How to determine the transformation of the function?

The equation of the function is given as

y = x

Express as a function

f(x) = x

The sequence of transformations is given as follows:

Vertically stretched by a factor of 1/10

When the above transformations are combined, we have:

Vertically stretched by a factor of 4: g(x) = 1/10f(x)

So, we have

g(x) = 1/10f(x)

Substitute x for f(x)

So, we have

g(x) = 1/10 * x

Evaluate

g(x) = x/10

Hence, the function g(x) is g(x) = x/10