please help with geometry proof

Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

Radical form is rather simple. It refers to the form of a number or algebraic expression where the number or expression is contained under a radical. The answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

A radical notation is an expression that makes use of a root, such as the square or cube root.

The fundamentals of radical form are simple. When a numerical or algebraic expression is under a radical, the term refers to that version of the expression. To improve that, we can manipulate a number or an algebraic expression in radical form to convert it to simplest radical form.

[tex]\text { Simplify }-x \sqrt{2} 8+10 \sqrt{6} 3 x^2:-\\\\8 \sqrt{2} x+30 \sqrt{6} x^2 -x \sqrt{2} \cdot 8+10 \sqrt{6} \cdot 3 x^2 \\\\& =-8 \sqrt{2} x+30 \sqrt{6} x^2\end{aligned}$$[/tex]

Therefore, the answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].

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Therefore, the result of the above linear equation problem's solution is hence The lines do not intersect, hence there are no solutions and an inconsistent system.

In algebra, a linear equation is one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are linear equations with two variables. Linear equations can be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear.

Here,

The lines in this system have the same slope even though the values of b vary.

This indicates the parallel lines.

The lines do not intersect, hence there are no solutions and an inconsistent system.

Since the lines are different, the equations are independent.

The result of the above graph problem's solution is hence The lines do not intersect, hence there are no solutions and an inconsistent system.

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It's a good idea to utilize the 13 cm measurement that Martha used for her scale illustration. This is because it would be simpler to measure the flag's stripes. The American flag has 13 stripes, thus each one is 1 centimeter wide.

Flags can be as big as 20 feet by 38 feet, although most are between 3 feet by 5 feet and 5 feet by 8 feet in size. The standard size for an American flag flown outside a home is 3 x 5.

A flag's rectangular design assures that even a moderate breeze would cause it to move, making it readily apparent to everyone else. Additionally, the shape is efficient in terms of production costs, according to a number of flag designers.

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Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25[tex]b^{2}[/tex] + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25[tex]b^{2}[/tex]  = -(5)(5) * [tex]b^{2}[/tex]

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * [tex]b^{2}[/tex] +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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On solving the provided question, we can say that - the answer of the following equation is = [tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex] = 25.2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex]

630000/25000

25.2

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17. The triangles can be proven congruent by the SSS theorem.

18. The triangles cannot be proven congruent by the HL theorem, as it is not known if the triangles are right triangles.

The side-side-side congruence theorem, abbreviated as SSS, means that if two triangles have three equal side lengths, then the triangles are congruent.

In item 17, we have that:

As the three triangles are equal, then the SSS theorem can be used to prove the congruence of the two triangles.

The HL theorem represents the hypotenuse and leg theorem, which means that if two right triangles share a hypotenuse measure along with a leg measure, then they are congruent.

Hence item 18 cannot be proven congruent by the HL theorem, as there is no information regarding whether the triangles are right triangles.

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Therefore , the solution of the problem of expression comes out to be

9.12 x 10 ^-2.

An algebraic expression must be checked via replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is comparable to 6, since 6 + 6 equal 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Given : 0.0912 in scientific notation

=> 9.12 /100

By using scientific notation

=> 9.12 × 10^-2

=> 9.12 x 10 ^-2

So, we get 9.12 x 10 ^-2 as the scientific notation for the given expression

Therefore , the solution of the problem of expression comes out to be

9.12 x 10 ^-2.

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The range of the function will be;

⇒ { 4, 2, 0, - 2, - 4 }

or, { - 4, - 2, 0, 2, 4 }

A relation between a set of inputs having one output each is called a function.

Given that;

The relation is,

⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)

Now,

Since, The relation is,

⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)

We know that;

The range of relation is the value of y.

Hence, The range of relation = { 4, 2, 0, - 2, - 4 }

Thus, The range of the function will be;

⇒ { - 4, - 2, 0, 2, 4 }

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The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

X now has 300 mg of sodium in it.

[tex]x = 300[/tex]

Y also has 450 mg of sodium in it.

[tex]y = 450[/tex]

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

a(300) + b(450) = 6000 .

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]

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37.5% of the cars have a fuel efficiency of at least 35 miles per gallon.

To find the percentage of cars that have a fuel efficiency of at least 35 miles per gallon,

We first need to determine how many of the eight cars meet that threshold.

To do this, we can compare each car's fuel efficiency to 35 miles per gallon, and count the number that is greater than or equal to 35.

Identify the cars that have a fuel efficiency of at least 35 mpg: 42, 42, 54,

count the number of cars which is 3

divide it by 8 which is the total number of cars

Multiply the result by 100 to get the percentage, so:

3/8 * 100 = 37.5%

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Answer:

If she played on the swings for 24 minutes and on the slide for 13, then she was at the playground for 37 minutes.

If she left the playground at 4:28, then you want to subtract 37 minutes from 4:28.

4:28 - :37 = 3:51.

She arrived at the playground at 3:51

Step-by-step explanation:

Hope it helps! =D

Answer:

3:51 p.m.

Step-by-step explanation:

Add the two amounts of time:

24 minutes + 13 minutes = 37 minutes

She was at the park for 37 minutes. She arrived at the park 37 minutes before 4:28 p.m.

Now we subtract 37 minutes from 4:28 p.m.

Remember that 1 hour = 60 minutes, so when you borrow 1 hour to do the subtraction, you add 60 minutes to the minutes of the time of day.

Borrow 1 hour from 4 hours as 60 minutes. You end up with 3 hours. Then add the 60 minutes to the 28 minutes to get 88 minutes.

4:28 p.m. is the same as 3:88 p.m.

     4:28 p.m.                             3:88 p.m.

-     0:37                 ----->         -  0:37

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

                                                  3:51 p.m.

Answer: 3:51 p.m.

a. The model represents exponential growth.

b. The annual percentage increase is 3%.

c. After 2390 decades the population was about 590000.

The formula for exponential growth is [tex]y = y_₀.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_₀.e^{(-kt)}.[/tex]

Given, The population P(in thousands) of Austin Texas during a recent decade is approximated by [tex]y = 492(1.03)^t[/tex].

The model represents exponential growth as time can not be negative.

The annual percentage increase in the model [tex]y = 492(1.03)^t[/tex] is 3%

as 1.03×100% = 103%.

The time when the population was about 590000 since the beginning of a decade is,

[tex]590000 = 492(1.03)^t[/tex].

[tex](1.03)^t = 590000/492[/tex].

[tex](1.03)^t = 1199.1869[/tex].

[tex]log_{1.03}1.03^t = log_{1.03}1199.1869[/tex].

t = 2389.84 Or 2390 decades.

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Therefore , the solution of the given problem of function comes out to be 2.

A function connects various inputs together or produces a single output from each input. Simply explained, a function is a collection of equations that are linked to a single, identifiable output. A statement, rule, or law which explains the connection between two variables is known as a function in mathematics (the dependent variable). When a rule of this type is applied, there is just one output. by photographer Alex Federspiel. 

Here,

=> (1−α)(1−β)(1+α)(1+β)

​=>(1−α−β+αβ)​ /(1+α+β=αβ)

=> (1−(α+β)+αβ ) / ( 1+(α+β)+αβ)

=>(1 + 2/3 + 1/3 )/ (1 -2/3 + 1/3)

​=> 2 x 3 /2  =3

=> (1−α)(1+β)+(1−β)(1+α) / (1+α+β+αβ)

=> 3(2−2αβ)/2

​

=>3(1−αβ)

=>3(1− 1/3 )

=>2

Therefore , the solution of the given problem of function comes out to be 2.

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The solution for the given system of equations:

x = 6 and y = 6.

Kana is incorrect about the solutions of the given equations.

Algebraic expressions and equations follow the same set of rules as numerical expressions and equations. The order of operations is preserved, and the laws governing addition and multiplication still apply.

Associative: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c

Identity: a + 0 = a , a ⋅ 1 = a

Inverse: a + ( − a ) = 0 , a ⋅ 1 a = 1

Distributive: a ( b + c ) = a b + a c

Given equations,

4x-2y=12        -----(a)

2x+2y=24            -----(b)

Multiplying -2 to the equation (b) like kana solution

-2 (2x+2y=24 )

By Distributive property

-2(2x+2y) = -2(24)

- 4x - 4y = - 48     ---------(c)

Now adding equation (a) and equation(c)

    4x - 2y = 12

  - 4x - 4y = - 48

__+___+____+__

         - 6y  =  -36

⇒ y = 36/6 = 6.

Putting value of y in equation (b).

2(x) + 2(6) = 24

2x + 12 = 24

2x = 24 - 12

2x = 12

x =12/2 = 6

By the above calculation,

Value of x = 6 and

value of y = 6.

Hence, for the system of equations given

the solutions are:

x = 6 and y = 6

which proves that Kana is incorrect that there are no solutions.

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The cost of a one mile ride is given as follows:

$6.

The cost per mile is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

A taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:

m = 4, b = 2.

Thus the function that gives the cost for a x mile ride is:

y = 4x + 2.

The cost for a one mile ride is of:

y = 4(1) + 2 = $6.

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Answer:

R=17

Step-by-step explanation:

R=17

It says the whale has swam upwards and jumps to a heigh less then 17 and it says model the possible change in the number of feet, (R)

Thus R=17 Will Be correct

a. The table for the relation is given by the image shown at the end of the answer.

b. The domain and range of the relation are given as follows:

c. The relation is a function, as it value of the input is mapped to a single value of the output.

The ratio between the total cost and the number of vehicles is obtained as follows:

k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.

Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:

y = 0.75x.

For which:

The domain and range are given as follows:

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Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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The  polynomial has the zeros 1,-2i and 3 is =  x³ - 5x² + 11x -15.

A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, as well as division (No division operation by a variable).

A polynomial function is a function that only uses non-negative numeric powers or only positive integer exponents of something like a variable in an equation, such as the quadratic equation, cubic equation, etc. As an illustration, the polynomial 2x+5 has an exponent of 1.

given zeros are 1-2i and 3 .

The polynomial function  p(x) is

[x - (1+2i)] × [x - (1 - 2i)] × (x - 3)

[(x - 1) - 2i] × [(x - 1) + 2i] × (x - 3)

[(x - 1)² - (2i)² × (x - 3)]

∴ (x² - 2x + 1 + 4)(x - 3)

∴  (x² - 2x + 5)(x - 3)

The  polynomial has the zeros 1,-2i and 3 is =  x³ - 5x² + 11x -15.

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Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.

Based on the information you provided, the two-way table would look like this:

More than 4 people | 6 | 10

4 or fewer people | 4 | 30

It should be noted that the information you provided does not add up to 50 students.

Total for students living with grandparents: 10,

Total for students with more than 4 people: 6+10 =16.

Let me know if this table is incorrect and I'll provide you with more information

Step-by-step explanation:

The equation of the least squares regression line for the data set is (b) ŷ = -2.984x + 112.38

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

Volunteer 15 11 22 35 18 41 27 18

Trees 77 99 4 11 44 14 2 90

Using a graphing calculator, we have the following calculation summary

The regression equation is represented as

ŷ = bX + a

Where

b = SP/SSX = -2213.88/741.88 = -2.98416

a = MY - bMX = 42.63 - (-2.98*23.38) = 112.37978

So, we have

ŷ = -2.98416X + 112.37978

Approximate

ŷ = -2.984x + 112.38

Hence, the equation  is ŷ = -2.984x + 112.38

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Answer:

  See attached

Step-by-step explanation:

You want the solution to the inequality -12x < -48 shown on a number line.

The solution to the inequality is found by dividing by the x-coefficient

  -12x < -48

  x > 4 . . . . . . . divide by -12

When working with inequalities, you need to know that multiplying or dividing by a negative number reverses the inequality symbol.

The value x=4 is not included in the solution set, so an open circle is plotted at that point. All values of x greater than x=4 are included in the solution set, so the number line is shaded to the right of the open circle.

The graph of the solution is shown in the attachment.

__

Additional comment

Often, you can avoid multiplying or dividing an inequality by a negative number by rearranging it. Here, adding 12x+48 to both sides makes it be ...

  48 < 12x

Now, you can divide by 12 without worrying about the inequality symbol:

  4 < x . . . . . same as above

Proportion of cars which are yellow -

= 1 - (0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10)

= 1 - 0.96

= 0.04

Answer:

A) 0.04

Step-by-step explanation:

edge 2023

[tex]m-16[/tex] when m is 30

Substitute for m with given value:

[tex](30)-16[/tex]

[tex]=\fbox{14}[/tex]

Answer:

Step-by-step explanation:

a.we can get the equation is m-16 = 30-16=10+20-10-6=10-6+20-10=4+10=14

answer is 14

The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.

An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.

y=mx+c

Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.

[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]

[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]

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