What is the value of the expression below?
−2
1
3
− 3
5
6
+ 1
1
3
?

Answer:

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

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]  ( cross- multiply )

2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

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

Step-by-step explanation:

SOHCAHTOA

CAH-

Cosine●= adj/hyp

cos30= y/8

0.8660=y/8

Cross multiply

0.8660×8=y

y=8×0.8660

y=6.928

By basic algebra, the part to be cut is equal to 17/45. When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions. Each fraction has two components.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Let x part is cut to shorten

then,

[tex]\frac{3}{2}-x=\frac{2}{9}\\\\x=\frac{3}{5} -\frac{2}{9} \\\\x=\frac{17}{45}[/tex]

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Answer:

The Sweet and Sour company

Step-by-step explanation:

Convert both types of lemonades into gallons and divide by the price.

For the loving lemon company you divide 24 by 4 and get a unit price of $6 per gallon

For the sweet and sour company change the 8 quarts into 2 gallons and divide 16 by 2, which gets you a unit price of $8 per gallon

The answer is A (x,y) -> (2x, 2y) it is representing the dilation.

Dilation is a medical procedure that involves widening a part of the body, such as the cervix or esophagus, by stretching and enlarging it. This can be done for a variety of reasons, including to allow for the passage of a baby during childbirth or to facilitate the insertion of a medical instrument or device. Dilation is usually done using dilators, which are cylindrical tools with a tapered end that can be inserted into the body and then gradually increased in size.

Dilation is a geometric transformation that enlarges or reduces the size of a shape by a factor. In this case, the shape is enlarged, with the resulting shape being twice the size of the original black figure. This is represented by the equation A (x,y) -> (2x, 2y), where the x and y coordinates of each point in the figure are multiplied by two.

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Answer:

0.23 is the answer

I wish you luck in your assignments.

2) {(-5,2), (5,2), (0, -3), (3,-8)} is a function.

3) {(-2, 7), (6, 2), (-2,-3), (0, 9)} is not a function.

4) {(7,2), (4,-6), (2,-2), (4, -9)} is not a function.

5) {(2, 3), (2, 4), (2, 5), (2,6)} is not a function.

6) {(1,-4), (2,-4), (3,-4), (4-4)} is a many to one function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one and many-to-one.

But a function can not be one to many means the same value of x can not lead to different values of y.

2) {(- 5, 2), (5, 2), (0, -3), (3,- 8)} is a fuction as different values of x leads to different values of y.

3) {(-2, 7), (6, 2), (-2,-3), (0, 9)} is not a function as the input - 2 leads to two different outputs 7 and - 3.

4) {(7, 2), (4, -6), (2, -2), (4, -9)} is also not a function as input 4 leads to two different outputs - 6 and - 9.

5) {(2, 3), (2, 4), (2, 5), (2,6)} is not a function as input 2 leads to different outputs.

6) {(1, - 4), (2, - 4), (3, - 4), (4, - 4)} is a function and it is a many-one function.

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The design of a simulation that would allow Ian to determine how likely it would

be to guess all answers correctly on this quiz can be Illustrated through a coin.

Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.

He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.

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The right triangles are congruent by HL theorem.

The triangles having congruent corresponding parts are called congruent triangles.

Given are two right triangles, with equal hypotenuse and one of the bases.

The question is by which theorem do they are congruent,

HL theorem :-

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.

Here, both the right triangles are following the condition of the HL theorem.

Hence, the correct option is HL.

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The number of months Mark can have the phone is given by the equation

A = 11.4 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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Step-by-step explanation:

c = 12m - 17

m = 2

c = 12×2 - 17 = 24 - 17 = 7

m = 4

c = 12×4 - 17 = 48 - 17 = 31

m = 8

c = 12×8 - 17 = 96 - 17 = 79

Mr.West ate 23 ounces of grapes in 11 days by eating 2 1/11 ounces of grapes each day.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day.

Therefore, The total number of grapes Mr.West ate is,

= 11×(2 1/11) grapes.

= 11×(23/11) grapes.

= 23 grapes.
So, He ate 23 ounces of grapes in 11 days.

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Answer:

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

4 1/2% of 50 is 4.5% of 50 which is same as:

or substituting % with 1/100,

The matching choices are A and B.

The statement five less than four times a number is greater than or equal

to 3 indeed has a solution results to 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement five less than four times a number is greater than or equal to 3.

Let, The unknown number be 'n'.

Therefore, The numerical form of the statement is,

4n - 5 ≥ 3.

4n ≥ 8.

n ≥ 2.

So, Yes 2 is a solution.

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Answer:2024

Step-by-step explanation: 44x46

On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

here,

(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)

=|  -cos(t)+2cosec(t) |

= -cos(t)+2cosec(t)

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The image for P(9, 1.5) after Translation is P'( 12, 1).

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

P(9, 1.5) with Translating Vector (3, -0.5).

So, Applying the Translation we get

P(9 + 3, 1.5 + (-0.5))

= P(12 , 1.5- 0.5)

= P(12, 1)

hence, the image is P'( 12, 1).

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The complete statement is f(2) = 8+5√7

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=2x²+5√7

Thus f(1) = 2×4+5√7

              = 8+5√7

Hence, The complete statement is f(2) = 8+5√7

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Answer: A. Quadrilateral

Step-by-step explanation:

The name for a polygon with 4 sides is a quadrilateral. Quadrilateral is a two-dimensional shape with four straight sides and four angles. The most common type of quadrilateral is the rectangle, which has four right angles. Other types of quadrilaterals include squares, parallelograms, trapezoids, and rhombuses.

Answer:

quadrilateral!!

Step-by-step explanation:

look at the beginning of the word, quad. Quad means 4 and is referring to a 4 sided figure.

Step-by-step explanation:

try this option:

[tex]a) \ log_{15}5+log_{15}3=log_{15}15;\\b) \ log_{1/2}log_{49}7=log_77;\\c) \ log_44=log_22.[/tex]

Answer:

4

Step-by-step explanation:

The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.

Hope this helps! :)

Answer:

Shop B

Step-by-step explanation:

First, find the number of scarves that Shop A sold: 15% of 120 scarves is 15/100 * 120 scarves = 18 scarves.

Then, find the number of scarves that Shop B sold: an eighth of 152 scarves is 152/8 = 152/8 = 19 scarves.

Since 18 scarves is less than 19 scarves, Shop B sold more scarves.

Answer:

To calculate XYZ Company's total assets minus liabilities, you would need to add up all of the assets listed on the balance sheet and then subtract the sum of all the liabilities.

In this case, the total assets would be $45,000 + $41,000 + $134,000 = $220,000. The total liabilities would be $55,000 + $56,000 + $50,000 = $161,000.

So, the total assets minus liabilities would be $220,000 - $161,000 = $59,000.

Step-by-step explanation:

The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]

The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]

We know that any number raised to the power of 0 is 1.

Therefore,[tex]a^0 = 1[/tex].

Also, any number raised to the power of -1 is its reciprocal.

Therefore, [tex]b^-4 = 1/b^4[/tex]

Simplifying the above expression we get

[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]

Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]

So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]

Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]

Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]

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Answer:

[tex]\boxed{\boxed{\sf x=1}}[/tex]

Step-by-step explanation:

[tex]\sf 25x^2=-25+50x[/tex]

Simplify both sides of the equation:-

[tex]\sf 25x^2-50x=-25[/tex]

Subtract 50x-25 from both sides:-

[tex]\sf 25x^2-(50x-25)=50x-25-(50x-25)[/tex]

[tex]\sf 25x^2-50x+25=0[/tex]

Factor left side of equation:-

[tex]\sf 25(x-1)(x-1)=0[/tex]

Set factors equal to 0:-

[tex]\sf x-1=0\: or\: x-1=0[/tex]

[tex]\sf x=1[/tex]

___________________

Hope this helps!

Have a great day!

Answer:

−1 < y < 3

Step-by-step explanation:

The area of the hot tub is 6079.04 in²

To determine the approximate area required for the installation of the hot tub. You can use the area of  a circle.

The area of  a circle is given by A = πr²

where r is the radius of the circle

Since the hot tub to have a diameter of 88 inches, the radius will be  88/2 = 44 inches. π = 3.14.

Thus, area of  the hot tub will be:

Area of hot tub = 3.14 × 44² = 6079.04 in²

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Answer:

congruent

Step-by-step explanation:

The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;

g(x) ≥ x

when x = 30, we have;

g(30) ≥ 20

Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.

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Complete Question:

Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.

What does g(30) ≥ 20 tell you?

It took at least 20 minutes for Mona to find 30 seashells.

Mona found at least 20 seashells in the first 30 minutes.

It took at least 30 minutes for Mona to find 20 seashells.

Mona found no more than 20 seashells in the first 30 minutes.

Answer:

10x10x10 or 10*3......

Answer:

(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!

Step-by-step explanation:

Given the system of equation, [tex]\left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.[/tex], solve by elimination.

[tex]\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.[/tex] , multiply the top equation by -2.

We get,  [tex]\left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex]

[tex]+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex], add the equations together.

We get, [tex]-15y=75[/tex], we just eliminated the variable, x, we can now solve this equation for y.

[tex]-15y=-75 = > y=\frac{-75}{-15}[/tex], [tex]y=\frac{75}{15} = > y=5[/tex]

We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...

[tex]x+6y=28 = > x+6(5)=28 = > x+30=28[/tex], subtract the value, 30, from both sides. We get, [tex]x=-2[/tex].

We found the value x, x=-2.

Thus the solution to the given system of equations is (-2,5).

Answer:

(-2, 5)

Step-by-step explanation:

Given linear system of equations:

[tex]\begin{cases}x+6y=28\\2x-3y=-19\end{cases}[/tex]

To solve by the method of elimination, first multiply the first equation by -2:

[tex]\implies -2 (x+6y=28)[/tex]

[tex]\implies -2x-12y=-56[/tex]

Add this to the second equation to eliminate the term in x:

[tex]\begin{array}{lrcrcr}& 2x & - & 3y & = & -19\\+\vphantom{\dfrac12}&(-2x & - & 12y & = & -56\\\cline{2-6}&\vphantom{\dfrac12}&- & 15y & = &-75\end{array}[/tex]

Solve the expression for y:

[tex]\implies -15y=-75[/tex]

[tex]\implies y=5[/tex]

Substitute the found value of y into the expression for x and solve for x:

[tex]\implies x=28-6(5)[/tex]

[tex]\implies x=28-30[/tex]

[tex]\implies x=-2[/tex]

Check by substituting the found values of x and y into both equations.

Equation 1

[tex]\implies -2+6(5)=-2+30=28[/tex]

Equation 2

[tex]\implies 2(-2)-3(5)=-4-15=-19[/tex]

Hence proving that the solution (-2, 5) is true.