(X+6)+(7x+4)+(2x)=180

Answer:

6 drinks

2 boxes of candy

==================================================

Explanation:

x = number of drinks

y = number of boxes of candy

These two variables represent positive integers.

"He bought 3 times as many drinks as candies" which means we can set up the equation x = 3y

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

1 drink costs $4.50

x drinks cost 4.50x dollars

1 box of candy costs $3

y boxes of candy cost 3y dollars.

4.50x + 3y = total cost = 33 dollars

Therefore, we arrive at the second equation of 4.50x+3y = 33

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

We have this system of equations

[tex]\begin{cases}x = 3y\\4.50x+3y = 33\end{cases}[/tex]

I'll use substitution to solve. Replace x with 3y in the second equation, then isolate y.

[tex]4.50x+3y = 33\\\\4.50(3y)+3y = 33\\\\13.50y+3y = 33\\\\16.50y = 33\\\\y = 33/16.50\\\\y = 2\\\\[/tex]

This tells us he bought 2 boxes of candy.

Use that value to find x.

[tex]x = 3y\\\\x = 3*2\\\\x = 6\\\\[/tex]

Carter also bought 6 drinks.

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

Check:

The answers are confirmed.

Another way to confirm the answers is to plug (x,y) = (6,2) into each equation of the system I mentioned earlier. After simplifying, you should get the same thing on both sides.

A visual way to confirm the answers is to graph each equation on the same xy grid. The two lines intersect at (6,2). You can use a graphing tool such as Desmos or GeoGebra.

To find the value of K, we need to find the point at which the line Y=2x+K is tangent to the parabola Y=x^2-4x+4. This means that the line and the parabola will have the same y-value at this point, and the line will be tangent to the parabola (meaning it will just touch the parabola at this point, without intersecting it).

To find the point at which the line and parabola are tangent, we can set Y=2x+K equal to Y=x^2-4x+4 and solve for x:

2x + K = x^2 - 4x + 4

x^2 - 4x + 4 - 2x - K = 0

(x-2)^2 = K

x = 2 +/- sqrt(K)

Since the line is tangent to the parabola, it will just touch the parabola at this point, which means that the parabola will have a minimum value at this point. This means that the value of K must be nonnegative, because the square root of a negative number is not a real number. Therefore, K must be equal to or greater than 0.

So, the value of K for which Y=2x+K is tangent to Y=x^2-4x+4 is K >= 0.

Answer:

132

Step-by-step explanation: Supplementary=180 So all you have to do is subtract 48 from 180 and should give you 132.

Hope that helps!

Answer:

see explanation

Step-by-step explanation:

vertical angles are congruent , then

2x - 3 = x + 16 ( subtract x from both sides )

x - 3 = 16 ( add 3 to both sides )

x = 19

Then

x + 16 = 19 + 16 = 35°

since the angles are congruent , then

the measure of each angle is 35°

Answer:

x=

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

Step-by-step explanation:

because tan30⁰=

[tex] \frac{ \sqrt{3} }{3 } \\ \[/tex]

3/x=root 3 over3

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

If a rubber ball is dropped from a height of 10 feet, The height of the 5th bounce and the population in 12 years

Generally, For the first problem, the height of the 5th bounce can be calculated by plugging in 5 for x in the function

f(x) = 20 (0.6)^x:

f(5) = 20 (0.6)^5

= 20 (0.12)

= 2.4 feet

For the second problem, the population in 12 years can be calculated by plugging in 12 for x in the function f(x) = 1000 (1.04)^x:

f(12) = 1000 (1.04)^12

= 1000 (1.70)

= 1700 pigs

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Answer:

0.7

Step-by-step explanation:

The equation is equivalent to the r = d/t.

There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

We have to find which equation is equivalent to the formula d = rt.

Formula given: d = rt

Divide both sides by t

d/t = rt / t

d/t = r

Thus, the equation is equivalent to the r = d/t.

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Lines a, b, and c are parallel, and d and e are also parallel to each other.

No matter how far they may reach in either direction, parallel lines are ones that are equidistant from one another and never cross. Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines.

Given the 5 lines and the angles made by them,

if ∠1 = ∠3 then a║b Because they intersect on the same line.

if ∠4 = ∠6 then c║b Because they intersect on the same line.

if ∠1 = ∠7, ∠2 = ∠8,  ∠23 = ∠5, ∠11 = ∠17, ∠2 = ∠8, ∠24 = ∠18, ∠6 = ∠12, and some more than d║e Because they intersect on the same line.

Therefore from the above figure, if two lines intersect another line with the same angle then they are parallel lines.

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Answer:

3,112,136

Step-by-step explanation:

x=2

replace x with 2

2+2=4

150-4= 146

146 to the third power is 146 x 146 x 146

146 x 146 x 146 = 3112136

hope this helps, tell me if i'm wrong

The given expression is simplified as -4/7. So, the correct option is D.

To simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Given that, (8-(4)(3))/(∛8 +5).

The given expression can be simplified as follows

Numerator of fraction simplified as 8-(4)(3)

= 8-12

= -4

Numerator of fraction simplified as (∛8 +5)

We know that, cube root of 8 (∛8) is 2

=(2 +5)

= 7

Thus, the fraction is -4/7

So, the expression (8-(4)(3))/(∛8 +5) is reduced to -4/7.

The simplified form of expression is -4/7. Therefore, option D is the correct answer.

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In linear equation,3 whole pizzas should they order .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

total people = 4

Each person always eats 3/4 of a cheese pizza.

   3/4 + 3/4 + 3/4 + 3/4  

= 3 + 3 + 3 + 3 /4

= 12/4

= 3

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Answer:

m = 2/5

:)))))))))))))))))))))))))))

Therefore the solution to the given question equation will shift the graph of the original equation up 2 units in  y=2x + 9

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Here,

It follows a linear function. y=mx + b

If A is the location where the y-axis intersects, then x = 0 and y = b are the coordinates of A.

In order to move the graph up by 2 units, you must add 2 units to b.

In our case, b was originally equal to 7, so shifting it up makes b become 7+2=9, and the new function is y=2x + 9.

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Step-by-step explanation:

Formula 1: V = lwh

V = 10 x 8 x 6

V = 480

Formula 2: V = 2lw + 2lh + 2wh

V = 2(10 x 8) + 2(10 x 6) + 2(8 x 6)

V = 480

Answer:

its c

Step-by-step explanation:

It will take the sales of 381 necklaces to reach break-even.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that Tony invest an initial amount of $381 for advertising, and materials cost $8 for each necklace he makes. Tony can sell his creations for $9 per necklace.

Let the number of necklace be x then;

8x + 381 = 9x

Solving;

9x - 8x = 381

x = 381

Therefore, Total expenses = 8x + 381

8(381) + 381

= 3429

Thus, Total sale = 9x = 3429

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The direct distance from your house to school as calculated from the given data is 0.9434 miles.

Let

the distance walked North = A = 0.8 miles

the distance walked East= B = 0.5 miles

the direct distance between house and school be C

On using pythagoras theorem,

C² = A² + B²

   = 0.8 ²+ 0.5 ²

   = 0.89

C =0.9434 miles

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem.

According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c , C² = A² + B².

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Answer:

Each egg costs $0.60

Each piece of toast costs $0.30

Step-by-step explanation:

Let's assume that the cost of a single egg is E

And the price of a toast as T

Kendra charges $1.50 for one toast and two eggs

The equation above will be

2E + T = $1.50

And the other equation is

E + T = $0.90

For the second equation, we make E the subject of the formula

E = 0.90 - T

Now substitute for this in equation 1

2E + T = 1.50

It will now be 2(0.90 - T) + T = 1.50

1.80 - 2T + T = 1.50

T= $0.30

price of one toast is $0.30

And now, for the price of an egg, we substitute T = 0.30 in the equation

E= $0.60

The function's range is in the interval (1, ∞).

Members of a set can congregate in mathematics.

These sets' constituents are referred to as elements. The correspondence between the two groups is known as a relation when the elements of each group are paired up together.

So, between two sets, a relation is a collection of ordered pairs of elements.

The term "function" refers to a particular type of relation where each element in the first group, referred to as the domain, corresponds to exactly one element in the second group, referred to as the range.

The elements in the domain couple with exactly one element in the range, and this is how a function is a pairing between two sets.

According to our question-

[7, ] is the interval notation.

The function's range falls between the numbers (1, ).

provided function

Determine the function's domain:

You do not want to use a counterargument to the square root in this situation (you cannot find the solution of a negative square root, at least as a real number).

What you actually do is "impose" that the argument always ends in a yes or a no (you know the square root of a positive number or zero).

You then solve for x to determine the variable's ALLOWED values by setting the argument greater than or equal to zero:

Consequently, the function is in the domain.

Find the function's range:

The set of all y values in the function's range is when,

range of the function is in the interval  (1, ∞).

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Answer: first 7,1 second 7, -1

Step-by-step explanation: edge 2023

The values of given functions are Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119.

Trigonometric equation is a condition including at least one trigonometric ratios of obscure points. It is communicated as proportions of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) points. For instance, cos2 x + 5 sin x = 0 is a mathematical condition.

We have,

Cosx = 12/13

Use sin^2(x) + Cos^2(x) = 1

sinx = [tex]\sqrt{1-cos^{2}x}[/tex] = 5/13

We know that

Sin2x = 2sinxcosx

Sin2x = 2(5/13)(12/13)

Sin2x = 120/169

Using cos2x = 2cos^2x - 1

cos2x = 2(12/13)^2 - 1

Cos2x = 119/169

Then, using tanx = sinx/cosx

tan2x = sin2x/cos2x

tan2x = [tex]\frac{\frac{120}{169} }{\frac{119}{169} }[/tex] = 120/119

Thus, required values Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119

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Required solution is

[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]

What is trigonometric ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

[tex]cos2x=cos^2x-sin^2x[/tex]

[tex]sin2x=2sinxcosx\\\\tan2x=(2tanx)/(1-tan2x)[/tex]

..

[tex]sinx= -\frac{12}{13}[/tex]

you are working with a (5-12-13) reference right triangle in quadrant IV where sin<0,cos>0,tan<0

[tex]sinx=-\frac{12}{13} (given)\\\\\cosx=\frac{5}{13} \\\\tanx=-\frac{12}{5}[/tex]

..

[tex]cos2x=cos^2x-sin^2x=\frac{25}{169-144} \times \frac{1}{69} =-\frac{119}{169} \\\\\\sin2x=2sinxcosx=2\times(-\frac{12}{13}) \times (\frac{5}{13} )=-\frac{120}{169} \\\\\\tan2x=\frac{2tanx}{1-tan^{2}x } \\\\\\=2(-12/5)/(1-(144/25))=(-24/5)/(-119/25)=(-24/5)(25/119)=\frac{120}{119}[/tex]

required solution is

[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]

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Because the value of x is 126° and the value of cos 2x is -0.301, which is fractionally identical to -7/25, the value of cos 2x will be -7/25.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.

Here,

sin x=4/5

x=126°

Cos 126°=-0.588

cos (2*126)=-0.310

The value of cos 2x will be -7/25 because value of x is 126° and that of cos 2x is -0.301 that is fractionally equal to -7/25.

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Answer:

B

Step-by-step explanation:

on edge

Increasing the given sample size will decreases the probability because σx will decreases as n value increases.

In Statistitics whenever we test a hypothesis for testing a statistic, we use confidence interval. Confidence interval is on either side of an assumed value a margin of error. Margin of error is calculated as critical value * sigma/sqrt of n. Thus we find that whenever n increases, margin of error decreases.

Thus making confidence interval narrower and thus making probability for accepting null hypothesis a less value. As the pattern sizes increase, the range of every sampling distribution decreases so they emerge as more and more leptokurtic. The variety of the sampling distribution is smaller than the variety of the authentic populace. Therefore, as a pattern length increases, the pattern imply and general deviation might be nearer in fee to the populace imply μ and general deviation σ.

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Answer: False

Step-by-step explanation:

The statement you are giving is for the Geometric Sequence, not the arithmetic sequence. So this is false!

Answer:117.7

Step-by-step explanation: m is 13/40, I converted that to decimal form which was .325. I then multiplied 362 by .325 to get 117.65, then rounded to the nearest tenth

Answer:

2,570,869,636 more tickets

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

: in this context, the y-intercept represents the volume of water already in the tank

Answer: 3150 is the answer

Step-by-step explanation:

Answer:

155 feet

Step-by-step explanation:

the building is 85 feet high that's where drone starts

the drone flies to 120 feet in 10 seconds from 85 feet so the rate equals 35 feet per 10 second

in 20 seconds the drone would be 70 feet higher.

so the final height would be 85 feet plus 70 feet which equals 155 feet.

hope that helps