PLEASE HELP!!
Solve for y 4y+5/3=y-10/2

The vertex form of the equation of the parabola is (y - 6) = - 2 · (x + 6).

Parabolae can be described by quadratic equations, whose forms are standard form and standard form. The vertex form of the equation of the parabola is shown below (please notice that parabolas are parallel to y-axis when its axis of symmetry is a vertical line):

y - k = C · (x - h)²

Where:

If we know h = - 6, k = 6 and (x, y) = (- 5, 4), then the vertex constant is:

C = (y - k) / (x - h)²

C = (4 - 6) / [- 5 - (- 6)]²

C = - 2 / 1²

C = - 2

The equation of the parabola in vertex form is (y - 6) = - 2 · (x + 6).

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Answer:

flagpole is sqrt(7h)

Step-by-step explanation:

We can use similar triangles to find the height of the flagpole.

Since Justin can see the top of the pole in the mirror, we can assume that the mirror and the ground form a right angle and the flagpole, mirror and Justin form a right triangle.

We can use the concept of similar triangles to find the height of the flagpole.

Let h be the height of the flagpole.

We can set up a proportion:

(7+h)/h = h/(7)

Cross-multiply and solve for h:

7h + h^2 = 7h

h^2 = 7*h - 7h

h^2 = 7h

h = sqrt(7h)

So the height of the flagpole is sqrt(7h)

It is worth noting that this answer is a square root of a variable and not a numerical value, thus we can't find an exact value of the height of the flagpole.

Answer:

Step-by-step explanation:

The f(9) means that the value of x would be 9 in any given equations or functions.

For example:

[tex]f(x) = 2x^{2} + 5\\f(9) = 2(9)^{2} + 5\\f(9) = 2(81) + 5\\f(9) = 162 + 5\\f(9) = 167[/tex]

On the other hand, f(x) = 9 means that the value of a certain function is simply equal to 9.

Answer:

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

Mark's weight is 75 pounds ad his sister's weight is w.

Together, he and his sister weigh 10 pounds more than two times the weight of his sister,

Set up equation:

Solve it for w:

The margin of error for this survey is 8% (0.08*100) rounded to the nearest tenth.

What is the margin of error?

The margin of error is a measure of the precision of a sample estimate. It is used to indicate the degree of uncertainty associated with a sample estimate.

The formula to calculate the margin of error at the 95% confidence level for a sample proportion is:

Margin of error = z* √(p*(1-p)/n)

Where:

z is the z-score for the 95% confidence level (1.96)

p is the sample proportion (36%)

n is the sample size (75)

So the margin of error for this survey would be:

Margin of error = 1.96 * √((0.36 * (1 - 0.36)) / 75)

Margin of error = 0.08

Hence, the margin of error for this survey is 8% (0.08*100) rounded to the nearest tenth.

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Answer:

Step-by-step explanation:

Q1)

A toffee costs $0.15 + $0.10 = $0.25

If you buy 15 candies, it will cost you 15* $0.15 = $2.25

If you buy 12 toffees, it will cost you 12* $0.25 = $3.00

So buying 15 candies is $3.00 - $2.25 = $0.75 cheaper than buying 12 toffees.

Q2)

The original price of two tennis rackets is $120 x 2 = $240

The original price of three cans of tennis balls is $15 x 3 = $45

So the original price of two tennis rackets and three cans of balls is $240 + $45 = $285

By buying two tennis rackets and three cans of balls at the sale price of $255, you save $285 - $255 = $30 off the original price.

Answer:

1

Step-by-step explanation:

(-1,2) and (2,6)

d=√[2-(-1)] ^+ [2-6]^

d=√3+(-4)^

d=√-1^

d=1

The required values are ∠B ≈ 59° and ∠C ≈ 31° for the given triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The triangle is given in the question, as shown

As per the tangent function,

tan ∠B = AC/AB

tan ∠B = 35/21

∠B = tan ⁻¹(35/21)

∠B = tan ⁻¹(1.667)

∠B ≈ 59°

tan ∠C = AB/AC

tan ∠C = 21/35

∠C = tan ⁻¹(21/35)

∠C = tan ⁻¹(0.6)

∠C ≈ 31°

Thus, the required values are ∠B ≈ 59° and ∠C ≈ 31°.

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Answer:

a)

i) To calculate the profit if 0 cakes are made per day, we can substitute x = 0 into the function:

P(x) = -x²+36x - 40

P(0) = -0² + 36(0) - 40 = -40 dollars

So, the profit from making 0 cakes per day is -40 dollars.

ii) To calculate the profit if 20 cakes are made per day, we can substitute x = 20 into the function:

P(x) = -x²+36x - 40

P(20) = -20² + 36(20) - 40 = 760 dollars

So, the profit from making 20 cakes per day is 760 dollars.

b) To find out how many cakes need to be made per day for the profit to be $270, we need to solve the equation P(x) = 270.

We can substitute the function P(x) into this equation:

-x²+36x - 40 = 270

Next we can solve this equation for x by using any method you prefer ( factoring, Quadratic formula, etc)

x = (36 +/- √(36² -4*(-40)(-1)))/ 2(-1)

x = (36 +/- √(1296 + 320))/ -2

x = (36 +/- √1616)/ -2

x = (36 +/- 40)/ -2

x = -2 +/- 20

x = 18 or -22

The number of cakes need to be made per day for the profit to be $270 is 18 or -22, but -22 is not a valid solution because the number of cakes must be a non-negative value, so the number of cakes need to be 18

The area of a triangle can be calculated if we know the lengths of all three sides of the triangle or the lengths of two sides and the measure of the included angle. In this case, we are given the lengths of two sides of the triangle (7 yards and 9 yards) and the measure of the included angle (49 degrees).

To find the length of the third side we can use the Law of Cosines. Which states that, in a triangle with sides a, b and c, and an angle C opposite to side c, c² = a² + b² - 2ab * cos(C).

In this case, a = 7, b = 9 and C = 49. So, we can calculate the value of c which is the length of the third side. Once we have this value, we can use Heron's formula, which states that the area of the triangle is equal to √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle (s = (a+b+c)/2).

By using these formulas we can calculate the area of the triangle which is approximately 25.38 square yards.

I hope this helps :)

The equation that models the scenario and number of years for the population to reach 656,000 will be option A.

i.e. y=100(3)^t and 8 years.

What are equations?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:

Linear equations

Quadratic equations

Cubic equations

Quartic equations

Differential equations

Parametric equations

Now,

The equation as the population is compounding annually for the scenario

will be y=P*(1+R)^t

Here p=Initial population

R=rate of increment/ decrement of population

t=time

Hence,

y=100*(1+2)^t                    (R=2 )

y=100*3^t

Time for which the population will be 656,000 will be

656000=100*3^t

6560=3^t

therefore,

t=8 years.

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Circle the equation that models the scenario and the number of years it takes for the population to reach 656,000 is y = 100(3)^x, 8 years.

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The expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In a right triangle, the hypotenuse (the longest side) is opposite the right angle, and the other two sides are called the legs. In this case, the hypotenuse is 2p + 8 and one of the legs (the base) is p - 5.

To find the third side (the other leg), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. In other words:

(hypotenuse)^2 = (leg 1)^2 + (leg 2)^2

Substituting the given values, we get:

(2p + 8)^2 = (p - 5)^2 + (leg 2)^2

Simplifying and solving for leg 2, we get:

leg 2 = sqrt((2p + 8)^2 - (p - 5)^2)

Now we can use the perimeter formula, which is the sum of the lengths of all the sides of the triangle. In this case, the perimeter of the triangle is:

perimeter = (leg 1) + (leg 2) + (hypotenuse)

Substituting the given values and the expression we found for leg 2, we get:

perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

Therefore, the expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

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The number of Cloud cupcakes that each person will be 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

I'm on a team of 9 people and we told our teacher that together we could eat 36 Cloud cupcakes.

The number of Cloud cupcakes that each person will be given as,

⇒ 36 / 9

⇒ 4

The number of Cloud cupcakes that each person will be 4.

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If there are 135 people in a sport centre. The number of people  that use exactly one of these facilities is 49.

Number of people that uses gym= 73- ( 32-14+ 36-14 + 14)

Number of people that uses gym = 73 - 54

Number of people that uses gym = 19

Number of people that use pool only = 73-(36-14+35-14+14)

Number of people that use pool only= 73-57

Number of people that use pool only = 16

Number of people that use track only = 67-(32-14+35-14+14)

Number of people that use track only = 67-53

Number of people that use track only = 14

Number of people  that use exactly one of these facilities =19+16+14

Number of people  that use exactly one of these facilities = 49

Therefore we can conclude that the number of people  that use exactly one of these facilities is 49.

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Answer:

[tex]\sqrt{6}[/tex]

Step-by-step explanation:

In a 45-45-90 triangle to find the two shorter sides (a and b) are represented as the number n in this case n is [tex]\sqrt{3\\[/tex] . The hypotenuse on the other hand is can be found by doing n[tex]\sqrt{2\\}[/tex] so you multiply [tex]\sqrt{3}(\sqrt{2} )[/tex] to get [tex]\sqrt{6}[/tex]

The solution is 9x - 36u + 27.

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We have given

-9(-×+4u-3)

When you multiply a negative number by another negative number, the result is positive.

So, to solve this problem, we can use the distributive property and simplify:

-9(-x + 4u - 3) = -9(-x) + -9(4u) + -9(-3)

= 9x - 36u + 27

Hence, the solution is 9x - 36u + 27.

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Answer: -2

Step-by-step explanation:

Given, aₙ = aₙ - ₁ - 3

so,

a₂ = a₁ - 3 = 7 - 3 = 4

a₃ = a₂ - 3 = 4 - 3 = 1

a₄ = 1 - 3 = -2

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The measure of ∠RQP is, 45°

The measure of ∠SPR is, 50°

The measure of ∠PSR is, 50°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

In trapezoid PQRS,

PQ is parallel to SR, and diagonal PR is drawn.

And, SP = SR, SRP = 50°, and PRQ = 85°

Here, SP = SR

So, We get;

In Δ PSR; ∠PRS = ∠SPR = 50°

And, PQ is parallel to SR.

Hence, We get;

⇒ ∠SRP = ∠RPQ = 50°

Now, In Δ PQR;

⇒ ∠PRQ + ∠QPR + ∠PQR = 180°

⇒ 85° + 50° + ∠PQR = 180°

⇒ 135° + ∠PQR = 180°

⇒ ∠PQR = 180° - 135°

⇒ ∠PQR = 45°

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The solution is

a) The diagram can represent the equation A = 10 ( 4 ) + 10 ( 10 ) = 140 and Andre's explanation is True

b) The diagram cannot represent 410 and Diego's explanation is False

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 equation be represented as A

Now , the value of A is

The number of small squares = 4 squares

The number of squares in the rectangle = 10 squares

So , the total number of squares = 10 + 4 = 14 squares

Now , the equation will be

a)

Andre's explanation says that diagram can represent 140

So , when A = 140

The total number of squares = 14

when one square = 10 ,

On simplifying the equation , we get

A = 10 ( 10 ) + 4 ( 10 )

The value of A = 100 + 40 = 140

So , each square can have a value of 10

And , Andre's explanation is True

b)

Diego's explanations says that diagram can represent 410

So , when A = 140

The total number of squares = 14

when one square = 10 ,

The value of A = 410 / 14

On simplifying the equation , we get

A = 29.28571..

So , each square cannot have an equal value

And , Diego's explanation is False

Hence , the equations are solved

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Answer:

-27

Step-by-step explanation:

3a - 4b
-3 - 4b
-3 - 24
-27

well, the subtotal cost will be 48.30 + 17.75 = 66.05, now let's add the tax to that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 66.05}}{\left( \cfrac{6}{100} \right)66.05} ~~ \approx ~~ 3.96~\hfill \underset{total~cost}{\stackrel{66.05~~ + ~~3.96}{\approx \text{\LARGE 70.01}}}[/tex]

The total cost of the purchase is $70.013.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Set of baseball cleats = $48.30

Baseball gloves = $17.75.

Sales tax = 6%.

This means,

6% of (48.30 + 17.75)

= 6/100 x 66.05

= $3.963

Now,

Total cost.

= 48.30 + 17.75 + 3.963

= $70.013

Thus,

The total cost is $70.013.

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The resulting stack of items :

[3,6,9,10,14,16,17].

It is a linear data structure that carries out the operations in a certain order.

Because we can only access the elements on the top of the stack, maintaining the reference to the top of the stack, which is the last element to be placed, is necessary to implement the stack.

Given:

Stack = [3,6,9,10,14,17].

Now we know in Stack elements are added or removed from the rear end of a stack or a queue.

So,

(1)  Add/push a new number : 10

Resulting stack :[3,6,9,10,14,17,10]

(2)  Add/push another number : 16

Resulting Stack :[3,6,9,10,14,17,10,16]

(3)  You remove/pop a number

Resulting stack : [3,6,9,10,14,16,17].

Therefore, resulting stack : [3,6,9,10,14,16,17].

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a) When Ozzie Foster deposits $2,000 at the end of each year,

amount in account after 25 years = $126571.43

b) If Ozzie had deposited the $2,000 at the beginning of each year,

amount in account after 25 years = $135431.43

An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees.

Given,

Value of each payment P = $2000

Rate of interest per period in decimal r = 7% = 0.07 per year

Number of years n = 25

a) future value of ordinary annuity

FV = P×((1+r)ⁿ−1) / r

FV = 2000×((1+0.07)²⁵−1) / 0.07

FV = 2000×((1.07)²⁵−1) / 0.07

FV = 2000×(5.43 - 1 )/ 0.07

FV = 2000×4.43/ 0.07

FV = 8860/0.07

FV = $126571.43

b) future value of annuity due

FV = (1+r)P×((1+r)ⁿ−1) / r

FV = (1+0.07) × $2000((1+0.07)²⁵ - 1)/0.07

FV = 1.07 × 2000×((1.07)²⁵−1) / 0.07

FV = 1.07 × 2000×(5.43 - 1 )/ 0.07

FV = 1.07 × 2000 × 4.43 / 0.07

FV = 2140 × 4.43 / 0.07

FV = 9480.2 / 0.07

FV = $135431.43

Hence,

a) $126571.43 is the amount in the account when Ozzie Foster deposits $2,000 at the end of each year.

b) $135431.43 is the amount in the account If Ozzie had deposited the $2,000 at the beginning of each year.

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Check the picture below.

so each row has a few gaps, but also has a few surplusses, so we can use the surplusses to fill up the gaps, and that will give us more or less 3 + 5 + 4 + 4 units, namekly 16 units.

Answer:

Step-by-step explanation:

²

a. 72² - 28² = (72 + 28)(72 - 28) = 100 × 44 = 4,400

b. 85² - 25² = (85 + 25)(85 - 25) = 110 × 60 = 6,600

Answer: Here it is

1) The range is {y | y ≥ 11.5}. This is true.

2) The domain is all real numbers. This is true.

3) The y-intercept is 4.5. This is False. The y-intercept is 7.

4) There is no X-intercept. This is true.

5) The rate of change is $4.5 per mug. This is true.

C(m) = 4.50m + 7 is a linear function, and the slope of a linear function represents the rate of change (or the unit rate of change) which is 4.5 dollars per mug. The y-intercept represents the cost when no mugs are ordered which is 7 dollars. As the domain is all real numbers this means that Marta can order any number of mugs. And as the range is {y | y ≥ 11.5} this means that the minimum cost for any order will be 11.5 dollars.

And as there is no X-intercept, this means that the function never crosses the x-axis, this means that the function can never have a y value of zero, which confirms that it doesn't have an X-intercept.

The solution of 2³ + 7 x 4 using PEDMAS is 36.

According to the PEMDAS rule, the computation wrapped in brackets or the parenthesis comes first in the order of operation. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and finally addition and subtraction.

Given:

2to the 3rd power +7 x 4

The mathematical expression is

= 2³ + 7 x 4

We know by PEDMAS rule is one of the rules which is exactly equal to BODMAS rule. The full form of PEMDAS is given below:

P – Parentheses  [{()}]

E – Exponents (Powers and Roots)

MD- Multiplication and Division (left to right) (× and ÷)

AS – Addition  and Subtraction (left to right) (+ and -)

According to the rule

2³ + 7 x 4

= 8 + 7 x 4

= 8 + 28

= 36

Hence, the answer is 36.

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The intercept, b of the line is 20

It is important to note that the general equation of a line is expressed as;

y = mx + c

Given that;

From the information, we have that;

Now, substitute the values to determine the intercept

50 = 5(6) + c

expand the bracket

50 = 30 + c

collect like terms

c = 50 - 30

c = 20

Hence, the value is 20

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Answer:

30 unit angles

Step-by-step explanation:

A unit angle is defined as an angle that measures 1 degree. To find the number of unit angles that the smaller angle 30° of a small pattern block goes through, we can divide the measure of the angle by the measure of a unit angle.

30° ÷ 1° = 30 unit angles

So, the smaller angle 30° of a small pattern block goes through 30 unit angles.

Answer:

B

Step-by-step explanation:

They put the decimal point in the wrong place.

Answer:

the answer is that 2.5 - 0.8 = 1.7