What is the quadratic function of 5 and 7?

Answer:

-8

Step-by-step explanation:

The length of the lighthouse shadow is:      61.2 ft

______________________________________

To find the length of the lighthouse shadow given similar triangles, solve a proportion with corresponding sides.

Let's follow these steps:

In the diagram, LH is the lighthouse. TY is Tommy. HE is the lighthouse shadow. YE is Tommy's shadow. Notice that the green triangle, ΔTYE, fits onto the larger triangle, ΔLHE.

Using AA similarity, we know that the two triangles in the diagram are similar. To say the triangles are similar, write:      ΔLHE ~ ΔTYE

Similar triangles have proportionate sides. This means that the length of corresponding sides will be longer or shorter by the same multiplication factor, which we can write as K.

Our pairs of corresponding sides are:

Corresponding sides are related to each other by the multiplication factor, K:

This makes any pair of corresponding sides written as a fraction equal to each other. Thus, we can write a proportion using these pairs.

We should choose two pairs of corresponding sides to write a proportion from:

[tex]\displaystyle { \frac{LH}{TY} = \frac{HE}{YE} }[/tex]

Note that this works because:    [tex]\displaystyle { K = \frac{LH}{TY} = \frac{HE}{YE} }[/tex]  

[tex]\displaystyle { \frac{LH}{TY} = \frac{HE}{YE} }[/tex]                   Write the proportion.

[tex]\displaystyle { \frac{170}{5} = \frac{HE}{1.8} }[/tex]                   Substitute known lengths.

[tex]\displaystyle { 34= \frac{HE}{1.8} }[/tex]                     Simplify. Now, isolate HE.

[tex]\displaystyle { 34*1.8 = \frac{HE}{1.8}*1.8}[/tex]    Multiply both sides by 1.8.

[tex]\displaystyle { 34*1.8= HE}[/tex]             1.8 cancels out on the right side.

[tex]\displaystyle { HE = 34*1.8}[/tex]             Keep the missing variable on the left side.

[tex]HE = 61.2[/tex]                  Solved for HE.

Remember to write the final answer with units.

Therefore, the lighthouse shadow is 61.2 ft long.

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Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation

- 3 = [tex]\frac{1}{3}[/tex] (- 9) + c = - 3 + c ( add 3 to both sides )

0 = c

y = [tex]\frac{1}{3}[/tex] x + 0 , that is

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

It will take approximately 4.3 years for the account value to reach $36,700 with an 8.75% annual interest rate.

1. Calculate the interest rate per period (year):

8.75%

= 0.0875

2. Calculate the number of periods (years) required to reach the desired total:

(36700-3500)/3500

= 10.2857

3. Calculate the final number of years to the nearest tenth of a year: 10.2857/0.0875

= 117.1429 or 4.3 years

To calculate the time it will take for the account value to reach $36,700, we need to first calculate the interest rate per period. In this case, the interest rate is 8.75% per year. This can be converted to a decimal by dividing 8.75 by 100 to get 0.0875. Next, we need to calculate the number of periods (years) required to reach the desired total. To do this, we subtract the initial account value of $3,500 from the desired account value of $36,700 and then divide this difference by the initial account value of $3,500. This gives us 10.2857. Finally, we need to calculate the final number of years to the nearest tenth of a year, which can be done by dividing 10.2857 by 0.0875. This gives us a result of 117.1429, which is equivalent to 4.3 years.

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The 95% confidence interval for the population standard deviation of the number of rooms rented would be (4.82, 7.90).

1. Calculate sample standard deviation: 5.86 rooms

2. Calculate the degrees of freedom: 26

3. Calculate the t-critical value using the t-distribution table with a 95% confidence level and 26 degrees of freedom: 2.056

4. Calculate the margin of error: t-critical value x sample standard deviation/square root of sample size: 2.056 x 5.86/√27 = 1.08

5. Calculate the confidence interval: sample standard deviation +/- margin of error: 5.86 +/- 1.08 = (4.82, 7.90)

The 95% confidence interval for the population standard deviation of the number of rooms rented would be (4.82, 7.90).

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The solutions to the systems of linear equations by elimination method are listed below:

In this problem we find four cases of two linear equations with two variables. There are different methods to solve the system, herein we must use elimination method to find the solution to each system of linear equations, which takes advantage of adding / subtracting linear equations and multiplying linear equations by scalars in order to get every solution set.

Case 1

x - y = 1

x + y = 3

First, add the two equations:

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

2 · x = 4

x = 2

Second, determine the variable y:

y = 3 - x

y = 3 - 2

y = 1

Point (x, y) = (2, 1) is a solution of the system of equations.

Case 2

x + y = 1

x + y = 11

Subtract the second equation from the first one:

(x + y) - (x + y) = 1 - 11

0 = - 10 (CRASH!)

The system of linear equations has no solution.

Case 3

x + 4 · y = 11

x - 6 · y = 11

First, subtract the second equation from the first equation:

(x + 4 · y) - (x - 6 · y) = 11 - 11

10 · y = 0

y = 0

Second, determine the variable y:

x = 11 + 6 · y

x = 11 + 6 · 0

x = 11 + 0

x = 11

Point (x, y) = (0, 11) is a solution of the system of equations.

Case 4

- 3 · x + 3 · y = 6

x + 3 · y = 18

First, subtract the second equation from the first equation:

(- 3 · x + 3 · y) - (x + 3 · y) = 6 - 18

- 4 · x = - 12

x = 3

Second, determine the variable y:

3 · y = 18 - x

3 · y = 18 - 3

3 · y = 15

y = 5

Point (x, y) = (3, 5) is a solution of the system of equations.

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Answer:

See below for proof.

Step-by-step explanation:

Given:

[tex]\log_ab \times \log_ba=1[/tex]

To prove the given equation, begin by changing the base of the two logs so that they have the same base.

[tex]\boxed{\textsf{Change of base}: \quad \log_pr=\dfrac{\log_xr}{\log_xp}}[/tex]

Change the base of both logs to x by using the change of base formula:

[tex]\implies \log_ab=\dfrac{\log_xb}{\log_xa}[/tex]

[tex]\implies \log_ba=\dfrac{\log_xa}{\log_xb}[/tex]

Substitute into the equation:

[tex]\implies \log_ab \times \log_ba=\dfrac{\log_xb}{\log_xa} \times \dfrac{\log_xa}{\log_xb}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times \dfrac{b}{d}=\dfrac{a \times b}{c \times d}:[/tex]

[tex]\implies \dfrac{\log_xb \times \log_xa}{\log_xa \times \log_xb}[/tex]

Apply the commutative property of multiplication to the numerator:

[tex]\implies \dfrac{\log_xa \times \log_xb}{\log_xa \times \log_xb}[/tex]

Cancel the common factor logₓb:

[tex]\implies \dfrac{\log_xa}{\log_xa}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{n}{n}=1:[/tex]

[tex]\implies \dfrac{\log_xa}{\log_xa}=1[/tex]

Hence proving that:

In one calculation:

[tex]\begin{aligned}\implies \log_ab \times \log_ba & =\dfrac{\log_xb}{\log_xa} \times \dfrac{\log_xa}{\log_xb}\\\\&=\dfrac{\log_xb \times \log_xa}{\log_xa \times \log_xb}\\\\&=\dfrac{\log_xa \times \log_xb}{\log_xa \times \log_xb}\\\\&=\dfrac{\log_xa}{\log_xa}\\\\&=1\end{aligned}[/tex]

Every quadrilateral has 4 vertices, 4 angles, and 4 sides.

A quadrilateral is a 4-sided plane figure. Below are some important properties of quadrilaterals :

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The graph of the given polynomial function representing a baseball card is shown.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,
Graph of  the polynomial function of f(x) = x³-13x² + 40x + 15, is shown,
From the graph,

a.
The card's starting value is 15.

b.
It reaches it maximum value when x is 2 and 9, the value at that point is 51.

c. It reaches it minimum value when x is 6.67, the value at that point is 0.

d.
As shown in the graph at the end worth of the card is 51.

Thus, the graph of the given polynomial function representing a baseball card is shown.

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Answer:

George is 149 centimeters

Step-by-step explanation:

We need to change meters to centimeters

1.58 meters * 100 cm/meters

158 cm

158 cm - 9 cm = 149 cm

George is 149 centimeters

Answer:

8x+11

Step-by-step explanation:

3(2x+1)+2(x+4)

distribute

3(2x)+3(1)+2(x)+2(4)

6x+3+2x+8

combine like terms

6x+2x+3+8

8x+11

this can't be simplified anymore

hopes this helps

Answer:

[tex] \sf \: 8x + 11 [/tex]

Step-by-step explanation:

Given expression,

→ 3(2x + 1) + 2(x + 4)

Let's simplify the expression,

→ 3(2x + 1) + 2(x + 4)

→ 6x + 3 + 2x + 8

→ (6x + 2x) + (3 + 8)

→ (8x) + (11)

→ 8x + 11

Hence, the answer is 8x + 11.

The transformation that maps triangle ABC to A'B'C' is given by :

1. Reflection across is given by option c. y = x line.

2. Translation of triangle ABC is done by option D. 10 units to the right and 4 units to the up.

Figure is attached.

As given in the question,

Transformation of the triangle ABC maps to the triangle A'B'C' is given by:

Coordinate of point C is ( -4 , 2 ) after reflection across the line y = x coordinate changes to ( 2, -4 ).

Therefore, the reflection and translation of the triangle ABC to A'B'C' after transformation is given by :

1. reflection across option C. line y = x.

2. Translation option D. 10 units to the right and 4 units to the up.

The above question is incomplete, the complete question is :

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the (1.)_____ followed by a translation (2.)_____ .

Answers for (1.)

* y-axis

* x-axis

* Line y = x

* Line y = -x

Answers for (2.)

* 4 units to the right and 10 units up

* 8 units to the right and 4 units up

* 10 unit to the right and 2 units up

* 10 units to the right and 4 unit s up

Required Figure is attached.

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Answer:

40

Step-by-step explanation:

Using the alternate exterior angles theorem,

[tex]4x-30=3x+10 \\ \\ x-30=10 \\ \\ x=40[/tex]

Answer:

So in the first case we buy the candy which costs 1 and take candies worth 3 and 4 for free, also you buy candy worth 2 as well. So min cost = 1 + 2 = 3. In the second case we buy the candy which costs 4 and take candies worth 1 and 2 for free, also We buy candy worth 3 as well. So max cost = 3 + 4 = 7.

Step-by-step explanation:

The x-variable is not referred to as the dependent variable when formulating a regression equation.

There are dependent and independent variables in statistical modeling, experimental sciences, and mathematical modeling. Dependent variables are so-called because, during an experiment, their values are assessed under the presumption or requirement that they are dependent on the values of other variables as a result of a certain law or rule (for example, a mathematical function). Independent variables are ones that are not seen as being reliant on any other variables in the context of the experiment in question.

Common independent variables that can be used to forecast include time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (such the size of the human population).

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The inequalities' solutions are -6x + 15 10 - 5x, and at 5 there is an open circle. A bold line begins at 5 and points to the right.

An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.

Given the inequality expression below:

–3(2x – 5) < 5(2 – x)

Expand to have:

-6x + 15 < 10- 5x

-6x + 5x < 10 - 15

-x <-5

x > 5

Hence the solutions to the inequalities are –6x + 15 < 10 – 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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The height of the flagpole with a shadow cast of 85 feet is 51 feet.

Given the data in the question;

To find the height of the flagpole, we can use the ratio of the flagpole's shadow length to Idris's shadow length, which is equal to the ratio of the flagpole's height to Idris's height.

Hence;

85 feet : 10 feet = flagpole's height : 6 feet

Solve for the flagpole's height by cross-multiplying and simplifying:

Flag pole height × 10 = 85 × 6

Flag pole height × 10 = 510

Flag pole height = 510 / 10

Flag pole height = 51 feet

Therefore, the height of the flagpole is 51 feet.

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The percent​ increase is 25%.

To calculate the percent increase from an original quantity to a new quantity, we can use the following formula:

percent increase = [(new quantity - original quantity) / original quantity] * 100

In this case, the original quantity is 12 and the new quantity is 15, so the percent increase would be:

percent increase = (15 - 12) / 12 * 100 = 3 / 12 * 100 = 25%.

This means that the new quantity is 25% larger than the original quantity.

Equation A = 384, where Tran has 8 pounds of butter, yields the total number of fasnacht doughnuts.

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions.  An equation's constituent parts include coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

given the data,

Let A represent the total number of fasnacht doughnuts.

The equation will now be

8 pounds of butter are in Tran's possession.

2 cups of butter from 1 pound

8 pounds of butter therefore equal 8 x 2 cups.

16 cups of butter from 8 pounds

Additionally, the recipe calls for 2 dozen fasnachts and 1 cup of butter.

Consequently, 16 cups of butter equal 16 dozen fasnachts.

16 cups of butter equal 32 dozens of fasnachts when the equation is simplified.

Additionally, there are 32 dozens of fasnacht doughnuts in all.

A = 32 x 12 = the total number of fasnacht doughnuts.

A total of 384 fasnacht doughnuts make up the entire batch.

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The value of n that makes the sixth term in the expansion contains x²⁵ is n = 5.

What is binomial expansion?

The binomial theorem (or binomial expansion) is a result of expanding the powers of binomials or sums of two terms. The coefficients of the terms in the expansion are the binomial coefficients (kn).

The general term in the binomial expansion of (a + b)ⁿ is given by:

[tex]T(r+1) = (n \, choose \, r) * a^{(n-r)} * b^r[/tex]

where "n choose r" represents the binomial coefficient, which is given by:

(n choose r) = n! / (r! * (n-r)!)

In this case, a = 2/x² and b = -5x⁵. We want to find the value of n such that the sixth term in the expansion contains x²⁵.

To find the term that contains x²⁵, we need to set the exponent of x in the general term equal to 25 and solve for r:

(n-r) = 25

n = r + 25

The exponent of x in the general term is given by:

[tex](2/x^2)^{(n-r)} * (-5x^5)^r = 2^{(n-r)} * (-5)^r * x^{(5r - 2(n-r))}[/tex]

Setting 5r - 2(n-r) = 25, we get:

7r - 2n = 25

We know that the sixth term has r = 5, so we can substitute this into the equation:

7(5) - 2n = 25

35 - 2n = 25

2n = 10

n = 5

Therefore, the value of n that makes the sixth term in the expansion contains x²⁵ is n = 5.

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The constant value in the polynomial expression is 12

The roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero. If a is the root of the polynomial p(x), then p(a) = 0.

Given here, the expression as (x+2)(x-2)-(x+4)(x-4) now using the identity  a²-b²=(a+b) (a-b) we get

(x+2)(x-2)-(x+4)(x-4) = x²-4-x²+16

                                 =12

Hence, The constant value in the polynomial expression is 12

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Answer: The answer is about 12 miles.

Step-by-step explanation:

The total was $25.78 so 25.78=

The initial value is 5 so +5

1.75 per mile so 1.75x (since thats the missing value)

equation= 25.78=1.75x+5

25.78-5=1.75x+5-5

25.78=1.75x

25.78/1.75=1.75/1.75x

12=x

You would travel about 12 miles.

The polygon tool to graph the dilated figure will be drawn below.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.

The polygon tool to graph the dilated figure will be drawn below.

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6 to the -1st power is 1/6

6 to the -2nd power is 1/36

6 to the -3rd power is 1/216

and 6 to the -4th power is 1/1296

Answer:

1) The radius of the circle is 3 units.

2) The center of the circle lies on the x-axis.

5) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

[tex]x^2+y^2-2x-8=0\\x^2-2x-8+y^2=0\\x^2-2x-8+9+y^2=0+9\\x^2-2x+1+y^2=9\\(x-1)^2+y^2=9[/tex]

By completing the square, we can see that the circle has its center at (1,0) and that its radius is 3 units. Thus, the 1st, 2nd, and 5th answers are all true.

Answer:

The height is 5 cm.

Step-by-step explanation:

a = 1/2([tex]base_{1}[/tex] + [tex]base_{2}[/tex])h

27.5 = 1/2(7+ 4) h

27.5 = 1/2 (11) h

27.5 = 5.5 h  Divide both sides by 5.5

5 = h

Answer:

5cm

Step-by-step explanation:

Given ,

To Find : The height of the Trapezoid

In order to find the height of the trapezoid we

[tex]27.5 = \frac{1}{2} X ( 7+4)h[/tex]

[tex]27.5X2 = 11 X h[/tex]

[tex]55 = 11h\\\frac{55}{11}= h\\ 5 = h[/tex]

Hence, the height of the trapezoid is 5cm

Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

The value upto two decimal is 18.73.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number.

Given digit 18.7347

to round off to two decimals

for rounding off we need to check the next digit of digit upto we round

the digit after 3 is 4 which is less than 5 then there is no change in digit,

so 18.73447 = 18.73

Hence the round 18.7347 is 18.73.

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Answer:

y + 11 = -8(x - 9)

y + 11 = -8x + 72

y = -8x + 61

Step-by-step explanation:

Answer:

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