nora is 5'3" tall and standing near the 252 foot tall pilgrim monument in Massachusetts. if she casts 9 foot long shadow, find the length of the shadow casted by the monument.​
show steps pls

Answer:

The value of discriminant is 384

There are two different real roots for the equation

Step-by-step explanation:

* Lets explain what is the discriminant

- In the quadratic equation ax² + bx + c = 0, the roots of the

 equation has three cases:

1- Two different real roots

2- One real root or two equal real roots

3- No real roots means imaginary roots

- All of these cases depend on the value of a , b , c

∵ The rule of the finding the roots is  

   x = [-b ± √(b² - 4ac)]/2a

- The effective term is b² - 4ac to tell us what is the types of

 the roots

# If the value of b² - 4ac is positive means greater than 0

∴ There are two different real roots

# If the value of b² - 4ac = 0

∴ There are two equal real roots means one real root

# If the value of b² - 4ac is negative means smaller than 0

∴ There is no real roots but the roots will be imaginary roots

∴ We use the discriminant to describe the number and type of roots

* Now lets solve the problem

∵ -3x² - 18x + 5 = 0

∴ a = -3 , b = -18 , c = 5

∵ Δ = b² - 4ac ⇒ (Δ is the discriminant symbol)

∴ Δ = (-18)² - 4(-3)(5) = 324 - (-60) = 324 + 60 = 384

∴ The value of discriminant is 384

∵ The value of discriminant greater then 0

∴ There are two different real roots for the equation

Answer: 32

Step-by-step explanation:

This ones a bit tricky but the answer is A

Answer:

$14

Step-by-step explanation:

Wages earned by daniel in one hour = $8

Number of working hours spend by daniel in each week = 35

Wages earned by daniel in each week without pay increase = [tex]35\times 8 = 280[/tex]

Increase in pay per week = [tex]\frac{5}{100} \times 280= 14[/tex]

Therefore extra wages earned by Daniel will be $14.

$14

Step-by-step explanation:

Wages earned by daniel in one hour = $8

Number of working hours spend by daniel in each week = 35

Wages earned by daniel in each week without pay increase =

Increase in pay per week =

Therefore extra wages earned by Daniel will be $14.

If the cone are similar, the volume ratio of Cone A to Cone B will be 1:25.

The right circular cone is one in which the line from the cone's peak to the center of the circle's base is perpendicular to the base's surface.

Assume that the radius of the right circular cone under consideration is 'r' units, and the height 'h' units. Then the volume is then expressed as;

[tex]\rm V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

If the cone are similar, the volume ratio of Cone A to Cone B;

[tex]\rm \frac{V_A}{V_B}=(\frac{R_A}{R_B})^3 } \\\\\ \frac{V_A}{V_B}=( \frac{5}{25} )^3 \\\\\ \frac{V_A}{V_B}=\frac{1}{125}[/tex]

If the cone are similar, the volume ratio of Cone A to Cone B will be 1:25.

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Answer:

• discriminant: 73

• # of real solutions: 2

Step-by-step explanation:

Comparing the equation ...

2x^2 -9x +1 = 0

to the generic form ...

ax^2 +bx +c = 0

we find the coefficient values to be ...

a = 2; b = -9; c = 1

That makes the value of the discriminant, (b^2 -4ac), be ...

(-9)^2 -4(2)(1) = 81 -8 = 73

Since the discriminant is positive, the number of real solutions is 2.

Answer:

x = 0

Step-by-step explanation:

Given

x² = - 4y ( divide both sides by - 4 )

y = - [tex]\frac{1}{4}[/tex] x²

Which is a parabola opening vertically down with it's vertex at (0, 0) and symmetrical about the y- axis

Hence equation of axis of symmetry is x = 0

Hoi there!

First, we can open parenthesis.

10+6x+x+10

Then combine like terms.

20+4x

We can put it in parenthesis (if you need it that way).

4(5+x)

So, your answer would be:

20+4x in not factored form.

4(5+x) in factored form.

Hope I helped, sorry if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Trademark Potato 2019.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+3&(1)\\y=4x+6&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\5x+3=4x+6\qquad\text{subtract 3 from both sides}\\5x=4x+3\qquad\text{subtract 4x from both sides}\\x=3\\\\\text{Put the value of x to (1):}\\\\y=5(3)+3\\y=15+3\\y=18[/tex]

Answer:

Step-by-step explanation:

(-)(-) = (+)

(+)(+) = (+)

(-)(+) = (+)(-) = (-)

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

16 - (-53) = 16 + 53 = 69

Answer:

130.5

Step-by-step explanation:

145% of 90 = 145% * 90

145% = 1.45

Substitute: 1.45 * 90

Multiply: 130.5

Answer:

[tex]x=55[/tex]

Step-by-step explanation:

The given equation is [tex]\sqrt{x-6}+3=10[/tex]

Group similar terms to get:

[tex]\sqrt{x-6}=10-3[/tex]

[tex]\sqrt{x-6}=7[/tex]

Square both sides to obtain:

[tex]x-6=7^2[/tex]

[tex]x-6=49[/tex]

Add 6 to both sides

[tex]x=49+6[/tex]

Simplify the right hand side to obtain;

[tex]x=55[/tex]

Answer:

The entry has an area of __44___ square feet

The total area of the tree house is __345__ square feet

Step-by-step explanation:

Let's first calculate the area of the trapezoid entrance:

The area of a trapezoid is given by:

A =((b1 + b2) * h) / 2

Where b1 and b2 are the bases or parallel sides.  So, we have:

A = ((6 + 16) * 4) / 2 = (22 * 4) / 2 = 44 sq ft

Now, let's look at the other areas... which are all rectangles, so easy to calculate (b * h).

Playroom: 16 x 14 = 224 sq ft

Side Deck: 3 x 14 = 42 sq ft

Back Porch: 6 x6 = 35 sq ft

So, in the total area of the tree house is:

TA = 44 + 224 + 42 + 35 = 345 sq ft

Answer:

The entry terrace has an area of

48

square feet. The total area of the tree house including the entrance, porch, and side deck is

350

square feet.

Step-by-step explanation:

I just took a test with this question and this was the right answer

~Please mark me as brainliest :)

It is an acute angle and it is more likelt to be B. 42 degrees

Pls mark brainliest answer

Answer:

Step-by-step explanation:

-3 is the number u will get. Hope this helps!!

To represent the expression -8 + 5 on a number line, start at -8 and move 5 units to the right, ending at -3.

To represent the expression -8 + 5 on a number line, we start at -8 and move 5 units to the right. Since we are adding a positive number, the arrow on the number line will point to the right.

So the number line that represents the expression -8 + 5 would start at -8 and have an arrow pointing to the right, ending at -3.

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Answer:

[tex]x^{2}+y^{2} +4x-2y+1=0[/tex]

Step-by-step explanation:

we know that

The general form of the equation of a circle is

[tex]x^{2} +y^{2}+ Dx + Ey + F=0[/tex]

where D, E, F are constants

step 1

Find the radius of the circle

Remember that the distance from the center to any point on the circle is equal to the radius

so

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex](-2,1)\\(-4,1)[/tex]  

substitute the values

[tex]r=\sqrt{(1-1)^{2}+(-4+2)^{2}}[/tex]

[tex]r=\sqrt{(0)^{2}+(-2)^{2}}[/tex]

[tex]r=2\ units[/tex]

step 2

Find the equation of the circle in standard form

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( -2,1)

radius r=2 units

substitute

[tex](x+2)^{2} +(y-1)^{2}=2^{2}[/tex]

[tex](x+2)^{2} +(y-1)^{2}=4[/tex]

Step 3

Convert to general form

[tex](x+2)^{2} +(y-1)^{2}=4\\ \\x^{2}+4x+4+y^{2}-2y+1=4\\ \\x^{2}+y^{2} +4x-2y+1=0[/tex]

Equation of line whose slope is 3 and passing point (2, 5) is y = 3x - 1.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

Here, Slope of line = 3

          Passing point (2, 5)

Equation of line

          (y - y₁) = m (x - x₁)

          y - 5 = 3 (x - 2)

          y - 5 = 3x - 6

          y = 3x - 6 + 5

          y = 3x - 1

Thus, equation of line whose slope is 3 and passing point (2, 5) is y = 3x - 1.

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Answer:

300cm

Step-by-step explanation:

First you get the length, width, and height. The length is 15, the width is 12, and the height is 10.

15*12=180

Since their is 2 you multiply by 2

180*2=360

12*10=120

Since their is 2 you multiply by 2

120*2=240

Then you divide by 2 since it is a triangle but before that you add the products up

360+240=600

600/2=300

Answer: The answer to 3.25÷0.5 is 6.5 :)

Step-by-step explanation:

Final answer:

The value 0.9 represents the 90% of the original price a customer pays after applying a 10% discount. It is used to calculate the discounted price by multiplying the original price by 0.9.

Explanation:

In the context of this question, 0.9 (or 0.90) represents the remainder of the original price G after a 10% discount is applied. When Ray uses his coupon for 10% off the price of ginger roots, this discount factors out 10% of the cost, leaving him to pay just 90% of the original price. This is why the price he pays can be represented as 0.9G, which is the same as saying 90% of G.

The 0.9 is a decimal representation of the percentage that remains after the discount. So, if the original price G is, for example, $10.00, with a 10% discount Ray would be saving $1.00, and thereby paying 90% of the original price, or $9.00. So, 0.9 in this calculation effectively means 90% of the original price.

Representing changes in price using decimals and percentages is a common method in mathematics to describe percentage change or discounts succinctly.

using the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] as defined by the table, we get that [tex]\((f \circ g)(1) = 17\).[/tex]

To find [tex]\((f \circ g)(1)\)[/tex], we need to first find  and then find the value of [tex]\(f\)[/tex] at that result.

1. Identify [tex]\(g(1)\)[/tex]: We need to evaluate the function [tex]\(g\)[/tex] at [tex]\(x = 1\)[/tex]. Looking at the table under the row for [tex]\(g(x)\)[/tex] and the column where \(x = 1\), we find that [tex]\(g(1) = 6\).[/tex]

2. Evaluate [tex]\(f\)[/tex] at [tex]\(g(1)\)[/tex]: Now that we have that [tex]\(g(1) = 6\)[/tex], we need to evaluate the function [tex]\(f\)[/tex] at [tex]\(x = 6\)[/tex]. Looking at the table under the row for [tex]f(x)\)[/tex] and the column where [tex]\(x = 6\)[/tex], we find that [tex]\(f(6) = 17\).[/tex]

3. **Combine the results**: We have [tex]\(f(g(1)) = f(6)\)[/tex]. Since we found out that [tex]\(f(6) = 17\)[/tex], we can conclude that [tex]\((f \circ g)(1) = 17\).[/tex]

So, using the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] as defined by the table, we get that [tex]\((f \circ g)(1) = 17\).[/tex]

Answer:

Part 1)  [tex]f^{-1}(x)=3(x+17)/2[/tex] ----> [tex]f(x)=\frac{2x}{3}-17[/tex]

Part 2) [tex]f^{-1}(x)=x+10[/tex] -----> [tex]f(x)=x-10[/tex]

Part 3) [tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex] ----> [tex]f(x)=\sqrt[3]{2x}[/tex]

Part 4) [tex]f^{-1}(x)=5x[/tex] ----> [tex]f(x)=x/5[/tex]

Step-by-step explanation:

Part 1) we have

[tex]f(x)=\frac{2x}{3}-17[/tex]

Find the inverse

Let

y=f(x)

[tex]y=\frac{2x}{3}-17[/tex]

Exchange the variables, x for y and y for x

[tex]x=\frac{2y}{3}-17[/tex]

Isolate the variable y

Adds 17 both sides

[tex]x+17=\frac{2y}{3}[/tex]

Multiply by 3 both sides

[tex]3(x+17)=2y[/tex]

Divide by 2 both sides

[tex]y=3(x+17)/2[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=3(x+17)/2[/tex]

Part 2) we have

[tex]f(x)=x-10[/tex]

Find the inverse

Let

y=f(x)

[tex]y=x-10[/tex]

Exchange the variables, x for y and y for x

[tex]x=y-10[/tex]

Isolate the variable y

Adds 10 both sides

[tex]y=x+10[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=x+10[/tex]

Part 3) we have

[tex]f(x)=\sqrt[3]{2x}[/tex]

Find the inverse

Let

y=f(x)

[tex]y=\sqrt[3]{2x}[/tex]

Exchange the variables, x for y and y for x

[tex]x=\sqrt[3]{2y}[/tex]

Isolate the variable y

elevated to the cube both sides

[tex]x^{3}=2y[/tex]

Divide by 2 both sides

[tex]y=\frac{x^{3}}{2}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex]

Part 4) we have

[tex]f(x)=x/5[/tex]

Find the inverse

Let

y=f(x)

[tex]y=x/5[/tex]

Exchange the variables, x for y and y for x

[tex]x=y/5[/tex]

Isolate the variable y

Multiply by 5 both sides

[tex]y=5x[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=5x[/tex]

The inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

Functions are shown in the picture.

We have to find the inverse of a function.

[tex]\rm f(x) = \dfrac{2x}{3}-17[/tex]

To find the inverse of a function plug in the place of f(x)→x and x→f(x) ⁻¹

[tex]\rm x = \dfrac{2f^-^1(x)}{3}-17[/tex]

f(x) ⁻¹ = 3(x + 17)/2

Similarly, we can find the rest of the inverse of the function as follows:

f(x) = x - 10

f(x) ⁻¹ = x + 10

f(x) = ∛2x

f(x) ⁻¹ = x³/2

f(x) = x/5

f(x) ⁻¹ = 5x

Thus, the inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

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Answer:

C) 110.

Step-by-step explanation:

To find it you must multiply in number by 5.

22*5=110.

To prove it you must divide it into 5, since 20 is the fifth part of 110.

110/5=22.

Answer:

Step-by-step explanation:

[tex]\bold{Method\ 1}\\\\\begin{array}{ccc}22&-&20\%\\x&-&100\%\end{array}\qquad\text{cross multiply}\\\\20x=(22)(100)\\20x=2200\qquad\text{divide both sides by 20}\\x=110[/tex]

[tex]\bold{Method\ 2}\\\\\begin{array}{cccc}22&-&20\%&\text{multiply both sides by 5}\\5\cdot22&-&5\cdot20\%\\110&-&100\%\end{array}[/tex]

[tex]\bold{Method\ 3}\\\\p\%=\dfrac{p}{100}\to 20\%=\dfrac{20}{100}=0.2\\\\n-number\\\\20\%\ of\ n\ is\ 22\to0.2x=22\qquad\text{divide both sides by 0.2}\\\\x=\dfrac{22}{0.2}\\\\x=\dfrac{220}{2}\\\\x=110[/tex]

Answer:

c 8700

Step-by-step explanation:

Answer:

The answer is (C. 8700

Step-by-step explanation:

I took the test

Answer:

- [tex]\frac{2}{729}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

Given a₁ = 6 and r = - [tex]\frac{1}{3}[/tex], then

[tex]a_{8}[/tex] = 6 × [tex](-1/3)^{7}[/tex] = 6 × - [tex]\frac{1}{3^{7} }[/tex] = 6 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{2}{729}[/tex]

The unit price of the 9-kilogram cement bag, rounded to the nearest cent, is $1.36.

Here's the complete answer:

1. **Unit Price Formula: Unit price is calculated by dividing the total cost by the quantity. It represents the cost per unit of the item.

2. **Given Information**:

  - Weight of cement bag = 9 kilograms

  - Cost of cement bag = $12.22

3. **Calculation**:

  - Unit price = Total cost / Quantity

  - Unit price = $12.22 / 9 kilograms

4. **Calculate Unit Price**:

  - Unit price = $1.358888... (dividing $12.22 by 9)

5. **Rounded to Nearest Cent**:

  - Since we're asked to round to the nearest cent:

    - $1.358888... is closer to $1.36 than $1.35.

6. **Final Answer**:

  - The unit price of the cement bag, rounded to the nearest cent, is **$1.36**.

The values of 12C4 and 11P4 are 495 and 7920, respectively

The expressions are illustrations of permutation and combination, and they are calculated using:

[tex]^nC_r = \frac{n!}{(n -r)!r!}[/tex]

and

[tex]^nP_r = \frac{n!}{(n -r)!}[/tex]

So, we have:

[tex]^{12}C_4 = \frac{12!}{(12 -4)!4!}[/tex]

Evaluate the difference

[tex]^{12}C_4 = \frac{12!}{8!4!}[/tex]

Evaluate the factorials

[tex]^{12}C_4 = \frac{479001600}{967680}[/tex]

Divide

[tex]^{12}C_4 = 495[/tex]

Also, we have:

[tex]^{11}P_4 = \frac{11!}{(11 -4)!}[/tex]

Evaluate the difference

[tex]^{11}P_4 = \frac{11!}{7!}[/tex]

Evaluate the quotient

[tex]^{11}P_4 = 7920[/tex]

Hence, the values of 12C4 and 11P4 are 495 and 7920, respectively

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Among the given options, only ((-196)^(1/4)) is equivalent to a real number, as it involves the fourth root of a negative number, which results in a real value.

The correct answer is option B.

To determine which expression is equivalent to a real number, we need to consider the roots involved and whether they result in a real value.

Let's analyze each option:

A. (-1503)^(1/6): The expression involves the sixth root of a negative number. Odd roots of negative numbers are real, but even roots are not. Therefore, this expression is not guaranteed to be real.

B. (-196)^(1/4): The expression involves the fourth root of a negative number. Similar to option A, the fourth root of a negative number is real, so this expression is valid.

C. (-144)^(1/2): This expression involves the square root of a negative number. Square roots of negative numbers are not real; hence, this expression is not equivalent to a real number.

D. (-1024)^(1/2): The expression involves the square root of a negative number as well. Like option C, this expression is not equivalent to a real number.

In summary, option B ((-196)^(1/4)) is equivalent to a real number because it involves the fourth root of a negative number, and odd roots of negative numbers are real.

Answer:

[tex]553\ acres[/tex]

Step-by-step explanation:

Let

z------> the crop yield

x----> the number of bushels harvested

y----> the number of acres used for the harvest

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=94,010\ bushels[/tex]

[tex]z=170\ bushels/acre[/tex]

substitute and solve for y

[tex]170=\frac{94,010}{y}[/tex]

[tex]y=\frac{94,010}{170}=553\ acres[/tex]

Answer:

553

Step-by-step explanation:

Answer:251.2m^2

Step-by-step explanation:

8^2+2*8*11.7