A student is solving a system of equations by substitution and comes up with the solution 3=3. Assuming that he solved the problem correctly, which of the following can be said about this system of equations?

A) The system has exactly 1 solution.
B) The system has exactly 2 solutions.
C) The system has infinitely many solutions.
D) The system has no solution.

HELLP MEEEEE PLZZZZ

Answer:

Slant height (s)= 12.1 cm

Step-by-step explanation:

Given: Base= 4.5 cm.

           Surface area of right square pyramid= 129.5 cm.

First, calculating slant height (s) of right square pyramid.

Surface area of square pyramid= [tex](a^{2} +2\times a\times s)[/tex]

a= side of square base.

s= slant height

∴ [tex]129.5= (4.5^{2} + 2\times 4.5\times s)[/tex]

⇒ [tex]129.5= (20.25+2\times 4.5\times s)[/tex]

⇒ [tex]129.5= (20.25+9\times s)[/tex]

Now, opening the parenthesis and subtracting both side by 20.25.

⇒ [tex]109.25=9\times s[/tex]

cross multiplying both side

∴ Slant height (s)= 12.1

Final answer:

To find the slant height of the right square pyramid, subtract the base area from the total surface area, divide by four to find the area of one triangular side, and then solve for the slant height using the triangle area formula. The calculated slant height is = 12.1 cm

Explanation:

The student is asking how to find the slant height of a right square pyramid when given the surface area and the base length. To solve this, we need to take into account the formula for the total surface area of a right square pyramid, which is the sum of the base area and the area of the four triangles forming the sides. We know the total surface area is 129.5 cm2 and the base length is 4.5 cm. The area of the base is simply the square of the base length since it's a square base.

Base area = base length2 = (4.5 cm)2 = 20.25 cm2

Total area of four triangular sides = 129.5 cm2 (total surface area) - 20.25 cm2 (base area) = 109.25 cm2

Area of one triangular side = 109.25 cm2 / 4 = 27.3125 cm2

Now, using the formula for the area of a triangle, A = 1/2 × base × height, we can substitute the area of one triangular side and the base length to solve for the slant height:

27.3125 cm2 = 1/2 × 4.5 cm × slant height (s)

Slant height (s) = (2 × 27.3125 cm2) / 4.5 cm = 12.139 cm

Rounded slant height = 12.1 cm

Answer:

Kenja could travel a certain number of miles in 1 hour depending the speedometer. So, it is not necessary that she may always take the same number of hours it takes to travel 1 mile.

For example, If Kenja has traveled 120 miles in three hours. It means it would take 5 hours to travel 200 miles. The reason is that her unit rate is 40 miles per hour. So, it would take her 1/40 hours to travel one mile.

Step-by-step explanation:

Kenja could travel a certain number of miles in 1 hour depending the speedometer.

If she is traveling at the rate of 5 miles per hour, it would take her 12 minutes to travel one mile. The only way she can take the same number of hours to travel 1 miles if she travels at the rate of 1 mile per hour.

For example, if Kenja has traveled 120 miles in three hours. It means it would take 5 hours to travel 200 miles. The reason is that her unit rate is 40 miles per hour.

As

[tex]\frac{120}{3} = 40 mph[/tex]  

So, if the unit rate is 40 mph, then it would take her 1/40 hours to travel one mile.

So, it is not necessary that she may always take the same number of hours it takes to travel 1 mile.

Keywords: miles per hour, speed, unit time

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Answer:

Number of rocks and fossils collected by you is 1 and  24 respectively

Number of rocks and fossils collected by your friend is 3 and 12 respectively

Step-by-step explanation:

Let  the number of Rocks you collect be x

Let  the number of Fossils you collect be y

Then the total number pf objects you collected will be

x + y = 25

x = 25 - y------------------------------(1)

Your friend collects three times as many rocks and half as many fossils as you.

This can be written as

[tex]3x + y(\frac{1}{2}) = 15[/tex]

[tex]3x + (\frac{y}{2}) = 15[/tex]-------------------(2)

Substituting (1) in (2)

[tex]3(25 -y) + (\frac{y}{2}) = 15[/tex]

[tex] 75 - 3y + (\frac{y}{2}) = 15[/tex]

Grouping the like terms we get,

[tex] 75 - 15 = 3y - (\frac{y}{2})[/tex]

[tex] 60= \frac{6y-y}{2})[/tex]

[tex] 60 \times 2= 6y-y[/tex]

[tex] 120= 5y[/tex]

[tex] y = \frac{120}{5}[/tex]

y= 24

Substituting  y value in equation(1) we get

x = 25 - 24

x= 1

Friends collects 3 times rock

so collects 3x =3(1) = 3rocks

Also he collects half as many fossils

That is

[tex]\frac{y}{2} = \frac{24}{2} =12 fossils[/tex]

You collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.

Let's assign variables to represent the number of rocks and fossils that you and your friend collect.

Let x represent the number of rocks you collect.

Since your friend collects three times as many rocks as you, we can represent the number of rocks your friend collects as 3x.

Let y represent the number of fossils you collect.

Since your friend collects half as many fossils as you, we can represent the number of fossils your friend collects as y/2.

From the information given, we know that you collect 25 objects, so we have the equation:

x + y = 25

We also know that your friend collects 15 objects, so we have the equation:

3x + y/2 = 15

Simplifying the second equation by multiplying both sides by 2, we get:

6x + y = 30

We now have a system of equations:

x + y = 25

6x + y = 30

Solving this system of equations, we can subtract the first equation from the second equation to eliminate y:

(6x + y) - (x + y) = 30 - 25

5x = 5

x = 1

Substituting the value of x into the first equation, we find:

1 + y = 25

y = 24

Therefore, you collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.

Answer:

n = 1

Step-by-step explanation:

First, rearrange the equation to standard form 0 = ax² + bx + c, when everything equals 0.

5n² = 5

5n² - 5 = 0

State the variables a, b and c.

a = 5;  b = 0;  c = -5

Substitute a, b, and c into the quadratic formula.

[tex]n = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]

[tex]n = \frac{-0 ±\sqrt{0^{2}-4(5)(-5)} }{2(5)}[/tex]   Substitute

[tex]n = \frac{\sqrt{100} }{10}[/tex]   Simplify inside the √ and bottom

[tex]n = \frac{10}{10}[/tex]  Simplify the top

[tex]n = 1[/tex]  Final answer

Therefore the solution is n = 1.

The quadratic formula usually is written with x, but it can be solved with any variable in standard form.

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

This is most easily solved by writing the factored form:

[tex]f(x) = (x + 9)(x + 1)[/tex]

Notice how, if we were to substitute -9 for x, the left part would be -9 + 9 = 0. Since (x + 1) × 0 = 0, this makes the function 0. The same logic applies for the right part.

Final answer:

A quadratic function with zeros at -9 and -1 can be written as f(x) = (x + 9)(x + 1) or f(x) = x^2 + 10x + 9 when expanded.

Explanation:

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical phrase or statement. Expressions can consist of variables, constants, arithmetic operations (such as addition, subtraction, multiplication, and division), exponents, and functions.

To write a quadratic function f with zeros at -9 and -1, we use the fact that a quadratic function f(x) can be represented in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the zeros of the function and a is a nonzero coefficient. In this case, our zeros are -9 and -1, giving us f(x) = a(x + 9)(x + 1). To keep the function in simplest form, we can choose a = 1, which gives us the quadratic function f(x) = (x + 9)(x + 1) or f(x) = x2 + 10x + 9 after expanding the expression.

Final answer:

A quadratic function with zeros at -9 and -1 can be written as f(x) = (x + 9)(x + 1) or f(x) = x^2 + 10x + 9 when expanded.

Explanation:

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical phrase or statement. Expressions can consist of variables, constants, arithmetic operations (such as addition, subtraction, multiplication, and division), exponents, and functions.

To write a quadratic function f with zeros at -9 and -1, we use the fact that a quadratic function f(x) can be represented in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the zeros of the function and a is a nonzero coefficient. In this case, our zeros are -9 and -1, giving us f(x) = a(x + 9)(x + 1). To keep the function in simplest form, we can choose a = 1, which gives us the quadratic function f(x) = (x + 9)(x + 1) or f(x) = x2 + 10x + 9 after expanding the expression.

Answer:

First option is correct.

[tex]\sqrt[10]{4}[/tex]

Step-by-step explanation:

Given:

The given expression is [tex](4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]

We write the given expression with a rational exponent as a radical expression such as.

[tex]=(4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]

Simplify the above equation by multiplication of powers.

[tex]=(4^{\frac{2}{5}\times \frac{1}{4}})[/tex]

[tex]=(4^{\frac{1}{5}\times \frac{1}{2}})[/tex]

[tex]=(4^{\frac{1}{5\times 2}})[/tex]

[tex]=(4^{\frac{1}{10}})[/tex]

[tex]=\sqrt[10]{4}[/tex]

Therefore, The answer is [tex]=\sqrt[10]{4}[/tex].

Answer:

lol

Step-by-step explanation:

Answer:

D) 34

Step-by-step explanation:

Since B is the midpoint, AB = BC

Plug the two in:

7x - 4 = 4x + 5

Solve for x:

3x = 9, x = 3

Find AB + BC

since BC = AB

AC = 4x + 5 + 4x + 5

AC = 8x + 10

AC = 8(3) + 10

AC = 24 + 10

AC = 34

The calculated length of the segment AC is () 34

From the question, we have the following parameters that can be used in our computation:

AB = 7x - 4

BC = 4x + 5

B is the midpoint of AC

So, we have

7x - 4 = 4x + 5

Evaluate

3x = 9

So, we have

x = 3

This means that

AC = 2 * (7 * 3 - 4)

Evaluate

AC = 34

HEnce, the length of the segment AC is () 34

Read more about midpoint at

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The value of x is 4.

Step-by-step explanation:

Consider a Rectangle ABCD

AB as Top

CD as Bottom

AB = -1 + 4x

CD = 3x + 3

To Find:

x = ?

Solution:

In a Rectangle ABCD

Opposite sides of rectangle congruent,

AB = CD

Top = Bottom

on substituting we get

[tex]-1+4x=3x+3\\\\4x-3x=3+1\\\\x=4\\\therefore x =4[/tex]

The value of x is 4.

Answer:

Choosing a 6 and then a prime number: 2/21

Choosing two odd numbers: 2/7

Step-by-step explanation:

Choosing a 6 and then a prime number:

The probability of choosing 6 out of 1, 2, 3, 4, 5, 6 and 7 is one event divided by number of total events (which is equal to 7). That results in 1/7. Once 6 is chosen, the probability of choosing a prime number (prime number is a number that can only be divided by 1 and itself) out of 1, 2, 3, 4, 5 and 7 is 4/6 (prime numbers are 2, 3, 5, 7 in total there are 4 number and total number of events are 6). Finally, the probability of choosing a 6 and then a prime number is (1/7)*(4/6)=2/21.

Choosing two odd numbers:

The probability of choosing 1st odd number is 4/7 (number of odd numbers is 4 which includes 1, 3, 5, 7 and the number of total events is 7). Once 1st odd number is chosen, the probability of choosing 2nd odd number is 3/6 (number of odd numbers is 3 - because 1 odd number is already chosen and the number of total events is 6). Finally, the probability of choosing two odd numbers in a sequence is (4/7)*(3/6)=2/7.

Answer:

[tex]2\sqrt{2}\ units[/tex]

Step-by-step explanation:

we know that

In a 45-45-90 right triangle, the length of the two legs are equal

so

Applying the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse

a and b are the legs

we have

[tex]a=2\ units\\b=2\ units[/tex]

substitute

[tex]c^2=2^2+2^2[/tex]

[tex]c^2=4+4[/tex]

[tex]c^2=8[/tex]

[tex]c=\sqrt{8}\ units[/tex]

simplify

[tex]c=2\sqrt{2}\ units[/tex]

20 times 4 add 5 is

20*4+5

20*4=80

80+5=85

85 is your answer

Answer: 85.

Step-by-step explanation: 20 times 4 equals 80, add 5 to that makes 85.

And the equation in mathematical form: ( 20 X 4 ) = 80 + 5 = 85.

Hope this helps, if not, comment below please!!!!!

I need this answer too, did you figure it out?

Answer:

91 1/4%

Step-by-step explanation:

To find the percentage of the discount, just divide the new selling price cost from the previous selling price over 100

73/80*100 = 91 1/4%

Answer:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c.

Step-by-step explanation:

Answer:

X = 117.9°

Step-by-step explanation:

Rearranging the cosine rule to obtain C

cosC = [tex]\frac{a^2+b^2-c^2}{2ab}[/tex]

Here C = X, a = 50, b = 55, c = 90

cosX = [tex]\frac{50^2+55^2-90^2}{2(50)(55)}[/tex]

        = [tex]\frac{2500+3025-8100}{5500}[/tex]

        = [tex]\frac{-2575}{5500}[/tex], thus

X = [tex]cos^{-1}[/tex]( - [tex]\frac{2575}{5500}[/tex] ≈ 117.9°

Final answer:

The variable x represents the unknown number, and the inequality is 4x - 6 < -2. Solving it step-by-step, we find that x < 1, which means any number less than 1 satisfies the inequality.

Explanation:

To solve the inequality 'four times a number decreased by 6 is less than -2', let's define a variable x as the number. Expressing the given condition as an inequality, we get 4x - 6 < -2. To solve for x, follow these steps:

Add 6 to both sides of the inequality to isolate the term with the variable: 4x - 6 + 6 < -2 + 6, which simplifies to 4x < 4.

Divide both sides of the inequality by 4 to solve for x: 4x/4 < 4/4, which gives us x < 1.

Check the answer to ensure it is reasonable. Since multiplying a number by four and subtracting six should result in a number less than -2, a number less than 1 seems reasonable.

Therefore, any number less than 1 satisfies the inequality.

Answer: 10 three points questions and 14 five points questions

Step-by-step explanation: Please see attachment for explanation.

Answer:

$25 - c(p)

Step-by-step explanation:

C = amount of comic books

P = price of comic books

$25 - c(p)

Hope this helps :)

Answer:

depends on the price of each book

Step-by-step explanation:

For instance if you have ...

one book sold for $5

you divide the total ($25) by the cost  for each book ($5) and you will get the number of comic books (25/5 = 5 comic books)

Answer:

[tex]3.5 - 1.4 + 2.9 \\ = 5[/tex]

hope this helps you

Answer:

3.5 - 1.4 + 2.9 = 5

Step-by-step explanation:

 3. 5 - 1.4 + 2.9

At first, we will add 3.5 and 2.9 and then we will subtract 1.4 from the sum of 3.5 and 2.9.

So, 3.5 - 1.4 + 2.9

= (3.5 + 2.9) - 1.4

= 6.4 - 1.4

= 5

So, the value of 3.5 - 1.4 + 2.9 is 5.

Answer:

$124.42

Step-by-step explanation:

look at the attachment for the formula I used

Because she needs 3 blankets and it takes 15 day per blanket(rate is given), she needs 3x15 or 45 days. She has 60 days so she can volunteer at most 15 days.

answer: s≤15

Answer:

Therefore the Minimum value of f(x) is 2.

Step-by-step explanation:

Given:

[tex]f(x)=x^{2} + 6x+11[/tex]

To Find:

minimum or maximum value of f(x)

Solution:

To find minimum or maximum value of f(x)

Step 1 . Find f'(x) and f"(x)

[tex]f(x)=x^{2} + 6x+11[/tex]

Applying Derivative on both the side we get

[tex]f'(x)=\dfrac{d(x^{2})}{dx}+\dfrac{d(6x)}{dx}+\dfrac{d(11)}{dx}[/tex]

[tex]f'(x)=2x+6+0[/tex]

Again Applying Derivative on both the side we get

[tex]f''(x)=\dfrac{d(2x)}{dx}+\dfrac{d(6)}{dx}[/tex]

[tex]f''(x)=2[/tex]

Step 2. For Maximum or Minimum f'(x) = 0 to find 'x'

[tex]2x+6=0\\\\2x=-6\\\\x=\dfrac{-6}{2}=-3[/tex]

Step 3. IF f"(x) > 0 then f(x) is f(x) is Minimum at x

            IFf"(x) < 0 then f(x) is f(x) is Maximum at x

Step 4. We have

[tex]f''(x)=2[/tex]

Which is grater than zero

then f(x) is Minimum at x= -3

Therefore the Minimum value of f(x) is 2.

The minimum value is 2 when x = -3.

The minimum or maximum value of the function f(x) = x^2 + 6x +11, we need to complete the square or use the vertex formula for a quadratic function.

The function is a parabola that opens upwards (since the coefficient of the x2 term is positive). To complete the square, we group the x-terms and add and subtract the square of half the coefficient of x:

f(x) = (x^2 + 6x + 9) + 11 - 9

f(x) = (x + 3)^2 + 2

The minimum value of this parabola occurs at the vertex, which is (-3, 2).

Answer:

He will earn 45.50 in five hours.

Step-by-step explanation:

Answer:

45.5

Step-by-step explanation:

9.10*5

The total amount paid for vase is $ 41

Solution:

Given that

Cost of vase = $ 34.99

Shipping charge = 3 dollars

Sales tax = 8.25 % was paid on the subtotal which included the shipping charge

To find: total amount paid for vase

total amount paid for vase = Cost of vase + Shipping charge + sales tax

Let us first find the sales tax

Given that 8.25 % was paid on the subtotal which included the shipping charge

Subtotal = 34.99 + 3 = 37.99

So 8.25 % of 37.99 was paid as sales tax

[tex]\text{ sales tax } = \frac{8.25}{100} \times 37.99 = 3.1341[/tex]

Therefore sales tax amount paid = $ 3.1341

total amount paid for vase = Cost of vase + Shipping charge + sales tax

total amount paid for vase = 34.99 + 3 + 3.1341 = 41.1241 ≈ 41

Therefore total amount paid for vase is $ 41

Answer:

The Correct option is

A) Additive Inverse Property .

Step-by-step explanation:

Identity Property of Addition :

In math, an identity is a number, n, that when added to other numbers, gives the same number, n.

The additive identity is always zero.

This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Statement                                      Reasons

1. -(a+b)+a = -a+(-b)+a                   1.Distributive Property

                = -a+a+(-b)                    2.Commutative Property of Addition

                = 0+(-b)                         3. Additive Inverse Property

                = -b                               4. Identity Property of Addition

Answer:

They will work together and print 200 T-shirts in 37.5 minutes.

Step-by-step explanation:

One machine can print 200 T-shirts in 50 minutes.

So, in one minute that machine can print [tex]\frac{200}{50} = 4[/tex] T-shirts.

Again, the other machine can print 200 T-shirts in 150 minutes.

So, in one minute the other machine can print [tex]\frac{200}{150} = 1.33[/tex] T-shirts.

Therefore, working together for one minute both the machines will print (4 + 1.33) = 5.33 number of T-shirts.

Hence, they will work together and print 200 T-shirts in [tex]\frac{200}{5.33} = 37.5[/tex] minutes. (Answer)

Answer:

It can be represented by a ≥ 17.

Step-by-step explanation:

The rules concerning the age of a soccer player in a recreational league mandate that a player is 17 years of age or older.  

Therefore, if the age of a player is a years, then the condition for a soccer player to participate in the league is that a must be equal to 17 or more than 17 years old.

Hence, mathematically it can be represented by a ≥ 17. (Answer)

(1, 12)

(420, 12)

Any coordinate with a y value of 12 lies on the line y = 12.

-----

(-5, 69)

(-5, 13)

Any coordinate with an x value of -5 lies on the line x = -5.

-----

Since the equation must be perpendicular to the line x = 4, which is a vertical line, it must also be written in the form x = a.

Since the x coordinate is 3, the equation of the line is simply x = 3.