3.
A hardware store sells three types of shovels, spade, flat, and square. The spade costs $16.00, the flat costs $9.60, and the square costs $12.80 each. The store keeps an inventory of 80 shovels. They always buy twice as many spade shovels as square. One day, after selling out of shovels, the store had receipts totaling $1,072.00. Find how many of each type of shovel were sold that day.

a. Write a system of equations to represent the information given.
b. Put the system into a matrix. Name the matrix using dimensions.
c. What is the determinant of the coefficients?
d. Use Cramer’s rule to solve the system.
e. If the store doubled all prices and inventory, what would the new matrix be?

whenever we have an amount to be divided in ratios, we simply divide the total amount by the sum of those ratios and then distribute accordingly.  In this case, let's divide 77.40 by (1+3+5) and then distribute accordingly to each chap.

[tex]\bf \stackrel{Paul}{1}~~:~~\stackrel{Colin}{3}~~:~~\stackrel{Brian}{5}~\hfill \cfrac{77.40}{1+3+5}\implies 8.6 \\\\\\ \stackrel{Paul}{1\cdot 8.6}~~:~~\stackrel{Colin}{3\cdot 8.6}~~:~~\stackrel{Brian}{5\cdot 8.6}\qquad \implies \qquad \stackrel{Paul}{8.6}~~:~~\stackrel{Colin}{25.8}~~:~~\stackrel{Brian}{43} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{Brian get this much more than Paul}}{43-8.6\implies 34.4}~\hfill[/tex]

Answer:

£34.40

Step-by-step explanation:

Paul, Colin and Brian are waiters.

One night the restaurant earns tips totalling £77.40

They share the tips in the ratio 1:3:5

Paul gets [tex]\frac{1}{9}[/tex] × £77.40 = £8.60

Brian gets [tex]\frac{5}{9}[/tex] × £77.40 = £43.00

Brian gets £43.00 - £8.60 = £34.40 more than Paul.

Answer:

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

[tex]\dfrac{1}{2}\times\underbrace{(6\times4)}_{1}+3+2\\\\=\underbrace{\dfrac{1}{2}\times24}_{2}+3+2\\\\=12+3+2=17[/tex]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept (0, b)

We have the slope m = -9 and the y-intercept (0, -2) → b = -2.

Substitute:

y = -9x + (-2) = -9x - 2

The slope-intercept equation of a line with a slope of -9 and a y-intercept of (0, -2) is y = -9x - 2.

The slope-intercept equation of a line is in the form y = mx + b, where m is the slope and b is the y-intercept.

Given a slope of -9 and a y-intercept of (0, -2), the slope-intercept equation is y = -9x - 2.

Therefore, the slope-intercept equation of the line is y = -9x - 2.

Answer:

Step-by-step explanation:

sqrt(28): sqrt(4*7)

sqrt(4) = 2;

sqrt28)=2*sqrt(7)

sqrt(343): sqrt(7 * 7 * 7) = 7 * sqrt(7)

Note: the rule is if you have 3 equal primes under the root sign, you leave one, you throw one away, and you put one outside the root sign.

2 sqrt(63) = 2 sqrt(3*3*7)  The above rule gets modified to throw 1 three away and take the other one outside the root sign.

2sqrt(63) = 2*3 sqrt(7)

Numerator: 2*sqrt(7) + 7sqrt(7) = 9sqrt(7)

9sqrt(7)

======

6 sqrt(7)

3/2

Note without brackets I cannot be certain that I have interpreted this correctly. The division only apply to sqrt(343) / 2 sqrt(63). If this is so please leave a note.

Answer:

$0.08 (rounded to nearest hundredth, 2 decimals)

Step-by-step explanation:

This is very easy if we setup a unitary method ratio.

" If 12.8 pesos equal 1 dollar, 1 peso is HOW MANY (let it be x) dollars?"

We translate the above sentence in ratio and solve for x:

[tex]\frac{Peso}{Dollar}=\frac{12.8}{1}=\frac{1}{x}\\12.8x=1\\x=\frac{1}{12.8}\\x=0.08[/tex]

Thus, it is worth about $0.08

Answer:

slope is -5

y-intercept is -5

Step-by-step explanation:

Solve for y to write in y=mx+b

m is slope

b is y-intercept

5x+y=-5

Subtract 5x on both sides

    y=-5x-5

slope is -5

y-intercept is -5

Answer:

B

Step-by-step explanation:

Given the expression

2n + 3

To determine the terms in the sequence generated by this expression

Substitute n = 1, 2, 3, 4, ... into it

a₁ = (2 × 1) + 3 = 2 + 3 = 5

a₂ = (2 × 2) + 3 = 4 + 3 = 7

a₃ = (2 × 3) + 3 = 6 + 3 = 9

a₄ = (2 × 4) + 3 = 8 + 3 = 11

a₅ = (2 × 5) + 3 = 10 + 3 = 13

The first 5 terms of the sequence are 5, 7, 9, 11, 13

Answer: No, because 1/3 is smaller than 2/3

Hope this helps :)

Step-by-step explanation:

The answer is:

The correct option is the first option, the average speed in blocks per minute is 1.5 blocks per minute.

[tex]AverageSpeed=1.5\frac{Block}{minute}[/tex]

To calculate the average speed we need to calculate the total distance traveled and the total time taken to cover that distance.

From the statement we know that:

[tex]Distance_{1}=3blocks\\Distance_{2}=9blocks-3blocks=6blocks\\time_{1}=2minutes\\time_{2}=6minutes[/tex]

So, we need to use the following formula in order to calculate the average speed:

[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]

Then, substituting we have:

[tex]AverageSpeed=\frac{3blocks+9blocks}{2minutes+6minutes}[/tex]

[tex]AverageSpeed=\frac{12blocks}{8minutes}=1.5\frac{blocks}{minutes}[/tex]

Hence, we have that the correct option is the first option, the average speed in blocks per minute is 1.5 blocks per minute.

[tex]AverageSpeed=1.5\frac{Block}{minute}[/tex]

Have a nice day!

Answer:

6

Step-by-step explanation:

Plug in 3 into both expressions

Then add those results

2(3)+21=6+21=27

3-24             =-21

                    -------

                         6  is the sum of 27 and -21

ANSWER

[tex]g(f( - 1)) = \frac{1}{5 }[/tex]

EXPLANATION

The given function is:

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

and

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

[tex]g(f(x)) = g( {x}^{2} )[/tex]

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

To find g(f(-1)), we substitute x=-1, to obtain;

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

We simplify the square in the denominator to get,

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

We now add the denominator to obtain;

[tex]g(f( - 1)) = \frac{1}{5 } [/tex]

Answer:

Part 1) [tex]m=0[/tex]

Part 2) The slope is undefined

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Part 1

we have

[tex]A(-2,-5)\ B(8,-5)[/tex]

Substitute the values

[tex]m=\frac{-5+5}{8+2}[/tex]

[tex]m=\frac{0}{10}[/tex]

[tex]m=0[/tex]  ----> is a horizontal line (parallel to x-axis)

Part 2

we have

[tex]A(4,9)\ B(4,-7)[/tex]

Substitute the values

[tex]m=\frac{-7-9}{4-4}[/tex]

[tex]m=\frac{-16}{0}[/tex]   ----> is a vertical line (parallel to y-axis)

The slope is undefined

Answer:

1/6

Step-by-step explanation:

To find the common ratio, you compare a few pairs of consecutive terms, by dividing an element by its predecessor.

12 / 72 = 1/6

2 / 12 = 1 / 6

1/3 / 2 = 1 / 6

The ratio is constant... so that's your common ratio to go from one term to the next.  

To go from one term to the next, you have to multiply by 1/6.

Answer:

Number of different operations

Step-by-step explanation:

Answer:

Option A.

Step-by-step explanation:

If you look closely at the graph, we can notice that the function is not defined at two different points.

If you look at functions B and C, you will notice that both functions are not defined at just one point. The function B is not defined at x= -5/2 and function C is not defined at x=-5. Both options are discarded, given that our function should not be defined at two fiferent points.

Now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

By analyzing the vertical asymptotes, we will see that the correct option is A.

We know that the vertical asymptotes in the graph of a rational function are at the values of x that make the denominator equal to zero.

Here, we can see that we have the asymptotes at x = -2 and at x = 5, so we can assume that the denominator is of the form:

d(x) = (x + 2)*(x - 5)

Now if you look at the options, there is only one that has this denominator, which is A:

[tex]f(x) = \frac{1}{(x + 2)*(x - 5)}[/tex]

If you want to learn more about rational functions, you can read:

https://brainly.com/question/1851758

For this case we must find an expression equivalent to:

[tex](x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, rewriting the expression we have:

[tex]x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =[/tex]

[tex]x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =[/tex]

By definition of multiplication of powers of the same base, we put the same base and add the exponents:

[tex]x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}[/tex]

Answer:

Option B

Answer:

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

Step-by-step explanation:

The question is on rules of rational exponents

Here we apply the formulae for product rule where;

[tex]= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}[/tex]

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

Answer:

In this case, you can use the concept of cosine to calculate y, and things are even easier when you have one of the special angles which is a 45° angle.

So we know that: cos45° = √2/2

This fact will always be true. In our case, we have:

cos45° = 7/y

Therefore, we have the equation:

7/y = √2/2

⇔ 14 = y√2

⇔ y   = 14/√2

⇔ y   = √196/√2 = √(196/2) = √98 = 7√2

So y is equal to 7√2

Answer:

7√2

Step-by-step explanation:

By observation, we can determine that because this is a right angle triangle with one of the internal angles = 45°, that the remaining unknown angle is also 45°, which makes this an isosceles triangle.

This means that x = 7

we can find y by using the Pythagorean equation:

y² = x² + 7²

y² = 7² + 7²

y² = 98

y = √98 = 7√2

Answer:

f(g(x)) = g(f(x)) = x

Step-by-step explanation:

Lemma;

If f(x) and g(x) are inverses, then the compositions  f(g(x)) = g(f(x)) = x

Answer:

54°

Step-by-step explanation:

Since the triangle is right use the cosine ratio to solve for angle

cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{26}{44}[/tex], hence

? = [tex]cos^{-1}[/tex] ( [tex]\frac{26}{44}[/tex] ) ≈ 54° ( nearest degree )

Answer:

6n

Step-by-step explanation:

Lesson:  ⇒ Algebric Expression

Product: ⇒ multiply

6n is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

B

Step-by-step explanation:

Area of a triangle is given by the formula:

[tex]A=\frac{1}{2}bh[/tex]

Now, we need to solve for b. We multiply the right side, cross multiply, and follow rules of algebra to isolate b. Shown below:

[tex]A=\frac{1}{2}bh\\A=\frac{bh}{2}\\2A=bh\\b=\frac{2A}{h}[/tex]

Thus, b is 2 times A over h, the answer choice B is right.

Answer:

The Answer is B. b equals two times A over h

Hope This Helps!

Answer:

Without any other information the answers could be a and c because they contain the factor x+5

Step-by-step explanation:

f(-5)=0 means that x=-5 is a zero which means x+5 is a factor

Without any other information f can be any of the expressions that have the factor (x+5)

Answer:

A. (x-2)(x+5)(x-3) is the correct answer to this question

Hope it helps!

Answer:

Step-by-step explanation:

16+(-4)-7=16 -(4+7)=16-28 = -12

Answer:

y = 5

Step-by-step explanation:

Given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 2.5 when x = 5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2.5}{5}[/tex] = 0.5

y = 0.5x ← equation of variation

When x = 10, then

y = 0.5 × 10 = 5

Answer:  The correct answer is:  " 5% increase " .

_________________________________________

Step-by-step explanation:

_________________________________________

Note:  The particular "percentage change" is a "percent increase" ; since we are going from "20" to "21" which is an "increased value of "1" .

_________________________________________

Note the formula for "percent increase" ; as follows:

_________________________________________

Percent increase = [(new value - original value)/original value] * 100 ;

_________________________________________

So;  let us "plug in" our known values; to solve for the "percentage change"    

                 →  [i.e. "percent increase" (in this case)] :

_________________________________________

 Percent increase  =  [(21 - 20)/20] * 100 ;

                                =  [1/20] * 100 ;

                                = [100/20] ;

                                = 5.

_________________________________________

The correct answer is:  " 5 % increase" .

_________________________________________

Hope this helps!

  Best wishes to you!

_________________________________________

Answer:

f(g(x)) = x² + 2x +1

Step-by-step explanation:

The given functions are:

f(x) = 4x²

g(x) = x+1

 f(x) = 4x²

(fog)(x) = f(g(x))

f(g(x)) = 4(x+1)²                 [f(x) = x² ]

 we know that (a+b)² = a² + b² + 2ab

f(g(x))  = 4(x²+1²+2(x)(1))

f(g(x))  = 4(x² + 1 + 2x )

f(g(x)) = 4x² + 8x +4

Answer:

y = -4x + 15

Step-by-step explanation:

Slope-intercept form is y = mx + b

m = slope ([tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex])

b = y-intercept (where the line crosses the y-axis)

It doesn't matter which coordinate pair you use for (x₁,y₁).

(x₁,y₁) = (2,7)

(x₂,y₂) = (4,-1)

[tex]\frac{-1 - 7}{4 - 2}[/tex]   Simplify

[tex]\frac{-8}{2}[/tex]   Simplify

-4 = your slope (m)

To get this information into slope-intercept form, you have to plug it into point-slope form, y - y₁ = m(x - x₁). It doesn't matter which coordinate pair you use for (x₁,y₁).

y - y₁ = m(x - x₁)   Let's use (2,7) since it doesn't have negatives.

y - 7 = -4 (x - 2)   Distribute

y - 7 = -4x + 8   Add 7 to both sides

y = -4x + 15

Check your answer by plugging both coordinate pairs in.

y = -4x + 15

7 = -4(2) + 15

7 = -8 + 15

7 = 7

and

-1 = -4(4) + 15

-1 = -16 + 15

-1 = -1

Answer:

y = -4x + 15

Step-by-step explanation:

m = -y₁ + y₂\-x₁ + x₂

Find the Rate of change [Slope] using the above formula:

-7 - 1\-2 + 4 = -4

Next, we use the Point-Slope Formula [y - y₁ = m(x - x₁)] to convert to Slope-Intercept Formula [y = mx + b]:

y + 1 = -4[x - 4]

y + 1 = -4x + 16

- 1 - 1

________________

[tex]y = - 4x + 15[/tex]

I am joyous to assist you anytime.

The multiplicative inverse (or reciprocal) is the number by which you multiply another to get a product of 1.  For any fraction, simply switch the numerator and the denominator. For any whole number, place it under 1.

The reciprocal of 5/9 is 9/5.

Hope this helps!!

Hello There!

To find the reciprocal of a number, just flip the numerator and the denominator so if the numerator is 5 and the denominator is 9, the new numerator would be 9 and the new denominator would be 5.

Our multiplicative inverse of 5/9 is

[tex]\frac{9}{5}[/tex]

Answer: alternate exterior angles

Step-by-step explanation:

Answer:

The answer is the second figure and the vertices of Δ R'S'T' are:

R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

- Now we can solve the problem

∵ R = (6 , 6) , S = (3 , -6) , T = (0 , 3), they are the vertices of ΔRST

- The triangle RST is reflected over the y-axis

- According to the rule above the signs of x-coordinates will change

∵ R = (6 , 6)

∴ Its image is (-6 , 6)

∵ S = (3 , -6)

∴ Its image is (-3 , -6)

∵ T = (0 , 3)

∴ Its image is (0 , 3)

* Now lets look to the figure to find the correct answers

- The image of Δ RST is ΔR'S'T'

∵ The vertices of the image of ΔRST are:

  R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

* The answer is the second figure