Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.

Answer:

1) Let D be the number of dimes and Q be the number of quarters. We can set up the following system of equations to represent the given information:

D + Q = 65

0.1D + 0.25Q = 10.70

The first equation represents the total number of coins Victoria has, and the second equation represents the total value of those coins in dollars. Solving this system of equations will give us the number of dimes and quarters Victoria has.

2) Let M be the number of hours Max spends mowing lawns and T be the number of hours he spends tutoring. We can set up the following system of equations to represent the given information:

M + T = 14

12M + 15T = 192

The first equation represents the total number of hours Max worked over the weekend, and the second equation represents the total amount of money he made during that time. Solving this system of equations will give us the number of hours Max spent on each job.

The additional expense brought on by reducing the quantity is known as the cost. An additional expense "at the margin" is another name for this. The extra income that results from raising the supply is known as the marginal revenue.

Profit is defined as the difference of revenue and cost (determined by deducting cost from revenue. when revenue exceeds operational expenses, the difference between them is called the operating profit.

The additional money "at the margin" is another name for this.The money left over after a corporation pays its bills and expenses is known as its profit. Costs are the out-of-pocket expenditures comes to making, producing, and marketing the company's goods and services.

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Answer:

Step-by-step explanation:

0.124

Answer:14 a

Step-by-step explanation:

The explanation is that it is E

Answer: 48 cm

Step-by-step explanation:

12 + 12 + 12 + 12 = 48

Answer:

(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!

Step-by-step explanation:

Given the system of equation, [tex]\left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.[/tex], solve by elimination.

[tex]\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.[/tex] , multiply the top equation by -2.

We get,  [tex]\left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex]

[tex]+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex], add the equations together.

We get, [tex]-15y=75[/tex], we just eliminated the variable, x, we can now solve this equation for y.

[tex]-15y=-75 = > y=\frac{-75}{-15}[/tex], [tex]y=\frac{75}{15} = > y=5[/tex]

We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...

[tex]x+6y=28 = > x+6(5)=28 = > x+30=28[/tex], subtract the value, 30, from both sides. We get, [tex]x=-2[/tex].

We found the value x, x=-2.

Thus the solution to the given system of equations is (-2,5).

Answer:

(-2, 5)

Step-by-step explanation:

Given linear system of equations:

[tex]\begin{cases}x+6y=28\\2x-3y=-19\end{cases}[/tex]

To solve by the method of elimination, first multiply the first equation by -2:

[tex]\implies -2 (x+6y=28)[/tex]

[tex]\implies -2x-12y=-56[/tex]

Add this to the second equation to eliminate the term in x:

[tex]\begin{array}{lrcrcr}& 2x & - & 3y & = & -19\\+\vphantom{\dfrac12}&(-2x & - & 12y & = & -56\\\cline{2-6}&\vphantom{\dfrac12}&- & 15y & = &-75\end{array}[/tex]

Solve the expression for y:

[tex]\implies -15y=-75[/tex]

[tex]\implies y=5[/tex]

Substitute the found value of y into the expression for x and solve for x:

[tex]\implies x=28-6(5)[/tex]

[tex]\implies x=28-30[/tex]

[tex]\implies x=-2[/tex]

Check by substituting the found values of x and y into both equations.

Equation 1

[tex]\implies -2+6(5)=-2+30=28[/tex]

Equation 2

[tex]\implies 2(-2)-3(5)=-4-15=-19[/tex]

Hence proving that the solution (-2, 5) is true.

A percentage of Bashir's commute that would be shorter than 32 minutes, to the nearest 10th is 50%.

Mathematically, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

Substituting the parameters into the z-score formula, we have;

Z-score, z = (32 - 32)/3

Z-score, z = 0/3

Z-score, z = 0

Since a commute of 32 minutes on a test has a z-score of 0, the percentage of Bahir's commute that would be shorter than 32 minutes can be calculated as follows:

P(x > 32) = P(z > 0)

P(z > 0) = 0.5

P(z > 0) = 50%.

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Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 137

x= y + 47

To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.

In this case, substituting the second equation in the first one you get:

y + 47 + y= 137

Solving:

y+ y= 137 -47

2y= 90

y= 90÷2

y= 45

Replacing this value in the second equation, you get:

x= 45 + 47

x= 92

Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.

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The amount of money that was spent is $120.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this case, the women went to Shopping and first she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining.

The fraction of money left will be:

= 1 - 4/5 - (2/3 × 1/5)

= 1 - 4/5 - 2/15

= 1/15

Since she had $10 left the original amount will be:

= $10 ÷ 1/15

= $10 × 15

= $150

The amount spent will be:

= 4/5 × $150

= $120

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The value of x and y in equations 17x - y = 40 and 2x + 4y = 50 are x = 3 and y = 11.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

17x - y = 40  ⇒ (1)

2x + 4y = 50 ⇒ (2)

(1)* 4

68x - 4y = 160

Adding equation (1) and (2)

68x - 4y = 160

2x + 4y = 50

⇒ 70 x = 210

        x = 3

Substituting the value of x in equation (1)

17*3 - y = 40

51 - y = 40

-y = 40 - 51

-y = -11

y = 11

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Answer:

From left to right picture,

Scale factor = 2/3

x = 24

y = 12

z = 21

Step-by-step explanation:

Look at the two figures and identify the sides where both lengths are known.

That is the top right-hand side.

Scale factor is hence 18/27 = 2/3

Next, find x, y and z:

Bottom left-hand side:   16/x = 2/3

                                            x = 3/2 x 16

                                             x = 24

Bottom right-hand side:    y/18 = 2/3

                                            y = 18 x 2/3

                                             y = 12

Top left-hand side:       14/z = 2/3

                                           z = 3/2 x 14

                                            z = 21

The line that passes through these two points is y=x-2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here function whose graph contains the points (9, 7) and (4, −8)

Thus using the two point formula for a line we get the equation as              y-7=(x-9)

y=x-2

Hence, The line that passes through these two points is y=x-2

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Answer:

70

Step-by-step explanation:

for every 5 $20 notes is $100 70 notes is $1400 and the other 20 is $2000 which makes 3400

If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that mean of 100 nummerical observations is 51.82

We need to find the sum of all the observations

The formula to find mean is mean=Sum of observations/ Number of observation

From given mean=51.82

Number of observations =100

Let us take x as sum of all 100 numbers

So 51.82=x/100

Now apply cross multiplication

x=51.82×100

x=5182

Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.

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So the expanded form of the odometer reading 35,467.219 is:

5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000

A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.

5 stands for 5 x 1,000 miles

3 stands for 3 x 100 miles

4 stands for 4 x 10 miles

6 stands for 6 x 1 miles

7 stands for 7 x 1/10 of a mile

2 stands for 2 x 1/100 of a mile

1 stands for 1 x 1/1000 of a mile

9 stands for 9 x 1/10000 of a mile

So the expanded form of the odometer reading 35,467.219 is:

5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000

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Work Shown:

area = length*width

length = area/width

length = 3162/51

length = 62 meters

Answer:

A 0.9102

Step-by-step explanation:

A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.

The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.

A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.

A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.

Hence, the correlation coefficient is A, 0.9102

We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -

[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]

Given is the inequality -

3 (m + n)! ≥ m! + n!

We have -

3 (m + n)!

3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}

3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)

3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)

Now, for (m! + n!) --

(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

It can be seen that -

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥

m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

Hence, it can be seen that -

3 (m + n)! ≥ m! + n!

Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.

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Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

A. A function that represents the attendance after t years can be written as y = 20,000(1 + 0.05t)

What does a math function mean?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

This function represents the initial attendance of 20,000, multiplied by 1 + 5% increase each year (0.05) times the number of years (t).

B. To find out about how many people will attend the festival in the fifth year, we can substitute t = 5 into the function.

y = 20,000(1 + 0.05 * 5)

y = 20,000(1 + 0.25)

y = 20,000(1.25)

y = 25,000

So, approximately 25,000 people will attend the festival in the fifth year.

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Using equations, the weights of the four fish are as follows:

Equations are mathematical statements showing the equality of two mathematical expressions.

Using the equation sign (=), equations depict that expressions are equal or equivalent.

The total weight of the four fish = 1,032

Let the weight of the Amberjack = x

Weight of the Tarpon = 2x

Weight of the White Marlin = 4x (2 x 2x)

Weight of the Tuna = 5x

x + 2x + 4x + 5x = 1,032

12x = 1,032

x = 86

Amberjack = 86 pounds (x)

Tarpon = 172 pounds (2x)

White Marlin = 344 pounds (4x)

Tuna = 430 pounds (5x)

Total weight = 1,032 pounds (86 + 172 + 344 + 430)

Thus, we solved the weight of each fish using equations.

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How much did each fish weigh?

Answer:

25

Step-by-step explanation:

5x5 = 25

Answer:

25

Step-by-step explanation:

Let's go through our times tables really quick!

5x1 = 5 (5 + 0)

5x2 = 10 (5 + 5)

5x3 = 15 (5 + 5 + 5 [10 + 5])

5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)

As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5

So, 5x5 is 25

Hope this helped!

[tex]\dfrac{s}{4} +5=13[/tex]

Simplify:

[tex]\dfrac{1}{4} s+5=13[/tex]

Subtract 5 from both sides:

[tex]\dfrac{1}{4} s+5-5=13-5[/tex]

[tex]\dfrac{1}{4} s=8[/tex]

Multiply both sides by 4:

[tex]4\times(\dfrac{1}{4} s)=4\times(8)[/tex]

[tex]\fbox{s = 32}[/tex]

s = 32.

[tex]\frac{s}{4} +5=13[/tex]

[tex]\frac{s}{4} +5-5=13-5\\ \\\frac{s}{4} =8[/tex]

[tex]\frac{s}{4}*4 =8*4\\ \\s=32[/tex]

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "s" by it's calculated value, 32.

[tex]\frac{(32)}{4} +5=13\\ \\8+5=13\\ \\13=13[/tex]

As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!

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The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Advantages include:

Disadvantages:

Additional expenses include

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Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Step-by-step explanation:

Let x = number of ounces of 63% solution.

Let y = number of ounces of 33% solution.

The total solution to be made is 100 oz.

x + y = 100

x ounces of 63% solution is 0.63x ounces of acid.

y ounces of 33% solution is 0.33y ounces of acid.

100 ounces of 39% solution is 39 ounces of acid

0.63x + 0.33y = 39

The system of equations is

x + y = 100

0.63x + 0.33y = 39

Multiply the both sides of the first equation by -0.33. Then add it to the second equation.

         -0.33x - 0.33y = -33

    +    0.63x + 0.33y = 39

   ---------------------------------

             0.3x             = 6

x = 6/0.3

x = 20

x + y = 100

20 + y = 100

y = 80

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Answer:

Dylan should purchase the 10-lens boxes in packs of 4 for $120, as this is the better deal. This option provides 40 lenses for $120, which works out to be $3 per lens. The 8-lens boxes in packs of 2 for $52 only provides 16 lenses for $52, which works out to be $3.25 per lens Therefore, the 10-lens boxes in packs of 4 is the better deal.

Step-by-step explanation:

Answer:

he should buy the 10-lens boxes in packs of 4 for $120

Step-by-step explanation:

22/7×14×14×12

the answer is 7392

The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.

An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.

y=mx+c

Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.

[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]

[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]

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Answer:

Step-by-step explanation:buordjkdkeek