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Mary is three times as old as her son. In 12 years, Mary's age will be one year less than her son's age. How old is each now?

OC represents vector a and b drawn using the head-to-tail method.

A vector is an object that has both magnitude and direction.

The given vectors are

a =<5, −1> and b =<2,−2>

Representing vector a +b using the head and tail method

Here in the image attached with the answer ,

The vector a is represented by OA and the vector b is represented by OB

By head and tail method , the OC is drawn by extending the vector a towards b and b towards a

Vector OC = Vector OA + Vector OB

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Answer:

6/6

Step-by-step explanation:

6/6 not equal -1/1 so these lines intersect each other at only one point hence these have only one solution.

Answer:

I can give you the answer if you can answer a question

Step-by-step explanation:

Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,

Area of triangle = 0.5 × 4cm × 11cm

Area of triangle = 22 cm²

Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,

Volume of the triangular prism = 22cm² × 3cm = 66cm³

Hence, the volume of the triangular prism is 66cm².

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Answer:

32 km/hr

Step-by-step explanation:

Firstly, you need to find the speed of both trains in km/hr.

Paolo's train= (70km x 60hr)/35= 120 km/hr

Monika's train= 684km/4.5hr= 152 km/hr

Then find the difference in speed:

152-120=32 km/hr

Using translation concepts, it is found that this transformation can be described as a reflection across the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, considering the vertices of quadrilateral 1 and quadrilateral 2, the transformation from quadrilateral 1 to quadrilateral 2 has the following format:

(x,y) -> (x, -y).

Which means that it can be described as a reflection across the x-axis.

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Answer:

15cm

Step-by-step explanation:

PC = 15

BR = 15

.

............................................

Answer:

Step-by-step explanation:

Remark

An altitude is a very special line. It must start from one of the angles and connect with the side opposite that angle. The connection must form a right angle.

It cannot start anywhere else -- certainly not in the middle of a line which would make the altitude of random importance. It could not be accurately reproduced.

Answer:

You can make 10 tortillas with one and a half kilograms of ground meat

Step-by-step explanation:

one and a half kilograms to grams

1.5kg x 1000 = 1500g

150 grams prepared to make 1 hamburger

than, 150 x h = 1500

h = 1500 / 150

h = 10

Answer:

10 tortillas

Step-by-step explanation:

First convert kilograms to grams:

   1 kg = 1000 g

⇒ 1.5 kg = 1500 g

Let x = number of tortillas made with 1500 g of meat

Set up a ratio of tortillas and meat and solve for x:

⇒ 1 tortilla : x tortillas = 150 g meat : 1500 g meat

[tex]\sf \implies \dfrac{1}{x}=\dfrac{150}{1500}[/tex]

[tex]\sf \implies 1 \cdot 1500= 150 \cdot x[/tex]

[tex]\sf \implies 1500=150x[/tex]

[tex]\implies \sf x=\dfrac{1500}{150}[/tex]

[tex]\implies \sf x=10[/tex]

Therefore, 10 tortillas can be made with 1.5 kg of ground meat.

Sin3A=Cos3A

Cos(90-3A)=Cos3A

90-3A=3A

90=3A+3A

90=6A

90/6=A

^•^

The answer is A=15

The value of t is 6.65

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.

Given:

A= 210 million

P= A e^(kt)

225 = 210 * e ^ (0.0069t)

225/210=  e ^ (0.0069t)

1.07 =  e ^ (0.0069t)

Taking log on both side

log  1.047 = 0.0069 t log e

[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]

t= log ( 1.047) / 0.0069

t= 6.65

Hence, value of t is 6.65.

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Answer:

Step-by-step explanation:

In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.

It is a polygon with four sides. The total interior angle is 360 degrees.

Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.

Kyle's claim is Incorrect. Because the shapes are square and rhombus.

In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.

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The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.

The climate in which these mice live has slowly gotten colder.

The change in the environment most likely affect the mouse population will be

The adjustment of thicker fur will be selected over thinner fur, and the population will develop.

Then the correct option is D.

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Answer:

  14.7 quarts

Step-by-step explanation:

Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.

__

  quarts/liters = x/14 = 1/0.95 . . . . . the conversion is given as 1 qt = 0.95 L

Multiply by 14 to find x.

  x = 14(1/0.95) ≈ 14.7

There are about 14.7 quarts in 14 liters.

_____

Additional comment

You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.

  [tex](14\text{ liters})\times\dfrac{1\text{ quart}}{0.95\text{ liter}}=\dfrac{14}{0.95}\text{ quarts}\approx14.7\text{ quarts}[/tex]

This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)

You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.

Answer:

(a) = 13

(b) = 8

(c) = 5

Step-by-step explanation:

Addition theorems on sets are

Theorem 1 :

n(AuB) = n(A) + n(B) - n(AnB)

Theorem 2 :

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Total number of students in the school is not given

so let there are 60 students in the school

using theorem 2

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

   60             =    40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)

60 +73 -120 = n(AnBnC)

         13         = n(AnBnC)

therefore, there are total 13 students who take all three subjects

Number of students who had taken only Mathematics  =
n(A) - n(AnB) - n(AnC) + n(AnBnC)

40 - 20 - 25 + 13

53 - 45 = 8 students

Number of students who had taken only Physics  =

n(B) - n(BnA) - n(BnC) + n(AnBnC)

42 - 20 - 28 + 13

53 - 48 = 5 students

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Answer:

No solution

Step-by-step explanation:

 7x + 2y = 16 ----------------(I)

-21x - 6y = 24 -----------------(II)

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{7}{-21}=\dfrac{-1}{3}\\[/tex]

[tex]\sf \dfrac{b_1}{b_2}=\dfrac{2}{-6}=\dfrac{-1}{3}[/tex]

[tex]\sf \dfrac{c_1}{c_2} =\dfrac{16}{24}=\dfrac{2}{3}\\\\ \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}[/tex]

So, the lines are parallel and has no solution

Answer:

parameter

Step-by-step explanation:

Answer:

  B. II  (6, 8, 10)

Step-by-step explanation:

A set of triangle side lengths will form a right triangle if they satisfy the Pythagorean theorem. The sum of squares of the shortest two sides must equal the square of the longest side.

__

Sets of integers that satisfy the Pythagorean theorem are called "Pythagorean triples." Some of these for smaller integers are ...

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)

If small integer side lengths are not one of these triples, or a multiple of one of these triples, they will not form a right triangle.

I. not a match to any triple

II. matches (3, 4, 5) multiplied by 2 -- a right triangle

III. not a match to any triple

IV. not a match to any triple

_____

Of course, you can actually compute the squares to see if they satisfy the Pythagorean theorem:

I. 4² +5² = 41 ≠ 6² (acute triangle)

II. 6² +8² = 100 = 10² -- right triangle

III. 5² +13² = 194 ≠ 14² (obtuse triangle)

IV. 7² +11² = 170 ≠ 13² (acute triangle)

__

The sum f = a² +b² -c² (where c is the longest side) can be considered to be a "form factor" for the triangle. For ...

This "form factor" is related to the largest angle (C) by ...

  cos(C) = f/(2ab)

Answer:

s. p = 270 Rs

discount = 10%

mp.= ?

Mp = s. p + discount

= 270 + 10/100*270

= 270 + 27

= 297 Rs

Answer:

[tex]\huge\boxed{\sf Rs.\ 297}[/tex]

Step-by-step explanation:

Selling Price = Rs. 270

Discount = 10%

= 10% of 250

[tex]\displaystyle =\frac{10}{100} \times 270[/tex]

= 1 × 27

= Rs. 27

= Selling Price + Discount

= 270 + 27

= Rs. 297

[tex]\rule[225]{225}{2}[/tex]

Answer:

Ok ya sure I would love to. :)

Step-by-step explanation:

Oh wait….

*Crickets chirping*

The complete question is

"Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?"

The solution is the intersection region of all the solutions in the system of inequalities.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

We know that the lines are given as;

x + 3y = -3

y = 1/2 x + 1

Solving for "y" from the first line;

3y = -3 - x

y = -1 - x/3

For the line x + 3y = -3  the x-intercepts;

y = 0

y = -1 - x/3

0 = -1 - x/3

x/3 = -1

x = -3

And the y-intercept;

y = -1

For the line y = 1/2 x + 1 the x-intercepts;

y = 0

0= 1/2 x + 1

1/2x = -1

x = -2

And the y-intercept

x = 0

y = 1

Now we can graph both lines,

The solution is the intersection region of all the solutions in the system of inequalities.

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Answer:

[tex]\huge\boxed{2400}[/tex]

Useful Information:

The formula for compound interest is: [tex]initial.amount*interest.rate^{no.years}[/tex]

Step-by-step explanation:

To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 5% by 100, which gives you 0.05. This is because percentages are out of 100.

The next step is to add 1 to 0.05, this gives you 1.05. This is because you are working out the percentage increase.

The next step is to substitute the values into the formula. This gives you[tex]initial.amount*1.05^{3}=2778.30[/tex]

To work out the initial value, you would divide the final amount of 2778.30 by [tex]1.05^3[/tex], which gives you 2400. This is because you are rearranging the formula to find the initial investment.

1) Divide 5 by 100.

[tex]\frac{5}{100}=0.05[/tex]

2) Add 1 to 0.05.

[tex]1+0.05=1.05[/tex]

3) Substitute the values into the formula.

[tex]initial.amount*1.05^{3}=2778.30[/tex]

4) Divide 2778.30 by [tex]1.05^3[/tex].

[tex]\frac{2778.30}{1.05^3}=2400[/tex]

Answer:

Jim:  2/9

Step-by-step explanation:

8/9-4/6

48/54-36/54          [Convert each fraction to a common denominator:  54

                              Multiply (8/9)*(6/6)=48/54;  Multiply (4/6)*(9/9) = 36/54]

 48/54-36/54 = 12/54

12/54 can be reduced to 2/9

Jim also has 2/9

Sue- 8/9-4/6=4/3 or 1 1/3:  Sue subtracted both the numerator and denominator.  This is not correct.

Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9:  Good Job Jim

Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27:  Bob converted both denominators to 54, but did not multiply the numerators by the same numbers.  Bad Bob.

The proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The proof will be given as:-

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{tanx}{coscxCosx}+\dfrac{Cosx}{CoscxCosx}\\\\[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =\dfrac{\dfrac{Sinx}{Cosx}}{\dfrac{Cosx}{Sinx}}+\dfrac{\dfrac{Cosx}{Sinx}}{\dfrac{Cosx}{Sinx}}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{Sin^2x}{Cos^2x}+1[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = tan^2x+1}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =Sec^2x[/tex]

Therefore the proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

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Answer:

[tex]\dfrac{26}{3}[/tex]

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

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

Given interval:  1 ≤ x ≤ 4

Therefore, a = 1 and b = 4

Therefore, find the value of the given function when x = 1 and x = 4:

[tex]\begin{aligned}\implies f(1) & =3^{1-1}+2\\ & = 3^0+2\\ & = 1+2\\ & = 3 \end{aligned}[/tex]

[tex]\begin{aligned} \implies f(4) & = 3^{4-1}+2 \\ & = 3^3+2\\ & = 27+2\\ & = 29 \end{aligned}[/tex]

Substitute the found values into the formula:

[tex]\begin{aligned}\implies \dfrac{f(b)-f(a)}{b-a} & =\dfrac{f(4)-f(1)}{4-1}\\\\ & =\dfrac{29-3}{4-1}\\\\ & = \dfrac{26}{3} \end{aligned}[/tex]

Answer:

(−∞,1)

Step-by-step explanation:

Answer:

The rectangular table

Step-by-step explanation:

Square table: 36*36=1296

Rectangular table: 20*42=1460 [tex]in^{2}[/tex]

Circular table: [tex]\pi * 21^{2}[/tex]≅1384

Answer:

minimum value is 3, maximum value is 4.459

Step-by-step explanation:

[tex] log_{2}(8) = \frac{ log(8) }{ log(2) } = 3[/tex]

[tex] log_{2}(22) = \frac{ log(22) }{ log(2) } = 4.459[/tex]