EXERCISE 2.1
(a)
1.
An agent sells some articles for Rs 5,500. What commission does he get at 5%?

Answer:

la respuesta es 25

Step-by-step explanation:

para calcular este tanto ciento, sugerimos usar esta formula:

%/100 = parte/total

realizando la multiplicatión en cruz:

25% x 100 = 100 x parte, o

2500 = 100 x parte

ahora es sólo dividir por 100 y obtener la respuesta:

parte = 2500/100 = 25

Greetings from Brasil...

Here, just apply the Metric Relationships to the Rectangle Triangle

AB² = BC · BD

10² = 16 · X

16X = 100

X = 100/16

        simplify

          100 ÷ 4 = 25

          16 ÷ 4 = 4

X = 25/4

In triangles ABD and CAD, The value of x in the figure is,

⇒ x = 25 / 4

Triangle is a three sided polygon, that has three vertices and three angles which has the sum 180 degrees, is called a triangle.

We have to given that;

Two triangles ABD and CAD are similar.

⇒ Δ ABD ≈ Δ CAD

Hence, We can Just apply the Metric Relationships to the Rectangle Triangle as;

⇒ AB² = BC · BD

Substitute all the values , we get;

⇒ 10² = 16 × x

⇒ 16x = 100

Divide by 16 both side, we get;

⇒ x = 100/16

⇒ x = 25/4

Therefore, In triangles ABD and CAD,

We get;

The value of x in the figure is,

⇒ x = 25 / 4

Learn more about the triangle visit;

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Answer:

  a +b -3c +15

Step-by-step explanation:

Write the subtraction you want to perform, use the distributive property, collect terms:

  (3a-4b-c+6) -(2a-5b+2c-9)

  = 3a -4b -c +6 -2a +5b -2c +9 . . . . . . distribute the minus sign

  = a(3-2) +b(-4+5) +c(-1-2) +(6+9) . . . . find and group like terms

  = a +b -3c +15

Answer:

a - b -3c + 15

Step-by-step explanation:

Answer:

CD = √11 and CE = √11

Step-by-step explanation:

We know that m∠D is 45° (by using the sum of interior angles in a triangle) so therefore, ΔDCE is a 45 - 45 - 90 triangle (the 45, 45, and 90 refer to the angle measures). The ratio of sides in a 45 - 45 - 90 triangle is 1 : 1 : √2 where the 1s are the sides and the √2 is the hypotenuse. We need to solve for x in x : x : √22. If you notice that √22 = √2 * √11, we can use this to find x, therefore, x = 1 * √11 = √11 so CD = √11 and CE = √11.

Answer:

[tex]\huge \boxed{CD =\sqrt{11} } \\ \\ \huge \boxed{CE =\sqrt{11} }[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can apply trigonometric functions to solve for the missing sides.

sin θ  = opp/hyp

sin 45 = CD /√22

Multiply both sides by √22.

√22 sin 45 = CD

√11 = CD

cos θ = adj/hyp

cos 45 = CE /√22

Multiply both sides by √22.

√22 cos 45 = CE

√11 = CE

Answer:

the answer is 15

Step-by-step explanation:

f(x)=5(2-x)

f(-1)=5(2-(-1))

f(-1)=5(2+1)

f(-1)=5(3)

f(-1)=15

Answer:

Step-by-step explanation:

Given , x = 7

let's find :

[tex] \sf{5 - 3(x - 1)}[/tex]

Plug the value of x

⇒[tex] \sf{5 - 3(7 - 1)}[/tex]

Subtract 1 from 7

⇒[tex] \sf{5 - 3 \times 6}[/tex]

Multiply the numbers

⇒[tex] \sf{5 - 18}[/tex]

Calculate

⇒[tex] \sf{ - 13}[/tex]

Hope I helped!

Best regards!!

The value of 5-3(x-1) when x=7 is -13.

Evaluation is nothing but to solve an algebraic expression means to find the value of an expression by replacing the value of the variable in it.

To evaluate the expression value, we simply substitute the variable from its given value and simplify the expression by using order of operations.  

In our case, the given expression is:

5-3(x-1)

Substitute the given number i.e., 7 for the variable in the expression:

5-3(7-1)

Solve the bracket first:

5-3(6)

Now solve the multiplication part:

5 - 18

Finally Subtract 5 from -18, we get:

-13

Hence the final value of the expression is -13 at x=7.

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Answer:

Q1)i) Q= 7p

ii) Q= 35

iii) P= 6

Q2)x= 3

Q3) B=4

Answer:

392

Step-by-step explanation:

m = 8 and n = 14

Substituting the values of m and n in the question, we get :

7m + 3mn

=( 7 x 8) +(3 x 8 x 14)

= 56 + 336

= 392

Answer:

356

Step-by-step explanation:

7x8+56

3x8=24

24x14=336

Add everything up

Answer:

[tex]\bold{21.07^\circ}[/tex]

Step-by-step explanation:

The given values can be mapped to an isosceles [tex]\triangle ABC[/tex].

Side AB = AC

Vertical height, AD = 2.1 m

The distance between one side to the other side of ceiling = 10.9 m

To find:

Pitch (Angle of the roof ) = ?

i.e. [tex]\angle B[/tex] or [tex]\angle C[/tex] = ? (because it is isosceles triangle, so both will be equal)

Solution:

As [tex]\triangle ABC[/tex] is isosceles, so vertical height will divide the side BC in two equal parts

i.e. [tex]BD = DC = \frac{1}{2} BC[/tex]

[tex]\therefore BD = \frac{10.9}{2} = 5.45 m[/tex]

In [tex]\triangle ABD[/tex], let us use tangent trigonometric property.

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tanB = \dfrac{AD}{BD}\\\Rightarrow tanB = \dfrac{2.1}{5.45}\\\Rightarrow tanB = 0.385\\\Rightarrow \angle B = tan^{-1}( 0.385)\\\Rightarrow \bold{\angle B = 21.07^\circ}[/tex]

Answer:

c = - [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

The product of the zeros = [tex]\frac{c}{a}[/tex] = [tex]\frac{1}{2}[/tex]

Given

2x² - 3x - 5c

with a = 2 and c = - 5c , then

[tex]\frac{-5c}{2}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

- 10c = 2 ( divide both sides by - 10 )

c = [tex]\frac{2}{-10}[/tex] = - [tex]\frac{1}{5}[/tex]

Answer:

y=1/5x

Step-by-step explanation:

y=mx+c

find m

m = rise/run

m = 2/10

   = 1/5

find c , sub in a co-ordinate (10,2)

2 = 10/5 + c

2 = 2 + c

c = 0

Answer:

jklfhgugt

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Given the illustration in the question

Required:

Use deductive reasoning to prove (a)

From your question, you need only the (b) part and this is done as follows;

Step 1: Represent the number with: n

Step 2: Multiply n by 4: 4n

Step 3: Add 10 to (2) above: 4n + 10

Step 4: Divide (3) above by 2: (4n + 10)/2 = 4n/2 + 10/2 = 2n + 5

Step 5: Subtract 5 from (4): 2n + 5 - 5 = n

Hence, the end result is proved to be 2n

Test this with any of the given illustration in (a) part, your answer will always be 2n

Answer:

The correct option is;

B. The difference of 2 perfect squares

Step-by-step explanation:

Solving a quadratic equation using factoring involves finding the factors of the equation that would yield the result of the quadratic equation

In order to find the roots of the quadratic equation, then the result of the factoring must be equal to zero, in which case, the constant terms in the factors are the solutions of the quadratic equation in opposite sign.

For example, we have;

x² - 5² = 11

We subtract 11 from both sides to get;

x² - 5² - 11  = 11 - 11

x² - 36 = 0

x² - 6² = 0

(x - 6) × (x + 6) = 0

Therefore, x = 6 or -6 which are the opposite sign of the constant terms in the factor.

Answer:

a. and e.

Step-by-step explanation:

Hello, there are two ways to handle this kind of question.

... Either you solve the equation ...

[tex]x^2+4x-9=x+1\\\\x^2+3x-10=0\\\\x^2-2x+5x-10=x(x-2)+5(x-2)=(x+5)(x-2)=0\\\\x= -5 \ \ or \ \ x = 2[/tex]

So the right answers are a. and e.

... Or, you check which answer can be right.

We replace x by 2 and the two expressions are equal.

[tex]2^2+4*2-9=4+8-9=3 \ and \ 2+1=3[/tex]

So this is a. 2

We replace x by 4 and the two expressions are not equal.

[tex]4^2+4*4-9=16+16-9=23 \ and \ 4+1=5[/tex]

So this is not b. 4

We replace x by -7 and the two expressions are not equal.

[tex]7^2-4*7+9=49-28+9=30 \ and \ -7+1=-6[/tex]

So this is not c. -7

We replace x by -3 and the two expressions are not equal.

[tex]3^2-4*3-9=9-12-9=-12 \ and \ -3+1=-2[/tex]

So this is not d. -3

We replace x by -5 and the two expressions are equal.

[tex]5^2-4*5-9=25-20-9=-4 \ and \ -5+1=-4[/tex]

So this is e. -5

We replace x by -4 and the two expressions are not equal.

[tex]4^2-4*4-9=16-16-9=-9 \ and \ -4+1=-3[/tex]

So this is not f. -4

Thank you.

Answer:

Step-by-step explanation:

[tex]3\sqrt{3}\times\sqrt{3}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a\\\\\sqrt{3}\sqrt{3}=3\\\\=3\times\:3\\\\=9[/tex]

Answer:

x = 68 degrees

Step-by-step explanation:

Step 1: We know this is a isosceles triangle

Since we know it is a isosceles triangle it has 2 of the same angle so the unknown side(not x) is 59

Step 2: Use the 2 angles to find 'x'

Angles in a triangle add up to 180 so we subtract 59 x 2 from 180 to get 68

Therefore angle x is 68 degrees

Answer:

Step-by-step explanation:

This is because u have to do the math - LOL

So

- an isosceles has 2 same sides. The pic shows an isosceles triangle

- 2 sides are the same which is 4

- 1 side is different and is 1.5

Same length = Same angles

So

- 4 = 4

- 56 = 56

Total angle - angle 1 - angle 2 = angle 3 or ?

- Total angle = 180

- Angle 1 = 56

- Angle 2 = 56

- Angle 3 = ?

180 - 56 - 56 = 68

Hope this helped,

Kavitha

Answer:

  2.0

Step-by-step explanation:

Subtract the smaller number from the larger to find their difference:

  1.5 -(-0.5) = 2.0

The distance between the given values is 2.0.

Answer:

Step-by-step explanation:

1) Why is f(x)=(3x+1/3)^2+8/9 not the vertex form of f(x)=9x^2+2x+1?

A.The expression has a constant outside of the squared term.

B. The expression is not the product of two binomials.

C. The variable x has a coefficient.

D. Some of the terms are fractions instead of integers.

Vertex form is a(x -h)^2 +k. The coefficient of x inside parentheses is 1. The given form is not vertex form because the leading coefficient has not been removed to outside parentheses.

__

2) What is the vertex of the parabola with the equation y=(x−2)^2+10?

A. (−2, −10)

B. (2, 10)

C. (−2, 10)

D. (2, −10)

Vertex form is a(x -h)^2 +k. Comparing to the given equation, we find the vertex (h, k) = (2, 10).

__

3) For the given function, identify the x- and y-intercepts if any, the vertex, the axis of symmetry, and the maximum or minimum value. f(x)=−x^2+25

A. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,−25). The vertex is (0,−25). The axis of symmetry is x=0. The minimum value of the function is −25.

B. There are no x-intercepts. The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is y=0. The maximum value of the function is 25.

C. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.

D. The x-intercepts are (−25,0) and (25,0). The y-intercept is (0,5). The vertex is (0,5). The axis of symmetry is x=0. The maximum value of the function is 5.

The x-intercepts are the values of x that make y=0. They are (±5, 0). The y-intercept is the value of y when x=0. It is (0, 25).

__

4) A student says that the function f(x)=−x^2−9 has the x-intercepts (−3,0) and (3,0). Is the student correct? If not, explain why.

A. The student is correct.

B. The student is not correct. The equation f(x)=0 has one real solution, so the x-intercept is (9,0).

C. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph has only one x-intercept, (0,0).

D. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph does not have any x-intercepts.

The parabola opens downward and has a maximum value of -9, so cannot cross the x-axis. There are no x-intercepts, hence no real solutions.

Answer:

0

Step-by-step explanation:

The chart shows k(x) and the value of x.

So when x is -3, k(-3) is 0.

Answer:

the answer would be -6 because that is the output of k(-3)

Answer:

3/5

Step-by-step explanation:

A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

[tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex]

Given the conic equation   [tex]r=\frac{3}{5-3cos(\theta)}[/tex]

We have to make the conic equation to be in the form [tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex].

[tex]r=\frac{3}{5-3cos(\theta)}\\\\Multiply\ the\ numerator\ and \ denominator\ by \ 1/5\\r=\frac{3*\frac{1}{5} }{(5-3cos(\theta))*\frac{1}{5}}\\\\r=\frac{3*\frac{1}{5} }{5*\frac{1}{5}-3cos(\theta)*\frac{1}{5}}\\\\r=\frac{\frac{3}{5} }{1-\frac{3}{5}cos(\theta)}[/tex]

Comparing with  [tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex]. gives:

e = 3/5, p = 1

The eccentricity is 3/5

Answer: x<-12

Step-by-step explanation:

let x= the number

2x+9<-15

    2x<-24

      x<-12

Hope this helps!! :)

You may ask any further questions

Step-by-step explanation:

Hello!

        Part A            

Peter can use the fact that 10% of 87 is 8.70 to find the amount he would save because 40% is just 4 times bigger than 10% so he can take 8.70 from to total of the coat 4 times to find out how much it cost.

        Part B            

Using the same method we know that 10% of 64 is 6.40 so we subtract that from the price of the coat 4 times to find out how much it cost

64 - 6.40 = 57.6

57.6 - 6.40 = 51.2

51.2 - 6.40 = 44.8

44.8 - 6.40 - 38.4

The price of the coat is $38.4

Hope this helps!

Answer:

[tex]-\frac{2}{21}[/tex]

Step-by-step explanation:

Step 1: Have a common denominator

[tex]\frac{12}{21}a -\frac{14}{21}a\\[/tex]

Step 2: Subtract to get answer

[tex]\frac{12}{21}a -\frac{14}{21}a = \frac{-2}{21}a[/tex]

Therefore the answer is [tex]\frac{-2}{21}a[/tex]

Answer:

-2/21a

Step-by-step explanation:

The common number  for this two denominator, 7 and 3, is 21.

21/7=3, so you multiply 3 with the numerator 4. giving 12/21a.

You do the same you -2/3a, and you end up getting the equation of:

12/21a-14/21a=-2/21a.

Hope this helps, have a nice day!

Answer:

One solution.

Step-by-step explanation:

Given that the equation is:

[tex]3(y+9)=12y+13[/tex]

To find:

The number of solutions of the given equation = ?

Solution:

First of all, let us learn a concept for number of solutions of a polynomial.

Number of solutions of a polynomial is equal to its degree.

Degree means the highest power of the variable.

Here, the variable is [tex]y[/tex] and it is observable that the highest power of

Therefore, only one solution will be there for the given equation.

Solving the equation:

[tex]3(y+9)=12y+13\\\Rightarrow 3y+27=12y+13\\\Rightarrow 12y-3y=27-13\\\Rightarrow 9y =14\\\Rightarrow \bold{y = \dfrac{14}{9}}[/tex]

The one solution is [tex]\bold{y=\frac{14}{9}}[/tex].

Hence, only one solution.

Hey There Answer  One Solutions

Step-by-step explanation:

Answer:

[tex] Quotient = \frac{8 - 2t}{3} [/tex]

Step-by-step explanation:

Quotient, in maths, is what you get when two number or expressions together. That is, dividend over the divisor.

Thus, from what we're given:

dividend is 8 decreased by 2 times t, which can be expressed as [tex] 8 - 2*t = 8 - 2t [/tex].

The divisor is 3.

[tex] Quotient = \frac{8 - 2t}{3} [/tex]

Answer:

x = 4

Step-by-step explanation:

16 × 7 = 112

2^4 = 16

so that is the answer

Quilt

Step-by-step explanation: