4. A rectangle measures 20cm by 15cm If each dimension is increased by 2.5cm by what percentage is a) The perimeter of the rectangle increased b) The area of the rectangle is increased​

Answer:

hello

Step-by-step explanation:

there is my answer

hope it helps

Answer:

the range in interval notation is (-4, 4).

Step-by-step explanation:

"Range" refers to the set of numbers that contains all possible values of y that a given function can take on.  In this diagram we see that the smallest possible y-value is -4 and the largest is +4, not inclusive (the set does not contain either -4 or +4).  Thus, the range in interval notation is (-4, 4).

Answer:

Step-by-step explanation:

Properties of an Isosceles Triangle

(Most of this can be found in Chapter 1 of B&B.)

Definition: A triangle is isosceles if two if its sides are equal.

We want to prove the following properties of isosceles triangles.

Theorem: Let ABC be an isosceles triangle with AB = AC.  Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC).  Then

a)      Triangle ABM is congruent to triangle ACM.

b)      Angle ABC = Angle ACB (base angles are equal)

c)      Angle AMB = Angle AMC = right angle.

d)      Angle BAM = angle CAM

Corollary: Consequently, from these facts and the definitions:

Ray AM is the angle bisector of angle BAC.

Line AM is the altitude of triangle ABC through A.

Line AM is the perpendicular bisector of B

Segment AM is the median of triangle ABC through A.

Proof #1 of Theorem (after B&B)

Let the angle bisector of BAC intersect segment BC at point D.  

Since ray AD is the angle bisector, angle BAD = angle CAD.  

The segment AD = AD = itself.

Also, AB = AC since the triangle is isosceles.

Thus, triangle BAD is congruent to CAD by SAS (side-angle-side).

This means that triangle BAD = triangle CAD, and corresponding sides and angles are equal, namely:

DB = DC,

angle ABD = angle ACD,

angle ADB = angle ADC.

(Proof of a).  Since DB = DC, this means D = M by definition of the midpoint.  Thus triangle ABM = triangle ACM.

(Proof of b) Since angle ABD = angle ABC (same angle) and also angle ACD = angle ACB, this implies angle ABC = angle ACB.

(Proof of c) From congruence of triangles, angle AMB = angle AMC.  But by addition of angles, angle AMB + angle AMC = straight angle = 180 degrees.  Thus 2 angle AMB = straight angle and angle AMB = right angle.

(Proof of d) Since D = M, the congruence angle BAM = angle CAM follows from the definition of D.  (These are also corresponding angles in congruent triangles ABM and ACM.)

QED*

*Note:  There is one point of this proof that needs a more careful “protractor axiom”.  When we constructed the angle bisector of BAC, we assumed that this ray intersects segment BC.  This can’t be quite deduced from the B&B form of the axioms.  One of the axioms needs a little strengthening.

The other statements are immediate consequence of these relations and the definitions of angle bisector, altitude, perpendicular bisector, and median.  (Look them up!)

Definition:  We will call the special line AM the line of symmetry of the isosceles triangle.  Thus we can construct AM as the line through A and the midpoint, or the angle bisector, or altitude or perpendicular bisector of BC. Shortly we will give a general definition of line of symmetry that applies to many kinds of figure.

Proof #2 (This is a slick use of SAS, not presented Monday.  We may discuss in class Wednesday.)

The hypothesis of the theorem is that AB = AC.  Also, AC = AB (!) and angle BAC = angle CAB (same angle).  Thus triangle BAC is congruent to triangle BAC by SAS.

The corresponding angles and sides are equal, so the base angle ABC = angle ACB.

Let M be the midpoint of BC.  By definition of midpoint, MB = MC. Also the equality of base angles gives angle ABM = angle ABC = angle ACB = angle ACM.  Since we already are given BA = CA, this means that triangle ABM = triangle ACM by SAS.

From these congruent triangles then we conclude as before:

Angle BAM = angle CAM (so ray AM is the bisector of angle BAC)

Angle AMB = angle AMC = right angle (so line MA is the perpendicular bisector of  BC and also the altitude of ABC through A)

QED

Faulty Proof #3.  Can you find the hole in this proof?)

In triangle ABC, AB = AC.  Let M be the midpoint and MA be the perpendicular bisector of BC.

Then angle BMA = angle CMA = right angle, since MA is perpendicular bisector.  

MB = MC by definition of midpoint. (M is midpoint since MA is perpendicular bisector.)

AM = AM (self).

So triangle AMB = triangle AMC by SAS.

Then the other equal angles ABC = ACB and angle BAM = angle CAM follow from corresponding parts of congruent triangles.  And the rest is as before.

QED??

Yes, This statement is valid.

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

Given that;

The two sides of a triangle are congruent.

Then, In ΔABC;

⇒ AB ≅ BC

So, ΔABC is isosceles.

Now,

Since, The two sides of a triangle are congruent.

We know that;

In a triangle if two sides are equal then it is an Isosceles triangle.

So, The given statement '' ΔABC is isosceles'' is valid.

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Answer:

c: 35/2

Step-by-step explanation:

70/4 = 35/2

35/2 is the simplest answer and how much Jacob earns for each yard he mows.

Answer:

[tex]-(\frac{3}{7})^3[/tex]

Step-by-step explanation:

Since we see that 3/7 is multiplied by itself three times, we can use exponents as a shorter way to write this. The expontent tells us how many times the base number, 3/7, is multiplied by itself.

[tex]-1 * (\frac{3}{7})^3[/tex]= [tex]-1 * \frac{3}{7} * \frac{3}{7} * \frac{3}{7}[/tex]

We then multiply by -1 to (3/7)^3 to get the exact answer.

[tex]-(\frac{3}{7})^3[/tex]

Answers and Step-by-step explanation:

a. The independent variable is the variable being manually changed by the experimenter. The dependent variable is the variable being affected by the independent variable. X (members joining the fitness club) is the independent variable. Y (total monthly cost) is the dependent variable.

b. The domain is 6, because x is always the domain. The range is 77, because Y is always the range. You plug in 6 (the domain which is x), and get 77.

c. Yes, this relation is a function. Relations are only not functions when one singular input (domain) goes to 2 outputs (range).

    A domain can not have multiple ranges. A range can have multiple domains though.

The y is the dependent variable and the x is the independent variable, in the equation y = 7x + 35, The domain is 6 and the range is 77 for the given equation. Yes, it is a function.

In other terms, it is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

y = 7x + 35, x members joining the fitness club and y is cost.

(a) As you can see from the equation, y depends on the value of x,

(b) Calculate the amount of x = 6 (as given)

y = 7 × 6 + 35

y = 42 + 35

y = $77

The domain of the function is 6 and the range is 77.

(c) Yes, as we put the values in x, y also changes, so it is a function.

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Answer:

y = 0x - 5 or just y = -5

Step-by-step explanation:

use the slope intercept equation

y2 - y1

x2 - x1

- 5 - 9 = 14

-3 + 3 = 0

14 / 0 = 0

so the slope is undefined

take one of the points (let's use -3, -5) and plug that in the slope intercept form (y = mx+b)

so -5 = 0(-3)+b

0 • 3 = 0 so the b (or y intercept) equals -5

so the equation is y = -5

Answer:

$200

Step-by-step explanation:

first you find the percentage of the money

so 60% of $500

second add/subtract the answer you get to/from the amount given

in this case subtract the answer you get from 500 and thats it there's your answer.

Answer:0.012345

Step-by-step explanation: km=mm/1000000 so 12345/1000000=0.012345mm

The direct distance from the school to the library, travelled by Alice can be

found using Pythagoras's theorem.

The number of miles Britney travelled more than Alice is; 8 miles

Reason:

The distance, d, between points given their coordinates, (x₁, y₁), (x₂, y₂) can

be found with the formula;

[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]

The above formula can be obtained using Pythagoras's theorem.

The distances travelled by Britney are;

Distance from the school to the mall = [tex]\sqrt{(10 - 10)^2 + (6 - (-4))^2}[/tex] = 10

Distance from the mall to the library = [tex]\sqrt{(-14 - 10)^2 + (6 - 6)^2}[/tex] = 24

Total distance travelled by Britney = 24 miles + 10 miles = 34 miles

The distance travelled by Alice is from the school to the library, which

gives; Alice's distance = [tex]\sqrt{(10 - (-14))^2 + (-4 - 6)^2}[/tex] = 26

Distance travelled by Alice from the school to the library is 26 miles

The number of miles more Britney traveled is 34 miles - 26 miles = 8 miles

Therefore;

Britney traveled 8 miles more than Alice

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Answer:

28.914

Step-by-step explanation:

Answer: $165

Step-by-step explanation: Divide the new price by 1, + the percent of increase. 198 / 1.20 = 165

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Answer:

Well to calculate percentage decrease

(Starting value- ending value / starting value)* 100

so 30-18=12

12/30= 2/5

2/5*100= 200/5

40 percent

Now thats the amount lost so

100%-40%=60%

60% reduction

plug the points into y2-y1/x2-x1:

[tex] \frac{7 - 7}{8 - 0} [/tex]

Now do the subtraction on both the bottom and top:

[tex] \frac{7 - 7 }{8 - 0} = \frac{0}{8} [/tex]

0 divided by a number will equal 0, so the slope is 0.

Answer:

[tex]f( - 9) = - 3 |( - 9) + 5| = - 3 | - 4| \\ = - 3 \times 4 = - 12[/tex]

Answer:

The answer is 9/10.

Step-by-step explanation:

Step 1: 3/4/5/6. This means, 3/4 is being divided by 5/6 and so you write it in that form. Take this for an example. 2/4 divided by 3 is 2/4/3.

Step 2: 3/4 ÷ 5/6. This is because, we want the question to be easy to simplify. Also, we want to write the division question as a multiplication problem. And this sign ( / ) means to divide.

Step 3: 3/4 × 6/5. This is because in Maths, when a fraction is dividing another fraction, that fraction is reciprocated ( the fraction at the right side.) Reciprocated here means the denominator is made the numerator and the numerator is made the denominator.

Step 4: 3/2 × 3/5. How? We cancelled out. 2 goes into 4 twice and into 6 thrice.

Step 5: 9/10. We multiplied 3/2 × 3/5 to get 9/10.

Step-by-step explanation:

3x3x3x3x3x3 = 3^6

3x3x3 = none

6x6x6 = 6^3

6+6+6 = 6x3

3 + 6 = none

3+3+3+3+3+3 = none

Answer:

For box 3^6:

3×3×3×3×3×3

For box 6^3:

6×6×6

For box 6×3:

6+6+6

3+3+3+3+3+3

For None:

6+3

3×3×3

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Answer:

D. x = 12

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

69 divided be 3

= 23

step 2

23 + 23 = 46 ( Alvin age)

step 3

69 -46= 23 Elga age

Answer:

Elga's age is 23

Step-by-step explanation:

To solve this, we need to make our equation.

2x+x=69

In this equation, 2x is Alvin's age, while Elga's age is x. The 69 is the sum of their ages.

Combine the like terms in this equation.

3x=69

Divide both sides by 3

3/3x=69/3

x=23

Elga's age is 23, but we still need to check to make sure we are correct.

To do this, plug in 23 for x.

2(23)+23=69

46+23=69

69=69

Do we get a true statement? Yes, so we are correct.

The sets can either be presented in set builder form or roaster form. The

given sets presented in the required form are;

a. The set B is the set of days in the week that starts with letter S

Therefore;

The elements of B are; Saturday, Sunday

In roster method, we have; B = {Saturday, Sunday}

In set builder notation, we have; B = {x | x is a days in the week that starts with letter S}

b. C is the set of letters in PHILIPPINES

In roster form, we have; C = {P, H, I, L, I, P, P, I, N, E, S}

In set builder notation, we have; C = {Letters in the word PHILLIPINES}

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The expression that could be used to calculate the perimeter of the following circle is 2π(5)

The perimeter is also known as the circumference of a circle. The formula for calculating the perimeter of a circle is expressed as;
C =2πr

where

r is the radius of the circle

Determine the radius

r = 10/2

r = 5cm

Substitute

C = 2π(5)

Hence the expression that could be used to calculate the perimeter of the following circle is 2π(5)

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Answer:

GIVEN :

SOLUTION :

[tex] \large{ \tt{A \times B = \{ \: 1 \:, 2 \: ,3 \} \: \times \: \{ \: i, \: o ,\: u \}}}[/tex]

[tex] \large{ \tt{= \{ \: (1 \:, i \: ) \: (1 \: ,o \: ) \: (1 \: ,u \: ) \: (2 \:, i) \: (2 \: ,o \: ) \: (2 \:, u) \: (3 \:, i) \: (3 \:, o) \: (3 \: ,u) \}}}[/tex]

-Hope I helped! ~

Please feel free to leave any comments if any! :)

Answer:

soit n un nombre entier quelconque; 2n sera pair et 2n+1 sera impair.

1) (2n)² = 4n² = 2 * 2n²

2) (2n+1)² = 4n² + 4n + 1 = 2*(2n² + 2n) + 1

3) 2n + 2m = 2*(n+m)

la somme de 2 nombres pairs est paire

(2n + 1) + (2m + 1) = 2n + 2m + 2 = 2 *(n + m + 1)

la somme de 2 nombres impairs est paire

Step-by-step explanation:

Answer:

15 minutes

Step-by-step explanation:

725 - 710 = 15

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Answer:

Is y

[tex]y = \sqrt{ - } 5 \times + 1[/tex]

Answer:

Hello,

Here is your answer.

Vertex: (5, -2)

Focus: (19/4, -2)

Directrix: x = 21/4

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

[tex]f(x) = 2|x + 6| -4[/tex]

Step 1: Substitute [tex]x[/tex] for the given function.

6 is the given function.

[tex]f(x) = 2|x + 6| -4\\=f(x) = 2|6 + 6| -4\\\\f(x) = 2|6 + 6| -4\\=24-4\\\\=20[/tex]

Answer:

126

Step-by-step explanation: