Challenge Yossi used to have a square garage with 230 ft2 of floor space. He recently built an addition to it. The garage is still a​ square, but now it has​ 50% more floor space. What was the length of one side of the garage​ originally? What is the length of one side of the garage​ now? What was the percent increase in the length of one​ side?

Przykład 5.

a) The plot cross the horizontal line [tex]y=2[/tex] when the time is [tex]t=5,5[/tex], so it took 5,5 s to cover the first 2 m.

b) If [tex]f(x)[/tex] denotes the distance from the starting position of the object, then its average speed over the entire 6-s period is

[tex]v_{\rm ave} = \dfrac{3\,\mathrm m - 0\,\mathrm m}{6\,\mathrm s - 0 \,\mathrm s} = \dfrac36 \dfrac{\rm m}{\rm s} = \boxed{0,5 \dfrac{\rm m}{\rm s}}[/tex]

c) In the last 3 seconds, the object covers a distance of

[tex]3\,\mathrm m - 1\,\mathrm m = \boxed{2\,\mathrm m}[/tex]

d) False. The average speed over the first 3-s period is

[tex]v_{\rm ave[0,3]} = \dfrac{1\,\mathrm m - 0\,\mathrm m}{3\,\mathrm s - 0\,\mathrm s} = \dfrac13 \dfrac{\rm m}{\rm s} \approx 0,33 \dfrac{\rm m}{\rm s}[/tex]

while over the second 3-s period, it is

[tex]v_{\rm ave[3,6]} = \dfrac{3\,\mathrm m - 1\,\mathrm m}{6\,\mathrm s - 3\,\mathrm s} = \dfrac23 \dfrac{\rm m}{\rm s} \approx 0,66\dfrac{\rm m}{\rm s} \neq 0,33\dfrac{\rm m}{\rm s}[/tex]

Przykład 2.

In total there are

8 + 24 + 28 + 16 + 4 = 80

graded assignments. Compute the percentages of students whose scores fall into the given categories:

• 0-8 : 8/80 = 1/10 = 10/100 = 10%

• 9-16 : 24/80 = 3/10 = 30/100 = 30%

• 17-24 : 28/80 = 7/20 = 35/100 = 35%

• 25-32 : 16/80 = 1/5 = 20/100 = 20%

• 33-40 : 4/80 = 1/20 = 5/100 = 5%

See the attached pie chart.

Zadanie 3.

From the plot, it appears that Mateusz

• took 6 min to reach the bus stop

• waited for 2 min

• took 5 min to return home

• took 1 min to grab his notebook

• took 5 min to return to the bus stop

• waited for 3 min

• and after the bus arrives, moves further away over the next 4 min

This means the total time Mateusz needed to (1) return home to get the notebook, (2) find the notebook, and (3) return to the bus stop is

5 min + 1 min + 5 min = 11 min

Zadanie 4.

True. Mateusz walks the distance between his house and the bus stop within the first 6 min, which is 2/5 of 1 km = 0,4 km = 400 m.

True. The bus arrives after 22 min, and its average speed is equal to Mateusz's average speed over the next 4 min. At 22 min, he is 0,4 km from home, and at 26 min, he is 4 km away from home, so the average speed is

[tex]v_{\rm ave} = \dfrac{4\,\mathrm{km} - 0,4\,\mathrm{km}}{26\,\mathrm{min} - 22\,\mathrm{min}} = \dfrac9{10} \dfrac{\rm km}{\rm min} = 0,9\dfrac{\rm km}{\rm min}[/tex]

Convert the speed to km/h.

[tex]\dfrac9{10} \dfrac{\rm km}{\rm min} \times \dfrac{60\,\rm min}{1\,\rm h} = 54 \dfrac{\rm km}{\rm h}[/tex]

The correct way of writing the equation of the line that passes through the points are y = -3x - 5.

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

The slope-intercept form, point-slope form, and standard form are the three primary types of equations. These equations provide sufficient details about the line to make graphing them simple.

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A population with 6 elements and mean 5 is given by:

4, 4, 5, 5, 6, 6

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, for this problem, we need 6 observations which add to 30, hence one possible population is:

4, 4, 5, 5, 6, 6

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Answer:

[tex]5 { \\ }^{2} [/tex]

Step-by-step explanation:

exponents are ways to write multiplication powers 5

[tex]5 {}^{2} [/tex]

= 5×5 = 25

Answer:

Step-by-step explanation:

You want to know how multiplication and powers are related, and how powers can be evaluated.

You may be familiar with the fact that a coefficient is used to signify repeated addition:

  y + y + y + y = 4y

The coefficient of 4 in 4y signifies that y is in the sum that many times.

An exponent is used to signify repeated multiplication:

  y × y × y × y = y⁴ . . . . y to the fourth power

The exponent of 4 signifies that y is a factor in the product that many times.

In typeset text, the exponent is rendered in a superscript font. In plain text, the exponent (power) is identified using a caret (^):

  y⁴ = y^4

The rules of exponents derive from the idea of exponents signifying repeated multiplication:

  [tex](x\cdot x)=x^2\\(x\cdot x\cdot x)=x^3\\(x\cdot x)\cdot(x\cdot x\cdot x)=(x\cdot x\cdot x\cdot x\cdot x)\ \Longrightarrow\ x^2\cdot x^3=x^{2+3}=x^5[/tex]

Division has a similar rule.

  [tex]\dfrac{(x\cdot x\cdot x\cdot x\cdot x)}{(x\cdot x)}=(x\cdot x\cdot x)\ \Longrightarrow\ \dfrac{x^5}{x^2}=x^{5-2}=x^3[/tex]

This supports the idea that a positive exponent in the denominator is the same as a negative exponent in the numerator, and vice versa.

Powers can be evaluated in a straightforward way by carrying out the multiplications.

In general, the number of significant digits in the result will be the product of the exponent and the number of significant digits in the base.

For example, 9.2^5 could be expected to have 2×5 = 10 significant digits:

  9.2^5 = 9.2×9.2×9.2×9.2×9.2 = 65,908.15232

Most calculators are limited to 12 digits or less, and most spreadsheets are limited to 16 digits or less. Some special-purpose calculators have "variable" precision, so are able to properly render higher powers of numbers with more than 1 or 2 significant digits.

A calculator may use any of several techniques for evaluating powers. Among them might be ...

Logarithms turn a power problem into a multiplication problem:

  log(9.2^5) = 5·log(9.2)

Of course, once the logarithm is found, the issue of evaluating powers comes back:

  9.2^5 = 10^(5×log(9.2)) ≈ 10^(4.818939136727776)

Fortunately, there are methods of evaluating antilogs that simplify this part of raising to a power. The difficulty is that precision may be lost. Here, using the rounded value 10^(4.81893913673) gives the result 65,908.152320337..., which is in error after the 10th digit.

An integer power can be written as a sum of powers of 2. For example, ...

  37 = 32 +4 +1 = (8 +1)4 +1

Then ...

  9.2^37 = (((((9.2^2)^2)^2 · 9.2)^2)^2) · 9.2

This requires only 7 multiplications, not 36

__

Additional comment

Only the first token after the caret is considered to be the exponent:

  y^4x = (y^4)(x) . . . . . the first token is 4

  y^1/2 = (y^1)/2 = y/2 . . . . the first token is 1

If the exponent has multiple parts, they should be enclosed in parentheses:

  [tex]y^{3x+1}[/tex]

will be written in plain text as ...

  y^(3x+1)

and ...

  y^(1/2) = √y

You also need to be careful writing multiple exponents using the caret symbol. Parentheses are usually required. The Order of Operations has you evaluate multiple exponents right to left.

  3^4^5 = 3^(4^5) = 3^1024

  (3^4)^5 = 3^20

The equation shows a slope of 5 for the line the equation represents of that given line will be y = 5x:

Given that

To find

So according the question

We have

We know that

Slope-intercept form of a line's equation is written as

Where

From question

so the equation of that given line will be

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Answer:

1.) 9

2.) 15

3.) 7

Step-by-step explanation:

1.) There are no repeat letters, so the cardinality is the number of letters, here 9

2.) There's half the numbers from 1 to 30 in the set, so 30/2 = 15

3.) There are 7 distinct days of the week, so the answer is 7

Answer:

No Solution

Step-by-step explanation:

Answer: look at the graph below

Step-by-step explanation:

Consider the given system of equation

x + y = -7     ........(1)

4x + y = 19   ..........(2)

Consider the equation (1)

x + y = -7

We first find different values of x and y that satisfies (1),

1) x = 1 , y = -7-1 = -8  

We get one point as (1,-8)

2) x= 2 , y = -7 -2 = -9

We get  point as (2 ,-9)

3) x = 0 , y = -7

We get point as (0 ,-7)

Similarly, find different values of x and y that satisfies (2),

4x + y = 19  

1) x = 2 , y = 19 -  8 = 11

We get  point as (0,11)

2)  x= 3 , y = 19 - 12 = 7

We get  point as (3 , 7)

3) x= 4 , y = 19 - 16 = 3

We get  point as (4 ,3)

Now , we plot these point on the graph paper,  we obtained graph as, (as attached below)

Answer:

(-5, 5)

Step-by-step explanation:

The function increases from x = -11 to x = -5.

The function decreases from x = -5 to x = 5.

the function increases from x = 5 to x = 11.

Answer: (-5, 5)

Answer: x=13

Step-by-step explanation: i think

The value of Sin 496.4° is 0.6896.

Trigonometry functions:

Trigonometry is a type of mathematics that deals with the specific function of angles and their application.

There are six functions of an angle used in trigonometry sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec) and cosecant(cosec). All these functions are based on the measurement of the triangle.

Given,

Sin 496.4°

Here we need to find the value of it.

While using the sine table,

The value of 496.4° = 0.6896

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Answer: 15. f(1)=3

16. g(3)=1

Step-by-step explanation:

15. (fog)(1)=

f(g(1))=

f(1)=3

16. (gof)(5)=

g(f(5))=

g(3)=1

If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).

As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.

We are required to calculate the coordinates of B'.

To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].

Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at [tex][(1+2), (5+(-7)]=[3, (-2)][/tex].

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Answer: D (3,-12)

Step-by-step explanation:

Answer:

3 is the common factor

Step-by-step explanation:

3 x 3 =9

3 x 4= 12

3 x 5 =15

3 x 6 =18

hope it helps

Answer:

Factors for 9: 1, 3, and 9

Factors for 12: 1, 2, 3, 4, 6, and 12

Factors for 15: 1, 3, 5, and 15

Prime Factors for 9: 3 and 3

Prime Factors for 12: 2, 2, and 3

Prime Factors for 15: 3 and 5

GCF = 3

Answer:

$350.00

Step-by-step explanation:

80 + 6(45) = ?

(A) Undefined terms are Point and Line.

(B)  Each point has at least two separate lines.

(C)  "P" does not lay on "m," hence the statement is contradictory.

A set of axioms from which one or more theorems may be logically deduced is known as an axiomatic system in mathematics and logic. A theory is a coherent, mostly self-contained body of knowledge that typically includes an axiomatic framework and all of the theorems that are deduced from it.

(A) Undefined terms are :

A location is a point. It is empty, meaning it has no width, length, or depth. A dot indicates a point.

A line is described as a collection of points that stretches in both directions indefinitely.

(B) Each point now has at least two separate lines.

A line 's' that is not incident on point 'P' must exist according to axiom 4 if we use point 'P' as our starting point.

Axiom 2 states that if a line exists, it must have the two points "R" and "S" on it.

(C) Since "P" does not lie on "m." P thus differs from 'e' and 's'

Points that stand out. They are different because they would be referred to as "m" if both lines "n" and I passed via "r" and "s."

However, "P" does not lay on "m," hence the statement is contradictory.

So it is proved

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Answer:

i the middle

Step-by-step explanation:

The fraction that represents the parts shaded red (indicated by "R*) is 7/9

The figure is represented by the following list of characters

RRRRRWRRW

In the above list of characters, we have

n(R) = 7

Total = 9

The fraction that represents the parts shaded red (indicated by "R*) is then calculated as

Fraction = n(R)/Total

So, we have

Fraction = 7/9

Hence, the fraction that represents the parts shaded red (indicated by "R*) is 7/9

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Answer:

2/100*40290

=805.8

40290 - 805.8

=$39484. 2

Step-by-step explanation:

the diagonals in a square are intersecting each other at 90°.

that means that G1 + G2 = 90

and because of the symmetry of a kite, it also means that G1 = G2.

combined this tells us

G1 = G2 = 90/2 = 45°.

also due to its symmetry one of the rules of a kite is that its diagonals are also intersecting each other at 90°.

so,

E1 = E2 = 90°.

the sum of all angles in a triangle is always 180°.

so,

180 = F1 + G1 + (D2 + D3) = F1 + 45 + 110

F1 = 180 - 45 - 110 = 180 - 155 = 25°

again, due to the symmetry of the kite

F1 = F2 = 25°.

also

C2 + C3 = D2 + D3 = 110°

due to the properties of a square (e.g. the angle in every corner is 90°, the diagonals are splitting each corner angle in half) we know that

D1 = D2 = 45°.

and again, therefore

C1 = C2 = D1 = D2 = 45°

and so

(1)

due to the law of the angles of a line intersecting parallel lines are equal for every parallel line, we see that

the line BD intersects the lines AD and GEF equally at 45°. therefore, GEF || AD.

(2)

as we know that F1 = F2 = 25°,

F1 + F2 = 2×25 = 50°

(3)

the angles in the triangle GDE are

E1 = 90°

D2 = 45°

G1 = 45°

the angles of GE and DE with their baseline GD are equal, that means this is an isoceles triangle, meaning the legs have an identical length, and therefore

DE = GE.

(4)

as GDE is a right-angled triangle we can use Pythagoras :

GD² = GE² + DE² = 2×DE² = 2×GE²

GD = 3×sqrt(2)

GD² = 9×2 = 18

18 = 2×DE² = 2×GE²

DE² = GE² = 18/2 = 9

DE = GE = 3

By consideration of congruence and collinearity, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.

Two line segments are congruent when the line segments have the same length, then the following condition has to be fulfilled:

AB = BC      (1)

Where AB and BC are the lengths of the line segments AB and BC.

If we know that AB = 4 · x + 1 and BC = 20 · x - 5, then we solve the equation for x is:

4 · x + 1 = 20 · x - 5

6 = 16 · x

16 · x = 6

x = 6 / 16

x = 3 / 8

Then, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.

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Answer:

12x + 9 = 4x + 7

Group likely terms

12x - 4x = 7 - 9

8x = -2

Now we need to isolate x

Therefore; Divide both side by the coefficient of x thus 8

Hence x = -1/4

Answer:

[tex]x = \bf -\frac{1}{4}[/tex]    

Step-by-step explanation:

We are given the following equation:

[tex]12x + 9 = 4x + 7[/tex]

In order to solve this equation, we have to rearrange it to make [tex]x[/tex] the subject of the equation:

[tex]12x + 9 = 4x + 7[/tex]

⇒ [tex]12x + 9 - 4x = 4x + 7 - 4x[/tex]       [Subtracting [tex]4x[/tex] from both sides]

⇒ [tex]8x + 9 = 7[/tex]

⇒ [tex]8x + 9 - 9 = 7 - 9[/tex]                     [Subtracting 9 from both sides]

⇒ [tex]8x = -2[/tex]

⇒ [tex]\frac{8}{8} x = -\frac{2}{8}[/tex]                                     [Dividing both sides by 8]

⇒ [tex]x = -\frac{2}{8}[/tex]

⇒ [tex]x = \bf -\frac{1}{4}[/tex]                                     [Simplifying the fraction]

The total number of Cubes that can be packed in the Rectangular Prism will be 84 Cubes

In the picture mentioned below, We have a Rectangular prism with the dimensions Length = [tex]3\frac{1}{2}[/tex] in, Breadth = 2 in, Height =  [tex]1\frac{1}{2}[/tex] in

Also, It is given that cubes of Dimension [tex]\frac{1}{2}[/tex] inches are to be packed in the Rectangular Prism.

Firstly, We need to find the volume of Both the Prism & the Cube.

Since, The it is a Rectangular Prism, Volume of cuboid = ( l*b*h )

Volume of Prism, V1 = l*b*h => l =[tex]3\frac{1}{2}[/tex], b = 2, h = [tex]1\frac{1}{2}[/tex]

                        => V1 = [tex]3\frac{1}{2} * 2 * 1\frac{1}{2}[/tex]    => V1 = 10.5 [tex]in^{3}[/tex]

Volume of Cube, V2 = l * l * l => l = [tex]\frac{1}{2}[/tex]

                       => V2 = [tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex]       => V2 = 0.125 [tex]in^{3}[/tex]

To find out the number of cubes that can fit inside the prism we need to divide the volume of the prism by the volume of cube => V1/V2

                       =>  N =  [tex]\frac{V1}{V2}[/tex]  =>  [tex]\frac{10.5}{0.125}[/tex]

                       =>  N = 84 Cubes.

Hence, the Total number of cubes that can fit inside the Prism will be 84.

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The answer to the given question is 169.

13 * (((6 square) / (( 5 squared ) - (4 square))) + 9)

= 169

Therefore,  the correct value of the given question is 169

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Answer:

8

Step-by-step explanation:

you first do operation in the brackets and then multiply and then divide:

2*2*2*2*2 / 4 = 8