with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.
We are given that Yossi has a garage of area = 230 feet²
We know that area of square is:
A = side²
230 = s²
s = √ 230
s = 15.17 feet
Now area is increased by 50 %
New area = 230 + 50% of 230
A' = 230 + 115
A' = 345 feet²
s² = 345
s = √ 345
s = 18.57 feet
Percent increase in length = 18.57 - 15.17 / 15.17 × 100
Percent increase in length = 22.41 %
Therefore, with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.
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Pomoże ktoś z matematyki?
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]
sin 496.4 degrees
Please don’t give just the answer! I would like to fully understand how you got to your answer, thank you!
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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please help!
maths geometry
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
geometry NEED HELP ASAP THX
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.
What is the value of the variable behind a geometric system formed by two collinear line segments?
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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2 x 2 x 2 x 2 ( 5.2 - 3.2 ) divided by 4
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
90.97 ÷ 8.6 =
please help me!
a scuba trip costs $80 plus $45 for each diver. write and evaluate an expression to find the total cost for 6 divers
Answer:
$350.00
Step-by-step explanation:
80 + 6(45) = ?
What do we get when we break apart 818+167 using place value?
Write 5 x 10^-4 in standard notation
Consider the axiomatic system and theorem below:
• Axiom 1: If there is a pair of points, then they are on a line together.
• Axiom 2: If there is a line, then there must be at least two points on it.
• Axiom 3: There exist at least two distinct points.
• Axiom 4: If there is a line, then not all the points can be on it.
Theorem 1: Each point is on at least two distinct lines.
A. List all undefined terms involved in the given axiomatic system, including all elements and relations.
B. Explain how the axioms require that the system has three distinct points.
Note: The use of models may be helpful in developing this explanation.
C. Prove theorem 1 for three points, using only the provided axioms.
Note: You do not need to use all four axioms.
(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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find last years salary if after a 2% pay raise this years salary is $40,290
Answer:
2/100*40290
=805.8
40290 - 805.8
=$39484. 2
Ahmad is loading a pallet with boxes that each
weighs 45 pounds. The pallet can safely
support no more than 900 pounds. How many
boxes can Ahmad safely load onto the pallet?
Solve F(x)=2x²+3x+5
Help please, very difficult.
Answer:
No Solution
Step-by-step explanation:
Determine the number of 1/2 inch cubes that can pack the prism shown
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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how to construct a population data set for which N=6 u=5
A population with 6 elements and mean 5 is given by:
4, 4, 5, 5, 6, 6
What is the mean?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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Which of the following equations shows a slope of 5 for the line the equation represents
The equation shows a slope of 5 for the line the equation represents of that given line will be y = 5x:
Given that
slope of the line = 5To find
The equation of lineSo according the question
We have
slope = 5We know that
Slope-intercept form of a line's equation is written as
y = mx+c.Where
The slope of the line is m, andc is the intercept.From question
m = 5 , and c = 0.so the equation of that given line will be
y = 5x + 0 ory = 5xThe equation of that given line will be y = 5xTo learn more about Equation of line please click on the link:
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Which is a correct way of writing the equation of the line that passes through the points shown in the
table?
XY
-2-2
02
26
The correct way of writing the equation of the line that passes through the points are y = -3x - 5.
What are equation ?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 square with side lengths of 4 units is translated on
the coordinate plane. One vertex of the image is at (2,
1).
Which ordered pair could represent another vertex of
the image?
Write fraction that represents the parts shaded red (indicated by "R*) in the figure shown below.
R
R
R
R
R
W
R
R
W
The fraction that represents the parts shaded red (indicated by "R*) is 7/9
How to write the fraction that represents the parts shaded red (indicated by "R*)?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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i need a equation for 4x + 12 = 64
thanks :)
Answer: x=13
Step-by-step explanation: i think
What is the equation solve it
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]
what is the common fact or 9 12 15 and 18
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
13[6 squared divided by (5 squared minus 4 squared)+9]
The answer to the given question is 169.
A subfield of mathematics called algebra uses mathematical expressions to depict issues or circumstances. To create a meaningful mathematical expression, variables like x, y, and z are used together with operations like addition, subtraction, multiplication, and division. All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, involve the use of algebra. A simple example of an expression in algebra is 2x + 4 = 8. Algebra deals with symbols, which are linked together using operators It is not just a mathematical concept, but a skill that we all use in our daily lives without even realizing it.These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to determine their values..
13 * (((6 square) / (( 5 squared ) - (4 square))) + 9)
= 169
Therefore, the correct value of the given question is 169
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Determine the cardinality of the given set.
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
how do we write repeated multiplication as powers and how do we evaluate powers
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:
the exponent signifies the number of times the base is a factorpowers can be evaluated by performing the multiplicationsStep-by-step explanation:
You want to know how multiplication and powers are related, and how powers can be evaluated.
Repeated additionYou 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.
Repeated multiplicationAn 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
Rules of exponentsThe 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.
Evaluating powersPowers 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 ...
logarithmsrepeated squaring.LogarithmsLogarithms 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.
Repeated squaringAn 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
a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'?
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].
Translation: In Coordinate Geometry, a translation is a repositioning of a point or a figure from one location to another location without changing its size, shape or orientation.Coordinates: The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional coordinate plane by using the horizontal and vertical distances from the two reference axesTo learn more about Translation, click on the link below.
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Answer: D (3,-12)
Step-by-step explanation:
can someone please help me with this hw question for pre calc
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
Solve the system of equations by graphing.
x+y=-7
4x+1=19
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)
Can you figure out the sequence/progression of the circle?
Answer:
i the middle
Step-by-step explanation:
I need help with this question
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)