Answer: The perimeter of rectangle is [tex]1.58\times 10^6[/tex]
Step-by-step explanation:
Given: Area of rectangle = [tex]1.45 \times 10^{11}[/tex]
Width of rectangle = [tex]2.9 \times 10^{5}[/tex]
As we know area of a rectangle is given by
[tex]Area = Length \times Breadth[/tex]
So we have
[tex]1.45 \times 10^{11}= Length \times 2.9 \times 10^{5}\\\\\Rightarrow Length = \dfrac{1.45 \times 10^{11}}{2.9 \times 10^{5}} \\\\\Rightarrow Length = 0.5 \times 10^6 = 5 \times 10 ^5[/tex]
Now as we know
[tex]Perimeter = 2(Length +breadth)\\\\\[/tex]
Length = [tex]5 \times 10^5[/tex]
Breadth = [tex]2.9 \times 10^{5}[/tex]
Therefore
[tex]Perimeter = 2(5 \times 10^5+ 2.9 \times 10^5)\\\\\Rightarrow Perimeter = 2\times 10^5(5+2.9)\\\\\Rightarrow Perimeter = 15.8 \times 10^5 = 1.58 \times 10^6[/tex]
Hence,the perimeter of rectangle is [tex]1.58\times 10^6[/tex]
Answer:
1.58*10^6
Step-by-step explanation:
Two rival companies began the same year. The equations below model the number of employees, y, at these companies x years after the companies began.
Company R: y = 3x + 24
Company T: y= 4x + 10
Company R stated, “We have 42 employees, the same number of employees as company T has this year.” Determine if company R’s claim is possible. Explain your reasoning.
Company T stated, “After 15 years, we will have the same year of employees as company R.” Determine if company T’s claim is possible. Explain your reasoning.
Answer:
Both the claims by the companies are not possible.
Step-by-step explanation:
Equations modeling number of employees 'y' after 'x' years of the start are,
For company R: y = 3x +24
For company T: y = 4x + 10
If Company R states that this year they have 42 employees,
42 = 3x + 24
3x = 42 - 24
x = [tex]\frac{18}{3}[/tex]
x = 6 years
So company has completed 6 years this year.
Now we put x = 6 years in the equation for company T.
y = (4×6) + 10
y = 24 + 10
y = 34
Which doesn't match with the number of employees of the company R.
Therefore, claim of company R is not possible.
Company T stated that after 15 years they will have the same number of employees as company R.
For company T : y = 4(15) + 10
y = 70 employees
For company R : y = 3(15) + 10
y = 45 + 10
y = 55 employees
Therefore, claim of the company T is also not possible.
Given the equations that model the number of employees y, at these companies x years after the companies began expressed as:
Company R: y = 3x + 24
Company T: y= 4x + 10
If both companies has the same number of employees, then;
3x + 24 = 4x + 10
3x - 4x = 10 - 24
-x = -14
x = 14
Since 14 ≠ 42 that company R claimed, hence the company does not have the same number of employees as company T has this year.
Functions and values
Given the equations that model the number of employees y, at these companies x years after the companies began expressed as:
Company R: y = 3x + 24
Company T: y= 4x + 10
If both companies has the same number of employees, then;
3x + 24 = 4x + 10
3x - 4x = 10 - 24
-x = -14
x = 14
Since 14 ≠ 42 that company R claimed, hence the company does not have the same number of employees as company T has this year.
Since 14 ≠ 15 that company T also claimed, hence the company does not have the same number of employees as company T has this year.
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A triangle has side lengths 1.5 cm, 2 cm, and 3 cm. Is this a right triangle? Explain.
Answer:
No
Step-by-step explanation:
To figure out whether a triangle is a right triangle using only the side lengths, you can use the Pythagorean theorem:
a^2 + b^2 = c^2
1.5^2 + 2^2 = 3^2
2.25 + 4 = 9
Since this equation isn't true, these numbers cannot be the side lengths of a right triangle.
After applying the Pythagorean theorem to the triangle with sides 1.5 cm, 2 cm, and 3 cm, it is determined that the triangle is not a right triangle because the squares of the shorter sides do not sum up to the square of the longest side.
Explanation:To determine if a triangle with sides measuring 1.5 cm, 2 cm, and 3 cm is a right triangle, we can apply the Pythagorean theorem. The theorem states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In mathematical terms, this is expressed as c² = a² + b².
Let's check if our triangle meets this condition:
Assume the longest side, 3 cm, is the hypotenuse (c).Square the lengths of the shorter sides: 1.5² + 2² = 2.25 + 4 = 6.25 cm².Square the length of the assumed hypotenuse: 3² = 9 cm².Since 6.25 cm² does not equal 9 cm², the sides do not satisfy the Pythagorean theorem, so the triangle is not a right triangle.
Based on the housing data below, which equation can be used to calculate
fair housing prices?
Square Feet
2156
2040
2050
House Price
(in thousands)
210
200
204
Answer: y=0.074x+50.48
Step-by-step explanation:
The solution is : B. y = 0.097x + 11.142
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
In order to find the best equation to descibe the housing price, we have to calculate the slope of the line first.
The equation of the line can be written as
y = mx + q
where m is the slope and q the y-intercept.
In order to have the most accurate estimate for the slope, we use the first point and the last point, that are:
(1900, 196)
and
(2200, 225)
The slope of the line is calculated as:
m = y2-y1/x2-x2 = 0.097
So, the slope of the line is 0.097.
Therefore, the correct option is the only one having a slope of 0.097, which is:
B. y = 0.097x + 11.142
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complete question:
Based on housing data below which equation can be used to calculate fair housing prices?
Square feet
1900
2000
2200
house price (in the thousands 19)
196
205
225
A. y = 0.087x + 9.286
B. y = 0.097x + 11.142
C. y = 0.074x - 50.48
D. y = 0.087x - 9.286
Select the number that completes the sentence. 20 is 1/10 of
0.02
O 0.2
2
200
O2,000
Answer:
the answer is 200
Step-by-step explanation:
We can write 1/10 of 200 in the form of equation as follows:
\frac{1}{10} * 200 = x
Where x represents that number we want to find.
so the answer is 20
The function f(x) = 3(1.9)x gives the length (in inches) of an image after being enlarged by 10% x times. What is the length of the image after it has been enlarged 3 times? Round your answer to the nearest hundredth.
The length of the image is how many
inches?
Answer:
20.58 inches
Step-by-step explanation:
As the variable x represents the number of times the figure is enlarged, to find the length of the image after it has been enlarged 3 times, we just need to use the function f(x) with the value of x = 3:
f(x) = 3 * (1.9)^x
f(3) = 3 * (1.9)^3
f(3) = 3 * 6.859
f(3) = 20.577 inches
Rounding to nearest hundredth, we have f(3) = 20.58 inches
So the length of the image after being enlarged 3 times is 20.58 inches
34 more than the quotient of a number and 15 is 53
Answer:
x=285
Step-by-step explanation:
34 more than ( +34)
quotient of number and 15 (x/15)
is 53 (=53)
(-34)x/15+34=53(-34)
(15)x/15=19(15)
x=285
pls helppp this is so urgent:
The 7th graders at DEMS are going to help set the playground for the kindergartners at the new school. School Safety regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started.
The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches.
How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing sets?
Answer:
90 bags of sand
Step-by-step explanation:
9 feet × 1.5 = 13.5
12 feet × 1.5 = 18
Large pit area= 13.5 × 18 = 243ft squared
The small pit area=9 × 12 = 108ft squared
243 / 108 = 2.25 times larger
This means the large pit needs 2.25 times more sand.
40 × 2.25 = 90 bags of sand
Answer 114.8
ILS
What type of triangle is shown below?
630
4.50
O
A. Acute
O
B. Obtuse
O
c. right
Find the area of the trapezoid shown below and choose the appropriate result.
Answer:
13.5 in²
Step-by-step explanation:
We can use the area formula for a trapezoid.
Area = [tex]\frac{1}{2}(b_{1}+b_{2} )h[/tex]
To solve, we find and plug in the variables. According to the trapezoid, we know
h (height) = 3 in
[tex]b_{1}[/tex] (base 1) = 4in
[tex]b_{2}[/tex] (base 2) = 5in
1/2(4 + 5) ·3 = 13.5 in²
The area of a trapezium is 13.5 in².
Option B is the correct answer.
We have,
The area of a trapezium.
= 1/2 x (sum of the parallel sides) x height
Now,
height = 3 in
Parallel sides = 5 in and 4 in
Now,
Substituting the values.
The area of a trapezium.
= 1/2 x (sum of the parallel sides) x height
= 1/2 x (5 + 4) x 3
= 1/2 x 9 x 3
= 27/2
= 13.5 in²
Thus,
The area of a trapezium is 13.5 in².
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530 : 34 =?
Write your answer as a whole number and remainder.
To divide 530 by 34, divide the quotient and the remainder. The whole number part of the quotient is 14 and the remainder is 54.
Explanation:To divide 530 by 34, we start by determining how many times 34 can fit into 530. We find that 34 can fit into 530 fourteen times. So, the whole number in the answer is 14. Now we calculate the remainder by subtracting 14 times 34 from 530. The remainder is 530 - (14 * 34) = 530 - 476 = 54.
Therefore, the answer to 530 divided by 34 is 14 with a remainder of 54.
What is the simplified form of the square root of 45?
A. the square root of 5
B. the square root of 9 x 5
C. 3 and the square root of 5
D. 5 and the square root of 3
Answer:
3sqrt(5)
Step-by-step explanation:
sqrt(45)
sqrt(9*5)
We know the sqrt(ab) = sqrt(a) sqrt(b)
sqrt(9) sqrt(5)
3sqrt(5)
Answer:
C. 3 and the square root of 5
Step-by-step explanation:
45/9=5
Square root of 9 is 3
Left over: rad 5
3 and the square root of 5
What is the greatest common factor of 4k, 18 Kº, and 12?
A 2
B 4
C 2k.
D
4K
The number 2 is a factor of 4k, 18k and 12 since
4k = 2*2k
18k = 2*9k
12 = 2*6
It is also the largest common factor of all three expressions.
4 wouldn't work because 4 is not a factor of 18
2k doesn't work, and neither does 4k, since k is not present in 12.
Which expression can be used to find the surface area of the following rectangular prism?
O 4+4+8+8+1+1
O 8+8+4+4+2+2
O 8+8+8+8
O 2+4
Answer:
8+8+4+4+2+2
Step-by-step explanation:
4×2=8
4×1=4
1×2=2
An angle whose measure is 40° is in standard position. In which quadrant does the terminal side of the angle fall? Quadrant I Quadrant II Quadrant III Quadrant IV
Answer:
Quadrant 1
Step-by-step explanation:
The terminal side of the angle whose measure is 40° falls in quadrant I.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To determine the quadrant in which the terminal side of an angle falls, we need to look at the direction in which the terminal side moves from the origin.
If the terminal side moves to the right of the origin, it is in quadrant I or IV; if it moves to the left of the origin, it is in quadrant II or III.
The angle whose measure is 40° starts on the positive x-axis and moves in a counterclockwise direction.
Since 40° is less than 90° the angle will move less than 90° counterclockwise from the x-axis.
The terminal side of the angle will fall in quadrant I, which is the quadrant that lies to the right of the positive x-axis and above the positive y-axis.
Hence, the terminal side of the angle whose measure is 40° falls in quadrant I.
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How do the temperatures compare? Order the temperatures from coldest to warmest. 42, -36.3, -15, 41.4, 36.1, -41.5
Answer:
-41.5, -36.3, -15, 36.1, 41.4, 42
Step-by-step explanation:
Final answer:
To order temperatures from coldest to warmest, place negative values first from smallest to largest, followed by positive values from smallest to largest. The correct order is -41.5, -36.3, -15, 36.1, 41.4, 42.
Explanation:
When comparing temperatures and ordering them from coldest to warmest, we need to recognize that negative temperatures are colder than positive temperatures. In °C or °F, lower negative values represent colder temperatures, and higher positive values represent warmer temperatures. Thus, to order the given temperatures from coldest to warmest: -41.5, -36.3, -15, 36.1, 41.4, 42.
A doctor has found that the number of hours students sleep each night is inversely related to the amount of time they spend playing video games. He collected the data below.
If the trend the doctor has observed holds true, how many hours of sleep would you expect of a student who plays video games for 6 hours?
A. 6.5 hours
B. 7.5 hours
C. 7.25 hours
D. 6.25 hours
Answer: 6.25
Step-by-step explanation:
What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places
Answer:
r ≈ 6.71
Step-by-step explanation:
The distance from the centre of the circle to a point on it is the radius.
Calculate the radius r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (8, 2) and (x₂, y₂ ) = (14, - 1)
r = [tex]\sqrt{(14-8)^2+(-1-2)^2}[/tex]
= [tex]\sqrt{6^2+(-3)^2}[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex] ≈ 6.71 ( to 2 dec. places )
Final answer:
The radius of the circle with the center at (8, 2) and a point on the circle at (14, -1) is 6.71 units, after rounding to two decimal places.
Explanation:
To find the radius of a circle with a given center and point on the circle, we need to calculate the distance between these two points. This distance represents the radius. The center of the circle is at (8, 2) and the point on the circle is at (14, -1).
Using the distance formula, which is d = √((x_2 - x_1)^2 + (y_2 - y_1)^2), where (x_1, y_1) is the first point and (x_2, y_2) is the second point:
[tex]d = √((14 - 8)^2 + (-1 - 2)^2) = √((6)^2 + (-3)^2) = √(36 + 9) = √45[/tex]
When using a calculator that has an eight-digit output, √45 is approximately 6.70820393. However, if we are to report the answer with only two decimal places, we get the radius as 6.71 units.
It's important to note that significant figures play a role in determining the precision of our result. Even though the calculator can give us many decimal places, we often round the number to either preserve significant figures or because the extra precision is not materially important for estimation purposes. In this case, the radius to two decimal places is 6.71, despite the calculator's eight-digit output.
Find the area of the rectangle.
square feet:
Answer:
4x9=36
Step-by-step explanation:
36
Answer:
36 sq ft.
Step-by-step explanation:
To solve for the area of a rectangle, all you need to do is multiply the length by the width which gives you:
4×9= 36 sq ft.
Which expression represents 11 less than the sum of y and 13? Will choose brainliest, plz include explanation.
Answer:
D
Step-by-step explanation:
A sum is adding so first you add (y+13)
then its says to subtract 11 so the correct expression is (y+13) - 11
Answer:
D (y+13) -11
Step-by-step explanation:
Less than means subtract from so we need the second part first
sum of y and 13
(y+13)
Less than means subtract from
(y+13) -11
two owls leave the same tree at 9:00 p.m. One owl flies west at 7 miles per hour and the other flies east at 13 miles per hour. In how many hours will they be 60 miles apart?
Answer:
3 hours.
Step-by-step explanation:
Trust me...
How many solutions does this equation have
1. In a sample of 300 high school
seniors, 78 reported that they do not
have a driver's license. What is the
sample proportion?
Answer:
13 to 50
Step-by-step explanation:
1). 78 / 300 = 13 / 50 or 26 %
Which could be the cross section of a square pyramid? Select all that
apply.
Choose all that apply:
trapezoid
triangle
circle
pentagon
square
Final answer:
Cross sections of a square pyramid can include a trapezoid, a triangle, or a square. A circle or a pentagon are not possible shapes for these cross sections because they don't align with the pyramid's geometric structure.
Explanation:
The cross section of a square pyramid could be either a trapezoid, a triangle, or a square, depending on the plane's angle relative to the pyramid's base and sides. A circle or a pentagon cannot be cross sections of a square pyramid since they do not conform to the sides or base of a square pyramid.
A trapezoid cross-section can be obtained if the cutting plane is parallel to one base edge and intersects the other three edges of the pyramid. A triangle appears when the cutting plane passes through one vertex and cuts through the base, creating a cross section congruent to the faces of the pyramid. Lastly, a square section results when the cutting plane is parallel to the base and slices through the pyramid.
Quick answer please ddd
Answer:
C
Step-by-step explanation:
It makes the most sense.
Answer:
honestly it seems as if c is a reasonable answer
Step-by-step explanation:
Which figure has a greater volume, and how much greater is it?
361
Figure 1
Figure 2
The volume of figure 1 is 97213 greater than the volume of figure 2.
The volume of figure 2 is 9721? greater than the volume of figure 1.
The volume of figure 1 is 1.134 ft greater than the volume of figure 2.
The volume of figure 2 is 1.134f greater than the volume of figure 1.
Mark this and retum
Save and Exit
TER
Submit
Answer:
the last one
Step-by-step explanation:
George Washington had been impatient since his departure from Philadelphia in early September. When he left the stricken city, he had put Secretary of War Henry Knox in charge of the government, giving the former general clear instructions to report to him weekly concerning the spread of yellow fever. —An American Plague, Jim Murphy What two benefits does the fictional account of events provide that the nonfiction does not? characters readers can connect with George Washington’s feelings about the event details of what it was like to experience the event Mr. Carris’s thoughts on Secretary of War Henry Knox a biography of George Washington
A fictional account offers benefits such as readers connecting emotionally with characters, like understanding George Washington's feelings, and provides immersive details on what experiencing historical events may have felt like, unlike nonfiction accounts which focus on factual precision.
A fictional account like the one in An American Plague by Jim Murphy offers two main benefits that a nonfictional account may not typically provide. First, it includes detailed characterization, which allows readers to connect with the characters on an emotional level. In this case, it's the portrayal of George Washington's feelings and his impatience as he left the city of Philadelphia. Second, a fictional account can offer vivid, imaginative details of what it was like to experience the event, thus bringing history to life in a way that purely factual retellings may not.
While nonfiction focuses on presenting the facts as accurately as possible, fiction can delve into the personal experiences and emotional journeys of historical figures, providing a different layer of understanding.
Which ordered pair would form a proportional relationship with the point graphed below?
PLZ HELPPP MEEE
On a coordinate plane, a line with negative slope goes through points (negative 20, 10), (0, 0), and (20, negative 10).
(10, –20)
(–30, 20)
(–10, 5)
(35, –20)
Answer:
( -10, 5 )
Step-by-step explanation:
( i used Desmos, you should try it )
:)
Answer:
its c
Step-by-step explanation:
HELPPP PLEASEEEEEEEEE
Answer:
the missing side is the same thing as the existing side. if you just take that triangle you see and flip it over, it will make a square. therefore, the length of the missing side is the same as the length of the existing side. sorry if this doesn't make sense haha
Step-by-step explanation:
What are the solutions of 3(x – 4)(2x - 3) = 0? Check all that apply.
Answer:
x=4 x = 3/2
Step-by-step explanation:
3(x – 4)(2x - 3) = 0
We can use the zero product property
x-4 =0 2x-3=0
Solve each equation
x-4 =0 2x-3=0
x=4 2x=3
x =3/2
can someone please help me?
Answer:
The answer is 27
Step-by-step explanation:
The reason being, you can solve this 2 ways.
1) Combine like terms, 7a-4a = 3a.
Now just substitute (a=9) into 3a.
3 * (9) = 27.
2) Or just substitute a = 9 into the original expression.
7 * (9) - 4 * (9)
= 63 - 36 = 27
Hello!
Answer:The correct answer is option four, 27.
Explanation:We know that a = 9.
Because the a is right next to the 7 and the 4, this indicates that it is being multiplied.
7a - 4a
Substitute for the 'a'.
= 7(9) - 4(9)
= 63 - 36
= 27