Answer:
The answer is 4.9cmStep-by-step explanation:
To find the perpendicular distance between them that's the height we use the formula
[tex]Area \: \: of \: \: a \: \: trapezium = \frac{1}{2} (a + b) \times h[/tex]
where
a and b are the parallel sides of the trapezium
h is the perpendicular distance
From the question
Area = 31.5cm²
a = 7.5 cm
b = 5.3 cm
Substituting the values into the above formula we have
[tex]31 .5 = \frac{1}{2} (7.5 + 5.3) \times h[/tex]
[tex]31.5 = \frac{1}{2} \times 12.8h[/tex]
[tex]31.5 = 6.4h[/tex]
Divide both sides by 6.4
[tex]h = \frac{31.5}{6.4} [/tex]
h = 4.921875
We have the final answer
h = 4.9cmHope this helps you
Which number is in the 3rd position after ordering in
descending order. V220,-10, V100, 11.5
Answer:
√100
Step-by-step explanation:
Given the following numbers: √220, -10, √100, 11.5,
Let's arrange the numbers from the largest to the smallest (in descending order).
Note: √220 ≈ 14.8
√100 = 10
From the largest to the smallest number, we have: √220, 11.5, √100, -10
Therefore, the number in the third position is √100
The point-slope form of the equation of the line that passes through points (-5,-1) and (10, -7 ) is y-4=1/4 (x-8) what is the slope intercept form of the equation for this line ?
Answer:
y = [tex]\frac{1}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
y - 4 = [tex]\frac{1}{4}[/tex] (x - 8) ← distribute
y - 4 = [tex]\frac{1}4}[/tex] x - 2 ( add 4 to both sides )
y = [tex]\frac{1}{4}[/tex] x + 2 ← in slope- intercept form
how do i solve this ?(x+3)(x-5)=
[tex](x+3)(x-5)=x^2-5x+3x-15=x^2-2x-15[/tex]
Answer:
Step-by-step explanation:
Use FOIL method
(x + 3)(x - 5) = x*x + x *(-5) + 3*x + 3*(-5)
= x² - 5x +3x - 15 {add like terms}
= x² - 2x -15
the sum of 48 and itself its half and half of the hal is added to 18
Answer:
150
Step-by-step explanation:
We are carrying out Addition
a) The sum of 48 and itself
= 48 + 48 = 96
b) Its half and half of the half
96 + (1/2 × 48) + (1/2 ×( 1/2 × 48)
= 96 + 24 +(1/2 × 24)
= 96 + 24 + 12
= 132
c) is added to 18
= 132 + 18
= 150
Therefore, the sum of 48 and itself, its half and half of the half is added to 18 is 150
The sum of 48 and itself its half and half of the half is added to 18 is 150.
Given, we have a number 48.
We have to find the sum of 48 and itself its half and half of the half is added to 18.
So, the half of the 48 is 24 and half of the half becomes 12.
Now the equation becomes,
[tex]48+48+24+12+18=150[/tex]
Hence the required sum is 150.
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In the figure below, triangle DOG, triangle ION, and triangle IDO are congruent and isosceles, each with perimeter 55. The quadrilaterals FLIN, DIES, and DRAG are all squares. The perimeter of the 11-sided polygon $DRAGONFLIES$ is 127. What is the area of DRAG?
Answer:
81 sq units.
Step-by-step explanation:
Given that Triangles DOG, ION and IDO are congruent and isosceles.
Let Sides NO = IO = DO = GO = [tex]x[/tex] units
Let the sides of squares FLIN, DIES and DRAG = [tex]a[/tex] units
So, NF = FL = LI = NI = IE = ES = SD = DI = DR = RA = AG = GD = [tex]a[/tex] units
Given that perimeter of each of Triangles DOG, ION and IDO = 55 units
Sum of sides of triangle = [tex]2x+a=55 ...... (1)[/tex]
and Perimeter of 11 sided polygon DRAGONFLIES = 127 units
The perimeter of the polygon includes the sides (only outer sides are included):
DR, RA, AG, GO, ON, NF, FL, LI, IE, ES and SD
[tex]2x+9a = 127......(2)[/tex]
Solving equations (2) and (1) by subtracting (1) from equation (2):
[tex]8a = 72\\\Rightarrow a = 9 units[/tex]
Area of a square DRAG = [tex]Side^2[/tex] = [tex]9^2 = \bold{81\ sq\ units}[/tex]
Answer:
81
Step-by-step explanation:
dont ask, i just know
An empty row in a frequency table is a mistake True or false
Answer:
False I think
Step-by-step explanation:
Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared?
Answer:
[tex]\dfrac{1}{6561}[/tex]
Step-by-step explanation:
Given the expression [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex], Using the laws of indices to simplify the expression. The following laws will be applicable;
[tex]a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\[/tex]
[tex]a^{-m} = 1/a^m[/tex]
Given [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex]
open the parenthesis
[tex]= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}[/tex]
Please someone help ASAP!!!!!!
Answer:
1.7 million in Northern Ireland
Step-by-step explanation:
Simply do the difference between the number of people in the UK, minus the number of people in everywhere else except northern Ireland. That is:
60.2 M - 50.4 M - 5.1 M - 3.0 M = 1.7 M
Answer:
[tex]\boxed{1.7 million}[/tex]
Step-by-step explanation:
Hey there!
To find the amount of people who lived in Northern Ireland in 2005 we need to subtract the total 60.2 mil by the England, Scotland, and Wales people.
50.4 + 5.1 + 3
= 58.5
Now we can set up the following equation,
NI = 60.2 - 58.5
NI = 1.7 million
Hope this helps :)
A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the length of her shadow increasing when she is 50 ft from the base of the pole
Answer:
4 ft/sec
Step-by-step explanation:
Hope it helps
The temperature in Anchorage, Alaska at 6:00 am was 2°C. If the temperature drops 2 degrees each hour, what is the temperature in degrees celsius at 2:00 pm
Answer:
-12°C
Step-by-step explanation:
6AM = 2°C
8AM= -2°C
10AM= -6°C
12AM= -8°C
2PM= -12°C
the temperature in degrees Celsius at 2:00 pm would be -14°C.
To find the temperature in degrees Celsius at 2:00 pm, we need to determine the number of hours that have passed from 6:00 am to 2:00 pm, and then calculate the temperature decrease accordingly.
From 6:00 am to 2:00 pm, a total of 8 hours have passed (6 hours from 6:00 am to 12:00 pm, and 2 hours from 12:00 pm to 2:00 pm).
Given that the temperature drops 2 degrees Celsius each hour, we can multiply the number of hours (8) by the rate of temperature decrease (2 degrees/hour):
Temperature decrease = 8 hours × 2 degrees/hour = 16 degrees
Starting with a temperature of 2°C at 6:00 am, if the temperature drops 16 degrees Celsius over 8 hours, we can subtract 16 from the initial temperature:
Temperature at 2:00 pm = 2°C - 16°C = -14°C
Therefore, the temperature in degrees Celsius at 2:00 pm would be -14°C.
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The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,224.00 for 264 square feet, what is the size of a kitchen that costs $3,824.00? A. 239 square feet B. 256 square feet C. 7,648 square feet D. 63,096 square feet
Answer:
The answer is option AStep-by-step explanation:
Let the price of the room be p
Let the size of the room be s
To find the size of a kitchen that costs $3,824.00 we must first find the relationship between them
The statement
The price of tiling a room varies directly as the size of the room is written as
p = kswhere k is the constant of proportionality
when
p = $4,224.00
s = 264 square feet
Substitute the values into the expression to find k
That's
4224 = 264k
Divide both sides by 264
k = 16
So the formula for the variation is
p = 16swhen
p = 3824
[tex]s = \frac{p}{16} [/tex]
[tex]s = \frac{3824}{16} [/tex]
s = 239
The final answer is
239 square feet
Hope this helps you
A certain forest covers an area of 2600 km^2. Suppose that each year this area decreases by 4.75%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1522km^2
Step-by-step explanation:
To solve this, first convert the percentage to a decimal. That would be .0475.
Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525
Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2
Answer:
The area will be 1292.98 km² after 11 years.
Step-by-step explanation:
To find what decreases by 4.57% each year in kilometers:
2600 × 4.57/100 = 26 × 4.57
= 118.82 km²
To find the area after 11 years:
118.82 × 11 = 1307.02
2600 - 1307.02 = 1292.98 km²
1292.98 km² is the answer.
Your fixed expenses are $1,235. 78/month. You want to save 5 months' worth for an emergency
fund over a year's time. How much must you save each month?
Answer:
$514.91
Step-by-step explanation:
You want to save a total of ...
5 × $1235.78
You want to do this over a 12-month period. So, you want to save 1/12 of this total each month. The amount you're saving each month is ...
5(1235.78)/12 = 514.908333... ≈ 514.91
You must save $514.91 each month to reach the goal.
Answer: $514.91
Step-by-step explanation:
($1,235.78)(5 months)=$6,178.90
6,178.90/12 months=$514.91
(just for clarity: the other person is right, just wanted to show a simpler way to achieve the answer. gl :)
name four points that are not coplanar
Answer: U, W, Z and Y
Step-by-step explanation:
4 points are not coplanar if there does not exist any plane that contains the 4 points.
So, a plane is formed by a line and one point outside of it.
Then, we want to select the last point in such a way that it lies outside of the plane generated by the first 3 points selected.
For example:
If first we select Point U and Point W, we will have a line, as shown in the image.
Now we can select the Point Z, that is outside the line, and now we have the plane M that you can see in the image.
Now we need to select a point that is not in the plane, the only two options are Point X and Point Y, we can select any of those two, let's take the Point Y.
So, here we have that:
Points U, W, Z and Y are not coplanar.
What is the LCD of 1/2 and 3/5
Answer:
10
Step-by-step explanation:
How you find LCD (lowest common denominator) is that you have to look at the denominator (the bottom number) and try to find the lowest multiple between both of the numbers that is on the bottom (in this case it is 2 and 5). Sometimes you have to multiply both denominators together to get a LCD.
Example of multiplying two denominators together to get an LCD:
1/3 and 1/13 LCD is 39 because you multiply 3 and 13.
1/5 and 1/4 LCD is 20 because you multiply 5 and 4.
The pair of figures is similar. Find x. Round to the nearest tenth if necessary.
Answer:
x ≈ 4.125 ft
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{11}{x}[/tex] = [tex]\frac{8}{3}[/tex] ( cross- multiply )
8x = 33 ( divide both sides by 8 )
x = 4.125 ft
Simplify the expression a-2b, when a=1.4 - 2x and b=-0.2x + 1.7 *
Answer:
a-2b= -1.6x-2.0
Step-by-step explanation:
[tex]a=1.4-2x\\b=-0.2x+1.7\\a-2b= (1.4-2x)-2(-0.2x+1.7)\\a-2b= 1.4-2x+0.4x-3.4\\a-2b=-1.6x-2.0\\[/tex]
{By, substituting the values of a and b in a-2b , we can find the value of a-2b}
Celine is Drake’s granddaughter. Her age is 4 years greater than of Drake’s age. If Celine is 28 years old, how old is Drake?
Answer:32
Step-by-step explanation:
if selling is 28 and she is 4 years greater than Drake then that is 28-4 which is 32 so Drake is 32 years old
Answer:
The answer is 32.
Step-by-step explanation:
If Celine is 28 and Drake is four years older than her, we do 28+4.
Select the correct answer. The velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C. What is the distance from A to C (the velocity of the ball relative to the ground), correct to two decimal places? Assume that all the points in the diagram lie in the same plane. A. 21.14 m/s B. 18.03 m/s C. 17.20 m/s D. 15.00 m/s
Answer:
Step-by-step explanation:
we use cosine formula
2×15×10×cos(180-66)=15²+10²-AC²
-300 cos 66=225+100-AC²
AC²=325+300 cos 66
[tex]AC=\sqrt{325+300 cos 66} \approx 21.14 ~m/s[/tex]
The distance from A to C is 21.14. The correct option is A.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.
Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that the velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C.
The distance A to C will be calculated as,
2×15×10×cos(180-66)=15²+10²-AC²
-300 cos 66=225+100-AC²
AC=√(325+300 cos 66)
AC = 21.17 m/s
Therefore, the distance from A to C is 21.14. The correct option is A.
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Combine like terms to simplify the expression: -5.55-8.55c+4.35c
Answer:
-5.55 - 4.2c
Step-by-step explanation:
-5.55 - 8.55c + 4.35c
'-8.55c' and '4.35c' are like terms because of them containing the same variable of 'c'.
Combine:
-5.55 - 8.55c + 4.35c
-8.55 + 4.35 = -4.2-5.55 - 4.2c
Hope this helps.
find the Perimeter Of a circle whose radius is 14cm
Answer:
88 cm
Step-by-step explanation:
Perimeter = 2πr
=2(14)(22/7)
= 88 cm
Answer:
87.97cm
Step-by-step explanation:
This question is asking to solve for the circumference.
The formula for the circumference of a circle is: [tex]\pi*diameter[/tex]
To work this out you would first need to multiply the radius of 14 by 2, this gives you 28cm. This is because the radius is half of the diameter.
The final step is to multiply pi by the diameter of 28, this gives you 87.97cm (87.9645943). This is because the formula for the circumference of a circle is [tex]\pi * diameter[/tex].
1) Multiply 14 by 2.
[tex]14*2=28[/tex]
2) Multiply pi by the diameter.
[tex]\pi*28^2=87.97 cm[/tex]
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
What is the formula for finding mean or average?
Answer:
LOOK BELOW
Step-by-step explanation:
I would not call the explanation a formula
All you have to do to solve mean or average is add all of the numbers up and divide by the total amount of numbers
so for example
0,2,4,0,2,3,2,8,6 <-------- lets find the mean/average
0+2+4+2+3+2+8+6= 27/amount of numbers
amount of numbers=9
(count the zeros too!)
27/9=3
3 is the mean or average!!!
What is the LCD for x/4 - 2/3 = 7/12?
Answer:
12
Step-by-step explanation:
All the denominators are factors of 12.
f(x) = x+ bx + 5 In the given function, b is a constant. If f(1) = 0, what is the value of f(3) ?
Answer:
f(x)= x+bx+5
f(1) = 1+ b(1) +5 =0
f(1) = 6 +b =0
6+b=0
b=-6
so we get,
f(3)= 3 -6(3)+5
f(3) = 3-18+5
f(3) = -10
hope it helps ^°^
Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long. What is the approximate angle, x, that the second tree makes with the ground? A 0.6° B 35.0° C 39.0° D 58.0°
Answer:
C 39.0
Step-by-step explanation:
To find the approximate angle, x, that the second tree makes with the ground, we can use the concept of similar triangles Therefore the correct option is B.
Let's calculate the height of the first tree using the given information. We can use the formula for the opposite side in a right triangle: opposite = adjacent * tan(angle). Therefore, the height of the first tree is approximately [tex]19 * tan(32°) = 19 * 0.6249 ≈ 11.873[/tex] feet. Now, we can set up a proportion between the two trees based on their heights. Let x be the angle the second tree makes with the ground.
We have the following proportion: (height of first tree)/(height of second tree) = (length of first tree)/(length of second tree). Substituting the known values, we have [tex]11.873/16 = 19/x[/tex]. Cross-multiplying gives us [tex]11.873x = 304,[/tex] and dividing both sides by 11.873 yields[tex]x ≈ 25.63°.[/tex] The approximate angle, x, that the second tree makes with the ground is closest to 35.0°.
Hence the correct option is B
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An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?
Each edge of the cube is 20cm. If it stayed on the edges it would need to walk on 3 edges for a total distance of 3 x 20 = 60 cm.
If it walked diagonally across the front face and then one edge it would travel:
Diagonal = sqrt(20^2 + 20^2) = 28.28
Total distance waling a diagonal and then an edge = 28.28 + 20 = 48.28 cm
The shortest distance would be diagonally across the front face then the edge to point B and the distance would be 48.28 cm.
Kyle stood on a bridge and threw a rock up and over the side. The height of the rocks in meters can be approximated by approximated by -5t^2+5t+24, where T is the time in seconds after car through it completely factor the expression
Answer:
The factorized expression is (-5) × (t - 2.747) ×(t - 1.747)
Step-by-step explanation:
The given expression is -5·t² + 5·t + 24
To factorize the expression by completing the square method, we equate the expression to zero to get;
-5·t² + 5·t + 24 = 0
WE divide by -5 to get;
t² - t - 24/5 = 0
t² - t = 24/5
t² - t + 1/4 = 24/5 + 1/4
(t - 1/2)² = 5.05
t - 1/2 = ±√5.05
t = 1/2 + √5.05, 1/2 - √5.05
The factorized expression becomes;
(t - 1/2 + √5.05) and (t - 1/2 - √5.05)
Which gives;
(t - 2.747) ×(t - 1.747)
The factorized expression is (-5) × (t - 2.747) ×(t - 1.747).
5/8 divided by 11/9 divided by 1/4=
Answer:
45/22
Step-by-step explanation:
(a/b)/(c/d) = (a*d)/(b*c)
then
{(5/8)/(11/9)} / {1/4)}
= {(5*9)/(8*11)} / {1/4)
= {45/88} / {1/4}
= {45*4} / {88*1}
= 180/88
= 45 / 22
Lucy reads 450 words in 3 minutes.
This is an equation that can be used to
find w, the number of words Lucy can
read in 20 minutes if she continues to
read at the same rate?
Answer:
3000 words
Step-by-step explanation:
450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.
1 minute = 150 words so 150 words times 20 minutes = 3000 words.
