Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
[tex]y=a(x-h)^2+k[/tex]
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:
[tex]y=-\frac{4}{21}x^2+84[/tex]
Answer:
x² = -21y
Step-by-step explanation:
THIS IS THE RIGHT ANSWER I TOOK THE TEST
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 :)
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!!!
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
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).
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.
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
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]
Compute the range and interquartile range for the data collected for boys and girls. Describe their differences in detail using specific terms of spread. (4 points)
Answer:
The measure of central tendency, mean and median are approximately equal for the boys indicating that the data of the boys is more evenly spread while standard deviation of the girls data is less than those of the boys indicating that the data for the girls is less widely spread.
Step-by-step explanation:
The given data are;
, 1 2 3 4 5 6 7 8 9 10
Girls, 50 32 15 56 81 50 18 81 22 55
Boys, 75 41 25 22 7 0 43 12 45 70
Sorting the data gives;
Girls, 15, 18, 22, 32, 50, 50, 55, 56, 81, 81
Boys, 0, 7, 12, 22, 25, 41, 43, 45, 70, 75
For the even numbered sample data size, the first quartile, Q₁ is found by sharing the data into two and finding the median of the left half which gives;
10/2 = 5 on each half
The first quartile, Q₁, is the median of the left 5 data points which is the 3rd data point = 22 for girls and 12 for boys
The third quartile, Q₃, is found in similar method to be the 8th data point which is 56 for girls and 45 for boys
The median = 50 for girls and 33 for boys
Therefore, the interquartile ranges are;
IQR = 56 - 22 = 34 for girls, 45 - 12 = 33 for boys
We check for outliers.
Q₁ - 1.5×IQR = 22 - 1.5*34 = -29
Q₃ + 1.5×IQR = 56 + 1.5*34 = 107
We check the mean of both data samples as follows;
Average for the girls = 46
Average for the boys = 34
Standard deviation for girls = 23.99
Standard deviation for girls = 25.43
Therefore, the measure of central tendency is more accurate for the boys indicating that the data of the boys is more evenly spread while the data for the girls is less widely spread.
What are the solutions to the equation 3(x – 4)(x + 5) = 0? x = –4 or x = 5 x = 3, x = 4, or x = –5 x = 3, x = –4, or x = 5 x = 4 or x = –5
Answer:
x= 4 x = -5
Step-by-step explanation:
3(x – 4)(x + 5) = 0
Using the zero product property
(x – 4)=0 (x + 5) = 0
x= 4 x = -5
What are the solutions to the equation 3(x – 4)(x + 5) = 0?
x = –4 or x = 5
x = 3, x = 4, or x = –5
x = 3, x = –4, or x = 5
x = 4 or x = –5
Answer:
D. x = 4 or x = –5
Step-by-step explanation:
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.
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
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]
Sandra spotted the sailboat from the shore and measured the angle from the waterline to the top of the boats mast to be 7° if the top of the mask is 23 feet above the water how far is the middle of the sailboat from the shore? Estimate your answer to the nearest tenth.
Answer:
The middle of the sailboat is approximately 268.8 feet from the shore.
Step-by-step explanation:
Let the distance from shore to the middle of the boat be represented by x, the angle of elevation of Sandra from the shore to the top of the boat mast is 7°. Applying the required trigonometric function to this question, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 7° = [tex]\frac{23}{x}[/tex]
⇒ x = [tex]\frac{23}{Tan 7^{0} }[/tex]
= [tex]\frac{23}{0.12279}[/tex]
= 268.7515
∴ x = 268.8 feet
The middle of the sailboat is approximately 268.8 feet from the shore.
solution for 2x is equal to 10
Answer:
The answer is 5
Step-by-step explanation:
divide 10 by two and get 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
We have the equation [tex]2x = 10[/tex], we can try and isolate x by dividing both sides by 2.
[tex]2x \div 2 = 10\div2\\x = 5[/tex]
Hope this helped!
Which of the following best describes the graph shown below?
16
A1
1
14
O A This is the graph of a linear function
B. This is the graph of a one-to-one function
C. This is the graph of a function, but it is not one to one
D. This is not the graph of a function
The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.
The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.
The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.
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.
A 250.0 kg rock falls off a 40.0 m cliff. What is the kinetic energy of the rock just before it hits the ground (hint: conservation of energy)?
Answer:
kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Step-by-step explanation:
conservation of energy states that total energy of a system remains constant.
Potential energy of body = mgh
m = mass
g = gravitational pull = 9/8 m/s^2
h = height
kinetic energy = 1/2 mv^2
where v is the velocity of body
________________________________________
Total energy for this at any point is sum of potential energy and kinetic energy
total energy at height h
v= 0
PE = 250*9.8*40= 98,000
KE = 1/2 m0^2 = 0
total energy at when ball hits the ground
h=0
PE = 250*9.8*0 =
KE = 1/2 mv^2
_______________________________________\
Applying conservation of energy
Total energy at height h = total energy at ground
98000 = KE
Thus, kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
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}
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
For a ,a relationship to be a function, which values cannot repeat: the x-
values or the y-values? *
Answer:
The x - valuesThe y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)
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 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
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 LCD for x/4 - 2/3 = 7/12?
Answer:
12
Step-by-step explanation:
All the denominators are factors of 12.
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
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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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.
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 :)
An empty row in a frequency table is a mistake True or false
Answer:
False I think
Step-by-step explanation:
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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