Answer:
98
Step-by-step explaination:
For this question, it is a direct variation. Hence, the equation would be formed accordingly, and the constant k would also be used.
z varies directly as x²
z= kx² where k is the constant
z = 8
x = 2
Putting the figures in the equation, we have
8=2²(k)
8= 4k
Dividing both sides by 4, we have
k = 8/4
k = 2
Solving for z now, we substitute k with 2. And x with 7
z=kx²
z = 2(7²)
z= 2(49)
z= 98
If it were indirect variation, the constant would have been 1/k. We also have other types of variation, Indirect variation, partial variation and joint variation.
The maximum sustained winds reached by a hurricane were 230 km per hour. a. What is this wind speed in miles per hour? b. What is this wind speed in meters per hour? c. What is this wind speed in meters per minute? d. Use the Internet to determine the highest category attained by hurricanes.
How many gram in one pound
There are 453.592grams in 1 pound
in one pound their are 453.59237 grams.
and as my estimate is 454 grams
I hope this helps
Simply the equation
1/4(-16x+8)
ill give whoever solves it ten points helppp
Answer:
-4x+2
Step-by-step explanation:
rewright factor and reduce
Danny deposits $12,500 into a pension fund that invests in stocks. After a successful two years of investing in the stock market, the fund agrees to pay a simple interest rate of 12% per year. What will the balance on the account be after two years earning interest at this rate? Round your answer to the nearest dollar.
Answer: while earning interest at this rate, the total balance that will be found in the account will be $15,500
Step-by-step explanation:
Before calculating the amount that the sum will grow to after two years, we need to input the formula for calculating simple interest since what the pension fund agreed to pay is a simple if interest if 12%.
Simple interest (S.I) = [Principal(P) × Rate(R) × Time(T)]/100
In this case, the amount deposited initially us $12,500, this is therefore the principal (P). The pension fund agreed to pay a simple interest of 12%, this is then the rate(R). The investment is for a period of two years, this is the time, (t).
S.I = (12,500 × 12 × 2)/100
= $3,000
This is the total interest the deposit will yield. We then add this interest to the initial deposit of $12,500 to find the total amount that will now be in the account after the two years.
$12,500 + $3,000
= $15,500
The total balance in the account after the period of two years is $15,500
Final answer:
$15,500.
Explanation:
Danny is looking to calculate the final balance of his pension fund after two years of earning simple interest at a rate of 12% annually on a principal investment of $12,500. To determine the final balance, we need to use the formula for calculating simple interest:
Simple Interest = Principal × Interest Rate × Time
In this case, Principal is $12,500, the Interest Rate is 12% per year (or 0.12 when converted to a decimal), and Time is 2 years. So the calculation would be as follows:
$12,500 × 0.12 × 2 = $3,000
This means that the interest earned over two years is $3,000. To find the total balance after two years, this interest amount is added to the original deposit:
$12,500 + $3,000 = $15,500
Consider the system of equations.
3x - y = 5,
2x + 3y = -15
Which value can the first equation be multiplied by to form opposite values on the y-term?
The solution to the system of equations is
Answer:
3x − y = 5,
2x + 3y = −15
Which value can the first equation be multiplied by to form opposite values on the y-term? 3
The solution to the system of equations is (0, -5).
Multiply by 3.
Solution is x=0, y=-5.
The coefficients of y are -1 and 3.
If we multiply the first equation by 3. Then the coefficients of y will be 3 and -3. They are opposite values.
After multiplying the first equation by 3 we get:
[tex]3(3x - y) = 3(5)\\9x-3y=15[/tex]
Then we add it with the second equation.
[tex]9x-3y+2x+3y=15-15\\11x=0\\x=0[/tex]
Using x=0 in 3x - y = 5 we get:
[tex]3(0) - y = 5\\0-y=5\\y=-5\\[/tex]
Solution is x=0, y=-5.
Learn more: https://brainly.com/question/13769924
Figure ABCD is reflected across the x-axis. What are the coordinates of A' , B' , C' , and D' ? Enter your answer in each box.
A' ( , )
B' ( , )
C' ( , )
D' ( , )
Answer:
The coordinates of ABCD after the reflection across the x-axis would become:
A'(2, -3) B'(5, -5)C'(7, -3)D'(5, -2)Step-by-step explanation:
The rule of reflection implies that when we reflect a point, let say P(x, y), is reflected across the x-axis:
x-coordinate of the point does not change, buty-coordinate of the point changes its signIn other words:
The point P(x, y) after reflection across x-axis would be P'(x, -y)
P(x, y) → P'(x, -y)
Given the diagram, the points of the figure ABCD after the reflection across the x-axis would be as follows:
P(x, y) → P'(x, -y)
A(2, 3) → A'(2, -3)
B(5, 5) → B'(5, -5)
C(7, 3) → C'(7, -3)
D(5, 2) → D'(5, -2)
Therefore, the coordinates of ABCD after the reflection across the x-axis would become:
A'(2, -3) B'(5, -5)C'(7, -3)D'(5, -2)Can you guys help me please???
Mr. Reynolds used 2 pounds of
peanuts to make trail mix. How many ounces
of peanuts did he use?
Answer:
Mr. Reynolds used 32 ounces of peanuts to make trail mix.
Step-by-step explanation:
One pound is equal to sixteen ounces! Simply, multiply the number of pounds by 16!
2 pounds x 16 ounces = 32 ounces
Hope this helps! :)
lim tend to 0 1 minus cosx divided be x^2
-1
Step-by-step explanation:
because 1 - 2 is -1
John wants to measure the height of a tree.he walks exactly 100 ft from the base of the tree and looks up.the angle from the ground to the top of the tree is 33 degrees.how tall is the tree
Answer: The height of the tree is 64.94ft
Step-by-step explanation:
Using the trigonometry of angles
Tan theta = opposite/adjacent
Tan 33° = height of the tree/100
Height of the tree= tan 33° * 100
= 0.6494*100
= 64.94ft
The height of the tree is 64.94ft
what is 28 1/2 of 120
Answer:
3,420
Step-by-step explanation:
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 28\frac{1}{2}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:120=\frac{120}{1}\\=\frac{57}{2}\cdot \frac{120}{1}[/tex]
[tex]\mathrm{Cross-cancel\:common\:factor:}\:2\\=\frac{57}{1}\cdot \frac{60}{1}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}\\=\frac{57\cdot \:60}{1\cdot \:1}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:57\cdot \:60=3420\\=\frac{3420}{1\cdot \:1}\\ \\\mathrm{Apply\:rule}\:\frac{a}{1}=a\\3420[/tex]
Hope this helps you!
Have a good night!
The equation of line p is y= –9/8x − 6 Line
q ,
which is perpendicular to line
p ,
includes the point
(7, 7) . What
is the equation of line
q ?
Answer:
the equasion of q is y=8/9x + 7/9
Step-by-step explanation:
1. to find the slope perpendicular to the slope of the first equasion, you have to find the negative recipocal, an easy way to find that is to switch the numerator and denominator of the slope as well as multiplying it by -1
2. now that you have found the slope that is perpendicular, your second equasion so far is y= 8/9x, to find the y-intercept, you plug in (7, 7) to x and y, making the equasion 7=8/9(7) + x, in this equasion x is the y intercept
3. when you solve for x for finding the y-intercept, x=7/9, which makes the equasion y=8/9x + 7/9
The sum of two numbers is 1. Five times the larger number plus four times the smaller number is 20. Find the numbers.
Answer:
16 and -15
Step-by-step explanation:
Let the numbers be x and y
x+y = 1 ..............(1)
5x + 4y = 20 .........(2)
Solve simultaneously using elimination method by multiplying equation 1 by 5 to eliminate x
5x + 5y = 5
5x + 4y = 20. Subtract the eqns from each other
---------------------
5y - 4y = 5-20
y = -15
Put value of y into equation 1
x+y = 1
x -15 = 1
Add 15 to both sides
x = 1+15
x = 16
Therefore the numbers are 16 and -15
I hope this was helpful, please mark as brainliest
find the value of n such that (-5)-(-7)>(+9)+(n)
Answer:
The answer is n < -7
Step-by-step explanation:
First, you have to move all the numbers to one side:
(-5) - (-7) > 9 + n
-5 + 7 > 9 + n
9 + n < 2
n < -7
(Hope this can help)
PLEASE ANSWERR
Which equation represents the line of best fit?
A. y= 10x + 45
B. y = x + 45
C. y = −10x+ 45
D. y = 45x + 10
Y-intercept is 45
Slope: (50-45)/(0.5-0)=5/0.5=10
y=10x+45
Answer: a) y=10x+45
the angle of elevation from point c to the top of the cliff is 34°. if point c is 1,000 ft from the base of the cliff, how high is the cliff.
Answer:
675 ft (3 s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
Given rectangle ABCD below,
a. Find the measure of the angles labeled below.
b. If the length of AB=3x–21, DC=34, BC=4y+32, and AD=62, find the values of x and y.
c. Find the perimeter and area of rectangle ABCD.
Answer:
(x, y) = (18 1/3, 7 1/2)perimeter = 192area = 2108Step-by-step explanation:
a) no angles are described or shown
__
b) Opposite sides are the same length, so we have ...
3x -21 = 34
3x = 55 . . . . . . . add 21
x = 55/3 = 18 1/3 . . . . . divide by 3
and
4y +32 = 62
4y = 30 . . . . . . . . subtract 32
y = 15/2 = 7 1/2 . . . . divide by 4
__
c) The perimeter is the sum of the side lengths, so is ...
P = 2(L+W) = 2(62 +34) = 192 . . . units
The area is the product of adjacent side lengths, so is ...
A = LW = 62·34 = 2108 . . . square units
PLEASE HELP 8th GRADE MATH QUESTION OVER HERE!!!
The side AB measures option 2. [tex]\sqrt{20}}[/tex] units long.
Step-by-step explanation:
Step 1:
The coordinates of the given triangle ABC are A (4, 5), B (2, 1), and C (4, 1).
The sides of the triangle are AB, BC, and CA. We need to determine the length of AB.
To calculate the distance between two points, we use the formula [tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}.[/tex]
where ([tex]x_{1},y_{1}[/tex]) are the coordinates of the first point and ([tex]x_{2},y_{2}[/tex]) are the coordinates of the second point.
Step 2:
For A (4, 5) and B (2, 1), ([tex]x_{1},y_{1}[/tex]) = (4, 5) and ([tex]x_{2},y_{2}[/tex]) = (2, 1). Substituting these values in the distance formula, we get
[tex]d=\sqrt{\left(2-4\right)^{2}+\left(1-5}\right)^{2}} = \sqrt{\left(2\right)^{2}+\left(4}\right)^{2}}=\sqrt{20}}.[/tex]
So the side AB measures [tex]\sqrt{20}}[/tex] units long which is the second option.
A software company is selling a new game in a standard edition and a collector's edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector's edition has a volume of 30 cubic inches, the company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which system of equations can be used to determine the number of standard edition games, s, and collector's edition games, c, that were ordered?
A) 75 − s = c
20s + 30c = 1,870
B) 75 + s = c
20s + 30c = 1,870
C) s − c = 75
25(s + c) = 1,870
D) s − c = 75
30s + 20c = 1,870
Answer:
A) 75 − s = c
20s + 30c = 1,870
Step-by-step explanation:
Let us call [tex]s[/tex] the number of standard edition games and [tex]c[/tex] the number of collectors edition games.
Each standard edition game has volume of 20 in³ and each collectors edition game has volume of 30 in³, together the shipping volume is 1870 in³; therefore,
[tex]20s+30c = 1870[/tex].
Also, the company receives a total of 75 copies of the game, which means
[tex]s+c =75.[/tex]
Thus, the system of equations representing the describing the situation are
[tex]20s+30c = 1870[/tex]
[tex]s+c =75,[/tex]
which from the given choices, matches choice A. ([tex]75-s=c[/tex] can be rewritten as [tex]s+c =75[/tex])
If a stone is thrown and travels at a steady speed and covers x metres in 0.2
seconds, what is its speed in metres per seconds and kilometres per hour?
Answer:
speed in meters per seconds = 5x
speed in kilometers per hour = 18
Step-by-step explanation:
The speed is the distance over the time
Given the speed of the stone x meters in 0.2 seconds
So, speed = [tex]\frac{x}{0.2}[/tex] = [tex]\frac{5*x}{5*0.2} = \frac{5x}{1}[/tex] = 5x meters per seconds
To convert from meters per seconds to kilometers per hour :
1 kilometer = 1000 meters ⇒ 1 meters = 0.001 kilometer
1 hour = 3600 seconds ⇒ 1 second = 1/3600 hour
[tex]\frac{meter }{second } = \frac{0.001\ km }{(1 /3600) \ hour} =\frac{3600}{1000} \frac{km}{hour} = 3.6 \ km/hour[/tex]
So, 5x meters per seconds = 5x * 3.6 = 18 kilometers per hour
Final answer:
Calculate the speed of the stone in meters per second and kilometers per hour based on the given distance and time traveled.
Explanation:
The speed of the stone can be calculated as follows:
Speed in meters per second = Distance / Time = x / 0.2 seconds
Speed in kilometers per hour = (x / 0.2) * 3.6
write 5/9 AS A DECIMAL to the nearest tenth
5x + 8 + 3x = 26 + 6x
Answer:
X = 9
Step-by-step explanation:
15 points if you get this question right for me
m∠R = 110° and m∠S = 110°
Solution:
Given data:
RSWY is a parallelogram.
∠R = (5x – 90)° and ∠S = (2x + 30)°
In RSWY, ∠R and ∠S are opposite angles.
Opposite angles of a parallelogram are congruent.
m∠R = m∠S
(5x – 90°) = (2x + 30)°
5x° – 90° = 2x° + 30°
Add 90° on both sides of the equation, we get
5x° = 2x° + 120°
Subtract 2x° on both sides of the equation, we get
3x° = 120°
Divide by 3 on both sides of the equation.
x° = 40°
Substitute x = 40 in m∠R and m∠S.
m∠R = (5x – 90)°
= 5(40°) – 90°
m∠R = 110°
m∠S = (2x + 30)°
= 2(40°) + 30°
m∠S = 110°
Hence m∠R = 110° and m∠S = 110°.
9x1 + 4x1/100 +7x1/1000 in decimal form
The given terms combine to form 9.047 in decimal form. The mathematical conversions are based on division by powers of ten and understanding how to move the decimal point for correct place value representation.
Explanation:The question asks us to express a sum of three terms in decimal form. The terms are: 9x1, 4x1/100, and 7x1/1000.
To simplify, the first term is just 9, as anything multiplied by one remains unchanged.
The second term, when simplified, is 4 divided by 100, which is 0.04.
The third term, 7 divided by 1000, simplifies to 0.007. Adding these three numbers together gives us the decimal form of the expression.
Using the knowledge of powers of ten, we know that dividing by powers of 10 moves the decimal point to the left a number of places equal to the exponent.
For instance, when we divide 1.9436 by 1000, we get 0.0019436.
Converting whole numbers to decimals and vice versa involves moving the decimal point and keeping track of the moves with powers of ten, as seen with the example of 965 becoming 9.65 x 10².
With this understanding, the sum of the terms is as follows: 9 + 0.04 + 0.007, which equals 9.047. This combines whole numbers and decimal fractions into one rounded decimal form.
Please help asap!! Will give brainlist :)
Each students in Ms. Wangs class will use a keyboard with 5 buttons on it to enter a 3-digit nunber. Each button has a different digit on it, from 1 through 5. (Some possible numbers are 111, 123, and 552.) How many different 3-digit numbers are possible for a student to enter?
Answer:
The answer is 12 x 5= 60
Step-by-step explanation:
Each number from the 5 digits becomes used with each other number that is used 5 x. This creates 4*2 =16 3^3=27 +2^3=16 +1^1 = 60
2. The accessory choices of 143 people are recorded in the table.
wearing a watch
no watch
wearing a belt
62
32
no belt
29
20
Create a relative frequency table that could be used to show the percentages of belt
wearers who wear a watch or not, as well as the percentages of people without belts
who wear a watch or not.
| | Wearing a Watch | Not Wearing a Watch |
|------------|-----------------|---------------------|
| Wearing a Belt | 43.36% | 22.38% |
| No Belt | 20.28% | 13.99%
The Breakdown
To create a relative frequency table, we need to calculate the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not.
First, let's calculate the total number of people:
Total = 62 + 32 + 29 + 20 = 143
Now, let's calculate the percentages:
Percentage of belt wearers who wear a watch:
= (Number of belt wearers who wear a watch / Total) × 100
= (62 / 143) *×100
≈ 43.36%
Percentage of belt wearers who do not wear a watch:
= (Number of belt wearers who do not wear a watch / Total) × 100
= (32 / 143) × 100
≈ 22.38%
Percentage of people without belts who wear a watch:
= (Number of people without belts who wear a watch / Total) × 100
= (29 / 143) × 100
≈ 20.28%
Percentage of people without belts who do not wear a watch:
= (Number of people without belts who do not wear a watch / Total) × 100
= (20 / 143) × 100
≈ 13.99%
Using these percentages, we can create the relative frequency table:
| | Wearing a Watch | Not Wearing a Watch |
|------------|-----------------|---------------------|
| Wearing a Belt | 43.36% | 22.38% |
| No Belt | 20.28% | 13.99% |
This table shows the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not.
The diameter is 10ft what is the radius
Radius- 5
The radius is half, so if you want to find the radius, you have to see what if half of the diameter, which is 10. So 10 divided by 2 is 5 which is the radius. Easy.
What is the radius and diameter or the TONU
7 cm
Radius -
Answer:
Radius = 7 cm
Diameter = 7 cm × 2 = 14 cm
Step-by-step explanation:
The radius of the circle is 7 cm, and the diameter is 14 cm.
Given that the radius (R) of a circle is 7 cm, we can determine both the radius and diameter of the circle.
Radius: The radius is the distance from the center of the circle to any point on its boundary. Thus, the radius provided is 7 cm.
Diameter: The diameter is twice the radius, as it stretches from one edge of the circle to the other, passing through the center. Therefore, the diameter is calculated as follows:
Diameter = 2 × Radius
Diameter = 2 × 7 cm
Diameter = 14 cm
So, the diameter of the circle is 14 cm.
To summarize, the radius is 7 cm and the diameter is 14 cm.
Write the fraction equivalent of each decimal 36.90
Answer:
36.90 = (369/10)