Answer:
C) Going from A to C to D and it is shorter by 3 miles.
Step-by-step explanation:
Angles
AB is 6 miles
BD is _12__ miles
AC is 5 miles
CD is 10 miles
First you need to find BD, so AB times CD. 6(10) = 60. then divide 60 with AC. 60/5 = 12. So BD = 12.
Now add
AB and BD,
{ 6+ 12 = 18} ABD = 18
Now add
AC and CD
{ 5 + 10 = 15 } ACD = 15
18 - 15 = 3
So ACD is 3 miles shorter then ABD.
Got right on the test
The shortest route is to take segment AD which is 8 miles long.
Explanation:To determine the shortest route, we need to find the length of segment AD and compare it to the combined length of segments AC and CD. Since segment AD bisects LA, we can use the properties of a line segment bisector to find its length.
AC = 6 milesCD = 10 milesSince segment AD bisects LA, we can say that AC = CD
Therefore, the shortest route is to take segment AD, which is 8 miles long, since it is equal to the combined length of segments AC and CD.
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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.
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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)The HCF of 2 numbers is 75 and their LCM is 1500. If one of the numbers is 300, find the other.
The other number is 375.
Step-by-step explanation:
The given information are,
The HCF of two numbers is 75.The LCM of the two numbers is 1500.The one number out of the two numbers is 300.
Let, the another number be assumed as 'x'.
The first number = 300 and the second number = x.
To find the number x :
The HCF × LCM = product of two Numbers is a logic to used to find the unknown number.
We know the values of HCF = 75 , LCM = 1500 and one number = 300 and the second number is x.
Therefore, substituting those values in the above formula, we get
⇒ 75 × 1500 = 300 × x
⇒ 1125 / 3 = x
⇒ 375 = x
Therefore, the second number is 375.
5x + 8 + 3x = 26 + 6x
Answer:
X = 9
Step-by-step explanation:
a car dealership pays 8,350 for a car. they mark up the price by 17.4% to get the retail price. what is the retail price at this dealership
Answer:
9802.9
Step-by-step explanation:
find 17.4% of 8350 and then add that to the original price
Write the fraction equivalent of each decimal 36.90
Answer:
36.90 = (369/10)
lim tend to 0 1 minus cosx divided be x^2
-1
Step-by-step explanation:
because 1 - 2 is -1
Roxanne has $3,000 that she plans to invest into an account that earns 7% simple interest.Assuming she makes no additional deposits or withdrawals, how much interest will Roxanne earn after 15 years? *
Answer:
$3150
Step-by-step explanation:
I = P • R • T
Intrest Equals Principal Amout times Rate of Intrest times Amount of Time
P is our Principal amount of $3,000
R is our Rate of 7%
T is the time span of years
Now if we plug in the values and solve the equation we get $3150 dollars in intrest.
Final answer:
Roxanne will earn $3,150 in interest after 15 years.
Explanation:
To calculate the interest Roxanne will earn, we can use the formula:
Interest = Principal x Rate x Time
Where Principal is the initial amount invested, Rate is the interest rate, and Time is the number of years.
Plugging in the given values, we get:
Interest = $3,000 x 0.07 x 15
Interest = $3,150
Therefore, Roxanne will earn $3,150 in interest after 15 years. This implies that Roxanne will accumulate $3,150 in interest after 15 years, illustrating the straightforward application of the interest formula to quantify the financial growth derived from the initial investment over the specified period.
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
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
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])
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
4,6, 12, 5, 8 mean, median,mode
Answer:
mean: 7
median: 6
mode: no mode
Step-by-step explanation:
To find the mean, add all numbers together and subtract by how many numbers there are:
4 + 6 + 12 + 5 + 8 = 35
35/5 = 7
To find the median, you put the numbers in order from smallest to largest and find the very center number:
4, 5, 6, 8, 12
The very center number is 6
To find the mode, you choose the number that appears most often. Since every number in this set only appears once, there is no mode.
Answer:
median=6, mean=5, mode=none
Step-by-step explanation:
median= number in the middle, mean= add up all numbers then divide by how many numbers there are, mode= most common number
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
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! :)
Find the equation of the line that passes through the points (-800, 200) and (-400, 300).
Answer:
y=1/4x+400
Step-by-step explanation:
Slope=Rise/Run=(300-200)/(-400-(-800))=100/400=1/4
Now we have the slope, making our equation:
y=1/4x+b
We need b, the y-intercept, which we can use any ordered pair to plug in:
200=1/4(-800)+b
200=-200+b
400=b
So the equation that passes through the points (-800, 200) and (-400, 300) is: y=1/4x+400
The equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.
What is the general equation of straight line?
The general equation of straight line is -
y = mx + c
Given is a line that passes through the points P(-800, 200) and
Q(-400, 300).
First we will find the slope of the line -
m = (y₂ - y₁)/(x₂ - x₁)
m = (300 - 200)/(-400 + 800)
m = 100/400
m = 1/4
Now, the line passes through the point Q(-400, 300). Therefore -
300 = (1/4) x (- 400) + c
300 = - 100 + c
c = 400
The final equation of the line will be -
y = x/4 + 400
Therefore, the equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.
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Can you guys help me please???
write 5/9 AS A DECIMAL to the nearest tenth
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.
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
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.
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 help asap!! Will give brainlist :)
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.
HELP PLSSSSSSSSSSSSSSSSSSSSSQ
[tex]m\angle B= 41^{\circ},[/tex] [tex]m\angle F= 70^{\circ},[/tex] [tex]m\angle H = 61^{\circ},[/tex] [tex]m\angle K= 56^{\circ}.[/tex]
Step-by-step explanation:
Step 1:
The total of the angles in any triangle is 180°.
So to determine the third angle of the given triangles, we subtract the sum of the other two sides from, 180°.
The third angle = 180° - (the first angle + the second angle).
Step 2:
For triangle ABC,
[tex]m\angle B=180^{\circ}-(\angle A+\angle C)[/tex],
[tex]m\angle B=180^{\circ}-(83^{\circ} + 56^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}.[/tex]
So [tex]m\angle B= 41^{\circ}.[/tex]
For triangle DEF,
[tex]m\angle F=180^{\circ}-(\angle D+\angle E)[/tex],
[tex]m\angle F=180^{\circ}-(61^{\circ} + 49^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}.[/tex]
So [tex]m\angle F= 70^{\circ}.[/tex]
Step 3:
For triangle GHI,
[tex]m\angle H=180^{\circ}-(\angle G+\angle I)[/tex],
[tex]m\angle H=180^{\circ}-(49^{\circ} + 70^{\circ}) = 180^{\circ} - 119^{\circ} = 61^{\circ}.[/tex]
So [tex]m\angle H = 61^{\circ}.[/tex]
For triangle JKL,
[tex]m\angle K=180^{\circ}-(\angle J+\angle L)[/tex],
[tex]m\angle K=180^{\circ}-(83^{\circ} + 41^{\circ}) = 180^{\circ} - 124^{\circ} = 56^{\circ}.[/tex]
So [tex]m\angle K= 56^{\circ}.[/tex]
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.
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
find P(A or B),if the events are disjointed
P(A)=9/25
P(B)=9/25
A 4/25
B 18/25
C 0
D 9/25
Answer: I dont know
Step-by-step explanation:
He is almost dead and wants the pp
Antoine manages a number of apartment buildings that use natural gas for heating, cooking, and laundry. The scatter plot shows the correlation between the outside air temperature and Antoine’s natural gas bill. Which type of correlation does the plot illustrate? A. strong negative B. strong positive C. weak negative D. weak positive Scatter plot is attached
Answer:
A. Strong negative
General Formulas and Concepts:
Statistics
Positive Correlation - trend of data points has a best line of fit that is positive (sloping up)Negative Correlation - trend of data points has a best line of fit that is negative (sloping down)No Correlation - trend of data points does not have a best line of fitStep-by-step explanation:
According to the graph and the data set, we can see that we do indeed have a negative correlation trend. Therefore, options B and D can be eliminated.
Looking at the graph, we can see that we can definitely tell that it is a negative slope and it would be pretty steep. Therefore, the best answer choice would be A. Strong negative.
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°.