Answer:
[tex]\displaystyle \large{x=\dfrac{1}{7}}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle \large{7x=1}[/tex]
Divide both sides by 7:
[tex]\displaystyle \large{\dfrac{7x}{7}=\dfrac{1}{7}}\\\displaystyle \large{x=\dfrac{1}{7}}[/tex]
Therefore, the solution is x = 1/7
Answer:
[tex]x =\frac{1}{7}[/tex]
Step-by-step explanation:
Find the value of x in 7x = 1
[tex]7x = 1 < == divide\ both\ sides\ by\ 7\\\\\frac{7x}{7}=\frac{1}{7}\\\\ x =\frac{1}{7}[/tex]
Hope this helps!
Nadia walks at an average speed of (x + 2) km/h for (x – 3) hours and cycles at an average speed of (3x + 5) km/h for x hours. She covers a total distance of 74 km. (i) Form an equation in x and show that it reduces to 4x2 + 4x - 80 = 0. (ii) Solve the equation 4x2 + 4x – 80 = 0. (iii) Find the time taken for her entire journey.
The time taken by Nadia for her entire journey is 5 hours
Speed and distance
Speed is the rate at which an object is moving, and it is defined as the distance traveled per unit of time. The formula for speed is:
Speed = Distance/Time
Where distance is the distance traveled by an object and time is the time taken to travel that distance.
From the fomrula, we can write as
Distance = Speed × Time
Here we have
Nadia walks at an average speed of (x + 2) km/h for (x – 3) hours and cycles at an average speed of (3x + 5) km/h for x hours.
As we know, Distance = Speed x Time
Distance walked = (x + 2)(x - 3)
Distance cycled = (3x + 5)(x)
The total distance covered is given as 74 km,
=> (x + 2)(x - 3) + (3x + 5)(x) = 74
=> x² - 3x + 2x - 6 + 3x² + 5x = 74
=> 4x² + 4x - 80 = 0
Hence, the final equation is 4x² + 4x - 80 = 0
(ii) The quadratic equation, can be solved as follows
=> x² + x - 20 = 0
=> x² + 5x - 4x - 20 = 0
=> x(x + 5) -4(x + 5) = 0
=> (x + 5) (x - 4) = 0
=> x = - 5 and x = 4
Here we cant take time as negative so take x = 4 hours
(iii) To find the time taken for her entire journey, we need to add up the time taken for walking and cycling:
Total time = (x - 3) + x
Total time = 2x - 3
Substituting the value of x
Total time = 2(4) - 3 = 8 - 3 = 5
Therefore,
The time taken by Nadia for her entire journey is 5 hours
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Juan has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $265.36.
He buys 2 bicycle reflectors for $13.61 each and a pair of bike gloves for $37.11.
He plans to spend some or all of the money he has left to buy new biking outfits for $54.87 each.
What is the greatest number of outfits Juan can buy with the money that's left over?
Answer:
Juan can buy 6 outfits with the money that's left over.
Step-by-step explanation:
Take $640-$265.36-$13.61-$37.11 and then divide
the answer, $332.92 by $54.87.
Juan spent a total of $316.08 on the bicycle, reflectors, and gloves. With the remaining $323.92, he can buy a maximum of 6 biking outfits priced at $54.87 each.
Given that,
Juan has $640 to spend at a bicycle store for new gear and biking outfits.
He buys a new bicycle for $265.36.
He buys 2 bicycle reflectors for $13.61 each.
He buys a pair of bike gloves for $37.11.
To determine the greatest number of outfits Juan can buy with the money he has left,
Calculate the remaining amount after purchasing the bicycle, reflectors, and gloves.
Juan's initial budget is $640.
After buying the bicycle for $265.36, the remaining amount is,
$640 - $265.36 = $374.64.
Next, he buys 2 bicycle reflectors for $13.61 each, which is a total of
2 x $13.61 = $27.22.
Subtracting this amount from the remaining budget, we have
$374.64 - $27.22 = $347.42.
Additionally, he purchases a pair of bike gloves for $37.11, leaving him with $347.42 - $37.11 = $310.31.
Finally, dividing the remaining budget by the cost of each biking outfit, which is $54.87,
Then Juan can buy a maximum of $310.31 / $54.87 ≈ 6 outfits.
Therefore, the greatest number of biking outfits Juan can buy with the money left over is 6.
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A pharmacist orders medications for a total of $6,439.65.a 6 44% discount is given if payment is made within
15 days, and a 2.5% discount is given if payment is made within 30 days. how much money can be saved by paying in 15 days instead of 30 days?
Answer:
2,672.45475 (round if needed)
Step-by-step explanation:
44 percent to a decimal is 0.44
2.5 percent to a decimal is 0.025
6,439.65 × 0.44 = 2833.446 (within 15 days)
6,439.65 × 0.025 = 160.99125 (within 30 days)
2833.446 - 160.99125 = 2,672.45475
Complete the table and then graph the function.
y = 5x
Answer:
Coordinates: (0,0) ; (1,5) ; (2,10)
Step-by-step explanation:
x | y
0 0
1 5
2 10
Coordinates: (0,0) ; (1,5) ; (2,10)
This should be a straight line that is going diagonally with a positive slope.
What us the diameter of a hemisphere with a volume of 5403ft³, to the nearest tenth of a foot?
Answer:
Volume of a sphere is 4/3πr^3
Determine r for the radius and multiply by 2 for diameter
INSECT CONTROL Mr. Malone used 40 pounds of insecticide to cover 1,760 square feet of lawn and 60 pounds to cover an additional 2,640 square feet. How many pounds of insecticide would Mr. Malone need to cover his whole lawn of 4,480 square feet
Answer:
101.8 lb
Step-by-step explanation:
1760 sq ft are covered by 40 lb
4480 sq ft are covered by x
1760/40 = 4480/x
1760x = 40 × 4480
x = 179,200/1760
x = 101.818181...
Answer: 101.8 lb
i really need the help with this multiple choice question for geometry.
Answer:
A. 50°
Step-by-step explanation:
The external angle ACB created by tangents CA and CB is the supplement of arc AB it intercepts.
∠ACB = 180° -AB
∠ACB = 180° -130°
∠ACB = 50°
Select the correct answer.
What is the range of the function shown on the graph?
у
1
6
2-
4
-8
-6
x
х
-2
2
8
-21
64
8
The range of the function shown on the graph is 20≤y≤60
What is a function?A relation is a function if it has only One y-value for each x-value.
What can go into a function is called the Domain.
What may possibly come out of a function is called the Codomain.
What actually comes out of a function is called the Range.
Range is all the possible values of 'y'.
When we observe the graph, the smallest value of 'y' is 20, where the point is (6, 20), and the largest value of 'y' is 60, where the point is (1, 60).
Therefore, the range of the function shown on the graph is 20≤y≤60
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What is the range of the function in the graph?
. 1≤x≤6
B. 20≤y≤60
C. 20≤x≤60
D. 1≤y≤60
Hello, I need help with my work, someone ANYONE please help me, you will make my day if you help me.
Answer:
2.5, 3, 6, 9, 2.8, 6, 1.5
Is this what you're asking for?
Step-by-step explanation:
Write a two-column proof on a space provided
Answer:
Step-by-step explanation:
The vertices of a rectangle are E(−1, 1), F(−1, 3), G(−5, 3), and H(−5, 1). Find the coordinates of the figure after reflecting in the x-axis, and then translating 3 units right.
The resulting points of the rectangle after applying rigid transformations are E'(x, y) = (2, -1), F(x, y) = (2, -3), G(x, y) = (-2, -3), H(x, y) = (-2, -1).
How to apply rigid transformations on geometrical loci
Rigid transformations are transformations in which Euclidean distances are conserved in every point of the geometrical locus. Reflections and translations are sound examples of rigid transformations.
Based on all the information given in the statement, we must apply the following vectorial formula to each vertex of the rectangle EFGH:
(x', y') = (x + 3, -y) (1)
If we know that E(x, y) = (-1, 1), F(x, y) = (-1, 3), G(x, y) = (-5, 3) and H(x, y) = (-5, 1), then the new coordinates are calculated below:
E'(x, y) = (2, -1), F(x, y) = (2, -3), G(x, y) = (-2, -3), H(x, y) = (-2, -1)
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4+3÷3(67)-5×8
What is the answer
What's the answer for this!
The options for each paragraph are listed below:
First paragraph50100001000Second paragraph0maximum18.498.6017.2How to fill the blanks in paragraphs on applications of second order polynomialsIn this question we are supposed to understand and apply concepts related to second order polynomials to fill the blanks when required in the following two paragraphs.
First paragraph talks about second order polynomials applied to economics and the second paragraph talks about second order polynomials applied to kinematics.
First paragraphThe roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x = 0 and x = 100. The vertex is (50, 1000).
The maximum profit of $ 50 is reached when 1000 items are produced.
The first root tells us that the profit will be 0 when 0 products are produced. The second root says once 1000 items are made, the company is no longer making any profit. (They do not have production capacity and have to outsource for anything over 50)
Second paragraphThe trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x) = -0.25 · x² + 4.3 · x, where x is the number of feet away from the golf club (along the ground) the ball is.
The ball starts 0 feet above the ground.
The ball reaches a maximum height of 18.49 feet at a horizontal distance of 8.60 feet away from the golf club its was hit with.
The ball returns to the ground at about 17.2 feet away.
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Find the third side, round the nearest 10th
Answer:
11.9
Step-by-step explanation:
Pythagorean theorem:
[tex]a^2+b^2 = c^2[/tex]. where a and b are the sides and c is the hypotehnus (the side in front of the 90 degree angle)
[tex]22^2 + b^2 = 25^2\\484 + b^2 = 625\\b^2 = 625-484\\b^2 = 141\\b = \sqrt{141} \\b = 11.9[/tex]
Answer:
11.9
Step-by-step explanation:
This is a right triangle so I can solve this with the pythagorean theorem.
Set up the equation 22²+x²=25² x would be the third side
Simplify, 484+x²=625
Subtract from both sides 484-484+x²=625-484
x²=141
Find the square root of 141 to get x
The square root of 141 is approximately 11.9 rounded to the nearest tenth.
What pair of factors of -28 has a sum of -3
Answer:
4 and -7
Step-by-step explanation:
Factors of -28: - 1, 1, - 2, 2, -4,4 ,-7,7,-14,14,-28,28
Factors with a sum of -3 = 4 and -7.
B
An athlete ran uphill at 3 metres per second for x seconds , downhill
at 6 metres per second for y seconds and covered a total distance
of 375 metres . If the athlete took 5 seconds longer to run uphill than
downhill, calculate the values of xandy.
(5)
Step-by-step explanation:
- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.
- Only the speed of going up the hill and down the hill will be different.
pls help ill kiss u
Write a recursive sequence that represents the sequence defined by the following
explicit formula:
an=-5(3)n+1
Answer:
a1= -45
an= -5 ⋅ 3^n+1
Step-by-step explanation:
A substance requires 310 J of heat to raise the temperature from 19
°C to 42 °C.. If the mass of the substance is 20 g, what is the specific
heat of the substance?
Answer:
.674 j / (g-C)
Step-by-step explanation:
Spec heat = heat required to raise 1 gram of substance 1 degree celsius
Spec heat units : j / (gm-C)
soooo 310 j / (20g * (42-19)C = .674
what's 2 to the -3rd power
Two sides of a triangle are 8 inches and 12 inches long each. Which of the following could be the length of the third side that would form a triangle?
Answer: All except 3 in.
Step-by-step explanation:
Two shorter sides of a triangle are equal to or bigger than the longest side. So the answer is all of them except 3 inches.
Sheila is biking at a constant speed. She travels 54 meters in 9 seconds.
How long in seconds would it take Sheila to travel 90 meters at this speed?
Enter the number in the box.
please answer quickly!! what is the exact value of x and y? please leave an answer if you’re going to comment!! (i’ve posted this 3 times)
To solve this problem
⇒ need to use the special right triangle theorem
⇒ 30-60-90 triangle theorem (look at diagram attached for the property)
(we can use this theorem because the square on one of the angles indicates that the angle is 90 degrees. The other angle is indicated as 60 degrees. All the angles of a triangle should add up to 180, so the last angle is 30 degrees)Using the theorem:
the side facing opposite the 60-degree angle is equal ⇒ [tex]x\sqrt{3}[/tex][tex]x\sqrt{3} =17\sqrt{3} \\x = 17[/tex]
the side facing opposite the 90-degree angle is twice the value of x[tex]y = 2x = 2 * 17 =34[/tex]
Answers:
x = 17 and y = 34
Hope that helps!
1. what can you say about the sum of the measures of <1 and <3?
Statement.
Reason.
i really need help
[tex]\huge\tt \underline{Question}[/tex]
1. what can you say about the sum of the measures of <1 and <3?[tex]\huge\tt\underline{Answer}[/tex]
[tex]\tt{Statements:}[/tex]
[tex]m < 1 + m < 3 = 90[/tex][tex]\tt{Reasons:}[/tex]
Definition of perpendicularity[tex] \\ \\ [/tex]
see the picture above
= "i hope it's help"
Find the area of the figure. Use 3.14 as π.
area triangle:
b×h/2
= 11 in×10 in/2
=55 in²
area half-circle:
pi×r² /2
= 3.14×5in² /2
=78.5in² /2
=39.25 in²
Total area: area triangle+ area half-circle
= 55 in²+39.25 in²
=94.25 in²
WRITE INEQUALITY AND SOLVE• Lamar weighs 250 pounds. If he loses 10 pounds
and then 2 pounds per week after that, how many
weeks will it take him to weigh less than 175 pounds?
Answer:
40 weeks
Step-by-step explanation:
2 x 40 = 80
240-80=160
so for him to get under 175 it could be 40
i am so sorry if this is inccorect.
What is the perimeter of the triangle shown below, if side a = 6 cm and side b = 8 cm?
Answer:
The answer is 24 cm.
Step-by-step explanation:
Since we know two sides, we can find the third side. Using the pythagorean theorm, a^2 + b^2 = c^2, this gives us:
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
Square root of 100 = c
10 = c.
Hope this helps!
how much would $500 invested at a 4% interest compounded continuosly be worth after 7 years round your answer to the nearest cent
Answer: F = 661.56
Step-by-step explanation: interest formula: F = Pe^(rt)
F = future value
P = present value = 500
r = interest rate = 0.04
t = years = 7
F = 500e^(0.04 * 7)
Yo I need to bring up my grade bad so
-3x-9=-3y
(please show it graphed already :D)
Answer:
Step-by-step explanation:
Find the area of this figure! (Don’t give me a big explanation, i have 30 mins to get this ixl to 90, currently at 74)
315 m²
area of rec + area of rec + area of rec + area of triangle
⇒ length + width + length + width + length + width + 1/2 * base * height
⇒ 19 * 6 + 9 * 9 + 18 * 5 + 1/2 * 12 * 5
⇒ 90 + 30 + 81 + 114
⇒ 315 m²
Answer:
315 m²
Step-by-step explanation:
As this figure may seem complicated, we can split it into four separate figures.
Area
Area of vertical rectangle + Area of left horizontal rectangle + Area of right horizontal rectangle + Area of triangle6 x 10 + (9 + 6) x (19 - 10) + 18 x 5 + 1/2 x 12 x (18 + 9 + 6 - 17 - 11)60 + 15 x 9 + 90 + 6 x 560 + 135 + 90 + 30180 + 135315 m²A cylinder has volume 45 pie and radius 3. What is its height?
Answer:
5 units
Step-by-step explanation:
The volume of the cylinder is the area of the circle multiplied by it's height. Therefore, the volume of the cylinder is πr² × h, which when simplified, gives us πr²h. Let's substitute the volume and the radius in the formula to find the height.
⇒ πr²h = Volume of cylinder
⇒ (π)(3²)(h) = 45π
Now, simplify the equation to evaluate the area of the cylinder.
⇒ (π)(3²)(h)/(3²)(π) = 45π/(3²)(π)
⇒ (h) = 45π/(9)(π) = 45/(9) = 5 units