Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (4, 1) and (x₂, y₂ ) = (x, - 6)
m = [tex]\frac{-6-1}{x-4}[/tex] = 1
m = [tex]\frac{-7}{x-4}[/tex] = 1 ( cross- multiply )
x - 4 = - 7 ( add 4 to both sides )
x = - 3 → A
The value of 'x' is -3 and this can be determined by using the two point slope formula and also by using the given data.
Given :
The points (4, 1) and (x, -6) lie on the same line.The slope of the line is 1.When two points are given then to determine the slope of the given line below formula can be used:
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the same line.
Now, substitute the value of slope m and points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above equation in order to determine the value of 'x'.
[tex]\rm 1 = \dfrac{-6-1}{x-4}[/tex]
x - 4 = -7
x = -3
So, the value of x is -3.
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prove that there are real numbers a and b such that square root of a + square root of b equals square root of a + b
Answer:
Lets firts mention that the rule presented in the question does not apply for all real numbers
But, we can see that in some cases it might be true.
Let
a = 1
b = 0
√1 + √0 = 1 + 0 = 1
Likewise,
√(1 + 0) = √(1) = 1
And we see that the result is the same.
Use the net to find the approximate surface area of the cylinder to the nearest square meter.
Radius=5
Height=9
Answer:
S.A. = 440 m²Step-by-step explanation:
Look at the picture.
We have the rectangle 2πr × h and two circles.
Therefore the formula of a Surface Area is:
[tex]S.A.=2\pi rh+2\pi r^2[/tex]
We have r = 5m and h = 9m. Substitute:
[tex]S.A.=2\pi(5)(9)+2\pi(5^2)=90\pi+50\pi=140\pi\ m^2[/tex]
[tex]\pi\approx3.14\to S.A.\approx(140)(3.14)\approx440\ m^2[/tex]
Final answer:
To calculate the surface area of the cylinder, use the formula 2π(radius)(height) + 2π(radius)², with radius = 5m and height = 9m. The answer is approximately 440 square meters when rounded to the nearest square meter.
Explanation:
To find the approximate surface area of the cylinder, we can use the formula: Surface area = 2π(radius)(height) + 2π(radius)². Given a radius of 5 meters and a height of 9 meters, we can plug these values into our formula.
The area of the two circular bases is 2π(radius)² = 2π(5)² = 2π(25) = 50π square meters.
The area of the side (the rectangular part when the cylinder is unrolled) is 2π(radius)(height) = 2π(5)(9) = 90π square meters.
Adding both of these areas together gives us the total surface area:
50π + 90π = 140π square meters.
Using 3.14159 as an approximation for π, we get 140π = 140(3.14159) ≈ 439.8226 square meters, which can be rounded to the nearest square meter as 440 square meters.
I NEED HELP DUE TONIGHT!!
Answer:
(-2 , -2)
Step-by-step explanation:
Solution of the system of equations is where the lines intersect
So they intersect at x = - 2 and y = -2
Answer (-2 , -2)
Answer:
(-2, -2) ⇒ x = -2 and y = -2Step-by-step explanation:
The solution of the system of equations is the point of the intersection of a lines.
The dance committee of Pine Bluff Middle School earns $72 from a bake sale and will earn $4 for each ticket they sell to the Spring Fling dance. The dance will cost $400
Write an inequality to determine the number, ttt, of tickets the committee could sell to have money left over after they pay for this year's dance.
AND
What is the solution set of the inequality?
Choose 1 answer:
A) t<82
B) t≤82
C) t>82
D) t≥82
Answer:
c
Step-by-step explanation:
Help me accidentally checked it in !!!!!!!!!
Answer: 16
Step-by-step explanation:
[tex]64^{\frac{2}{3}}=(2^6)^{\frac{2}{3}}=2^{\frac{12}{3}}=2^4=\boxed{16}[/tex]
A map of a highway has a scale of 2 inchesequals39 miles. The length of the highway on the map is 9 inches. There are 7 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch equals 30 miles. How far apart are the rest stops on the new map?
The distance between rest stops on the new map is approximately 4.262 miles.
Explanation:To find the distance between the rest stops on the new map, we need to determine the distance between each rest stop on the original map and then convert it to the new scale. The original map has a scale of 2 inches = 39 miles, so the distance between each rest stop on the original map is (9 inches / 7 rest stops) * 39 miles. Simplifying this gives us 5.571 miles. To convert this distance to the new scale, we use the scale of 1 inch = 30 miles. So, the distance between each rest stop on the new map is (5.571 miles / 39 miles) * 30 miles, which equals approximately 4.262 miles.
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The rest stops on the new map are approximately 19.2857 miles apart.
Explanation:To find the distance between the rest stops on the new map, we need to determine the distance between the rest stops on the original map and then convert it to the new scale.
In the original map, the length of the highway is 9 inches and there are 7 rest stops.
Therefore, the distance between each rest stop on the original map is 9 inches / 7 rest stops = 1.2857 inches.
To convert this distance to the new scale, we multiply it by the ratio of the scales: 1.2857 inches * (1 inch / 2 inches) * (30 miles / 1 inch) = 19.2857 miles.
So, the rest stops on the new map are approximately 19.2857 miles apart.
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Find the exact circumference of a circle with the given radius. x/2 miles C =
¼x miles x miles 2x miles
Answer:
[tex]\pi[/tex] x miles
Step-by-step explanation:
Circumference, C= 2[tex]\pi r[/tex]
r=radius = x/2
C= 2×[tex]\pi[/tex] × x/2
C=[tex]\pi[/tex] x
Answer:
πx miles
Step-by-step explanation:
Given in the question,
radius of a circle = x/2 miles
To find circumference of a circle we will use following formula
2π * r
where π is constant = 3.14
r is radius of circle
Plug values in the formula
2(3.14)(x/2)
2 will cancel out
So we are left with 3.14x miles or πx milesTranslate this sentence into an equation. The product of Mabel's score and 6 is 90 . Use the variable m to represent Mabel's score.
product is the answer to a multiplication problem mx6=90
The sentence 'The product of Mabel's score and 6 is 90' translates into the equation 'm * 6 = 90' in mathematics, where m represents Mabel's score.
Explanation:The sentence provided can be translated into an equation. In mathematics, the phrase 'the product of' means to multiply. Here, Mabel's score is represented by the variable m. The 'product of Mabel's score and 6' is the same as saying 'm multiplied by 6'. This is said to be equal to 90. Therefore, the equation that represents this sentence is m * 6 = 90.
To translate the sentence 'The product of Mabel's score and 6 is 90' into an equation using the variable m to represent Mabel's score, we can write:
6m = 90
This equation states that the product of Mabel's score (m) and 6 is equal to 90.
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a rectangle has a perimeter of 72 ft the side lengths are whole numbers what is the area
Answer:
Minimum area is : 1 * 35 = 35
Maximum area is : 19 * 17 = 323
Step-by-step explanation:
The parameter (P) of rectangle is calculated using:
P = 2(a+b)
We are given that,
P = 72
=> 2(a+b) = 72
=> a+b = 36
In rectangle, the lengths of both sides are different and a whole number (as mentioned in question), Therefore, the length of smaller side a can be varied from 1 to 17. Similarly, the length of larger side varies from 19 to 35.
The area can be easily calculated using a*b.
Minimum area is : 1 * 35 = 35
Maximum area is : 19 * 17 = 323
I got these wrong help needed plz !!
tiene que sacar la raiz nena
Answer: π and √5
Step-by-step explanation:
π is irrational
√5 is irrational
0.3333 is rational (repeating decimal)
√-4 is imaginary (equal to 2i) so is not a Real Number
1/9 is rational (repeating decimal) equal to 0.11111
help on 8, 9, and 12?
Answer:
8.) x = 15
Step-by-step explanation:
8.) divide 40 by 2 = 20 to only find half the triangle..
20^2 + b^2 = 25^2
400 + b^2 = 625
-400 -400
√b^2 = √225
b = 15
The button on Monica's shirt has a radius of 1 centimeter. What is the button's diameter?
Final answer:
To find the diameter of Monica's shirt button with a radius of 1 centimeter, we multiply the radius by 2, resulting in a diameter of 2 centimeters.
Explanation:
The question asks to determine the diameter of a button given its radius. The radius of Monica's shirt button is 1 centimeter. In geometry, the diameter of a circle is defined as twice the radius. Therefore, to find the button's diameter, you simply multiply the radius by 2.
Formula: Diameter = 2 × Radius
Calculation: Diameter = 2 × 1 cm = 2 cm.
Thus, the diameter of Monica's shirt button is 2 centimeters
The price of a plane ticket has increased from $150 to $200. By what percent has the price increased? A) 15% Eliminate B) 25% C) 33% D) 50%
Answer:
c
Step-by-step explanation:
The price of a plane ticket has increased by 33% from $150 to $200, determined by computing the difference between the new and old prices, dividing by the original price, and converting to a percentage.
Explanation:The question is asking by what percent the price of a plane ticket has increased from $150 to $200. To calculate the percentage increase, you subtract the original price from the new price and divide by the original price. Then multiply by 100 to convert it to a percentage. Using this method:
Price Increase = New Price - Original Price = $200 - $150 = $50Percentage Increase = (Price Increase ÷ Original Price) × 100 = ($50 ÷ $150) × 100 = 33.33%So, the price of the plane ticket has increased by 33%, which means the correct answer is C) 33%.
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Find the volume of the cylinder. Use 3.14 for (π Pi) 34 m on top and 27 m down on the right.
Is 34 the diameter or radius?
PLEASE HELP ME I WILL MARK YOU BRAINLIEST!!!!!
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has oil and the test predicts it?
A. 0.09
B. 0.11
C. 0.36
D. 0.44
Answer: A. 0.09
Step-by-step explanation:
So if you subtract 45% from 80% and thats when you get 0.09
The length a rectangle is 2 cm grater than its width .the area is the rectangle is 80 cm square what is the width of the rectangle
Answer:
Step-by-step explanation:
If breadth =x
length =x+2
Area =length *breadth
Area =x(x+2)=80
X^2+2x-80=0
X^2 +10x - 8x - 80=0
X(x+10)- 8(x+10)=0
(X-8)(x+10)=0
X=8 or x=-10
X=8(since breadth cannot be a negative value x cannot be negative)
What is the sum of the geometric sequence 1,3,9.. if there are 12 terms?
Answer:
The sum of terms 12 the geometric sequence 1,3,9... = 265720
Step-by-step explanation:
Formula:-
Sₙ = a₁(1 - rⁿ)/(1 - r)
Where Sₙ - sum of n terms in the GP
a - First term of GP
r - Common ratio
n - Number
It is given the geometric sequence 1,3,9....
To find the sum of 12 terms
Here a = 1, r = 3 and n = 12
Sₙ = a₁(1 - rⁿ)/(1 - r) = 1(1 - 3¹²)/(1- 3) = 265720
Answer:
The sum of the 12 terms = 265720
Step-by-step explanation:
* Lets study the geometric sequence rule
- If a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , .........................
∴ an = a[(r)^(n-1)]
- Where a is the first term and r is the common ratio and
n is the position of the term in the sequence
- The rule of the sum of some terms is Sn = [a(1 - r^n)]/(1 - r)
- Where n is the number of terms we want to add
* Lets check our terms in the sequence
- The terms are 1 , 3 , 9 , ..........
- To find the common ratio divide the 2nd term by 1st term
∵ the second term is 3 and the first term is 1
∴ 3/1 = 3
∴ The common ratio is 3
∵ n = 12 and a = 1
* Lets substitute the values of a , r , n in the rule of the sum to
find the sum of the 12 terms
∴ S12 = [1(1 - 3^12)]/(1 - 3) = (1 - 3^12)/-2 = 265720
* The sum of the 12 terms = 265720
What is the measure of angle 4
Answer:
35 degress
Step-by-step explanation:
Answer: 108 degress
Step-by-step explanation:
I need help with this anybody know it?
3(2n-7)=9
Answer:
5
Step-by-step explanation:
3(2n-7)=9
^ ^
6n-21=9
+21 +21
6n=30
6 6
n=5 :)
If A=3x^2+5x−6 and B=−2x−6x+7, then what is A-B
Answer:
A=3x^2+5x-6
B=-2x^2-6x+7
A-B=(3x^2+5x-6)-(-2x^2-6x+7)
remove parentheses
A-B=3x^2+5x-6+2x^2+6x-7
combine like terms
A-B=5x^2+11x-13
Select the numbers which should be hyphenated when written in words. 17 20 23 46 99 1/3 1/2 7/8
Answer:
23
46
99
1/3
1/2
7/8
Step-by-step explanation:
Let's find out by writing out each of the numbers.
17 = Seventeen (Seventeen stands alone)
20 = Twenty (Twenty stands alone)
23 = Twenty-three will be hyphenated
46 = Forty-six will be hyphenated
99 = Ninety-nine will be hyphenated
1/3 = one-third will be hyphenated
1/2 = one-half will be hyphenated
7/8 = seven-eights will be hyphenated
Now we ask ourselves why are they hyphenated?
We hyphenate because we need the two words to be glued together to show readers that the two or more elements of a sentence are link to each other.
Answer:
23
46
99
1/3
1/2
7/8
Find the area of triangle AOB
Answer:
9√3 unit^2.
Step-by-step explanation:
The area = 1/2 6^2 sin 60
= 1/2 * 36 * √3/2
= 9√3
The area is [tex]9\sqrt{3}un^2.[/tex]
Note that: triangle AOB is an equilateral triangle because:
OA = OB (both are radius)
So ∠OAB = ∠OBA
Given that ∠AOB=60 degree.
The sum of three angles of a triangle is 180 degrees.
So,
∠OAB + ∠OBA + ∠AOB = 180
∠OAB + ∠OBA + 60 = 180
∠OAB + ∠OBA = 120
∠OAB + ∠OAB = 120
2∠OAB = 120
∠OAB = 60
It means ∠OAB = ∠OBA =60.
Since all the angles of these triangle is 60 degree, so triangle AOB is an equilateral triangle.
Given: side length = a = 6.
The area of the triangle is: [tex]\frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{3}}{4}\left(6^{2}\right)=\frac{\sqrt{3}}{4}\left(36\right)=9\sqrt{3}[/tex]
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If sheena buys 5 bags of apples that cost for $12.25, what is the unit price for the apples
Answer:
It should be $2.45.
Step-by-step explanation:
12.25 divided by 5 equals 2.45.
what fraction is equal .20%
Answer: 1/5
Step-by-step explanation:
Answer:
1/500
Step-by-step explanation:
if you add a %, multiply the number by 100 (or move to the right 2 decimal places)
if you remove the %, divide the number by 100 (or move to the left 2 decimal places)
example .5 to a percent is .5(100) = 50%
to make this a fraction, first change the number to a decimal, then divide by 100, or multiply by 1/100.
.20 is the fractional number of two tenths or 2/10%.
(2/10)(1/100) = 2 / 1000 this can reduce to 1/500
A rectangular prism has a height of 8 meters and a volume of 640cubic meters. What is the area of the base of the prism?
Write a fraction that is equivalent to 8
8/1 or 16/2 or 24/3 or 32/4 or 40/5
Jason and Shawn both begin riding their bikes from different points away from the ranger station. They both ride their bikes in the direction away from the station along the same trail.
Jason starts biking 1 mile away from the station. Jason rides at a constant speed of 20 miles per hour.
Shawn starts biking 2 miles away from the station. Shawn rides at the same constant speed as Jason.
Let y represent the total miles away from the station.
At how many hours, x, will it take Shawn to catch up with Jason?
Based on the information provided, complete each expression below and determine the number of solutions.
The answer is: There is no solution, it's not possible for Shawn to catch up with Jason since both are riding at the same constant speed, there is always be a distance of 1 mile between.
Why?If it's possible to Shawn to catch up with Jason, the following equation will be true:
Let be the station our origin, so:
[tex]ShawnPosition=JasonPosition\\20mph.x-2miles=20mph.x-1mile\\-2=-1[/tex]
So, since the equation is not fulfilled, there is not solution, meaning that it's not possible to Shawn to catch up with Jason since both started riding from different points keeping the same constant speed, there will always be a distance of 1 mile between them if they keep the speed constant.
Also, Shawn could have caught up with Jason if he were started with a speed of 21mph instead the Jason speeds (20mph), let's prove that:
[tex]ShawnPosition=JasonPosition\\21mph.x-2miles=20mph.x-1mile\\\\21mph.x-20mph.x=2miles-1mile\\\\mph.x=1mile\\x=1h[/tex]
So, by substituting "x" into the equations, we have:
[tex]ShawnPosition=JasonPosition\\21mph.1h-2mile=20mph.1h-1mile\\21miles-2miles=20miles-1mile\\19miles=19miles[/tex]
So, Shawn could have caught up with Jason if he were started with a 21 mph speed instead starting with the Jason speed (20 mph).
Have a nice day!
(20 points!) Delisa is designing a website that will be viewable on both computers and mobile devices, so the website as it is seen on a mobile device is proportional to the website as it is seen on a computer. The diagonal of Delisa's computer monitor is 21 inches, and the diagonal of Delisa's tablet is 9.7 inches.
If an image is 16 centimeters wide on the website when it's displayed on Delisa's computer, how wide should the image be on the tablet? Round to the nearest tenth of a millimeter, if necessary.
To determine the image width for Delisa's tablet, the width on the computer is divided by the ratio of the diagonals of the devices. The calculated width on the tablet is 7.4cm (74.0mm) when rounded to the nearest tenth of a millimeter.
Explanation:Delisa is tasked with ensuring that the website is proportional on both computers and mobile devices.
Given the diagonal of her computer monitor (21 inches) and tablet (9.7 inches), we know that the scale of the image on the tablet should be in the same ratio as the diagonals.
Since the image is 16 centimeters wide on the computer, we can calculate the width on the tablet using the ratio of the diagonals.
The ratio of the tablet size to the computer size is 9.7/21.
To find the width of the image on the tablet, we use the proportionality:
Width on computer / Width on tablet = Diagonal of computer / Diagonal of tablet
We can then solve for the unknown width on the tablet:
16cm / Width on tablet = 21 / 9.7
By cross-multiplying and solving the equation, we get:
Width on tablet = 16cm * (9.7 / 21)
Width on tablet = 7.390476 cm
Rounded to the nearest tenth of a millimeter, the width on the tablet will be approximately 7.4cm or 74.0mm.
Final answer:
The width of the image on the tablet is calculated using a proportion based on the diagonal screen sizes of the computer and tablet. After converting the image width from centimeters to inches, and using the ratio of the diagonals (9.7 inches to 21 inches), the width on the tablet is determined and then converted back to centimeters, rounded to the nearest tenth of a millimeter.
Explanation:
Delisa is designing a website and wants to ensure that an image displayed on different devices remains proportional. The diagonal of her computer monitor is 21 inches, and the diagonal of her tablet is 9.7 inches. When scaled down, the image width on the tablet should maintain the same proportion to the tablet's screen size as the image on the computer does to the computer's screen size.
To find the proportional width of the image on the tablet, we use the ratio of the diagonals of the two devices. The ratio is the diagonal of the tablet (9.7 inches) to the diagonal of the computer (21 inches), which simplifies to 9.7/21. Since we know the width of the image on the computer is 16 centimeters, we can set up a proportion:
(Width on tablet / 9.7 inches) = (16 cm / 21 inches)
To solve for the width on the tablet, we cross-multiply and divide:
Width on tablet = 16 cm × (9.7 inches / 21 inches)
Before solving, we need to convert 16 cm to inches, since the diagonal measurements are in inches. There are approximately 2.54 cm in an inch, so:
16 cm ÷ 2.54 cm/inch = 6.2992 inches
Now, we can calculate the width for the tablet:
Width on tablet = 6.2992 inches × (9.7 inches / 21 inches)
Performing the multiplication gives us the width on the tablet in inches. To convert back to centimeters, we multiply the result by 2.54 cm/inch. Finally, we round the answer to the nearest tenth of a millimeter.
3 A classroom is arranged with 8 seats in the front row, 10 seats in the middle row, and 12 seats in the back row. The teacher randomly assigns seats to students as they enter the classroom. What is the probability that the first student who enters the classroom will be assigned a seat in the front row? 2 5 A 2 3 B 4 11 4 15
Answer:
0.266
Step-by-step explanation:
Total No of seats in class = 8+10+12 = 30
probability that first student will be assigned first row will be: 8/30 = 0.266
because there are 8 front row seats and total seats are 30.
The probability that the first student who enters the classroom will be assigned a seat in the front row is; Option D; 4/15
We are told;
Number of front row seats = 8 seats
Number of middle row seats = 10 seats
Number of back row seats = 12 seats
Thus;
Total number of seats in classroom = 8 + 10 + 12
>> 30 seats
Now, we want to find the probability that the first student who enters the classroom will be assigned a seat in the front row.
Thus;
P(1st student sits in front row) = 8/30
This can be reduced to get;
P(1st student sits in front row) = 4/15
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The names Jessica,Joshua,Jill,and Jimmy are written on slips of paper. The slips of paper are placed in a bag. One name is picked. Name an event that is impossible. Name an event that is certain. Name an event that is as likely as not. Name an event that is more likely than not.
Answer:
Name an event that is impossible: Drawing the name "John" out of the bag
Name and event that is certain: Drawing a name that starts with the letter "J"
Name an event that is as likely as not: Drawing a girl's name or a boy's name
Name an event that is more likely than not: Drawing a name that is longer than 4 letters.
Step-by-step explanation: