Answer:
No
Step-by-step explanation:
First subtract 16 from both sides
y + 4 < 16y + 4 - 16 < 16 - 16y - 12 < 0 So 0 has to be greater than whatever is on the leftIf y = 13 is put into the inequality you get 13 - 12 < 0.What is ultimately true is that 1 < 0 Is 1 smaller than 0?No13 is not a solution to the original inequality.
A space probe flies by a planet in an hyperbolic orbit. It reaches the vertex of its orbit at (5,0) and then travels along a 2 path that gets closer and closer to the line y=-x. Write an equation that describes the path of the space probe if the 5 center of its hyperbolic orbit is at (0,0).
Answer:
[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]
Step-by-step explanation:
Since the required hyperbola has its vertex at (5,0), its transverse axis is on the x-axis and center at (0,0).
So, we use the equation in standard form
[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex]
Also, since the path of the space probe gets closer to y = -x, this is the asymptote to the hyperbola.
Our standard asymptote equation is y = ±bx/a taking the negative sign and comparing with y = -x,
-bx/a = -x ⇒ b/a = 1 ⇒ a = b
Also, the coordinate of the vertex (c, 0) = (5, 0) and c² = a² + b²
substituting c = 5 and a = b into the equation, we have
c² = a² + b²
5² = a² + a²
25 = 2a²
a² = 25/2
a = √(25/2)
a = ±5/√2
rationalizing, we have
a = ±5/√2 × √2/√2
a = ±5√2/2
Since a = b, b = ±5√2/2
Inserting a and b into the equation for the hyperbola, we have
[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\\\frac{x^{2} }{(\frac{5\sqrt{2} }{2} )^{2} } + \frac{y^{2} }{\frac{5\sqrt{2} }{2} ^{2} } = 1\\\frac{x^{2} }{\frac{25 X 2 }{4} } + \frac{y^{2} }{\frac{25X2 }{4} } = 1\\\frac{x^{2} }{\frac{25}{2} } + \frac{y^{2} }{\frac{25}{2} } = 1\\\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]
So, the required equation is
[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]
I need help ppl this is due tomorrow thank yooou
Answer:
8.62
Step-by-step explanation:
Use the Pythagorean theorem.
b= [tex]\sqrt{c^{2}-a^{2} }[/tex]
b=[tex]\sqrt{10.5^{2}-6^{2} }[/tex]
b= [tex]\sqrt{110.25-36[/tex]
b=[tex]\sqrt{74.25}[/tex]
b= 8.62
The ratio of dogs is 5:3. If there are 12 cats, how many dogs are there? PLS HELP
Answer:
First of all, is it the ratio cats to dogs or dogs to cats?
Step-by-step explanation:
?????
What is the area of this triangle?
Answer:
The answer would be 14 units.
Step-by-step explanation:
Count each of the units to find the height and base.
Height - 4 units
Base - 7 units.
Then use the formula A = 1/2*h*b
A = 1/2*7*4
A = 1/2*28
A = 14 units.
The area of the given triangle is 14 units².
Use the concept of the triangle defined as:
A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
And area of triangle = (1/2)x base x height
In the given triangle:
Width = 5 units + 2 units
Width = 7 units
Height = 2 units + 2 units
Height = 4 units
Put the values into the above formula of area,
Area of triangle = (1/2)x 7 x 4
Area of triangle = 14 unit²
Hence,
The area of the given triangle is 14 units².
Learn more about the triangle visit;
brainly.com/question/1058720
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Sue wants to know whether wearing sunglasses improves driving performance. If she uses an independent groups design, she would manipulate the variable by randomly requiring half the drivers to drive with sunglasses and the other half to drive without sunglasses. having all drivers first drive without sunglasses and then with sunglasses. having half the drivers first drive without sunglasses and then with sunglasses and having the other half first drive with sunglasses and then without sunglasses. requiring all drivers to first drive with sunglasses and then without sunglasses.
Answer:
randomly requiring half the drivers to drive with sunglasses and the other half to drive without sunglasses.
Step-by-step explanation:
When employing an independent group design in a research or experimental study, the different groups in the study are assigned entirely different subjects such that, subjects in the treatment group are different from those in the control group. Therfore, adopting an independent group design in the scenario described above means diving the subjects into two at random with one half driving with sunglasses and the other half having to drive without it.
someone please please help me with this ! I would really appreciate it
Answer:
Both volumes are the same
Step-by-step explanation:
Volume of cylinder = [tex]\pi[/tex][tex]r^{2} h[/tex]
r = radius
h = height
Since area of the circle is given on top,
Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
We know the area is 12
12 = [tex]\pi[/tex][tex]r^{2}[/tex] (we need to find r)
r = [tex]\sqrt{\frac{12}{\pi} }[/tex]
r = 1.954
Now we can find the cylinder's volume:
Volume of cylinder = [tex]\pi[/tex][tex](1.954)^{2}[/tex] (6)
Volume of cylinder = 72
To find the volume of the cuboid, we use
Volume of cuboid = lwh
l = length
w = width
h = height
Volume of cuboid = 6 x 4 x 3
Volume of cuboid = 72
This proves that both the volumes are the same.
plz answer this ill give 10pts
whats the question....?
54 can be divided with no remainder by which of the following numbers 2 3 4 5 6 9 10
LINKS WILL BE REPORTED NOT HAVING IT
Answer:
6 and 9
Step-by-step explanation:
6 x 9 = 54
A dozen cookies is on sale for $1.92. How much is one cookie?
Select the answer that shows what you need to do mathematically to answer this question.
Reminder: There are 12 cookies in a dozen.
Divide total price by number of cookies:
1.92/12 = 0.16
Each cookie cost $0.16
Answer:
Step-by-step explanation:
16 cents each cookie :3
*PLEASE HELP ASAP ITS A TEST* How many solutions does the system of linear equations represented in the graph below have?
Answer:
0
Step-by-step explanation:
The 2 lines never intersect so there are 0 solutions
4 divided by 1/6 with explanation !
What is the approximate surface area of a cylinder that's base has a radius of 2, and it's lateral rectangle has a length of 6.28, and a width of 4?
Answer:
Surface area of cylinder = 50.26 unit² (Approx.)
Step-by-step explanation:
Given:
Radius of base r = 2 units
Width of lateral rectangle = 4 units
Length of lateral rectangle = 6.28 units
Find:
Surface area of cylinder
Computation:
Surface area of cylinder = 2[Area of base] + Area of lateral rectangle
Surface area of cylinder = 2[πr²] + [l][b]
Surface area of cylinder = 2[(22/7)(2)²] + [6.28][4]
Surface area of cylinder = 2[(22/7)(4)] + 25.12
Surface area of cylinder = 25.14 + 25.12
Surface area of cylinder = 50.26
Surface area of cylinder = 50.26 unit² (Approx.)
Which other expression has the same value as (-4) - (-8) ?
A. (-4) + 8
B. -4 - (-8)
C. 4 + (-8)
D. (-4 ) + (-8)
Answer:
the answer is option (A) . (-4) + 8
it’s geometry, help plz
Answer:
i think its 18(DONT TRUST ME)
Step-by-step explanatioN:
6 x 3
A number multiplied by 7 is less than 21. Which of the following expressions correctly identifies this sentence?
Answer:
Step-by-step explanation:
Find the missing length indicated in the figure.
Answer:
45
Step-by-step explanation:
Since the lines of hypotenuse are parallel,the triangles are similar
20/8 = x/18
cross multiplication
8x = 20x18
8x=360
x=45
answer question for 10 points and brainilest
Answer:
343
Step-by-step explanation:
[tex]\frac{(7^4)^2}{7^5}[/tex]
[tex]=\frac{7^4^*^2}{7^5}[/tex]
[tex]=\frac{7^8}{7^5}[/tex]
[tex]=7^8^-^5[/tex]
[tex]=7^3[/tex]
[tex]=7*7*7[/tex]
[tex]=343[/tex]
I don't know this questions so pls help
Answer:
The distance between the two points is 6.3 units
Step-by-step explanation:
Here, we want to find the distance between the two points
We have the equation to find this as follows;
D = √((x2-x1)^2 + (y2-y1)^2
where (x1,y1) = (-4,2) and (x2,y2) = ((2,4)
so we have the length calculated as follows;
D = √(2-(-4))^2 + (4-2)^2
D = √6^2 + 2^2
D = √36 + 4
D = √40
D = 6.3 units
find the measure of each angle
Answer:
Step-by-step explanation:
m∠ 1 = 180 - 117
m∠ 1 = 63
m∠2 = the same as m∠ 1
m∠2 = 63
m∠3 is also the same b/c of the same length of the "legs" of the triangle
m∠3 = 63
If Charlie has 50 apples but devin ate 25 how many does Charlie have left?
Answer:
25
Step-by-step explanation:
50-25=25
PLEASEE HELPPP ME I needdd helppp
Answer:
5
Step-by-step explanation:
divide the figure as a triangle and a rectangle first.
take away the rectangle part and if you just look at the triangle part,
you can get x using Pythagorean theorem.
Pythagorean theorem is a^2 + b^2 = c^2,
so 3^2 + 4^2 = x^2.
If you calculate it, x should be root 25, which equals 5.
So, the answer is 5.
A rectangle has a height of 5 inches and a area of 35 squared inches what is the length of the base of the rectangle? Please help I dont get it.
Answer:
The length of the base of the rectangle is 7 inches
Step-by-step explanation:
The Area of the rectangle can be found out by multiplying length with the breadth
Area= length * breadth
35 squared inches= x *5
5x= 35
x= 35/5
x= 7inches
Hence the length of the base of the rectangle is 7 inches.
If the area and one side are known then we can simply find the 2nd side by simply substituting x in its place and solving the equation.
A circle has a circumference of 2 x cm. Which statement about the circumference and area is true?
O A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical values of the circumference and area of the circle are equal.
O The numerical value of the circumference is greater than the numerical value of the area.
O The numerical value of the circumference is less than the numerical value of the area.
Vx
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Answer:
O The numerical value of the circumference is less than the numerical value of the area.
Step-by-step explanation:
as pi>2, therefore, only 'the numerical value of the circumference is greater than the numerical value of the area. The numerical value of the circumference is less than the numerical value of the area' is correct.
The parent function y = -2x^2+5 is translated down 12 units and left 8 units. What is the new equation in vertex form?
Answer:
y=-2(x+8)²-7
Step-by-step explanation:
Given: y=-2x²+5
After transformations: y=-2(x+8)²-7
Vertex would be (h,k) -> (-8,-7) instead of (0,5)
Help me plz I don’t get it
Answer:
3.33
Step-by-step explanation:
each cube represents 1, so each flat represents 0.1 and each unit represents 0.01. so if there are 3 of each, it would be 3+0.3+0.03 which equals 3.33
Answer:
3.33
Step-by-step explanation:
Each cube in this picture is equal to 1 unit as the diagram in the upper right corner shows.
We have 3 cubes so -> 1 + 1 + 1 = 3
We also have 3 squares that are 1/10th of a cube.
1/10 * 1 = 0.1 so each square is equal to 0.1 unit.
We have 3 squares so it would be 0.1 + 0.1 + 0.1 = 0.3
We have 3 tiny squares that are 1/100th of a cube.
1/100 * 1 = 0.01 so each tiny square is equal to 0.01 unit.
We have 3 tiny squares so it would be 0.01 + 0.01 + 0.01 = 0.03
Add everything up: 3 + 0.3 + 0.03 = 3.33
Simplify:............
[tex] - \frac{4 {m}^{2} }{1 + {m}^{4} + {m}^{8} } [/tex]
is your answer
Answer:
jshdgdhdhdhdhdhdhd English project work
True or false
A chance event with probability 1 is certain to happen
Answer:
True, since 1 is 1/1, which is 100%
Hope that helps! :)
Step-by-step explanation:
the volume of the square pyramid is ___ cubic feet.
28ft
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ddjdjddddddddddddddddddddddddddddddddddddddddd
Melissa has started training for a race. The first time she trains, she bikes 5 miles. Each subsequent time she trains, she bikes 0.5 mile farther than she did the previous time.
A. Use summation notation to write an arithmetic series to represent the total distance Melissa has biked after she has trained n times.
B. Use the formula for a partial sum of the series you wrote in part a, above, to answer this question: What is the least number of times Melissa must bike for her total distance biked during training to exceed 60 miles? (3 points)
9514 1404 393
Answer:
A. d = ∑[k=1,n] (4.5+0.5k)
B. 9
Step-by-step explanation:
A) The series has first term 5 and common difference 0.5. The general term is given by ...
an = a1 +d(n -1)
an = 5 + 0.5(n -1) . . . . substitute numbers for this series
an = 4.5 +0.5n . . . . . . simplify
The sum is the sum of these terms:
[tex]\displaystyle \boxed{d_n=\sum_{k=1}^n(4.5+0.5k)}[/tex]
__
B) The sum of terms of an arithmetic series is the average of the first and last, multiplied by the number of terms. We want to solve for n to make the sum greater than 60.
[tex]\displaystyle d_n=\frac{n}{2}(5 +4.5 +0.5n)\\\\\dfrac{n}{2}(9.5+0.5n)>60\\\\n(19+n)>240\qquad\text{multiply by 4}\\\\n^2+19n+9.5^2>240+9.5^2\qquad\text{complete the square}\\\\n+9.5>\sqrt{330.25}\qquad\text{square root}\\\\n>18.17-9.5=8.67\qquad\text{positive root, subtract 9.5}[/tex]
Melissa's total distance will first exceed 60 miles the 9th time she trains.
Answer:
A. d = ∑[k=1,n] (4.5+0.5k)
B. 9
Step-by-step explanation:
A) The series has first term 5 and common difference 0.5. The general term is given by ...
an = a1 +d(n -1)
an = 5 + 0.5(n -1) . . . . substitute numbers for this series
an = 4.5 +0.5n . . . . . . simplify
Ginny has a cell phone plan that charges a flat fee of $20 per month plus $.10 per minute used talking on the phone. Which expression will calculate Ginny’s bill if she spends (t) minutes on the phone each month?
Answer:
20 + 0.10t
Step-by-step explanation:
The 20 is the flat rate, the .10 is the per minuet rate meaning the answer is 20 + 0.10t. plz 5 str and thx, and brailiest.