Answer:
Step-by-step explanation:
One of the important things to remember about parabolas is that the vertex is directly in between the focus and the directrix. Our focus is at (4, 0) and the directrix is at (-4, 0), so that means that the vertex (h, k) is at the origin (0, 0). Another important thing to remember is that the distance between either the vertex and the focus or the vertex and the directrix is the p value, the value that tells us how stretched or compressed the parabola is. Another thing to remember is that a parabola will always wrap itself around the focus away from the directrix. So here's what we know then:
Our parabola opens to the right, the equation for that is
[tex](y-k)^2=4p(x-h)[/tex],
p = 4, and the vertex is (0, 0). Filling in the formula for the parabola using that info:
[tex](y-0)^2=4(4)(x-0)[/tex] which simplifies a bit to
[tex]y^2=16x[/tex] and solving it for x:
[tex]\frac{1}{16}y^2=x[/tex]
Answer:
y^2 = 16x
Step-by-step explanation:
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
Answer:
0.723 seconds
Step-by-step explanation:
Let h = 0
0 = -16t² + 6t + 4
Let’s solve by completing the square.
Subtract 4 from both sides.
-4 = -16t² + 6t
Since the coefficient of -16t² is -16, divide both sides by -16.
1/4 = t² - 3/8t
The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.
Then we need to add (b/2)² = 9/256 to both sides to complete the square.
Add 9/256 to both sides.
73/256 = t² - 3/8t + 9/256
Factor right side.
73/255 = (t-3/16)²
Take the square root on both sides.
±√(73/255) = t-3/16
Add 3/16 to both sides.
3/16 ± √(73/255) = t
The answer has to be positive, not negative.
0.72254626884 = t
0.723 ≈ t
Answer:
Rounding to the nearest hundredth, it is 0.72
Write the given expression in terms of x and y only. tan(sin^-1(x)+cos^-1(y))
Answer:
[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]
Step-by-step explanation:
tan(sin⁻¹x + cos⁻¹y)
Use angle sum formula:
[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]
To evaluate these expressions, I suggest drawing right triangles.
For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1. Therefore:
sin θ = x/1
θ = sin⁻¹x
Using Pythagorean theorem, the adjacent side is √(1−x²). Therefore:
tan θ = x / √(1−x²)
tan(sin⁻¹x) = x / √(1−x²)
Draw a new triangle. This time we'll make y the adjacent side to angle θ.
cos θ = y/1
θ = cos⁻¹y
Using Pythagorean theorem, the opposite side is √(1−y²). Therefore:
tan θ = √(1−y²) / y
tan(cos⁻¹y) = √(1−y²) / y
Substituting:
[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]
Multiply top and bottom by √(1−x²).
[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]
Multiply top and bottom by y.
[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]
Rewrite 4 − 5 using the additive inverse and display the new expression on a number line. (5 points) 4 + 5 An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 4 − (−5) An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 5 − 4 An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1. 4 + (−5) An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Answer: 4 + (−5)
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Step-by-step explanation: The arrow from 0 running to 4 is the graph of how the point on the line is a positive 4: Four added to 0
The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5
4 + (-5) = -1 is the additive inverse of 4-5= -1
The descriptions of the number lines are well done, but difficult to sort out.
Answer:
4 + (−5)
Step-by-step explanation:
it is got it correct
help me with this question please.
Answer:
B. cylinder
Step-by-step explanation:
Any cross section of a cylinder that is parallel to the base will be a circle of the same radius as the cylinder.
__
Various cross sections of any of these figures can be made to be non-uniform. They can also be made to be uniform, if you put restrictions on how the section is done.
For example, a right pyramid will have uniform cross sections, if they are all through the point and perpendicular to the base and one edge. Similarly, a sphere will have uniform cross sections if they are all taken at the same distance from the center of the sphere.
We assume the problem intends no particular restrictions, though we would like to note that cylinder cross sections are uniform only when parallel to each other without intersecting a base.
A delivery company estimates that it will take 4 minutes for their drone to fly 7 km how long will it take the drone to fly 21 km
Answer: 12 minutes
Step-by-step explanation:
7 km ........ 4 minutes
21 km ...... ?
21/7 x 4= 12 minutes
Answer: 12 minutes.
Step-by-step explanation:
It is easy to put the numbers into a ratio form to work it out. So-
4 minutes for 7 km = 4 : 7
Then ? minutes for 21 km = ? : 21
You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.
Therefore your answer is 12 minutes.
Which pair of quantities is LEAST likely to be directly proportional?
1. Hours worked and money earned
2. Distance and time when speed is constant
3. Area and side length of a square
4. Total cost and the number of hats purchased
Answer:
A
Step-by-step explanation:
Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)
4. If 30 locusts eat 420 grams of grass in a week. How many days will it
take 21 locusts to consume 420 grams of grass if they eat at the same
rate
Answer:
The amount one locust eats in a week is 420/30 = 14 grams so it eats 14/7 = 2 grams per day, therefore 21 locusts can eat 21 * 14 = 42 grams per day. 420 / 42 = 10 so the answer is 10 days or 1 week and 3 days.
How can we write 0.7 in words?
Step-by-step explanation:
You could simply say the numbers in 0.7 one at a time like this:
=> zero point seven
OR
You can also see 0.7 as a fraction (7/10) and should therefore be said and written as follows:
=> seven tenths
Hope this helps.. Good Luck
0.7 means the same thing as 7 tenths.
Below, I have made a place value chart.
You will see that 0.7 means 0 units and 7 tenths.
the function g(x)=-5x-6
Answer:
D. the slope of f(x) is greater than the slope of g(x)
Step-by-step explanation:
slope of f(x) =rise/run
=y2 -y1 / x2 -x1
slope of f(x)= -1-2/1-0= -3
g(x)= -5x-6
slope of g(x)= -5
-3>-5
D. the slope og f(x) is greater than the slope of g(x)
Please answer this question now in two minutes
Answer:
D
Step-by-step explanation:
For the lines to be parallel, the corresponding angles must be congruent which means:
12x - 4 = 10x + 10
2x = 14
x = 7 degrees
Need help with this. The question is on this image, thanks!
Answer: y = 5/8x + 0.5
Step-by-step explanation:
5/8 is the slope if you could 5 up and 8 to the side
slope form is y=mx+b
y = 5/8x + 0.5
<!> Brainliest is appreciated! <!>
If g(x) = 3x2 - 4x + 1, what is the value of g(-2)?
Answer:
21
Step-by-step explanation:
substitution
Answer:
21
Step-by-step explanation:
Plug in x as -2.
3(-2)² - 4(-2) + 1
3(4) - - 8 + 1
12 + 8 + 1
= 21
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
Find the least number which must be added to 6203 to obtain a perfect square.
Also, find the square root of the number so obtained.
Answer:
78.7591264553
Step-by-step explanation:
search google
copy answer sorry that is all I got
Solve for x 7 x − 4 = 6 Give your answer as an improper fraction in its simplest form.
Answer:
10\7
Step-by-step explanation:
7x-4=6
7x=6+4
7x=10
7x\7=10\7
x=10\7
Answer:-13/3
Step-by-step explanation:
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answer:
Slope would equal 3.
slope= (y2-y1)/(x2-x1)
Plug in you get (8-2)/8-6)
Simplify (6)/(2)=3
Step-by-step explanation:
True or false
The diagonal of a square are congruent
Answer:
True
Step-by-step explanation:
As we know that all four sides and angles of a square are equal to each other plus the diagonal is right angled to each other as they intersect at 90 degree i.e perpendicular
It contains the identical length i.e congruent
Hence the given statement is true i.e diagonal of a square are congruent to each other
What is the slope of the line that passes through the points (-3,2) and (6, -9)?
Answer:
-11/9 is the slope
Step-by-step explanation:
Use the formula and u will find this is the answer, hope this helped!
Y2 - Y1 / X2 - X1
(-9 - 2) / (6 - (-3))
<!> Brainliest is appreciated!
Answer:
-11/9
Step-by-step explanation:
In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:
[tex]\frac{-9-2}{6-(-3)}[/tex]
The negatives cancel out and become postive, so the denominator will then read to be 6+3:
[tex]\frac{-9-2}{6+3}[/tex]
[tex]-\frac{11}{9}[/tex]
Four whole numbers are rounded to the nearest 10 The sum of the four rounded numbers is 90 What is the maximum possible sum of the original four numbers
Answer:
110
Step-by-step explanation:
example:
rounded 20+20+20+30 = 90
original 25+25+25+35 = 110
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answer:
y=3/4 x+2
Step-by-step explanation:
y=mx+b
take two points from graph
(0,2) and (4,5)
find b when x=0 then y=b=2
find m : y2-y1/x2-x1=5-2/4-0
m=3/4
y=3/4 x +2
Solve the system of equations using substitution.
3x + 7y = 19
-X + 8y = -27
Answer:
x= 11
y= -2
Step-by-step explanation:
8y + 27 =x
3(8y+27) + 7y =19
24y + 81 + 7y =19
31y + 81 =19
-81 -81
31y = -62
31 31
y = -2
-x + 8(-2) = -27
-x - 16 = -27
+16 +16
-x = -11
x= 11
Irene is making a patchwork quilt. She has completed a rectangular section that is 2 patches long and 3 patches wide. Each week, she plans to make the quilt one patch longer and 2 patches wider. The total number of patches in the quilt after x weeks is given by the product: (___) • (___) The total number of patches in the quilt after x weeks is given by the product: (___) • (___) What goes in the blanks?
Answer:
[tex](2+x).(3+2x)[/tex] is the total number of patches in the quilt after 'x ' weeks.
Step-by-step explanation:
Given:
Irene has completed rectangular section which is 2 patches long and 3 patches wide.
To find:
Formula for number of patches after x weeks.
Solution:
Total number of patches in the first week = 2 + 2 +2 = 6
OR
we can simply calculate the number of patches by multiplying 2 with 3.
Given that every week,
The quilt will be one patch longer and 2 patches wider.
After [tex]x[/tex] number of weeks,
The quilt will be [tex]x \times 1[/tex] patches longer and [tex]x \times 2[/tex] patches wider.
OR
The quilt will be [tex]x[/tex] patches longer and [tex]2x[/tex] patches wider.
Initially, it was 2 patches long and 3 patches wide.
So, after x weeks:
The quilt will be [tex]2+x[/tex] patches longer and [tex]3+2x[/tex] patches wider.
And total number of patches, after x weeks will be given as:
[tex](2+x).(3+2x)[/tex]
Answer:
The total number of patches in the quilt after x weeks is given by the product:
length times width
The total number of patches in the quilt after weeks is given by the product:
2+x times 3+2x
Let T be the set of things found in a toy store, and V be the set of things that cost more than $50. The set T∪V is the set of things that found in a toy store or cost more than $50 . The set T∩V is the set of things that found in a toy store and cost more than $50 . The set T′ is the set of things that_____ A cost under $50 B not found in a toy store C not found in a toy store and cost more than $50
Answer:
B. not found in a toy store
Step-by-step explanation:
Given:
T = the set of things found in a toy store.
V = the set of things that cost more than $50.
T∪V = the set of things that found in a toy store or cost more than $50.
T∩V = the set of things that found in a toy store and cost more than $50.
The set T′ is the complement of the set T and it consists of the set of things that are not found in a toy store.
The correct option is B
D. Is no solution please help
Answer:
B
Step-by-step explanation:
I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.
Answer:
B
Step-by-step explanation:
It is too blurry BTW but B is correct
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
(a) after 1 s
(b) after 3 s
(c) after 7 s
Answer:
1.) 15,708cm^2/s
2) 47,124cm^2/s
3.) 109,956cm^2/s
Step-by-step explanation:
Given the following:
50cm/s is the radius of the ripple per second , that is, radius(r) of ripple after t seconds = speed * time(t)
Speed = 50cm/s
r = 50t
.area of a circle(A) = πr^2
Rate of change of area with radius :
dA/dt = π2r . dr/dt
Speed of ripple created = 50cm/s; this is the rate at which the radius changes with time (dr/dt)
dr/dt = 50cm/s
Rate at which area is increasing with time:
dA/dt = π2r . dr/dt
dA/dt = π2(50t).50
dA/dt = 5000πt
After 1 second:
dA/dt = 5000π(1)
= 15,707.963cm^2/s
After 3 second:
dA/dt = 5000π(3)
= 47,123.889cm^2/s
After 7 second:
dA/dt = 5000π(7)
= 109,955.74cm^2/s
The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?
Answer:
The diameter is 91.
Step-by-step explanation:
The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91
Answer:
91 yards
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c=π * d
We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.
285.74= 3.14 *d
We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14
285.74/3.14= 3.14*d/3.14
285.74/3.14=d
Divide
91=d
d= 91 yards
The diameter of the field is 91 yards.
for the function F(x)=1/x,which of these could be a value of F(x) when x is close to zero
Answer:
C. -10,000
Step-by-step explanation:
As x approaches zero, f(x) approaches infinity or negative infinity.
Answer: C. -10,000
Answer:
-10,000
Step-by-step explanation:
Use the first four terms of the binomial theorem to approximate 2.2^7
Answer:
248.96 which is approximately 249
Step-by-step explanation:
2.2^7
The coefficients are;
1,7,21,35,35,21,7,1
So the terms we want to use are 1,7,21 and 35
We can write 2.2 as 2+ 0.2
So the approximations are;
1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3
= 128 + 89.6 + 26.88 + 4.48 = 248.96
what is the explicit formula for this sequence? 2,10,50,250,1250
Answer:
[tex]a_n = 2(5)^{n-1}[/tex]
Step-by-step explanation:
Explicit Geometric Formula: [tex]a_n = a_1r^{n-1}[/tex]
a₁ is 1st term
r is common ratio
n is term number
Step 1: Find common ratio r
r = 10/2 = 5
Step 2: Plug variables into formula
[tex]a_n = 2(5)^{n-1}[/tex]
Answer:
This is a geometric sequence with a₁ = 2 and r = 5 where a₁ is the first term and r is the common ratio.
Explicit formula: aₙ = a₁ * r ⁿ⁻¹
The answer is aₙ = 2 * (5ⁿ⁻¹)
Solve for x 8x−6=15 Give your answer as an improper fraction in its simplest form
Answer:
[tex]\boxed{x = \frac{21}{8} }[/tex]
Step-by-step explanation:
=> 8x-6 = 15
Adding 6 to both sides
=> 8x = 15+6
=> 8x = 21
Dividing both sides by 8
=> x = 21/8 (In its simplest form)