Answer:
x = 2
Step-by-step explanation:
Since you didn't attach an image of the graph I'll have to do this the long way and use a strategy called "completing the square" to find the vertex. The x-coordinate of the vertex is the axis of symmetry.
x² - 4x + 6
= (x - 2)² - 4 + 6
= (x - 2)² + 2, therefore the vertex is (2, 2) so the axis of symmetry is x = 2.
Is the following statement true or false? The intersection of a plane and a ray can be a line segment.
Answer:
False
Step-by-step explanation:
Is the following statement true or false?
The intersection of a plane and a ray can be a line segment.
It is false. Correct one is the point.What is the slope of the line in the graph? On a coordinate plane, a line goes through points (negative 2, negative 1) and (0, 1). slope =
Answer:
1
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= (1 - -1)/(0- -2)
= (1+1)/(0+2)
2/2
=1
Answer:
1
Step-by-step explanation:
by using rise over run
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B? (1 point)
A. {2, 4}
B. {1, 2, 3}
C. {1, 2, 3, 4}
D. {1, 2, 3, 4, 5}
Answer:
{2, 4}.
Step-by-step explanation:
A = {1, 2, 3, 4, 5} and B = {2, 4}.
A ∩ B?
This means intersection or what is in common
A ∩ B = {2, 4}.
Find the value of x.
Answer:
x= 42
Step-by-step explanation:
(2x +1)°= 85° (vert. opp. ∠s)
2x +1= 85
2x= 85 -1 (bring constant to 1 side)
2x= 84 (simplify)
x= 84 ÷2
x= 42
Important!!!
That is the distance between (-5, 4) and (-1, 4)?
-5 units
-4 units
4 units
5 units
Answer:
4 units
Step-by-step explanation:
Since the y value is the same, we only have to look at the x value
-1 - -5
-1 +5
4
The distance is 4 units
Answer:
4 units
Step-by-step explanation:
if you graph these 2 points, they'll be on the same line of the graph separated by 4 units
can someone help me please? thanks!
Answer:
V = 11/21
Step-by-step explanation:
Formula: V = 4/3πr³
Simply plug in r to find volume
V = 4/3π(1/2)³
V = 0.52381
And we have our answer!
Based on the given angle measures, which triangle has side length measures that could be correct? A right triangle is shown. The length of the hypotenuse is 16, the base is 8, and the other side is 13.9. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 13.9, the base is 8, and the other side is 16. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 13.9, the base is 16, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Answer:
A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Step-by-step explanation:
The measures of the angles of in a triangle should correspond to the length size of the side opposite each angle in a triangle.
In simple terms, this means that the larger the measure of an angle, the longer the length of the side opposite that angle. Therefore, the smallest measure of an the 3 angles in the triangle should correspond with the shortest length.
Therefore, the triangle with the correct side length would be "A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees." Check the attachment below to see how each side length corresponds with each angle opposite them.
Answer:
D
Step-by-step explanation:
your welcome
Ashley and Beth drove from city A to city B in exactly 5 hours, not taking rest stops. Ashley drove up to the area located halfway between the two cities at the average speed of 40 miles per hour and then Beth drove the other half at an average speed of 60 miles per hour. How many hours did Beth drive on their trip?
Answer:
2 hours
Step-by-step explanation:
Time= 5 hrs
Ashley's speed= 40 mph
Beth's speed= 60 mph
Beth's time in travel= x
Since they drove the same distance, we have this equation:
60x=40(5-x)60x=200-40x100x=200x=200/100x=2 hoursWhat is the area of the composite figure? -70 cm2 -100 cm2 -105 cm2 -130 cm2
Make two shapes out of it.
The bottom is a rectangle 14 x 5 = 70 square cm
The top is a triangle 1/2 x 12 x 5 = 30 square cm
Total area = 70 + 30 = 100 square cm
Answer:
100 cm²
Step-by-step explanation:
The composite shape can be cut into two shapes. One triangle and one rectangle. The sum of their areas is the area of the whole composite shape.
The area of the triangle:
b × h × 1/2
(14 - 2) × 5 × 1/2
60 × 1/2
= 30 cm²
The area of the rectangle:
l × w
14 × 5
= 70 cm²
Add the areas of the two shapes.
30 cm² + 70 cm²
= 100 cm²
The area of the composite shape is 100 cm².
A water balloon is tossed vertically from a window at an initial height (s-sub zero) of 37 feet and with an initial velocity(v-subzero) of 41 feet per second. Answer the following using the fact that h(t)=-16T^2+v-sub zer0t+s sub zero. a) Determine a formula, h)t), for the function that models the height of the water balloon at time t . b)Plot the function in Desmos in an appropriate window. Use the graph to estimate the time the water balloon lands c)Use algebra to find the exact time the water balloon lands. Show your work. No decimals in your answer. d)Determine the exact time the water balloon reaches its highest point and its height at that time. e)4 pts] Compute the average rate of change of on the intervals . Include units on your answers and write a sentence to explain the meaning of the values you found. Arc{1.5,2}____________________________. Explanation: Arc{2,2.5}____________________________. Explanation: årc{2.5,3}____________________________. Explanation:
Answer:
a) h(t) = -16t^2 +41t +37
b) see attached (3.270 seconds)
c) (41+√4049)/32 seconds
d) 1.28125 seconds; 63.265625 feet
e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47
Step-by-step explanation:
a) The formula and initial values are given. Putting those values into the formula, we get ...
h(t) = -16t^2 +41t +37
__
b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.
__
c) Using the quadratic formula, we can find the landing time as ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]
The exact landing time is (41+√4049)/32 seconds.
__
d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.
The value of the function at that point is ...
h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64
The maximum height is 4049/64 = 63.265625 feet.
__
e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...
h'(t) = -32t +41 . . . in feet per second
Then the average rates of change are ...
arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s
arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s
arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s
These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.
Answer:
(a) h(t) = -16t² + 41t + 37
(b) About 3.3 s
[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]
(d) -15 ft/s; -31 ft/s; -47 ft/s
Step-by-step explanation:
(a) The function
h(t) = -16t² + v₀t + s₀
v₀ = 41 ft·s⁻¹
s₀ = 37 ft
The function is
h(t) = -16t² + 41t + 37
(b) The graph
See Fig. 1.
It looks like the water balloon lands after about 3.3 s.
(c) Time of landing
h = -16t² + 41t + 37
a = -16; b = 41; c = 37
We can use the quadratic formula to solve the equation:
[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
(i) Evaluate the discriminant D
D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368 = 4049
(ii) Solve for t
[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]
[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]
(d) Time and maximum height
(i) Time
The axis of symmetry (time of maximum height) is at t = -b/(2a)
[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]
(ii) Maximum height
The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37 = 63.27 ft
(e) Average rate of change
(i) Arc{1.5,2}
h(1.5) = 62.5
h(2) = 55
m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s
The water balloon has started to fall after it has reached peak height, so it is not going very fast
(ii) Arc{2,2.5}
h(2.5) =39.5
m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s
The balloon is in mid-fall, so gravity has caused it to speed up.
(iii) Arc{2.5,3}
h(3) = 16
m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s
The balloon is about to hit the ground, so it is falling at almost its maximum velocity.
Fig. 2 shows the height of the balloon at the above times.
Anybody know this ? Please help :(
Answer:
D
Step-by-step explanation:
5.50. 5.50+0.25= 5.75, 5.75+0.25= 6.00, 6.00+0.25= 6.25, 6.25+0.25= 6.50
Option D is the answer:
5.50, 5.75, 6.00, 6.25, 6.50...
Can someone answer this question thanks
Answer:
80 = x
Step-by-step explanation:
The base angles are the same if the side lengths are the same
The unmarked angle is 50 degrees
The sum of the angles is a triangle is 180 degrees
180= 50+50+x
180 = 100 +x
180 -100 = 100+x-100
80 = x
Answer:
80°
Step-by-step explanation:
In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.
The other angle on the base line is also equal to 50°.
Angles in a triangle add up to 180°.
x° + 50° + 50° = 180°
x° + 100° = 180°
x° = 180° - 100°
x° = 80°
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Answer:
11 is the answer
Step-by-step explanation: i hope so cuz my calculations gives this answer
What is the value of the power a if 5^a = 1/125
Answer:
a = -3
Step-by-step explanation:
5^a = 1/125
The fraction 1/125 can be written as a power with base 5.
5^a = 5^(-3)
Cancel the same bases on both sides.
a = -3
Answer:
a = -3.
Step-by-step explanation:
5^a = 1/125
1/125 = 1 / 5^3
= 5^-3
5^a = 5^-3
so a = -3.
th
Write an explicit formula for An, the nth
term of the sequence 15, 23, 31, ....
Answer:
a₁ = 15 and common difference = 8 so the formula is:
aₙ = 15 + (n - 1) * 8
= 8n + 7
Brandee makes an hourly wage. In the last pay period, she earned $800 for regular hours and $240 for overtime hours. Her overtime rate of pay is 50% more than her regular rate of pay "r". Write and simplify an expression in terms of "r" that represents the number of hours "h" Brandee worked in the pay period. Show your work.
Step-by-step explanation:
Overtime rate= r+50%= 1.5r
Regular hours= 800/r
Overtime hours= 240/1.5r
Total hours worked
h=800/r+240/1.5rh= 800/r+160/rh=960/rr=960/hAn account pays 7%per year simple interest. In 1 year, the amount in the account is 950. How much is in the account in year 6
Answer:
First year's interest is already given.
There are 5 more payments of interest
= 5 * 0.07 * 950 = 332.5
so amount in the account after 6 years = 950 + 332.5 = 1282.5
Answer:
The answer is 1282.50
Step-by-step explanation:
What shape best describes the cross section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
Answer:
Rectangle.
Step-by-step explanation:
The 2 dimensional section would be a rectangle.
Answer:
rectangle
Step-by-step explanation:
How do you write this quadratic equation using substitution
Answer:
u^2 +7u -8=0 where u = 3x+2
Step-by-step explanation:
(3x+2)^2 + 7(3x+2) - 8=0
Let 3x+2 = u
u^2 +7u -8=0
What is the domain of g(x)?
Answer:
-2 ≤x≤5
Step-by-step explanation:
The domain is the inputs
The lowest value of x is -2 and every value of x is valid up to 5
-2 ≤x≤5
What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is positive Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive Negative, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is negative Negative, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is negative
Answer:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Step-by-step explanation:
There are an even number of negative factors, so the product is positive:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Which functions graph is a translation of the graph of f(x)= 3x^2 + 4 seven units down?
A. F(x)= -4x^2 +4
B. F(x)= 10x^2+4
C. F(x)= 3x^2-3
D. F(x)= 3x^2 +11
Answer:
Option C
Step-by-step explanation:
Consider the function f ( x ) = 3x^2 + 4;
[tex]f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\[/tex]
Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;
[tex]4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C[/tex]
* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane
Hope that helps!
Circumference of circles
Answer:
The circumference formula is 2πr and we know r = 1 so the answer is 2π.
Answer: 6.28 feet
Step-by-step explanation:
The formula for circumference is C= πd Diameter is radius times two. So use a value of π which is usually 3.14 or 3.1416 for practical purposes. Multiply by the diameter. 3.14×2=6.28.
Which of the following equations is the translation 2 units up of the graph of y = |x|?
A. y = |x| - 2
B. y = |x| + 2
C. y = |x + 2|
D. y= |x - 2|
Answer:
its y = |x| + 2
Step-by-step explanation:
When planning road development, the road commission
estimates the future population using the function
represented in the table, where x is the time in years and
f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the population in years
Answer:
C
Step-by-step explanation:
Got 100% on edge.
Can someone please help me with this geometry question
Answer:
A. q = 39
Step-by-step explanation:
Since the lines are parallel, their sides will be proportional,
So,
Taking their proportion
=> [tex]\frac{60}{40} = \frac{q}{26}[/tex]
Cross Multiplying
q × 40 = 26 × 60
q = [tex]\frac{1560}{40}[/tex]
q = 39
Solve the equation 4x2 – 27x – 5 = –10x to the nearest tenth.
Please answer this ASAP ❤️
Answer:
4
Step-by-step explanation:
just change the x into -6
-(-6)-2 = 6 - 2 = 4
Answer:
f(x)=-x-2
f(-6)=-(-6)-2
f(-6)=4
Step-by-step explanation:
2x + 3y = 13
4x - y = -2
Answer:
x=1/2. y=4
Step-by-step explanation:
4(2x+3y=13)=8x+12y=52
2(4x-y=-2)=8x-2y=-4
subtract equation one from equation two to get
14y=56 then u will divide bothe sides by 14. for x u substitute y in equation one
Answer:
x = 1/2 y = 4
Step-by-step explanation:
Equation 1
2x + 3y = 13
Equation 2
4x - y = -2
Multiply equation 2 by 3
12x - 3y = -6
Add equation 1 to 3
14x = 7
x = 7/14
x = 1/2
Substitute x into equation 1
2(1/2) + 3y = 13
3y = 13 -1
3y = 12
y= 12/3
y = 4
x =1/2 y = 4
Hope this helps.
On Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4. Write a mathematical statement that represents the situation and determine the price at the end of the week.
Answer:
The price at the end of the week is $33.
Step-by-step explanation:
We are given that on Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4.
The price of a company’s stock on Monday = $30 per share
So, the mathematical statement that represents the situation is given by;
Price of company’s stock on Monday = $30
On Tuesday, the stock price drops $3, so the price of company’s stock on Tuesday = Price of company’s stock on Monday - Drop in price on Tuesday
= $30 - $3 = $27
On Wednesday, the stock price rises $7, so the price of company’s stock on Wednesday = Price of company’s stock on Tuesday + Rise in price on Wednesday
= $27 + $7 = $34
On Thursday, the stock price rises $3, so the price of company’s stock on Thursday = Price of company’s stock on Wednesday + Rise in price on Thursday
= $34 + $3 = $37
On Friday, the stock price drops $4, so the price of company’s stock on Friday = Price of company’s stock on Thursday - Drop in price on Friday
= $37 - $4 = $33
Hence, the price at the end of the week is $33.