The equation is equivalent to −10r−6 = 115 will be B. -10r = 115 + 6.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The equation is equivalent to −10r−6 = 115
Add 6 on both side;
−10r−6 = 115
−10r−6 + 6 = 115 + 6
-10r = 115 + 6
Hence, the equation is equivalent to −10r−6 = 115 will be B. -10r = 115 + 6.
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if twice the raju age is 6 years more than raman age. if raju age is 10 years then raman age is
Help please with this awnser
Answer:
use the Theorem Pythagoras method
Whats is the diference of:
Answer:
[tex]2h^2[/tex]
Step-by-step explanation:
=> [tex](10h^4+h^2)-(10h^4-h^2)[/tex]
=> [tex]10h^4+h^2-10h^4+h^2[/tex]
=> [tex]h^2+h^2[/tex]
=> [tex]2h^2[/tex]
Jamaal has 20 models of planes and cars. He has three times as many cars as planes. What is the ratio of his cars to total models? 1/4 3/1 3/4 4/3
Answer: 3/4
Step-by-step explanation:
If Jamal has 3 times as many cars as planes then we could represent it by the equation x + 3x = 20 where x is the number of planes and 3x is the number of cars.
x+ 3x =20 solve for x
4x = 20
x = 5
Number of planes = 5
Number of cars = 3(5) = 15
Now the ratio of his cars to the total model will be [tex]\frac{15}{20}[/tex] which reduces to 3/4.
Jayden is running laps at track practice. The track is 25 kilometers around. Jayden runs 1 lap in 2 minutes. How many minutes does it take Jayden to run 1 kilometer?
Answer:
0.08 minutes for a kilometer.
Step-by-step explanation:
If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.
I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.
Find the values of x and y.
Answer:
x=6, y=75
Step-by-step explanation:
Since the diameter of the circle is a perpendicular bisector to the chord, x and 6 must be equal and therefore x=6. It also bisects the arc, meaning that y=75. Hope this helps!
The angle of elevation of the top of a tower from a point 100m away from the base of the tower is 45°. The angle of elevation of the top of the flag staff mounted on the top of the tower is 60°. The height of the flag staff is.......... (Use √3 =1.73)
Answer:
The height of the flag staff is 73 m
Step-by-step explanation:
Let H₁ be the height of the building.
Since the angle of elevation of the top of the tower is 45° from a point 100 m away from the base of the tower,
From tan45° = H₁/100
H₁ = 100tan45° = 100 m
Let H₂ be the height of the building plus flag staff.
Since the angle of elevation of the top of the flag staff is 60° from the same point 100 m away from the base of the tower,
From tan60° = H₂/100
H₂ = 100tan60°
= 100√3
= 100 × 1.73
= 173 m.
So, the height of the flag staff is h = H₂ - H₁
= 173 m - 100 m
= 73 m.
So, the height of the flag staff is 73 m
f(x) = x2 - 4x - 21.
What will the function have at the y-intercept and where would the vertex be ?
Answer:
vertex is (2,-25) Y-intercept is -21
Step-by-step explanation:
Answer: EDMENTUM USERS!
I got this correct on the tutorial. Hope this helps!
Step-by-step explanation:
Find the values of a and b such that
x^2 + 3x + 4 = (x + a)^2 + b
URGENT!
*silly answers will be reported
Answer:
a = 1.5
b = 1.75
Step-by-step explanation:
First, we need to solve [tex](x+a)^2[/tex] and replace the result in the initial equation as:
[tex]x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b[/tex]
Then, this equality apply only if the coefficient of [tex]x[/tex] is equal in both sides and the constant is equal in both sides.
It means that we have two equations:
[tex]3x=2ax\\4=a^2+b[/tex]
So, using the first equation and solving for a, we get:
[tex]3x=2ax\\3=2a\\a=\frac{3}{2}=1.5[/tex]
Finally, replacing the value of a in the second equation and solving for b, we get:
[tex]4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75[/tex]
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.
Find the volume of this right rectangular
prism.
3 ft
15 ft
10 ft
[? ]ft?
Answer:
450 ft³
Step-by-step explanation:
V= lwh= 15*10*3= 450 ft³
Answer:
450 ft³
Step-by-step explanation:
Volume of a rectangular prism is lwh.
length × width × height
15 × 10 × 3
150 × 3
= 450
The volume of the right rectangular prism is 450 ft³.
which number line represents the solution to the inequality
What is the domain of this function?
{x|x>0}
{x|x < 8) {x|0< x 8)
{x|x < 0x>8)
Answer:
Step-by-step explanation:
x can take on values as small as 0, as large as 8 and all values in between. The third answer choice is the correct one.
Answer:
It's A.
Step-by-step explanation:
I took the test.
Which coordinate grid shows Point A at (0.75, −1.50)? Coordinate grid shown from negative 2 to positive 2 on the axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 6 grid lines to the left of the y-axis and 3 grid lines above the x-axis. Coordinate grid shown from negative 2 to positive 2 on the axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 6 grid lines to the right of the y-axis and 3 grid lines below the x-axis. Coordinate grid shown from negative 2 to positive 2 on the axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 3 grid lines to the left of the y-axis and 6 grid lines above the x-axis. Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 3 grid lines to the right of the y-axis and 6 grid lines below the x-axis.
Answer:
( fraction negative 1 over 4, fraction 1 and 3 over 4 )
Step-by-step explanation:
Answer:
1st one will be it!
Step-by-step explanation:
The height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet. Find the length of the base and the height of the triangle
Answer:
Step-by-step explanation:
The length of the base is 3 feet and the height of the triangle is 6 feet.
What is the area of a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.
Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.
The dimensions of the triangle will be calculated as,
A = (1/2) x b x h
A = (1/2) x b x ( b + 3 )
54 = ( 1 / 2 ) x ( b² + 3b )
108 = ( b² + 3b )
( b² + 3b - 108) = 0
( b² + 12b -3b -108 ) = 0
(b - 3 ) ( b+ 12 ) = 0
b = 3 and b = -12 ignore negative value.
The height will be calculated as,
h = b + 3
h = 3 + 3
h = 6 feet
Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.
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pls help i need help pls
Answer:
1. x = 32°
2. x = 28°
3. x = 15°
4. x = 30°
5. x = 40°
6. x = 20°
Step-by-step explanation:
All the angles should add up to 90° as they are complementary.
Solve application using algebra. Write your equation or inequality and show your solving steps. The sum of 3 consecutive integers is 147. Find the 3 integers.
Answer:
Integers are 48, 49, 50
Step-by-step explanation:
x+(x+1)+(x+2) = 147
3x + 3 = 147
3x = 147-3
x = 144 / 3 = 48
This probability distribution shows the typical distribution of pitches thrown to a batter in a given at bat in a baseball game. Find the probability that the pitcher will throw fewer than 3 pitches to a batter.
Answer:
0.35
Step-by-step explanation:
This probability distribution is shown below:
Pitch 1 2 3 4 5
Frequency 15 20 40 15 10
Probability 0.15 0.2 0.4 0.15 0.1
The probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 3)
X is the number of pitches thrown. Therefore:
P(X < 3) = P(X = 1) or P(X = 2)
The additive rule pf probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.
P(X < 3) = P(X = 1) or P(X = 2) = P(X = 1) + P(X = 2) = 0.15 + 0.2 = 0.35
The probability that the pitcher will throw fewer than 3 pitches to a batter = 0.35
Answer:
.35
Step-by-step explanation:
a. 1
b. 0
c. Infinitely many
d. Cannot be determined
Answer:
0
Step-by-step explanation:
The lines are parallel, they will never intersect
Answer:
no solution ( 0)
Step-by-step explanation:
If the lines have the same slope by different y intercepts, the lines are parallel
They will never intersect, so they have no solution
Pls help
First box choices : 9x^2-15x
-9x^2-15x
-9x^2+15x
Second box choices:
3x
-3x
X
Answer:
first box : -9x^2-15x
second box: -3x
Step-by-step explanation:
(63x^3y+105x^2y)/(-7xy)=-9x^2-15x/-3x= 3x+5
Which of the binomials below is a factor of this trinomial?
X2-16x + 28
O A. x+7
O B. x2 + 7
O c. x+4
O D. X-14
Answer:
x-14
Step-by-step explanation:
The binomial which is a factor of this trinomial is (x- 14).
What is Trinomial?An algebraic expression with three terms is called a trinomial.
Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z.
Given:
p(x) = x²-16x + 28
If x+ a is factor of any polynomial p(x) then x= -a satisfy the polynomial.
factorizing p(x)
x²-16x + 28
= x²-14x + 2x + 28
= x( x- 14) + 2 (x+ 14)
= (x- 14)(x+ 2)
Hence, the binomial is (x- 14).
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Penny buys 3 bouquets of flowers for $3 each and 4 bouquets for $2 each. Which expression gives the total cost of the bouquets that Penny buys?
A.
33 + 42
B.
33 + 24
C.
33 + 4 × 2
D.
32 + 4 × 2
Its neither of the above(maybe you type something wrong?)
The total cost is
$(3 x 3 + 4 x 2)
Determine the unknown angle measures of ADEF.
Round to the nearest degree.
m2D
23.5
m2 =
24.3
D
33.8
F
Answer:
m∠D = 46°
m∠F = 44°
Step-by-step explanation:
cos D =base/hypo
cosD =23.5/33.8 = 0.695
so and D = 45.97°
thus angle F = 180-(90+45.97) =44.03°
Using relations in a right triangle, it is found that:
The measure of angle D is of 46º.The measure of angle F is of 44º.What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem:
The hypotenuse is of 33.8.The side opposite to angle D is of 24.3.The side opposite to angle F is of 23.5.Hence:
[tex]\sin{D} = \frac{24.3}{33.8}[/tex]
[tex]D = \sin^{-1}{\left(\frac{24.3}{33.8}\right)}[/tex]
[tex]D = 46^\circ[/tex]
[tex]\sin{F} = \frac{23.5}{33.8}[/tex]
[tex]F = \sin^{-1}{\left(\frac{23.5}{33.8}\right)}[/tex]
[tex]F = 44^\circ[/tex]
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calculate the surface area of an open cuboid which is 12 cm long,8cm wide,6cm high
Answer:
432 cm²
Step-by-step explanation:
To find the surface area of a cuboid, there is a formula.
2lw+2lh+2hw
Length is l, height is h, and width is w.
2(12)(8)+2(12)(6)+2(6)(8)
Multiply all the terms.
336+96
Add both the terms.
= 432
The surface area of the open cuboid is 432cm².
Answer:
432 cm²
Step-by-step explanation:
The formula.
2lw+2lh+2hw
Length is l, height is h, and width is w.
2(12)(8)+2(12)(6)+2(6)(8)
336+96
= 432
The surface area of the open cuboid is 432cm²
could someone help me with this question.
Answer:
D
Step-by-step explanation:
The measure of an inscribed angle is half the measure of its intercepted arc, that is
∠ GHI = 0.5 × arc GI = 0.5 × 80° = 40° → D
which expression represents five more than one-third y?
Answer:
1/3 y +5
Step-by-step explanation:
five more than one-third y
1/3 y +5
Answer:
5+1/3y
Step-by-step explanation:
Hope it helps
Derive the explicit rule for the pattern 3,0 -3,-6-9
Answer:
Each term is previous term minus 3
Answer:
Explicit rule: -3
Step-by-step explanation:
3-3=0
0-3=-3
-3-3=-6
-6-3=-9
Each number is subtracting by 3 to get the next number
Therefore your answer would be -3
Hope this helps!
Find the sum. Round your answer to match the less precise measurement. 7.4 L + 1.16 L Answer Choice A. 8.56 L B. 9 L C. 8.5 L D. 8.56 L
Answer: 9 L - B
Step-by-step explanation:
Sum means "add" so you add 7.4 and 1.16. Then it asks for a less precise measurement (or apporaxmate) probably meaning after you've rounded up. That would be 9 L or B. Hope that helps!
Answer:
B
Step-by-step explanation:
Someone plz help me XX
Answer:
-2<x<2
Step-by-step explanation:
its wrong but ur from britain luv innit xxx
One vertex of a polygon is located at (3, –2). After a rotation, the vertex is located at (2, 3). Which transformations could have taken place? Select two options.
Answer:
1) Rotation of the polygon -90° clockwise
2) Rotation of the polygon 270° clockwise
Step-by-step explanation:
Given that the result of the transformation is as follows;
p = (3, -2)
p' = (2, 3)
Therefore, given by the rules of rotation, we have;
When the type of rotation is 90° counterclockwise, which is -90° clockwise
The point of image before rotation = (x, y)
The point of rotated image after the rotation = (-y, x)
Similarly, we have;
When the type of rotation is 270° clockwise,
The point of image before rotation = (x, y)
The point of rotated image after the rotation = (-y, x)
Therefore, the transformations that could have taken place are;
1) Rotation of the polygon -90° clockwise or
2) Rotation of the polygon 270° clockwise
Answer:
1) Rotation of the polygon -90° clockwise
2) Rotation of the polygon 270° clockwise
Step-by-step explanation:
hope this helps
