Answer:
18 + √3
Step-by-step explanation:
The product of a surd and its conjugate gives a rational number. Hence;
(18 - √3) (18 + √3)
=324 + 18√3 - 18√3 - 3
=321
A rational number does not contain any surd, hence the answer.
Answer: cube root 1/18 & cube root 12
Please solve, -8-2(7r+1)=-94
Answer:
r = 6
Step-by-step explanation:
Hello!
-8 - 2(7r + 1) = -94
Add 8 to both sides
-2(7r + 1) = -86
Divide both sides by -2
7r + 1 = 43
Subtract 1 from both sides
7r = 42
Divide both sides by 7
r = 6
Hope this Helps
A ball is thrown straight up, from 3 m above the ground, with a velocity
of 14 m/s. The equation to model this path is h(t)= -5t^2 + 14t + 3. How
would you find when the ball is 8 m above the ground?
Your answer
O This is a required question
If you can, find the solution to the above problem and briefly describe
how you found your solution.
Your answer
Answer:
probably the 2.38 seconds answer
Step-by-step explanation:
start by setting the entire equation equal to 8, since h(t) is the height and 8m is the height we are looking at right now.
[tex]8=-5t^{2}+14t+3[/tex]
subtract 8 from both sides to get: [tex]0=-5t^{2}+14t-5[/tex]
use the Quadratic equation to find the time, the negative answer does not count.
when you do the quadratic equation you get [tex]\frac{7+2\sqrt{6} }{5},\frac{7-2\sqrt{6} }{5}[/tex]
In decimal form that's about 2.38 and 0.42 You'd probably go with the 2.38 seconds because the ball starts at 0 seconds, so the lower number is probably to close to the start point.
The solution of the problem is
Given that:
The equation is [tex]h(t)=-5t^2+14t+3[/tex] , where [tex]h(t)[/tex] is height .
The ball is [tex]8m[/tex] above the ground so [tex]h=8m[/tex] .
Now,
Substitute the value of height in given equation,
[tex]h=-5t^2+14t+3\\\\8=-5t^2+14t+3[/tex]
Subtract [tex]8[/tex] on both side to obtain the quadratic equation,
[tex]-5t^2+14t+3-8=8-8\\\\-5t^2+14t-5=0[/tex]
Multiply minus sign in both sides,
[tex]5t^2-14t+5=0[/tex]
Solve the quadratic equation ,
Where,
[tex]a=5,b=-14,c=5[/tex]
[tex]x=-b +\frac{\sqrt{b^{2}-4ac } }{2a} \\\\ x=-b -\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
Substitute the known values in the formula,
[tex]x=\frac{14+\sqrt{(-14)^2-4(5)(5)} }{2(5)} \\x=\frac{14+\sqrt{196-100} }{10} \\\\x=\frac{14+\sqrt{96} }{10} \\\\x=\frac{14+\sqrt{2*2*2*2*2*3} }{10} \\\\x=\frac{14+(4\sqrt{6}) }{10} \\\\x=\frac{7+2\sqrt{6} }{5}[/tex]
Similarly,
[tex]x=\frac{7-2\sqrt{6} }{5}[/tex]
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2/7 What is the value of x?
Answer:
42
Step-by-step explanation:
If the scale factor is 2/7 divide 12 by 2 which is 6. 6 is 1/7 and if Figure a is 7/7
multiply 6 by 7 to get x. That would be 42.
Answer:
42
Step-by-step explanation:
Since the scale factor is [tex]\frac{2}{7}[/tex], we know that the bigger shape went to the smaller shape.
If we know that the smaller shape's side, 12, is [tex]\frac{2}{7}[/tex] of the bigger one, we can make the equation
[tex]\frac{2}{7}x = 12[/tex].
To solve for x, we can divide both sides by [tex]\frac{2}{7}[/tex].
[tex]x = 12\div{\frac{2}{7}}[/tex]
We can multiply by the reciprocal:
[tex]\frac{12}{1} \cdot \frac{7}{2} = \frac{84}{2} = 42[/tex]
Hope this helped!
Identify the rate of change and term 0
1. 3, 5, 7, 9, 11, 13, 15....
Answer:
-1
mark me brainliest
Simplify the expression. (3x2 – 4x + 1) + (-x2 + x – 9)
Answer: 2x2−3x−8
Step-by-step explanation:
A square has an area of 18.49 square yards. What is the length of each side in yards?
Answer:
4.6225
Step-by-step explanation: It would be too long to get an exact
Answer:
Step-by-step explanation:
Area of square = 18.49 square yards
side² = 18.49
side = √18.49
side = 4.3 yards
The altitude a
(in feet) of a plane i minutes after liftoff is given by
a = 34001 + 600. How many minutes
after liftoff is the plane
at an altitude of
21.000 feet?
Answer:
Step-by-step explanation:
a=3400t+600, we put in 21,000 for a. Because we have to find 't' when 'a' is 21,000.
which will give us 21,000 = 3400t+600.
Then,Subtract 600 to both sides to get 20,400 = 3400t
Divide both sides by 3,400 and you get 6 = t.
The ans is 6 minutes. The plane will take 6 min to reach the altitude 21,000 feet
A body of mass 50kg moves with a velocity of 2m5-1. calculate the kinetic energy of the body
Answer:
K.E = 100 J
Step-by-step explanation:
Here, we are interested in calculating the kinetic energy of the body.
Mathematically;
Kinetic energy K.E = 1/2 * m * v^2
From the question, m = 50kg and v = 2 ms^-1
Substituting these values into the equation, we have;
K.E = 1/2 * 50 * 2^2 = 200/2 = 100 J
i will mark brainlist!!
Answer:
3/5 + 2 3/4 = 3 7/20
Step-by-step explanation:
2 = 8/4
2 3/4 = 2 + 3/4
then:
3/5 + 2 3/4 = 3/5 + 8/4 + 3/4
= 3/5 + (8+3)/4
= 3/5 + 11/4
3/5 = 12/20
11/4 = 55/20
then:
3/5 + 11/4 = 12/20 + 55/20 = 67/20
67/20 = 60/20 + 7/20 = 3 + 7/20
= 3 7/20
he Boston public school district has had difficulty maintaining on-time bus service for its students. Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 10 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement using a two tailed test—students were not as late. Assume a population standard deviation for bus arrival time of 10 minutes. The test statistic is 1.20 based on this and an alpha of .05 which of the following statements is not correct?
Answer:
Fail to reject the null hypothesis.
Step-by-step explanation:
The hypothesis test is conducted for Boston public school. They have used z-value table and the value of test statistics is 1.20. AT the significance level of 0.05, the null hypothesis is accepted. We cannot reject the null hypothesis. The p-value is greater than alpha so there is no evidence to support the claim of Boston Public School.
Determine algebraically whether f(x) = x2(x2 + 9)(x3 + 2x) is even or odd.
Answer:
[tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex] is an odd function.
Step-by-step explanation:
Let be [tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex], by Algebra this expression can be rewritten as:
[tex]f(x) = x^{3}\cdot (x^{2}+9)\cdot (x^{2}+2)[/tex]
Where [tex]x^{2} + 9[/tex] and [tex]x^{2}+ 2[/tex] are even functions, because they satisfy the condition that [tex]g(x) = g(-x)[/tex], whereas [tex]x^{3}[/tex] is an odd function, as the condition of [tex]h(-x) = - h(x)[/tex] is observed. Then, the overall function is odd.
solve for x 15x + 6 = 10x + 21
Answer:
15x+6=10x+21
15x-10x=21-6
5x=15
divide by 5
5x/5=15/5
x=3
Answer:
x=3
Step-by-step explanation:
15x+6=10x+21
-10x
5x+6=21
-6
5x=15
divided by 5
x=3
help meh wit this bruh♂️
Answer:
a) m∠BPD = 120°
b) m∠BC + m∠AD = 120°
Step-by-step explanation:
a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:
The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.
The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2
The larger exterior arc (m∠BD) = 170°
The small exterior arc (m∠CA) = 70°
m∠BPD = m∠BD + m∠CA/2
m∠BPD = 170° + 70°/2
= 240°/2
= 120°
b) We are to find m∠BC + m∠AD
The sum of exterior angles in a circle = 360°
360° = m∠BD + m∠CA + m∠BC + m∠AD
360° = 170° + 70° + m∠BC + m∠AD
360° = 240 + m∠BC + m∠AD
360 - 240° = m∠BC + m∠AD
Thererefore,
m∠BC + m∠AD = 120°
Answer:
1. m∠BPD = 120°
2. m∠BC + m∠AD = 120°
Answer ASAP, Will give brainliest.
Answer:
[tex]\huge\boxed{10.4\ units\²}[/tex]
Step-by-step explanation:
Area of circle:
=> [tex]\pi r^2[/tex]
Where r = 2.8
=> [tex](3.14)(2.8)^2[/tex]
=> (3.14)(7.84)
=> 24.6 units²
Area of Triangle:
=> 1/2 (Base)(Height)
=> 1/2 (10)(7)
=> 5 * 7
=> 35 units²
Area of the shaded region:
=> 35 - 24.6
=> 10.4 units²
Answer for Brainiest, 25 points and 5 stars with thanks
Range: 71.9
Spread out above the median
The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.
Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.
Hope that helped,
-sirswagger21
Find the value of m∠ADC.
A. 90º
B. 117º
C. 18º
D. 24º
Answer:
A. 90°
Step-by-step explanation:
Any angle that has a box on it denotes that the angle is a right angle.
Definition of a right angle is 90°.
So our answer must be 90°
Answer:
A
Step-by-step explanation:
∠ADC is the same thing as ∠D. ∠D has the little right-angle symbol. Thus, ∠D is a right angle. All right angles are 90°. Therefore, ∠D or ∠ADC is 90°.
Help pleaseeeee. Tyyy
Answer:
Option B.
Step-by-step explanation:
The measure of cage is 90 feet by 40 feet.
Length of rope [tex]=40\sqrt{2}[/tex] foot
It is clear that, length of rope is greater than one side of cage and raw a line which divides the cage in two parts as shown in below figure.
We need to find the shaded area.
By Pythagoras theorem:
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex](40\sqrt{2})^2=(40)^2+perpendicular^2[/tex]
[tex]3200=1600+perpendicular^2[/tex]
[tex]3200-1600=perpendicular^2[/tex]
[tex]1600=perpendicular^2[/tex]
[tex]40=perpendicular[/tex]
So, it is a square.
From the figure it is clear that the shaded area contains 1/8th part of circle are half part of square.
Area of circle is
[tex]A_1=\pi r^2[/tex]
[tex]A_1=\pi (40\sqrt{2})^2[/tex]
[tex]A_1=3200\pi[/tex]
Area of square is
[tex]A_2=a^2[/tex]
[tex]A_2=(40)^2[/tex]
[tex]A_2=1600[/tex]
Area of shaded portion is
[tex]A=\dfrac{A_1}{8}+\dfrac{A_2}{2}[/tex]
[tex]A=\dfrac{3200\pi}{8}+\dfrac{1600}{2}[/tex]
[tex]A=400\pi+800[/tex]
[tex]A=400(\pi+2)[/tex]
The required area is [tex]400(\pi+2)[/tex] sq. ft.
Therefore, the correct option is B.
What is the answer please
Answer:
I think it should be (C)
Answer:
B
Step-by-step explanation:
The fastest way to solve this would to plug in a number for x such as 1 in both equations to find which 2 are equivalent.
When you plug 1 into the top equation it equals 3.5, so now we need to find the correct equation below that equals 3.5 when 1 is plugged in for x.
When you plug 1 into equation B you are also left with 3.5.
Figure a is a scale image of figure b. Figure a maps to figure b with a scale factor of 0.75 What is the value of x? please answer asap!
Answer:
x = 7.5
Step-by-step explanation:
Step 1: Create a fraction with the known sides
[tex]\frac{x}{10}[/tex]
Step 2: Set the fraction equal to the scale factor
[tex]\frac{x}{10}=\frac{0.75}{1}[/tex]
Cross multiple to solve for x
[tex]x = 7.5[/tex]
Therefore x is equal to 7.5
Answer:
7.5
Step-by-step explanation:
did it on khan
0 is the multiplicative identity of the set of rational numbers true or false
if [tex] x\times e=x[/tex] for all x, then e is the Multiplicative Identity.
is this enough for you to get the answer?
Answer:
FALSE.
Step-by-step explanation:
1 is the multiplicative identity of the set of rationals.
7 people out of the 99 visitors bought a gift. About ___% of the visitors bought a gift.
Answer:
About 7.07% of the visitors bought a gift.
Step-by-step explanation:
7/99 = 0.0707
0.0707 *100 = 7.07%
then:
About 7.07% of the visitors bought a gift.
if A+B+C=π prove that sinA+sinB+sinC=4cosA/2 cosB/2 cosC/2
Answer:
oyo archer comes here in answer your real answer it is 7 divided by 7 divided / 2 / to the answer X to other words if you're into Google with answers in churches of students
PLEASE HELP ME WITH THIS QUESTION
Answer:
answer is 90°
Step-by-step explanation:
it's simple , these both angles are complementary so sum of both is 90°
I hope it helped:)
Answer:
see below
Step-by-step explanation:
58+32 = 90
The angles add to 90 degrees, so the angles are complementary
Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(250)?
Answer:
Hey There!! The Correct answer C: ) is the average number of days a house stays on the market before being sold for price p in $1,000s
A little more clearer explanation:
p is the price in $1000s, and
f(p) is the number of days before its sold for p
Hence, f(250) would be the number of days before its sold for 250,000 (since p is in $1000s)
Answer choice C is the correct one.
Hope It Helped!~ ♡
ItsNobody~ ☆
Answer: C
Step-by-step explanation: This is the average number of days the house stayed on the market before being sold for $250,000
Rewrite the equation by completing the square. x^2−4x+3=0
Answer:
x=1 or x=3
Step-by-step explanation:
Hello, please consider the following.
[tex]x^2-4x+3=0\\\\\text{Step 1 - complete the square}\\\\x^2-4x+3=x^2-2*2*x+3=(x-2)^2-4+3=(x-2)^2-1=0\\\\\text{Step 2 - move the constant to the right side, meaning adding 1 here.}\\\\(x-2)^2=1\\\\\text{Step 3 - take the root}\\\\x-2=\pm1\\\\x=2-1=1 \ \ or \ \ x=2+1=3[/tex]
Thank you
answers are -2,1
.
......
Two trees are growing in a clearing. The first tree is 17 feet tall and casts a 10 foot shadow. The second tree casts a 35 foot shadow. How tall is the
second tree to the nearest tenth of a foot?
Answer:
59.5 feet
Step-by-step explanation:
The second tree is 59.5 feet tall.
GivenTwo trees are growing in a clearing.
The first tree is 17 feet tall and casts a 10-foot shadow.
The second tree casts a 35-foot shadow.
Let x be the tall is the second tree.
Then,
The ratio of the height of the tree is;
[tex]\rm \dfrac{17}{10} = \dfrac{x}{35}\\\\17 \times 35 = x \times 10\\\\595 = 10x\\\\x = \dfrac{595}{10}\\\\x = 59.5 \ feet[/tex]
Hence, the second tree is 59.5 feet tall.
To know more about Ratio click the link given below.
https://brainly.com/question/8677748
or what value of g does the function f(g) = g2 + 3g equal 18?
Answer:
The 2 values that makes the function equal to 18 is 3 and -6
Step-by-step explanation:
First you can convert the quadratic equation from standard form to root form
Step 1: Substitute f(g) = 18
Step 2: Move 18 to the other side to create
0 = g² + 3g - 18
Step 3: Now we rearrange equation from standard form into root form
Step 4: Find what adds to 3 and multiples to -18
-3 and 6 adds to 3 and multiples to -18
Step 5: Now we substitute -3 and 6 into the root equation
0 = (g-3)(g+6)
Step 6: Set the brackets to 0 and solve
g - 3 = 0
g = 3
g + 6 = 0
g = -6
10
19 Solve the simultaneous equations.
You must show all your working.
x = 7 – 3y
x2 - y2 = 39
Answer:
x= -8 , y = 5
x= 25/4 , y = 1/4
Step-by-step explanation:
substitute first eqn into the second eqn:
(7 - 3y)^2 -y^2 = 39
49 - 42y + 9y^2 - y^2 = 39
8y^2 - 42y +10 =0
4y^2 - 21y + 5 = 0
(4y-1) (y-5) = 0
y= 1/4 , 5
when y=1/4
x = 7- 3/4
=25/4
when y= 5
x = 7- 15
= -8
The required solution of the given simultaneous equations are x = -8, 25/4 and y = 5, 1/4.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
x = 7 – 3y - - - - -(1)
x² - y² = 39 - - - - (2)
Put x from equation 1 in equation 2
(7 - 3y)² -y² = 39
49 - 42y + 9y² - y² = 39
8y² - 42y +10 =0
4y² - 21y + 5 = 0
(4y-1) (y-5) = 0
y= 1/4 , 5
Substitute this values in the equation 1,
x = -8 and 25/4
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ5
what is 45/99 simply
Answer:
5/11
Step-by-step explanation:
divide numerator and denominator by 9
5/11
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Answer:
5/11
Step-by-step explanation:
45/99
Divide the top and bottom by 9
45/9 = 5
99/9 = 11
5/11
What is |3| = ? -3 0 3
Answer:
3
Step-by-step explanation:
the absolute meaning of a number is never a negative number
