Answer:
[tex] { \tt{8 \sqrt{2} + 2 \sqrt{8} }}[/tex]
separate the biggest root ( √8 ):
[tex]{ \tt{ = 8 \sqrt{2} + 2 \sqrt{4 \times 2} }} \\ = { \tt{ 8 \sqrt{2} + (2 \times 2) \sqrt{2} }} \\ = { \tt{8 \sqrt{2} + 4 \sqrt{2} }}[/tex]
factorise √2 out:
[tex] = { \tt{(8 + 4) \sqrt{2} }} \\ \\ = { \bf{12 \sqrt{2} }}[/tex]
1. Identify the following numbers as rational or irrational.
a. -15.4
b. 27/5
c. 0.99999....
d. V
Given m||n, find the value of x and y
Answer:
x=20,y=34
Step-by-step explanation:
x+14=2x-6 (vertically opposite angles)
x-2x = -6-14
-x = -20
x=20
x+14=y (corresponding angles)
20+14=y
y=34
Answer:
x = 20, y = 34
Step-by-step explanation:
(2x - 6) and (x + 14) are vertical angles and are congruent, then
2x - 6 = x + 14 ( subtract x from both sides )
x - 6 = 14 ( add 6 to both sides )
x = 20
Then
2x - 6 = 2(20) - 6 = 40 - 6 = 34
y and (2x - 6) are alternate angles and are congruent , so
y = 34
Three times a number x minus a half a second number y
Answer:
3x - y/2
Step-by-step explanation:
The parabola described by the equation -1/16(x-3)^2 + 4 = y has the directrix at y=8. What is the focus of the parabola?
Answer:
(3, 0)
Step-by-step explanation:
A parabola is the locus of a point such that the distance from a fixed line called directrix and the distance from a fixed point called focus is constant.
The equation of a parabola with a vertex at (h, k) with axis of symmetry parallel to the y axis is given as:
[tex]4p(y-k)=(x-h)^2[/tex]
The directrix is at y = k - p, and focus is at (h, k + p).
Given an equation -1/16(x-3)^2 + 4 = y, expressing it in standard form is:
[tex]-\frac{1}{16}(x-3)^2+4=y\\\\(y-4)= -\frac{1}{16}(x-3)^2\\\\-16(y-4)=(x-3)^2\\\\[/tex]
Comparing with the standard form:
The center = (h, k) = (3, 4)
Also, -16 = 4p
p = -4
Directrix is at y = k - p = 4 - (-4) = 8
Directrix is at y = 8
The focus is at (h, k + p) = (3, 4 + (-4)) = (3, 0)
The focus is at (3, 0)
Evaluate: 5 + 2 • 42?
5 + ( 2 × 42 ) =
5 + 84 =
89
.....
.....
Answer:
89
Step-by-step explanation:
So we will follow PEMDAS in this exact order:
P- Parentheses
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction
5 + 2 • 42 Equation
5 + (2 • 42) We have no parentheses or exponents so we move on to multiplication
5 + 84 We have no division so we move on to addition
= 89 We have no subtraction so this is our final answer
What is the range of the function?
O all real numbers
O all real numbers greater than 0
O all real number less than or equal to 0
O all real numbers greater than or equal to 0
Which gives the correct values for points A,B,C, and D?
Answer:
The answer would be A
Step-by-step explanation:
Daniel trabalha em um zoológico e cuida da parte tá comida dos leões . nesse zoológico, a quantidade de carne que eles consomem é proporciao ao seu peso. Se um dos leões pesa 18arroubas, qual o corespondente em kg
Answer:
270kg!
Step-by-step explanation:
Which graph represents y as a function of x?
Answer:
A
Step-by-step explanation:
By vertical line test, if you draw any vertical line, except for A, all graph meet at more than two points. So, graph A represents y as a function of x.
plz help me I will give u branist and like u back plz help me I will also follow u
Answer:
hi, the answer is Nu5000
250×20=5000
During a single day at radio station WMZH, the probability that a particular song is played is 6/7. What is the probability that this song will be played on at least 5 days out of 6 days? Round your answer to the nearest thousandth.
Answer:
The required probability is 0.462.
Step-by-step explanation:
Probability to play the song = 6/7
Probability not to play the song = 1 - 6/7 = 1/7
Required probability
= Probability to play 5 days x probability not to play 1 one + Probability to play 6 days
[tex]=\left (\frac{6}{7} \right ) ^5\times \frac{1}{7} + \left (\frac{6}{7} \right ) ^6\\\\= \frac{6^5 +6^6}{7^6}\\\\=0.462[/tex]
in isosceles Triangle RST below what is the value of y
Answer:
second option
Step-by-step explanation:
y + y + 38 = 180 degree ( sum of interior angle of a triangle is 180 degree)
2y = 180 - 38
y = 142/2
y = 71 degree
Answer:
71 degrees
Step-by-step explanation:
Hi there!
All the interior angles of a triangle add up to 180 degrees.
Knowing this, we can construct the following equation:
[tex]180=y+y+38\\180=2y+38[/tex]
Subtract 38 from both sides
[tex]180-38=2y+38-38\\142=2y\\71=y[/tex]
I hope this helps!
I’ve never understood this, please help!
Answer:
-80
Step-by-step explanation:
So basically what we need to do is find the value of x that satisfies the equation.
When I mean satisfy, I basically mean a value of x that makes one side of the equals sign equal to the other side of the equals sign.
So in this case, we need -6 = -6.
To find this lets solve the equaion step by step:
-6=x/8+4
So first off, you always want to get the variable on one side, and the number on the other.
This means you want to subtract the 4 from both sides, leaving x/8:
-6=x/8+4
-4 -4
-10=x/8
Whenever x is not 1x, you have to divide or multiply to get it equal to 1x.
If this is a bit confusing, here is an example:
100=10x
We need 1x, but above is 10x. The reason why we want 1x is because it is the lowest ratio, and most accurate x value.
You can think of it like a 1 dollar bill. Its easier and better to use than per say a 3 dollar bill.
So in the example above you would divide by 10, since 10x/10 would equal 1x.
Remember the rule however, that what you do on one side you must do on the other. This emans you would divide both sides by 10:
100/10 =10x/10
=
10=1x
We have in our equation:
-10=x/8
Our x is lower than 1. It x/8. Whenever we have a value of x greater than 1, we divide, like we did in the example. However here, it is below x. So we multiply.
In this case we multiply by 8, since its x/8:
-10 * 8 = x/8 * 8
=
-80=x
So x is equal to -80.
I hope you understand it better now :D
peter collects antique marbles. he has these two boxes full of marbles
Answer:
3 marbles
Step-by-step explanation:
and they have died inside too
The lengths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in, find the width, perimeter, and area of this rectangle.
Answer:
L = 31.5 w = (4/7)31.5 = 18 p = 2 * 31.5 + 2 * 18 A = 31.5 * 18
Step-by-step explanation:
Find the size of the angle below
Answer:
i wish i could tell you
Step-by-step explanation:
[tex]{(\frac{4}{3}) ^{-1} - (\frac{1}{4} )^{-1})}^{-1}[/tex]
Pls include steps
Step-by-step explanation:
(4/3)–1 = 3/4 and (1/4)–1 = 4/1
now we have,
(3/4 - 4)–1 = (-13/4)–1
= -4/13
Simplify 6V 80.
0 6+16 51
0 6+415
0 6+1615
O 6+4v5i
Answer:
2nd option
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i
Simplifying the radical
[tex]\sqrt{-80}[/tex]
= [tex]\sqrt{16(5)(-1)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex]
= 4 × [tex]\sqrt{5}[/tex] × i
= 4i[tex]\sqrt{5}[/tex]
Then
6 + [tex]\sqrt{-80}[/tex]
= 6 + 4i[tex]\sqrt{5}[/tex]
y=5/2x-5/6
find the slope and simplify
Answer:
5/2
Step-by-step explanation:
The slope of this equation is 5/2
Students are asked to estimate the number of gumballs in a jar. Sam says there are 228 gumballs. In actuality, there are 240 gumballs. What is the percent error
Answer:
5%
Step-by-step explanation:
Percent error = (actual - estimated) / actual x 100
(240 - 228) / 240 x 100 = 5%
Which expression can be used to convert 100 USD to Japanese?
Answer:The expression that can be used to convert 100 USD to Japanese Yen is 100 USD = 100/Y Japanese Yen.
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 46°
Step-by-step explanation:
64° + 70° + x = 180°
x = 180° - 64° - 70°
x = 46°
what is 5\8 divided by 1\4
Answer:
2.5
Step-by-step explanation:
Answer:
2 1/2
Step-by-step explanation:
5/8 ÷ 1/4
Copy dot flip
5/8 * 4/1
Rewriting
5/1 * 4/8
5/1 * 1/2
5/2
Writing as a mixed number
2 1/2
find the area of a circle diameter equals to 30 cm
Answer:
225Pi (in terms of Pi)
Or
706.5cm
Step-by-step explanation:
Area = Pi * radius^2
Radius is half of the diameter, so it is 15.
Area = Pi*15^2
Which is:
225Pi
Or
706.5
Answer:
The area of the circle is
[tex]225\pi[/tex]
Step-by-step explanation:
The diameter equals 30 cm, so the radio equals 15 cm.
The formula of the circle area is
[tex]\pi \times {r}^{2} [/tex]
Then,
[tex]\pi \times {15}^{2} = 225\pi[/tex]
In the circle below, AD is a diameter and AB is tangent at A. suppose mADC=228. Find the measures of mCAB and mCAD. Type your numerical answers without units in each blank
Answer:
m∠CAB = 66°
m∠CAD = 24°
Step-by-step explanation:
m∠CAB
The given parameters are;
The measure of arc m[tex]\widehat{ADC}[/tex] = 228°
The diameter of the given circle = [tex]\overline{AD}[/tex]
The tangent to the circle = [tex]\underset{AB}{\leftrightarrow}[/tex]
The measure of m∠CAB and m∠CAD = Required
By the tangent and chord circle theorem, we have;
m∠CAB = (1/2) × m[tex]\widehat{AC}[/tex]
However, we have;
m[tex]\widehat{AC}[/tex] + m[tex]\widehat{ADC}[/tex] = 360° the sum of angles at the center of a circle is 360°
∴ m[tex]\widehat{AC}[/tex] = 360° - m[tex]\widehat{ADC}[/tex]
Which gives;
m[tex]\widehat{AC}[/tex] = 360° - 228° = 132°
m[tex]\widehat{AC}[/tex] = 132°
Therefore;
m∠CAB = (1/2) × 132° = 66°
m∠CAB = 66°
m∠CAD
Given that [tex]\overline{AD}[/tex] is the diameter of the given circle, we have
The tangent, [tex]\underset{AB}{\leftrightarrow}[/tex], is perpendicular to the radius of the circle, and therefore [tex]\underset{AB}{\leftrightarrow}[/tex] is also perpendicular to the diameter of the circle
∴ m∠DAB = 90° which is the measure of the angle formed by two perpendicular lines
By angle addition property, we have;
m∠DAB = m∠CAB + m∠CAD
∴ m∠CAD = m∠DAB - m∠CAB
By substitution, we have;
m∠CAD = 90° - 66° = 24°
m∠CAD = 24°
A boy standing between two pillars of equal height observes the angle of a
elevation of the top of pillars to be 30°. Approaching 15m towards any one
of the pillar, the angle of elevation is 45°. Find the height of the pillars and the distance between them
Answer:
15m
Step-by-step explanation:
did the math
calculate (4.8×10⁵)÷(1.2×10³),give your answer in standard form to 3 significant figures
Step-by-step explanation:
pleae mark as brain list please give me some thanks please
The sum of $4500 is divided among Anesha, Sian and Joanne in the ratio 7: 11: 12
respectively.
Calculate
(i) The amount of money each person received
(ii) The percentage of the total that Joanne received.
Which function is a quadratic function?
O p(x) = 2x(x2 + 6) + 1
m(x) = -4(x + 3) - 2
Ot(x) = -8x²(x2 – 6) + 1
Oh(x) = 3x(x - 2) - 4
what is energy efficiency
Answer:
The goal to reduce the amount of energy used to provide products and services; saving the earth vibes.