1. √7 × √7 = √[7×7] = √[7²] = 7
2. √18 × √2 = √[18×2] = √36 = √[6²] = 6
3. √45 = √[9×5] = √9 × √5 = √[3²] × √5 = 3√5
4. [tex]\dfrac{\sqrt{50}}{5}=\dfrac{\sqrt{25\cdot2}}{5}=\dfrac{\sqrt{25}\cdot\sqrt2}{5}=\dfrac{5\cdot\sqrt2}{5}=\bold{\sqrt2}[/tex]
5. 2√2 × 4√5 = (2×4) × (√2×√5) = 8×√[2×5] = 8√10
6. √48 - √12 = √[16×3] - √[4×3] = √16×√3 - √4×√3 = 4√3 - 2√3 = 2√3
7. (2 - √3)(1 + √3) = 2×1 + 2×√3 + (-√3)×1 + (-√3)×√3 =
= 2 + 2√3 - √3 - √[3×3] = 2 + √3 - 3 = √3 - 1
Solve by Cross multiplication method x+2y+1=0 and 2x-3y-12=0
Answer:
x = 3
y = -2
Step-by-step explanation:
x + 2y + 1 = 0
2x - 3y - 12 = 0
Multiply first equation by -2.
-2x + -4y + -2 = 0
2x - 3y - 12 = 0
Add equations.
0x + -7y - 14 = 0
Solve for y.
-7y = 14
y =-2
Put y as -2 in the first equation and solve for x.
x+2(-2)+1=0
x + -4 + 1 = 0
x = 0 + 4 - 1
x = 3
Answer:
[tex]\boxed{x = 3, y = -2}[/tex]
Step-by-step explanation:
[tex]x+2y +1 = 0[/tex]
=> [tex]x+2y = -1[/tex] -------------------(1)
[tex]2x-3y-12 = 0[/tex]
=> [tex]2x-3y = 12[/tex] -------------------(2)
Multiplying (1) by 2
=> [tex]2(x+2y) = 2(-1)[/tex]
=> [tex]2x+4y = -2[/tex] ------------------(3)
Subtracting (3) from (2)
=> [tex]2x-3y+2x-4y = 12+2[/tex]
=> -3y-4y = 14
=> -7y = 14
Dividing both sides by -7
=> y = -2
Now, Put y = -2 in Eq (1)
=> x+2(-2)+1 = 0
=> x -4+1 = 0
=> x - 3= 0
Adding 1 to both sides
=> x = 3
multiply c^2(c^2-10c+25)
Step-by-step explanation:
c^2( c^2-10c+25)
=c^4 - 10c^3 + 25c^2
PLEASE HELP! I WILL GIVE BRAINIEST! Look at the figure below: A triangle ABC is drawn. D is a point on BC such that BD is equal to DC. A straight line joins points A and D. This line extend Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? a Triangle ABD and triangle ECD b Triangle ABC and triangle ECD c Triangle ABD and triangle ADC d Triangle ADC and triangle ABC
Answer:
ADB and ADC
Step-by-step explanation:
SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.
Answer:
ABD and ECD
Step-by-step explanation:
EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.
SB
Compare the process of solving
|x - 11 +1 < 15 to that of solving
|x - 11 +1 > 15.
DONE
Answer:
x = 0
Step-by-step explanation:
i) x - 11 + 1 < 15
x - 10 < 15
x < 10 + 15
x < 25
ii) x - 11 + 1 > 15
x - 10 > 15
x > 25
Therefore to compare (i) and (ii)
25 < x < 25
In any case, x = 0
What is the length of chord ML? 20 units 24 units 26 units 30 units
Answer: 24 units
Step-by-step explanation:
MO, NO and LO are radii.
If MO = 13, THEN LO = NO = 13
IF NO = 13 and NP = 8, THEREFORE,
PO = NO - NP
PO = 13 - 8 = 5
USING PYTHAGORAS, WE CAN FIND MP:
MP = Sqrt(MO^2 - PO^2)
MP = sqrt(13^2 - 5^2)
MP = sqrt(169 - 25)
MP = sqrt(144)
MP = 12 units
P is the midpoint of Segment ML,
THEREFORE,
MP = PL
ML = MP + PL
ML = 12 + 12
ML = 24 units
Answer: 24
Step-by-step explanation:
edge
Given: DF and DE are midsegments of ∆ABC Prove: DE= 1/2 AC (PLEASE HELP)
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Step-by-step explanation:
–3(6 – 2x) ≥ 4x + 12? PLZ HELP
Answer:
x ≥ 15Step-by-step explanation:
–3(6 – 2x) ≥ 4x + 12
Expand the terms in the bracket
We have
- 18 + 6x ≥ 4x + 12
Group like terms
that's
6x - 4x ≥ 12 + 18
2x ≥ 30
Divide both sides by 2
x ≥ 15
Hope this helps you
Step-by-step explanation:
no worries
if u multiply by a negative number the sign changes
so it can -18 + 6x <= 4x + 12
take x to one side and others to other side
6x - 4x <= 18 + 12
2x <= 30
x<= 15
so solutions can be from ....-2,-1,0,1,2,3....
What the answer now
Answer:
57°
Step-by-step explanation:
There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:
m∠K = 90° -m∠J = 90° -33°
m∠K = 57°
Added to Six Flags St. Louis in the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet above the ground. Determine an equation that relates a rider's height above the ground at time . Assume the passenger begins the ride at the bottom of the wheel.
Answer:
The height of the rider as a function of time is [tex]h(t) = 15 + 82.5\cdot (1-\cos 0.168t) \,[ft][/tex], where time is measured in seconds.
Step-by-step explanation:
Given that Ferris wheel rotates at constant rate and rider begins at the bottom of the wheel, the height of the rider as a function of time is modelled after this expression:
[tex]h(t) = h_{bottom} + (1-\cos \omega t)\cdot r_{w}[/tex]
Where:
[tex]h_{bottom}[/tex] - Height of the bottom with respect to ground, measured in feet.
[tex]\omega[/tex] - Angular speed of the ferris wheel, measured in radians per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]r_{w}[/tex] - Radius of the Ferris wheel, measured in feet.
The angular speed of the ferris wheel, measured in radians per second, is obtained from the following expression:
[tex]\omega = \frac{\pi}{30}\cdot \dot n[/tex]
Where:
[tex]\dot n[/tex] - Angular speed of the ferris wheel, measured in revolutions per minute.
If [tex]\dot n = 1.6\,rpm[/tex], then:
[tex]\omega = \frac{\pi}{30}\cdot (1.6\,rpm)[/tex]
[tex]\omega \approx 0.168\,\frac{rad}{s}[/tex]
Now, given that [tex]h_{bottom} = 15\,ft[/tex], [tex]r_{w} = 82.5\,ft[/tex] and [tex]\omega \approx 0.168\,\frac{rad}{s}[/tex], the height of the rider as a function of time is:
[tex]h(t) = 15 + 82.5\cdot (1-\cos 0.168t) \,[ft][/tex]
Please Help!!! Will get brainiest if answer correctly with an explanation. Name the postulate or theorem you can use to prove wzv=wzy. given:
Answer:
AAS
Step-by-step explanation:
Δwzy=Δwzv
to prove the equality:
1- wz is a common side
angle: wzv=wzy=90 degrees ( height of triangle)
angle v= angle y
Since WZ bisects W, it's good to say that vwz and zwy
prove one side is equal and two angles
so ASA or AAS is the answer
The app store is offering 15 percent off any purchase for one day, only you decide to buy a game app that cost 12 dollars and 90 cents. If you buy it during the sale, what is the amount of the discount?
Answer:
$1.935
Step-by-step explanation:
As the store is offering a 15% discount, you have to calculate the 15% of the price of the game app to find the amount of the discount:
Price of the game app= 12.90
12.90*15%=1.935
According to this, the answer is that the amount of the discount if you buy the game app during the sale is $1.935 and you would have to pay: 12.90-1.935= $10.965.
Plzzzzz Help I really need help
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
(1.5,-3) and (4.5,-3)
Step-by-step explanation:
BRAINLIEST!!! MATH HELP ME ASAP PLS!!!
Answer:
-0.0062 and 27.5
Step-by-step explanation:
You can write the equation of the line using the 2-point form:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
The given values of the variables are ...
(h, T) = (10000, -34.5) and (15000, -65.5)
Putting these into the formula, we have ...
T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)
T = -31/5000(h -10000) -34.5
T = -0.0062h +62 -34.5
T = -0.0062h +27.5
The appropriate choice is ...
-0.0062 and 27.5
PLSSSSS HELLLLLLP!!!!!
Answer:
[tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex] will be the answer.
Step-by-step explanation:
The given expression is,
[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]
By solving this expression,
[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]
= [tex]\frac{3n(n-4)}{(n+3)(n-4)}+\frac{5(n+3)}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n(n-4)+5(n+3)}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n^2-12n+5n+15}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex]
Therefore, fraction given in option (2) will be the answer.
98 percent of all babies survive delivery. However, 15 percent of all births involveCesarean (C) sections, and when a C section is performed, the baby survives 96percent of the time. If a randomly chosen pregnant woman does not have a Csection, what is the probability that her baby survives?
S - a randomly chosen pregnancy result in a successful delivery
C - a randomly chosen pregnancy ending in a C section
The graph shows the distance Ted traveled from the market in miles (y) as a function of time in seconds (x). The graph is divided into four segments labeled P, Q.
R. and S
S
Distance
(mi)
R
P
Time (sec)
Which segment shows Ted waiting for a cab?
A) P
B) Q
C) R
D) S
Explanation:
The flat horizontal portion S is where the distance (y) does not increase or decrease. So Ted is stationary during this time frame.
In terms of speed, we would say speed = distance/time = (change in y)/(change in x). Note how this is the slope.
Rise = 0 because the horizontal line does not go up or down. The run is any positive number, though convention usually has Run = 1. Therefore, slope = rise/run = 0/1 = 0. All flat horizontal lines have a slope of 0 to indicate no upward or downward movement.
Can someone help me with this?
Answer:
9 = k :)
Step-by-step explanation:
1. distribute 3 to the -1/4 k and to the 3 and get -3/4 k + 9 = 1/4 k
2. add 3/4 k to both sides and get 9 = k
Describe the process you would use to explain to your parents (or other significant adults in your life) how you could calculate the sum of the interior angles of a 12-sided object without measuring them
Answer:
Sum of interior angles of 12 sided object = 1800°
Step-by-step explanation:
Formula to calculate the sum of interior angles of a polygon is,
Sum of the interior angles of a polygon = (n - 2) × 180°
Where n = number of sides of the polygon.
If number of sides of a polygon are 12,
For n = 12,
Sum of interior angles = (12 - 2) × 180°
= 10 × 180°
= 1800°
Therefore, sum of interior angles of a 12 sided polygon will be 1800°.
A 5×5×5 wooden cube was painted and then sawed into 1×1×1 cubes. How many 1×1×1 cubes are there? HELPPPPP!!!!!!!!!!!!!!!!!!!!!! QUIKE
Answer:
125
Step-by-step explanation:
1 x 1 x 1 = 1
5 x 5 x 5 = 125
125 / 1 = 125
125 is your answer
what must be divided to 43659 to get a perfect square
Answer:
11
Step-by-step explanation:
Prime factor: 43659 = 3*3*3*3*7*7*11
Pair: √43659 = √3²×3²×7²×11
11 is odd therefore 11 must be divided by 43659
Uma makes a scale drawing of a patio. The drawing below shows the two scales she used to plan two patios of different sizes.
Scale 1: 1 centimeter = 3 meters.
Scale 2: 1 centimeters = 4 meters.
Options
A)Scale 1: 45 m; Scale 2: 60 m
B)Scale 1: 60 m; Scale 2: 45 m
C)Scale 1: 36 m; Scale 2: 27 m
D)Scale 1: 27 m; Scale 2: 36 m
Answer:
Scale 1: 1 centimeter = 3 meters.
Scale 2: 1 centimeters = 4 meters.
Step-by-step explanation:
your answer should be A
15*3=45
15*4=60
Answer:
A.)Scale 1: 45 m; Scale 2: 60 m
Step-by-step explanation:
bcuz......uhhhhhhh, ummmmmm:/
The vertices of triangle ABC are A(5,2), B(-1,-6), and C(1,5). If triangle DEF is similar to triangle ABC and AB/DE = 5, which could be the coordinates of D and E
Answer:
im pretty sure its the third one
Step-by-step explanation:
i guessed but it might be right
Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle. Which statements describes how the location of segment EG affects the area of EFGH? A.) the area of EFGH is 1/4 of the area of the rectangle if E and G are not midpoints B.) The area of EFGH is 1/2 of the area of the rectangle only if E and G are midpoints C.) The area of EFGH is always 1/2 of the area of the rectangle. D.) The area of EFGH is always 1/4 of the area of the rectangle.
Answer:
C.) The area of EFGH is always ¹/₂ of the area of the rectangle.Step-by-step explanation:
If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.
If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.
Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].
So the area of the rectangle: [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]
The area of the kite:
[tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]
No matter the height of the triangles, so no matter the location of the EG
Increased by 75% is 35 ?
Answer:
20
Step-by-step explanation:
20 + (75% × 20) =
20 + 75% × 20 =
(1 + 75%) × 20 =
(100% + 75%) × 20 =
175% × 20 =
175 ÷ 100 × 20 =
175 × 20 ÷ 100 =
3,500 ÷ 100 =
35;
how to solve 10 + (2 × 3)^2 ÷ 4 × (1/2)^3
Answer:
11.125Step-by-step explanation:
[tex]10 + {(2 \times 3)}^{2} \div 4 \times {( \frac{1}{2}) }^{3} [/tex]
To raise a product to a power, raise each factor to that power
[tex] = 10 + 4 \times 9 \div 4 \times {( \frac{1}{2} )}^{3} [/tex]
To raise a fraction to a power, raise the numerator and denominator to that power
[tex] = 10 + 4 \times 9 \div 4 \times \frac{1}{8} [/tex]
Any expression divided by itself equals 1
[tex] = 10 + 1 \times 9 \times \frac{1}{8} [/tex]
Any expression multiplied by 1 remains the same
[tex] = 10 + 9 \times \frac{1}{8} [/tex]
Calculate the product
[tex] = 10 + \frac{9}{8} [/tex]
Write all numerators above the common denominator
[tex] = \frac{80 + 9}{8} [/tex]
Add the numbers
[tex] = \frac{89}{8} [/tex]
Divide
[tex] = 11.125[/tex]
Hope this helps..
Best regards!!
Answer:
11 1/8
Step-by-step explanation:
Okay so I messed up big time. So I had to edit this! I am really sorry if you read mine before. I fixed mine. So this is the right answer. Sorry!
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
2
Step-by-step explanation:
In order to make the equation undefined, you should make the denominator 0. Remember that dividing anything by 0 will become undefined.
[tex]2x-4=0\\\frac{2x=4}{2} \\x=2[/tex]
Answer:
[tex]\boxed{x = 2}[/tex]
Step-by-step explanation:
A rational expression is undefined when Denominator = 0
Here Denominator = 2x-4
So,
=> 2x - 4 = 0
Adding 4 to both sides
=> 2x = 4
Dividing both sides by 2
=> x = 2
HELP PLS WITH BRAINLIEST
Answer:
cos C
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
simplify the expression without negative exponents
Answer: [tex]-50a^{11}b^{9}[/tex]
Step-by-step explanation:
Any negative exponent can be moved to the other side of the fraction as a positive exponent.[tex]\frac{1}{x^{-3}}=x^3\\ \frac{x^{-3}}{1}=\frac{1}{x^3}[/tex]
Thus, simply move the negative exponents from the bottom into the numerator to get. -10a^2*b^4*5a^9*b^5. Then, use the exponent rule to get [tex]-50a^{11}b^{9}[/tex]
Hope it helps <3
If y is inversely proportional to x and y = 5, when x = 7, find the value of y when x = 70
Answer:
y = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given y is inversely proportional to x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = 5 when x = 7, then
5 = [tex]\frac{k}{7}[/tex] ( multiply both sides by 7 )
35 = k
y = [tex]\frac{35}{x}[/tex] ← equation of variation
When x = 70, then
y = [tex]\frac{35}{70}[/tex] = [tex]\frac{1}{2}[/tex]
La suma de dos números es 50 y la diferencia es 22. ¿Cuáles son los números?
Answer:
(3,2)
Step-by-step explanation:
Just took the test