Answer:
pythagorean theorem - The length of the hypotenuse squared will always equal the sum of A squared and B sqaured. The equation is A^2 + B^2 = C^2.
Step-by-step explanation:
For Example
A = 4 A^2 = 16
B = 2 B^2 = 4
C = ? C^2 = ?
16 + 4 = 20
[tex]\sqrt{20}[/tex] ≈ 4.5
C/Hypotenuse = 4.5
If g (x) is the inverse of f (x) and f (x) = 4 x + 12, what is g (x)
g (x) = 12 x + 4
g (x) = one-fourth x minus 12
g (x) = x minus 3
g (x) = one-fourth x minus
Answer:
[tex]g(x) = \frac{1}{4} x - 3[/tex]Step-by-step explanation:
Since g(x) is the inverse of f (x) to find g(x) must first find f-¹(x)
To find f-¹(x) equate f(x) to y
That's
f(x) = y
y = 4x + 12
Next interchange the terms x becomes y and y becomes x
That's
x = 4y + 12
Next make y the subject
4y = x - 12
Divide both sides by 4
[tex]y = \frac{1}{4} x - 3[/tex]Therefore
[tex]g(x) = \frac{1}{4} x - 3[/tex]Hope this helps you
Two birds start from the same nest and head off in opposite directions. The speed of the first bird is 15mph more than the speed of the second.After 6 hours the two birds are 402 miles apart. Find the speed of each bird?
Answer:
41 mph26 mphStep-by-step explanation:
The rate at which distance is increasing between the birds is ...
r = d/t = (402 mi)/(6 h) = 67 mi/h
This is the sum of the speeds of the two birds, so is 15 mph more than double the speed of the slower bird. That bird's speed is then ...
(67 -15)/2 = 26 . . . miles per hour
The faster bird is 15 mph faster so is 26+15 = 41 mph.
The slower bird's speed is 26 mph; the faster bird's speed is 41 mph.
find a^4 + b^4 + c^4
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------------
Question: "Prove that a^{4} + b^{4} + c^{4} > abc(a + b + c) , where a, b, c are different positive real numbers."
------------------------------------------------------------------------------------------------------------
From the AM and GM inequality, we have:
a^4 + b^4 ≥ 2a^2b^2
b^4 + c^4 ≥ 2b^2c^2
c^4 + a^4 ≥ 2a^2c^2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From adding the inequalities we have above and dividing by 2, we have:
a^4 + b^4 + c^4 ≥ a^2b^2 + b^2c^2 + c^2a^2......1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now we need to repeat the process of a^2b^2, b^2c^2, and c^2a^2 to get:
a^2b^2 + b^2c^2 ≥ 2b^2ac
b^2c^2 + c^2a^2 ≥ 2c^2ab
c^2a^2 + a^2b^2 ≥ 2a^2bc
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now, we add from what we have above and divide by 2 to get:
a^2b^2 + b^2c^2 + c^2a^2 ≥ (b^2ac + c^2ab + a^2bc) or abc(b + c + a).....2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So, from (1) and (2) it follows:
a^4 + b^4 + c^4 ≥ abc( a + b + c)
Answer:
0.5
Step-by-step explanation:
a+b+c=0—(1)
a2+b2+c2=1—(2)
We know that:
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca—(3)
Substituting (1) and (2) in (3) , 0=1+2(ab+bc+ca)
=>ab+bc+ca=−0.5—(4)
Squaring: (ab+bc+ca)2=0.25
=>a2b2+b2c2+c2a2+2ab2c+2bc2a+2a2bc=0.25
=>a2b2+b2c2+c2a2+2abc(a+b+c)=0.25
Since a+b+c=0 ,
a2b2+b2c2+c2a2=0.25—(4)
squaring (2) :
(a2+b2+c2)2=12
=>a4+b4+c4+2a2b2+2b2c2+2c2a2=1
=>a4+b4+c4+2(a2b2+b2c2+c2a2)=1—(5)
Substituting (4) in (5),
a4+b4+c4+2(0.25)=1
=>a4+b4+c4=0.5
Hope this helps :D
Find the equation of a line that is perpendicular to line g that contains (P, Q).
coordinate plane with line g that passes through the points negative (3, 6) and (0, 5)
3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P
Answer:
x-y is parallel, im confused on what your asking for and what you mean by "negative"
Step-by-step explanation:
The equation of a line that is perpendicular to line g that contains (P, Q). is 3x − y = 3P − Q
What is Equation of line?The general form of the equation of a line with a slope m and passing through the point (x1, y1) is given as: y - y1 = m ( x- x1)
Further, this equation can be solved and simplified into the standard form of the equation of a line.
Given:
Line g passes through (3,6) and (0,5).
Slope of lone= y2 - y1/ (x2 - x1)
Perpendicular lines have opposite, reciprocal slopes, so negative change in x over change in y.
slope of line= -(-3 - 0)/(6 - 5)
= - -(-3)/1 =
slope of line = 3
Now, Two lines are perpendicular if they have the same slope.
Line parallel to line g has a slope of 1. Since it passes through (P, Q),
y - y1 = m ( x- x1)
y- Q =3 ( x- P)
y- Q = 3x- 3P
3x − y = 3P − Q
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Kitty buys hot chocolate sachets. There are 14 hot chocolate sachets in a small box. A small box costs £3.49. Kitty uses 3 hot chocolate sachets each day. Work out the how much Kitty spends on hot chocolate sachets in a four-week period.
Answer:
24.43
Step-by-step explanation:
first find the price of One sachets
next Find the no. of sachets consumed for four weeks..
and at last the product of the price of one sachet and no. of sachets consumed will give the answer...
Mathematical operation are above...
Help and show work please.
Any rectangle is also a parallelogram (but not the other way around). So AB is parallel to CD. The angles BAC and ACD are alternate interior angles that are congruent due to the parallel sides mentioned.
(angle BAC) = (angle ACD)
3x+4 = x+28
3x-x = 28-4
2x = 24
x = 24/2
x = 12
So,
angle BAC = 3x+4 = 3*12+4 = 40 degrees
and
angle CAD = 90 - (angle BAC) = 90 - 40 = 50 degrees
With any rectangle, the four interior angles are always 90 degrees. So that's why angles BAC and CAD add to 90.
What are the coordinates of the vertices of the polygon in the graph that are in Quadrant II? A) (4,–2) B) (4,3), (0,5), (0,1) C) (–5,2), (–3,2), (–3,4) D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)
Answer:
C) (–5,2), (–3,2), (–3,4)
Step-by-step explanation:
A) (4,–2)
B) (4,3), (0,5), (0,1)
C) (–5,2), (–3,2), (–3,4)
D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)
For quadrant two the points are always (-x,y) and x is always negative.
Image shows quadrant places.
8. Mark chose a number between 0.437 and 0.436 and multiplied it by 4. Then, he
subtracted 20 from this product. Next, he took three-fourths of this difference and got y.
Finally, he took the original number, added twelve to it, tripled it, and subtracted it from y.
What was his final answer?
A. -56
B. -51
C. 16
D. 21
E. Not enough information
Answer:
y=¾(4x-20)
y=3x-15
Final answer= y - 3(x+12)
=y - 3x-36
=3x-15-3x-36
= -51
Answer:
The answer is -51
Step-by-step explanation:
Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14 9 2 km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride. What was the cost per kilometer? \$Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14
9
2
km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride.
What was the cost per kilometer?
Answer:
$2.25/km
Step-by-step explanation:
The cost charged for a total taxi ride of [tex]14\frac{2}{9}\ km[/tex] was $32. To get the cost per km, we divide the cost charged for the total taxi ride by the total distance that was traveled by the taxi. The cost per km is given by:
Cost per km = [tex]\frac{Cost \ of\ money\ charged}{Total\ distance}=\frac{\$ 32}{14\frac{2}{9} \ km}=\frac{32}{\frac{128}{9} }= \$2.25/km[/tex]
Therefore the cost per kilometer is $2.25 per kilometer. Each kilometer traveled by the taxi cost $2.25.
What is the determinant of H = 2 4 9
3 3 1
4 5 3
Answer:5,3,7
2,4,9
3,6,4
Step-by-step explanation:he determinant of a 2 x 2 matrix A,
EVALUATING A 2 X 2 DETERMINANT,
DETERMINANT OF A 3 X 3 MATRIXFINDING THE DETERMINANT OF' A MATRIX,
FINDING THE COFACTOR OF AN ELEMENT, ,EVALUATING A 3 X 3 DETERMINAN,
EVALUATING A 4 X 4 DETERMINANT
voila
Answer: The answer is 15. You can use the calculator in Edge2020
Step-by-step explanation:
Edg2020
Match each number with its place in order from smallest (1st) to largest (6th). 1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48 HELP ASAP IM GETTING GRADED ON THIS
Answer:
1st -842nd -803rd -564th 485th 59 6th 90Step-by-step explanation:
To match each number with its place in order from smallest (1st) to largest (6th).
1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48
First we write all numbers: -56, 90, -84, 59, -80, 48
In Ascending order ( from smallest to largest): -84, -80,-56, 48, 59, 90
Here, the required arrangement:
1st -842nd -803rd -564th 485th 59 6th 90
Sheila cuts 60 foot wire cable in equal stripes of [tex]\frac{4}{5}[/tex] of a feet each. how many strips does she make?
a) 48 b) 51 c)60 d) 70 e) 75
Answer:
e) 75
Step-by-step explanation:
Given the following :
Total length of cable = 60 foot
Length of each stripe = (4/5) of a feet
Number of stripes = ( total cable length / length of each stripe)
Number of stripes = ( 60 / (4/5))
Number of stripes = 60 ÷ 4/5
Number of stripes = (60 * (5/4)
= (60 * 5) / 4
= 300 / 4
= 75
Number of stripes made = 75
Find the value of r. A. 24 B. 12 C. 2 D. 3
Answer:
[tex]\boxed{r=3}[/tex]
Step-by-step explanation:
We can use SAS ≅ SAS congruence to validate that the triangles are similar (both share the same side, have another congruent side, and have a congruent angle).
Because the sides are congruent, set them equal to each other and solve for r.
18 - 2r = 4r
18 = 6r
3 = r ⇒ [tex]\boxed{\bold r = 3}[/tex]
Therefore, the answer is D.
Answer:
r = 3
Step-by-step explanation:
Here Triangle ALR is divided precisely in half by the vertical side LU. The two triangles thus formed are therefore congruent.
Thus, 18 - 2r = 4r, and 6r = 18. Then r = 3.
Of a group of boys and girls at Central Middle School’s after-school party, 15 girls left early to play in a volleyball game. The ratio of boys to girls then remaining was 2 to 1. Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1. How many students attended the party?
Answer:
90
Step-by-step explanation:
Let g and b represent the number of girls and boys attending, respectively.
After 15 girls left, the ratio of boys to girls was ...
b/(g -15) = 2/1
b = 2g -30 . . . . . multiply by (g-15)
__
After 45 boys left, the ratio of girls to boys was ...
(g -15)/(b -45) = 5/1
g -15 = 5b -225 . . . . . . multiply by (b-45)
g = 5b -210
Using the latter to substitute into the former, we have ...
b = 2(5b -210) -30
450 = 9b . . . . . add 450-b
50 = b . . . . . . 50 boys attended
g = 5(50) -210 = 40 . . . . . 40 girls attended
The number of students who attended the party was 50 +40 = 90.
_____
Check
After 15 girls left, the ratio of boys to girls was 50/25 = 2/1.
After 45 boys left, the ratio of girls to boys was 25/5 = 5/1.
Answer:
let b = original number of boys
let g = original number of girls
:
Of a group of boys and girls at Central Middle School's after-school party, 15 girls left early to play in a volleyball game.
The ratio of boys to girls then remaining was 2 to 1.
b%2F%28%28g-15%29%29 = 2%2F1
Cross multiply
b = 2(g-15)
b = 2g - 30
:
Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1.
%28%28g-15%29%29%2F%28%28b-45%29%29 = 5%2F1
cross multiply
g - 15 = 5(b-45)
g - 15 = 5b - 225
g = 5b - 225 + 15
g = 5b - 210
Replace b with (2g-30)
g = 5(2g-30) - 210
g = 10g - 150 - 210
g = 10g - 360
360 = 10g - g
360 = 9g
g = 360/9
g = 40 girls originally
find b
b = 2(40) - 30
b = 50 boys originally
" How many students attended the party?"
40 + 50 = 90 students
Question 8(Multiple Choice Worth 1 points)
(06.05 MC)
A paper cup is dropped and its landing position is recorded. The cup can land on the side, on the open end, or on the closed end. The results of 20 trials are shown in the table below:
Paper Cup Experiment
# of times occurred
Open
HT III
Closed
Side
HT III
Based on the table, which of the following best compares the experimental probability of the cup landing on its open end with the experimental probability of the cup landing on its closed end?
The probabilities are equal.
The probability of landing on the open end is greater.
The probability of landing on the closed end is greater.
O No conclusion can be made.
Table Given in the question :
Open = HT 111 = 8
Side = 1111 = 4
Side = HT 111 = 8
Answer:
The probability of landing on the open end is greater.
Step-by-step explanation:
Given the experimental probability distribution :
Open = HT 111 = 8
Side = 1111 = 4
Side = HT 111 = 8
The experimental probability is the ratio of the number of times an event occurs and the total number of trials.
P(A) = number of times A occurs / total number of trials
Where A is defined event.
COMPARING the probabilities of open and closed events
P(open) = 8 / 20 = 2 / 5
P(closed) = 4 / 20 = 1/5
2/5 > 1/5
P(open) > P(closed)
Find the value of x.
Answer:
I think it is 32 hopes its right
find the Area and perimeter. Write your answer in terms of pie.
Area of a quarter of circle
A = 1/4 * π * R²
A = 1/4 * π * 12²
A = 36 * π cm²
Perimeter of a quarter of circle
P = 1/4 * 2 * π * R²
P = 1/4 * 2 * π * 12²
P = 72 * π cm
Area of a right triangle
A = b * h / 2
A = 12 * 12 / 2
A = 72 cm²
Length of hypotenuse
L = 12√2 cm
Area of blue
A = 36 * π - 72
A = 36 * ( π - 2) cm²Perimeter of blue
P = 12 * (6 * π + √2 ) cmHope it helps
xxx
Choose the function whose graph is given by
C)
Because if you choose some points for example x = 0 and x = 3.14 (≈ pi)
you will see that there's only one match.
Answer:
Option C. y = cos x -2
Step-by-step explanation:
For triangle DEF, angle D = 42 degrees, line e = 30 meters and line d = 25 meters. Determine the number of possible triangles that can be constructed. Show work.
Answer:
2 triangles
Step-by-step explanation:
The given angle is opposite the shorter of the given sides, so the number of triangles is 2. (30/25·sin(42°) ≈ 0.8 < 1)
_____
Additional comment
For the case where the shorter given side is opposite the given angle, there is the possibility that the triangle could be a right triangle (1 solution) or that there may be no solutions. You can tell the difference by computing ...
(long side)/(short side) × sin(given angle)
If this result is exactly 1, the triangle is a right triangle. If it is greater than 1, the triangle cannot exist (no solutions). Since the sines of most angles are irrational, it is unlikely you will see this result be exactly 1 (except for a 30°-60°-90° right triangle).
These observations are a consequence of the Law of Sines, which tells you ...
sin(A) = (a/b)sin(B)
For real angles, sin(A) ≤ 1.
what is 3 2/7 x 2 4/5 (Answer with a mixed number in simplest form) Thankyou!!
Answer:
9 1/5
Step-by-step explanation:
3 2/7 * 2 4/5
Change to improper fractions
( 7*3+2)/7 * ( 5*2+4)/5
23/7 * 14/5
Rewriting
14/7 * 23/5
2 * 23/5
46/5
Changing back to a mixed number
5 goes into 45 9 times with 1 left over
9 1/5
The product of 3 2/7 and 2 4/5 is 9 1/5 in simplest form as per the concept of simplifying fractions.
To multiply the mixed numbers 3 2/7 and 2 4/5, we need to convert them to improper fractions and then perform the multiplication.
First, convert 3 2/7 to an improper fraction:
3 2/7
= (3 x 7 + 2) / 7
= 23/7
Next, convert 2 4/5 to an improper fraction:
2 4/5
= (2 x 5 + 4) / 5
= 14/5
Now, multiply the two improper fractions:
(23/7) x (14/5) = (23 x 14) / (7 x 5)
= 322/35
To simplify the resulting fraction, we find the greatest common divisor (GCD) of the numerator (322) and the denominator (35), which is 7. Divide both the numerator and the denominator by the GCD:
322/35
= (322/7) / (35/7)
= 46/5
Now, express the improper fraction as a mixed number:
46/5 = 9 1/5
Therefore, the product of 3 2/7 and 2 4/5 is 9 1/5 in simplest form.
To learn more about the fractions;
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A ladder is leaning against a wall. The ladder is 5 metres long. The top of the ladder is 3 metres above the ground. The top of the ladder is sliding down at 8 metres/second. At what rate is the bottom of the ladder moving away from the wall?
Answer:
it is moved away in .625 seconds
Step-by-step explanation:
i did 5 divided by 8 though this question is weriod
Assuming the ladder is leaning against the wall and there are no spaces in between (that doesn't make sense sorry), it is still at a rate of 8 meters per second because it is standing straight up. It is moving at the same rate, since it is the same ladder.
HELP QUICK!
A parabola, (y + 2)2 = 8(x - 3), is changed to (y + 10)2 = 8(x - 3). How will this affect the graph of the parabola?
A)
The vertex will shift up.
B)
The vertex will shift down.
C)
The vertex will shift to the left.
D)
The vertex will shift to the right.
Answer:
B) The vertex will shift down.
Step-by-step explanation:
In the equation of a parabola, (y - k)² = 4p(x - h), (h, k) is the vertex.
The original parabola's vertex was (3, -2).
In the new parabola, the y-coordinate changed to -10, making the new vertex (3, -10).
So, the parabola's vertex shifted down 8 units from -2 to -10.
The number of radians in a 720-degree angle can be
written as an, where a is a constant. What is the
value of a ?
Answer:
a=4
Step-by-step explanation:
When going from degrees to radians, 180 degrees is always going to equal π radians
That means 2π would be 360 degrees, and 4π would be 720
And since we're trying to find a in aπ when it's a 720 degree angle, we can conclude that a=4
Answer:
4
Step-by-step explanation:
We know that:
π rad= 180°Then:
720° = 4*180° = 4π radianThe value of a:
4π = aπ ⇒ a= 4The product (5+ i) (5 – i) is a real number, 26. What are the factors (5 + i) and (5 – i) called? (1 point)
o complex numbers
O imaginary units
complex conjugates
O imaginary numbers
please help :( suck at math all the way
Answer:
complex conjugates
Step-by-step explanation:
The factors (5 + i) and (5 – i) are called complex conjugates.
Answer:
complex conjugates
Step-by-step explanation:
Numbers of the form a+ bi and a - bi are complex conjugates.
Their product is real.
Please find the perimeter!
Answer:
1. half circle: C = (2πr) / 2
a. C = (2π4) / 2 ≈ 12.566
2. triangle:
a. find slant / hypotenuse.
i. 4² + 10² = c²
ii. 16 + 100 = c²
iii. c² = 116
iv. c ≈ 10.770
b. add both slants to find triangular area
i. 10.77 + 10.77 ≈ 21.54
3. add:
a. 12.566 + 21.54 ≈ 34.106 cm
hope this helps :)
The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The children’s path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. Hypotenuse: 32 ft , Short leg: x , Long leg: x+6
Answer:
[tex]x= \sqrt{503}-3[/tex]
Step-by-step explanation:
Hypotenuse = 32 feet
Short leg = x
Long leg = x+6
We will use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]32^2=x^2+(x+6)^2[/tex]
[tex]1024=x^2+x^2+36+12x[/tex]
[tex]2x^2+12x-988=0[/tex]
[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]
Since the distance cannot be negative
So,[tex]x= \sqrt{503}-3[/tex]
Round the number 53.18474629
a) To the nearest tenth
b) To the nearest thousandth
c) To the nearest whole number
Answer:
Step-by-step explanation:
To the nearest tenth: 53.2
To the nearest thousandth: 53.185
To the nearest whole number: 53
Translate the following into an algebraic expression: The number that is 40% more than five more than a number a.
Answer:
1.4a > 5+a
Step-by-step explanation:
If the number is increased by 40% of that number, then it multiplies by 1.4. So, the left side of the equation is 1.4a.
On the right side of the equation, if the number is increased by 5, then the equation is a + 5.
Since the left side of the equation is more than the right side of the equation, we add a greater than sign. So the expression is 1.4a > 5+a
The coefficient of 6x is
1
6
Х
Answer:
6
Step-by-step explanation:
If a number and a variable were together in a term, the number would the the coefficient. The coefficient would multiply the variable.
In '6x', the number '6' is the coefficient. '6' would be multiplying 'x'.
The correct answer should be 6.
solve the following inequality for v. 4v-8≤5v+5
[tex]\text{Solve for v:}\\\\4v-8\leq5v+5\\\\\text{Subtract 5v from both sides}\\\\-v-8\leq5\\\\\text{Add 8 to both sides}\\\\-v\leq13\\\\\text{Divide both sides by -1, while also flipping the inequality}\\\\\boxed{v\geq-13}[/tex]
Answer:
v>=-13
Step-by-step explanation:
4v-8<=5v+5
4v-5v-8<=5
-v-8<=5
-v<=5+8
-v<=13
v<=-13
v>=-13
