Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{16.27 \: \: units}}}}}[/tex]Step-by-step explanation:
Given,
A ( - 1 , - 3 )⇒( x₁ , y₁ )
B ( 11 , 8 )⇒( x₂ , y₂ )
Using distance formula to find the length of AB
[tex] \sf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
plug the values
⇒[tex] \sf{ \sqrt{ {(11 - ( - 1))}^{2} + {( 8 - ( - 3))}^{2} } }[/tex]
We know that [tex] \sf{( - ) \times ( - ) = ( + )}[/tex]
⇒[tex] \sf{ \sqrt{ {(11 + 1)}^{2} + {(8 + 3)}^{2} } }[/tex]
Add the numbers
⇒[tex] \sf{ \sqrt{ {12}^{2} + {11}^{2} } }[/tex]
Evaluate the power
⇒[tex] \sf{ \sqrt{144 + 121} }[/tex]
Add the numbers and calculate
⇒[tex] \sf{\sqrt{265} }[/tex]
⇒[tex] \sf{16.27}[/tex] units
Hope I helped!
Best regards!!
Pls help with question 5 will mark braineliest
Answer:
Last year there were 1070 students.
Step-by-step explanation:
Since 856 students represent a 20% drop from last year's number of students, then 856 students is 80% of last year's number.
80% of x = 856
0.8x = 856
x = 856/0.8
x = 1070
Answer: Last year there were 1070 students.
Answer:
1070
Step-by-step explanation:
p = previous years populations
p - p 20% = 856
p - .20*p = 856
Combine like terms
.80p = 856
Divide each side by .8
.80p/.8 - 856/.8
p =1070
Members of a community center have decided to paint a large circular mural in the middle of the parking lot. The radius of the mural is to be 11 yards. Before they begin painting the mural, they use a rope to form the outline. How many yards of rope will they need?
Answer:
69.124 yards of ropeStep-by-step explanation:
This problem bothers on the mensuration of flat shapes, circles.
given that the members of the community used rope as outline for the circular shape mural.
we can tell that the perimeter of the mural is same as the perimeter of the rope.
Hence the length of rope used is same as the perimeter of the circular mural.
we know that the perimeter of a circle is given as
[tex]C=2\pi r\\\\[/tex]
substituting radius r= 11 yards
we have
[tex]C= 2*3.142*11\\\\C= 69.124 yards[/tex]
A cube has a side length of 14 meters. What is the volume of the cube?
Volume of cube = side length^3
Volume = 14^3
Volume = 2,744 cubic meters
Answer:
v=x^3
14^3=2744
.....
Determine the form of the following quadratic equation, and identify the values for the key characteristic of the parabola revealed by that form. f(x)=(2x−1)(x+6)
Answer:
1) The equation is given in factored form
2) The key characteristics of the parabola are;
a. The parabola has 2 real roots and extends to infinity on both sides
b. The x-intercepts of the parabola are (1/2, 0) and (-6, 0)
c. The y intercept is (0, -6)
d. The vertex point is (-2.75, -21.125)
Step-by-step explanation:
The given equation is f(x) = (2·x -1)(x + 6)
Therefore the equation is given in factored form
The key characteristic of the parabola revealed from the form f(x) = (2·x -1)(x + 6) are;
1) Writing the parabola in the intercept form, a(x - p)(x -q) we have;
f(x) = (2·x -1)(x + 6) = 2·(x - 1/2)(x + 6)
p = 1/2, q = -6
Therefore;
Given that a is positive the parabola is concave upwards
2) a. The parabola has 2 real roots and extends to infinity on both sides
b. The x-intercepts of the parabola are p and q which are (1/2, 0) and (-6, 0)
c. The y intercept is a·(-p)·(-q) = 2×(-1/2)×6 = -6
The y intercept is (0, -6)
d. Expanding we get;
f(x) = 2·x² + 11·x - 6
From the
The vertex is h = -b/(2·a) = -11/(2×2) = -2.75
h(2.75) = 2×(-2.75)² + 11×(-2.75) - 6 = -21.125
Therefore, the function is symmetrical about the vertex point (-2.75, -21.125)
Jesse works in construction and is planning the layout of a client’s garage. The only requirement is for the length to be twice as long as the width. If the area of the garage must be 288 square feet, what must the dimensions be?
Answer:
Width = 12 foot
Length = 24 foot
Step-by-step explanation:
Let
Width=x
Length=2x
Area = 288 square feet
Area of the garage = Length × width
288 = 2x * x
288= 2x^2
Divide both sides by 2
288 / 2 = x^2
144= x^2
Find the square root of both sides
√144 = √x^2
12 = x
Therefore,
x=12
The dimensions will be:
Width = x
= 12
Length = 2x
=2(12)
=24
Width = 12 foot
Length = 24 foot
Kyle challenges you to a game. Each player rolls a standard number cube twice. If the sum of the results is divisible by 3, you win. If it is not, Kyle wins. What is your probability of winning? Is this a fair game?
Answer:
[tex]P(M) = \frac{1}{3}[/tex]
The game is not a fair game
Step-by-step explanation:
We start by listing out the sample space
Number Cube 1: {1,2,3,4,5,6}
Number Cube 2: {1,2,3,4,5,6}
Sample Space (S) of the sum of the 2 cubes;
[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]
[tex]n(S) = 36[/tex]
Next, is to list out all multiples of 3; Represent this with M
[tex]M = \{3,6,3,6,6,9,6,9,6,9,9,12\}[/tex]
[tex]n(M) = 12[/tex]
Your probability of winning is the probability of M and is calculated as thus;
[tex]P(M) = \frac{n(M)}{n(S)}[/tex]
[tex]P(M) = \frac{12}{36}[/tex]
[tex]P(M) = \frac{1}{3}[/tex]
The probability of Kyle winning, P(K) = 1 - P(M)
[tex]P(K) = 1 - \frac{1}{3}[/tex]
[tex]P(K) = \frac{2}{3}[/tex]
The game is not a fair game because;
The probability of you winning and the probability of Kyle winning are not equal;
good morning god loves you all :) please help Which is the expanded form of 124,750,000? A. 124,000 + 750,000 B. 100,000,000 + 20,000,000 + 4,000,000 + 700,000 + 50,000 C. 124,000 + 750 D. 124 x 1000 + 75 x 1000
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Answer : (B) [tex]100,000,000 + 20,000,000 + 4,000,000 + 700,000 + 50,000 = 124,750,000[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
B.
Step-by-step explanation:
124,750,000=100,000,000
20,000,000
4,000,000
700,000
+50,000
Hope this helps ;) ❤❤❤
how to calculate rational numbers
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
The simplest method to find a rational number between two rational numbers x and y is to divide their sum by 2.
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
1. Which range of numbers is most appropriate for the y-axis scale and interval on a graph given the
Range: 10 - 35; Interval 10
Range: 0-35; Interval: 5
Range: 0 - 30; Interval 5
Range: 10 - 30; Interval: 5
Answer:
Option B.
Step-by-step explanation:
We need to find the range of numbers is most appropriate for the y-axis scale and interval on a graph for given table.
From the given table it is clear that the minimum value of y is 10 and the maximum value of y is 34.
It means 10 and 34 must be included in the Range.
In option C and D 34 in not included in the range, so these options are incorrect.
In option A, 10 is the minimum value of range and interval of 10 is not possible for the range 10-35, because it contains only multiple of 10 on the y-axis. So, this option is incorrect.
In option B, both 10 and 34 are included and interval of 5 is possible for range 0-35.
Therefore, the correct option is B.
Both the Galapagos Islands and the island of Naura are on the equator, but the Galapagos Islands are at 90.30°W whereas the island of Naura is at 166.56°E. How far is it from the Galapagos Islands to Naura traveling over the Pacific ocean along the equator, correct to the nearest km?
Answer:
11521 km
Step-by-step explanation:
The computation is given below:
But prior to reaching the final solution first the following calculations need to be computed
Angle between the Galapagos and Nauru is
= 90.30° + 166.56°
= 256.86°
As we know that the total of angles is 360 degrees
Now the major arc and the minor arc is
= 360° - 256.86°
= 103.14°
So, the angles between galapagos islands is
= 180° - 90.30°
= 89.70°
And, angles between the naura island is
= 180° - 166.56°
= 13.44°
Now the sum of this two island is
= 89.70° + 13.44°
= 103.14°
Therefore The length is
[tex]= \frac{\pi r}{180^{\circ}} \times \theta \\\\ = \frac{6,400 \pi}{180^{\circ}} \times 103.14^{\circ}[/tex]
= 11521 km
2. A, B, and C are the centers of the 3 circles. How many
equilateral triangles are there in this diagram?
5 equilateral triangles.
Hope this helps.
A bottle of 150 vitamins costs $5.25. What should a bottle with 250 vitamins cost?
Answer:
8.75
Step-by-step explanation:
because it had increase in percent is about 70 % which is 70% do the same to 5.25 which is 8.75
Answer:
$8.75
Step-by-step explanation:
We can use ratios to solve
150 vitamins 250 vitamins
------------------ = ------------------
$5.25 $x
Using cross products
150x = 250 (5.25)
150x =1312.5
Divide each side by 150
x =1312.5/150
x =8.75
Use the i formation major of 1..... look at picture
Explanation:
You basically plug in x = 20, which is the same as saying "replace x with 20". Then you perform arithmetic to simplify each expression. Both simplify to 90, so angle 1 and angle 2 are the same measure. These angles are alternate interior angles, so we'll use the converse alternate interior angle theorem to conclude the lines are parallel.
Note: the alternate interior angle theorem says that if we have parallel lines, then the alternate interior angles are congruent. So the converse goes in reverse of this.
The vertices A, B, C of a triangle are (2,1),(5,2),and (3,4) respectively . Find the coordinate of the circumcentre and also the radius of the circum-circle of the triangle
Answer:
Circumcenter = (4,0)
Circumcircle = √5
Step-by-step explanation:
The circumcentre is the point of intersection of the perpendicular bisectors of a triangle. The vertices of the triangle are equidistant to the circumcentre.
Let us assume the coordinate of the circumcentre is at O(x, y). Therefore the distance between the cirmcumcenter and the vertices are:
[tex]AO=\sqrt{(x-2)^2+(y-1)^2} =\sqrt{x^2-4x+4+(y^2-2y+1)}\\=\sqrt{x^2+y^2-4x-2y+5} \\\\BO=\sqrt{(x-5)^2+(y-2)^2} =\sqrt{x^2-10x+25+(y^2-4y+4)}\\=\sqrt{x^2+y^2-10x-4y+29} \\\\CO=\sqrt{(x-3)^2+(y-4)^2} \\=\sqrt{x^2-9x+9+(y^2-8y+16)}=\sqrt{x^2+y^2-9x-8y+25} \\[/tex]
AO = BO, therefore
√(x² + y²-4x-2y+5) = √(x² + y² - 10x - 4y + 29)
x² + y²-4x-2y+5 = x² + y² - 10x - 4y + 29
6x + 2y = 24 (1)
BO = CO
√(x² + y² - 10x - 4y + 29) = √(x² + y² - 9x - 8y + 25)
x² + y² - 10x - 4y + 29 = x² + y² - 9x - 8y + 25
-x + 4y = -4 (2)
Multiply equation 2 by 6 and add to equation 1:
26y = 0
y=0
Put y = 0 in -x + 4y = -4
-x + 4(0) = -4
x = 4
The cicumcenter is at (4, 0)
The radius of the circumcircle = AO = BO = CO. Therefore:
[tex]Radius=AO=\sqrt{(4-2)^2+(0-1)^2} =\sqrt{4+1}=\sqrt{5}[/tex]
Convert 955.234 kg to dg
Which of the following correctly describes the end behavior of the polynomial function f(x) = -3x^4+2x^2-x
A. Both ends go up
B. Both ends go down
C. The left end goes down and the right end goes up
D. The left end goes up and the right end goes down
Answer: B
Step-by-step explanation:
The end behavior of f(x) is that both ends go down. The correct answer is B.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
f(x) = -3x^4+2x^2-x
Now,
we can find the end behavior of f(x) = -3x^4 + 2x^2 - x:
The degree of f(x) is 4, which is even. Therefore, both ends of the graph will either go up or go down.
The leading coefficient of f(x) is -3, which is negative. Therefore, the right end of the graph will go down.
Since both ends have to go in the same direction, and the right end goes down, then the left end must also go down.
Therefore, by the given function the answer will be both ends go down
Learn more about function here:
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i need help ASP. f(x)=1-3X and g (x)=x+4 calculate fg(-2)
First replace x with -2 in the g(x) equation and solve:
G(x) = x + 4 = -2 + 4 = 2
Now replace x in the f(x) equation with the solution of g(x).
F(x) = 1-3(2) = 1-6 = -5
Fg(-2) = -5
If the lengths of PW and PQ are given, can the length of QW be determined?
Answer:
Yes
Step-by-step explanation:
The length of QW can be determined from PW and PQ by figuring out what the lengths are for Q and W in PW and PQ.
1/8x-5/6=2x solve for X
Answer:
x= -4/9
Step-by-step explanation:
HOPE THIS HELPS!!!! :)
<3333333333
Chiang is filling a 50 ft3 container with water at a rate of 0.5 ft3/min. Interpret
the key features for this situation.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the expression :
Chiang is filling a 50 ft3 container with water at a rate of 0.5 ft3/min. Interpret
50 ft^3 represents the volume of the container which is a product of its length, width and height. The rate is said to be 0.5ft^3 /min. The stated rate represents the volume of the container which Chiang fills each minute. The rate could be obtained by taking the proportion of the entire volume of the container and the time it takes Chiang to fill it.
Here, it will be :
Rate = ( volume of container (ft^3) / time taken (minutes))
Hence 0.5ft^3/min means on average Chiang's fills a volume of 0.5ft^3 of the container each minute.
Pls help I will mark brainliest
Elle and Jude formed a company and agreed that their annual profit will be shared in the ratio 4:5 respectively.If the end of the year Jude received $5000.00 more than Elle how much was Elle's share
Answer:
$20000
Step-by-step explanation:
Let Elle received $x
Therefore, Jude received (x + 5000)$
[tex] \because x : (x + 5000) = 4 :5[/tex]
[tex] \therefore \frac{x}{(x + 5000)} = \frac {4}{5}[/tex]
[tex] \therefore 5x = 4(x + 5000)[/tex]
[tex] \therefore 5x = 4x + 20000[/tex]
[tex] \therefore 5x - 4x = 20000[/tex]
[tex] \therefore x = \$20000[/tex]
Therefore, Elle's share = $20000
pls answer fast i need help
Answer:
The value of k is 46°.
Step-by-step explanation:
Given that when 2 angles add up together, they will form 75°.
So in order to find the value of k, you have to subtract 29° from 75° :
[tex]k + 29 = 75[/tex]
[tex]k = 75 - 29[/tex]
[tex]k = 46[/tex]
Answer:
46 degrees.
Step-by-step explanation:
The whole angle is 75 degrees. So you subtract the given value with the total angle. 75-29=46 degrees.
1) 5x + 12 = -33
whats the answer to this ?? please help
Answer:
[tex]x=-9[/tex]
Step-by-step explanation:
[tex]5x+12=-33[/tex]
Subtract 12 from both sides. The left side cancels:
[tex](5x+12)-12=(-33)-12\\5x=-45[/tex]
Divide both sides by 5. The left side cancels:
[tex](5x)/5=(-45)/5\\x=-9[/tex]
The value of x is -9.
what number is the opposite of 0
Answer:
No opposite
Step-by-step explanation:
Zero has no opposite because it is neither positive or negative.
The value of the number that is the opposite of 0 is 0
How to determine the number that is the opposite of 0From the question, we have the following parameters that can be used in our computation:
Number = 0
By definition:
The number that is the opposite of a number x is -x
using the above as a guide, we have the following:
Opposite = -0
Evaluate
Opposite = 0
Hence, the number that is the opposite of 0 is 0
Read more about expressions at
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Evaluate −5+(−2). The solution is .
Answer:
-7
Step-by-step explanation:
-5 + (-2)
You are adding two negative numbers, -5 and -2.
Find their absolute values: 5 and 2.
Add the absolute values: 5 + 2 = 7
The answer is negative: -7
-5 + (-2) = -7
another math question ! write 16 to the 8th power as a power with a base of 4
Answer:
[tex]\Huge \boxed{4^{16} }[/tex]
Step-by-step explanation:
[tex]16^8[/tex]
Rewrite 16 with base 4.
16 is also written as 4².
[tex](4^2)^8[/tex]
We can apply an exponent rule :
[tex](a^b)^c=a^{bc}[/tex]
Multiply the exponents.
[tex]4^{2 \times 8}[/tex]
[tex]4^{16}[/tex]
Find m∠1. the sides are 56 , 62, and 1
a 62
b 72
c 58
d 67°
Answer:
c 58
Step-by-step explanation:
Answer:
62
Step-by-step explanation:
Add all of them and it’s 180
A 4-pack of monster cards $6.56 what is the unit price
Answer: 1.64
Step-by-step explanation: You need to do 6.56/4 which is 1.64
#_Factor the quadratic binomial 3x2 - 48.
Then, find one of its factors.
Answer:
3(x - 4)(x + 4)
Step-by-step explanation:
[tex]3 {x}^{2} - 48 \\ = 3( {x}^{2} - 16) \\ = 3( {x}^{2} - {4}^{2} ) \\ = 3(x - 4)(x + 4)[/tex]
PLEASE HELP ASAP PLEASE
Answer:
t = (q - r) / rs
Step-by-step explanation:
Right now you have q=rst+r so if you want to find t you must move the variables around. Like this:
q=rst+r (or r+rst)
so so get rid of the r first
like this: (q-r)=rst
divide by rs to find t
so t=(q-r)/rs