Answer:
The equation
[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
Write the equation for the line that passes through the points (4, 5) and
(6,9). *
Answer:
y = 2x + 1
Step-by-step explanation:
first find slops
(9-5)/(6-4) = 4/2 = 2 = m
y = mx + b
5 = 2(2) + b
1 = b
y = 2x + 1
Answer:
y = 2x - 3
Step-by-step explanation:
gradient of the line is
[tex] \frac{9 - 5}{6 - 4 } = 2[/tex]
equation will be:
[tex] \frac{y - 5}{ x - 4} = 2[/tex]
y - 5 = 2x - 8
y = 2x - 3
Prime factors of 2601
Answer:
The prime factors are: 3 x 3 x 17 x 17. or also written as { 3, 3, 17, 17 }
Step-by-step explanation:
Person above agrees
When solving the system of equations by graphing, what is the solution of 3x + 2y = 2 and 2x – y=6?
A (-2,2)
B. (2.-2)
C. (-2,-2)
D. (2, 2)
Answer:
answer B: (2,-2)
Step-by-step explanation:
First, write the equations on top of each other:
[tex]3x+2y=2\\2x-y=6[/tex]
Then, multiply the the second equation by 2 so that we can use elimination of the y-variable:
[tex]3x+2y=2\\2(2x-y)=2(6)\\\\3x+2y=2\\4x-2y=12[/tex]
Next, use elimination to find the value of "x":
[tex]3x+2y=2\\+(4x-2y=12)\\\\7x+0=14\\7x=14\\\frac{7x}{7}=\frac{14}{7}\\x=2[/tex]
So, your x-value is 2.
Now, substitute your x-value into one of your equations, let's take the second equation, 2x-y=6:
[tex]2x-y=6\\2(2)-y=6\\4-y=6\\4-4-y=6-4\\-y=2\\\frac{-y}{1}=\frac{2}{-1}\\y=-2[/tex]
Your y-value is -2.
With all your information gathered, you find that the solution to this system of equation is (2,-2).
Find the area of the triangle ABC given A = 30°, b = 5, and c = 2 [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex]
3[tex]\frac{1}{8}[/tex]
4[tex]\frac{1}{8}[/tex]
12[tex]\frac{1}{2}[/tex]
Answer:
a=6.25 unit^2
Step-by-step explanation:
Given:
A=30°
b=5
c=2½
Required:
a=?
Formula:
a=½b*h
Solution:
a=½b*h
=½5*2½
=½*5*5/2
=0.2*5*5/2
=2.5*5/2
=2.5*2.5
=6.25 unit^2
Hope this helps ;) ❤❤❤
Answer:
The answer is B or 3 1/8
Step-by-step explanation:
In the diagram, TC represents a vertical building. The points, A and B, are on the same level as the foot C of the building such that ATC = 40° and BTC = 56°. If BT is 29 m longer than AT, find
(a) the height of the building,
(b) the distance AB.
Answer:
(a) The height of the building is 60.06 m
(b) The distance AB is 139.43 m
Step-by-step explanation:
The given parameters are
Given that segment BT = segment AT + 29
By trigonometric ratios, we have;
cos∠ATC = CT/AT
cos∠BTC = CT/BT
Therefore, we have;
cos(40°) = CT/AT.................................(1)
cos(56°) = CT/BT = CT/(AT + 29).....(2)
cos(56°) = CT/(AT + 29)......................(3)
From equation (1)
CT = AT×cos(40°)
From equation (3)
AT×cos(56°) + 29 × cos(56°) = CT
Therefore;
AT×cos(40°) = AT×cos(56°) + 29 × cos(56°)
AT×cos(40°) - AT×cos(56°) = 29 × cos(56°)
AT×(cos(40°) - cos(56°)) = 29 × cos(56°)
AT = 29 × cos(56°)/(cos(40°) - cos(56°)) = 78.4 m
TC = CT = AT×cos(40°) = 78.4×cos(40°) = 60.06 m
The height of the building = 60.06 m
(b) BT = AT + 29 = 78.4 m + 29 m= 107.4 m
AB = AT×sin(∠ATC ) + BT×sin(∠BTC) = 78.4×sin(40°) + 107.4×sin(56°) = 139.43 m
The distance AB = 139.43 m.
Line N passes through the points (–1, 4) and (–1, –4).Which is true of line N? Line N is a vertical line with an undefined slope. Line N is a vertical line with a slope of zero. Line N is a horizontal line with an undefined slope. Line N is a horizontal line with a slope of zero.
Answer:
Line N is a vertical line with an undefined slope.
Step-by-step explanation:
When the points that line N passes through are graphed, they form a vertical line.
All vertical lines have an undefined slope.
We can also check if it's undefined by finding the slope.
[tex]m=\frac{-4-4}{-1+1}=\frac{-8}{0}[/tex]
The quotient would be undefined. You cannot divide by zero.
Hope this helps.
Answer:
Line N is a vertical line with an undefined slope.
Step-by-step explanation:
Did the quiz wanted to help people.
Create a figure with half the perimeter of a given figure.
you don't have to actually make a shape, can someone explain how to do this pls
Step-by-step explanation:
First you have to add up all of the numbers that make up the perimeter of this arrow.
3+3+1+.5+.5+1.8+1.8=11.6
You than want to divide this number by 2 to find the half perimeter you have to work with, which is 5.8.
A simple shape you can make is a square, with each side being 1.45 m.
perform the indicated operations. express the answer as a polynomial written in standard form.
(2x+5y)^2
Answer:
Step-by-step explanation:
If the cost of fencing a rectangular garden per meter is rupees 5 . Find the amount needed to do the fencing of the garden with length 400 m and breadth 150 m .
Answer:
6500 rupees
Step-by-step explanation:
We are given a rectangular garden is the dimensions of:
Length = 400 m
Breadth = 150 m
Perimeter of a rectangle = 2(L + B)
= 2(400 + 150)
= 2(650)
= 1300m
We are told that the cost of fencing a rectangular garden per meter is rupees 5
1 m = 5 rupees
1300m =
Hence, the cost to fence the entire garden = 1300 × 5 rupees
= 6500rupees
find the distance between the pair of points (2, -5) and (3, -7)
Step-by-step explanation:
Using distance formula:
√(- 7 - (-5))² + (3 - 2)²
√(- 7 + 5)³ + 1²
√(-2)² + 1
√4+1
√5
Form a group of 17 women and 11 men, a researcher wants to randomly
select 5 women and 5 men for a study. In how many ways can the study
group be selected.
Answer:
17C5+11C5
Step-by-step explanation:
Well there are 17 and chooses 5 that's 17C5
there are 11 men abd chooses 5 that's 11C5
so add them up
17C5+11C5
The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.
What is Permutation and Combination?Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.
Now, the number of ways for selection can be written as,
Number of ways in which men can be selected = ¹¹C₅ = 462
Number of ways in which women can be selected = ¹⁷C₅ = 6188
Further, the number of ways for selection can be written as,
Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected
Number of ways = 462 × 6188
Number of ways = 2,858,856
Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.
Learn more about Permutation and Combination here:
https://brainly.com/question/11732255
#SPJ2
Factorize
4a^2-24a^2b^2+9b^2
another question what's the formula for an open end of a cylinder??
Answer:
Formula for an opened end of a cylinder =
[tex]\pi r^2 +2\pi rh\\[/tex]
Closed at both end =
[tex]2\pi r^2 +2\pi r h[/tex]
Opened at both end =
[tex]2\pi rh[/tex]
Step-by-step explanation:
An apartment complex has several 9-story buildings, and every apartment in the complex has a unique number. On the first floor of one of the buildings, you see four apartments numbered 109, 110, 111, and 112. In which building and on which floor is apartment 207?
Answer:
Apartment 207 is a second floor apartment in Building 2.
Step-by-step explanation:
Since one building has four first floor apartments, then I'd think all buildings have 4 apartments per floor. Since one building has first floor apartment numbers 109, 110, 111, and 112, then I'd think there is a building with first floor apartment numbers 101, 102, 103, and 104, and another building with first floor apartment numbers 105, 106, 107, 108.
Building 1 First floor: 101, 102, 103, 104
Building 2 First floor: 105, 106, 107, 108
Building 3 First floor: 109, 110, 111, 112
Building 2 Second floor: 205, 206, 207, 208
Apartment 207 is a second floor apartment in Building 2.
2.3 repeating as a fraction or percentage
Find the sum of 91.8+0.964+5.09 and correct your answer to one decimal place.
Answer:
97.85
I hope this helps!
5000 X 10 X 10 X 50
Answer:
25000000
5000 X 10 is 50000
50000 X 10 is 500000
500000 X 50 is 25000000
Step-by-step explanation:
Answer:
25000000
Step-by-step explanation:
A way to tackle this is to split all the numbers up into a digit and a power of 10.
5000 = 5*1000, and 1000 can be written as 10^3
10 = 1*10, and obviously 10 is 10^1
50 = 5*10, where 10 is 10^1
Now we have (5*10^3) * (1 * 10) *(1 *10)*(5 *10)
Gathering all the digits, we have 5*1*1*5, giving us 25
Gathering all the powers of 10, we have 10^3*10*10*10 = 10^6
expanding and multiplying gives us the final answer of 25000000
Find the range of f(x) = –x + 4 for the domain {–3, –2, –1, 1}.
Answer:
[tex]\boxed{ \{7, 6, 5, 3 \} }[/tex]
Step-by-step explanation:
The domain is all possible values for x.
The range is all possible values for f(x) or y.
The domain given is {-3, -2, -1, 1}.
Plug x as {-3, -2, -1, 1} and find the f(x) or y values.
[tex]f(-3)=-(-3)+4=7\\f(-2)=-(-2)+4=6\\f(-1)=-(-1)+4=5\\f(1)=-(1)+4=3[/tex]
The range is {7, 6, 5, 3}, when the domain is {-3, -2, -1, 1}.
Simplify 7^ -5/6 x 7^-7/6
Answer:
1/49
Step-by-step explanation:
If you add this is the calculator, I think it will come out.
━━━━━━━☆☆━━━━━━━
▹ Answer
1/49
▹ Step-by-Step Explanation
7^-5/6 * 7^-7/6
= 1/7²
= 1/49
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Determine if the event described is independent or dependent. You pick a marble at random from a group of marbles, don't replace the marble, and pick a second marble.
Answer:
dependent
Step-by-step explanation:
This is a dependent event. There is one less marble in the bag to choose from
Say there was 1 red marble and 4 blue marble. You drew the red marble on the first pick, now you cannot get a red marble on your second pick.
If you drew a blue marble on the first pick you could get a red marble on the second pick.
So what happens on the first pick affects the second pick
PLEASE HELP!!!
10. Write the formula of the function f(x) whose graph is shown.
A
f(x) = 4 - 4
х
B
f(x)=
1
= - +4
X
с
f(x) = 24
D
1
f(x) =
X +4
Step-by-step explanation:
c
Pls help, I don’t know how to fo
frustum of a cone is: = pi * l(R + r)
(l) = slant height of the frustum.
from 2929.645714 - 506.1257143
= 2423.52
= 2423.5cm
Answer:
from 2929.645714 - 506.1257143
= 2423.52
= 2423.5cm
How many solutions are there for the absolute value equation, |16 + t| = – 3
Answer:
no solutions
Step-by-step explanation:
|16 + t| = – 3
Absolute values are greater than or equal to zero
They cannot be negative so there are no solutions
Answer:
no solutions
Step-by-step explanation:
|16 + t| = – 3
Absolute values are greater than or equal to zero
They cannot be negative so there are no solutions
1782/3 = and why the answer
Answer:
594
Step-by-step explanation:
1782/3 = 594.
To if the answer is correct, you do this:
594 × 3 = 1782.
If Paul and Steve are the same height and they are both correct, write an equation to represent this relationship. Put Paul's expression on the left side of the equal sign and Steve's expression on the right.
Answer:
Theresa's height=60 inches
Paul's height= Steve's height=74 inches
Step-by-step explanation:
Theresa has two brothers,Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. If they're both right, how tall is Theresa ?
Let
p=paul's height
s=steve's height
t=theresa's height
Paul's height = Steve's height
p=s
Paul says he is 16 inches shorter than 1 1/2 times Theresa's height
1 1/2 * t -16
=3/2t -16
Steve says he is 6 inches shorter than 1 1/3 times Theresa's height
1 1/3 * t - 6
=4/3t - 6
P=S
3/2t -16 = 4/3t - 6
Collect like terms
3/2t-4/3t= -6+16
9t-8t/6 =10
t/6=10
Cross product
t=60
Theresa's height=60 inches
P=3/2t -16
=3/2(60) -16
=180/2 -16
=90-16
=74 inches
p=s
Paul's height=74 inches
Please answer question now
Answer:
3
Step-by-step explanation:
2 tangents of a circle drawn from an external point are said to be congruent, according to the two-tangents theorem. Thus:
MN = ML (both tangents from external point M)
ML = 6 - KL
KL = KJ (tangents from point K)
PQ = QJ = 1 (tangents from point Q)
Therefore, KJ = 4 - 1 = 3
Since kJ = KL = 3,
ML = 6 - KL = 6 - 3
ML = MN = 3
Brad invests $3700 in an account paying 3% compounded monthly. How much is in the account after 8 months?
Answer:
Amount after 8 month (A) = $3775 (Approx)
Step-by-step explanation:
Given:
Amount invested (P) = $3,700
Rate of interest (r) = 3% = 0.03 / 12 = 0.0025 monthly
Number of month (n) = 8 month
Find:
Amount after 8 month (A)
Computation:
[tex]A=P(1+r)^n\\\\ A=3700(1+0.0025)^8\\\\A=3700(1.02017588)\\\\ A = 3774.650676[/tex]
Amount after 8 month (A) = $3775 (Approx)
PLEASE HELP ILL LOVE U FOREVER
In Exercise 4, find the surface area of the solid
formed by the net.
Round the approximate value however you need to
Units are in square centimeters.
===================================================
Work Shown:
You have the 160 portions correct since 20*8 = 160.
The other pieces are equilateral triangles, in which we use the formula
[tex]A = \frac{\sqrt{3}}{4}x^2[/tex]
where x is the side length of the triangle. Plug in x = 8 to get
[tex]A = \frac{\sqrt{3}}{4}x^2\\\\A = \frac{\sqrt{3}}{4}8^2\\\\A = \sqrt{3}*\frac{1}{4}*64\\\\A = \sqrt{3}*16\\\\A = 16\sqrt{3}\\\\[/tex]
That's the exact area of one triangle, but we have two of them. Double the result to get [tex]2*16*\sqrt{3} = 32\sqrt{3}[/tex]
The total surface area is the sum of all the smaller areas
[tex]160+160+160+32\sqrt{3} = 480+32\sqrt{3}[/tex]
--------------------------
The exact surface area is [tex]480+32\sqrt{3}[/tex] square cm.
Using a calculator, you should get [tex]480+32\sqrt{3} \approx 535.425625842204[/tex]
Round this however you need to.
PLEASE HELP ME WILL MARK BRAINLIEST! Town planners are planning a 500 foot by 700 foot parking lot by making a scale drawing that is 90 inches by 126 inches. What is the scale of inches in the drawing to inches in the actual object?
Answer:
The approximate value of the scale is 1:67
or the actual value without approximation is 1: 66 2/3 ( 66 while number , two over three)
Step-by-step explanation:
Here, we want to figure out the scale in inches of the drawing to the actual object.
The actual object is 500 ft by 700 ft
while the drawing is 90 inches by 126 inches
Mathematically, we know that 12 inches = 1 foot
So the actual object will be;
500(12) by 700(12)
= 6000 inches by 8400 inches
Now let’s make a division to get the scale;
6000/90 by 8400/126
we get 66.67 as answers on both ends
This is approximately equal to 67
So the scale we have here is 1:67
How many cubes with side lengths of \dfrac12 \text{ cm} 2 1 cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism? Cubes
Answer:
24
Step-by-step explanation:
Answer
24!
Step-by-step explanation:
Person above me is correct :)
