Answer:
Given,
[tex] \sqrt{ {x}^{2} + 4x + 4} - 3 = 0 \\ = > \sqrt{ {x}^{2} + 4x + 4} = 3 \\ = > {( \sqrt{ {x}^{2} + 4x + 4} })^{2} = {3}^{2} \\ = > {x}^{2} + 4x + 4 = 9 \\ = > {x}^{2} + 4x + 4 - 9 = 0 \\ = > {x}^{2} + 4x - 5 = 0 \\ = > {x}^{2} + 5x - x - 5 = 0 \\ = > x(x + 5) - 1(x + 5) = 0 \\ = > (x - 1)(x + 5) = 0 \\ \\ \sf \: either \: x - 1 = 0 \: \: \: \: \\ = > x = 1 \: \: \\ \\ \sf \: or \\ x + 5 = 0 \\ = > x = - 5 \\ \\ \green{ \boxed{ \bf \: \: \: \: \: x = 1 \: \: or \: - 5}}[/tex]
But if we put the value of x = 5 then it doesn’t satisfy the equation.
So,
X = 1
Answer:
The answer is [tex]x=1[/tex].
Step-by-step explanation:
To solve this problem, start by factoring the equation using the perfect square trinomial rule, which is states that the middle term is the first term multiplied by the last term, and then multiplied by 2. The formula for the perfect square trinomial rule looks like [tex]a^2+2ab+b^2[/tex], where [tex]a=x[/tex] and [tex]b=2[/tex]. The equation will look like [tex]\sqrt{(x+2)^2}-3=0[/tex].
Next, pull out the terms from under the radical, assuming positive real numbers, which will look like [tex]x+2-3=0[/tex]. Then, simplify the equation by subtracting 3 from 2, which will look like [tex]x-1=0[/tex]. Finally, add 1 to both sides of the equation, and the answer will be [tex]x=1[/tex].
What is the distance in units between the points (4, -7) and (1, -7)?
Step-by-step explanation:
To evaluate such, the following formula is required:
Distance Formula: d(P, Q) = √ (x2 − x1)^2 + (y2 − y1)^2
Denote the following points as the following,
(4, -7). (1, -7)
X1 Y1. X2. Y2
D(P, Q) = √(1 - 4)^2 + (-7 + 7)^2. <== Since there is a double negative, such will be considered addition.
√(-3)^2 + (0)^2
√9 = 3
Thus, the agglomerate distance of such points on the Cartesian plane is disclosed as 3 units.
Câu 2. Cho hình thang cân ABCD (AB // CD, AB CD). Gọi O là giao điểm của AD và BC, E là giao điểm của AC và BD. Chứng minh rằng: | a) Tam giác AOB cân ở O.
b) Các tam giác ABD và BAC bằng nhau. C) EC = ED
d) OE là trung trực của AB và CD.
Answer:
Step-by-step explanation:
Simplify the following, leaving your answer with a positive exponent:
x^-12/ x^-7
Answer:
[tex]\frac{1}{x^{5} }[/tex]
Step-by-step explanation:
x^-12/ x^-7
= x^(-12-(-7))
= x^-5
= 1/x^5
Một người gửi tiết kiệm 100 triệu đồng theo kỳ hạn gửi là 1 năm. Sau 5 năm người người đó nhận được số tiền là 153,86 triệu đồng. Hỏi lãi suất người này gửi là bao nhiêu (lãi kép hàng năm):
Answer:
no
Step-by-step explanation:
Given that 3=a+r/a-r,make r the subject of the formula?
Answer:
Step-by-step explanation:
[tex]3=\frac{a+r}{a-r} \\3a-3r=a+r\\3a-a=r+3r\\4r=2a\\r=\frac{1}{2} a[/tex]
Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!Please Help!
Answer:
(a) no solution
Step-by-step explanation:
Writing the second equation in slope-intercept form, it becomes ...
3x -y = 2 . . . . given
y = 3x -2 . . . . add y-2 to both sides
The first equation is already in slope-intercept form:
y = 3x +3 . . . . first equation
The coefficients of x in the two equations are both 3, so the lines they describe are parallel. They do not intersect, so there is no solution.
The number seventeen and seven thousand in decimal form is
Answer:
17.00 and 17,000.00
this is your answer to ur question
La señora Angélica fue al mercado y compró 2 visores protectores y 1 mascarilla, pagó $55.00, en total. En el mismo puesto, la señora Silvia compró 1 visor protector y 2 mascarillas y pagó $50.00. ¿Cuál es el precio de una mascarilla? ¿Cuáles el precio de un visor protector?
Answer:
Cost of 1 goggles = $20
Cost of 1 mask = 15
Step-by-step explanation:
Given:
Cost of 2 goggles and 1 mask = $55
Cost of 1 goggles and 2 mask = $50
Find:
Cost of each goggles and mask
Computation:
Assume;
Cost of 1 goggles = a
Cost of 1 mask = b
So,
2a + b = 55.....EQ1
a + 2b = 50.......EQ2
EQ1 x 2
4a + 2b = 110 ......EQ3
EQ3 - EQ2
3a = 60
a = 20
Cost of 1 goggles = $20
a + 2a = 50
20 + 2b = 50
2b = 30
b = 15
Cost of 1 mask = 15
.
What is the y-intercept of the line shown?
1
0
10
2
4
-10
ОО
01
03
3.5
Answer:
y-intercept = 3
Step-by-step explanation:
value that's on the y - axis
Meg initially has 3 hours of pop music and 2 hours of classical music in her collection. Every month onwards, the hours of pop music in her collection is 5% more than what she had the previous month. Her classical music does not change. Which function shows the total hours of music she will have in her collection after x months
Answer:
The answer is "[tex]f(x) = 3(1.05)x + 2[/tex]".
Step-by-step explanation:
She starts off with 3 hours with pop music.
Next month, she will have 3 hours she has had and + 3*0.05.
3hrs + 3*0.05hrs = 3*1.05 hrs
We add 2 hours of classical music to the 3 * 1.05 hours to achieve 3 * (1.05) hours + 2 hours of classical music.
Answer: f(x):2(0.05)^x+3
What shape is this? I’m so confused and I need to get this done really quickly!
The shape is an irregular pentagon
WILL GIVE BRAINLISEST Solve for m∠NLM
GOOD LUCKJ!
Answer:
[tex]m<NLM = 30[/tex]
Step-by-step explanation:
1. Approach
The easiest way to solve this problem is to find the degree measure of the parameter (x). Use the fact that line (LN) is a diameter to solve for (x), beacause the angle measure of a circle on either side of the diameter is (180) degrees. One can then find the measure of arc (mNM), and then find the measure of the angle (<NLM) using the inscribed angles theory.
2. Find the measure of (x)
A diameter is the largest chord or segment in a circle. It intersects a circle at two points and runs through the center of a circle. The degree measure of a circle on either side of the diameter is (180) degrees. As per the given image, line (LN) is a diameter. The arcs (mLM) and (mNM) make up half of the circle, or rather one side of the diameter. With this information, one can form an equation and solve for the parameter (x) using this information:
[tex](mLM)+(mNM)=180[/tex]
Substitute,
[tex](mLM)+(mNM)=180[/tex]
[tex](13x-10)+(7x-10)=180[/tex]
Simplify,
[tex](13x-10)+(7x-10)=180[/tex]
[tex]20x-20=180[/tex]
Inverse operations,
[tex]20x-20=180[/tex]
[tex]20x=200[/tex]
[tex]x=10[/tex]
3. Find the measure of angle (<NLM)
The inscribed angles theorem states that an angle with its vertex on the circumference (outer edge) of a circle is equal to half of the surrounding arc. One can form an equation and solve for the measure of angle (<NLM).
[tex]m<NLM=\frac{1}{2}(mNM)[/tex]
Substitute,
[tex]m<NLM=\frac{1}{2}(mNM)[/tex]
[tex]=\frac{1}{2}(7x-10)[/tex]
[tex]=\frac{1}{2}(7(10)-10)\\\\=\frac{1}{2}(70-10)\\\\=\frac{1}{2}(60)\\\\=30[/tex]
a) In a group of 60 students, 15 liked maths only, 20 liked science only and 5 did not like
any of two subjects?
(i) How many of them liked at least one subject?
(ii) Find the number of students who liked both the subjects.
(iii) How many of them liked maths?
(iv) How many of them liked science?
(v) Represent the result in a Venn diagram.
PLZ PLZ HELP.........
Part (i)
We have 60 students total, and 5 didn't like any of the two subjects, so that must mean 60-5 = 55 students liked at least one subject.
Answer: 55=========================================================
Part (ii)
We have 15 who like math only, 20 who like science only, and 55 who like either (or both). Let x be the number of people who like both classes.
We can then say
15+20+x = 55
x+35 = 55
x = 55-35
x = 20
This means 20 people liked both subjects
Answer: 20=========================================================
Part (iii)
There are 15 people who like math only, and 20 who like both. Therefore, there are 15+20 = 35 people who like math (and some of these people also like science)
Answer: 35=========================================================
Part (iv)
We'll follow the same idea as the previous part. There are 20 people who like science only and 20 who like both subjects. That yields 40 people total who like science (and some of these people also like math).
Answer: 40=========================================================
Part (v)
We'll draw a rectangle to represent the entire group of 60 students. This is considered the universal set. Inside the rectangle will be two overlapping circles to represent math (M) and science (S).
We'll have 15 go in circle M, but outside circle S to represent the 15 people who like math only. Then we have 20 go in circle S but outside circle M to show the 20 people who like science only. We have another copy of 20 go in the overlapped region between the circles. This is the 20 people who like both classes. And finally, we have 5 go outside both circles, but inside the rectangle. These are the 5 people who don't like either subject.
Note how all of the values in the diagram add up to 60
15+20+20+5 = 60
This helps confirm we have the correct values.
Answer: See the venn diagram belowSolve the following equation |2x+3|+|x-2|=6x
Recall the definition of absolute value:
• |x| = x if x ≥ 0
• |x| = -x if x < 0
So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).
(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then
|2x + 3| + |x - 2| = 6x
-(2x + 3) - (x - 2) = 6x
-2x - 3 - x + 2 = 6x
-3x - 1 = 6x
9x = -1
x = -1/9
But -1/9 is not smaller than -3/2, so this case provides no valid solution.
(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,
|2x + 3| + |x - 2| = 6x
(2x + 3) - (x - 2) = 6x
2x + 3 - x + 2 = 6x
x + 5 = 6x
5x = 5
x = 1
This solution is valid because it does fall in the interval -3/2 ≤ x < 2.
(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So
|2x + 3| + |x - 2| = 6x
-(2x + 3) + (x - 2) = 6x
-2x - 3 + x - 2 = 6x
-x - 5 = 6x
7x = -5
x = -5/7
This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.
(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.
|2x + 3| + |x - 2| = 6x
(2x + 3) + (x - 2) = 6x
2x + 3 + x - 2 = 6x
3x + 1 = 6x
3x = 1
x = 1/3
This is yet another invalid solution since 1/3 is smaller than 2.
So there is one solution at x = 1.
Out of 120 students in exam, 2/3 of them passed. How many students passed?
Out of 120 students in exam, 2/3 of them passed. How many students passed?
now,
no of students passed = 2/3×120
= 0.66×120
=80...
therefore 80 students were passed....
Answer:
80
Step-by-step explanation:
A square has an area of 49 cm squared what is the length of each side
Answer:
7
Step-by-step explanation:
[tex]s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7[/tex]
if f(x) = 2x/2x+1 and g(x) = 1/2x+1, find f(x) / g(x)
Answer:
2x
Step-by-step explanation:
Just solve the function operation:
f/g=(2x/2x+1)/(1/2x+1) = 2x since (2x/1)/(2x+1/2x+1) simplifies to 2x/1 the answer is 2x
A man was traveling by air is allowed a maximum of 20kg luggages .The man has four bags weighing 3.5kg ,15 kg ,2kg and 1.5kg .Find excess weight of his luggage. 2 . Express the excess weight as a percentage of his maximum weight allowed.
Answer:
See explanation
Step-by-step explanation:
Maximum weight = 20 kg
Bag 1 = 3.5kg
Bag 2 = 15 kg
Bag 3 = 2kg
Bag 4 = 1.5kg
Total weight of bags = 22 kg
Excess weight of his luggage = Total weight of bags - Maximum weight
= 22 kg - 20 kg
= 2 kg
Express the excess weight as a percentage of his maximum weight allowed = excess weight / maximum weight × 100
= 2/20 × 100
= 0.1 × 100
= 10%
Express the excess weight as a percentage of his maximum weight allowed = 10%
Find g(5)+h(2)
g(x)=2x-5
h(x)=4x+5
Step-by-step explanation:
g(5)=2(5)-5=5
h(2)=4(2)+5=13
g(5)+h(2)=5+13=18
Write these sums as decimals:
2/100 + 3/1,000 =
1/10 + 4/10,000 =
Answer:
1 ) 0.023
2 ) 0.1004
Step-by-step explanation:
2 / 100 + 3 / 1000
= 0.02 + 0.003
= 0.020 + 0.003
= 0.023
1 / 10 + 4 / 10,000
= 0.1 + 0.0004
= 0.1000 + 0.0004
= 0.1004
What is 2:50 is simplest form
Answer:
0.04
Step-by-step explanation:
2 / 50 is the same as 1 / 25.
1 / 25 = 0.04
Answer:
0.04
Step-by-step explanation:
A set of composite number less than 12.Express it in listing and set-builder methods
composite numbers less than 12={1,3,4,6,8,9,10}
1 point Write the equation of the line that is parallel to the line given and through the given point. Do not use spaces in your equation y=-x-3 (-3,4)
Answer:
y=3x+9......(i)
y=-4x-12...(ii)
these are the equation
Find the real or imaginary solutions by factoring.
X^4 -3x^2 = -2x^2
Look in the images it is solved.
help me please it easy.
Answer: there is no picture attached or equation? what's the question?
Step-by-step explanation:
ok, what do you need help with?
could someone help me with this (picture) please explain if you could I don't really understand.
Answer:
10t + D = 40
Step-by-step explanation:
y = mx + b is the equation of a line in slope intercept form. We'll be using this equation since the slope, or distance traveled, is steady (linear). In this case, the slope is 10 since Sarah's pace is 10 km/hr. m is the slope, so m = 10.
y = 10x + b. However, she needs to run 40 km. So we're going to substitute 40 in for y.
40 = 10x + b. Now, we need to use t instead of x since that's what's been asked of us. (The slope represents the distance traveled over time, so t fits.)
10t + b = 40
b needs to become D, the distance in kilometers.
So now we have 10t + D = 40
Answer:
D(t)= 40-10t
Step-by-step explanation:
#KmNn
ASAP!! can i get help on this one and can i please get a vivid explanation thank you.
Answer:
3x + 11
Step-by-step explanation:
1) Remove Parentheses:
x + 4 + 2x + 7
2) Combine Like Terms:
(2x + x) and (4 + 7)
3) Simplify:
3x + 11
Hope this helps, good luck! Have a good day. :)
Which of the following numbers are solutions of the sentence x-3 < 2?
I -3
II 0
III 2
IV 5
O ll only
O III only
O I and III only
O I, II, and III only
O I, II, III, and IV
Answer:
O I, II, and III only
Step-by-step explanation:
x-3 < 2
Add 3 to each side
x-3+3< 2+5
x<5
-3 is less than 5
0 is less than 5
2 is less than 5
5 is not less than 5
I , II , II are true
PLEASE HELP ME ASAP!!!
Answer:
5.30
Step-by-step explanation:
Total cost = flat fee + cost per mile * number of miles
c(m) = 3.50 + .60m
Let m=3
c(3) = 3.50 + .60(3)
= 3.50 + 1.80
=5.30
Answer:
B: $5.30
Step-by-step explanation:
Each mile is $0.6, to get the result for 3 miles we would need to multiply $0.6 by 3. $0.60 * 3 = $1.8. Finally we would need to add the 3.50 to $1.8 resulting in $5.30
20 points PLEASE HELP IT'S DUE TODAY
Answer:
Step-by-step explanation:
Arc length of the circle is given by,
Arc length = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]
Area of the sector of a circle = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]
22). Arc length of the circle having central angle = [tex]\frac{\pi}{3}[/tex]
= 60°
Arc length = [tex]\frac{60^{\circ}}{360^{\circ}}(2\pi )(7)[/tex]
= [tex]\frac{14\pi }{6}[/tex]
= 7.33 cm
23). Arc length of the circle having central angle = 225°
Arc length = [tex]\frac{225^{\circ}}{360^{\circ}}(2\pi )(10)[/tex]
= 12.5π
= 39.27 km
24). Central angle = [tex]\frac{5\pi }{4}[/tex]
= [tex]\frac{5\times 180^{\circ}}{4}[/tex]
= 225°
Area of the sector = [tex]\frac{225^{\circ}}{360^{\circ}}(2\pi )(11)[/tex]
= 43.20 yd²
25). Area of the sector = [tex]\frac{270^{\circ}}{360^{\circ}}(2\pi )(14)[/tex]
= 65.97 yd²
