raAnswer:
x = 5
Step-by-step explanation:
Original equation = [tex]\sqrt{2x+6}[/tex] - [tex]\sqrt{x+4}[/tex] = 1
Remove square roots
[tex]x^{2}[/tex] + 2x +1 = 4x +16
Subtract 16 from both sides
[tex]x^{2}[/tex]+ 2x +1 = 4x +16
-16 -16
---------------------------
[tex]x^{2}[/tex] + 2x- 15= 4x
Subtract 4x from both sides
[tex]x^{2}[/tex] + 2x - 15 - 4x= 4x - 4x
= [tex]x^{2}[/tex] - 2x - 15 = 0
THIS EQUATION HAS 2 rational roots. {x1,x2} = {5,-3}
CHECK THAT THE FIRST SOLUTION IS CORRECT (5)
Original equation, root isolated, after tidy up
[tex]\sqrt{2x+6}[/tex] = [tex]\sqrt{x+4}[/tex]
Plug in 5 for x
[tex]\sqrt{2\cdot (5)+6}[/tex] = [tex]\sqrt{(5)+4+1}[/tex]
Simplify
[tex]\sqrt16}[/tex] = 4
Solution checks !!
Solution is: x = 5
CHECK THAT THE SECOND SOLUTION IS CORRECT (-3)
Original equation, root isolated, after tidy up
[tex]\sqrt{2x+6}[/tex] = [tex]\sqrt{x+4}[/tex]
Plug in -3 for x
[tex]\sqrt{2\cdot (-3) +6}[/tex] = [tex]\sqrt{(-3)+4+1}[/tex]
Simplify
[tex]\sqrt{0}[/tex] = 2
Solution does not check
0 ≠ 2
So, the answer is x = 5
Hope this helps!
The variable b varies directly as the square root of c. If b = 100 when c = 4, which equation can be used to find other combinations of b and c? A. B. C. D.
Answer:
b. b=50√c
Step-by-step explanation:
The equation can be used to find other combinations of b and c will be b = 50√c. Then the correct option is B.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The variable b varies directly as the square root of c.
b ∝ √c
If the proportionality sign is removed with the equal sign, then a constant (k) is introduced.
b = k√c
If b = 100 when c = 4.
Then the value of k will be
100 = k√4
100 = 2k
100 / 2 = k
k = 50
Substitute the value of k in equation, then the equation will be
b = 50√c
The equation can be used to find other combinations of b and c will be b = 50√c.
Then the correct option is B.
The complete question is given below.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5
If x = 24 and y = 74, what is x when y = 19?
Round to the nearest hundredths place (two decimal places)
Answer:
Step-by-step explanation:bbbbb
Answer:
-31
Step-by-step explanation:
74-24=50
19-50=-31
suppose you can type 60 words per minute. what is the total number of words typed after 5, 10, 15, and 20 minutes?
Please help me with 4/a, b, c and 5/b
Answer:
4:
a.) 49x^2-36y^2
b.) 9a^2-25b^2
c.) 1/25x^2-49
5: b.) -5x^2-4xy+4y^2
Step-by-step explanation:
__________________________________
4a.) [tex]\bold{(7x-6y)(7x+6y)}[/tex]:- Multiplication can be transformed into difference of squares using the rule: [tex](a-b)(a+b)=a^2-b^2[/tex].
- So change the equation using the rule:
[tex](7x)^2-(6y)^2[/tex]- Expand [tex](7x)^2[/tex] and [tex](6y)^2[/tex]:
[tex](7x)^2=7^2x^2[/tex][tex](6y)^2=6^2y^2[/tex]- Calculate [tex]7^2[/tex] and [tex]6^2[/tex]:
[tex]7^2=49[/tex][tex]6^2=36[/tex]So the end equation would be: [tex]49x^2-36y^2[/tex].
4b.) [tex]\bold{(3a+5b)(3a-5b)}[/tex]:- Multiplication can be transformed into difference of squares using the rule: [tex](a-b)(a+b)=a^2-b^2[/tex].
- So change the equation using the rule:
[tex](3a)^2-(5b)^2[/tex]- Expand [tex](3a)^2[/tex] and [tex](5b)^2[/tex] :
[tex](3a)^2=3^2a^2[/tex][tex](5b)^2=5^2b^2[/tex]- Calculate [tex]3^2[/tex] and [tex]5^2[/tex]:
[tex]3^2=9[/tex][tex]5^2=25[/tex]So the end equation would be: [tex]9a^2-25b^2[/tex].
4c.) [tex]\bold{(\frac{1}{5}x-7)}[/tex] × [tex]\bold{(\frac{1}{5}+7)}[/tex]:- Multiplication can be transformed into difference of squares using the rule: [tex](a-b)(a+b)=a^2-b^2[/tex].
- So change the equation using the rule:
[tex](\frac{1}{5}x)^2-7^2[/tex]- Expand [tex](\frac{1}{5}x)^2[/tex]:
[tex](\frac{1}{5})^2x^2[/tex]- Calculate [tex](\frac{1}{5})^2[/tex] and [tex]7^2[/tex] :
[tex](\frac{1}{5})^2=\frac{1}{25}[/tex][tex]7^2=49[/tex]So the end equation would be: [tex]\frac{1}{25}x^2-49[/tex].
5b.) [tex]\bold{(4x-y)(4x+y)+(2x-y)^2-(5x+2y)(5x-2y)}[/tex]:- Consider [tex](4x-y)(4x+y)[/tex]. Multiplication can be transformed into difference of squares using the rule: [tex](a-b)(a+b)=a^2-b^2[/tex].
- So change the equation using the rule:
[tex](4x)^2-y^2[/tex]- Expand [tex](4x)^2[/tex]:
[tex](4x)^2=4^2x^2[/tex]- Calculate [tex]4^2[/tex]:
[tex]4^2=16[/tex]- Use binomial theorem [tex](a-b)^2=a^2-2ab+b^2[/tex] to expand [tex](2x-y)^2[/tex]:
[tex]4x^2-4xy+y^2[/tex]- Combine [tex]-y^2[/tex] and [tex]y^2[/tex]:
[tex]-y^2+y^2=0[/tex]- Consider [tex](5x+2y)(5x-2y)[/tex]. Multiplication can be transformed into difference of squares using the rule: [tex](a-b)(a+b)=a^2-b^2[/tex].
So change the equation using the rule:
[tex](5x)^2-(2y)^2[/tex]- Expand [tex](5x)^2[/tex] and [tex](2y)^2[/tex]:
[tex](5x)^2=5^2x^2[/tex][tex](2y)^2=2^2y^2[/tex]- Calculate [tex]5^2[/tex] and [tex]2^2[/tex]:
[tex]5^2=25[/tex][tex]2^2=4[/tex]- Combine [tex]20x^2[/tex] and [tex]-25x^2[/tex]:
[tex]20x^2+(-25x^2)=-5x^2[/tex]So the end equation would be: [tex]4y^2-4xy-5x^2[/tex].
__________________________________
One-fourth the sum of 1 and what number is one-half the sum of 2 and 1/2 ?
Answer:a 1
Lesson 3-1
Translate each sentence into an equation.
1
Step-by-step explanation:
Which expression is the same as (2a + b)3?
Answer:
I guess it's A
Step-by-step explanation:
2*2*2+b*b*b
that's 8a³+b³
PLS HELP ILL GIVE BRAINLIEST
Hi there.
The answer is f(0) = 3.
Explanation:
Given 2 functions with given domains.
[tex]f(x) = 5x - 1[/tex]
where x < -2
[tex]f(x) = x + 3[/tex]
where x >= -2
Evaluate the value of f(x) when x = 0. Therefore, f(x)= 5x-1 cannot be used as the given x = 0 is greater than its domain.
Thus, our main function is f(x) = x+3
Evaluate the value by substituting x = 0 in the function.
[tex]f(0) = 0 + 3 \\ f(0) = 3[/tex]
Thus, the answer is f(0) = 3
The circumference of a circular garden is approximately 24 feet. What is the approximate area inside the circular garden? What is the approximate area inside the garden? Solve on paper. Then, enter your answer on Zearn.
Answer:
45.86 ft²
Step-by-step explanation:
Circumference of a circle = 2 * pi * r
Circumference = 24
24 = 2 * 3.14 * r
24 = 6.28r
r = 24 / 6.28
r = 3.8216 ft
Approximate area of garden :
Area of circle :
pi * r^2
Area = 3.14 * 3.8216^2
Area = 45.8585273984
Area = 45.86 ft²
someone please help if ur good with math!
The answer is C.
A is wrong in y-intercept part.
B is wrong in slope value part.
C is absolutely correct.
D is wrong in y-intercept part.
18. (1) The value of cot π/4+Q)cot
(π/4 - Q
) is
d. Not-defined.
a. - 1
C. 1
b. 0
solving systems by elimination
2x+3y=6
2y=5-x
Step-by-step explanation:
2x + y = 6/3
x+y = 1
x=1-y
now,
y=5-(-1)/2
y=3
again,
x=1-3
x=-2
therefore, x= -2 and y = 3
What do you say when a trinomial is not factorable
Answer:
I think you just say non-factorable or simply not factorable
Determine the
the fourth
the geometric sequence. x; 2x+2; 3x+3.
numerical
value
Of
term
OF
Answer:
a₄ = - [tex]\frac{27}{2}[/tex]
Step-by-step explanation:
In a geometric sequence, the common ratio r is calculated as
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] , substitute values
[tex]\frac{2x+2}{x}[/tex] = [tex]\frac{3x+3}{2x+2}[/tex] ( cross- multiply )
(2x + 2)² = x(3x + 3) ← expand both sides
4x² + 8x + 4 = 3x² + 3x ( subtract 3x² + 3x from both sides )
x² + 5x + 4 = 0 ← in standard form
(x + 1)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
However x ≠ - 1 as this would make the denominator of the second term equal to zero and therefore undefined.
Thus x = - 4 and
r = [tex]\frac{2(-4)+2}{-4}[/tex] = [tex]\frac{-8+2}{-4}[/tex] = [tex]\frac{-6}{-4}[/tex] = [tex]\frac{3}{2}[/tex]
Then
a₁ = - 4
a₂ = - 4 × [tex]\frac{3}{2}[/tex] = - 6
a₃ = - 6 × [tex]\frac{3}{2}[/tex] = - 9
a₄ = - 9 × [tex]\frac{3}{2}[/tex] = - [tex]\frac{27}{2}[/tex]
Which of the following is a measure used to describe the typical distance of a
data value from the mean value for a given spread of data, as shown in red
below?
A. Skew
B. Mode
C. Standard deviation
D. Median
Answer:
The correct answer is: Option C: Standard Deviation
Step-by-step explanation:
In a dataset, there are several methods that are used to determine the attributes of the data. One of them is standard deviation.
Deviation is derived from the word "Deviate" which means to move far.
Standard deviation is used to measure the distance of a data value from the mean i.e. how far a data value is from mean.
Hence,
The correct answer is: Option C: Standard Deviation
What expression is equal to 3/7 divided by 5/12?
Answer:
The answer is 6/77
Step-by-step explanation:
The sum of two numbers is 48. The smaller number is 8 less than the larger number. What are the numbers?
Answer:
x=28
y=20
Step-by-step explanation:
x+y=48
x=x
y=x-8 (y is the smaller number)
x+(x-8)=48
2x=56
x=28
(28)+y=48
y=20
Given: Cosine (x minus y)
1. = sine (pi/2 - (x minus y))
2. = sine (pi/2 - x + y)
3. = sine ((pi/2 - x) + y )
4. = sine ((pi/2 - x) - (-y))
5. = sine (pi/x - x) cosine (-y) - cosine (pi/2 - x) sine (-y)
6. = cosine (x) cosine (-y) - sine (x) sine (-y)
7. = cosine (X) cosine (y) + sine (x) sine (y)
Choose a justification for each step in the derivation of the sine difference identity.
Step 1:
Step 2: Distributive property
Step 3: Associative property
Step 4: Factoring out –1
Step 5:
Step 6:
Step 7:
Answer:
Step 1- cofunction identity
Step 5- sine difference identity
Step 6- cofunction identity
Step 7- cosine function is even, some is odd
Step-by-step explanation:
edge2020
I really need help I'm to the point of tears please help
A line that includes the points (g,–7) and (7,2) has a slope of –9. What is the value of g?
Answer:
g = 8
Step-by-step explanation:
The image below shows when g equals 8 and creates the point (8,-7), both that and (7,2) fall on the line of the equation y = -9x + 65, which has a slope of -9.
line p goes through points (-2 6) and (4 -3) what is the equation of line p
Answer:
y = -2/3x + 3
5. What is the range of the relation below?
Step-by-step explanation:
The answer is option D.
If the total value of the coins is $0.78, what are the missing coins?
Answer:
1 Quarter, 1 Dime, 1 Nickel, a 2 Pennies
Step-by-step explanation:
x+ 0.36=0.78
x=0.42
So, 1 Quarter, 1 Dime, 1 Nickel, and 2 Pennies
0.25 + 0.10+ 0.05+ 0.02= 0.42
0.42 + 0.36 equals 0.78
Hope this helps!!!
Brianna can buy 14 pencils for $1.50 at the school store. At that rate, about how much would 100 pencils cost?
Answer:
we conclude that the cost of 100 pencils = $11
Step-by-step explanation:
Brianna can buy 14 pencils for $1.50 at the school store.
so
unit rate = $1.50 / 14 pencils
= 0.11 USD per pencil
Thus,
The cost of 1 pencil = $0.11
The cost of 100 pencils = $0.11 × 100
= $11
Therefore, we conclude that the cost of 100 pencils = $11
Dash asked Lily to cut 5 equal-sized pieces of string for the holiday balloons. Lily only has 3 4/5 meters of string total. What length does each piece of cut string need to be?
Answer:
19/25 metres
Step-by-step explanation:
From the question, we are given;
Total length of the string = 3 4/5 metres
If the string is cut into 5 equal size, the length of each piece will be expressed as;
Length of each piece = Total string length/5
Length of each piece = (3 4/5)/5
Length of each piece = 19/5 ÷ 5
Length of each piece = 19/5 ×1/5
Length of each piece = 19/25 metres
Hence the length of each piece she cut is 19/25 metres
-30=5(x+1)−30=5(x+1) proszę szybką odpowiedź :)
Answer:
x = -7
Step-by-step explanation:
The given equation is :
-30=5(x+1)
We need to solve the equation.
Use associative property on RHS.
-30 = 5x+5
Subtract 5 from both the sides.
-30-5 = 5x+5-5
-35 = 5x
x = -7
Hence, the value of x is -7.
Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to find the number of games, g, that Roberto can buy. Enter your answer in the box.
Answer:
The inequality will be 25.50x ≤ 200
he could by 7 video games.
Step-by-step explanation:
25.50x ≤ 200
x ≤ 200/25.50
x ≤ 7.84
Answer:
7 Games
Step-by-step explanation:
Number of games (g) times price per game (25.50) has to be less than or equal to what Roberto has to spend ($200). So
25.50g< or = 200, solving for g = 7.8 so he can buy 7 games with some left over for a milk shake.
In Ellen’s sixth grade class there are 14 boys and 11 girls write each ratio using numbers in two ways
please help:))) I’ll give brainliest
Answer:
289???????????????? :( or :)
Step-by-step explanation:
A rectangle is transformed according to the rule R0, 90º. The image of the rectangle has vertices located at R'(–4, 4), S'(–4, 1), P'(–3, 1), and Q'(–3, 4). What is the location of Q?
(–4, –3)
(–3, –4)
(3, 4)
(4, 3)
Answer:
A
Step-by-step explanation:
i think...
The transformation is (4, 3)
what is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation
If the there is rotation of 90° around the origin (0,0), that can be expressed as
(x, y) => (-y, x)
Which means a 90° rotation that can done by changing coordinates positions and inverting the sign of y-coordinate.
However, the problem is giving the transformed coordinates where
Q'(–3, 4)
Hence, the transformation is (4, 3)
Learn more about transformations here:
https://brainly.com/question/10519316
#SPJ6
what quantity of pepper would you need to make a half recipe
Answer: 3/8
first divide 3/4 then divide that answer by 2 then turn it into a fraction
PLEASE HELP!!!
What is the solution to this system of equations?
-3x+5y=-2
3x+7y=26
1. (4,2)
2. (2, 3 1/3)
3. no solution
4.infinitely many solutions
Answer:
(4,2)
Step-by-step explanation:
-3x+5y=-2
3x+7y=26
I will add the two equations to eliminate x
-3x+5y=-2
3x+7y=26
---------------------
0x + 12y = 24
Divide by 12
12y/12 = 24/12
y =2
Now find x
3x+7y =26
3x+7*2 =26
3x+14= 26
Subtract 14 from each side
3x+14-14 =26-14
3x= 12
Divide by 3
3x/3 =12/3
x=4
Answer:
found:
x=−3
y=5
Explanation:
I would multiply the first equation by −4 and the second by 3 and add together the two equatins (in columns):
{−12x−28y=−104
{12x+15y=39
0−13y=−65
So: y=6513=5
Substitute back this value into the first equation:
3x+7⋅5=26
3x=26−35=−9
x=−93=−3
Step-by-step explanation:
Its second
