Answer: [tex]x= \frac{-1+\sqrt{97} }{8} , \frac{-1-\sqrt{97} }{8}[/tex]
Step-by-step explanation:
Use the Quadratic Formula .. if you use Completing the Square it'll take longer!!
In general, given [tex]ax^{2} +bx+c=0[/tex] , there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] , [tex]\frac{-b-\sqrt{b^{2} }-4ac}{2a}[/tex]
In this case, a=4 , b=1 and c= -6
[tex]x= \frac{-1+\sqrt{1-4*4*-6} }{2*4}[/tex] , [tex]\frac{-1-\sqrt{1-4*4*-6} }{2*4}[/tex]
Simplify.
[tex]x=\frac{-1+\sqrt{97} }{8}[/tex] , [tex]\frac{-1-\sqrt{97} }{8}[/tex]
Which ordered pair lies on the function f(x) = x^2 + 3?
Question 7 options:
A)
(–1,–4)
B)
(1,–4)
C)
(–1,4)
D)
(–4,–1)
Answer:
c
Step-by-step explanation:
The radius of the semicircle in the following composite figure is 8.5 millimeters. What is the total area of the composite figure rounded to the nearest hundredth?
Answer:
13.35 millimeter. (About)
Step-by-step explanation:
To find the area or circumference of any circle, you need to use pi. So, if we are trying to fine the area of a semicircle, you use the the formula:
πr²/2
So, if the radius is 8.5,
8.5 · 3.14 = 26.69
Now we divide it by 2.
26.69 = 13.345
Since the question is asking to round to the hundredths, the answer will be 13.35 millimeters.
Answer:
185.43 mm 2
Step-by-step explanation:
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Joshua has a rectangular vegetable garden with the dimensions shown below. If he doubles the length and width of the garden, how will the area of the new garden compare to the area of the original garden?
How many triangles???
Answer:
4
Step-by-step explanation:
The triangle itself
Also the 3 at the top
They are the only ones with 3 sides
Answer:
9 triangles
Step-by-step explanation:
Carly tried to solve an equation step by step.
Find Carly's mistake.
Answer:
Step 1 is incorrect
Step-by-step explanation:
Answer:
step 1
Step-by-step explanation:
Find the first five terms of the geometric sequence a1=0.3,an=10an-1
Answer:
{0.3, 3, 30, 300, 3000}
Step-by-step explanation:
Here a(1) = 0.3, and
a(2) = 3, and
a(3) = 30, and
a(4) = 300, and
a(5) = 3000
The first term (given) is 0.3, and the common ratio is 10.
Which statement about this figure is true?
a. it has rotational symmetry with an angle of rotation of 90°
b. it has no reflectional symmetry
c. it has reflectional symmetry with two lines of symmetry
d. it does not have symmetry point
Answer:
a. it has rotational symmetry with an angle of rotation of 90°
Step-by-step explanation:
the diameter of a circle is 5 ft. Find the circumference to the nearest tenth(urgent)
Answer:
15.71
Step-by-step explanation:
To find the radius, half the diameter because r x 2 = diameter. 5/2 = 2.5
Put in circumference formula C=2πr
c=2 x 3.14 x 2.5
c= 2 x 7.85
c=15.7
Put the value into the circle circumference formula C=2πr
Leticia is cutting a board to make a ramp for her skateboard. The ramp will slope from the ground up to a height of 4 feet. The board will make an angle of 25° with the ground. How long should she cut the board for her ramp? *
1 point
9.46 feet long
4.41 feet long
8.58 feet long
10 feet long
Answer:
Correct option: first one -> 9.46 feet long
Step-by-step explanation:
To find the length of the board for her ramp, we just need to use the sine relation of its angle with the ground.
The opposite side to the angle is the height of the ramp, and the hypotenuse of the triangle formed is the length of the board. So, we have that:
sin(25°) = height / length
0.4226 = 4 / length
length = 4 / 0.4226
length = 9.4652 feet
So the length of the board should be 9.46 feet (correct option: first one)
Which expression is equivalent to 2 (a + 3) when a = 3? 2 (3) 5 (3) 2 (3) + 3
Answer:
[tex]12[/tex]
Step-by-step explanation:
[tex]2 (a + 3)[/tex]
[tex]a=3[/tex]
[tex]2(3+3)[/tex]
[tex]2(6)[/tex]
[tex]=12[/tex]
Answer:
2 (3) + 6
Step-by-step explanation:
2( a + 3) if (a = 3)
then now is 2( 3 + 3 )
3+3 = 6........6 times 2 = 12
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
❌: 2(3) = 2 x 3 = 6 ←← not 12
❌: 5(3) = 5 x 3 = 15 ←← not 12
❌: 2(3)+3 = 2 x 3 = 6.... 6 + 3 = 9 ←← not 12
✅: 2(3)+6 = 2 x 3 = 6.... 6 + 6 = 12 ←← its 12
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Which is the graph of y?
Replace x with a number and solve for y. Plot the points out on a graph.
See the attached picture.
Rotate the image.
Which number produces an irrational number when multiplied by 1/4
Answer:
D
Step-by-step explanation:
1/4 x -36 = -9
1/4 x 4/3 = 1/3
1/4 x 12 = 3
But...
1/4 x 0.444444... = 0.111111...
So A is the answer
√12 produces an irrational number when multiplied by 1/4
What is an irrational number?A real number that cannot be expressed as a straightforward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to p/q if N is irrational.
Given Four numbers to find the number that will produce an irrational number after dividing by 4. We will check them one by one:
For A, 0.4444:
=> 0.444
After multiplying by 1/4
=> 0.1111111
That can also write as 1/9(Not an irrational number)
For C, -√36:
=> -√36
After multiplying by 1/4
=>-√9/4
That can also write as 3/2(Not an irrational number)
For D, 4/3:
=> 4/3
After multiplying by 1/4
=> 1/3
That can also write as 1/3(Not an irrational number)
For B. √12:
=> √12
After multiplying by 1/4
=> √12/4
=>√(3/4)
That can also writes as √(3/4)(yes, an irrational number)
Therefore, The irrational number in the given option is B √12
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Which function has a domain and range that includes all real values?
Answer:
Its c
Step-by-step explanation:
just did the quiz
18
What is the value of y?
10
2y + 4
10 + 2x
5
Step-by-step explanation:
8
ahhdhdvab ah a. b b b n n bk.
What is the explicit formula for the geometric sequence with this recursive formula?
Answer:
A
Step-by-step explanation:
The explicit formula for a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
The recursive formula gives a term in the sequence by multiplying the previous term by r
Given the recursive formula
a₁ = - 6
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] ([tex]\frac{1}{4}[/tex] )
with r = [tex]\frac{1}{4}[/tex]
Then explicit formula is
[tex]a_{n}[/tex] = - 6[tex](\frac{1}{4}) ^{n-1}[/tex] → A
For this graph, Mark the statements that are true.
Given: HJ =4x+9, JK=3x+3
and KH=33
Find: x, HJ, and JK
X= BLANK?
HJ=BLANK?
JK=BLANK?
The value of x=3, length of HJ=21 and JK=12 can be found out using Segment Addition Postulate.
What is Segment Addition Postulate?
If B is between A and B, then AB +BC = AC
Find the values of x, HJ and JK
Given that, HJ=4x+9
JK=3x+3
KH=33
According to the Segment Addition Postulate, we can say that
HJ+JK=KH
4x+9+3x+3=33
(4x+3x)+(9+3)=33
7x+12=33
7x=33-12=21
x=3HJ=4x+9=4(3)+9
HJ=12+9=21
JK=3x+3=3(3)+3
JK=9+3=12
The value of x=3, length of HJ=21 and JK=12 .
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A worker needs to create a 4-character password. The worker can use alphabet as well
as number(0-9) and 4 special characters. How many outcomes are possible?
Answer: 2560000
Step-by-step explanation:
Given, A worker needs to create a 4-character password.
Worker can use :
Alphabets, numbers and 4 special characters
Total alphabets = 26
Total digits = 10
So, total characters he can use = 26(alphabets) + 10 (digits) +4 (special characters)
= 26+10+4 = 40
Since, there is no pattern or condition is provided to choose them.
So, the total possible outcomes to create a 4-character password. = [tex](\text{Total characters})^4=40^4=2560000[/tex]
Hence, the total possible outcomes = 2560000
Penny received an unexpected $5,000.00 gift from a distant relative. She invests it
in a mutual fund that increases the value of the original investment by 8% each year.
You must show all calculations to earn credit.
How much will her original investment be worth in 10 years?
Answer:
$9,000.00 is her original investment worth in 10 yrs.
5000 x 1.08 ^10 = 10794.6249864
Then subtract -500000 = 5794.62498636
Step-by-step explanation:
Why, because the first year is proved 5000 x 0.08 = 400
= 400 year 1 but cna keep only if stays in investment for 10 years
400 x 10 = 4000 interest on investment
5000+ 4000 = $9,000.00 SI
+ 1,794.62 Interest on interest if applies (this is called CI) and makes $10794.62
Find the sum of the first 48 terms of the following series, to the nearest integer7,11,15,...
Answer:
7
Step-by-step explanation:
The sum of first 48 terms of the given series is 4848.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form sum of n terms of arithmetic sequence is Sₙ=n/2[2a+(n-1)d].
The given arithmetic sequence is 7,11,15,......
Here, a=7, d=11-7=4 and n=48
Now, S₄₈=48/2[2×7+(48-1)×4]
= 24(14+47×4)
= 24(14+188)
= 24×202
= 4848
Therefore, the sum of first 48 terms of the given series is 4848.
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What is the inverse of the function f(x) = 4x - 12
Answer:
y=x+12/4
Step-by-step explanation:
y=4x-12
x=4y-12 (then make y the subject)
x+12=4y(divide both sides by 4)
y=x+12/4
can someone help me on these 2 questions?
7. x=20
8. x=19
Step-by-step explanation:
7. The shape is a parallelogram and the angles that are labeled are opposite from each other, meaning that they are congruent. So, 4x-40=2x (and solve)
8. Same case as last time (parallelogram), and the angles labeled are congruent. So, 2x+19=3x (and solve)
After plotting the data where x=area, and f(x)=the length of one side of the square, Sam determined the model to approximate the side of a square was f(x)= *square root sign* x-5+3 Use the model Sam created to predict the side length of the square when the area is 86.
6
12
81
144
Answer:
12
Step-by-step explanation:
f(x) = sqrt( x-5)+3
Let x = 86
f(86) = sqrt(86 -5) +3
f(86) = sqrt(81) +3
f(86) = 9+3
f(86) = 12
The side length is 12
If x=5 and y=3, what is the value of 2(x+y)2 – (xy)0.
Answer:
32
Step-by-step explanation:
[tex]2(x+y)2-(xy)0\\2(5+3)2-((5)(3))0\\2(8)2-(15)0\\16(2)-0\\32-0\\32[/tex]
So the right answer is 113
please see the attached picture for full solution
Hope it helps
Good luck on your assignment...
Select the correct answer from each drop-down menu.
Shape I is similar to shape II.
Answer:
Translation (moving the figure) will map figure 1 onto figure 2 and then after this , dilation by a scale factor of "2"
Answer:
The first one is Translation 3 units down and8 units left, then a dialationby a scale factor of 2
Step-by-step explanation:
How does the graph of y = StartRoot x EndRoot + 2 compare to the graph of the parent square root function?
The graph is a horizontal shift of the parent function 2 units right.
The graph is a horizontal shift of the parent function 2 units left.
The graph is a vertical shift of the parent function 2 units up.
The graph is a vertical shift of the parent function 2 units down.
Answer:
The graph is a vertical shift of the parent function 2 units up.
Step-by-step explanation:
Our the function is:
y = √x + 2
Its parent function is: f(x) = √x
Answer:
The graph is a vertical shift of the parent function 2 units up.
Step-by-step explanation:
Our the function is:
y = √x + 2
Its parent function is: f(x) = √x
Then, the transformation can be rewritten as: f(x) + 2, which has the form f(x) + c, which is a vertical shift of f(x) c units up. Therefore, in this case, the parent function is shifted 2 units up.
This question is based on the concept of graph .Hence,the correct option is (c) i.e. the graph is a vertical shift of the parent function 2 units up.
Given:
The function of graph is [tex]\bold{y=\sqrt{x+2}}[/tex].
Its parent square root function is [tex]\bold{f(x)= \sqrt{x}}[/tex].
By the parent function we have to obtain given function ,So,we have to add on both sides 2,
f(x)+2 = [tex]\sqrt{x+2}[/tex]
Thus, we have to added 2 to transform the parent root function into given function.Therefore, graph is shifted vertically 2 units up.
Hence,the correct option is (c) i.e. the graph is a vertical shift of the parent function 2 units up.
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Which of the following has a prime factorization of 2 x 2 x 3 x 5?
Answer:
60
Step-by-step explanation:
Just multiply them all together.
2 * 2 * 3 * 5 = 60
Answer 60
Step-by-step explanation: 60 devided by 2 = 30
30 devided by 2 = 15
15 devided by 3 = 5
5 devided by 5 = 1
hence verified
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Find the mean of the data in this set.
9.4
6
8.5
8
Answer:
The mean is 7.975.
Step-by-step explanation:
Answer:
The correct answer is 9.4, Hope this helps!
Step-by-step explanation:
I took the test and this was the correct answer!
What is the solution of 3square root x+8 = -4?
• x=-72
• x=-66
• x=58
• no solution
Answer:
No solution
Step-by-step explanation:
I'd suggest you try to solve this first: 3√(x + 8) = 4. First, square both sides; this results in 9(x + 8) = 16, or x + 72 = 16/9, or x = -632/9. We cannot let x = -632/9 in √(x + 8) because -632/9 is not in the domain of the square root function. No solution.
If we now write 3√(x + 8) = -4 (note the negative sign), similar efforts at solution result in 9(x + 8) = -4, or x + 8 = -4/9, or x = -8 - 4/9. If we now substitute this result for (x + 8) in 3√(x + 8) = -4 (above), we get 3√(-8 + 8 - 4/9), which has no solution; -4/9 is not in the domain of the square root function.
The solution for the given equation is 16.
The given equation is 3√x+8=-4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The solution for the given equation can be determined as follows:
Now, 3√x+8=-4
⇒ 3√x=-4-8
⇒ 3√x=-12
⇒ √x=-12/3
⇒ √x=-4
Squaring both the sides, we get
x=16
Therefore, the solution for the given equation is 16.
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Can anyone solve this?
Answer:
[tex]x= \frac{20}{3}[/tex]
Step-by-step explanation:
Set up the equation
[tex]\frac{15}{10} =\frac{10}{x}[/tex]
and cross multiply to solve for x.