Final answer:
To solve the inequality x^2 + 36 > 12x, rearrange the terms to have all variables on one side and the constant on the other side. Subtracting 12x from both sides, we get x^2 - 12x + 36 > 0. This is now a quadratic inequality. The solution is x > 6 or x < 6.
Explanation:
To solve the inequality x^2 + 36 > 12x, we need to rearrange the terms to have all variables on one side and the constant on the other side. Subtracting 12x from both sides, we get x^2 - 12x + 36 > 0. This is now a quadratic inequality. To solve it, we can factor the expression into (x-6)(x-6) > 0. From this, we see that the inequality is satisfied when x > 6 or x < 6, since the parabola opens upwards and the expression is equal to zero at x = 6.
If sinx= sqrt(3)/2, and 90° < x < 180°, what is cos(x/2)?
Answer:
cos 60° = 1/2
Step-by-step explanation:
* Lets explain how to solve the question
- If angle Ф lies in the first quadrant then sin Ф , cos Ф and tan Ф
are positive values
- The equivalent angle of angle Ф in the second quadrant is 180° - Ф
and sin Ф is positive but cos Ф and tan Ф are negative
- The equivalent angle of angle Ф in the third quadrant is 180° + Ф
and tan Ф is positive but cos Ф and sin Ф are negative
- The equivalent angle of angle Ф in the fourth quadrant is 360° - Ф
and cos Ф is positive but sin Ф and tan Ф are negative
* Lets solve the problem
∵ sin x = √3/2
∵ 90° < x < 180°
∴ ∠ x lies in the second quadrant
∴ m∠ x = 180° - Ф
- Let sin Ф = √3/2
∴ Ф = sin^-1 (√3/2)
∴ Ф = 60°
∵ x = 180° - Ф
∴ x = 180° - 60°
∴ x = 120°
- To find cos(x/2) divide 120° by 2
∵ cos (120°/2) = cos (60°)
∴ cos 60° = 1/2
9 is 0.32% of what number?
Answer:
2812.5
Step-by-step explanation:
Is means equals and of means multiply
9 = .32% * W
Change the percent to a decimal
9 = .0032 * W
Divide each side by .0032
9/.0032 = .0032W/.0032
2812.5 = W
The number is 2812.5
Answer:
2,812.5
Step-by-step explanation:
pls help solve this problem
Answer:
166 mm²
Step-by-step explanation:
The area is given by ...
A = (1/2)Pa . . . . . where P is the perimeter and "a" is the apothem
One side of a 6-sided figure is shown as 8 mm, so the perimeter is ...
P = 6·(8 mm) = 48 mm
Filling in the apothem value, we have ...
A = (1/2)(48 mm)(4√3 mm) = 96√3 mm² ≈ 166 mm²
The area of the hexagon is about 166 mm².
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?
Answer:
6(3) - (4 - 3²) = 6(3) - 4 + 3²Step-by-step explanation:
[tex]f(x)=4-x^2,\ g(x)=6x\\\\(g-f)(x)=g(x)-f(x)\\\\(g-f)(x)=6x-(4-x^2)\\\\(g-f)(3)-\text{put x = 3 to the equation}\\\\(g-f)(3)=6(3)-(4-3^2)[/tex]
Solve the given inequality. If necessary, round to four decimal places.
134a < 19
Question 4 options:
a < 0.287
a < 4.2641
a < 1.3863
a < 2.5649
Answer:
[tex]a < 0.287[/tex]
Step-by-step explanation:
we have
[tex]13^{4a} < 19[/tex]
Solve for a
Apply log both sides
[tex]log(13^{4a}) < log(19)[/tex]
Remember the rule
㏒(a^n) = n ㏒(a)
so
[tex](4a)log(13) < log(19)[/tex]
Divide by 4 log(13) both sides
[tex]a < log(19)/[4log(13)][/tex]
[tex]a < 0.2870[/tex]
PLEASE HURRY
WILL GIVE BRAINLIEST
Answer:
1 and 4
Step-by-step explanation:
There are 2 shaded, and 2 even numbers
There are 2 unshaded, and 2 odd numbers.
Hope this helps
Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same length of ribbon to frame a circular clock. What is the maximum radius of the circular clock? Round to the nearest whole number.
(JUSTIFY)
Answer:
7 inches
Step-by-step explanation:
The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.
Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches
Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference of the clock should be no more than 44 inches.
[tex]2\pi r=44[/tex]
[tex]r=\frac{44}{2\pi }[/tex]
[tex]r=7.003[/tex]
Therefore, the maximum radius of the circular clock is 7 inches.
Answer:
= 7 inches
Step-by-step explanation:
The ribbon covers the perimeter of the gift.
Perimeter of a rectangle= 2L+2W
=2(12)+2(10)
=44 inches
If the same ribbon is used to frame a circular clock, the perimeter remains to be 44 inches.
Perimeter of a circle= 2πr where r is the radius of the circle.
44 inches= 2×π×r
r=44/2π
=7.0 inches
Radius of the circular clock is 7 inches
A triangle has vertices at L(2, 2), M(4,4), and N(1,6). The
Triangle is transformed according to the rule Ro 180°
Which statements are true regarding the
transformation? Select three options.
.
The rule for the transformation is (x, y) + (-X, -Y).
The coordinates of L'are (-2,-2).
The coordinates of M' are (4,4).
The coordinates of N' are (6,-1).
The coordinates of N' are (-1,-6).
Answer:
The rule for the transformation is (x, y) + (-X, -Y)
The coordinates of L'are (-2,-2).
The coordinates of N' are (-1,-6)
Step-by-step explanation:
90 degree rotation from (x,y) results in (-x, y) and 180 degree results in (-x,-y)
The coordinates will change accordingly
L(2,2) will become L'(-2,-2)
M(4,4) will become M'(-4,-4)
and
N(1,6) will become N'(-1,-6)
So the correct statements are:
The rule for the transformation is (x, y) + (-X, -Y)
The coordinates of L'are (-2,-2).
The coordinates of N' are (-1,-6) ..
The true options are:
The rule of transformation is [tex](x, y) \to (-x, -y)[/tex]The coordinates of L'are (-2,-2).The coordinates of N' are (-1,-6)The vertices of the triangle are given as:
L(2, 2), M(4,4), and N(1,6).
The rule of transformation is Ro 180°.
This is represented as:
[tex](x, y) \to (-x, -y)[/tex]
So, we have:
[tex]L' = (-2,-2)[/tex]
[tex]M' = (-4,-4)[/tex]
[tex]N' = (-1,-6)[/tex]
Hence, the true options are (a), (b) and (e)
Read more about transformation at:
https://brainly.com/question/4289712
which statement must be true about the diagram?
Answer:
It's the third choice.
Step-by-step explanation:
M < NKM and m < MKL both equal 61 degrees
so KM is a bisector of < NKL.
Answer:
C:ray MK is an angle bisector of angle NKL
Step-by-step explanation:
We have to find the true statement about the diagram
[tex]\angle JKN=58^{\circ}[/tex]
[tex]\angle NKM=61^{\circ}[/tex]
[tex]\angle MKL=61^{\circ}[/tex]
[tex]\angle NKM=\angle MKL=61^{\circ}[/tex]
When a ray is a bisector of any angle then the angles are equal which are made by bisection of the angle.
By using this definition
The ray MK is a bisector of angle NKL because angle NKM and MKL are equal.
Answer:C
Write quadratic equation whose roots are 1 and -3 and whose leading coefficient is 4
Answer:
4x^2 + 8x - 12 = 0.
Step-by-step explanation:
We first write it in factor form.
4(x - 1)(x + 3) = 0
4(x^2 + 2x - 3) = 0
4x^2 + 8x - 12 = 0 (answer).
Answer:
4x^2 + 8x - 12 = 0
Step-by-step explanation:
A quadratic equation with roots a and b has the equation (x - a)(x - b) = 0.
You roots are 1 and -3.
The equation is
(x - 1)(x - (3)) = 0
(x - 1)(x + 3) = 0
We can multiply it out.
x^2 + 3x - x - 3 = 0
x^2 + 2x - 3 = 0
Since we need the leading coefficient to be 4, we multiply both sides by 4.
4x^2 + 8x - 12 = 0
what is a reasonable estimate for the problem? 3 3/4 x -2/5
Answer:
You can not break that down any further if x does not equal anything and the equation is not equal to anything.
Step-by-step explanation:
Evaluate -x+4x when x=-2
Use the substitution method
-x+4x when x=-2
-(-2)+4(-2) Positive number * ( multiplying)Negative number=Negative number
2-8
=-6
Answer is -6
what is the slope of the line and y intercept of y = x + 1
The slope and y-intercept are both [tex]\bf{1}[/tex].
Explanation:This equation is written in slope-intercept form, or [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
Since there is no coefficient to [tex]x[/tex], which would have been [tex]m[/tex], [tex]m=1[/tex], so the slope is [tex]1[/tex].
[tex]b=1[/tex], so the y-intercept is also [tex]1[/tex].
Try this trick out on a friend. Tell your friend to place a dime in one hand and a penny in the other hand. Explain that you can determine which hand is holding the penny.
Here’s how to do it:
a. Ask the friend to multiply the value of the coin in his or her RIGHT hand by 4, 6, or 8 and then to multiply the value of the coin in his or her LEFT hand by 3, 5, or 7.
b. Now ask the friend to add the two results together and tell you the total.
c. If the total is EVEN, the penny is in the RIGHT hand. If the total is ODD, the penny is in the left hand.
The math trick described allows you to figure out which hand a friend is holding a penny in by having them multiply the value of the coins in their hands by specific numbers, adding the results, and determining whether the total is even or odd.
Explanation:The subject at hand pertains to a mathematical trick used to determine in which writing a friend is holding a penny. To execute the scheme, follow the procedure:
Ask your friend to multiply the coin's value in their right hand by 4, 6, or 8. Then, instruct them to bear the coin's weight in their left hand by 3, 5, or 7.Next, ask them to add the two results and the total.the penny is in the friend's right hand if the total is even. If the sum is odd, the penny is in their left hand. Here's why: When a dime (10 cents) is multiplied by any integer, the result will be an even number. But a penny (1 cent) multiplied by any number will keep its parity (odd or even). So, if the total sum is weird, the left-hand number, odd, must have been contributed by the penny.Learn more about math tricks here:
https://brainly.com/question/2273245
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What is the following simplified product? Assume x>/= 0
Answer: second option.
Step-by-step explanation:
We know that:
[tex]\sqrt[n]{a^n}=a[/tex]
[tex](a^m)(a^n)=a^{(m+n)[/tex]
Then we can simplify the radicals:
[tex]2\sqrt{8x^3}(3\sqrt{10x^4}-x\sqrt{5x^2})=(2\sqrt{2^2*2*x^2*x})(3\sqrt{10x^4}-x\sqrt{5x^2})=\\\\=2*2*x\sqrt{2x}=3x^2\sqrt{10}-x*x\sqrt{5}\\\\=4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})[/tex]
Since:
[tex](a\sqrt[n]{x})*(b\sqrt[n]{y})=ab\sqrt[n]{xy}[/tex]
We can apply Distributive property:
[tex]4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})\\\\12x^3\sqrt{20x}-4x^3\sqrt{10x}[/tex]
Simplifying:
[tex]12x^3*2\sqrt{5x}-4x^3\sqrt{10x}\\\\24x^3\sqrt{5x}-4x^3\sqrt{10x}[/tex]
Answer:
B
Step-by-step explanation:
edg2021
How do u do this please help!!
Answer:
C. 3 gal. 3 qt. 1 pt.Step-by-step explanation:
1 gallon = 4 quarts
5 gallons 2 quarts 1 pint = 4 gallons 6 quarts 1 pint
(5 gallons 2 quarts 1 pint) - (1 gallon 3 quarts)
= (4 gallons 6 quarts 1 pint) - (1 gallon 3 quarts)
= 3 gallons 3 quarts 1 pint
How would I solve for y?
Answer:
y=40
Step-by-step explanation:
Step 1: Add 1 to both sides.
3y−1+1=119+1
3y=120
Step 2: Divide both sides by 3.
3y /3 = 120 /3
y=40
Which expression are equivalent to the one below? Check all that apply. Log5 5+log5 125
Answer:
B. 4
C. Log₅ 625
Step-by-step explanation:
When given the sum of two logarithms to the same base, let us say
LogₐB +LogₐC, Then, the sum is equivalent to Logₐ(B×C)
=Logₐ BC
The sum given in the question is Log₅5 + Log₅125
This is equivalent to Log₅(5×125)=Log₅625
Log₅625=4 (Since 625=5⁴, the log of 625 to base 5 is 4)
Answer:4 Log5 625 Log5(5^4)
Step-by-step explanation:
The appropriate translation of the phrase 11 more than 20 percent of a number is:
0.2n+11
True or false?
Answer: True
Step-by-step explanation: 20% can also be written as 0.2 and if you know the number then you would multiply it by 0.2, then if you needed to add 11 that is exactly how you would write that equation
What’s the surface area of a regular pyramid if the base is 7 and the height is 10
Answer:
Step-by-step explanation:
the base is a square, and then there are four triangles that meet at their tip.
so you need to find the area of the base, and the four triangles.
base-l*w=7*7=49
triangles=1/2*b*h*4=1/2*7*10*4=35*4=140
140+49=189
Final answer:
The surface area of a regular pyramid with a square base of 7 units and a height of 10 units is approximately 197.26 square units. This is calculated by adding the area of the square base to the combined area of the four triangular faces.
Explanation:
To find the surface area of a regular pyramid with a square base, we need to calculate the area of the square base and the area of the four triangular faces. The formula for the area of a square is base x base. If the base is 7 (units unspecified, but assumed to be the same for both height and base), the area of the base is 7 x 7 = 49 square units. To find the area of a triangular face, we use the formula 1/2 x base x slant height.
To calculate the slant height, we need the half of the base of the triangle (which is 3.5 if the base of the square is 7), and the given perpendicular height of the pyramid, in this case, 10 units. We can use the Pythagorean theorem to find the slant height. The slant height (s) can be calculated as s = \\sqrt{(3.5)² + 10²} = \\sqrt{12.25 + 100} = \\sqrt{112.25}, which is approximately 10.59 units.
The area of one triangular face is 1/2 x 7 x 10.59 ≈ 37.065 square units. There are four triangular faces, so their total area is 37.065 x 4 ≈ 148.26 square units. Thus, the total surface area of the pyramid is the sum of the area of the base and the four triangular faces: 49 + 148.26 ≈ 197.26 square units.
If you bought a stock for $45 dollars and could sell it fifteen years later for three times what you originally paid. What was your return on owning this stock?
Answer:
90$
Step-by-step explanation:
45$
45*3=135
But your return was 3 times the price, so subtract a 45.
135-45=90$
Answer: $90
Step-by-step explanation:
Given : The cost of one stock = $45
And the value of that stock after 15 years is 3 times the paid price.
i.e. The value of that stock after 15 years = [tex]3\times45=\$135[/tex]
Then, the return on owning this stock = [tex]\text{Value after 15 years -Paid price}[/tex]
[tex]=\$135-\$45=\$90[/tex]
Therefore, the return on owning this stock = $90
Consider kite WXYZ.
What are the values of a and b?
a = 4; b = 10
a = 4; b = 40
a = 8; b = 10
a = 8; b = 40
Answer:
a = 8 ; b = 40
I just took the test and I got it right
Answer:
D
Step-by-step explanation:
D on edge :)
What is the slope of the line containing (6, -7) and (5, -9)?
A) 1
B) -2.
C) 2
D) 16
Answer: C
Step-by-step explanation:
y2-y1/x2-x1
-9+7/5-6 = 2
f(x) = x^2 - 5
g(x) = 4x - 4
Find (f-g) (5)
4
-5
-4
5
Answer:
The correct answer option is: 4.
Step-by-step explanation:
We are given the following two functions and we are to find the value of [tex] ( f - g ) ( 5 ) [/tex]:
[tex]f(x) = x^2 - 5[/tex]
[tex]g(x) = 4x - 4[/tex]
Finding [tex] ( f - g ) ( x ) [/tex]:
[tex] ( f - g ) ( x ) [/tex] [tex]= (x^2-5)-(4x-4) = x^2-4x-5+4[/tex]
[tex]( f - g ) ( x ) = x^2-4x-1[/tex]
So, [tex]( f - g ) ( 5 ) = (5)^2-4(5)-1 = 4[/tex]
Answer:
4
Step-by-step explanation:
f(x) = x^2 - 5
g(x) = 4x - 4
(f-g) (x)= x^2 - 5 - (4x - 4)
Distribute the minus sign
= x^2 - 5 - 4x + 4
= x^2 -4x-1
Let x = 5
(f-g) (5) = 5^2 -4(5) -1
=25 - 20 -1
=5-1
=4
Find the value of X in the picture
Answer:
The measure of the arc x is 80°
Step-by-step explanation:
we know that
The semi-inscribed angle is half that of the arc it comprises
so
40°=(1/2)[arc x]
solve for x
arc x=(2)(40°)=80°
/5×+4/ =/×+9/ solve for x
Answer:
[tex]\large\boxed{x=\dfrac{5}{4}\ \vee\ x=-\dfrac{13}{6}}[/tex]
Step-by-step explanation:
[tex]|5x+4|=|x+9|\iff5x+4=x+9\ or\ 5x+4=-(x+9)\\\\5x+4=x+9\qquad\text{subtract 4 from both sides}\\5x=x+5\qquad\text{subtract x from both sides}\\4x=5\qquad\text{divide both sides by 4}\\x=\dfrac{5}{4}\\\\5x+4=-(x+9)\\5x+4=-x-9\qquad\text{subtract 4 from both sides}\\5x=-x-13\qquad\text{add x to both sides}\\6x=-13\qquad\text{divide both sides by 6}\\x=-\dfrac{13}{6}[/tex]
if a + b + C = -1 and x + y + z = -8, what is -8z -8x + 5a + 5c - 8y + 5b
Answer:
59
Step-by-step explanation:
a + b + C = -1
x + y + z = -8
We want 5a so multiply the first equation by 5
5(a + b + c) = -1*5
5a+5b+5c = -5
We want -8x so multiply the second equation by -8
-8(x + y + z) = -8*-8
-8x-8y-8x = 64
Add these equations together
5a+5b+5c = -5
-8x-8y-8x = 64
---------------------------
-8x -8y-8x+5a+5b+5c = 59
Rearrange the order
-8z -8x + 5a + 5c - 8y + 5b = 59
Answer:
59
Step-by-step explanation:
The first step here is to rewrite -8z -8x + 5a + 5c - 8y + 5b as
-8x - 8y - 8z + 5a + 5b + 5c.
This is the same as -8(x + y + z) + 5(a + b + c).
Subbing -8 for (x + y + z) and -1 for (a + b + c), we get -8(-8) - 5, or 59.
Find the value of x if A, B, and C are collinear points and B is between A and C.
AB=x,BC=x+2,AC=14
A. 6
B. 10
C. 9
D. 5
When A, B, and C are collinear points and B is between A and C, value of AB(x) is 6. Therefore, option A is the correct answer.
If we know that points A, B, and C are collinear, with B between A and C, then we can use the given distances AB and BC to find the total distance AC.
Since AB is given as x, and BC as x+2, and we know AC is the sum of AB and BC< which is equal to 14, we can set up the equation:
AB + BC = AC
x + (x+2) = 14
Combining like terms gives us:
2x + 2 = 14
Subtracting 2 from both sides of the equation, we have:
2x = 12
Dividing both sides by 2 to isolate x:
x = 6
Therefore, the length of segment AB, which is x, is 6 units. Option A. 6 is the correct answer.
Solve the system of equations given below.
8x + 4y = 16
7y = 15
-
1
OA. (4,-2)
B. (-2,4)
C. (1.2)
:
D.
(2,1)
Reset
Next
Next
Answer:
Step-by-step explanation:
we have the system :
8x+4y=16
7y=15
the easiest unknown to find first is y because we have the second equation contains only y :
7y=15 we divide both sides by 7 we get : y=[tex]\frac{15}{7}[/tex]
then we can substitute this value in the first equation to find x :
8x+4 [tex]\frac{15}{7}[/tex] = 16
means : 8x+[tex]\frac{60}{7}[/tex] = 16
8x=16-[tex]\frac{60}{7}[/tex]
8x = [tex]\frac{52}{7}[/tex]
divide both sides by 8 :
x = [tex]\frac{13}{14}[/tex]
so the solution is ([tex]\frac{13}{14}[/tex],[tex]\frac{15}{7}[/tex])
this is the solution of the system you submitted
Now if you meant this system :
8x+4y=16
7y=15-1
we get :
7y=14 which gives us y=2
then 8x+4(2)=16 gives us : 8x+8=16
means 8x=8
means x=1
and in this case the solution will be (1,2) answer C
What is the slope of the line given by the equation below?
y = 4x-2
Answer:
slope: 4
Step-by-step explanation:
y = 4x-2 is in the form y = mx +b where m is the slope and b is the y intercept
4 is the slope and -2 is the y intercept
Answer:
4Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have [tex]y=4x-2[/tex].
Therefore
the slope [tex]m=4[/tex]
the y-intercept [tex]b=-2[/tex]