The correct representations of this solution are
(d) A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.(e) (3, ∞)How to determine the solution set?The inequality is given as:
6 + 2n > 12
The solution is given as:
n > 3
When the above inequality is represented as an interval, we have:
(3, ∞)
Also, the inequality symbol > is represented using an open circle.
This means that the number line would use an open circle and the arrow would point right
Hence, the correct representations of this solution are (d) and (e)
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Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to 73.7-57
0 72
0 77
17
글
Answer: [tex]\frac{1}{7^{2}}[/tex]
Step-by-step explanation:
Using the exponent rule [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex], we get that
[tex]7^{3} \cdot 7^{-5}=7^{-2}[/tex]
Then, using the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex], we get that
[tex]7^{-2}=\boxed{\frac{1}{7^{2}}}[/tex]
A rectangular aquarium is 1m 20cm long, 90cm wide and 50cm deep. How many cubic centimeters of water can it hold
Answer:
540,000 cubic centimeters
Step-by-step explanation:
1 meter and 20 centimeters is equal to 120 centimeters.
[tex]120 \times 90 \times 50 = 540000[/tex]
Need help with Math (Quadratic)
Answer:
f(x) = 2(x -3)² +5 or f(x) = 2x² -12x +23
Step-by-step explanation:
The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.
__
vertex formThe vertex form equation for a parabola is ...
f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'
equationFor vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...
f(x) = 2(x -3)² +5 . . . . . vertex form equation
Expanded to standard form, this is ...
f(x) = 2(x² -6x +9) +5
f(x) = 2x² -12x +23 . . . . . standard form equation
The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.
{n | n < 3}
{n | n ≥ 3}
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
(3, ∞)
The correct representations of this solution is {n | n > 3} an open circle appears at positive 3.
Solution to inequality expressionInequalities are expressions not separated by an equal sign. Given the inequality
6 + 2n > 12
Subtract 6 from both sides
2n > 12 - 6
2n >6
Divide both sides by 2
2n/2 >6/2
n >3
Hence the correct representations of this solution is {n | n > 3} an open circle appears at positive 3.
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What is the distance between the two end points in the graph below
Step-by-step explanation:
10 that's what my teacher told me
What is the product? Assume x≥0.
(√3x + √5)√15x+2√30)
A. 3x√√5 +3√165x+10√√6
B. 3x√5+6√10x +5√3x +10√6
C. 3x√√5+10√6
D. 6√3x+10√6
The product of (√3x + √5)(√15x+2√30) assuming x ≥ 0 is 3√5x² + 6√10x + 5√3x + 10√6
What is the product of the expression?It follows from the task content that the expression given whose product is to be evaluated is;
(√3x + √5)(√15x+2√30)
Hence, by multiplying the terms with each other accordingly; we have;
= (√45x² + 2√90x + √75x + 2√150)
= 3√5x² + 2√90x + √75x + 2√150
= 3√5x² + 2×3√10x + √75x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 10√6
= 3√5x² + 6√10x + 5√3x + 10√6
Ultimately, the product of the expression is; 3√5x² + 6√10x + 5√3x + 10√6
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What is the value of log5^125?
Step-by-step explanation:
I'm going to assume you mean
[tex]log(5^{125})[/tex] which can be rewritten as [tex]125 log(5)[/tex] since if you start with [tex]log(a) = x = > 10^x=a\\(10^x)^c=a^c\\c *log(a^c)[/tex]since when you do (10^x)^c you're just multiplying the exponent which is represented by the x but is equal to the log you just multiply the log which is why you can bring it in front.
You can then approximate the value of log(5) using a calculator and multiply by 125 to get around 87.371
Help solve and get 20 pts! (Math)
Two fire trucks on the ground on either side of a burning building or 1.3 miles apart. they each measure the angle of elevation to the fire which are 58° and 52°. How far is each truck from the fire? Please help ASAP thank you so much!
The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.
Distance of each truck from the fireUsing sine rule, we find the length of AB and BC as shown in the image.
a/sin A = b/sin B = c/sin C
Angle C = 180 - (58 + 52) = 70⁰
1.3/(sin 70) = b/(sin 52)
b = (1.3sin 52) / (sin 70)
b = 1.09 mile
c = (1.3sin 58) / (sin 70)
c = 1.1732 miles
Bisect angle C, and use sine rule again to find the lengths of bisected line AB.
1.09/(sin 90) = x/[sin (90 - 58)]
1.09/(sin 90) = x/(sin 32)
x = (1.09 sin 32)/(sin 90)
x = 0.578 mile
Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile
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Solve for B -9/3+ B equals -1
Answer:
-2
Step-by-step explanation:
-9/3=-3
-3+b=-1
b=-1+3
b=-2
Rob bought a pair of jeans at 30% off the original price. If the original price was $55, how much did he pay for the jeans?
Answer:
$38.50
Step-by-step explanation:
(100-30)% of $55
= 70% of $55
= $38.50
Hope this helps :)
juan tiene 400 y rosa 350. ambos se compran
Estimate the solution to the following system of equations by graphing.
9x + 8y=26
3x + 2y=9
Solution of 9x+8y=26 and 3x+2y=9 are given by (C) [tex]\mathbf{x=\frac{10}{3},y=-\frac{1}{2}}[/tex].
We have to plot the graphs of the given two lines or curves, then we have to find the intersection point(s) of the curves or lines. That point is the solution for the system of the equations.
Given equations are,
9x+8y=26 .................(1)
3x+2y=9 ...................(2)
Now multiplying 3 with (2) and then subtracting (1) from that we get,
3(3x+2y)-(9x+8y)=3(9)-26
9x+6y-9x-8y=27-26
-2y=1
y=-1/2, on dividing both sides by -2
Substituting the value of y in (1) we get,
9x+8(-1/2)=26
9x-4=26
9x=26+4
9x=30
x=30/9=10/3
Also if we draw the graphs of the given equations by using graphing calculator we get,
Here in the graph we can see that the lines represented by the given equations intersects each other at point [tex]\left(\frac{10}{3},-\frac{1}{2}\right)[/tex].
Hence the solution is [tex]x=\frac{10}{3},y=-\frac{1}{2}[/tex].
Thus the correct option is (C).
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only 2/3 of the school districts kindergarten teachers are women. if 59 are men, how many kindergarten teachers in all are employed by the school district
Answer:
177
Step-by-step explanation:
2/3 are women.
that means the remainder, 1/3, are men.
59 = 1/3 of all kindergarten teachers (3/3 = 1 representing the "whole").
so,
59×3 = 177
is the number of all kindergarten teachers employed by the school district.
Lily pads increase by 25% every 10 days.lf a pond starts with 22 lily pads,how many will there be after 50 days?
We conclude that after 50 days, there will be 67 lily pads.
how many will there be after 50 days?
We know that the number increases by 25% every 10 days.
In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.
We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:
N = 22*(1 + 25%/100)*...*(1 + 25%/100%)
( the factor (1 + 25%/100%) appears five times)
So we can rewrite:
N = 22*(1 + 25%/100%)⁵
N = 22*(1 + 0.25)⁵ = 67.1
Which can be rounded to the nearest whole number, which is 67.
So we conclude that after 50 days, there will be 67 lily pads.
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consider the quadratic function f(x)= x^2 -8x-4 what is the value of the leading coefficient
The leading coefficient of the quadratic equation f(x)= x² – 8x – 4 will be 1.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
Then we have the quadratic equation given below.
f(x)= x² – 8x – 4
f(x)= x² – 8x + 16 – 16 – 4
f(x)= (x – 4)² – 20
Then the leading coefficient will be 1.
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help Which statement describes the pattern shown?
*
1 point
Captionless Image
A. Each figure has 3 fewer squares than the one before it.
B. Each figure has 6 fewer squares than the one before it.
C. Each figure has 3 more squares than the one before it.
D. Each figure has 6 more squares than the one before it.
A pattern is a recurring arrangement of numbers, forms, colours, and so on.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
As per the pattern, Each figure has 3 more squares than the one before it.
Hence, the correct option is C.
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer: A
Step-by-step explanation:
We can rewrite [tex]8^x[/tex] as follows:
[tex]8^{x}=\left(8^{9} \right)^{x/9}=\left(\frac{1}{8^{9}} \right)^{-x/9}[/tex]
Hence, [tex]A=\frac{1}{8^{9}}=\boxed{8^{-9}}[/tex]
3x² - 2x + 1 = [?]
x=4
Answer:
3(4)² - 2(4) + 1 = 48 - 8 +1 = 41
x = 4
[tex] {3x}^{2} - 2x + 1 \\ \\ 3 \times {4}^{2} - 2 \times 4 + 1 \\ \\ 3 \times 16 -8 + 1 \\ \\ 48 - 8 + 1 \\ \\ 41.[/tex]
Which of the following is the graph of y = log3 x - 1
The options are not mentioned , but the correct graph is plotted and attached with the answer.
What is a function ?A function is a mathematical statement that relates a dependent variable with an independent variable .
It is given to find among the options which is the correct graph for
y = log₃ (x-1)
The options are not mentioned , but the correct graph is plotted and attached with the answer.
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Write the mathematical expression for cost of each item if y items cost a
total of $25.00.
A linear function on a coordinate plane passes through (minus 2, 3), (minus 1, 0), (0, minus 3), and (1, minus 6)
Which equation describes the line graphed above?
A.
B.
C.
D.
The equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The options are missing.
The options are:
A) y = 3x - 3
B) y = -3x + 3
C) y = 3x + 3
D) y = -3x - 3
From the points [tex]\left(-2,3\right)[/tex] and [tex]\left(-1,0\right)[/tex]:
[tex]\rm y\ =\ \dfrac{3}{-1+2}\left(x+1\right)[/tex]
y = 3(x + 1)
y = 3x + 3
Thus, the equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
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What is the value of x?
The value of x in the segment is 3
How to determine the value of x?Using the secant and segment theorem, we have:
x * (x + 21) = (x + 1) * (x + 1 + 14)
Evaluate the sum
x * (x + 21) = (x + 1) * (x + 15)
Expand
x^2 + 21x = x^2 + 15x + x + 15
Subtract x^2 from both sides
21x = 15x + x + 15
Evaluate the like terms
5x = 15
Divide both sides by 5
x = 3
Hence, the value of x is 3
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"If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c)."
Answer:
The commutative property of addition says that changing the order of addends does not change the sum.
(a+b)+c = a+ (b+c)
( -8 + -7) + 6 = -8 + ( -7 + 6)
-15 + 6 = -8 + -1
-9 = -9
Answer:
Hence, proved (a+b) + c = a + (b+c)."
Step-by-step explanation:
first take left hand side and insert the values of a, b, and c and similarly than take right hand side.
L.H.S
(a+b)+c
(-8+(-7))+6
(-8-7)+6
-15+6
-9
R.H.S
a+(b+c)
-8+(-7+6)
-8+(-1)
-8-1
-9
hence, proved (a+b) + c = a + (b+c)."
Simplify this expression:
12a−8−5a+12
12a - 8 -5a + 12
arranging like terms
12a - 5a - 8 + 12
a ( 12-5) - 8 - 12
a(7) - 4(2 - 3)
a(7) -4(-1)
a(7) + 4
7a + 4
simplifing the expressions
Answer:
12a-5a-8+12
=(12-5)a+4
=7a+4
Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?
D: [–1, 5]; R: [–7, 5]
D: [–5, 7]; R: [–5, 1]
D: [–5, 1]; R: [–5, 7]
D: [–7, 5]; R: [–1, 5]
The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have an ellipse equation:
[tex]\rm x^{2}+4y^{2}-2x+16y-19=0[/tex]
We can write the above equation as:
[tex]\rm \dfrac{\left(x-1\right)^{2}}{36}+\dfrac{\left(y+2\right)^{2}}{9}=1[/tex]
The domain will be:
D: [–5, 7]
The range will be:
R: [–5, 1]
Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]
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line / is parallel to line m. the slope of line / is 4/9. what is the slope of line m?
Answer: 4/9
Step-by-step explanation:
Parallel lines have equivalent slopes.
As line 'l' and line 'm' are parallel to each other ,then the slope of line 'm' is also 4/9.
Parallel lines have the same slope. The slope of line segments is identical because they are all similarly inclined with respect to the positive x-axis. If 'l', and 'm' are the slopes of two parallel lines,
then l = m
Slope-intercept notation for lines may be expressed as y=mx+b.
In this notation, b denotes the location of the line's y-axis intercept, and slope(m) indicates the slope of the line.
The slope of 'l'=4/9
The slope of the two parallel lines is the same.
Therefore, the slope of the parallel line "m" = 4/9.
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Fireside Shop offers chimney caps for $120 less trade discounts of 25/10. The same chimney cap is being offered at Builder's Supply for $111 less trade discounts of 25/5. What is the price difference between the two companies?
The difference in price between the two companies is $81-$79.56 = $1.44
Fire side Shop
Price of Chimney cap =$120
First Discount = 25% of(120)=$30
Price after 1st Discount = $120-$30=$90
Second Discount = 10% of 90=$9
Price after 2nd Discount = $90-$9=$81
Builders' Supply
Price of Chimney Cap= $111
First Discount= 25% of 111 = $27.75
Price after 1st Discount = $111 - $27.75 = $83.75
Second Discount = 5% of $83.75 = $ 4.1875
Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56
Therefore,
a) Builders supply offers the lower price.
b) Difference in price = $81-$79.56 = $1.44
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Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).
the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.Which statements are true about the function?
Here we have the function:
[tex]F(x) = -\sqrt[3]{x}[/tex]
First, this is a cubic root, so its domain is the set of all real numbers (same for the range). And we know that the cubic root is an increasing function, so if we put a negative sign before it, we will have a decreasing function.
Then the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.The fourth option is incomplete, so we can't conclude if it is true or not, it would be true if it said:
"The function is a reflection over the x-axis of y = ∛x"
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Answer:
b, c, d
Step-by-step explanation:
Helppppp meeeee pleaseeee?
Answer:
D
Step-by-step explanation:
A. The domain is not all real numbers since the domain of the inverse is the range of the square root function which is not all real numbers.
B and C. The domain is not x >= -4, that's the range since the domain and range are swapped relative to the original square root function which had a domain x >= 4 and a range x >= 0
D. This is true since the range of the square root function is x >= 0 which is now the range of the inverse.
