Answer:
3
Step-by-step explanation:
Start with the amount that he wants to pay with gigabytes and subtract the amount of his bill without gigabytes.
58.50-46.50=12
Then divide that amount by the price of each gigabyte to determine how many gigabytes he can use while staying in budget.
12/4=3
Answer: 3
Inequalities help us to compare two unequal expressions. The gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given that Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. Therefore, we can write the inequality for this condition as,
$46.50 + $4(x) ≤ $58.50
46.50 + 4x ≤ 58.50
4x ≤ 58.50 - 46.50
4x ≤ 12
x ≤ 12/4
x ≤ 3
Hence, the gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.
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a number b times 18 is greater than -10
The number b is b > -5/9
How to determine the number?The statement is given as:
a number b times 18 is greater than -10
This can be represented as:
b * 18 > -10
Divide both sides by 18
b > -10/18
Simplify
b > -5/9
Hence, the number b is b > -5/9
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Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?
3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units
Answer:
6 StartRoot 3 EndRoot units
Step-by-step explanation:
10. Which is the equation of a line that is perpendicular to the line represented by y=3/4x-1/2
a group of 31 friends gets together to play a sport. first person must be more be divided into teams . each team has to have exactly 3 players , and no one can be on more than one team .how many teams can make ?
The number of teams that can be made is 10.
How many teams can he make?
In order to determine the number of teams he can make, divide the number of friends by the total number of people that must be in the team. Division is the process of grouping a number into equal parts using another number.
31 / 3 = 10 remainder 1
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Which of the quotients are equivalent to -(48/17)
Answer:
Check the first box, third box and fifth box
Explanation:
1st box:
Rewrite the fraction: 48
- ----
17
Check equivalency: True
Answer: True
2nd box:
Check equivalency: False
Answer: False
3rd box:
Convert the improper fraction into a mixed number:
2 × 17 + 14
- -----------------
17
Calculate the product or quotient: 34 + 14
- -----------
17
Calculate the sum or difference: 48
- ----
17
Check equivalency: True
Answer: True
4th box:
Rewrite the fraction: 17
----
48
Check equivalency: False
Answer: False
5th box:
Rewrite the fraction: 48
- ----
17
Check equivalency: True
Answer: True
I hope this helps!
solve for n (please help i’ll do my best to get everyone the answers points)
Answer:
N = 18Step-by-step explanation:
Both triangles are similar by SAS property,
that means corresponding sides are proportional,so,
5/6 = 15/N
= 6/5 = N/15
N = (6×15)/5
N = 6×3
N = 18
The function g(x) is graphed.
On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- and y-axis at (0, 0), and leaves the plane at point (2.3, 5).
Which statements about the function are true? Choose three options.
The statements about the function that are true include:
g(0) = 0
g(1) = -1
g(-1) = 1
How to depict the function?From the information, the points include:
(x1, y1) = (-2, 2, 5).
(x2, y2) = (0, 0)
(x3, y3) = (2, 3, 5).
It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in ten graph.
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Answer: the answer is b, d, and e.
g(0) = 0
g(1) = 1
g(-1) = 1
Step-by-step explanation:
A local dry cleaner interviewed 15 candidates for the positions of cashier, washer, and delivery driver. How many ways can
they fill the 3 positions?
18
45
455
2,730
Answer:
D. 2730
Step-by-step explanation:
I just had this question on FLVS yesterday.
you use factorials for this:
15!/12!
15*14*13*12!/12!
15*14*13
2730
Number of ways in which 3 positions can be filled are 2730.
What is permutation and combinations?The number of ways in which objects from a set may be selected, generally without replacements, to form subsets. This selection of subset is called permutation when order of selection is a factor.
If n things taken r at a time and n! = n × (n-1) × (n-2) × (n-3)..........3 × 2 × 1
⇒Permutation,
[tex]P(n,r) =\frac{n!}{(n-r)!}[/tex]
Now it is given that number of candidates, n = 15
and number of position, r = 3
Hence number of ways positions can be filled-
[tex]P(n,r) =\frac{15!}{(15-3)!}[/tex]
⇒ [tex]P(15,3) =\frac{15!}{12!}[/tex]
⇒ P(15,3) = (15 × 14 × 13)12!/12!
⇒ P(15,3) = (15 × 14 × 13)
⇒ P(15,3) = 2730
∴ Number of ways in which 3 positions can be filled are 2730.
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What is the measure of RCD?
Find length CD first, which is the hypotenuse of the triangle.
PD = opposite
Opposite & hypotenuse = SOH or sin
Sin(27) = 15/H
x h, then ÷ sin(27)
H = 15/sin(27)
H = 33.04....
Move to triangle CDR:
15 is length opposite the angle we're after.
So far, we've got the hypotenuse (which we just found to be 33.04....) & the opposite of our triangle
Hypotenuse & opposite = SOH
Sin(x) = 15/33.04... but, to find the angle we do inverse of sin
sin-1(15/33.04...) = x
x = 27
(33.04... means I used the full numbers displayed on my calculator)
Thus, RCD is 27 degrees
Hope this helps!
9. Find all function values f(x) such that the distance
from f(x) to the value 8 is less than 0.03 units.
Express this using absolute value notation.
Answer: [tex]|f(x)-8| < 0.03[/tex]
bill is replacing his 15ft long by 12 ft wide deck. his new deck will add 5 feet to the length and 4 feet to the width. if a drawing of the new deck uses a scale of 1 inch =2.5 feet, fin the dimensions of the deck in the drawing
The dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.
Given that the length of the previous deck = 15 feet
The width of the previous deck = 12 feet
Since the new deck will add 5 feet to the length and 4 feet to the width,
The length of the new deck = 15 + 5 = 20 feet
The width of the new deck = 12 + 4 = 16 feet
Also given that a drawing of the new deck uses a scale of 1 inch = 2.5 feet.
So, The length of the deck in the drawing = 20/2.5 inches = 8 inches
The width of the deck in the drawing = 16/2.5 inches = 6.4 inches
Therefore, the dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.
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What is the additive inverse of the polynomial? –6x3 4x2 – 4x 6x3 4x2 4x 6x3 – 4x2 4x –6x3 – 4x2 – 4x 6x3 4x2 – 4x
The additive inverse of the polynomial is 6x³-4x²+4x.
Given The polynomial is -6x³+4x²-4x.
A polynomial is an expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It consists of indeterminates and coefficients.
The number that results in zero when a number is added to it is said to be a number's additive inverse. The opposite, a shift in the sign, and negation are other names for this number.
The given polynomial is -6x³+4x²-4x.
To find the additive inverse of the polynomial, multiply the polynomial with minus sign, we get
-(-6x³+4x²-4x)=6x³-4x²+4x.
Hence, the additive inverse of the polynomial -6x³+4x²-4x is 6x³-4x²+4x.
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Please help me with this LINEAR INEQUALITIES question:
Please enter 3 inequalities with the correct symbols. I'd really appreciate it!
The system of linear inequalities which satisfy the region R are:
y < x - 3.y ≤ -2x + 5.y ≥ x.How to find the inequalities?Mathematically, the standard equation of a straight line is given by y = mx + b.
In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which the lines passes through.
For the broken line, we have:
y-intercept = 3.
x-intercept = -3.
Points (x, y) = (0, 3) and (-3, 0).
Since the line is broken (not equal to), the inequality is given by:
y < x - 3.
For the other line, we have:
y-intercept = 5.
x-intercept = -5/2.
Points (x, y) = (0, 5) and (-5/2, 0).
(x/-5/2) + y/5 ≤ 1
-2x + y ≤ 5
y ≤ -2x + 5
For the line passing through the origin, we have:
y - x ≥ 0
y ≥ x.
In conclusion, the system of linear inequalities which satisfy the region R are:
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Select the correct texts in the table.
Consider function f.
f(x) =
=
(-x² + 6x + 36, x < -2
4x - 15,
35-4,
-2 ≤ x ≤ 4
> 4
Are the statements about the graph of function true or false?
The graph crosses the y-axis at (0,-15). True/false
The graph has a point of discontinuity at x = -2. True/false
The graph is increasing over the interval (4, ∞o). True/false
The graph is decreasing over the interval (-12, -2). True/false
The domain of the function is all real numbers. True/false
Based on the given texts in the table about the graph of the function, the true statements are:
The graph crosses the y-axis at (0,-15).The graph has a point of discontinuity at x = -2.The graph is increasing over the interval (4, ∞o).The domain of the function is all real numbers.Which statements are true of the graph of the function?The function, 4x - 15 shows that 15 is the y-intercept which means that the graph will cross the y-axis at (0,15).
The point of discontinuity is x = - 2 and we see this with the gap created at x < -2 and -2 ≤ x ≤ 4.
The graph is indeed increasing over the interval (4, ∞o) because any value of x that is greater than 4 will increase f(x) = [tex]3^x^-^4[/tex].
The domain of the function is also all real numbers as it begins at negative infinity and ends at infinity, (-∞, ∞).
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Side A B is parallel to Side D E in the map below. Triangle A B C. Side A B is 15 feet and side B C is 9 feet. Triangle C D E. Side C D is 6 feet and side D E is x feet. Which proportion solves for the distance between D and E? Start Fraction 9 Over 6 End Fraction = Start Fraction x Over 15 End Fraction Start Fraction 6 Over x End Fraction = Start Fraction 15 Over 9 End Fraction Start Fraction 9 Over 6 End Fraction = Start Fraction 15 Over x End Fraction Start Fraction 6 Over 15 End Fraction = Start Fraction 9 Over x End Fraction
The proportion that solves for the distance between D and E is x/15 = 6/9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Triangle ABC and CDE are similar triangles, hence the ratio of their corresponding sides are in the same proportion.
Hence:
x/15 = 6/9
The proportion that solves for the distance between D and E is x/15 = 6/9
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its timed help me please
Which of the following is the correct factorization of the polynomial below x3 - 12
a x+3 x-4
b x-3 x+4
c x+3 x^2-4x+4
d the polynomial is irreducible
Answer:this is all I could find
Step-by-step explanation:
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Reflection over the x-axis followed by a translation to the right by 2 units
Reflection over the y-axis followed by a translation to the left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 2 units
The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'
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PLS help asap!!!!!
Which equation represents the line that is perpendicular to y = 6 and passes through (-8,-2)?
Answer:
The answer is a since non of the other answer would go throught that point
Hope This Helps!!!
What is the volume of the carton?
Answer:
c.) 6 1/2
Step-by-step explanation:
Volume = length × width × height
2 1/6 × 1 1/5 × 2 1/2
13/6 × 6/5 × 5/2
13/5 × 5/2
13/2 = 6 1/2
A box has dimensions of 2.5 cm by 3.0 cm by 4.0 cm. The volume of the box in milliliters and liters is:
Answer:
30000 milliliters
0.03 liters
Step-by-step explanation:
The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
The volume of the box is 30 mL or 0.03 L.
What is volume?Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.
The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,
Volume= Dimension 1× Dimension 2× Dimension 3
The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
Hence, the volume of the box is 30 mL or 0.03 L.
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Complete the point-slope equation of the line through-8,-8) and (7, 9)
Answer:
[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]
Step-by-step explanation:
So the slope-intercept form is given as: y=mx+b where m is the slope and b is the y-intercept (since if you plug in 0 as x, mx will be 0 leaving only b). You can calculate the slope with the slope formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. So for this example (-8, -8) will be ([tex]x_1, y_1[/tex]) and (7, 9) will be ([tex]x_2, y_2[/tex]).
Plug values into equation:
[tex]\frac{9 - (-8)}{7 - (-8)}[/tex]
cancel out negatives
[tex]\frac{9+8}{7+8}\\[/tex]
Simplify
[tex]\frac{17}{15}[/tex]
The fraction is in the most simplified form unless you want to have a mixed fraction, otherwise you can't do anything else to the fraction.
so now we have the slope we have one part of the equation: [tex]y=\frac{17}{15}x + b[/tex], but now we need to solve for b. This can be done by using either of the points and plugging in x and y, but for this example I'll use (7, 9).
Plug in (7, 9) as (x, y)
[tex]9 = \frac{17}{15}(7) + b[/tex]
Multiply
[tex]9 = \frac{119}{15}+b[/tex]
Subtract
[tex]9-\frac{119}{15}=b[/tex]
Rewrite 9 as a fraction
[tex]\frac{135}{15} - \frac{119}{15} = b[/tex]
Subtract numerators
[tex]\frac{16}{15} = b[/tex]
now we have both pieces of information
[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]
Which graph represents an even function? A coordinate plane has 5 points. The points are (negative 6, negative 4), (negative 4, 2), (2, 4), (4, negative 2), (6, 2). A coordinate plane has 7 points. The points are (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6). A coordinate plane has 7 points. The points are (negative 5, 2), (negative 4, 1), (negative 3, 3), (negative 2, 5), (2, negative 2), (3, negative 5), (4, negative 6). A coordinate plane has 7 points. The points are (negative 4, negative 3), (negative 3, negative 5), (negative 2, 1), (0, 0), (2, 1), (3, negative 5), (4, negative 3).
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is D.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
For a function to be even, the graph of the function should be such that it should be symmetrical about the x-axis. Therefore, the points of the graph will be the opposite.
The 7 points of option D can be plotted as shown below, which is symmetrical about the X-axis. Hence, the correct option is D.
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Can someone do this whole page please? I REALLY NEED IT!
Answer:
1. A(-8,3) B(-8,-2) C(-4,-2)
2. A'(8,3) B'(8,-2) C'(4,-2)
3. A"(-12,1.5) B"(-12,-3) C"(-6,-3)
4. they give you the coordinates, haha. Just graph and connect the dots.
5. Coordinates of ABC: A(-8,3) B(-8,-2) C(-4,-2)
Coordinates of A'''B'''C''': A'''(-3,10) B'''(-3,5) C'''(1,5)
The correct coordinates for a 90 degree rotation is: A''''(3,8) B''''(-2,8) C''''(-2,4)
Most of these are formulas so I hope you have this memorized in preparation for tests! Good luck!
What is the fourth row of Pascal’s triangle?
Answer:
14641
Step-by-step explanation:
[tex]formular \: for \: the \: digits \: in \: each \\ row \: of \: a \: pascal \: triangle \: is \: = 11 {}^{n} \\ row \: 0 = \: 11 {}^{0} = 1 \: \\ row \: 1 \: = 11 {}^{1} = 11 \\ row \: \: 2 \: = 11 {}^{2} = 121 \\ row \: 3 = \: 11 {}^{3} = 1331 \\ row \: 4 = 11 {}^{4} = 14641 \\ therefore \: the \: fourth \: row \: is \: 14641[/tex]
65. Extensions
Find the equation of the line that passes through the following points: (a, b) and (a, b +1 )
Answer:
The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.
Step-by-step explanation:
It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).
It is asked to find the linear equation which passes through the given points.
To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.
Step 1 of 2
Determine the slope of the line.
The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute b+1&b for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and a&a for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$[/tex]
b+1. So the equation of the line cannot be found using the general point-slope form equation.
Step 2 of 2
Write the equation of the line.
So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.
Consider the following equation.
x^2-3x+2= √ x-2 + 2
Approximate the solution to the equation using three iterations of successive approximation. Use the graph below as a starting point.
please I really need this and I don't have more points to give but I will definitely MARK BRAINLIEST
The approximate solution of the above equation is: 55/15 (Option A). This is solved using the quartic formula, not quadratic equation.
What is the Quartic Formula?
The quartic formula has up to four various solutions including real and imaginary numbers. Read on for more explanation.
What is the solution to the above question?
First we restate the above equation:
x²-3x+2= √(x-2) + 2
Next we remove square roots
[tex]x^{4}[/tex] - 6x³ + 9x² = x - 2
Add two to both sides
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x - 2 +2
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x
Subtract X from both sides
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 -x = x -x
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 - x= 0
Using the Quartic formula to solve the fourth order equation:
a[tex]x^{4}[/tex] + bx³ + cx² + dx + e
The resolution of x is given as:
x = 2.691085, 3.346753
Because the fraction nearest to 3.4 is 55/16
hence, the correct answer is Option A.
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Pls help me I’m so stuck :(
Answer:
B
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
(x + 1)² + (x + 3)² = (x + 5)² ← expand all factors using FOIL
x² + 2x + 1 + x² + 6x + 9 = x² + 10x + 25 , that is
2x² + 8x + 10 = x² + 10x + 25 ← subtract x² + 10x + 25 from both sides
x² - 2x - 15 = 0 ← in standard form
(x - 5)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 3 = 0 ⇒ x = - 3
however, x > 0 , then x = 5
Answer:
B. 5
Step-by-step explanation:
[tex] \sf{C = \sqrt{ A {}^{2} + B {}^{2} }}[/tex]
[tex]\sf{x + 5 = \sqrt{ {(x + 3)}^{2} + {(x + 1)}^{2} }}[/tex]
[tex]\sf{x + 5 = \sqrt{ {(x {}^{2} + 6x + 9)} + {(x {}^{2} + 2x + 1)}}}[/tex]
[tex]\sf{x + 5 = \sqrt{ {(2x {}^{2} + 8x + 10)}}}[/tex]
[tex]\sf{(x + 5) {}^{2} = { {2x {}^{2} + 8x + 10}}}[/tex]
[tex]\sf{ {x}^{2} + 10x + 25= { {2x {}^{2} + 8x + 10}}}[/tex]
[tex]\sf{0= { {2x {}^{2} \red{ { - x}^{2} } + 8x \red{ - 10x} + 10 \red{ - 25}}}}[/tex]
[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]
[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]
[tex]\sf{0= (x - 5)(x + 3)}[/tex]
[tex] \sf{x_{1} - 5 = 0 }[/tex]
[tex] \sf{x_{1} = 0 + 5 }[/tex]
[tex] \sf{x_{1} = \boxed{5 }}[/tex]
[tex] \sf{x_{2} + 3 = 0 }[/tex]
[tex] \sf{x_{2} = 0 - 3 }[/tex]
[tex] \sf{x_{2} = \boxed{- 3 }}[/tex]
Option B. 5
Can someone help me out and show work
Answer: [tex]5(3)^{n-1}[/tex]
Step-by-step explanation:
The common ratio is 15/3 = 5.
The first term is 3.
So, the explicit rule is [tex]5(3)^{n-1}[/tex]
Two side lengths of a triangle are $11$ and $17$. What is the longest possible integer length of the third side of the triangle
The longest possible integer length of the third side of the triangle is 6 < x < 28
The sum of any two sides must be greater than the third side for a triangle to exist
let the third side be x
x + 11 > 17 and x + 17 > 11 and 11 + 17 > x
x > 6 and x > - 6 and x < 28
The longest possible integer length of the third side of the triangle is 6 < x < 28
The length of the 3 sides of a triangle needs to always be among (however no longer the same) the sum and the difference of the opposite two sides. As an example, take the instance of two, 6, and seven. and. consequently, the third side period should be extra than 4 and less than 8.
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Answer:
27
Step-by-step explanation:
Let the third side length be s. Then, by the Triangle Inequality, we know that s satisfies the inequalities
[tex]s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.[/tex]
[tex]\begin{align*} s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\end{align*}[/tex]
The first two inequalities hold as long as s > 6 and the third holds if s < 28. The largest possible integer s that satisfies all of these is 27.