Correct representations of the inequality -3(2x - 5) 5 are - 6x + 15 10 - 5x (2 – x)
What is Inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1]
The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.
There are two form of inequality relations that are not strict, in contrast to strict inequalities:
The indication of an or b denotes that.
According to our question-
The fourth response is shown by an open circle at 5, and a bold line that begins at 5 and points to the right (attached figure)
Detailed explanation
The difference is 5 (-3(2x - 5)). (2 - x)
First, make each side simpler.
∵ -3(2x - 5) = -3(2x) + -3(-5) (-5)
Recall that (+)=(-)
∴ -3(2x - 5) = - 6x + 15
∵ 5(2 - x) = 5(2) + 5(-x) (-x)
Recall that (+)(-) = (-)
∴ 5(2 - x) = 10 - 5x
∴ - 6x + 15 < 10 - 5x
Take 15 away from both sides.
∴ - 6x < -5 - 5x
5 times on both sides
∴ - x < - 5
Because the coefficient of x is negate, you must change the inequality's sign when you divide both sides by it.
The x coefficient is -1.
∴ Add -1 to both sides.
∴ x > 5
The appropriate answers are:
- 6x + 15 < 10 - 5x
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f(x) = x3 – 7x + 6 (a) Show that (x – 2) is a factor of f (x). (b) Hence, or otherwise, factorise f(x) completely.
Answer:
see explanation
Step-by-step explanation:
if (x - h) is a factor of f(x) then f(h) = 0
(a)
if (x - 2) is a factor of f(x) then f(2) = 0
f(2) = 2³ - 7(2) + 6
= 8 - 14 + 6
= - 6 + 6
= 0
since f(2) = 0 then (x - 2) is a factor of f(x)
(b)
using synthetic division to factor f(x)
insert a zero in the x² position on the table
2 | 1 0 - 7 6
↓ 2 4 - 6
-----------------------
1 2 - 3 0
quotient is
x² + 2x - 3 = (x + 3)(x - 1)
Then
f(x) = (x - 2)(x + 3)(x - 1)
If a segment is drawn perpendicular to a line, the point of intersection is called the ____ of the perpendicular.
Answer: Foot
Step-by-step explanation:
The point of intersection is called the foot of the perpendicular. I remember learning this in my Math class!
i need help Which of the points E , F , G , or H is the center of dilation?
Responses
E
F
G
H
segment EH and segment E'H' both pass through the center of dilation.
Which statement is true about the dilation?A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
The center, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).
In the figure attached, triangle EFG is shown.
H is located at (0, 1)
The center of dilation is located at (0, 2)
Then, H' is located at (0, 0), so that the distance between the center of dilation and H' is twice the distance between the center of dilation and H.
E is located at (0, 5)
Then, E' is located at (0, 8), so that the distance between the center of dilation and E' is twice the distance between the center of dilation and E.
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What is the answer to this problem?
Answer:
450x-9000
Step-by-step explanation:
You will be 9,000 dollars in debt, and it costs 300 dollars to make but sells for 750.
750-300 = 450 (profit per desk)
(5/6z+5) + (-1/2-4)?
.
Answer: [tex]\frac{5}{6}z+\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{5}{6}z+5-\frac{1}{2}-4\\\\\frac{5}{6}z+1-\frac{1}{2}\\\\\frac{5}{6}z+\frac{1}{2}[/tex]
PLS HELP
Assume that all grade-point averages are to be standardized on a scale between 0 and 5. How many grade-point averages must be obtained so that the sample mean is within 0.009 of the population mean? Assume that a 98% confidence level is desired. If using the range rule of thumb, o can be estimated as
Range/4 = 5-0/4 = 1.25. Does the sample size seem practical?
No, the sample size is not practical.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We need to find grade-point averages.
The sample mean is within 0.009 of the population mean.
98% confidence level is desired
The formula for sample size is n = (z alpha/2× S/E)²
where n = sample size
z alpha/2 = critical value for 98% confidence = 2.58
S = 1.25 and
E = 0.009
n = (2.58 × 1.25 / 0.009)² = 128401.5 ~ 128402
Sample size does not seem practical.
Hence, the sample size is not practical.
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A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h (t) = 104t-16t^2. After how long will it reach its maximum height?
Rewrite using a single exponent.
Answer:[tex]5^{18}[/tex]
Step-by-step explanation:
5^18
9. Sales: $50,000
Returns: $4,680
Net Sales: (a)
Cost of goods sold: $22,950
Gross profit: (b)
The gross profit of the Blog Inc would be $22,370.
What is gross profit?Gross profit is the profit of a company or an entity after subtracting all the costs that are related to manufacturing and selling its products or services. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that Sales: $50,000
Returns: $4,680
Cost of goods sold: $22,950
Therefore,
Net Sales: 50,000 - 4,680
= 45,320
We can calculate the Gross Profit;
Gross Profit = (Net Sales – Cost of Goods Sold)
= ($45,320- $22,950)
= $22,370
Hence, the gross profit would be $22,370.
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what's 2+2?
a. fish
b.3
c.4
d.6,472
Im just giving away points to anyone who needs some.
Answer:
what's 2+2?
a. fish
b.3
c.4
d.6,472
Im just giving away points to anyone who needs some.
c.4
Answer: 4
Step-by-step explanation:
2+2=4
Point m is located at (5,-1) on the coordinate plane. Point M is reflected over the y axis to create point M. What ordered pair describes the location of M
The ordered pair that describes the location of M' is (-5, -1)
How to determine the ordered pair that describes the location of M?From the question, we have the following parameters that can be used in our computation:
Point M = (5, -1)
This point can be represented as
(x, y) = (5, -1)
Also, from the question, we have the transformation to be:
Point M is reflected over the y axis
Mathematically, this can be expressed as
(x, y) = (-x, y)
So, we have
Point M' = (-5, -1)
Hence, the image is (-5, -1)
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PLEASE HELP much appreciated!
y>-2x+4 is the inequality of the given graph.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given line passes through (2,0) and (0,4)
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
m=4/-2=-2
4=-2(0)+b
b=4
Hence equation of line y=-2x+4
The shaded region is the above the line and line is dotted. so we have to use greater than symbol.
Hence, y>-2x+4 is the inequality of the given graph.
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19. find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm. what is the maximum volume?
A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
Here,
radius=10 cm
r²+h²/4=10²
r²=10²-h²/4
volume=πr²h
=π(10²-h²/4).h
V=π(10²h-h³/4)
dV/dh=π(10²-3h²/4)
dV/dh=0
10²=3h²/4
10²*2²/3=h²
20/√3=h
h=11.55 cm
r²=10²-h²/4
=10²-(10²*2²/3)/4
r²=(100-400/12)
r²=100-33.33
r²=66.67
r=√66.67
r=8.165 cm
volume=πr²h
=3.14*8.165*8.165*11.55
volume=2417.82 cm³
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.
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Given the table below, write a linear equation that defines the dependent variable, p, in terms of the independent variable, t.
t
p
0
4
1
7
2
10
3
13
Show your work here
Enter your answer
Given the table below, write a linear equation that defines the dependent variable, p, in terms of the independent variable, t.
t. P
0. 4
1 7
2 10
3 13
Show your work here
Enter your answer
The required linear equation that defines the dependent variable, p, in terms of the independent variable, t is p = 3t + 4.
Explain linear equation?A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the slant and b is the y-catch. Sometimes, the above is known as a "straight condition of two factors," where y and x are the factors.
According to question:Let linear equation be p = at + b
Where a and b are constant.
On putting the values from the table,
4 = 0×a + b
b = 4
and,
7 = 1×a + b ⇒ a + b = 7
a + 4 = 7
a = 3
Then,
p = 3t + 4
Thus, required equation is p = 3t + 4.
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Decide whether enough information is given to prove that the triangles are congruent using the HL Congruence Theorem. Explain.
Answer:
No
Step-by-step explanation:
You want to know if there is enough information to claim ∆PQT ≅ ∆SRT by the HL theorem.
HL theoremThe HL theorem tells you right triangles are congruent if they have one leg (L) and the hypotenuse (H) congruent.
Here, the triangles are not indicated as being right triangles, so the HL theorem cannot be applied.
__
Additional comment
There is not enough information here to permit the triangles to be declared congruent.
For congruence by any theorem, we'd need to know that angle T is the largest angle in each triangle, a condition not supported by the evidence.
Though rarely (if ever) seen in congruence discussions, a claim of SSA congruence can only be supported if the angle (A) is opposite the longest side. When the angle is 90°, this is called the HL congruence theorem. When the angle is known to be obtuse, it will always be opposite the longest side.
When the given angle is opposite the shortest of the two given sides, there are two possible triangles that can be constructed. Hence congruence cannot be guaranteed between two triangles with the same SSA dimensions.
What is the value of the expression 32.4 ÷ 6?
Group of answer choices
4.4
5.4
6.4
7.4
Answer:
If you divide 32.4 by 6, then you get 5.4 as an answer
Find all numbers whose absolute value is 3 .
Answer:
-3 and 3
Step-by-step explanation:
Absolute value makes a negative number positive and allows a positive number to stay the same. |-3| becomes 3, and |3| stays as 3, so the correct answers are -3 and 3.
A Question 8 (2 points) Retake question
Which equation would reflect the function over the Y-AXIS
f(x)= |x-31+2
Og(x) =
-x +31-2
g(x) = -x - 3| +2
) g(x) = |-x + 3| + 2
g(x) = -x - 3| + 2
A Question 9 (2 points) Retake question
The equation g(x) = |-x-3| + 2 would reflect the function over the y-axis.
The required value of f(3) is 10.
What is a reflection across the y-axis?Reflection across the y-axis is defined as reflecting a point across they = x, the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).
So reflected across the y-axis: f(x) → f(-x),
⇒ (x,y) → (-x , y)
As per the given question,
f(x) = |x-3| + 2
f(-x) = |-x-3| + 2 = g(x)
Thus, the equation g(x) = |-x-3| + 2 would reflect the function over the y-axis.
The function f(x) is given in the question,
f(x) = 4x - 2,
To determine the value of f(3)
Substitute the value of x = 3 in the given function,
f(3) = 4(3) - 2
f(3) = 12 - 2
f(3) = 10
Thus, the required value of f(3) is 10.
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- 5(-4) +3(5)| = ?
A. -35
B. -5
C. 5
D. 35
E. 36
please i need help
I need help on my test please help its 7th grade Im just bad at math
For the given inequality 14 - 3f > 2 the option that comes out be correct is
f < 4 i.e option 2.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.
Here, "Less than" and "Greater than" have new meanings.
Less-than sign is the symbol for such phrase.
14 - 3f > 2
adding 3f on both sides:
14 - 3f + 3f > 2 + 3f
14 > 2 + 3f
subtracting 2 on both sides:
14 - 2 > 2 + 3f - 2
12 > 3f
dividing 3 on both sides:
(12)/3 > (3f)/3
4 > f
which means f < 4
Therefore, option 2 is correct.
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Evaluate using the given values.
Answer:
8
Step-by-step explanation:
x^3/3-y
3^3/3-1
27/3-1
9-1
8
Hopes this helps please mark brainliest
liters/minute, where t is in minutes since the pump is started. if the holding tank contains 1000 liters of water when the pump is started, approximately how much water does it hold two hours later?
Approximately, water does it hold two hours later is = 248.72 liters
Given that,
The holding tank contains 1000 liters of water
Water does it hold two hours later,
Then,
1) Integrate the function, from t =0 to t = 120 minutes to obtain the number of liters pumped out in the entire interval, and
2) Substract the result from the initial content of the tank (1000 liters).
So
We can write,
Let us assume,
Integral of (6 - 6 [tex]e^{-0.13t}[/tex] ) dt ]from t =0 to t = 120 min
= 6t + 6 [tex]e^{-0.13t}[/tex] / 0.13
= 6t + 46.1538 6 [tex]e^{-0.13t}[/tex] ] from t =0 to t = 120 min
= 6*120 + 46.1538 e^(-0.13*120) - 0 - 46.1538
= 720 + 46.1538 (1.678) - 46.1538
= 720 + 77.44 - 46.1538 liters
= 751.28 liters
2) If the holding tank contains 1000 liters of water,
1000 liters - 751.28 liters = 248.72 liters
Therefore,
Approximately, water does it hold two hours later is = 248.72 liters
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Neeeeeeeeed help please please
Answer:
Step-by-step explanation:
how do you divide 9.51 by 6
Answer: 1.00585 or 1.585. Both are correct
Step-by-step explanation:
PLEASE HELP!!! i'm terrible at graphing.
The graph of the given function, g(x) = -5^x + 5, is shown below
Graphing a functionFrom the question, we are to graph the given function.
From the given information,
The given function is
g(x) = -5^x + 5
To graph the function, we will determine some of the points on the line
When x = -2
g(2) = -5^(-2) + 5
g(2) = -1/25 + 5
g(2) = 4 24/25 = 4.96
When x = -1
g(1) = -5^(-1) + 5
g(1) = -1/5 + 5
g(1) = 4 4/5 = 4.8
When x = 0
g(0) = -5^(0) + 5
g(0) = -1 + 5
g(0) = 4
When x = 1
g(1) = -5^(1) + 5
g(1) = -5 + 5
g(1) = 0
When x = 2
g(2) = -5^(2) + 5
g(2) = -25 + 5
g(2) = -20
Using the above points, the graph of the function is shown below.
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What is the value of x in the equation
8(x - 3) - 4x = 20?
A
x=−11
B
x=11
C
x=1
D
x=−1
Answer:
x = 11
Step-by-step explanation:
8(x-3) - 4x = 20
8x - 24 - 4x = 20
4x = 44
x = 11
Answer:
x=11
Step-by-step explanation:
8(x-3)-4x=20
8(x)+8(-3)-4x=20
8x-24-4x=20
4x-24=20
+24. +24
4x=44
/x. /x
x=11
Hopes this helps
Write the equation of 5x-y=15 after it is reflected in the y-axis and then translated (3 -1)
Answer: y=-5x-1. I need someone to tell me what translating equations is and how to get there.
The equation after the transformation is y = -5x - 1
How to determine the equation after the transformation?From the question, we have the following parameters that can be used in our computation:
Equation: 5x - y = 15
Make y the subject
So, we have
y = 5x + 15
The rule of reflection across the y-axis is
(x, y) = (-x, y)
So, we have the following equation
y = -5x + 15
The rule of translation by (3 -1) is
(x, y) = (x + 3, y - 1)
So, we have the following equation
y = -5(x + 3) + 15 - 1
Expand
y = -5x - 15 + 15 - 1
So, we have
y = -5x - 1
Hence, the equation is y = -5x - 1
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(0.25) to the power of 7 ⋅ 4 to the power of 7
The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.
What is the power of 7 to 4?The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.
To do this, you must multiply both the ordinates and the powers of ten portions of the two numbers (the mantissas).
In mathematics and algebra, multiplying seven occurrences of a given number by themselves yields the number's seventh power.
Consequently, n7 = n n n n n n.
Let's write 7 to the power of 4.0.2 to the power of 4 is 0.0016 one step at a time.
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What is the equation in slope-intercept form of the line that passes through the point (4, 7) and is parallel to the line represented by y = 2x - 5?
Step-by-step explanation:
please see the attachment
NUMBER 4 PLEASE THIS IS URGENT
Answer:
its 5
Step-by-step explanation: