Answer:
6
Step-by-step explanation:
4n - 12 < 2n + 2 is for n=6
4×6 -12 < 2×6 +2
24 - 12 < 12 + 2
12 < 14 correct
for n=7
4×7 - 12 < 2×7 + 2
16 < 16 incorrect
for n=8
4×8 - 12 < 2×8 + 2
20 < 18 incorrect
for n=9
4×9 - 12 < 2×9 + 2
24 < 20 incorrect
so, only for n=6 is the expression true.
Answer:
6
Step-by-step explanation:
4n - 12 < 2n + 2 is for n=6
4×6 -12 < 2×6 +2
24 - 12 < 12 + 2
12 < 14 correct
for n=7
4×7 - 12 < 2×7 + 2
16 < 16 incorrect
for n=8
4×8 - 12 < 2×8 + 2
20 < 18 incorrect
for n=9
4×9 - 12 < 2×9 + 2
24 < 20 incorrect
so, only for n=6 is the expression true.Step-by-step explanation:
Find range
of
f(x) =
[tex]1 \div ( |x| - x)[/tex]
Step-by-step explanation:
We need to find thr range if
[tex] \frac{1}{ (|x| - x)} [/tex]
The absoulte value of something is positive.
So
[tex] \frac{1}{x - x} = \frac{1}{0} [/tex]
This function isn't possible so no range exist.
Independent Practice
x
0
1
2
3
4
y
2
1.5
1
0.5
0
Which kind of function best models the data in the table? Write an equation to model the data.
A.
linear; y= 1 2 x+2
B.
quadratic; y=− x 2
C.
quadratic; y=− 1 2 x 2
D.
linear; y=− 1 2 x+2
Answer:
D. linear; y = - 1/2x + 2
Step-by-step explanation:
As the values of x increase by 1, the values of y decrease by 0.5. This means that we have a negative linear relationship of 1/2. In other words, the slope is -1/2. Our y-intercept is 2 since when x = 0, y = 2. So, D is the correct choice.
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
Answer:
Y =-10X +5
Step-by-step explanation:
x1 y1 x2 y2
1 -5 0 5
(Y2-Y1) (5)-(-5)= 10 ΔY 10
(X2-X1) (0)-(1)= -1 ΔX -1
slope= -10
B= 5
Y =-10X +5
Answer:
y = -2x2 + 8x + 5.
Step-by-step explanation:
PLEASE HELP HURRY!!!!!!!!!
What is the length of PC¯¯¯¯¯?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.
____ cm
Description of drawing:
Circle A with a tangent and a secant. Point B at 11 o clock, point C at 12 o clock, and point D at 7 o clock are on the circle. Point P is at 11 o clock outside of the circle. Tangent P C and secant B D intersect at point P. Segment P B is labeled as 4 centimeters. Segment B D is labeled as 52 centimeters.
Answer:
PC = 14.42 cm
Step-by-step explanation:
If a tangent and secant are drawn from a point outside a circle, then the product of the lengths of the segments of the secant is equal to the square of the length of the tangent.
PC² = PB × BD
PC² = 4 × 52
PC² = 208
PC = [tex]\sqrt{208}[/tex]
PC = 14.42 cm
The length of PC=14.42 cm.
when a tangent and secant are drawn from a point outside a circle, then the multiplication of the lengths of the segments of the secant is equal to the square of the length of the tangent.
What is the relation between the tangent and secant line?
PC² = PB × BD
Use the given value in above formula we get,
PC² = 4 × 52
PC² = 208
[tex]PC = \sqrt{208}[/tex]
Therefore we get the value of PC is,PC = 14.42 cm.
Therefor the length of PC=14.42 cm.
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Which of the following answer choices correctly expresses the number 64?
A. 4'6
B. 4'5
C. 4'4
D. 4'3
Answer:
4’3
Step-by-step explanation:
Took test
Answer:
4’3
Step-by-step explanation:
Rewrite the series as a sum (show all work)
Answer:
1144
Step-by-step explanation:
100 + 98 + 96 +.... + 78+76 =
(12-0)/2 (176)
(6.5) (176) = 1144
The sum of the series will be 1068.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
We have to rewrite the series as the sum.
What do you mean by Series ?A series in mathematics is the sum of a list of numbers that are generated according to some pattern.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
The terms of this series can be calculated by calculating the value of the function at different values of i.
The series is as follows -
100 + 98 + 96 +.... + 78+76
This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -
[tex]S = \frac{n}{2} \times {2a + (n-1)d}[/tex]
S = [tex]\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22][/tex]
S = 6 x 178 = 1068
The sum of the series will be 1068.
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Which equation represents a line that is perpendicular to line PQ?
A. y = 3x - 2
B. y = 1/3x + 4
C. y = -1/3x - 5
D. y = -3x + 6
Answer:
B. y=1/3x+4
Step-by-step explanation:
Hi there!
We are given the line PQ and we want to find the line that is perpendicular to it
Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1
So first, let's find the slope of the line PQ
The point P is given as (-8, 7) and the point Q is given as (-4, -5)
The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where ([tex]x_{1}[/tex] [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points
We have the needed information for the slope, but let's label the values of the points to avoid any confusion
x1=-8
y1=7
x2=-4
y2=-5
Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):
m=[tex]\frac{(-5-7)}{(-4--8)}[/tex]
simplify
m=[tex]\frac{-5-7}{-4+8}[/tex]
add
m=-12/4
divide
m=-3
So the slope of the line PQ is -3
As said above, perpendicular lines have slopes that have a product of -1
So to find the slope of the line perpendicular to PQ, use this formula:
-3m=-1
divide both sides by -3
m=1/3
The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.
Hope this helps!
Use a number line to represent the following. (a) {-4,-1, 0, 2, 3}
Step-by-step explanation:
sorry I couldn't draw it properly but that is it...
I hope it helps
Answer:
Step-by-step explanation:
Draw a line and divide it into 13 equal parts.
Mark 0 in the middle of number line.
Mark negative numbers to the left of zero and mark positive numbers to the right of zero.
A photographer needs a frame for an 5 x 7 inch picture, such that the total area is 80 in? Calculate the width of
the frame. Which of the following quadratic equations would be used when solving this?
4x^2 + 24x = 45
4x^2 + 12x = 45
2x^2 + 24 = 45
2x^2 + 12x = 45
Answer:
4·x² + 24·x = 45
Step-by-step explanation:
The total area of the frame and picture needed by the photographer = 80 in²
The size of the picture that will be in the frame = 5 × 7 inch
The length of the picture = 7 inches
The width of the picture = 5 inches
Let x represent the width of the frame, we get;
The width of the total area = The width of the picture + 2 × The width of the frame
Therefore, the width of the total area = 5 + 2·x
The length of the total area = The length of the picture + 2 × The width of the frame
Therefore, the length of the total area = 7 + 2·x
We get;
The total area = Total length × Total width
∴ The total area = (5 + 2·x) × (7 + 2·x)
We are given that the total area = 80, therefore, by transitive property of equality, we have;
(5 + 2·x) × (7 + 2·x) = 80
35 + 10·x + 14·x + 4·x² = 80
4·x² + 24·x = 80 - 35 = 45
∴ 4·x² + 24·x = 45
Therefore, the quadratic equation that can be used in solving for the width is 4·x² + 24·x = 45.
Answer:
The answer is 4x^2+24x=45
Step-by-step explanation:
I got it right on my test.
Help me to solve this fast ( prove it)
Step-by-step explanation:
sec⁴A + tan⁴A = 1 + (2tan²A/cos²A)
LHS = sec⁴A + tan⁴A
= (sec²A)² + (tan²A)² {using formula of a²+b²)
= (sec²A-tan²A) + 2tan²A.sec²A
= 1 + {2tan²A.(1/cos²A)}
= 1 + (2tan²A/cos²A)
Go Long Telephone Company charges a flat rate of $18.75 per month plus $0.18 per minute. To Call Telephone Company charges a flat rate of$12.51 per month plus $0.42 per minute. How many minutes would a customer need to use in order for the bill from Go Long and Via Call to be equal at the end of the month?
9514 1404 393
Answer:
26 minutes
Step-by-step explanation:
Let x represent the number of minutes used. The charges will be equal when ...
18.75 +0.18x = 12.51 +0.42x
6.24 = 0.24x . . . . . . . . . . . . . . . subtract 0.18x+12.51
26 = x . . . . . . . . . . . . . . . divide by 0.24
A customer using 26 minutes will receive the same bill from either company.
I need help I don't understand at all.
please mark this answer as brainlist
Could the cross-section of a square be a triangle? Explain and draw a diagram to justify your answer.
Yes
Step-by-step explanation:
As u can see in the diagram labelled 1-4 u can see 4 triangles ,
Can someone help me with this math homework please!
Answers:
A local maximum occurs over the interval (-2, 0)A local minimum occurs over the interval (0, 2)This is describing interval notation and not ordered pair notation.
==============================================================
Explanation:
Plot all of the points on the same xy coordinate grid. See the diagram below. The highest point seems to be point C located at (x,y) = (-1,2) showing that y = 2 is probably the local max. I use "probably" because there might be other values that the table isn't mentioning, due to the nature of continuous functions.
If we strictly go by what the table tells us, then y = 2 is the largest y output. This is considered a local maximum. It's the highest point in this specific region. That region being -2 < x < 0 which translates over to the interval notation (-2, 0). Be sure to not confuse this with ordered pair (x,y) notation, which unfortunately the notation is identical.
The same graph of points also shows us that y = -4 is the smallest y output (point E). This is over the interval 0 < x < 2 which gets us the interval notation (0, 2). Like before, this is not ordered pair notation.
What is the area of the obtuse triangle below?
11
13
A. 12 sq. units
7
B. 71.5 sq. units
C. 24.5 sq. units
D. 143 sq. units
find the length of x
Answer:
7/2 =x
Step-by-step explanation:
The triangles are similar so we can write a ratio to solve
2 4
---- = -------
x 7
Using cross products
2*7 = 4x
14 = 4x
14/4 = 4x/4
7/2 =x
Answer:
[tex]x=3\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{4}{2} :\frac{7}{x}[/tex]
x · 4 = 7 · 2
4x = 14
4x ÷ 4 = 14 ÷ 4
x = 3.5
Point T is the centroid. Find TE if XE =21
Answer:
7
Step-by-step explanation:
Thing about centroids is they create segments that are spilt with one piece [tex]\frac{1}{3}[/tex] and the larger piece [tex]\frac{2}{3}[/tex] .
So, if the whole segment is 21, then the large piece is [tex]\frac{2}{3}[/tex] of 21. The small piece is [tex]\frac{1}{3}[/tex] of 21.
TE = 21 · [tex]\frac{1}{3}[/tex] = [tex]\frac{21}{3}[/tex] = 7
can anyone answer this please
Answer:
4
Step-by-step explanation:
x=3
x2 means 3 square (+3)
3×3+3
=9+3
12÷3
4
Which graph represents an odd function?
y
6
4
.
2
.
O
-6..
4
-2.
2.
.
B
х
لند
4
9
TV
Answer:
the odd graph represented is
y
6
4
1st graph represents the odd function because it is symmetric about origin
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
For a function f to be odd, it should satisfy the following equation:
f(-x) = -f(x)
For a function f to be even
f(-x)=f(x)
The graph of an odd function will always be symmetric about the origin.
By observing the graphs we can say that:
1st graph is symmetric about origin and hence it is an odd function.
2nd graph is symmetric about y-axis.Hence it is not an odd function.
Hence, 1st graph represents the odd function because it is symmetric about origin
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pls help my test is timed!! Which of the following scatterplots would have a trend line with a negative slope?
x,y,
1
45
5
15
4
55
25
2
O
3+
25
5
2+
3
375
1+
35
35
35
x, y,
25
15 35
3
2
25425
2 25
OS
1
i
the first/upper one
the other point cloud is too compact to leave a clear clue about any slope
If a block weighs 8kg PLUS half a block.
What is the weight of a block and a half?
Answer:12kg
Step-by-step explanation:
8kg+4kg=12kg
the 4kg came from the half block
se um bloco pesa 8 kg meio bloco pesa 4 kg então é só juntar 8+4=12
If 1125 = 3^m × 5^n ;find the value of m and n.
9514 1404 393
Answer:
m = 2
n = 3
Step-by-step explanation:
1125 = 9·125 = 3^2 · 5^3
m = 2
n = 3
_____
Additional comment
Using divisibility rules, you can keep dividing by the obvious factors until the quotient is 1.
1125/5 = 225
225/5 = 45
45/5 = 9
9/3 = 3
3/3 = 1 . . . . . . 5 is a factor 3 times; 3 is a factor 2 times.
56s+8 write your answer as a product with a whole number greater than 1
Answer:
Hello,
Step-by-step explanation:
[tex]Factorizing \ the\ expression\ \\56s+8=7*8*s+1*8=8(7*s+1)\\[/tex]
Pls help me with this problem
[tex]3x - 8 = 4x - 17 \\ \\ \sf \longmapsto \: 3x + 4x = - 17 + 8 \\ \\ \sf \longmapsto \: 7x = - 9 \\ \\ \sf \longmapsto \: x = \frac{ - 9}{7} [/tex]
Triangle ABC is shown below with line DE passing through the center:
Triangle ABC is shown with line DE running horizontally through the center of the figure.
If triangle ABC is dilated by a scale factor of three about the center of the triangle, dilated line D'E' will (6 points)
be parallel to the original line
shift three units to the right
be perpendicular to the original line
pass through points D and E
Answer:
D'E' be parallel to the original line
Step-by-step explanation:
Given
[tex]\triangle ABC[/tex]
Line [tex]DE[/tex]
[tex]k = 3[/tex] -- scale factor
Required
The relationship between [tex]DE[/tex] and [tex]D'E'[/tex]
When [tex]\triangle ABC[/tex] is dilated by a scale factor of 3, [tex]\triangle A'B'C'[/tex] will be three times as big as [tex]\triangle ABC[/tex].
Also:
Line [tex]D'E'[/tex] will be three times as long as [tex]DE[/tex]
Since no further transformation is done on [tex]\triangle ABC[/tex] and line [tex]DE[/tex], then [tex]D'E'[/tex] will be parallel to [tex]DE[/tex]
What single percentage change is equivalent to a 8% increase followed by a 13% decrease?
А
93.96% increase
B
3.96% decrease
С
6.04% decrease
D
3.96% increase
E
6.04% increase
F
93.96% decrease
Answer:
D: 6.04
Step-by-step explanation:
100*1.08 = 108
108*0.87 = 93.96
100-93.96 = 6.04
Step-by-step explanation:
look at the link below
it really helps!
A pitcher of juice holds 6 cups. How many 2/3 -cup servings of juice are in the pitcher?
serving-
please help ill give brainliest
Answer:
Step-by-step explanation:
6 ÷ (⅔) = 6 × (3/2) = 9
There are nine ⅔-cup servings per pitcher.
Type the correct answer in each box. Use numerals instead of words.
The domain of this function is {-12, -6, 3, 15}.
y = -2/3x + 7
Complete the table based on the given domain.
Answer:
hope it helps plz mark me brainliest!
Step-by-step explanation:
4x² - 3, x less than/equal to 0
Step-by-step explanation:
y = (-1/2)[(x+3)^½]
(x+3)^½ = -2y
Square both sides,
(x+3) = (-2y)²
x+3 = 4y²
x = 4y²-3
Interswitch x and y
Inverse is 4x²-3
Domain of inverse is the range of f.
The range of f is less than/equal to 0
Because at x = -3, f(x) = 0
For x > -3, f(x) is negative
Domain of inverse is x less than/equal to 0
Which expression gives the surface area of a sphere with radius 3x?
Answer:
=> 12πr²
Step-by-step explanation:
The Surface area of sphere is 4πr²
so the surface area of sphere with radius 3x will be
=> 4×3πr²
=> 12πr²
what is -10/19÷-5/7 but not converted into a decimal please!
Answer:
14/19
Step-by-step explanation:
Dividing fractions is the same as multiplying by the reciprocal:
-10/19 ÷ -5/7
-10/19 x -7/5
Multiply the numerators by each other, as well as the denominators:
70/95
Simplify by dividing both the numerator and denominator by 5:
= 14/19
So, the answer is 14/19
