Answer:
Yes, the relation is proportional because the ratios are equivalent between each pair of values
Step-by-step explanation:
Proportional relationships are relationships with equal ratios.
Entries in the respective columns are:
column 1 (Minutes) column 2 (Blocks) Ratios
6 3 1/2
14 7 1/2
20 10 1/2
As the ratio of Blocks and Minutes is same for every row,
the given table represent a proportional relationship.
hence, option c is correct.
Yes, because the ratios are equivalent between each pair of values.
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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)
Simply the function f(x)=7(3Square root 54^x)
Answer:
54 = 2 × 3 × 3 × 3 = 2 × 3³
[tex] f(x) = 7(\sqrt[3]{54})^x [/tex]
[tex] f(x) = 7(\sqrt[3]{3^3 \times 2})^x [/tex]
[tex] f(x) = 7(3\sqrt[3]{2})^x [/tex]
Initial value: x = 0
[tex] f(0) = 7(3\sqrt[3]{2})^0 [/tex]
[tex] f(0) = 7(1) [/tex]
[tex] f(0) = 7 [/tex]
The initial value is 7.
The domain is all real numbers.
The range is all real numbers greater than zero.
Equation of a graph problem
Answer:
this quantity refers to the amount that a container can hold.
Determine the period.
The period of the graphed function is T = 8.
How to get the period?For a sinusoidal function, the period is the horizontal distance between two consecutive peaks.
Here we can see the first peak at x = 1, and the second peak is at x = 9.
The horizontal distance is: 9 - 1= 8.
Then we conclude that the period of the function is T = 8.
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Answer:
^ their right :)
Step-by-step explanation:
Its right on Acellus
have a great day!
Write and solve a proportion to complete the statement. Round to the nearest hundreth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
The conversion of the following units are done below.
6 km = 3.72 miles2.5 L = 0.65 gallons90 lb = 40.5 kgWhat is conversion?Conversion means to convert the same thing into different units.
We know the following unit's conversion.
1 km = 0.62 miles
6 km = 3.72 miles
1 L = 0.26 gallons
2.5 L = 0.65 gallons
1 lb = 0.45 kg
90 lb = 40.5 kg
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Can anyone explain how to do mathematical induction. The question is below. Brainliest awarded for the right answer. Thanks.
The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]
According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n
triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of series of equilateral triangle.
given series in the figure
1, 3, 6, 10, 15, . . . . . . ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex] for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒ ∑S
⇒ ∑[tex]\frac{n^2+n}{2}[/tex]
⇒ [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]
Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]
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For function f(x), which pair of limits would verify the existence of a vertical asymptote at x = –1?
The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
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What is the 25th term of this arithmetic sequence? 3,9,15,21,27
Answer:
75
Step-by-step explanation:
you need to divide numbers by 3
3×25=75
Answer:
147
Step-by-step explanation:
Arithmetic sequence:
a = first term = 3
d = common difference = second term - first term
= 9 - 3
d = 6
n = 25
[tex]\sf \boxed{\bf n^{th} \ term = a + (n-1) d}[/tex]
= 3 + (25 - 1)*6
= 3 + 24*6
= 3 + 144
= 147
can someone please help and explain its due in a littleee
[tex]f(x) = {x}^{2} - 3x + 2 [/tex]
••••••••••••••••••••••••••••••••••••••••put x = (-1)
[tex] f( - 1) = {( - 1)}^{2} - 3 \times ( - 1) + 2 \\ \\ 1 + 3 + 2 \\ \\ 6.[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (z)
[tex] f(z) = {z}^{2} - 3 \times z + 2 \\ \\ {z}^{2} - 3z + 2 \\ \\ {z}^{2} - 2z - z + 2 \\ \\ z(z - 2) - 1(z - 2) \\ \\ (z - 1)( z -2 ) \\ \\ (z - 1) = 0 \: \: , \: \: (z - 2) = 0\\ \\ z = 1 \:, \: 2[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (x+1)
[tex]f(x + 1) = {x}^{2} - 3x + 2 \\ \\ {(x + 1)}^{2} - 3 (x + 1) + 2 \\ \\ {x}^{2} + 1 + 2x - 3x - 3 + 2 \\ \\ {x}^{2} - x \\ \\ x(x - 1) \\ \\ x(x - 1) = 0 \\ \\ x - 1 = \frac{0}{x} \\ \\ x - 1 = 0 \\ \\ x = 1.[/tex]
•••••••••••••••••••••••••••••••••put x = (√2 + 1 )
[tex]f( \sqrt{2} + 1) = {x}^{2} - 3x + 2 \\ \\ {( \sqrt{2} + 1) }^{2} - 3( \sqrt{2} + 1) + 2 \\ \\ 2 + 1 + 2\sqrt{2} - 3 \sqrt{2} - 3 + 2 \\ \\ 3 - 1 \sqrt{2} - 1 \\ \\ 2 - \sqrt{2} \\ \\ 2 - 1.4 (optional \: \: \: steps)\\ \\ 0.6 \: \: [/tex]
What is the slope of the linear relationship shown in this table of values?
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table
m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2
12 identically sized pieces of timber are
x
cm long when put together. How long is each individual piece?
Answer:
[tex]\frac{x}{12}[/tex] (x/12)
Step-by-step explanation:
if 12 pieces combine to make x, [we know they are identical], each piece must be 1/12 of x [1/12·x = x/12]
(think of it like this: "x" length must be divided amongst 12 pieces, so, we divide x/ 12)
Answer:
Timber=x/12
Step-by-step explanation:
12 pieces long is x, if the length of each one is same, so the length of each one is x/12.
Simplify the expression –3(x 3)2 – 3 3x. what is the simplified expression in standard form?
[tex]-3(x^{2} +5x+10)[/tex] is the standard form of the given expression
The given expression is:
[tex]=-3(x+3)^{2} -3+3x\\\\=-3*(x^{2} +2*3*x+3^{2} )-3+3x\\\\=-3x^{2} -3*6x-3*9-3+3x\\\\=-3x^{2} -18x-27-3+3x\\\\=-3x^{2} -15x-30\\\\=-3(x^{2} +5x+10)[/tex]
This is the standard form of the given expression.
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Select the correct answer.
Consider function f.
f(x) = 2x²
What is the value of (ƒ•ƒ)(x)₂
O A.
8x4
OB. 16x4
OC. 4x4
4x2
D.
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} [/tex]
[tex] \: [/tex]
[tex] = (f \circ f)(x)[/tex]
[tex] = f(f(x))[/tex]
[tex] = 2 {x}^{2} [/tex]
[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]
[tex] = 2(4 {x}^{4} )[/tex]
[tex] = 2.4 {x}^{4} [/tex]
[tex] = 8 {x}^{4} [/tex]
The answer is A.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Which is the correct representation of the inequality?
Here we have.
-3(2x - 5) < 5*(2 - x)
First, we need to isolate x in one side, let's expand both sides:
-6x + 15 < 10 - 5x
15 - 10 < 6x - 5x
5 < x
This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:
"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."
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what is 1,000,000,000 divided by -1,000
-1000000 that is the answer
hope this helps!
give me the answer
Given below is a magic square. Place the numbers
70 – 21 25 24 , ,, 95 –133 95 38
in the appropriate squares so that sum in each row, column and
diagonal is equal
The appropriate numbers to fill in the magic squares are;
Row 2, Column 2 = 21/133
Row 2, Column 3 = 24/38
Row 3, Column 2 = 70/95
Row 3, Column 3 = 25/95
How to use magic squares?
To solve this magic square, we will follow the procedures below;
Step 1; Convert all the numbers into lowest forms.Step 2; Find the sum of any column or row which is 34/19.Step 3; Put the numbers given in such positions that the sum of each row, column and diagonal is equal.Step 4; Write the numbers in their original form.When we follow those steps above, we will arrive at the following figures;
Row 2, Column 2 = 21/133
Row 2, Column 3 = 24/38
Row 3, Column 2 = 70/95
Row 3, Column 3 = 25/95
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1. y = 5 x Reflected across the x-axis 2. y = 5 –x+ 5 Reflected across the y-axis 3. y = 5 –x + 5 Translated down by 5 units 4. y = 5 –x – 5 Translated up by 5 units 5. y = –5 –x Translated left 5 units 6. y = 5 –x – 5 Translated right by 5 units
The matchup are:
1. Translated left 5 units - y = 5⁻ ˣ ⁻ ⁵ 2. Translated right by 5 units - y= 5⁻ ˣ ⁺ ⁵3. Translated up by 5 units - y = 5⁻ˣ + 54. Translated down by 5 units - y = 5⁻ ˣ -5 5. Reflected across the x-axis - y= - 5 ⁻ ˣ6. Reflected across the y-axis -y = 5ˣWhat is Translation and reflection?Reflection is known to be the turning over an object across a line and it is one where we do not need to change its size or shape.
While Translation is said to be sliding a figure into another direction and it is one where we do not need to change its size, shape or make.
The Translation and reflection matchup are given:
1. Translated left 5 units - y = 5⁻ ˣ ⁻ ⁵ 2. Translated right by 5 units - y= 5⁻ ˣ ⁺ ⁵3. Translated up by 5 units - y = 5⁻ˣ + 54. Translated down by 5 units - y = 5⁻ ˣ -5 5. Reflected across the x-axis - y= - 5 ⁻ ˣ6. Reflected across the y-axis -y = 5ˣSee full question below
Match each function formula with the corresponding transformation of the parent function y = 5-^x Please help ASAP!!
1. y = 5x
Translated left 5 units
2. y = 5–x + 5
Translated right by 5 units
3. y = 5–x – 5
Translated up by 5 units
4. y = 5–x+ 5
Translated down by 5 units
5. y = –5–x
Reflected across the x-axis
6. y = 5–x – 5
Reflected across the y-axis
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can someone please help me
Answer:
-6, 14, -26, 10x -4, -8x + -2x - 6
Step-by-step explanation:
So F(x) is setting that the values before the lines are equal to x and should be applied to the problem. Dont forget PEMDAS with these tho, they'll try to trick u like that.
So for the first one, f(0) you plug 0 where the x's are.
1.) 8(0)^2 +2(0) -6
0 + 0 - 6 = -6
2.) 8(2) +2(2) - 6
16+ 4-6= 20 - 6= 14
3.) 8(-2) + 2(-2) -6
-16 + -4 -6 = -26
On the ones where they leave the x there, you just have to leave the x. But don't forget distribution tho.
4.) 8(x+1) +2(x+1) -6
8x +8 + 2x + 2 -6
10x +10 -6 = 10x -4
5.) 8(-x) + 2(-x) -6
-8x + -2x -6
Step-by-step explanation:
the given function is f(x) = 8x² + 2x -6
f(0) = 8(0)² + 2(0) -6 = -6
f(2) = 8 (2)² + 2 (2) - 6 = 30
f(-2) = 8 (-2)² + 2 (-2) - 6 = 22
f (x+1) = 8(x+1)² + 2 (x+1) -6
= 8(x² +2x +1 ) + 2x -4
8x² + 16x +8 +2x -4 = 8x² + 18x + 4
f(-x) = 8(-x)² + 2 (-x) - 6
= 8x² -2x -6
A large apartment complex has 1,500 units, which are filling up at a rate of 10% per month. If the apartment complex starts with 15 occupied units, how many months will pass before the complex has 800 occupied units? (Assume logistic growth). Round to the nearest tenth.
The number of months before the complex would have 800 occupied units is 40 months.
How many months before the complex has 800 occupied units?The formula that can be used to determine the required value is:
(In FV / PV) / r
Where:
FV = 800 PV = present occupancy rate = 15 r = rate of filling up = 10%(In 800 / 15) / 0.1 = 40 months
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Answer: 47.3 months
Step-by-step explanation:
-40 represents the height of a subway 40 feet below ground level. 40 represents the height of a kite 40 feet above ground level what does the zero rpresent in this situation
Answer:
0 represents the ground level
When f(a) = 227 + 32 - 3, evaluate f( - 1)
helpp
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} + 3x - 3[/tex]
[tex]f( - 1) = 2. {( - 1)}^{2} + 3.( - 1) - 3[/tex]
[tex]f( - 1) = 2 - 3 - 3[/tex]
[tex]f( - 1) = - 4[/tex]
If u(x) = -2x²+3 and v(x)=
X'
what is the range of (uv)(x)?
The answer is option D which is the range will be ( -∞, ∞ ).
What is the range?After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).
Given function is
u(x) = -2x²+3 and v(x) = ( 1 / x ).
The product of the function will give uv(x).
uv(x) = (-2x²+3 ) x [tex]\dfrac{1}{x}[/tex]
uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]
When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.
Therefore the answer is option D which is the range will be ( -∞, ∞ ).
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Which of these r-values represents the strongest correlation?
A. -0.7
B. -0.8
C. -0.6
D. -0.9
Answer:
D
Step-by-step explanation: the larger abs(r value) is, (abs of r closest to 1) the better the correlation. Negative values indicate a negative correlation (negative slope)
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:
[tex]\sqrt{69}[/tex]
Step-by-step explanation:
from the pythagorean theorem:
[tex]a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}[/tex]
An ice cube is freezing in such a way that the side length s, in inches, is s(t)=1/2t+4, where it is in hours. The surface area of the ice cube is the function A(s) = 6s²_
Part A: Write an equation that gives the volume at t hours after freezing begins. (2 points)
Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)
Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations. (4 points)
Help Please!!
The equation of volume will be V = [(1/2)t + 4]³. The surface area as a function of time will be A(s) = 3/2 t² + 24t + 96. The number of hours when the surface area equal 294 square inches will be 3 1/2 hours.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
Part A: The equation that gives the volume at t hours after freezing begins will be
V = s³
V = [(1/2)t + 4]³
Part B: The surface area as a function of time, using composition, and determine its range will be
A(s) = 6(1/2 t + 4)²
A(s) = 6 (t²/4 + 4t + 16)
A(s) = 3/2 t² + 24t + 96
Part C: The number of hours when the surface area equal 294 square inches will be
294 = 6(1/2 t + 4)²
49 = (1/2 t + 4)²
7 = 1/2 t + 4
1/2 t = 3
t = 3 1/2 hours
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A gas tank consists of a cylinder with a hemisphere on top. It is made of metal that is 1 cm
thick. It has an overall height of 90 cm and an external diameter of 20 cm. Calculate:
a the surface area of the tank
b the internal volume of the tank.
(Give answers correct to two significant figures)
The surface area of the cylinder is 5969.03 cm²
The internal volume is 23156.68 cm³
Given:
A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm
To Find
a) the surface area of the tank
We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.
So, the surface area of the cylinder is
[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)
= π×(1900)
= 5969.03 cm²
b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm
= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]
= 23156.68 cm³
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5. Use the law of Cosines to find each missing sides. Round to the nearest tenth
The measure of angle x will be 88 degrees. Then the correct option is C.
The complete question is attached below.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
2ab cos θ = a² + b² – c²
The triangle is shown below.
Then the value of the variable x will be
2 · 7 · 10 · cos x = 7² + 10² – 12²
140 · cos x = 49 + 100 – 144
cos x = (149 – 144) / 140
x = 87.95 ≈ 88°
Then the correct option is C.
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Helena sees this recipe for pastry. she says that the ratio of margarine to flour is 4:1 is Helena correct? explain your answer
pastry:200g flour pinch salt
50g margarine water to mix
50g lard
Answer:
NOsince it talks about a ratio of margarine to flour, we should write it in this form:
MARGARINE : FLOURSince we have a 50g margarine and a 200g flour, therefore, we write it as
➡️ 50 : 200 ➡️ 1 : 4
FINAL ANSWER SHOULD BE:
1 : 4Step-by-step explanation:
Ratio of MARGARINE TO FLOUR
Given that margarine is 50g and flour is 200g. Therefore,
Margarine:Flour ➡️ 50:200 = 1:4
To check:
A:B= C:D ➡️ 50:200= 1:4
▶️AD= BC ➡️ (50) (4) = (200) (1)
➡️ 200 = 200
☑️
Hope it helps
To hire a bicycle it costs $6 for each day plus a fixed charge of $15
a) Maria pays $39 to hire a bicycle. How many days does she hire it for.
Answer:
4 days
Step-by-step explanation:
1) Derive a formula.
Let b = bicycle
Let x = the number of days
A set up equation: b = 6x + 15
2) If she pays 39 to hire a bicycle, substitute 39 into b, then solve for x.
39 = 6x + 15
39 - 15 = 6x
24 = 6x
24/6 = x
4 = x
x = 4
Since x is the number of days, she hired the bicycle for 4 days.
I’m really stuck please can someone help
Answer:
Least, Median and Greatest height of boys are all higher then Least, Median and Greatest of girls height
Step-by-step explanation:
Least height of boys: 158cm > 150cm Least height of girls
Median height of boys: 168cm > 165cm Median height of girls
Greatest height of boys: 182cm > 170cm Greatest height of girls
Can someone help me with this, it’s urgent. It’s geometry.
Answer:
10. Ray ED and Ray EF (two rays)
11. DE and EF (two line segments)
Step-by-step explanation:
hope this helped
Answer:
Ray ED and Ray EF
DE and EF
Step-by-step explanation: