Answer:
y = 2x + 3; y = -1/3 x + 3
Step-by-step explanation:
Both lines have y-intercept 3.
The slopes are 2 and -1/3.
The equations are: y = 2x + 3; y = -1/3 x + 3
EXTREMELY URGENT!!! The angles of elevation of the top of two vertical towers as seen from the
middle point of the lines joining the foot of the towers are 45° & 60°. The ratio of the height of the towers is:
Since the angles of elevation of the top of two vertical towers is 45° & 60°, the ratio of the height of the towers is 0.58:1
How to find the ratio of the height of the towersSince the angles of elevation of the top of two vertical towers as seen from the middle point of the lines joining the foot of the towers are 45° & 60°.
The height of the tower, the line of sight and the ground form a right angled trangle
Height of first towerLet
h = height of first tower, d = distance of tower to middle point = L/2 where L = distance between tower and Ф = angle of elevation of tower from midpoint = 45°Using trigonometric ratios, we have that
tanФ = h/d
= h/L/2
= 2h/L
So, h = LtanФ/2
= Ltan45°/2
= L/2 × 1
= L/2
Height of second towerLet
h' = height of first tower, d = distance of tower to middle point = L/2 where L = distance between tower and Ф' = angle of elevation of tower from midpoint = 60°Using trigonometric ratios, we have that
tanФ' = h'/d
= h'/L/2
= 2h'/L
So, h' = LtanФ'/2
= Ltan60°/2
= L/2 × √3
= √3L/2
Ratio of the height of the towersSo, the ratio of the height of the towers is n = h/h'
= L/2 ÷ √3L/2
= 1/√3
= 1/1.732
= 0.577
≅ 0.58
So, the ratio of the height of the towers is 0.58:1
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f(x) = 3/x+2-√x-3
The domain for f(x) is all real numbers ___ than it equal to 3
The domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
The domain of a function f(x) is the set of all real values of x, for which real f(x) exists.
In the question, we are asked to find the domain of the function f(x) = 3/x + 2 - √(x - 3).
To find the domain of f(x), we need to check the real values of x, for which real f(x) exists.
We check each part of f(x):
For 3/x, every x gives a real value except x = 0.
For 2, every x gives a real value as it is not dependent on x.
For √(x - 3), real values exist when x - 3 ≥ 0, as negative square roots are not real.
Therefore, after assessing each term, we can say that the domain for f(x) is x - 3 ≥ 0, or x ≥ 3.
Therefore, the domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
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If the number of types of massages is represented by 4x + 3 and the number of
types of manicures is represented by -6x + 5 and the number of types of pedicures
is represented by 8x - 7, what is the expression for the total number of services they
have to choose from?
The expression for the total number of services the have to choose from is 6x - 1
Simplifying an expressionFrom the question, we are to determine the expression for the total number of services
From the given information,
Number of types of massages = 4x + 3
Number of types of manicures = -6x + 5
Number of types of pedicures = 8x - 7
Then,
Total number of services = 4x + 3 + (-6x + 5) + 8x - 7
Total number of services = 4x + 3 - 6x + 5 + 8x - 7
Total number of services = 4x - 6x + 8x - 7 + 3 + 5
Total number of services = 6x - 1
Hence, the expression for the total number of services the have to choose from is 6x - 1
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Answer: the answer is actually 6x+1, not 6x-1
There are currently 3000 moose in the state of Colorado. Their population is increasing at a rate of 2% per year. How many years will it be before there are 6000 moose in the state of Colorado. Round your answer to the nearest year.
Answer:
35 years from now.
Step-by-step explanation:
The quantity of moose as a function of time is as follows:
[tex]M(t) = 3000(1.02)^{t}.[/tex]
Thus, for [tex]M < 6000:[/tex]
[tex]3000(1.02)^{t} < 6000\\\\1.02^{t} < 2\\\\t < \frac{log\,2}{log\,1.02}\\\\ t < 35.003\,\,years.[/tex]
First accurate answer gets brainliest
Answer: C, (-1, -5)
Step-by-step explanation:
A = 2, B = 4, C = -3
We know the graph opens up because a is positive.
This rules out A and D
We are left with B and C as options.
Let's change this into vertex form
[tex]y=a(x-h)^2[/tex]
Complete the square
[tex]2(x+1)^2-5[/tex]
now a = 2, h = 1, k = -5
The vertex is (h, k)
plug in values:
(-1, -5)
100 POINTS!!! Find the exact length of side a.
Has to be one of the four options
Answer: a = 2√3
First method (Pythagoras theorem):
a² + b² = c²
a² + 2² = 4²
a² = 16 - 4
a = √12
a = 2√3
Second method (sine rule):
opposite/hypotenuse = sin(x)
a/4 = sin(60)
a = 4sin(60)
a = 2√3
Third method (tan rule):
opposite/adjacent = tan(x)
a/2 = tan(60)
a = 2tan(60)
a = 2√3
Answer:
2√3
Step-by-step explanation:
From inspection of the given triangle:
Side a is opposite angle A ⇒ a = BCSide b is opposite angle B ⇒ b = ACSide c is opposite angle C ⇒ c = ABAs we cannot be sure that ΔABC is a right triangle since it is not marked as such, use the cosine rule to find the exact length of side a.
Cosine Rule
[tex]a^2=b^2+c^2-2bc \cos A[/tex]
where a, b and c are the sides and A is the angle opposite side a
Given:
A = 60°b = 2c = 4Substitute the given values into the formula and solve for a:
[tex]\implies a^2=2^2+4^2-2(2)(4) \cos 60^{\circ}[/tex]
[tex]\implies a^2=4+16-16\left(\dfrac{1}{2}\right)[/tex]
[tex]\implies a^2=20-8[/tex]
[tex]\implies a^2=12[/tex]
[tex]\implies a=\sqrt{12}[/tex]
[tex]\implies a=\sqrt{4 \cdot 3}[/tex]
[tex]\implies a=\sqrt{4}{\sqrt{3}[/tex]
[tex]\implies a=2\sqrt{3}[/tex]
Therefore, the exact length of side a is 2√3.
To find out if ΔABC is a right triangle, use Pythagoras Theorem to solve for side a:
[tex]\implies a^2+b^2=c^2[/tex]
[tex]\implies a^2+2^2=4^2[/tex]
[tex]\implies a^2+4=16[/tex]
[tex]\implies a^2=12[/tex]
[tex]\implies a=\sqrt{12}[/tex]
[tex]\implies a=2\sqrt{3}[/tex]
As the measure of side a is the same as the solution found when using the cosine rule, we can conclude that ΔABC is a right triangle.
Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts.
He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture.
On day 1, he mixes 4 cans of blue and 6 cans of yellow.
On day 2, he mixes 6 cans of blue and 9 cans of yellow.
Fill in the blanks to find the highest number of cans of each color Marc can mix to make the same shade of green on day 3.
The ratio of blue paint to yellow paint is 2 : 3.
The total number of blue paint he used on the first and second day is 10.
The number of yellow paint he used on the first and second day is 15.
On the third day, the highest number of can of blue paint he can use is 2
On the third day, the highest number of can of yellow paint he can use is 3.
What is the highest number of blue and yellow paint he can use?The ratio of blue paint to yellow paint can be determined by determining the simplest form of the paints used: 4 : 6 = 2: 3
Total blue paint cans used on the first and second day = 4 + 6 = 10
Blue paint cans remaining = 14 - 10 = 4
Total yellow paint cans used on the first and second day = 6 + 9 = 15 cans
Yellow paint cans remaining = 20 - 15 = 5 cans
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Find the y-intercept of the line.
=y−2.1x5.9
The y-intercept given line equation is 5.9.
Given that, the line of the equation is y-2.1x+5.9.
We need to find the y-intercept of the line.
What is slope-intercept form?The standard form of slope-intercept form is y=mx+c.
Where, m=slope and c=y-intercept.
Using the slope-intercept form to find the y-intercept, we get c=5.9.
Hence, the y-intercept given line equation is 5.9.
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You start your working career when you are 24 years old. Each month, you deposit $144 into a pension plan. You continue making deposits into the plan you are 68 years old. What is the balance, in dollars, when the plan earns 6%, compounded monthlyRound your answer to the nearest cent
The balance, in dollars, (future value) when the pension plan earns 6% compounded monthly is $372,134.19.
What is future value?The future value refers to the compounded future value of an asset, for example, a pension plan, based on a growth rate of interest for a future period.
The future value can be determined with the FV formula, table, or using an online finance calculator as follows:
Data and Calculations:N (# of periods) = 528 months (68 - 24 x 12 months)
I/Y (Interest per year) = 6%
PV (Present Value) = $0
PMT (Periodic Payment) = $144
Results:
FV = $372,134.19
Sum of all periodic payments = $76,032 ($144 x 528)
Total Interest = $296,102.19
Thus, the balance, in dollars, (future value) when the pension plan earns 6% compounded monthly is $372,134.19.
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Please can somebody help me with this question
Answer:
the answer is=21
Step-by-step explanation:
u have to sum all of its sides
(length+breadth+height).
Please help me with problem 3 (a-d). Thank you!
Using the spread sheet we can easily get the answers:
The statistical section helps find answers by putting the accurate formula or the graphing calculator.
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1471.33 2 735.68 11.59 0.001072834 3.7389
Within Groups 888.55 14 63.4677
Total 2359.882 16
The APA style refers to Times New Roman Font 12 pts.
The effect size of the result is 0.6233 medium
Part A
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1471.33 2 735.68 11.59 0.001072834 3.7389
Within Groups 888.55 14 63.4677
Total 2359.882 16
1) The null and alternative hypotheses are
H0: u1=u2=u3
Ha: Not all means are equal
2) The significance level is alpha = 0.05
3) The test statistic F = sb²/sw²
Which if H0 is true has an F distribution with ν1=2 and v2= 14 degrees of freedom.
The computations are
Anova: Single Factor
Groups Count Sum Average Variance
Column 1 6 373 62.16666667 78.96666667
Column 2 4 324 81 60.66666667
Column 3 7 402 57.42857143 51.95238095
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1471.33 2 735.68 11.59 0.001072834 3.7389
Within Groups 888.55 14 63.46768707
Total 2359.882353 16
5) The critical region is F ≥ F(0.05)(2,14) = 3.74
6) Conclusion:
Since the computed value F= 3.73 does not fall in the critical region F> 3.74 so we accept H0 and conclude that there is no significant difference in the three means.
Part D: The effect size of the result is 0.6233 medium and calculated by
η²= ss between/ ss between + ss error
η²= 1471/1471+889
η²= 0.6233
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The graph of the function f(x)=log6(x) is stretched vertically by a factor of 7, reflected over the x-axis, reflected over the y-axis, and shifted up by 2 units.
The resulting function after all transformations have been carried out is; -7log6(-x) - 2.
Which function results from all the Transformations?The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 7; Hence, we have; 7f(x) = 7log6(x).Reflected over the x-axis; -7f(x) = -7log6(x).Reflected over the y-axis; -7f(x) = -7log6(-x).Shifted up by 2 units; -7f(x) -2 = -7log6(-x) - 2.On this note, it follows that the resulting function upon all the Transformations is; = -7log6(-x) - 2.
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On the coordinate plane below, what is the length of AB? A coordinate plane is shown with a rectangle with the following points A at negative 6, 5; B at 8, 5; C at 8, negative 4; D at negative 6, negative 4. All points are connected to create a rectangle. 8 units 9 units 13 units 14 units
The length of AB wit the coordinate (-6, 5) and (8,5). is 14 units
Distance between two pointsA rectangle is a quadrilateral with 4 sides and angles
Taking the length of AB.
Since AB is slant line, the length of AB will be determined using the distance formula as shown;
D = √(-6-8)² +(5-5)
D = √(-14)²
D = AB = 14 units
Hence the length of AB wit the coordinate (-6, 5) and (8,5). is 14 units
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HELP! ASAP!
Thank you in advance :)
By the corresponding angles theorem,
∠AFG, ∠BGD, and ∠CHD are congruent∠BAF, ∠CBG, and ∠DCH are congruentThus, triangles AFD, BGD, and CHD are similar by AA.
Answer:
If all of these are parralel and all touching a single line(FD), then they must be the same. Also, they are perpendicular. :/
Step-by-step explanation:
10.3 was subtracted from a number then that difference was multiplied by 7 after which the result was divided by 2.5. if the result of that divison is -7 then what was the initial number
Answer:
6
Step-by-step explanation:
i took the test
what is the reminder when X³ +4X² - 2X + I is divided by X + 1 what is the reminder when X³ + 4X² - 2X + I is divided by X + 1
Answer:
6
Step-by-step explanation:
Q. 2 Find the HCF of 16, 44 and 84 by listing the factors.
factor: (14.25r^4-24.375r^3+10.125)=0
Answer:
1, 1.5
Step-by-step explanation:
Use the rational roots theorem. Factor out until you get the maximum simplification.
0.375(x−1)(2x−3)(19x2+15x+9)
However, if you wanted to solve this equation for r, you will get 1, 1.5 using the quartic formula.
Identify a transformation of the function ƒ(x) = x2 by observing the equation of the function g(x) = (x – 6)2.
f(x) moves 6 unit towards right side along X-axis and forms the function g(x).
Given that, the original function is
[tex]f(x)=x^2[/tex]
and now the function is
[tex]g(x) =(x-6)^2[/tex]
When f(x)=0 then we can get by calculating that,
[tex]x^2=0[/tex]
x=0
So, the f(x) function satisfied by point (0,0).
Now when g(x)=0 then by calculating that we get,
[tex](x-6)^2=0[/tex]
x-6 = 0
x = 6
So g(x) function satisfied by (6,0).
In geometrical words we can say that if we transform from f(x) to g(x) then (0,0) tranformed to (6,0).
That suggests that the function moves 6 unit right along X axis, which is towards positive X axis.
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Blood contains three types of cells including red blood cells, white blood cells, and platelets. For approximately every 420 red blood cells in humans with certain medical conditions,
there are 30 platelets and 2 white blood cells. Write the ratio of red blood cells to platelet cells.
O Points:
a simplified fraction)
Step-by-step explanation:
Evalate the expression when m=4 and m=6
Solve for the missing item in the following. (Do not round intermediate calculations. Round your answer to the nearest whole percent.)
Principal 5,000 time 6 months simple interest 300
Rate?
The rate is 1.2%.
What is Simple interest?Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account.
Given:
P = 5000
T =6 month= 1/2 year
SI= 300
We know,
SI= P*R*T/100
300= 500* R * 1 /200
60000= 500R
R= 60000/500
R= 120
R= 1.2%
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Hey brainly gang I'm having trouble could someone help me out. Solve for x.
Answer: x=9
Step-by-step explanation:
Since this shape is a parallelogram, the diagonals perpendicularly bisect each other. So EH =HG
5x-3=2x+24
3x=27
x=9
Substituing x=9 to EH and HG
EH: 5(9)-3=42
HG: 2(9)+24=42
99 points answer fast!!!!
The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:
• There have been two turning points in sales this year.
• Sales are expected to increase in the long run.
• The least amount of sales during the year is about $250,000.
Which graph correctly shows the coffee shop’s sales?
Answer:
Step-by-step explanation:
So given the three bits of information you can conclude a couple of things. The end behavior towards the right should be increasing and since there is only two turning points this means it was previously going down but had a turning point and starting going up, and before that it was going up and then started going down, those will be the two turning points. So on the left side it should be decreasing and the right side it should be increasing. The last peace of information tells you that at the second turning point, should be equal to 250k when it turned back up OR the y-intercept is 250k. Given all this information the answer should be the first graph in the first picture
Answer: D
Step-by-step explanation:
A graph shows the proportional relationship between the number of test questions a student gets correct, x, and the student’s test score, y. The ordered pair (1,5/4) is on the graph. What does the y- coordinate of the ordered pair represent in this relationship.
Answer:
The y-coordinate is 5/4, it represents a test score for one correct answer
Step-by-step explanation:
Proportional relationship is:
y = kx, where k is coefficient of proportion.We have the ordered pair (1, 5/4), which represents:
5/4 = k*1 k = 5/4When x = 1, the y- coordinate is equal to the coefficient of proportionality.
In this case it represents a score for one correct answer.
60% of a rectangular garden measuring 3 by 6 is covered by snow. What area of the garden is not covered by snow?
If 15 buses can carry 795 passengers, what is the total number of passengers that can be carried by 18 buses?
Answer:
954 passengers
Step-by-step explanation:
We can use ratios to solve
15 buses 18 buses
-------------- = ---------------
795 passengers x passengers
Using cross products
15 * x = 18 * 795
15x = 14310
Divide each side by 15
15x/15 = 14310 /15
x =954
18 buses can carry 954 passengers
Given the graph of the function f(x) shown below, find the average rate of change of the function f(x) on the interval [5,15].
Step-by-step Expression;
- Given; The function f(x) on the interval [ 5,15]
- To find the average rate of change of the function f(x)=?
x = 5 , y = 15,
I can't solve it anymore,please can you solving?
4cos(-5B) sin3B is equivalent to
The trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]
How to find the trigonometric identity 4cos(-5B) sin3B is equivalent to?Since we have 4cos(-5B) sin3B
Using the trigonometric identity
sin(x + y) - sin(x - y) = 2cosxsiny
So, cosxsiny = [sin(x + y) - sin(x - y)]/2
Since we have 4cos(-5B) sin3B, comparing cos(-5B) sin3B with cosxsiny, we have
x = -5B and y = 3B
So, we have cos(-5B)sin3B = [sin(-5B + 3B) - sin(-5B - 3B)]/2
= [sin(-2B) - sin(-8B)]/2
= [-sin(2B) - {-sin(8B)}]/2 [since sin(-2B) = -sin(2B)]
= [-sin(2B) + sin(8B)]/2
= [sin(8B) - sin(2B)]/2
So, 4cos(-5B)sin3B = 4 × [sin(8B) - sin(2B)]/2
= 2[sin(8B) - sin(2B)]
So, the trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]
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Please help!! Simplify the following expression in terms of fractional exponents and write it in the following form.
Answer:
[tex]\huge{\boxed{ \huge{\sf 10^{\frac{4}{5} } x^\frac{1}{5} }}}[/tex]
Explanation:
Exponent rules:
[tex]\sqrt[\sf n]{\sf x^b} = \sf x^{\sf \frac{b}{n} }[/tex]Given expression:
[tex]\sqrt[\sf 5]{\sf 10^4 x}[/tex]breakdown
[tex]\sqrt[\sf 5]{\sf 10^4} \sqrt[\sf 5]{\sf x}[/tex]rewrite expression
[tex]\sf 10^{\frac{4}{5} } x^\frac{1}{5}[/tex]consider the functions f(x) = -2(x-3)² + 2 which is represented by the graph
drag each interval to the correct location in the table to describe key features of f(x) and g(x)
The intervals of the function on the graph are:
Domain = (-∝, ∝)Range = (-∝, 2]Increases (-∝, 3]Decreases [3, ∝)The key features of the function?The function is given as:
f(x) = -2(x-3)² + 2
See attachment for the graph.
From the graph, we have;
Domain = (-∝, ∝)
Because it takes all real values as its input
Range = (-∝, 2]
Because it has a vertex of (3, 2) and the vertex is a maximum
Also, it increases on the interval (-∝, 3] and decreases on the interval [3, ∝)
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