[tex]\begin{array}{ccll} \stackrel{hours}{t}&\stackrel{height}{h}\\ \cline{1-2} 3&20\\ 5&19 \end{array}[/tex] with those values provided from the table, let's get its equation
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{19}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{19}-\stackrel{y1}{20}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{19 -20}{5 -3} \implies -\cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{-\cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{3}) \implies y-20=-\cfrac{ 1 }{ 2 }x+\cfrac{3}{2} \\\\\\ y=-\cfrac{ 1 }{ 2 }x+\cfrac{3}{2}+20\implies y=-\cfrac{ 1 }{ 2 }x+\cfrac{43}{2}\implies \LARGE \begin{array}{llll} h=-\cfrac{ 1 }{ 2 }t+\cfrac{43}{2} \end{array}[/tex]
how talll will the candle be after 8 hours? namely when t = 8.
[tex]h=-\cfrac{ 1 }{ 2 }(8)+\cfrac{43}{2}\implies h=-4+\cfrac{43}{2}\implies h=\cfrac{35}{2}\implies \LARGE \begin{array}{llll} h=17\frac{1}{2} \end{array}[/tex]
Consider the following function.
Place the steps for finding f(x) in the correct order.
Answer:
[tex]\frac{x-7}{4} =f^{-1}( x)[/tex]
Step-by-step explanation:
→ Replace f(x) with y
y = 4x + 7
→ Minus 7 from both sides
y - 7 = 4x
→ Divide both sides by 4
[tex]\frac{y-7}{4} =x[/tex]
→ Replace y's with f⁻¹(x)
[tex]\frac{x-7}{4} =f^{-1}( x)[/tex]
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line in the given graph = rise/run = 3.
How to Find the Slope of a Line?To determine the value of the slope of a line on a coordinate plane, we can find the ratio of the rise of the line to that of its run. This means that, the formula for calculating the slope of a line would be:
Slope = rise/run.
Vertical distance across the line is the rise of the line
Horizontal distance across the line is the run of the line
In the graph given, we have:
The rise is labelled as the blue line = 9 units
The run is labelled as the red line = 3 units
Slope of the line (m) = 9 units/3 units
Slope (m) of the given line = 9/3 = 3
Therefore, the slope of the line in the given graph = rise/run = 3.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line shown is -2/5
Slope of a lineThe formula for calculating the slope of a line is expressed according to the formula
Slope = Rise/Run
Slope = y₂-y₁/x₂-x₁
Using the coordinate point (0,7) and (5, 5)
Slope = 5-7/5-0
Slope = -2/5
Hence the slope of the line shown is -2/5
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Honors Pre-Calculus
Please answer fast!
The desired odd function is sketched at the end of the question.
What is an odd function?An odd function is a function in which the following statement is true for all values of x.
f(-x) = -f(x).
What is the domain of a function?The domain of a function is the set that contains all possible input values for a function. In a graph, it is the set that contains the values of x for which the function is defined.
What is the range of a function?The domain of a function is the set that contains all possible output values for a function. In a graph, it is the set that contains the values of y for which the function is defined.
When a function is increasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y decreases.
When a function is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
Considering these definitions, the function with the desired characteristics is plotted at the end of the answer.
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Please answer both questions!
-
1. The measure of an angle is 177°. The measure of its supplementary angle is ___
degrees.
2. The measure of an angle is 47.1°. The measure of its complementary angle is ___
degrees.
Answer:
1. 3
2. 42.9
Step-by-step explanation:
1. 180 - 177 = 3
2. 90 - 47.1 = 42.9
Solve: 1 4/5 x 5/6 =
Group of answer choices
1 3/11
15/30
1 2/3
1 1/2
The multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2
In this question, we have been given an expression 1 4/5 x 5/6
We need solve given mathematical expression.
First we write improper fraction 1 4/5 as proper fraction.
1 4/5 = 9/5
So, given expression becomes,
1 4/5 x 5/6
= 9/5 x 5/6
= 9/6
= 3/2
Now we write 3/2 as improper fraction.
If we divide the 3 by 2,then we will get 1 as quotient and 1 as remainder.
3/2 = 1 1/2
Therefore, the multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2
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What is the value of the median? 8, 12, 14, 20
Answer: 14 ==> 3rd option
Step-by-step explanation:
The median is the middle value of a set of ordered numbers. Since this set of numbers from 8 to 20 are already ordered, the median would be the average number between 8 and 20.
(8+20)/2=
28/2=14 ==> 3rd option
Write the equation of the line parallel to the line and passing through
the point. Y=-2x-1, (4, 3)
Answer:
y = - 2x + 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x - 1 ← is in slope- intercept form
with slope m = - 2
• Parallel lines have equal slopes , then
y = - 2x + c ← is the partial equation of the parallel line
to find c substitute (4, 3 ) into the partial equation
3 = - 8 + c ⇒ c = 3 + 8 = 11
y = - 2x + 11 ← equation of parallel line
The length of a rectangular playground is 3x−2 feet while the width is 5x +12 feet. The perimeter of the playground is
The perimeter of the playground is 16x + 20
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l+w)
Given the following
l = 3x-2
w = 5x+12
Substitute to have:
P = 2(3x-2+5x+12)
P = 2(8x + 10)
p = 16x + 20
Hence the perimeter of the playground is 16x + 20
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Giovanni's tech fingerboard is about 25 mm wide and 100mm longe .giovanni wants to make a larger scale drawing of the tech deck on an 8 1/2 inch by 11-inch piece of paper.select a scale that is most appropriate for the scale drawing .
A scale factor of 2 would be the perfect scale for the scale drawing.
How to interpret Scale Drawing?We are given original dimensions of tech fingerboard as;
Length = 100 mm
Width = 25 mm
Now, from conversions we know that;
1 inch = 25.4 mm
Since Giovanni wants to make a larger scale drawing on an 8 1/2 inch by 11-inch piece of paper, then we can say that;
11-inch = 25.4 * 11 = 279.4 mm
8 1/2 inch = 8 1/2 * 25.4 = 215.9 mm
Thus;
New Length/old length = 279.4/100 = 2.794
Since that is the maximum scale for the drawing paper, then we can say that something lesser like a scale factor of 2 would be the perfect scale for the scale drawing.
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41. find the odds against selecting an ace when a card is drawn from a standard deck of cards. odds against
The odds against selecting an ace when a card is drawn from a standard deck of cards is 12:1.
The total number of cards in a deck is 52.The number of suits in the deck is 4.Each suit has its own ace card.So, the number of aces in the deck is 4.The probability (p) of selecting an ace card from the deck is the number of ace cards divided by the total number of cards.p = 4/52p = 1/13The probability (p') of not selecting an ace card from the deck is the number of non-ace cards divided by the total number of cards.p' = 48/52p' = 12/13The odds against selecting an ace card are equal to the probability (p') of not selecting an ace card divided by the probability (p) of selecting an ace card.The odds against selecting an ace card are p'/p.The odds against selecting an ace card are (12/13)/(1/13).The odds against selecting an ace card are 12/1.The odds against selecting an ace card are 12.To learn more about probability, visit :
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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
The final step of the given inequality is x < 3. Therefore, option C is the correct answer.
The given inequality is -2(5 - 4x) < 6x - 4.
We need to solve and write the final step of the given inequality.
What is inequality?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The inequality -2(5 - 4x) < 6x - 4 can be solved as follows:
⇒ -10 + 8x < 6x - 4
⇒ -10 + 8x-8x < 6x - 4-8x (Subtract 8x on both the side of the inequality)
⇒ -10 < -4 -2x
⇒ -10+4 < -4 -2x+4 (Add 4 on both the side of the inequality)
⇒ -6 < -2x
⇒ -6 < -2x (Divide -2 on both the side of the inequality)
⇒ x < 3
The final step of the given inequality is x < 3. Therefore, option C is the correct answer.
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I need help solving x. photo is attached below.
Explain if the student is correct about the following:
Jake says that 3 1/5 divided by 1/7 equals 16/30
is the student correct, explain why or why not?
Answer:
student is not correct
Step-by-step explanation:
3 1/5 ÷ 1/7 = 22/5
the mistake the student made was multiplying rather than dividing
I need help (If you know you get brainliest)
800 x 10
Answer:
8000
Step-by-step explanation:
800 × 10 = 8000
--------------
Answer:
8000
Step-by-step explanation:
= 800 × 10 ( adding 800 ten times )
= 8000 ( and got 8000)
Which of the following is a factor of the following expression? Select all that apply.
1/3x - 2
Answer:
2 is the factor i think
Step-by-step explanation:
can i get a brainlist?
A sight-seeing tour bus can carry 68 people. If 330 people want to go sight-seeing on the bus, what is the minimum number of trips the bus will have to make to accommodate everyone?
Answer:
5 trips
Step-by-step explanation:
330 people / 68 spots = 4.853
Because passengers cannot take 0.853 of a bus, it rounds up to 5.
The weight of the items in a truck is ton.
How many pounds do the items in the
truck weigh?
all combinations from 0-9 that equals 0
can you guys evaluate this function? I seem to be confused , thank you in advance.
k(z) = 7z^2 + 7 , find k(8z - 2)
z(q) = -10q^2 - 5 , find z(q^2)
Answer: k(8z - 2)=448z^2-224z+35
z(q^2)=-10q^4 - 5
Step-by-step explanation:
k(z) = 7z^2 + 7
k(8z - 2)=7(8z - 2)^2 + 7
k(8z - 2)=7(8z - 2)(8z - 2) + 7
k(8z - 2)=7(64z^2-16z-16z+4) + 7
k(8z - 2)=7(64z^2-32z+4) + 7
k(8z - 2)=7(64z^2-32z+4+1) ==> 7*1=7, so +1 is added in parentheses while +7 is removed outside of parentheses.
k(8z - 2)=7(64z^2-32z+5)
k(8z - 2)=448z^2-224z+35
z(q) = -10q^2 - 5
z(q^2)=-10(q^2)^2 - 5
z(q^2)=-10(q^(2*2)) - 5
z(q^2)=-10q^4 - 5
Please answer of the picture
Urgent
The side lengths of RS and PR are 12 units
What are similar triangles?Similar triangles are triangles whose corresponding sides are in proportion to one another.
In most cases, one triangle is dilated to form the other triangle
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the side length of PR?The corresponding triangles are given as:
PQR and PSQ
This means that
PQ corresponds to PS
PR corresponds to PQ
QR corresponds to QS
Where
PQ = 18
QR = 14
QS = 21
So, we have:
PR : QR = PQ : QS
This gives
PR : 14 = 18 : 21
Express as fraction
PR / 14 = 18 / 21
Multiply through by 14
PR = 14 * 18 / 21
Evaluate
PR = 12
How to determine the side length of RS?The corresponding triangles are given as:
PQR and PSQ
This means that
PQ corresponds to PS
PR corresponds to PQ
QR corresponds to QS
Where
PQ = 18
QR = 14
QS = 21
So, we have:
RS = PR
This gives
RS = 12
Hence, the side lengths of RS and PR are 12 units
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What is the slope of the line that passes through the points (2, 8) and (12, 20)?
Write your answer in simplest form.
Answer:
6/5
Step-by-step explanation:
m = (y_2 - y_1)/(x_2 - x_1) = (20 - 8)/(12 - 2) = 12/10 = 6/5
Find the value of x in each case
Answer: x = 23
Step-by-step explanation:
Angle in a X shape, the two 'opposite' eachother must be the same so angle HGC is 14
Angle in a Z shape where the lines of the Z are parralell, the two innercorner angles of the Z must be the same os angle GCE must be 14
In triangle GEC we now know two out of the three angles 78 and 14 and we know that angles in a trianlge add up to 180 so the missing angle GEC must be 180-78-14=88
Angles on a straight line must add up to 180 so 4x+88=180
Then this can be used to figure out x
4x+88=180
4x = 92
x = 23
NEED HELP ASAPP RADICALSSS
Applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.
How to Apply the Tangent Ratio?The tangent ratio is: tan ∅ = opposite side length / adjacent side length of the right triangle.
Given the following:
Reference angle (∅) = 30 degrees.
Opposite side length = 8
Adjacent side length = x = ?
Using the tangent ratio, we have: tan 30 = 8/x
x(tan 30) = 8
Divide both sides by tan 30
x(tan 30)/tan 30 = 8/tan 30
x = 8/tan 30
x = 8/1/√3
x = 8 × √3
x = 8√3
Therefore, applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.
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find the inverse funtion of p(t)=1+In(t)
Answer:
[tex]\mathsf e^{t-1}[/tex]
Step-by-step explanation:
Definition of an inverse function
[tex]\textsf {A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:[/tex]
In order to find the inverse of p(t) = 1 + ln(t)...
Set y = 1 + ln(t)Replace t with ygiven values of median, mean, mode, first and third quartiles for the observations of a numeric feature, what insights can we gain into the statistical distribution of its observations?
Median, mean, mode, first and third quartiles describe a statistical distribution because these are the measures of central tendency and dispersion of a distribution.
Median, mode and mean are known as the measures of central tendency of a statistical distribution. Because these three can even represent the whole data and its properties. Mean, median and mode gives the central value around which the whole distribution lies or its representative value.
Mean: It gives the average value of the distribution. That is the Total value/ Total number of values.
Median: It is a positional average and it is the middle value of the observations in a distribution.
Mode: Mode is also a positional average which gives the most repeated or frequent observation from the distribution
Now the first and third quartiles are measures of dispersion. It gives the variation of data values from the central value. It gives an idea of the scattering of the distribution around the central value.
First quartile: If the n observations are arranged in ascending order, then the n/4th value is the first quartile.
Third Quartile: It is the 3n/4th value in the ordered n observations.
These two are used to measure the quartile deviation from the central value. If the dispersion is large, then the measures of central tendency cannot be a representative value of the distribution.
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Cant answer this question
give the reason
75% of 210 =
Answer: 157.5
"Of" means to multiply. When multiplying percentages by whole numbers, the percentage becomes smaller. The commonly asked question in scenarios just like this is, "what is x% of y?" where x is the percentage and y is your number you want a percentage out of. This question requires you to use multiplication, because it uses the word, "of".
[tex]\bold{Step-by-step}[/tex]
[tex]\mathrm{"What}[/tex] [tex]\mathrm{is}[/tex] [tex]\mathrm{x\%}[/tex] [tex]\mathrm{of}[/tex] [tex]\mathrm{y?"}[/tex]
[tex]P = (x\% \times y)\\P = (75\% \times 210)\\p = 75\% = 0.75\\P = (0.75 \times 210)\\P = 157.5[/tex]
Any concerns, notify me. Have a good day!
1 7/16 as a decimal show work pls
Please help
Thanks in advance!
Answer:
x = 5
Step-by-step explanation:
7/17 = x/12
17x = (7)(12)
17x/17 = 84/17
x = 5
2. Find x.
F
(2x-18)
E
(4x)
GH
X=
Using composition formula we get the value of x is 9/16 for G(H(X)) = 32x - 18
What is the composition formula?In mathematics, composing a function is the process by which two functions, f and g, produce a new function, h, such that h(x) = g(f(x)). This indicates that the function of g is being applied to the function of x. In essence, a function is then applied to the outcome of another function.
We F (2x-18) and G (4x)
By using the composition formula
H(x) = g(f(x))
That is
H(x) = g(2x-18)
= 2(4x) - 18
= 8x - 18
If H(x) = 8x - 18
Then, G(H(x))
⇒ G(8x - 18)
⇒ 8(4x) - 18
⇒ 32x - 18
Now, we find x in G(H(x))
⇒ 32x - 18 = 0
⇒ 32x = 18
⇒ x = 18/32
⇒ x = 9/16
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