x f(x)
0 24
1 12
2 6
3 3
The table represents an exponential function given by:
[tex]f(x) = 24*(1/2)^x[/tex]
Is the function exponential or quadratic?Here we have the table:
x f(x)
0 24
1 12
2 6
3 3
First, notice that for each unit that x increases, the value of f(x) decreases by its half.
This is clearly an exponential equation, whose base must be equal to (1/2).
And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.
Then the exponential function is:
[tex]f(x) = 24*(1/2)^x[/tex]
Such that:
[tex]f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3[/tex]
Concluding, the table represents an exponential function.
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In isosceles ∆ABC, points M and N belong to base
BC
so that BM = CN. Prove:
∆BAM ≅ ∆CAN
∆AMN is an isosceles triangle.
From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN
How to prove an Isosceles Triangle?Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.
Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.
We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.
Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.
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Answer & Step-by-step explanation:
To prove ∆BAM ≅ ∆CAN:
1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.
2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.
3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.
4. Similarly, ∠BMA and ∠CNA are congruent.
5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.
To prove ∆AMN is an isosceles triangle:
1. From the given information, we know that BM = CN.
2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.
3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.
4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.
Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths.
The answer to the question that is modeled here is one sixth plus four sixths.
How to solve for the expression
We have the following fractions
1/6 and 5/6
We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have
1/6 + 4/6 = 5/6
Hence the correct answer to the question here is option a.
complete questionPLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths
one sixth plus four sixths
five sixths minus one sixth
five sixths minus four sixths
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Now, he wants to wrap it with wrapping paper. If the length of the shoebox measures 10 in, the width measures 5 in, and the height measures 3 in, how much wrapping paper does he need to cover the shoebox?
The amount of wrapping paper he need to cover the shoebox is 190 square inches
Surface area of a boxThe formula for calculating the surface area of a box is expressed as:
SA = 2(lw + wh + lh)
where
l is the length
w is the width
h is the height
Given the following parameters
l = 10in
w = 5in
h =3in
Substitute
S = 2(10*5 + 5*3 + 10*3)
S = 2(50+15+30)
S = 2(95)
S = 190 square inches
Hence the amount of wrapping paper he need to cover the shoebox is 190 square inches
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Solve for t in this equation and show steps please d = vt + 1/2(a)(t^2)
If f(x) = 8- 10x and g(x) = 5x + 4, what is the value of (fg) (-2)?
O -196
O -168
O 22
O 78
Identify the segments that are parallel, if any angle ABC equals angle HCB
Answer: A. DC||AB
Step-by-step explanation:
Line DC is parallel to AB so the correct answer is option B.
What is the similarity?
If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.
Therefore Line DC is parallel to AB so the correct answer is option B.
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look at this system of exquations. y=2x-1 4x +y=2 which shows a correct step using substitution to solve the system of equations?
The solution to the system of equations is x = 0.5, y = 0
How to solve the system of equations?The system of equations is given as:
y = 2x-1
4x + y=2
Substitute y = 2x-1 in 4x + y=2
4x + 2x-1 =2
Evaluate the like terms
6x = 3
Divide by 6
x = 0.5
Substitute x = 0.5 in y = 2x-1
y = 2 * 0.5 - 1
Evaluate
y = 0
Hence, the solution to the system of equations is x = 0.5, y = 0
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Find the value of x.
x = 2
x = 3
x = 33
x = 52
a. Write an ordered pair: (t, value), in which t is time from purchase and value is the current value of the car. In this case, it would be (0, Total Cash Price).
3. Find the amount of depreciation in 1 year. Determine the average rate of change (slope) in one year.
a. Write an ordered pair for the 1 - year value, which is (1, value after 1 year).
4. Find the total depreciation after 5 years.
a. Write an ordered pair for the 5 - year value, which is (5, value after 5 years).
5. Determine the following two average rates of change (slope) in the value of the car.
a. Average rate of change over 1 year
b. Average rate of change over 5 years
6. What is the practical meaning of the average rate of change over 5 years?
The value of the car decreases by $1430 per year over 5 years
The initial ordered pairThe given parameters are:
Total Cash Price: $13,7551 year depreciation: $1,811So, the ordered pair is (0, 13,755)
The amount in depreciation after 1 yearIn (a), we have:
Total Cash Price: $13,7551 year depreciation: $1,811The difference in the amounts is
Difference = 13755 - 1811
Difference = 11944
So, the ordered pair is (1, 11,944)
Total depreciation after 5 yearsWe have:
5 year depreciation = $7,150
The difference in the amounts is
Difference = 13755 - 7150
Difference = 6605
So, the ordered pair is (5, $6,605)
Average rates of changeThis is calculated as:
m = (y2 - y1)/(x2 - x1)
Over 1 year, we have:
m = (13,755-11,944)/(0-1)
m =-1811
Over 5 years, we have:
m = (13,755-6605)/(0-5)
m =-1430
The meaning of the average rate of change over 5 yearsThe average rate of change over 5 years is -1430
This means that the value of the car decreases by $1430 per year
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Missing information in the question
Total Cash Price: $13,755
1 year depreciation: $1,811
5 year depreciation: $7,150
What is the value of "y" that satisfies the expression below?
5 y + 14 = 9 ( 3 y + 1 )
Round your answer to 2 decimal points (i.e. #.##)
Answer:
0.23
Step-by-step explanation:
5y+14=27y+9
14-9=27y-5y
5=22y
dividing through by 22
y=0.23
Evaluate the fraction for x = 0. (x-1)² (1-x)² 01 0-1 02
Evaluating the given algebra fraction (x - 1)²/(1 - x)² at x = 0 gives; 1
How to Evaluate Algebra Fractions?
We want to evaluate the algebra fraction;
(x - 1)²/(1 - x)² at x = 0.
Now, let us first break down the expression to get;
[(x - 1) * (x - 1)]/[(1 - x) * (1 - x)]
At x = 0, we have;
[(0 - 1) * (0 - 1)]/[(1 - 0) * (1 - 0)]
⇒ (-1 * -1)/(1 * 1)
⇒ 1
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Melissa's mother asked her to buy a gallon of milk at the store. The store only had quarts of milk. How many quarts of milk does Melissa need to buy?
Answer:
4 quarts of milk
Step-by-step explanation:
4 quarts = 1 gallon
so, melissa needs to buy 4 quarts
Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1
The non-extraneous solutions are -6 and -5.
How to find non-extraneous solutions?By checking these solution values in the original equation.
[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]
Thus, -6 is non-extraneous.
[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]
Thus, -5 is non-extraneous.
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Identify the type of sequence and write the recursive rule −1,−2,−4,−8,
In a recent year, 27.2% of all registered doctors were female. If there were 55,900 female registered doctors that year, what was the total number of registere doctors? Round your answer to the nearest whole number. In a recent year , 27.2 % of all registered doctors were female . If there were 55,900 female registered doctors that year , what was the total number of registere doctors ? Round your answer to the nearest whole number .
it's B why they need me to write something long the answer is ez B
Step-by-step explanation:
it f common sense
Find f(2) and f(a + h) when f(x) = 3x2 + 2x + 4.
Step-by-step explanation:
[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]
[tex] \: [/tex]
[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]
[tex]f(2) = 3.4 + 4 + 4[/tex]
[tex]f(2) = 12 + 8[/tex]
[tex]f(2) = 20 \\ [/tex]
[tex] \: [/tex]
[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]
[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]
[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]
[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]
Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
ANSWER:
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance. This is a distance-time graph problem.
What is the proof for the above?
Recall that Josiah had a head start of 10 meters and he skates at 2 meters per second.
Since Y is the function that represents the distance in meters from the finished line, by observation, it is clear to see that all the factors that are related to his race are adequately represented in:
y = 10 + 2x
Where 10 is the head start in meters
2 is the rate at which he skates per second; and
x is the unknown amount of time in seconds.
Given that the point F sits over 25 seconds,
that is F(y) = 10 + 2 * 25
= 60 meters.
Hence, Point F is on line a, so it does represent Josiah's distance at exactly 25 seconds.
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find the measure of the exterior angle x
The measure of the exterior angle x is 90°.
We need to find the measure of the exterior angle x.
What is the exterior angle theorem formula?An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Now, x°=∠A+∠B
⇒x°=30°+60°=90°
Therefore, the measure of the exterior angle x is 90°.
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Dont Really need explanation Simply answer Just I didn’t understand Maybe I can get help
Based on the calculations, Tart & Sweet's total profit from April to June is equal to -2 dollars.
What is a bar chart?A bar chart can be defined as a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.
In order to determine Tart & Sweet's total profit, we would simply add the amount of money (in dollars) generated from April to June as follows:
April = -8.May = 2.June = 4.Total profit = -8 + 2 + 4
Total profit = -$2.
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Can anyone explain this answer, I'll give brainliest.
Where does the 0.693 and 2.303 come from?
The constants 0.693 is the natural log of 2 and the constant 2.303 is the multiplicative factor of converting log of a number to the natural log of that same number.
What are 0.693 and 2.303 used for?It follows from the task content that the calculation involves the use of the half-life of radioactive materials formula.
Hence, the constant 0.693 is the real number value of ln(2). Additionally, the constant 2.303 as used by convention is used to convert log value of a number x to its natural log value. Hence,. it follows that the relation which holds true is; ln(x) = 2.303 × log(x).
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Which expression is a non-real complex number?
-4 +√7
3
1 + √²
5-√15
27
28
The expression that represents a complex number is the one in the second option.
[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]
Which expression is a non-real complex number?Remember that the complex number i is given by:
[tex]i = \sqrt{-1}[/tex]
So we have complex numbers when we have negative arguments inside of square roots.
In this particular case, the only option with a negative argument on a square root is on the second option:
[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]
We conclude that the correct option is the second one.
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Answer:
(2)/(3)+\sqrt(-(27)/(28))
Step-by-step explanation:
Plato/Edmentum
Solve the following equation for m.
F=mv^2 / r
Answer:
Step-by-step explanation:
F = [tex]\frac{mv^2}{r}[/tex]
mv² = Fr
m = [tex]\frac{Fr}{v^2}[/tex]
For a normally distributed data set with a mean of 830 and a standard deviation of 96.7, calculate the z-score for a
data point of 915.
Round this however your teacher instructs.
=================================================
Work Shown:
mu = 830 = mean
sigma = 96.7 = standard deviation
x = 915 = given raw score we want to convert
z = (x - mu)/sigma
z = (915 - 830)/(96.7)
z = (85)/(96.7)
z = 0.8790072 approximately
Simplify the expression.
[tex]\huge\boxed{4x}[/tex]
Start by simplifying the power.
[tex](5x)^3=5^3x^3=125x^3[/tex]
[tex]\dfrac{500x^4}{125x^3}[/tex]
Cancel out the common factor of [tex]125[/tex].
[tex]\dfrac{4x^4}{x^3}[/tex]
Finally, cancel out the common factor of [tex]x^3[/tex].
[tex]\boxed{4x}[/tex]
what is w? 11w= 12 please be quick with the response.
Answer:
1.090909090909091
Step-by-step explanation:
12/11 = 1.090909090909091
W = 1.090909090909091
Answer:
w = [tex]\frac{12}{11}[/tex]
Step-by-step explanation:
11w = 12 ( isolate w by dividing both sides by 11 )
w = [tex]\frac{12}{11}[/tex]
One of the tables shows a proportional relationship.
Use the points from this table to graph the line representing the proportional
relationship.
Line
10-
9
8-
7
5
4
3
2
-2-
3 7 4
-3-
Undo
1 2
3
4
Redo
$
6
x Reset
7 8 9 10
X
y
x
y
X
y
X
y
2
1
2
1
0
2
1
3
2
4
3
2
2
2
4
5
6
3
4
6
4
5
3
7
27
6
4
8
4
5
8
9
6
Answer:
See attached
Step-by-step explanation:
The graph of a proportional linear relationship is a line that passes through the origin (0, 0).
From inspection of the given tables, the linear equations for each table of points is:
Table 1: y = x + 1Table 2: y = x/2Table 3: y = x + 2Table 4: y = 2x + 1The only equation for which y = 0 when x = 0 is y = x/2 → Table 2.
Given points from Table 2:
(2, 1)(4, 2)(6, 3)(8, 4)To graph the line, plot the given points and draw a line through them (see attached).
why is the derivative of a constant zero
A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.
That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then
[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]
Two parallel lines are cut by a transversal. What is the measure of angle 6?
[tex]\huge\boxed{\textsf{D.}\ 57^\circ}[/tex]
We know that angles 1 and 2 are supplementary angles that add up to 180 degrees.
Solve for angle 2:
[tex]\begin{aligned}\angle1+\angle2&=180^\circ\\123^\circ+\angle2&=180^\circ\\123^\circ-123^\circ+\angle2&=180^\circ-123^\circ\\\angle2&=57^\circ\end{aligned}[/tex]
We also know that angles 2 and 6 are corresponding angles, so they are equal to each other. This means that angle 6 is also 57 degrees.
For more information on this topic, search the Internet. There are many great resources on transversal lines and angles out there that expand on the few details I shared here.
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region.
The area of the shaded region is 29.5 square yards.
The following calculations are to be done:
Area of the triangle:
Base of the triangle is
= 5 + 4
= 9 yard.
Height of the triangle = 6 + 5
Height of the triangle= 11 yards.
The area of the triangle is,
[tex]\ Area \ of \ the\ rectangle=\frac{1}{2} \times height\times base[/tex]
[tex]\ Area \ of \ the\ rectangle=\frac{1}{2}\times 9\times 11[/tex]
= 49.5 square yards.
What is the formula for the area of a triangle?Area of the rectangle:
[tex]=Length\times width[/tex]
[tex]=4\times 5[/tex]
= 20 square yards.
Now finally the shaded region should be
= 49.5 square yards - 20 square yards
= 29.5 square yard
Therefore we can conclude that the area of the shaded region is 29.5 square yards.
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