Answer:
x = 6
Step-by-step explanation:
Given that the line segment is an angle bisector then the following ratios are equal
[tex]\frac{42}{78}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex], that is
[tex]\frac{7}{13}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex] ( cross- multiply )
13(6x - 1) = 7(10x +5) ← distribute parenthesis on both sides
78x - 13 = 70x + 35 ( subtract 70x from both sides )
8x - 13 = 35 ( add 13 to both sides )
8x = 48 ( divide both sides by 8 )
x = 6
The ABC Bagel Shop sells bagels for $0.85 each thus far today they have sold 47 bagels write an equation that represents the amount of money A they'll make if they an additional B bagels today
Answer: 47+B(.85) = A
Step-by-step explanation:
One bagel = $0.85
Sold 47 today
One bagel(.85) = profit
A = profit
B = additional bagels
47+B(.85) = A
Find the domain and range of f(x)=2x+cos x
Answer:
Domain = Range = All real numbers
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The equation is:
f(x)=2x+cos x
From the plot, we can see the answer is
Option a.
Domain = Range = (-∞,∞)
Answer: a
Step-by-step explanation:
right on edg
Alan learned 24 new vocabulary words in 4 weeks. which unit rate describes the situation? 6,8,20,28
Answer:
the person above me is correct
Step-by-step explanation:
by the way its 8 because 24 words divided by 4 weeks is 8.
The unit rate describing Alan's vocabulary acquisition is 6 words per week.
The unit rate that describes the situation where Alan learned 24 new vocabulary words in 4 weeks is 6 words per week.
To find the unit rate, divide the total number of words learned by the total number of weeks. In this case, 24 words / 4 weeks = 6 words per week.
What is the standard form of an ellipse with foci at (0, ±2), and vertices at (0, ±4)?
Answer:
B) x^2/12 +y^2/16 = 1
Step-by-step explanation:
The distance from focus to covertex is the same as the distance from the center to the vertex: 4. So, the Pythagorean theorem tells you ...
a^2 + 2^2 = b^2
a^2 +4 = 4^2 = 16
a^2 = 16 -4 = 12
So, the standard-form equation ...
x^2/a^2 +y^2/b^2 = 1
looks like this when the values are filled in:
x^2/12 +y^2/16 = 1
Select the functions that have identical graphs.
Answer:
c. 1 and 3
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.
Please see the attached image below, to find more information about the graph s
The equations are:
1) y = sin (3x + π/6)
2) y = cos (3x - π/6)
3) y = cos (3x - π/3)
Looking at the graphs, we can see that the identical ones
are equations one and three
Correct option:
c. 1 and 3
The correct option is:
option: c c. 1 and 3
Step-by-step explanation:The first trignometric function is given by:
[tex]y=\sin (3x+\dfrac{\pi}{6})[/tex]
and also we know that:
[tex]\sin \theta=\cos(\dfrac{\pi}{2}-\theta)[/tex]
This means that:
[tex]\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{2}-(3x+\dfrac{\pi}{6})\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{2}-3x-\dfrac{\pi}{6})\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{2}-\dfrac{\pi}{6}-3x)\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{2\pi}{6}-3x)\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{3}-3x)\\\\\\\sin (3x+\dfrac{\pi}{6})=cos (-(3x-\dfrac{\pi}{3}))[/tex]
As we know that:
[tex]\cos (-\theta)=cos(\theta)[/tex]
Hence, we have:
[tex]\sin (3x+\dfrac{\pi}{6})=\cos (3x-\dfrac{\pi}{3})[/tex]
Also, by the graph we may see that the graph of 1 and 2 function do not match.
Hence, they are not equivalent.
in the figure, AB||CD and BC||AE. Let ABD measure (3x+4), BCD measure (6x-8), and EDF measure (7x-20).
What does angle BCD measure?
Answer:
The measure of angle BCD is [tex]68.5\°[/tex]
Step-by-step explanation:
step 1
Find the value of x
In this problem
[tex]m<ABD+m<BCD+m<EDF=180\°[/tex] -----> is a straight line
substitute the values
[tex](3x+4)+(6x-8)+(7x-20)=180\°[/tex]
[tex](16x-24)=180\°[/tex]
[tex]16x=180\°+24\°[/tex]
[tex]x=12.75\°[/tex]
step 2
Find the measure of angle BCD
[tex]m<BCD+=(6x-8)\°[/tex]
substitute the value of x
[tex]m<BCD+=(6(12.75)-8)=68.5\°[/tex]
What is the sum of the first 703 terms of the sequence -5, -1, 3, 7, ...?
Answer:
983497
step-by-step explanation:
The sum formula of arithmetic sequence is given by:
[tex]S_n = \frac{n}{2}(2a_1 +(n - 1)d[/tex]
a_1 is the first term, n is the nth term and d is the common difference
From the given information
[tex]d = - 1 -( - 5) = - 1 + 5 = 4[/tex]
[tex]a_1 = - 5 \: and \: n = 703[/tex]
By substitution we obtain:
[tex]S_{703}= \frac{703}{2}(2( - 5) +(703- 1)4)[/tex]
[tex]S_{703}= \frac{703}{2}( - 10 + 2808)[/tex]
[tex]S_{703}= \frac{703}{2}(2798)[/tex]
[tex]S_{703}=98397[/tex]
Answer:
S = 983,497
Step-by-step explanation:
We are given the following sequence and we are to find the sum of the first 703 terms of this sequence:
[tex]-5, -1, 3, 7, ...[/tex]
Finding the common difference [tex]d[/tex] = [tex]-1-(-5)[/tex] = [tex]4[/tex]
[tex]a_1=-5[/tex]
[tex]a_n=?[/tex]
[tex]a_n=a_1+(n-1)d[/tex]
[tex] a_n = - 5 + ( 7 0 3 - 1 ) 4 [/tex]
[tex] a _ n = 2803 [/tex]
Finding the sum using the formula [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex].
[tex]S_n = \frac{703}{2}(-5+2803)[/tex]
S = 983,497
What is ∑n=14[100(−4)n−1] equal to? Enter your answer in the box.
The value of ∑n=14[100(−4)n−1] is -5368709100
How to evaluate the series?The sequence is given as:
∑n=14[100(−4)n−1]
The above sequence is a geometric sequence, with the following properties
First term, a = 100Common ratio, r = -4Number of terms = 14The sum of n terms of a geometric series is:
[tex]S_n = \frac{a* (r^n - 1)}{r - 1}[/tex]
So, we have:
[tex]S_n = \frac{100* ((-4)^{14} - 1)}{-4 - 1}[/tex]
Evaluate
[tex]S_{14} = -5368709100[/tex]
Hence, the value of ∑n=14[100(−4)n−1] is -5368709100
Read more about geometric series at:
https://brainly.com/question/24643676
The sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\)[/tex] is [tex]\[\boxed{-5100}\][/tex]
To find the sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\),[/tex] we will calculate the individual terms of the sequence and then sum them up.
The general term of the sequence is [tex]\(100(-4)^{n-1}\)[/tex]. Let's compute the terms from [tex]\(n = 1\) to \(n = 4\):[/tex]
1. For [tex]\(n = 1\):[/tex]
[tex]\[ 100(-4)^{1-1} = 100(-4)^0 = 100 \cdot 1 = 100 \][/tex]
2. For [tex]\(n = 2\):[/tex]
[tex]\[ 100(-4)^{2-1} = 100(-4)^1 = 100 \cdot (-4) = -400 \][/tex]
3. For [tex]\(n = 3\):[/tex]
[tex]\[ 100(-4)^{3-1} = 100(-4)^2 = 100 \cdot 16 = 1600 \][/tex]
4. For [tex]\(n = 4\):[/tex]
[tex]\[ 100(-4)^{4-1} = 100(-4)^3 = 100 \cdot (-64) = -6400 \][/tex]
Now, let's sum these terms:
[tex]\[100 + (-400) + 1600 + (-6400)\][/tex]
Perform the calculations step-by-step:
1. [tex]\(100 - 400 = -300\)[/tex]
2. [tex]\(-300 + 1600 = 1300\)[/tex]
3. [tex]\(1300 - 6400 = -5100\)[/tex]
Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth. From the least to the greatest, the solutions are: x ≈ and x ≈ .
Answer:
See the graph attachedx₁ ≈ - 2.1x₂ ≈ 0.2Explanation:
To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:
Equation 1: y = log (5.6x + 1.3)Equatin2: y = - 1 - x1) To graph the equation 1 you can use these features of logarithmfunctions:
Domain: positive values ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)Range: all real numbers (- ∞ , ∞)x-intercept:log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054
y-intercept:x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11
Pick some other values and build a table:x log (-5.6x + 1.3)
-1 0.8
-2 1.1
-3 1.3
You can see such graph on the picture attached: it is the red curve.2) Graphing the equation 2 is easier because it is a line: y = - 1 - x
slope, m = - 1 (the coeficient of x)y - intercept, b = - 1 (the constant term)x - intercept: y = 0 = - 1 - x ⇒ x = - 1The graph is the blue line on the picture.3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:
x₁ ≈ - 2.1x₂ ≈ 0.2Answer:
x = -2.1
& .2
Step-by-step explanation:
Find the slope of the line.
A-4
B--1/4
C-1/4
D--4
Answer:
slope=-1/4
Step-by-step explanation:
point 1: -4,-1
point 2: 0,-2
y1-y2/x1-x2
1/-4
-1/4
Apply the distributive property
1/4(16a+8b+c)
Answer:
4a + 2b + 1/4 c.
Step-by-step explanation:
1/4(16a+8b+c)
= 1/4 * 16a + 1/4 * 8b + 1/4 * c
= 4a + 2b + 1/4 c.
Final answer:
To apply the distributive property to the expression 1/4(16a+8b+c), we distribute the 1/4 to each term inside the parentheses and simplify the expression.
Explanation:
To apply the distributive property to the expression 1/4(16a+8b+c), we distribute the 1/4 to each term inside the parentheses. This means multiplying 1/4 by 16a, 1/4 by 8b, and 1/4 by c. The distributive property states that a (b + c) = ab + ac. So, the expression becomes:
1/4(16a) + 1/4(8b) + 1/4(c)
Since 1/4 times any number equals the number divided by 4, we can simplify further:
(16a/4) + (8b/4) + (c/4)
Which simplifies to:
4a + 2b + c/4
The school production of 'Our Town' was a big success. For opening night, 503 tickets were sold. Students paid $4.00 each, while non-students paid $6.00 each. If a total of $ 2296.00 was collected, how many students and how many non-students attended?
The number of students was
nothing. (Simplify your answer.)
The number of non-students was
nothing. (Simplify your answer.)
4x➕6(503-x)=2296
Distribute the 6 into the parentheses
Let x represent the students
503-x will represent the non-students
4x➕3018➖6x=2296
Then combine like terms
-2x➕3018=2296
Now since you move your constant your sign has to change as well,
-2x=2296➖3018
Then subtract
-2x=-722
Then divide both sides by -2
You are left with x=361
This represents the students
503➖361= 142 which equal the non-students
Therefore your answer is:
361=students
142=non-students
Hope this helps! :3
Answer:
361 students and 503-361=142 non students
Step-by-step explanation:
Let x = number of students. And 503-x = the number of non students. Therefore, 4x+6(503-x)=2296
LAST QUESTION GUYS PLEASE LORD HELP ME
ANSWER
D. 13
EXPLANATION
The given function is:
[tex]f(x) = \frac{2x + 1}{x -4} [/tex]
Let
[tex]y = \frac{2x + 1}{x -4} [/tex]
Interchange x and y.
[tex]x= \frac{2y + 1}{y-4} [/tex]
Solve for y.
[tex]x(y - 4)=2y + 1[/tex]
[tex]xy - 4x=2y + 1[/tex]
[tex]xy - 2y = 1 + 4x[/tex]
[tex](x - 2)y = 1 + 4x[/tex]
[tex]y = \frac{1 + 4x}{x - 2} [/tex]
[tex] {f}^{ - 1}(x) = \frac{1 + 4x}{x - 2} [/tex]
We put x=3,
[tex]{f}^{ - 1}(3) = \frac{1 + 4 \times 3}{3- 2}[/tex]
[tex]{f}^{ - 1}(3) = \frac{13}{1} = 13[/tex]
Calcule a area da superficie lateral e a capacidade de um cone de revolucao de altura 9 cm sabendo que sua area lateral vale o dobro da area da sua base
Answer:
The answer is -8.
Step-by-step explanation:
Mark all the statements that are true.
A. This graph is not a function because the value x = 3 is assigned to more than one y-value.
B. This graph is a function whose range is the set {3}
C. The equation fo this line is x=3.
D. This graph is a function whose domain is the set {3}
E. This graph is a function because the value of x is the same for every value of y.
Answer:
Option A
Option C
Step-by-step explanation:
A relationship is defined as a function if and only if each element of the "domain" set is assigned only one element of the "range" set. That is, there is only one output value y assigned to each input value x.
The relation x = 3 is not a function because there are infinite output values y, assigned to the same input element x.
(3, 2), (3, 5) (3, 9) (3,10000)
Then the option A is true
Option C is also true, the equation of the line shown is
[tex]x = 3[/tex]
The rest of the options are false because x = 3 is not a function
The function f(t) = 349.2(0.98)t models the relationship between t, the time an oven spends cooling and the temperature of the oven. For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
A function assigns the values. The temperature that will model most accurately predict the time spent cooling will be 300.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given function [tex]f(t)=349.2 (0.98)^t[/tex], the value of t which will lie within the given function range will be the value function that will model most accurately predict the time spent on cooling. Therefore, let's substitute the values and check,
A.) t = 0
[tex]f(t)=349.2 (0.98)^t\\\\0=349.2 (0.98)^t[/tex]
As the value of t will lie at infinite, therefore, this will not give an accurate prediction of the model.
B.) f(t) = 100
When the value of the function will be 100 then the value of t will be 61.6, therefore, this can not be the most accurate prediction.
C.) f(t) =300
When the value of the function will be 300 then the value of t will be 7.5, therefore, this is the most accurate prediction.
D) f(t) = 400
When the value of the function will be 400 then the value of t will be -6.724, therefore, this can not be the most accurate prediction.
Thus, the temperature that will model most accurately predict the time spent cooling will be 300.
Learn more about Function:
https://brainly.com/question/5245372
PLEASE HELP!!!
Given triangle QRS is congruent to triangle TUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV.
Answer:
The length of QS and TV is 8 units
Step-by-step explanation:
we know that
If triangle QRS is congruent with triangle TUV
then
QS=TV
QR=TU
RS=UV
In this problem
we have
QS=3v+2
TV=7v-6
so
QS=TV
3v+2=7v-6
Solve for v
7v-3v=2+6
4v=8
v=2
Find the length of QS
substitute the value of v
QS=3(2)+2=8 units
so
TS=8 units
Final answer:
Triangle QRS is congruent to triangle TUV, so side QS is equal to side TV. By setting the expressions for QS and TV equal and solving for 'v', we find that both lengths are 8 units.
Explanation:
To solve the problem of finding the length of QS and TV given that triangle QRS is congruent to triangle TUV, and being given the expressions QS = 3v + 2 and TV = 7v - 6, we must recognize that congruent triangles have corresponding sides of equal length. Thus, we can set the expressions for QS and TV equal to each other:
3v + 2 = 7v - 6
We then solve for 'v' by subtracting 3v from both sides:
2 = 4v - 6
Next, we add 6 to both sides:
8 = 4v
Divide both sides by 4 to find 'v':
v = 2
Now that we have the value of 'v', we can substitute it back into the expressions for QS and TV to find their lengths:
QS = 3(2) + 2 = 8
TV = 7(2) - 6 = 8
Therefore, the length of QS and TV is 8 units each.
PLEASE HELP ASAP! WILL GIVE BRAINLIEST! Thank you!
Given: mKP=2mIP, mIVK=120°
Find: m∠KJL
That is 99 degrees if you have the triangle facing the other way
the measure of angle KJL is [tex]\( 40^\circ \)[/tex].
Given information
[tex]\( m(KP) = 2 \cdot m(IP) \)\\\( m(IVK) = 120^\circ \)[/tex]
Using the fact that the sum of angles in a circle is [tex]\( 360^\circ \)[/tex], we have:
[tex]\[ m(KP) + m(IP) + m(IVK) = 360^\circ \][/tex]
Substituting the given values:
[tex]\[ 2 \cdot m(IP) + m(IP) + 120^\circ = 360^\circ \][/tex]
Solving for [tex]\( m(IP) \)[/tex]:
[tex]\[ 3 \cdot m(IP) = 360^\circ - 120^\circ \]\[ 3 \cdot m(IP) = 240^\circ \]\[ m(IP) = \frac{240^\circ}{3} \]\[ m(IP) = 80^\circ \][/tex]
Finding [tex]\( m(KP) \)[/tex]:
[tex]\[ m(KP) = 2 \cdot m(IP) = 2 \cdot 80^\circ = 160^\circ \][/tex]
Using the angle formed by a tangent and a secant theorem, we can find [tex]\( m(\angle KJL) \)[/tex]:
[tex]\[ m(\angle KJL) = \frac{1}{2} (m(KP) - m(IP)) \][/tex]
Substituting the known values:
[tex]\[ m(\angle KJL) = \frac{1}{2} (160^\circ - 80^\circ) \]\[ m(\angle KJL) = \frac{1}{2} (80^\circ) \]\[ m(\angle KJL) = 40^\circ \][/tex]
Therefore, the measure of angle KJL is [tex]\( 40^\circ \)[/tex].
The complete question is:
given: [tex]\( m(KP) = 2 \cdot m(IP) \)\\[/tex] and [tex]\( m(IVK) = 120^\circ \)[/tex]
find: m∠KJL.
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
[tex]4w^4-7z^4+6w^2z^2[/tex]
Step-by-step explanation:
We can reformat this equation so we can vertically add.
Then, we can just add down.
Since all the degrees and the variables are the same, we only have to worry about the coefficients.
5 - 1 = 4 --> [tex]4w^4[/tex]
-7 + 13 = 6 --> [tex]6w^2z^2[/tex]
-3 - 4 = -7 --> [tex]-7z^4[/tex]
Now let's rewrite this.
[tex]4w^4-7z^4+6w^2z^2[/tex]
Last weekend sanjay watched 3 television shows that were each 30 mins long he also watched one movie on television that was 90 mins long what is the total number of minutes Sanjay watched television last weekend
Answer:
Sanjay watched television last weekend for 180 minutes.
Step-by-step explanation:
Sanjay watched 3 television shows and one movie on television last week.
Time duration of 1 television shows = 30 mins
Time duration of 3 television shows = 3* 30 = 90 mins
Time duration of movie = 90 mins
Total number of minutes Sanjay watched television last weekend = Time duration of 3 television shows + Time duration of movie
= 90 + 90
= 180 min
So, Sanjay watched television last weekend for 180 minutes.
HELP PLEASE ASAP!!!!! BRAINLIEST+20 POINTS!!!!!!!
Which statements are true about parabolas represented by the equation
y=ax²+bx+c?
Select four that apply.
If a>0, then the parabola opens up.
If a>0, then the parabola has a minimum.
If a<0, then the parabola opens down.
If a>0, then the parabola has a maximum.
C. If a<0, then the parabola opens down
What is the value of matrix B if A+B=C?
Answer:
option B
Step-by-step explanation:
Step 1
A + B = C
[tex]A=\left[\begin{array}{ccc}8&-3\\3&y+2\end{array}\right][/tex][tex]+B=\left[\begin{array}{ccc}3x&z+4\\w&1/2y\end{array}\right][/tex]
=
[tex]C=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]
Step 2
[tex]\left[\begin{array}{ccc}8+3x&-3+z+4\\3+w&y+2+y/2\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]
Step 3
4 equations are form
Equation 1
8 + 3x = x
8 = -2x
x = -4
Equation 2
-3 + z + 4 = 2z
1 + z = 2z
1 = z
z = 1
Equation 3
3 + w = 4
w = 1
Equation 4
y + 2 + y/2 = y
2 + y/2 = 0
4 + y = 0
y = -4
Step 4
[tex]\left[\begin{array}{ccc}3(-4)&1+4\\1&1(-4)/2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-12&5\\1&-2\end{array}\right][/tex]
Answer:
B
Step-by-step explanation:
I got 100% on EDGE 2020 Unit test
Please check if ur able to help with these
The last ones answer is six
What is true about the dilation?
It has a scale factor between zero and one and is a reduction.
It has a scale factor greater than one and is a reduction.
It has a scale factor between zero and one and is an enlargement.
It has a scale factor greater than one and is an enlargement.
Answer:
im pretty sure its the first one
Answer with explanation:
When the size of Preimage is greater than size of Image than dilation factor will be less than 1 and greater than zero.
And, when Size of preimage is greater than Size of Image than dilation factor will be greater than 1.
In the given diagram
Size of Preimage > Size of Image
Dilation Factor=0 <Dilation factor <1
Option A: It has a scale factor between zero and one and is a reduction.
Simplify the algebraic expression: x(x + 3) + x(2x – 4) + 6
A. 3x2 + 5
B. 2x4 – x2 + 6
C. 3x2 + x + 6
D. 3x2 – x + 6
Thanks !! Will mark for Brainlest if answered correctly.
answer for this question is (d)3x2-x+6
This is the answer:)
The function f(x) = ?x2 + 16x ? 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
Answer:
Step-by-step explanation:
A
The vertex form: f(x) = a(x-h)^2 + k
f(x) = x^2 + 16x + 60 = (x^2 + 16x) + 60
We want to get a perfect square in the brackets, so we solve for our b^2 coefficient.
b^2 = (16/2)^2 = 64
f(x) = (x^2 + 16x + 64 - 64) + 60. Note we subtracted 60 right away to end up with an equivalent expression and not some other function.
f(x) = (x+8)^2 - 4, as you can see it matches the general vertex form.
The vertex form shows when the profit is minimal. The point (h, k) or f(h).
B. The x-intercepts or when the function is equal to 0, or the profit is 0 in the context of the problem.
f(x) = x^2 + 16x + 60 set = 0
x^2 + 16x + 60 = 0
[tex]x_{12} = \frac{-16 \pm \sqrt{256 - 4(1)(60)}}{2} = \frac{-16 \pm \sqrt{16}}{2} = \frac{-16 \pm 4}{2} = -8 \pm 2[/tex]
Answer:
the vertex is either the maximum or minimum value
since the leading coefinet is negative (the number in front of the x² term), the parabola opens down and is a maximum
so
A.
a hack version is to use the -b/(2a) form
if you have f(x)=ax²+bx+c, then the x value of the vertex is -b/(2a)
so
given
f(x)=-1x²+16x-60
the x value of the vertex is -16/(2*-1)=-16/-2=8
the y value is f(8)=-1(8)²+16(8)-60=
-1(64)+128-60=
4
the vertex is (8,4)
so you selll 8 candels to make the max profit which is $4
B.
x intercepts are where the line crosses the x axis or where f(x)=0
solve
0=-x²+16x-60
0=-1(x²-16x+60)
factor
what 2 numbers multiply to get 60 and add to get -16
-6 and -10
0=-1(x-6)(x-10)
set each factor to 0
0=x-6
x=6
0=x-10
10=x
x intercepts are at x=6 and 10
that is where you make 0 profit
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8. The trapezoids are similar. The area of the smaller trapezoid is 131 m2. Find the area of the larger trapezoid to the nearest whole number.
Answer:
[tex]3,726\ m^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z----> the scale factor
x----> corresponding side of the larger trapezoid
y----> corresponding side of the smaller trapezoid
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=64\ m[/tex]
[tex]y=12\ m[/tex]
substitute
[tex]z=\frac{64}{12}[/tex]
step 2
Find the area of the larger trapezoid
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z----> the scale factor
x----> area of the larger trapezoid
y----> area of the smaller trapezoid
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{64}{12}[/tex]
[tex]y=131\ m^{2}[/tex]
substitute
[tex](\frac{64}{12})^{2}=\frac{x}{131}[/tex]
[tex]x=(\frac{4,096}{144})(131)[/tex]
[tex]x=3,726\ m^{2}[/tex]
please i need help
i dont know how to do this
Do what? I can't see a question
repost and let me know once it’s up because I can’t see the picture
Good luck,
:)
Which function is represented by the graph below? graph begins in the second quadrant near the x−axis and increases slowly while crossing the ordered pair 0, 1. When the graph enters the first quadrant, it begins to increase quickly throughout the graph f(x) = 3x f(x) = 3x − 3 f(x) = 3x + 3 f(x) = 3(x + 3).
Answer:
[tex]f(x)=3^x[/tex]
Step-by-step explanation:
Given that the function is represented by the graph below, which begins in the second quadrant near the x−axis and increases slowly while crossing the ordered pair 0, 1. When the graph enters the first quadrant, it begins to increase quickly throughout the graph
Because it passes through (0,1) it is of the form
[tex]y=a^x[/tex]
Also for negative x large it is very near x axis, So a must be positive then only it increases faster in the I quadrant. Range is only posiitve real numbers
So the function is
[tex]f(x) =3^x[/tex]
HELP ASAP PLEASE!!!!
If f(x)= x^2 and g(x)= 2x+3, what is f (g(x))?
A. 4x^2+9
B. x^2+2x+3
C. 2x^2+3
D. 4x^2+12x+9
Answer:
D
Step-by-step explanation:
Substitute x = g(x) into f(x)
f(2x + 3) = (2x + 3)² ← expand factors
f(g(x)) = (2x)² + 6x + 6x + 3² = 4x² + 12x + 9 → D