Answer:
(x+5)^2-20
(-5,-20)
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term to complete the square.
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 ∑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:
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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]
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
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 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.
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
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
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:
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,
:)
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.
20 points!
Which transformations are rigid motions?
Check all that apply!
Question options:
Dilations
Rotations
Translations
Reflections
Translations, rotations, and reflections are all rigid transformations.
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]
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:
reposting this as a priority question worth 15 points help please ASAP
Answer:
3. f(x) = 5^x
4. f(x) = 3 (8)^x
Step-by-step explanation:
3. Which function represents the data 2=>25, 3=>125, 4 =>625
You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.
f(x) = x^4 + 9 - NO
for x = 2, 2^4 + 9 = 16 + 9 = 25 YES
for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125
f(x) = 4^x + 9 - NO
for x = 2, 4^2 + 9 = 16 + 9 = 25 YES
for x = 3, 4^3 + 9 = 64 + 9 = 73 NO, should be 125
f(x) = x^5 - NO
for x = 2, 2^5 = 32 NO, should be 25
f(x) = 5^x YES
for x = 2, 5^2 = 25 YES
for x = 3, 5^3 = 125 YES
for x = 4, 5^4 = 625 YES
4. Which of the options is equivalent to f(x) = 3(2)^(3x)
By property of the powers you can easily break down the 3x exponent into a much simpler way.
[tex](2)^{3x} = (2^{3} )^{x} = 8^{x}[/tex]
From (2)^(3x) we got to 8^x, so the equation can now be written:
f(x) = 3 (8)^x, which is the first choice.
You could easily verify it with x = 2 in each equation.
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:)
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
which house is worth more after two years?
Answer:
Hello cheaters lol jk, Answer is B.
Step-by-step explanation:
more interest equals more money, if you divide the amount of the house by 6% and do the same for the other by 5, the amount for B is greater.
The House A is more worth than House B .
What is compound interest?Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
Formula of Compound interest :
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
Where,
A = Final amount
P = initial principal
r = rate per annum
n = Time in years
According to the question
House A:
Principal = 125260
Rate = 5%
Time in years = 2
Applying Formula of Compound interest for final amount
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
[tex]A = 125260 (1+\frac{5}{100} )^{2}[/tex]
[tex]A = 125260 (1.05)^{2}[/tex]
A = 138,099.15
House B:
Principal = 120160
Rate = 6%
Time in years = 2
Applying Formula of Compound interest for final amount
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
[tex]A = 120160 (1+\frac{6}{100} )^{2}[/tex]
[tex]A = 120160(1.06)^{2}[/tex]
A = 135,011.776
Hence , House A is more worth than House B .
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Please help me out!!!!!
Answer:
Okay I might not be right on this one but, I believe you divide 27 and 3. As to the part about simplifying, you might want to give me so details.
Step-by-step explanation:
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]
im not good with geometry
Answer:
neither am i bro no worries
Step-by-step explanation:
no cap
Answer:
Step-by-step explanation:
It's parallel to the side BC, from a known theorem (the segment linking the midpoints of two sides of a triangle is parallel to the third, and its lenght is half of it.
What is the amplitude and period of f(t)=-cos t
Answer:
c. amplitude: 1; period: [tex]2\pi[/tex]
Step-by-step explanation:
The given function is [tex]f(t)=- \cos t[/tex]
This function is of the form;
[tex]y=A \cos Bt[/tex]
where [tex]|A|[/tex] is the amplitude.
When we compare [tex]f(t)=- \cos t[/tex] to [tex]y=A \cos Bt[/tex], we have
[tex]A=-1[/tex], therefore the amplitude of the given cosine function is [tex]|-1|=1[/tex]
The period is given by;
[tex]T=\frac{2\pi}{|B|}[/tex]
Since B=1, the period is [tex]T=\frac{2\pi}{|1|}=2\pi[/tex]
Answer:
c. amplitude: [tex]\displaystyle 1;[/tex]period: [tex]\displaystyle 2\pi[/tex]
Explanation:
[tex]\displaystyle f(t) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]
With the above information, you now should have an idea of how to interpret graphs like this.
I am joyous to assist you at any time.
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
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
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.
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
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.
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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 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
A salesperson set a goal to earn $2,800 in October. He receives a base salary of $1,400 per month as well as a 8% commission for all sales in that month. How many dollars of merchandise will he have to sell to meet his goal?
Answer:
[tex]\$17,500[/tex]
Step-by-step explanation:
Let
x----> that month's sales
y----> October earnings
we know that
[tex]8\%=8/100=0.08[/tex]
[tex]y=0.08x+1,400[/tex] -----> equation A
[tex]y=2,800[/tex] -----> equation B
Equate equation A and equation B and solve for x
[tex]2,800=0.08x+1,400[/tex]
[tex]0.08x=2,800-1,400[/tex]
[tex]x=1,400/0.08[/tex]
[tex]x=\$17,500[/tex]
Final answer:
The salesperson needs to earn an additional $1,400 on top of the base salary to meet the goal, which means they need to sell $17,500 worth of merchandise with an 8% commission rate.
Explanation:
To calculate the amount of merchandise the salesperson must sell to meet the goal of $2,800, we need first to understand how much more money is needed beyond the base salary. The salesperson receives a base salary of $1,400. Since the goal is $2,800, the additional amount needed from commission is $2,800 - $1,400 = $1,400.
With an 8% commission rate, we can set up an equation where the amount of merchandise sold (let's call it x) times the commission rate (0.08) equals the additional amount needed ($1,400). The equation is: 0.08x = $1,400. To find x, divide both sides by 0.08, therefore x = $1,400 / 0.08, which equals $17,500.
So, the salesperson will need to sell $17,500 worth of merchandise to meet the goal of earning $2,800 in October.
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