Tonia Sells Cars. Her yearly salary is $35,000 plus 8% of her sales. type and solve an equality to determine her necessary cells to earn over $50,000 step-by-step.
Step-By-Step Explanation:
Let x be the amount of sales of Tonia in a year.
8% of her sales is:
[tex]x\cdot\frac{8}{100}=0.08x[/tex]Her salary is this plus $35,000. If 'y' is the total yearly salary of Tonia, the equaltion is:
[tex]y=0.08x+35,000[/tex]We want y > 50,000. Replacing this value and solving for x:
[tex]\begin{gathered} 50,000<0.08x+35,000 \\ 50,000-35,000<0.08x \\ 15,000<0.08x \\ x>\frac{15,000}{0.08} \\ x>187,500 \end{gathered}[/tex]Answer:
The equality is 50,000 < 0.08x + 35,000
Tonia needs to sell over 187,500 sales to earn $50,000
QuestionDetermine the value(s) for which the rational expressionlist them separated by a comma, e.g. n = 2,3.-3n + 12is undefined. If there's more than one value,84n2 + 76n +16
A rational expression is defined for all real numbers except the zeros of the denominator.
Then, find the zeros of the denominator to find the values for which the given rational expression is undefined:
[tex]84n^2+76n+16=0[/tex]Use quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex][tex]\begin{gathered} n=\frac{-76\pm\sqrt[]{76^2-4(84)(16)}}{2(84)} \\ \\ n=\frac{-76\pm\sqrt[]{5776-5376}}{168} \\ \\ n=\frac{-76\pm\sqrt[]{400}}{168} \\ \\ n=\frac{-76\pm20}{168} \\ \\ n_1=\frac{-76+20}{168}=\frac{-56}{168}=-\frac{1}{3} \\ \\ n_2=\frac{-76-20}{168}=\frac{-96}{168}=-\frac{4}{7} \end{gathered}[/tex]Then, the given rational expression is undefined for:n= -1/3 , -4/7The graph of the function f(x)=log4(x) is stretched vertically by a factor of 2, reflected over the x-axis, reflected over the y-axis, and shifted down by 1 unit.Find the equation of the function g(x) described above.
Transformations on a lograrithmic function:
[tex]\begin{gathered} Reflections: \\ over\text{ x-axis: -}\log_bx \\ over\text{ y-axis:}\log_b(-x) \end{gathered}[/tex][tex]\begin{gathered} \text{Vertical stretching: }a\log_bx\text{ \lparen a is the factor of streatching\rparen} \\ \\ \end{gathered}[/tex][tex]Shift\text{ down k units:}\log_b(x)-k[/tex]Then, the given function after the given transformations is:[tex]g(x)=-2\log_4(-x)-1[/tex]reflect the point (2, -4) I very rhe y-axis
To reflect a point over the y-axis, you have to reverse the sign of the x-coordinate, the y-coordinate remains the same.
For example for a point P with coordinates (x,y) the reflection is
Original point → y-axis reflection
P(x,y) → P'(-x,y)
For the point (2,-4) the reflection over the y-axis is:
(2,-4) → (-2,-4)
Find the surface area of the pyramid . The surface area of the pyramid is _m2(Do not round until final answer .Then round to the nearest whole number as needed .)
surface area of the pyramid is
[tex]\begin{gathered} Atotal=Abase+\frac{Pbase\cdot Apothem}{2} \\ \end{gathered}[/tex]then
[tex]\begin{gathered} \text{Abase}=\frac{P\cdot\text{Apothembase}}{2} \\ \text{Abase}=\frac{18\cdot6\cdot9\sqrt[]{3}}{2}=841.77 \end{gathered}[/tex]and the total area is:
[tex]\text{Atotal}=841.77+\frac{6\cdot18\cdot18}{2}=841.77+\frac{1944}{2}=841.77+972=1814[/tex]answer: 1814 m^2
. When you carry a credit card, it is very easy to buy on impulse.
True
False
True. It is very easy to buy on impulse when we carry a credit card.
An impulse purchase is a case when we buy goods without any prior plan to do so instantly according to our own whims. This is more often than not done by the use of a credit card.
A credit card is an instrument that allows us to purchase goods/ services by borrowing within a certain limit from the bank.
Since when we use a credit card we do not have to pay instantly, we reason our purchase by a near raise in a job or some profit in business. Also, usually, we need to pay in installments for the items we used the credit for, the amount seems very small.
Therefore, we quickly decide to buy the item that might be unnecessary for us or might be too expensive.
To know more about impulse buying visit
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I need help with this math problem because I am having a hard time understanding the problem and finding the answer. Can u help me
Answer:
[tex]h(x)=\frac{x+1}{5x+7},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=-\frac{3}{2}\text{ }and\text{ }x=-\frac{7}{5}[/tex][tex]h^{-1}(x)=\frac{1-7x}{5x-1},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=\frac{1}{5}[/tex]
Explanation:
The notation for composition of functions is:
[tex](f\circ g)(x)=f(g(x))[/tex]In this case:
[tex]\begin{cases}f(x)={\frac{x}{x+2}} \\ g(x)={\frac{x+1}{2x+3}}\end{cases}[/tex]To do the composition, we replace the x in the f(x) with the function g(x):
[tex](f\circ g)(x)=f(g(x))=\frac{g(x)}{g(x)+3}=\frac{\frac{x+1}{2x+3}}{\frac{x+1}{2x+3}+2}[/tex]And solve:
[tex]=\frac{\frac{x+1}{2x+3}}{\frac{x+1}{2x+3}+2}=\frac{\frac{x+1}{2x+3}}{\frac{x+1}{2x+3}+\frac{2(2x+3)}{2x+3}}=\frac{\frac{x+1}{2x+3}}{\frac{5x+7}{2x+3}}=\frac{(x+1)(2x+3)}{(2x+3)(5x+7)}[/tex]Here, we can calcualte the domain. The function is not defined when teh denominator is 0, thus:
[tex]2x+3=0\Rightarrow x=-\frac{3}{2}[/tex][tex]5x+7=0\Rightarrow x=-\frac{7}{5}[/tex]Since the function can't be evaluated when x = -3/2, we can cancel the terms (2x+3) in the numerator and denominator:
[tex]\frac{(x+1)(2x+3)}{(2x+3)(5x+7)}=\frac{x+1}{5x+7}[/tex]Thus:
[tex]\begin{equation*} h(x)=\frac{x+1}{5x+7},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=-\frac{3}{2}\text{ }and\text{ }x=-\frac{7}{5} \end{equation*}[/tex]Now, to find the inverse of the function, we first switch the variables:
[tex]y=\frac{x+1}{5x+7}\Rightarrow x=\frac{y+1}{5y+7}[/tex]And solve for y:
[tex]\begin{gathered} \begin{equation*} x=\frac{y+1}{5y+7} \end{equation*} \\ . \\ x(5y+7)=y+1 \\ . \\ 5xy+7x=y+1 \\ . \\ 5xy-y=1-7x \\ . \\ y(5x-1)=1-7x \\ . \\ y=\frac{1-7x}{5x-1}\Rightarrow h^{-1}(x)=\frac{1-7x}{5x-1} \end{gathered}[/tex]And since the denominator can't be 0:
[tex]5x-1=0\Rightarrow x=\frac{1}{5}[/tex]Thus:
[tex]\begin{equation*} h^{-1}(x)=\frac{1-7x}{5x-1},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=\frac{1}{5} \end{equation*}[/tex]In a certain year, congress began debating a new health care bill. A poll of 1000 Americans at the time indicated that 434 opposed the bill, 248 favored the bill, and 318 were not sure. Based on these results assume you ask a randomly selected American this question. Express your answers as exact decimals. a) What is the probability that a randomly selected American was in favor of the bill?b) What is the probability that a randomly selected American was not in support of the bill?
Answer:
a) 0.248
b) 0.434
Explanation:
Given;
Total number of Americans in the poll = 1000
Number of Americans not in favor of the bill = 434
Number of Americans in favor of the bill = 248
Number of Americans that were not sure = 318
a) We can now go ahead and determine the probability that a randomly selected American was in favor of the bill using the below probability formula;
[tex]Probability\text{ of an event occurring = }\frac{Number\text{ of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex][tex]P(\text{Americans in favor of the bill) = }\frac{248}{1000}=0.248[/tex][tex]P(\text{Americans not in support of the bill) = }\frac{434}{1000}=0.434[/tex]find the absolute change and the percentage change for the given situation. 128 is increased to 704
SOLUTION
The absolute change is the difference between the final value and the initial value
[tex]\begin{gathered} \text{Absolute change =final value-initial value } \\ \text{ final value=704} \\ \text{ initial value=128} \end{gathered}[/tex]
If an employee makes $20.50 an hour and works 80 hours every 2 weeks, what is that employees annual income?
There are 52 weeks in a year.
The employee works 80 hours every 2 weeks. This means that his weekly hours worked wll be:
[tex]\frac{80}{2}=40\text{ hours per week}[/tex]If he earns $20.50 per hour, his weekly wages will be:
[tex]\Rightarrow20.50\times40=\$820[/tex]For 52 weeks in the year, he will earn:
[tex]52\times820=\$42640[/tex]The employee's annual income is $42,640.
you would probably use calculus to determine the area for which of the following shapes, I think it’s A
To determine the area of shape A we need to use calculus.
This comes from the fact that this is a curved figure. The other options don't need calculus since we can divide them in polygons from which we know how to determine the area.
The point A(8,-6) is reflected over the point (1, 1) and its image is point B. Whatare the coordinates of point B?
In point reflection, the distance from the preimage to the point of reflection is the same as the distance from the point of reflection to the image.
Hence, this means that if the preimage coordinates are
[tex](x,y)[/tex]and the image coordinates are
[tex](x\text{',y')}[/tex]and are reflected over a point
[tex](a,b)[/tex]It thus follows that
[tex]\begin{gathered} a=\frac{x+x^{\prime}}{2} \\ \text{and} \\ b=\frac{y+y^{\prime}}{2} \end{gathered}[/tex]From the question, the preimage is given as
[tex]A=(x,y)=(8,-6)[/tex]and it is reflected over the point
[tex](a,b)=(1,1)[/tex]Applying the formula above, we can calculate the coordinates of the image B
which expression will be easier to simplify if you use the associative property to change the groupingA.[-12+(-5)]+36B.[21+(-14)]+(-53)C.67+[3/2+(-1/2)]D.(70+30)+72
The expression:
[21+(-14)]+(-53)
will be easier to simplify using associative property as follows:
21 + [(-14) + (-53)]
So that, the two negative numbers are combined first.
what is HL? for kites and trapezoids
The HL means Hypotenuse Leg theorem which is useful when we have two right triangles inside a geometric figure.
The theorem tells us that two right triangles are congruent when
i need help with this question what does y represent?
In the given graph, we can observe the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included.
Then, we can say in the x-axis we have the number of boxes already included and in the y-axis, we have the allowed weight remaining.
So, when x=0, there is any box in the shipment, y=70, so the total allowed weight in the given shipment is 70.
Answer: y reprensents the allowed weight remaining in the shipment.
Vhat type of move takes Figure Ato Figure B? Explainyour reasoning
Figures A and B appear to be congruent, i.e. they are from equal size.
This is a reflection over the e line.
The image looks like it's a 180º rotation.
I need help with math
We are told that in the past month, ms Jeffers flew ( 1716 +984+2058) miles for work,
This month she flew 4 x ( 1716 +984+2058)miles.
If we were to compare the distance flown this month with last month, we see that
"Ms. Jeffers flew four times more distance this month than she flew last month".
if m is the midpoint of a line XY, find the coordinates of x if m(-3, -1) and Y(-8, 6)
ANSWER:
X(2, -8)
Given:
m(-3, -1), Y(-8, 6)
To find the coordinates of X, use the midpoint formula below:
[tex](x_{m.}y_m)\text{ = (}\frac{x1+x2}{2},\text{ }\frac{y1+y2}{2})[/tex]Where,
(xm, ym) = (-3, -1)
(x2, y2) = (-8, 6)
Let the coordinates of x be (x1, y1)
Therefore, we have:
[tex]\begin{gathered} x_m\text{ = }\frac{x1+x2}{2} \\ \text{Substitute values to solve for x}1 \\ -3\text{ =}\frac{x1+(-8)}{2} \\ -6\text{ = x1 - 8} \\ x1\text{ = -6 + 8} \\ x1\text{ = 2} \end{gathered}[/tex][tex]\begin{gathered} \text{For y1:} \\ y_m\text{ = }\frac{y1+y2}{2} \\ Substitute\text{ values in the equation to find y1:} \\ -1\text{ = }\frac{y1+6}{2} \\ 2(-1)\text{ = y1 + 6} \\ -2\text{ = y1 + 6} \\ y1\text{ = -6 - 2} \\ y1\text{ = -8} \end{gathered}[/tex]The coordinates of X(x1, y1) = X(2, -8)
I need help solving the volume of the triangular prism
In general, the volume of a triangular prism is given by the formula below
[tex]\begin{gathered} V=\frac{\text{bhl}}{2} \\ b\to\text{ basis of the triangular base} \\ h\to\text{ height of the triangular base} \\ l\to\text{ height of the prism} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} b=9,h=5.2,l=6 \\ \Rightarrow V=\frac{9\cdot5.2\cdot6}{2}=140.4 \end{gathered}[/tex]The volume of the prism is 140.4cm^3
I need help with this question please. The ending of the question says: give the leading coefficient.
Given the polynomial:
[tex]-x^3+10x-4x^5+3x^2+7x^4+14[/tex]You need to remember the following definitions:
- The degree of a polynomial is the highest exponent.
- The Leading Coefficient is the number that multiplies the variable with the highest exponent.
- The Standard Form of a polynomial shows the terms in descending numerical order.
In this case, you can identify that:
1. The highest exponent of the polynomial is 5. Therefore:
[tex]Degree\colon5[/tex]2. The Constant Term is:
[tex]14[/tex]Therefore, you can rewrite it in descending numerical order:
[tex]\begin{gathered} \\ =-4x^5+7x^4-x^3+3x^2+10x+14 \end{gathered}[/tex]Now you can identify that the Leading Coefficient is:
[tex]-4[/tex]Hence, the answer is: Last option.
The number of members for an e-commerce company was 1,700 in the year that the company started and has increased by 10% per year since then. Theexponential function of the number of members, M(f), in terms of t, the number of years since the year the company started, can be described by M(t) =1700(1.10). What is M(5) and its interpretation in the context of the problem?OM(5)-9350; After 5 years, there are approximately 9,350 members in the company.OM(5)=2737.867; After 5 years, there are approximately 2,737 members in the company.OM(5) 1786.717; After 5 years, there are approximately 1,786 members in the company.OM(5) 1870: After 5 years, there are approximately 1,8705 members in the company.W
Solution
Step 1
Given data
Initial members p = 1700
Rate of increase = 10% = 10/100 = 0.1
time t = 5
Step 2
Using exponential increase formula
[tex]\begin{gathered} A\text{ = p\lparen1 + r\rparen}^t \\ \\ A\text{ = 1700}\times(1\text{ + 0.1\rparen}^5 \end{gathered}[/tex]Step 3
Simplify the expression for the value of A
[tex]\begin{gathered} A\text{ = 1700}\times1.1^5 \\ \\ A\text{ = 2737.867} \end{gathered}[/tex]Final answer
After 5 years, there are approximately 2,737 members in the company.
The length of a rectangle is three times its width. If we decrease the length by two meters and increase the width by 4 meters, the surface increases by 52m².Find the dimensions of the rectangle
Let the length of rectangle is l and width of the rectangle is w.
The area of rectangle obtained is
[tex]A=l\times w[/tex]It is given that length of rectangle is three times the width.
[tex]l=3w[/tex]It is also given that the length decrease by 2 m and width increase by 4 m andsurface increases by 52 sq.m.
[tex]l\times w^{}+52=(l-2)(w+4)[/tex]Now susbtitute the length equals to 3w in the equation.
[tex]3w^2+52=lw+4l-2w-8[/tex][tex]3w^2+52=3w^2+12w-2w-8[/tex][tex]52=10w-8[/tex][tex]10w=60[/tex][tex]w=6m[/tex]Therefore , the length of the rectangle is
[tex]l=3\times6=18m[/tex]Hence the length of rectangle is 18 m and width is 6m.
Can you help me review these questions for Algebra I? I am trying to see which of my answers are possibly incorrect.
To find:
The value of given expression at x = 1 and y = 2.
[tex](3x\times x)^2-(\frac{x}{y})^{-2}[/tex]Solution:
It is known that
[tex]a^{-b}=(\frac{1}{a})^b[/tex]Substitute x = 1 and y = 2, in the expression and simplify as follows:
[tex]\begin{gathered} (3x\times x)^2-(\frac{x}{y})^{-2}=(3(1)\times1)^2-(\frac{1}{2})^{-2} \\ =(3)^2-(2)^2 \\ =9-4 \\ =5 \end{gathered}[/tex]Thus, the answer is 5.
an 1,020 + (n-1)(-20) find a12
we have the expression
an= 1,020 + (n-1)(-20)
find a12
For n=12
a12=1,020+(12-1)(-20)
a12=1,020+(11)(-20)
a12=1,020-220
a12=800What is the reference angle of -139 degrees
41º
1) Since we want to find the reference angle for a -139º angle, we need to resort to the following formula
[tex]Reference\:Angle\:\:Quadrant\:III=180^{\circ}-139^{\circ}=41^{\circ}[/tex]2) Note that a -139 angle is in quadrant III, since negative angles are clockwise oriented
3) Thus the Reference Angle is 41º
Answer:
41°
Step-by-step explanation:
Find the acute angle in the first quadrant used as a reference for
−139°.
41°
whats 1+1A. 2B. 4C. 7D.11
Given the equation :
[tex]1+1=\text{?}[/tex]So, by adding the numbers the result will be: 1 + 1 = 2
so, the answer is option A. 2
The accurate scale diagram shows a telephone mast and a box. Find an estimate for the real height, in metres, of the telephone mast. telephone mast +2.5 m box
The estimate for the real height of the telephone mast is of 9 meters, using proportions.
What is a proportion?A proportion is a fraction of a total amount, and equations are built with these fractions and estimates to find the desired measures in the problem using basic arithmetic operations such as multiplication and division.
In this problem, the telephone box and the mast are similar figures, hence their side lengths are proportional.
The, the following proportional relationship is established:
10.8 cm / 1.8 cm = x / 1.5 cm.
The left side of the relationship can be simplified, as follows:
6 = x / 1.5 cm.
Then the estimate is found applying cross multiplication, as follows:
x = 6 x 1.5 cm = 9.5 cm².
Missing InformationThe diagram is given by the image at the end of the answer.
More can be learned about proportions at https://brainly.com/question/24372153
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A company makes regular and tall boxes. The base area of each box is 5 ft. The volume of the regular box is 40 ft. The tall box is 3 ft taller. What is the volume of the tall box?
The base area of each box (regular and tall boxes) = 5 ft².
The volume of the regular box = 40 ft³.
The height of the regular box is given by:
[tex]\text{ height = }\frac{\text{ volume}}{a\text{rea}}=\frac{40}{5}=8\text{ ft.}[/tex]The tall box is 3 feet longer than the regular box.
Hence, the height of the tall box = 8 + 3 = 11 ft.
The volume of the tall box is given by:
[tex]\begin{gathered} \text{ Volume = Area x height} \\ =5ft^2\text{ x 11 ft} \\ =55ft^3 \end{gathered}[/tex]Therefore, the volume of the tall box is 55 ft³
a metal alloy weighing 6 mg and containing 32% gold is melted and mixed with 12 mg of a different alloy which contains 2% gold. what % of the resulting alloy is gold? explain all of your work.
12% of the resulting alloy is gold
Here, we want to calculate the percentage of the resulting alloy that is gold
We proceed as follows;
(32% of 6mg) + (2% of 12mg)
That would be;
1.92 + 0.24 = 2.16
What means that of the total (6mg + 12mg) , 2.16 mg is gold
Thus the gold percentage will be;
[tex]\frac{2.16}{18}\text{ }\times\text{ 100 = 12 percent}[/tex]1. Find the roots of x^2 + 5 = -5x
To find the roots of the equation:
[tex]x^2+5=-5x[/tex]we can use the general formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]First we need to write the equation in the form:
[tex]ax^2+bx+c=0[/tex]Then the equation given takes the form:
[tex]x^2+5x+5=0[/tex]now we identify that a=1, b=5 and c=5. Plugging this values into the general formual we have:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(1)(5)}}{2(1)} \\ =\frac{-5\pm\sqrt[]{25-20}}{2} \\ =\frac{-5\pm\sqrt[]{5}}{2} \end{gathered}[/tex]Hence the roots are:
[tex]\begin{gathered} x=\frac{-5+\sqrt[]{5}}{2} \\ \text{and} \\ x=\frac{-5-\sqrt[]{5}}{2} \end{gathered}[/tex]