Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD:
15.70(d-3)=2.30
3d - 15.70 = 2.30
15.70d-3=2.30
3(d-15.70)=2.30
Which inequality is represented by the graph?
Answer:
it's option c ............
Are the two triangles similar? If so, state the reason and the similarity statement
Two sides are in same proportion and the included angle is common as per SAS. Therefore, both the triangles are similar.
Triangle:
A triangle is the three-sided polygon, which has three vertices. The three sides are interconnected with each other end to end at a point, which forms the angles of the triangle.
Here there are two triangles KLP and KMN. And the sum of all three angles of the two triangle is equal to 180 degrees.
Given,
Here we have the two triangle and we need to find that they are similar or not.
For that we have to calculate the total length of the sides of the triangle,
That,
KM = KL + LM
KM = 8 + 2 = 10
Similarly,
KN = KP + PN
KN = 12 + 3 = 15
In triangles KLP & KMN,
KL/KP = 8/12 = 2/3
Similarly, for the triangle KMN,
KM/KN = 2/3
Here the angles have the same values so they are parallel. Which states that, Angle O is common in both the triangles.
Therefore, the two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.
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How much should be invested now at an interest rate of 7% per year, compounded continuously, to have 2000 dollars in three years? Do not round intermediate computations, and round your answer to the nearest cent
Answer:
The amount that should be invested is $1621.16
Explanation:
The formula for continuous compound interest is:
[tex]A=Pe^{rt}[/tex]Where:
A is the amount of money after t years
P is the invested amount (what we want to find, in this case)
r is the rate of compounding in decimal
t i the amount of time compounding, in years
Then, in this case:
A = $2000
r = 0.07 (to convert percentage to decimal, we divide by 100: 7% / 100 = 0.07)
t = 3 years
Then:
[tex]2000=Pe^{0.07\cdot3}[/tex][tex]2000=Pe^{0.21}[/tex][tex]P=\frac{2000}{e^{0.21}}\approx1621.16849[/tex]To the nearest cent, P = $1621.16
Solve the equation by working backward through the number trick.
x = 3
Explanations:The given equation is:
[tex]\frac{4(x+3)-6}{2}=\text{ 9}[/tex]Step 1: Cross multiply
4 ( x + 3) - 6 = 9(2)
Step 2: Remove the brackets by expanding the equation
4x + 12 - 6 = 18
4x + 6 = 18
Step 3: Collect like terms
4x = 18 - 6
4x = 12
Step 4: Divide both sides by 4
4x / 4 = 12 / 4
x = 3
points E,D and H are the midpoints of the sides of TUV, UV=100,TV=126,and HD=100, find HE.
Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:
[tex]\begin{gathered} \frac{VD}{VU}=\frac{HD}{TU} \\ \end{gathered}[/tex]Since D is the midpoint of VU, VD=50
[tex]\begin{gathered} \frac{50}{100}=\frac{100}{TU} \\ 50\times TU=100\times100 \\ TU=200 \end{gathered}[/tex]then
[tex]\begin{gathered} \frac{HE}{UV}=\frac{HD}{TU} \\ \frac{HE}{100}=\frac{100}{200} \\ HE=\frac{100}{200}\times100 \\ HE=50 \end{gathered}[/tex]The table shows the numbers of ships that visited a port in the past 5 years. Identify a polynomial function for thenumber of ships in thousands that visited the port in a given year.
The function is f(x) = 1.3x^2 + 0.1X
resents "three lessWrite the expression -- 5x(4 + 3x) using words,the sum of negative five times a number andfour minus three times the numberthe product of negative five times a numberand the quantity four plus three times thenumberthe product of three times a number plus thequantity four and five times the numberpresents "thetwo less than theDONE
Given:
[tex]=-5x(3x+4)[/tex]Sol:.
The product of negative five times a number and the quantity four plus three times the number.
A bucket can hold 26 litres of water when it is 8/9 full. How many litres can it hold when it is full?
Answer:
[tex]29.25\text{ liters}[/tex]Explanation:
Here, we want to know the amount of water the bucket can hold when full
Let us have the volume as x liters
Mathematically:
[tex]\begin{gathered} \frac{8}{9}\times x\text{ = 26} \\ \\ 8x\text{ = 9 }\times\text{ 26} \\ x=\text{ }\frac{9\times26}{8} \\ \\ x\text{ = 29.25 liters} \end{gathered}[/tex]Find the midpoint M of the line segment joining the points R = (-5. -9) and S = (1. -1).
Answer:
(-2,-5)
Step-by-step explanation:
(-5+1÷2, -9+(-1)÷2)
=(-4÷2, -10÷2)
=(-2,-5)
PLS HELP!!! Ill give 20 points!!!
Answer:
Step-by-step explanation:
22.57 cm inches are the net weight of the slope
A business could not collect $5,000 that it was owed. The total owed to the business was $100,000. What fraction of the total was not collected? (Express As Fraction)
Total owed to the business = $100,000
amount that could not be collected = $5000
Fraction of total not collected
[tex]\text{fraction not collected=}\frac{5000}{100000}=\frac{5}{100}=\frac{1}{20}[/tex]Which of the following is equal to the rational expression below when x+112x² – 121x +11A. +11B.X+ 11c. -11XD. X-11
SOLUTION
From the question we have
[tex]\frac{x^2-121}{x+11}[/tex]from difference of two squares, we have
[tex]\begin{gathered} \frac{(x-11)(x+11)}{x+11} \\ x+11\text{ above cancels the one below, we have } \\ x-11 \end{gathered}[/tex]Hence the answer is option D
In a data set, the median is less than the mean. What does that indicate about the data?A.It is skewed to the right.B.It is skewed to the left.C.It is symmetric.D.It is bell-shaped.
SOLUTION:
Step 1:
In this question, we are given the following:
In a data set, the median is less than the mean. What does that indicate about the data?
A. It is skewed to the right.
B. It is skewed to the left.
C. It is symmetric.
D. It is bell-shaped.
Step 2:
The diagram that explains the question above is:
A left-skewed distribution has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak.
A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions. That’s because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak.
Back to the question, in a data set, the median is less than the mean
It indicates that:
It is skewed to the right ( OPTION A )
Solve for y: 5 left parenthesis 3 y plus 4 right parenthesis equals 6 open parentheses 2 y minus 2 over 3 close parentheses The solution is Y = _______
ANSWER:
-8
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]5\cdot\mleft(3y+4\mright)=6\cdot\mleft(2y-\frac{2}{3}\mright)[/tex]Solving for y:
[tex]\begin{gathered} 15y+20=12y-4 \\ 15y-12y=-4-20 \\ 3y=-24 \\ y=-\frac{24}{3} \\ y=-8 \end{gathered}[/tex]The solution of y is equal to -8
Which relation is a function? choose all the correct answers.[1] (1, 0), (3, 0), (1, 1), (3, 1) (1, 3) [2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)[3] (2, 7), (6, 5), (4, 4), (3, 3), (2, 1)[4] (9, −3), (9, 3), (4, −2), (4, 2), (0, 0)
A relation is a function if an input value has only one output value. This means that a value of x must have only one value of y. Looking at the options,
1) for x = 1, there are different values of y. They include y = 0, 1, 3
for x = 3, y = 0, 1
This means that it is not a function
2) No value of x has more than one value of y. Thus, no input has more than one output. This means that it is a function
3) for x = 2, there are different values of y. They include y = 7, 1
This means that it is not a function
4) for x = 9, there are different values of y. They include y = - 3, 3
for x = 2, there are different values of y. They include y = - 2, 2
This means that it is not a function
Thus, the correct option is
[2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
f(x)=3x-4g(x)=-x^2+2x-5h(x)2x)^2+1j(x)=6x^2-8xk(x)=-x+7calculate (g+j)(x)
To calculate (g+j)(x) we need the function:
[tex]\begin{gathered} g(x)=-x^2+2x-5 \\ j(x)=6x^2-8x \end{gathered}[/tex]and we can made the addition so:
[tex]\begin{gathered} (g+j)(x)=g(x)+j(x) \\ (g+j)(x)=-x^2+2x-5+6x^2-8x \end{gathered}[/tex]and we can simplify
[tex](g+j)(x)=5x^2-6x-5[/tex]Make a tree diagram, Please complete number 18.Please be quick, I am in a hurry.
Explanation:
The question wants us to list out all the possible outcomes in question 18
From the question
We have a spinner that has 5 possible outcomes
[tex]\mleft\lbrace\text{Red, Orange, Green, Purple, Yellow}\mright\rbrace[/tex]The outcomes of flipping a coin are
[tex]\begin{gathered} \mleft\lbrace\text{Head, Tail}\mright\rbrace\text{ } \\ \text{which can be written as} \\ \mleft\lbrace H,T\mright\rbrace \end{gathered}[/tex]Thus, to get the possible outcomes, we will have
Someone help me please
Approximately 5 meters long.
What is the equation for this? I don't understand which piece of information is irrelevant.
It is given that she produce print of her photos at a cost of 4 dollar per print and a setup cost of 45 dollar per run.
Let the number of photos produced be x.
Then the equation formed is
[tex]C(x)=4x+45[/tex]The sellling cost given is the unnecessary data given in the question.
The total cost is determined by only the setup cost and cost produce per prints.
The graph formed for the total cost and number of photos produced is
X-axis represent the number of photos produced and Y-axis represent the total cost.
The population of the state of Colorado was about 5,846,000 people in 2020.
Which number best approximates the population as a single digit times a
power of 10?
OA. 6x 10-6
OB. 6 x 106
C. 5 × 105
D. 5 x 106
Answer: [tex]6 \times 10^6[/tex] which is choice B
==========================================
Method 1
5,846,000 rounds to 6,000,000 aka "6 million".
This converts to the scientific notation [tex]6 \times 10^6[/tex]
The first 6 is from "6 million", while the 6 as the exponent tells us to move the decimal point that many places to the right to go from 6.0 to 6,000,000
---------------
Method 2
Place a decimal point between the first two digits of 5,846,000 and erase the zeros at the end.
So we get 5.846
We must move the decimal point 6 spaces to the right to go from 5.846 back to 5,846,000 again
Therefore, [tex]5,846,000 = 5.846 \times 10^6[/tex]
Then the 5.846 rounds to 6.0 or simply 6 when rounding to the nearest whole number. This leads to [tex]6 \times 10^6[/tex]
suppose that z varies jointly with x and y. When x=2, y=2, z=7 write the equation that models the relationship
If the revenue function for a certain item is R(x)=20x−0.25x2, what is the marginal revenue for the 8th item? Do not include the dollar sign in your answer.
The marginal revenue of the 8th item from the revenue function is 16
How to determine the marginal revenue?From the question, the revenue function is given as
R(x) = 20x - 0.25x^2
To calculate the marginal revenue, we start by differentiating the revenue function
This is calculated as follows
R(x) = 20x - 0.25x^2
Differentiate the function
R'(x) = 20 - 0.5x
The above represents the marginal revenue function
So, we have
M(x) = 20 - 0.5x
For the 8th item, we have
M(8) = 20 - 0.5 x 8
Evaluate
M(8) = 20 - 4
Evaluate
M(8) = 16
Hence, the marginal revenue is 16
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when doing right triangle trigonometry how do you determine which sine you use like sin, cos etc?
Let's draw a right triangle to guide us:
Every right triangle will have one hypotenuse side and two leg sides. The hypotenuse is always the bigger one and it is always opposite to the right angle, so in this triangle the hypotenuse is a (the letter can change from exercise to exercise, but it is always the opposite to the rignt angle).
The legs can be classified as adjancent or opposite legs, but this is with respect to the angle we are using.
So, if we are using angle C, the opposite leg is the leg that is opposite to angle C, that is, c.
Thus, the adjancent leg is the leg that is touching the angle C, that is, b.
So, with respect to angle C, we have:
Hypotenuse - a
Opposite leg - c
Adjacent leg - b
The sine is the ratio between the opposite leg and the hypotenuse, always.
The cosine is the ratio between the adjacent leg and the hypotenuse, always.
The tangent is the ratio between the opposite leg and the adjacent leg, always.
For, for angle C, we have:
[tex]\begin{gathered} \sin C=\frac{c}{a} \\ \cos C=\frac{b}{a} \\ \tan C=\frac{c}{b} \end{gathered}[/tex]For angle B, we do the same, however now, the legs are switched, because the leg that is opposite to angle B is b and the leg that is adjance to angle B is c, so, for angle B:
Hypotenuse - a
Opposite leg - b
Adjacent leg - c
And we follow the same for sine, cosine and tangent but now for angle B and with the legs switched:
[tex]\begin{gathered} \sin B=\frac{b}{a} \\ \cos B=\frac{c}{a} \\ \tan B=\frac{b}{c} \end{gathered}[/tex]Questions regaring these ratios normally will present 2 values and ask for a third value. One of the values will be an angle, the other will be side (usually). So, we need to identify which angle are we working with and which sides are the hypotenuse, the opposite leg and adjancent leg with respect to the angle we will work with. Then we identify which of the side we will use and pick the ratio thet relates the sides we will use.
List all real values of x such that f(x) = 0, if there are no such real x, type DNE in the answer blank. If there is more than one real x, give a comma separated list (i.e: 1, 2) X =
Given the function defined as:
[tex]\begin{gathered} f(x)=-7+\frac{-8}{x-6} \\ \end{gathered}[/tex]The function can further be expressed as:
[tex]f(x)=-7-\frac{8}{x-6}[/tex]Find the LCM of the function;
[tex]\begin{gathered} f(x)=\frac{-7(x-6)-8}{x-6} \\ f(x)=\frac{-7x+42-8}{x-6} \\ f(x)=\frac{-7x+34}{x-6} \\ \end{gathered}[/tex]If f(x) = 0, then the value of x is calculated as:
[tex]\begin{gathered} \frac{-7x+34}{x-6}=0 \\ -7x+34=0 \\ -7x=0-34 \\ -7x=-34 \end{gathered}[/tex]Divide both sides of the equation by -7:
[tex]\begin{gathered} \frac{\cancel{-7}x}{\cancel{-7}}=\frac{\cancel{-}34}{\cancel{\square}7} \\ x=\frac{34}{7} \end{gathered}[/tex]Therefore the value of x if f(x) = 0 is 34/7
A dilation with a scale factor of 4 is applied to the 3 line segment show on the resulting image are P'Q', A'B', And M'N'. Drag and drop the measures to correctly match the lengths of The images
Given:
Scale factor = 4 (Dilation)
PQ = 2 cm
AB = 1.5 cm
MN = 3 cm
Find-:
[tex]P^{\prime}Q^{\prime},A^{\prime}B^{\prime}\text{ and }M^{\prime}N^{\prime}[/tex]Explanation-:
Scale factor = 4
So,
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ A^{\prime}B^{\prime}=4AB \\ \\ M^{\prime}N^{\prime}=4MN \end{gathered}[/tex]So the value is:
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ P^{\prime}Q^{\prime}=4\times2 \\ \\ P^{\prime}Q^{\prime}=8\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} A^{\prime}B^{\prime}=4AB \\ \\ A^{\prime}B^{\prime}=4\times1.5 \\ \\ A^{\prime}B^{\prime}=6\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} M^{\prime}N^{\prime}=4MN \\ \\ M^{\prime}N^{\prime}=4\times3 \\ \\ M^{\prime}N^{\prime}=12\text{ cm} \end{gathered}[/tex]Professor Torres is stucked in a burning building. He is leaning to the window on the 5th floor which is 60feets above the ground. For stability, the firefighter have to place the bottom of their ladder 15feet from the wall of the building. How long does the ladder needs to be to reach the window on the 5th floor and save professor Torres? round to 2 decimal place
The situation forms the right triangle above:
Where x is the length of the ladder.
Apply the Pythagorean theorem:
c^2 = a^2 +b^1
where:
c = hypotenuse = longest side = x
A &b = the other 2 legs of the triangle
Replacing:
x^2 = 60^2 + 15^2
Solve for x
x^2 = 3,600 + 225
x^2 = 3,825
x =√3,825
x = 61.85 ft
Sally wishes to purchase an IPhone 12. the price of the item is $849. the amount of money she save's per month is $70. The amount of money Sally already have's is $17. , , , : write your function and define your variables. your function should be in a slope-intercept form. what is ()input = number of months. and ()output = amount of money you need :: complete your input/output tabel. select 6 values for your input (). They can be consistent (, , , , , , ) Whatever the case, it should match your function. Substitute those values into your function to solve for your output () : create your graph. Clearly label your - and - axis and use an appropriation scale. Use the ordered pair from your input/output table to place on the graph. Connect your points with a straight line. : 1. how long will it take you to reach your goal and purchase your item? 2. looking at your data (table and graph) what is one observation you can make? 3. if you double your savings each month, how does this affect the time it takes to reach your goal amount? 4. how do you know your equation is a function?
How many 7 digit phone numbers can be created if the first digit cannot be a zero, and the lastnumber must be an odd number?
Given:
Number of digits = 7
The first digit cannot be zero
Last number = odd number
The possible numbers between other than zero is 9
and there are 5 odd numbers.
Hence, the number of possible combinations is:
[tex]\begin{gathered} =\text{ 9 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 5} \\ =\text{ 4500000} \end{gathered}[/tex]Answer: Option A
Mai works as a tutor for $12 an hour and as a waitress for $7 an hour. This month,she worked a combined total of 85 hours at her two jobs. Let t be the number of hours Mai worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.total earned (in dollars) = ?
Solution:
Let t be the number of hours Mai works as a tutor.
Given that She earns $12 a hour as a tutor, this implies that for t number of hours, she will earn
[tex]\begin{gathered} \$12\times t \\ =\$\text{ 12t} \end{gathered}[/tex]For the month, she worked a combined total of 85 hours. This implies that
[tex]\begin{gathered} 85=t\text{ + (number of hours worked as a waitress) } \\ \Rightarrow nu\text{mber of hours worked as a waitress = (85-t) hours} \end{gathered}[/tex]Her total eranings for the month is expressed as
[tex]\text{Total earnings = 12(number of hours worked as a tutor)+7(number of hours worked as a waitress)}[/tex]Recall that she earnes $7 an hour while working as a waitress.
Thus, we have her combined total amount in dollars expressed as
[tex]\text{Total earned (in dollars)=12t+7(85-t)}[/tex]Hence, the expression is
[tex]\begin{gathered} \text{12t+7(85-t) } \\ \text{open parentheses} \\ \Rightarrow12t+595-7t \\ \text{collect like terms.} \\ \text{thus, the expression is simplied to be} \\ 5t+595 \end{gathered}[/tex]Identify the rate, base, and portion.
21% of what number is 57?
Question content area bottom
Which values are given? Select the correct choice below and fill in any answer boxes in your choice. (Type an integer or a decimal. Do not perform the calculation.)
A.The base is (enter your response here) and the portion is (enter your response here). The rate is not given.
B.The rate is (enter your response here % ) and the portion is (enter your response here). The base is not given.
C. The rate is (enter your response here %) and the base is (enter your response here).
Given:
21% of what number is 57
Let the number = x
So, 21% of x = 57
so, the rate = 21%
and the base = x
and the portion = 57
So, the base is not given
so, the answer will be option B
B) the rate is 21% and the portion is 57. the base is not given.
