A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $165 (without tax) and thatthe calculator cost $25 more than thrice the cost of the textbook. Whatwas the cost of each item? Let x = the cost of a calculator andy = the cost of the textbook. The corresponding modeling system is { x = 3y + 25x + y =Solve the system by using the method of= 165substitution
Answers
We know that the calculator price (x) was 25 more than 3 times the price of the textbook (y).
This can be represented as:
[tex]x=3y+25[/tex]We also know that the sum of the prices of the two items is equal to $165:
[tex]x+y=165[/tex]We have to solve this system of equations with the method of substitution.
We can use the first equation, as we have already clear the value of x, to substitute x in the second equation and then solve for y:
[tex]\begin{gathered} x+y=165 \\ (3y+25)+y=165 \\ 4y+25=165 \\ 4y=165-25 \\ 4y=140 \\ y=\frac{140}{4} \\ y=35 \end{gathered}[/tex]With the value of y we can calculate x using the first equation:
[tex]\begin{gathered} x=3y+25 \\ x=3\cdot35+25 \\ x=105+25 \\ x=130 \end{gathered}[/tex]Answer: the solution as ordered pair is (x,y) = (130, 35)
Related Questions
solve the following equation for x..[tex]5x { }^{2} = 180[/tex]
Answers
The square root of 36 has 2 results, one positive and one negative.
[tex]\begin{gathered} x=\sqrt[]{36} \\ x=\pm6 \\ or \\ x_1=6\text{ and }x_2=-6\text{ } \end{gathered}[/tex]RecommendationsSkill plansMathLE Language artsScienceSocial studiesDE TX StandaAlgebra 10.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! Go toWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Students in a poetry class are writing poems for their portfolios. The teacher wants them towrite stanzas with certain numbers of lines each. Dan wrote 7 short stanzas and 6 longstanzas, for a total of 140 lines. Jim wrote 7 short stanzas and 2 long stanzas, for a total of84 lines. How many lines do the two sizes of stanzas contain?The short stanzas containlines and the long ones containlines.Submit
Answers
Answer:
Short stanzas contains 8 lines
Long stanzas contains 14 lines
Explanations:
Let the number of short stanzas be "x"
Let the number of long stanzas be "y"
If Dan wrote 7 short stanzas and 6 long stanzas, for a total of 140 lines, this is expressed mathematically as:
7x + 6y = 140 ............................ 1
Similarly, if Jim wrote 7 short stanzas and 2 long stanzas, for a total of
84 lines, this is expressed as:
7x + 2y = 84 ......................... 2
Solve both equations simultaneously using elimination method
7x + 6y = 140 ............................ 1
7x + 2y = 84 ......................... 2
Subtract both equations
6y - 2y = 140 - 84
4y = 56
y = 56/4
y = 14
Substitute y = 14 into equaton 1.
Recall that 7x + 6y = 140
7x + 6(14) = 140
7x + 84 = 140
7x = 140 - 84
7x = 56
x = 56/7
x = 8
This shows that the short stanzas contains 8 lines and the long ones contains 14 lines
Which of the following represents the LCM of 98 ab^ 3 and 231 a^ 3 ?
Answers
The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
Solution by using the division method:
This method consists of grouping by separating the numbers that will be decomposed on the right side by commas while on the left side we put the prime numbers that divide any of the numbers on the right side. We starting with the lowest prime numbers, divide all the row of numbers by a prime number that is evenly divisible into 'at least one' of the numbers. We stop when it is no longer possible to divide (the the last row of results is all 1's). See below how it works step-by-step.
2 | 98, 231
3 | 49, 231
7 | 49, 77
7 | 7, 11
11 | 1, 11
1 | 1, 1
The LCM is the product of the prime numbers in the first column, so:
LCM = 2 . 3 . 7 . 7 . 11 = 3234
Solution by listing multiples:
This method consists of listing the multiples of all the numbers that we want to find the LCM. Multiples of a number are calculated by multiplying that number by the natural numbers 2, 3, 4, ..., etc. See below:
* The multiples of 98 are 98, 196, 294, 392, 490, 588, ..., 3234
* The multiples of 231 are 231, 462, 693, 924, 1155, ..., 3234
Because 3234 is the first number to appear on both lists of multiples, 3234 is the LCM of 98 and 231.
Hence the answer is The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
To learn more about LCM click here https://brainly.com/question/233244
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i need help with this question parts c d and e
Answers
ANSWER :
c. None
d. 0
e. (-1, 0)
EXPLANATION :
c. Values of x in which f(x) = -2
From the illustration, the graph does not pass through the y = -2
So there's NO values of x that will give f(x) = -2
d. Values of x in which f(x) = -3
From the illustration, when x = 0, f(x) will be -3
So the value of x is 0
e. x-intercepts are the points in which the graph intersects the x-axis.
In this case, the graph intersects at point (-1, 0)
Graph the line x= -3 on the axes shown below. Type of line: Choose one
Answers
due to the equation that represents the line is a line with no slope defined and is drawn up and down and are parallel to the y-axis.
in this case, since x=-3 it means that this value won't change along the y-axis
The price of hamburger increased from .50 cent to .60 cent. What is the percent increase
Answers
The hamburguer was .50 cent and increased to 0.60 cent. Let's calculate the percent increase:
The percent increase may be calculated using the formula:
percent increase = [(final value - initial value)/initial value]*100
So:
[tex]\begin{gathered} \frac{0.6-0.5}{0.5}\cdot100= \\ \frac{0.1}{0.5}\cdot100= \\ 0.2\cdot100=20 \end{gathered}[/tex]So, the percent increase was 20%
if -x - 3y = 2 and -8x + 10y = 9 are true equations, what would would be the value of -9x + 7y?
Answers
To find the value we add both equations:
[tex]\begin{gathered} (-x-3y)+(-8x+10y)=2+9 \\ -9x+7y=11 \end{gathered}[/tex]Therefore the value of the expression given is 11.
The net of a rectangular prism is shown below. The surface area of each is labeled
Answers
Given:
Area of box I = 48 cm²
Area of box 2 = 24 cm²
Area of box 3 = 48 cm²
Area of box 4 = 24 cm²
Area of box 5 = 72 cm²
Area of box 6 = 72 cm²
• Let's find the values which represent the dimensions of the prism.
Let L represent the length.
Let w represent the width
Let h represent the height.
Now, to find the surface area of a rectangular prism apply the formula:
A = 2(wL + Lh + wh)
Now, given each rectangular face, we have:
Area of length and width, Lw = 72 cm²
Area of length and height, Lh = 48 cm²
Area of width and height, wh = 24 cm²
Now to find the dimensions, we have:
[tex]\begin{gathered} \frac{Lh}{wh}=\frac{48}{24} \\ \\ \frac{L}{w}=2 \\ \\ L=2w \end{gathered}[/tex]Now, substitute 2w for L in Lw:
[tex]\begin{gathered} Lw=72 \\ \\ 2w(w)=72 \\ \\ 2w^2=72 \\ \\ w^2=\frac{72}{2} \\ \\ w^2=36 \\ \\ \text{ take the square root of both sides:} \\ \sqrt{w^2}=\sqrt{36} \\ \\ w=6 \end{gathered}[/tex]Therefore, the width is 6 cm.
Now, substitute 6 for w in wh:
[tex]\begin{gathered} wh=24 \\ \\ 6*h=24 \\ \\ Divide\text{ both terms by:} \\ \frac{6*h}{6}=\frac{24}{6} \\ \\ h=4 \end{gathered}[/tex]Now, substitute 4 for h in Lh:
[tex]\begin{gathered} Lh=48 \\ \\ L*4=48 \\ \\ \text{ Divide both sides by 4:} \\ \frac{L*4}{4}=\frac{48}{4} \\ \\ L=12 \end{gathered}[/tex]Therefore, the values which represent the dimensions are:
4, 6, 12
ANSWER:
4, 6, 12
Determine the degree of the polynomial 2w with exponent of 2+ 2w:
Answers
The degree of the polynomial is 2, because the degree of a polynomial is defined as the same as the greater exponent on the polynomial.
In this case, w² is the greater, then the degree is 2.
There were 55.5 million people enrolled in Medicare in 2015. In 2009, there were 46.6million enrolled. Which value best represents the unit rate of change (slope) in millions per year?a)-1.48b) 1.48c) 19.1%d) -0.674
Answers
Let the number of people enrolled in Medicare be represented by y
Let the year be represented by x
So that,
[tex]\begin{gathered} (x_1,y_1)=(2015,55.5\text{ million)} \\ (x_2,y_2)=(2009,46.6\text{ million)} \end{gathered}[/tex]The unit rate of change (slope) in millions per year can be calculated by:
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \text{Hence,} \\ slope=\frac{46.6million_{}-55.5million_{}}{2009_{}-2015_{}} \\ slope=\frac{-8.9}{-6} \\ slope=1.48 \\ \end{gathered}[/tex]Therefore, the unit rate of change in millions per year is 1.48 [Option B]
xP(x)00.2510.0520.1530.55Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places
Answers
The Solution:
Given:
Required:
Find the standard deviation of the probability distribution.
Step 1:
Find the expected value of the probability distribution.
[tex]E(x)=\mu=\sum_{i\mathop{=}0}^3x_iP_(x_i)[/tex][tex]\begin{gathered} \mu=(0\times0.25)+(1\times0.05)+(2\times0.15)+(3\times0.55) \\ \\ \mu=0+0.05+0.30+1.65=2.0 \end{gathered}[/tex]Step 2:
Find the standard deviation.
[tex]Standard\text{ Deviation}=\sqrt{\sum_{i\mathop{=}0}^3(x_i-\mu)^2P_(x_i)}[/tex][tex]=(0-2)^2(0.25)+(1-2)^2(0.05)+(2-2)^2(0.15)+(3-2)^2(0.55)[/tex][tex]=4(0.25)+1(0.05)+0(0.15)+1(0.55)[/tex][tex]=1+0.05+0+0.55=1.60[/tex]Thus, the standard deviation is 1.60
Answer:
1.60
Which of the following numbers is irrational? (A)-1.325 (B)√8 (C)2 (D)4
Answers
Answer:
(B)√8
Explanation:
Irrational numbers are numbers which when converted to decimal can be written indefinitely without repeating.
Irrational Numbers are numbers that cannot be written as a terminating or repeating decimal.
Examples of Irrational Numbers are:
[tex]\sqrt{2},\text{ }\pi,\text{ }\frac{22}{7},\text{ }\sqrt{5}\text{, etc.}[/tex]From the given options, the number which is irrational is √8.
What is the future value of an ordinary annuity of ₱38,000 per year, for 7 years, at 8% interest compounded annually?
Answers
Annuities
The future value (FV) of an annuity is given by:
[tex]FV=A\cdot\frac{(1+i)^n-1}{i}[/tex]Where:
A is the value of the annuity or the regular payment
i is the interest rate adjusted to the compounding period
n is the number of periods of the investment (or payment)
The given values are:
A = $38,000
n = 7 years
i = 8% = 0.08
Substituting:
[tex]\begin{gathered} FV=\$38,000\cdot\frac{(1+0.08)^7-1}{0.08} \\ FV=\$38,000\cdot\frac{(1.08)^7-1}{0.08} \\ \text{Calculate:} \\ FV=\$38,000\cdot\frac{0.7138243}{0.08} \\ FV=\$38,000\cdot8.9228 \\ FV=\$339,066.53 \end{gathered}[/tex]The future value is $339,066.53
Find an equation of the line that has a slope of -1 and a y intercept of 2. Write your answer in the formy = mx + b.
Answers
Based on the information the equation would be:
y = -1x + 2
m=slope
b= y-intercept
When graphing an inequality in slope-intercept form, which of the folowing indicates that you have to shade ABOVE the boundary line? Select ALL that apply.
Answers
Explanation
When graphing an inequality in slope-intercept form, we are asked to find which of the folowing indicates that you have to shade ABOVE the boundary line. This can be seen below.
The symbols
[tex]>\text{ and }\ge[/tex]Indicates that one should shade above the boundary line, The only difference is that the boundary line is broken in the case of greater than and unbroken in the case of greater than or equal to.
Answer:
[tex]>\text{ and }\ge[/tex]
Suppose that E and F are independent P(E) = 0.8 and P(F) = 0.4What is P(E and F)?
Answers
Answer:
P(E and F) = 0.32
Explanation:
Given that E and F are independent, then
P(E and F) is the multiplication of P(E) and P(F).
P(E) = 0.8, and P(F) = 0.4
P(E and F) = 0.8 * 0.4 = 0.32
Which equation can be used to find the solution of (1/4)y+1=64 ? −y−1=3y−1=3−y+1=3y + 1 = 3
Answers
1/4 and 64 can be expressed as follows:
[tex]\begin{gathered} \frac{1}{4}=4^{-1} \\ 64=4^3 \end{gathered}[/tex]Substituting into the equation:
[tex]\begin{gathered} (4^{-1})^{y+1}=4^3 \\ 4^{(-1)(y+1)}=4^3 \\ 4^{-y-1}=4^3 \\ -y-1=3 \end{gathered}[/tex]A Use the information given to answer the question. A student works at a job in order to save money to buy a desktop computer. • The student works 80 hours each month. • The desktop computer costs $850. Part B If the student has already saved $150 and plans to save an additional $100 each week, the function g(w) = 100w + 150 represents the total amount of money, in dollars, saved after w weeks. What is the value of g(5)?
Answers
The function given is:
[tex]g\mleft(w\mright)=100w+150[/tex]Where
w represents the week
g(w) represents the total money
We want to fing g(5).
This means, put "5" into the function g.
Put "5" in place of "w" in the function g.
Shown below:
[tex]\begin{gathered} g(w)=100w+150 \\ g(5)=100(5)+150 \\ g(5)=500+150 \\ g(5)=650 \end{gathered}[/tex]Sketch the right triangle and find the length of the side not given if necessary approximate the light to the nearest thousandth
Answers
Let's take a look at our triangle:
Using the pythagorean theorem, we'll have that:
[tex]h^2=12^2+16^2[/tex]Solving for h,
[tex]\begin{gathered} h^2=12^2+16^2 \\ \rightarrow h=\sqrt[]{12^2+16^2} \\ \rightarrow h=\sqrt[]{400} \\ \\ \Rightarrow h=20 \end{gathered}[/tex]This way, we can conlcude that the missing side measures 20 units.
Solve the equation below 4X. If your answer is not a whole number enter it as a fraction in lowest terms, using the slash mark (/) as the fraction bar x-5=8x+9X=
Answers
Simplify the equation x - 5 = 8x + 9 to obtain the value of x.
[tex]\begin{gathered} x-5=8x+9 \\ x-8x=9+5 \\ -7x=14 \\ x=\frac{14}{-7} \\ =-2 \end{gathered}[/tex]So x = -2.
solve the equation1/4p-2/5=3/4p+7P=
Answers
Solve:
[tex]\frac{1}{4}p-\frac{2}{5}=\frac{3}{4}p+7[/tex]The LCM of the denominators is 4*5 = 20. So we multiply each term by 20 to eliminate denominators:
[tex]20\cdot\frac{1}{4}p-20\cdot\frac{2}{5}=20\cdot\frac{3}{4}p+20\cdot7[/tex]Operating:
[tex]5p-8=15p+140[/tex]Adding 8 and subtracting 15p:
[tex]5p-15p=8+140[/tex]Simplifying:
[tex]-10p=148[/tex]Dividing by -10:
[tex]p=\frac{148}{-10}[/tex]Simplifying:
[tex]p=-\frac{74}{5}[/tex]Which function could represent the height in feet, h, of a soccer ball t seconds after being kicked from an initial height of 1 foot?
Answers
Let h is the height of the ball after t seconds
The acceleration upward = -32 feet/sec.^2
This situation must be represented by a quadratic function
The form of the function is:
[tex]h=ut+\frac{1}{2}at^2+h_0[/tex]u is the initial velocity
a is the acceleration of gravity
t is the time
h0 is the initial height
From the given, the initial height is 1 foot
The acceleration of gravity is a constant value -32 ft/s^2
The initial velocity is unknown
Let us substitute the values given in the function
[tex]\begin{gathered} h=ut+\frac{1}{2}(-32)t^2+1 \\ h=ut-16t^2+1 \end{gathered}[/tex]Let us arrange the terms from greatest power of t
[tex]h=-16t^2+ut+1[/tex]We have only 1 function in the choices similar to our function
[tex]h=-16t^2+25t+1[/tex]The answer is the second choice
How many real solutions does the equation \displaystyle -2x^2-6x+15=2x+5−2x 2 −6x+15=2x+5 have?
Answers
-2x² - 6x + 15 = 2x +5
Re-arrange the equation
-2x² - 6x -2x+ 15-5=0
-2x² -8x + 10 = 0
Multiply through by negative one
2x² + 8x - 10 =0
Now;
solve by factorization
Find two numbers such that its product give -20x² and its sum gives 8x and 8x by them
That is;
2x² + 10x - 2x - 10 = 0
2x(x+5) -2(x+5) = 0
(2x - 2) (x+5) = 0
Either 2x - 2 = 0
2x = 2
x= 1
Or
x+5 = 0
x=-5
Hence it has 2 real solutions
Help me please don’t use me for pointsthis answer well be 12×
Answers
Answer:
9x + 3
Explanation:
Given the below expression;
[tex]1x-7+8x+10[/tex]The 1st to solving the above is to group like terms;
[tex]1x+8x-7+10[/tex]Let's go ahead and evaluate;
[tex]9x+3[/tex]Can someone please help me solve the following?Please put numbers on graph
Answers
Given:
The equation of the hyperbola is given as,
[tex]\frac{y^2}{25}-\frac{x^2}{4}=1........(1)^{}[/tex]The objective is to graph the equation of the hyperbola.
Explanation:
The general equation of hyperbola open in the vertical axis of up and down is,
[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\text{ . . . . . . . .(2)}[/tex]Here, (h,k) represents the center of the hyperbola.
The focal length can be calculated as,
[tex]c=\sqrt[]{a^2+b^2}\text{ . . . . (3)}[/tex]On plugging the values of a and b in equation (3),
[tex]\begin{gathered} c=\sqrt[]{5^2+2^2} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}[/tex]The foci can be calculated as,
[tex]\begin{gathered} F(h,k\pm c)=F(0,0\pm\sqrt[]{29}) \\ =F(0,\pm\sqrt[]{29}) \end{gathered}[/tex]The vertices can be calculated as,
[tex]\begin{gathered} V(h,k\pm a)=V(0,0\pm5) \\ =V(0,\pm5) \end{gathered}[/tex]To obtain graph:
The graph of the given hyperbola can be obtained as,
Hence, the graph of the given hyperbola is obtained.
a vector w has initial point (0,0) and terminal point (-5,-2) write w in the form w=ai+bj
Answers
The initial point is (0,0) and the terminal point (-5,-2).
First, graph the points:
Lets say that A= (0,0) and B = (-5,-2)
So my vector w= line(AB)
Use the component form
Replace the values <-5-0, -2-0>
Then <-5,-2>
In the form w=ai+bj
w = -5i -2j
Looking at the graph we have -2 on the y-axis and -5 on the x-axis.
Use the graph to write an equation for f(x).Oy=1(12)Oy=3(4)*Oy=12(4)*Oy=4(3)*
Answers
---------------------------------------------------------------------------------------------------------------
[tex]\begin{gathered} g(x)=36x-24 \\ g(1)=36(1)-24=36-24=12 \\ g(2)=36(2)-24=72-24=48 \end{gathered}[/tex][tex]y=36x-24[/tex]Macy is hosting a party to celebrate her son's baptism. There will be 6 children at the
party. Each child will receive 1/3 of a regular size adult portion. How many full adult
portions will be made to feed the 6 children?
Answers
Answer:
2
Step-by-step explanation:
three 1/3 makes a whole and there are 6 children so 3 and 3 is 6 so its 2
Suppose that the functions f and g are defined as follows.f(x) = x² +78g(x) =3x5x70Find the compositions ff and g9.Simplify your answers as much as possible.(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)
Answers
ANSWER
[tex]\begin{gathered} (f\cdot f)(x)=x^4+14x^2+49 \\ (g\cdot g)(x)=\frac{64}{9x^2} \end{gathered}[/tex]EXPLANATION
We are given the two functions:
[tex]\begin{gathered} f(x)=x^2+7 \\ g(x)=\frac{8}{3x} \end{gathered}[/tex]To find (f * f)(x), we have to find the product of f(x) with itself.
That is:
[tex](f\cdot f)(x)=f(x)\cdot f(x)[/tex]Therefore, we have:
[tex]\begin{gathered} (f\cdot f)(x)=(x^2+7)(x^2+7) \\ (f\cdot f)(x)=(x^2)(x^2)+(7)(x^2)+(7)(x^2)+(7)(7) \\ (f\cdot f)(x)=x^4+7x^2+7x^2+49 \\ (f\cdot f)(x)=x^4+14x^2+49 \end{gathered}[/tex]We apply the same procedure to (g * g)(x):
[tex]\begin{gathered} (g\cdot g)(x)=(\frac{8}{3x})(\frac{8}{3x}) \\ (g\cdot g)(x)=\frac{64}{9x^2} \end{gathered}[/tex]Those are the answers.
2 2. 8 friends are going on a camping trip. 5 friends own a sleeping bag. How many friends need a sleeping bag? + Il8-5=3
Answers
If 8 friends go camping and only 5 friends have sleeping bag
Then of the 8 friends, the number that need a sleeping bag would be
= 8 - 5
= 3
Hence 3 friends will be in need of a sleeping bag