Given that, they spent a total of 20 dollars.
Therefore, the first equation becomes,
[tex]x+y=20[/tex]Also, mom spent 8 more than 4 times the amount of daughter.
Therefore, the second equation becomes,
[tex]y=4x+8[/tex]Substitute 4x+8 for y in the equation x+y=20 implies,
[tex]\begin{gathered} x+4x+8=20 \\ 5x=12 \\ x=2.4 \end{gathered}[/tex]Use the equation x+y=20 to find the value of y.
[tex]\begin{gathered} y=20-x \\ y=20-2.4 \\ y=17.6 \end{gathered}[/tex]Therefore, daughter's spending is 2.4 dollars and mom's spending is 17.6 dollars
Line m has a y-intercept of cand a slope of 2, where p>0, q> 0, and p* q.What is the slope of a line that is parallel to line m?A.-OB. 2POC. -2OD. 2P
Step 1
Given; Line m has a y-intercept of cand a slope of 2, where p>0, q> 0, and p* q. What is the slope of a line that is parallel to line m?
Consider the line 5x-6y=1What is the slope of a line parallel to this line?What is the slope of a line perpendicular tothis line?
The equation of a line in slope-intercept form looks like this:
[tex]y=mx+b[/tex]Where m is known as the slope. All lines that have the same slope m are parallel whereas a line perpendicular to y=mx+b has a slope given by -1/m.
In this case we have the line 5x-6y=1. We should write it in slope-intercept form. In order to do this we can add 6y to both sides and substract 1 from both sides:
[tex]\begin{gathered} 5x-6y+6y-1=1+6y-1 \\ 5x-1=6y \end{gathered}[/tex]Then we divide both sides by 6:
[tex]\begin{gathered} \frac{6y}{6}=\frac{5x-1}{6} \\ y=\frac{5}{6}x-\frac{1}{6} \end{gathered}[/tex]Then the slope of this line is 5/6.
AnswerFollowing what we stated above we have these answers:
The slope of a line parallel to this is 5/6.
The slope of a line perpendicular to this is -6/5.
Could you help explain and work this out for me?
The equation of the Line L is 2x - y [tex]=[/tex] -1 .
In the question ,
a line graph is given ,
we can find two points from the line .
first point : when x = 1 , y is 3
the first coordinate is (1,3)
second point : when x = 2, y is 5 .
the second coordinate is (2,5)
the slope of the line passing through (1,3) , (2,5) is
m = (5-3)/(2-1)
m = 2/1
m = 2
the equation of line passing through (1,3) and slope as 2 is
y-3 = 2(x-1)
y - 3 = 2x - 2
2x - y = -3+2
2x - y = -1
Therefore , The equation of the Line L is 2x - y [tex]=[/tex] -1 .
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Find the exact interest for $180,000 at 7.5% for 180 days
Answer:
[tex]\text{ \$6,657.53}[/tex]Explanation:
Here, we want to calculate the interest value
Mathematically, we have this as:
[tex]\text{ I = }\frac{PRT}{100}[/tex]where:
P is the amount loaned which is given as $180,000
R is the interest rate which is 7.5%
T is the time given in days that will make us rewrite the equation above as follows:
[tex]\text{ I = P }\times\frac{R}{100}\times\frac{n}{365}[/tex]where n is the number of days in this context given as 180 days
Substituting the values, we have it that:
[tex]\text{ I = }\frac{180000\times7.5\times180}{100\times365}\text{ = \$6,657.53}[/tex]A coin is tossed upward with an initial velocity of 32 feet per second from a height of 16 feet above the ground.The equation giving the object's height h at any time t is h = 16 + 32t - 16t^2. Does the object ever reach a height of 32 feet?(Select an answer No or Yes! If so, when? (Answer "dne" if it does not.)It reaches 32 feet after___seconds.
Solution:
Given:
[tex]h=16+32t-16t^2[/tex]To get the maximum height, we differentiate. At maximum height, the velocity is zero.
Hence,
[tex]\begin{gathered} \frac{dh}{dt}=32-32t \\ when\text{ }\frac{dh}{dt}=0, \\ 0=32-32t \\ 32t=32 \\ t=\frac{32}{32} \\ t=1sec \end{gathered}[/tex]Thus, substitute t = 1 into the equation;
[tex]\begin{gathered} h=16+32(1)-16(1^2) \\ h=16+32-16 \\ h=32ft \end{gathered}[/tex]Since the maximum height is 32 feet, then the object reaches 32feet after 1 second.
Sharon wants to throw a baby shower for her sister. She is comparing two event halls to host the baby shower in. Event Hall A charges a hall rental fee of $300 plus $25 for each guest. Event Hall B charges $200 plus $35 for each guest. At how many guests will both companies charge the same amount? (Type only the numerical answer)
Let's call x to the number of guests.
Event Hall A cost: 300 + 25x
Event Hall B cost: 200 + 35x
If both companies charge the same amount:
300 + 25x = 200 + 35x
Solving for x:
300 - 200 = 35x - 25x
100 = 10x
100/10 = x
x = 10
Use a rectangular array to write the products in standard form
2x + 20
Explanation:Given:
[tex]2(x\text{ + 10\rparen}[/tex]To find:
To use a rectangular array to write the products in standard form
To use a rectangular array for the product, we will construct rectangles representing x and 10:
Next, we will multiply the expression outside by 2. The results will be in each box
The product in standard form will be the sum of each expression in the box = 2x + 20
[tex]2(x\text{ + 10\rparen = 2x + 20}[/tex]Find the equation of a line parallel to -3x - 5y = -6 that contains the point (-4,1). Write the equation in slope-intercept form.
Answer:
y=-0.6x+3.4
Explanation:
First, by definition, two lines are parallel if they have the same slope.
Given the equation of the line:
[tex]-3x-5y=-6[/tex]We find the slope by rewriting the line in the slope-intercept form:
[tex]y=mx+b\text{ where }\begin{cases}m={Slope} \\ b={y-intercept}\end{cases}[/tex]This gives:
[tex]\begin{gathered} -3x+6=5y \\ y=-\frac{3x}{5}+\frac{6}{5} \\ \implies\text{ The slope}=-\frac{3}{5} \end{gathered}[/tex]Since the two lines are to be parallel, the new line will have a slope of -3/5 and pass through the point (-4,1).
Substitute x=-4, y=1 and m=-3/5 into the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ 1=-4(\frac{3}{5})+b \\ b=1+\frac{12}{5} \\ b=3.4 \end{gathered}[/tex]The equation of the line is:
[tex]\begin{gathered} y=-\frac{3}{5}x+\frac{17}{5} \\ y=-0.6x+3.4 \end{gathered}[/tex]If f(x)=-3x-2, find each value
1. f(3)
2. f(-7)
3.f(-2)+9
Please and thanks!
Answer:
1. -11
2. 19
3. 13
Step-by-step explanation:
f(x) = -3x - 2
1. f(3) = -3(3) - 2
f(3) = -9 - 2
f(3) = -11
2. f(-7) = -3(-7) - 2
f(-7) = 21 - 2
f(-7) = 19
3. f(-2) + 9 = (-3(-2) - 2) + 9
f(-2) + 9 = (6 - 2) + 9
f(-2) + 9 = 4 + 9
f(-2) + 9 = 13
Find the maximum or minimum value of the product of two numbers whose difference is 14.49343-56-49
Given:
The difference between the two numbers is 14.
Required:
We need to find the maximum or minimum value of the product of two numbers whose difference is 14.
Explanation:
Let x be the first number.
The difference between the two numbers is 14.
The second number is x-14.
The product of the two numbers is
[tex]x(x-14)[/tex][tex]x^2-14x[/tex]Differentiate this with respect to x and equate it to zero.
[tex]2x-14=0[/tex][tex]2x-14+14=0+14[/tex][tex]2x=14[/tex]Divide both sides by 2.
[tex]\frac{2x}{2}=\frac{14}{2}[/tex][tex]x=7[/tex]Substitute x =7 in the product.
[tex](7)^2-14(7)=-49[/tex]Final answer:
The maximum or minimum value of the product of two numbers whose difference is 14 is -49.
The histogram below represents the prices of digital SLR camera models at a store. Describe the shape of thedistribution.
Unimodal and right-skewed
The mean of right-skewed data will be located to the right side of the graph and will be a greater value than either the median or the mode.
It is unimodal, with the mode closer to the right and greater than either mean or median.
What is the missing length of the side? 89 ft 80 ft A 120 ft B 9 39 ft D 30 ft
PythagoApply pythagorean theorem:
c^2 = a^2 + b^2
Where:
c = hypotenuse = 89 ft ( longest side)
a & b = the other 2 legs of the triangle = 80 ft & x
Replace:
89^2 = 80^2 + x^2
Solve for x ( missing side )
7,921 = 6,400+ x^2
7,921 - 6,400 = x^2
1,521 = x^2
√1,521 = x
39 = x
Missing side = 39 ft
State if the given binomial is a factor of the given polynomial [tex](10x ^{3} + 95x^{2} + 40x - 45) \div (x + 9)[/tex]
Answer:
The given binomial(x + 9) is a factor of the given polynomial by Factor Theorem
Explanation:
Given the below polynomial;
[tex]f(x)=10x^3+95x^2+40x-45[/tex]We're asked to state if the binomial (x + 9) is a factor of the above polynomial.
To do that, we have to apply the Factor Theorem, which states that if f(x) is a polynomial function, then (x - c) is a factor of f(x) if and only if f(c) = 0.
So let's go ahead and determine f(-9);
[tex]\begin{gathered} f(-9)=10(-9)^3+95(-9)^2+40(-9)-45 \\ =-7290+7695-360-45 \\ =0 \end{gathered}[/tex]Since f(-9) is 0, therefore by Factor Theorem, (x + 9) is a factor of the polynomial.
can you help me with this question? t = 10 please
Given:
Final Balance = $160,000
rate = 8% or 0.08
Compounding period = daily = 365 days
time in years = 10
Find: Principal or Initial Amount
Solution:
To determine the principal or the initial amount to be invested in order to have $160,000 at the end of 10 years with the given compounding rate, we have the formula below:
[tex]P=\frac{F}{(1+\frac{r}{m})^{mt}}[/tex]where:
P = Principal
F = Final Value = $160,000
r = annual rate = 0.08
m = compounding period = 365 days
t = time in years = 10
Let's plug into the formula above the given information.
[tex]P=\frac{160,000}{(1+\frac{0.08}{365})^{365\times10}}[/tex]Then, solve for P.
a. Add the terms inside the parenthesis and multiply its exponent.
[tex]P=\frac{160,000}{(1.000219178)^{3,650}}[/tex]b. Apply the exponent to the term in the denominator.
[tex]P=\frac{160,000}{2.22534585}[/tex]c. Divide the numerator by the denominator.
[tex]P\approx71,898.94[/tex]Answer:
Therefore, one must invest $71,898.94 in order to produce a final balance of $160,000 at the end of 10 years given that the rate is 8% compounded daily.
I need help with number twelve please and thank you for your help
Given:
The length of the extension cord is 5 feet.
We know that,
[tex]1\text{ foot = 12 inches}[/tex]So, the length of the extension cord in inches is,
[tex]\begin{gathered} 5\text{ feet= 5}\times12\text{ inches} \\ 5\text{ feet= 60 inches} \end{gathered}[/tex]Answer: Option A)
Find all solutions of the equation x+1+5/x=0 and give your answer as a list of complex numbers, such as 3-4i, 5+i.
Given:
[tex]x+1+\frac{5}{x}=0[/tex]Simplify the equation,
[tex]\begin{gathered} x+1+\frac{5}{x}=0 \\ x^2+x+5=0 \\ \text{Compare it with ax}^2+bx+c=0 \\ a=1,b=1,c=5 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-1\pm\sqrt{1^2-4\cdot\:1\cdot\:5}}{2\cdot\:1} \\ x=\frac{-1\pm\sqrt{19}i}{2\cdot\:1} \\ x=\frac{-1+\sqrt{19}i}{2},\: x_{}=\frac{-1-\sqrt{19}i}{2} \\ x=-\frac{1}{2}+i\frac{\sqrt{19}}{2},\: x=-\frac{1}{2}-i\frac{\sqrt{19}}{2} \end{gathered}[/tex]Answer: The root of equation is,
[tex]x=-\frac{1}{2}+i\frac{\sqrt[]{19}}{2},\: x=-\frac{1}{2}-i\frac{\sqrt[]{19}}{2}[/tex]Find an equation of the line containing the centers of the two circles whose equations are given below.x2+y2−4x+6y+4=0x2+y2+6x+4y+9=0
Given the first circle:
x²+ y² − 4x + 6y + 4 = 0
x²+ y² − 4x + 6y = - 4
x² − 4x + 4 + y² + 6y + 9 = - 4 + 4 + 9
(x - 2)² + (y + 3)² = 9
The center of the circle is the point (2, -3) and the radius r = 3
Now, for the second circle:
x² + y² + 6x + 4y + 9 = 0
x² + 6x + 9 + y² + 4y + 4 = - 9 + 9 + 4
(x + 3)² + (y + 2)² = 4.
The center of the circle is the point (- 3, - 2) and the radius r = 2
Finally, we need to find the equation of the line ( y = mx + b), that crosses through the points (- 3, - 2) and (2, -3):
[tex]\begin{gathered} \text{m = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{-3\text{ + 2}}{2\text{ + 3}}\text{ = }\frac{-1}{5} \end{gathered}[/tex]To find b, we replace one point on the linear equation:
y = mx + b
-3 = (-1/5)(2) + b
b = -13/5
So, the equation of the line is:
y = (-1/5)x - 13/5
The ticket sales for concert started at 4:00 the table shown the linear realashionship bewtween the number of tickets remaining and the number of hours since 4:00
Answer:
y = -3000x + 15000
Explanation:
To find the equation that represents the table, we will use two ordered pairs like (1, 12000) and (2, 9000)
The first coordinate represents the number of hours after 4 p.m. and the second coordinate represents the number of tickets remaining.
Then, to find the equation of a line that passes through the points (x1, y1) and (x2, y2) we can use:
[tex]y-y_1=m(x-x_1)[/tex]Where m is equal to:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (x1, y1) by (1, 12000) and (x2, y2) by (2, 9000), we get that m is equal to:
[tex]m=\frac{9000-12000}{2-1}=\frac{-3000}{1}=-3000[/tex]Then, the equation is:
[tex]\begin{gathered} y-12000=-3000(x-1) \\ y-12000=-3000x-3000(-1) \\ y-12000=-3000x+3000 \\ y-12000+12000=-3000x+3000+12000 \\ y=-3000x+15000 \end{gathered}[/tex]Therefore, the answer is:
y = -3000x + 15000
The line graph shown below is of the amount of money astudent earns at a part time job, per hour. What is the students wage rate (in terms of dollars per hour)?
SOLUTION
From the question let us take any two points.
Let's take (1, 10) and (2, 20)
We have rate as
[tex]\begin{gathered} =\frac{20-10}{2-1} \\ =\frac{10}{1} \\ =10 \end{gathered}[/tex]Hence the answer is $10 per hour
State whether the given scale factor would enlarge, reduce, or preserve the size of a figure
Scale factor = 0.75 Reduce
Scale factor = 4/5 Reduce
Scale factor = 4.2 Enlarge
Scale factor = 8/8 Preserve
Scale factor = 7/2 Enlarge
Scale factor = 1 Preserve
Scale factor = 0.1 Reduce
Scale factor = 12 Enlarge
A scale factor is usually a decimal which scales, or multiplies, some quantity.
What is 2 divided 5?Draw a diagram that explains how you know.
see the figure below to better understand the problem
I divided the segment between 0 and 2 into 5 spaces
The value of each space is
(2-0)/5=2/5
so
If you multiply the width of each space (2/5) by the number of spaces, the result must be equal to 2
Verify
(2/5)*5=2 is ok
so it’s the angle sun theory but i don’t understand it at all
ANSWER
[tex]30\degree[/tex]EXPLANATION
The angle sum theory states that:
This implies that:
[tex]x+x+60+60=180[/tex]Solve for x in the equation above:
[tex]\begin{gathered} 2x+120=180 \\ \Rightarrow2x=180-120=60 \\ x=\frac{60}{2} \\ x=30\degree \end{gathered}[/tex]That is the value of x.
in which of the following is y a function of x?
The answer will be only III which is letter C.
i need help In this work
After a sequence of reflections, translations and rotations, segment AB would be located in a different place and a different way, but its length would not change. It means, after these transformations, the segment will always be 4 units long, then, an image of segment AB could be each segment that measures 4 units. Those are:
line segment CD
line segment GH
line segment NP
Explain how solve 4^(x+3)=7 using the change of base formula: (imaged below). Include the solution for x in your answer and round to the nearest thousandth
we have the equation
[tex]4^{(x+3)}=7[/tex]Solve for x
Apply log of base 4 on both sides
so
[tex]\begin{gathered} \log_44^{(x+3)}=\log_47 \\ \\ (x+3)\operatorname{\log}_44=\operatorname{\log}_47 \\ \\ (x+3)=\log_47 \\ \\ x=\log_47-3 \\ \end{gathered}[/tex]Apply change of base
we have that
[tex]\log_47=\frac{log7}{log4}[/tex]substitute
[tex]\begin{gathered} x=\frac{log7}{log4}-3 \\ \\ x=-1.596 \end{gathered}[/tex]50.26 round to the nearest tenth
To round a number to the nearest tenth we look at the hundredth place
If the digit in the hundredth place is 5 or greater than 5, then we add the digit in the tenths place by 1 and remove the digits right to it
If the digit in the hundredth place is less than 5, we removed all the digits right to the tenth digit
Since the number is 50.26
The digit in the hundredth place is 6 (greater than 5)
Then add the digit in the tenths place by 1 and remove the digit in the hundredth place
The number is 50.3
50.26 is rounded to 50.3 to the nearest tenth
Carter plays 5/8 of a basketball game, The basketball games Is 40 minutes long. Which of the following shows how to find the number of minutes Carter plays?
Answer: C
[tex]\frac{5\times5}{8\times5}=\frac{25}{40}\text{ ; 25 minutes}[/tex]Explanation:
Given that Carter plays 5/8 of a basketball game.
Which means he play 5 out of every 8 minutes of the game.
Since a game is 40 minutes, the number of minutes he plays per game is;
[tex]\begin{gathered} \frac{5}{8}=\frac{5\times5}{8\times5}=\frac{25}{40}\text{ ; 25 minutes} \\ \text{which means he plays 25 minutes out of the 40 minutes of the game.} \end{gathered}[/tex]For every 40 minutes of the game he plays 25 minutes.
Write the following rational expression in lowest term
Given rational expression is
[tex]\frac{t^2-4}{6t-12}[/tex]Factor the numerator and denominator first.
[tex]\begin{gathered} t^2-4=t^2-2^2 \\ =(t+2)(t-2) \end{gathered}[/tex]Factor the denominator 6t-12:
[tex]\begin{gathered} 6t-12=6t-6\cdot2 \\ =6(t-2) \end{gathered}[/tex]So,
[tex]\begin{gathered} \frac{t^2-4}{6t-12}=\frac{(t+2)(t-2)}{6(t-2)} \\ =\frac{t+2}{6} \end{gathered}[/tex]Therefore, the given expression in lowest form is
[tex]\frac{t+2}{6}[/tex]What is the value of x that satisfies the equations?
ANSWER
x = 2
EXPLANATION
We have two graphs in the picture.
Each of them represents a linear function:
y = x
and
x + 2y = 6
For the graphs, the value of x that satisfies the linear equations is that value of x such that the value of y in the two equations are equal.
A simple way of obtaining it is to look at where the two graphs intersect one another and note the value of x.
From the graph, the value of x where the two lines intersect is 2.
So, the value of x that satisfies the equations is x = 2.
Note: One way to verify this is to put the value of x = 2 in both equations
Elizabeth sells 12 bows for 12.12 what is the cost of each bow?
Unit Price
The unit price can be calculated by dividing the total price of n items by n:
Elizabeth sold n=12 bows for $12.12, so the unit price is:
$12.12 / 12
=$1.01
The cost of each bow is $1.01
The long division requires us to arrange the number like:
12 | 12.12
The division starts by dividing 12 (of the dividend 12.12) by 12 (the divisor). We get 1. It must be placed atop the dividend::
| 1
12 | 12.12
Now multiply 1x12 and subtract from the dividend:
| 1
12 | 12.12
| -12
|----------
| 0.12
We have found the decimal point. Remove it and add it to the quotient.
| 1.
12 | 12.12
| -12
|----------
| 12
Divide 1 by 12. It's not possible, so we add a 0 to the quotient:
| 1.0
12 | 12.12
| -12
|----------
| 12
Now we divide 12 by 12 again and get 1. This is added to the quotient and subtract 1*12 from the dividend:
| 1.01
12 | 12.12
| -12
|----------
| 12
| -12
| ---------
| 0
The remainder is 0 and the quotient is 1.01