Answer
Cost of desktop = $1750
Cost of laptop = $1900
Explanation:
Let the price of the desktop computer be x
Let the price of laptop computer be y
Laptop cost $150 more than desktop
Therefore, the cost of laptop y is given mathematically below
y= x + 150 ------------ equation 1
The interest rate of laptop is 9.5%
The interest rate of desktop is 7%
A sum of $303 was paid for the total financial charges
This statement can be represented mathematically as
0.07x + 0.095y = 303 ------------------ equation 2
Combine the two system of equations together and solve simultaneously
y = x + 150 ------------ equation 1
0.07x + 0.095y = 303 ---equation 2
Substitute the value of y in equation 2
0.07x + 0.095(x + 150 ) = 303
Open the parentheses
0.07x + 0.095x + 14.25 = 303
Collect the like terms
0.07x + 0.095x = 303 - 14.25
0.165x = 288.75
Divide both sides by 0.165
0.165x / 0.165 = 288.75 / 0.165
x = $1750
Find y
Since y = x + 150
x = 1750
y = 1750 + 150
y = $1900
Therefore, the cost of a desktop is $1750 and the cost of a laptop is $1900Answer
The vertices of ABC are A(2,-5), B(-3, - 1), and C(3,2). For the translation below, give the vertices of AA'B'C'. T * - 1) (ABC) The vertices of AA'B'C' are A'B', and c'| (Simplify your answers. Type ordered pairs.)
In order to calculate the translation of <-4, -1> to the triangle ABC, we just need to add these coordinates to all vertices of the triangle, that is, add -4 to the x-coordinate and -1 to the y-coordinate. So we have that:
[tex]\begin{gathered} A(2,-5)\to A^{\prime}(2-4,-5-1)=A^{\prime}(-2,-6) \\ B(-3,-1)\to B^{\prime}(-3-4,-1-1)=B^{\prime}(-7,-2) \\ C(3,2)\to C^{\prime}(3-4,2-1)=C^{\prime}(-1,1) \end{gathered}[/tex]So the vertices after the translation are A'(-2, -6), B'(-7, -2) and C'(-1, 1).
The food service manager at a large hospital is concerned about maintaining reasonable food costs. The following table lists the cost per serving, in cents, for items on four menu's. On particular day, a dietician orders 68 meals from menu 1, 43 meals from menu 2, 97 meals from menu 3, and 55 meals from menu 4.Part AWrite the information in the table as a 4x5 matrix M. Maintain the ordering of foods and menu's from the table.M=[__]Part BWrite a row matrix N that represents the number of meals ordered from each menu. Maintain the ordering of menu's from the tableN=[___]Part CFind the product NMNM=[___]1st blank options (average or total)2nd blank (each food, food, or each menu)
Answer and step by step:
a) To write the information in the table as a 4x5 matrix:
b) Write a row matrix N that represents the number of meals ordered from each menu.
c) Find the product NM:
To find the product of two matrices, the matrices have to be the same number of columns and rows. Then it cannot be solved.
Dion makes and sells stained glass suncatchers in different shapes. For one of his designs, he attaches semicircles to each side of a square that has a side length of 4 centimeters. He builds a frame around the outside of each suncatcher to hold it together.What is the approximate length of the frame that Dion used on this suncatcher?
Designs shape is:
So length is :
Perimeter of half circle is:
[tex]\text{ Perimeter =}\pi r+2r[/tex]Radius of circle is:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]So the length is:
[tex]\begin{gathered} =4(\pi r+2r) \\ =4(2\pi+2(2)) \\ =4(2\pi+4) \\ =4(6.283+4) \\ =4\times10.283 \\ =41.132 \end{gathered}[/tex]So the approximate length is 41 centimeter.
use the trigonometric ratio to find the measure of θ in the triangle. Give your answer to the nearest degree
θ = 64°
Explanation:
Trigonometric ratio SOHCAHTOA
hypotenuse = 10cm
angle = θ
opposite = side opposite the angle = 9cm
adjacent = not given
Since we know the opposite and the hypotenuse, we would apply sine ratio (SOH)
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin \text{ }\theta\text{ = }\frac{9}{10} \end{gathered}[/tex][tex]\begin{gathered} \sin \theta\text{ = 0.9} \\ \theta=sin^{-1}(0.9) \\ \theta=\text{ 64.16}\degree \\ To\text{ the nearest degr}ee,\text{ }\theta=\text{ 64}\degree \end{gathered}[/tex]25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. developed at least tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure. A) how many only got tumors? B) how many didn't get a tumor? C) how many suffered from at least one of these effects?
Explanation:
The total number of mice for the experiment is
[tex]Universalset=25[/tex]How to know how many mice didn't have a tumor?
Identify the total mice who did not have any effects or the effects did not include a tumor.
The number of mice that had respiratory failur is
[tex]n(R)=9[/tex]Based on this, it can be concluded 9 mice did not have a tumor,
Hence,
The number of mice that didnt have a tumor is 9
To figure out the number that got only tutmor, we will consider the number that has both tumors and respiratory failure
[tex]n(T\cap R)=4[/tex]The number that developed tumors is given below as
[tex]n(T)=15[/tex]Hence,
The number that got
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 15 miles. If the two airplanes are 39 miles apart, the eastbound airplane has traveled __ miles.
Answer:
36 miles
Explanation:
Let's go ahead sketch the given problem as shown below;
From the above diagram, we can go ahead and determine x, which is the distance the eastbound plane has traveled, using the Pythagorean theorem;
[tex]\begin{gathered} 39^2=x^2+15^2 \\ 1521=x^2+225 \\ x^2=1521-225 \\ x=\sqrt[]{1296} \\ x=36\text{miles} \end{gathered}[/tex]The barrel of a rifle has a length of 0.983m. A bullet leaves the
muzzle of a rifle with a speed of 602m/s. What is the
acceleration of the bullet while in the barrel? A bullet in a rifle
barrel does not have constant acceleration, but constant
acceleration is to be assumed for this problem.
Answer in units of m/s^2
The acceleration of the bullet while in the barrel is 184335.7 m/s^2.
First, let us understand the acceleration:
Any action where the velocity changes are said to it as acceleration. There are only two ways to accelerate: altering your speed or altering your direction, or altering both. This happens because velocity is both a speed and a direction.
We are given;
The length of the barrel of the rifle is 0.983 m.
The speed of the bullet is 602m/s.
From the third equation of motion, we know that,
v^2 = u^2+ 2aS
Initial velocity, u=0
Final velocity, v = 602m/s.
Distance, S = 0.983 m.
Substitute the given values in the above formula,
v^2 = u^2 + 2aS
(602)^2 = 0 + 2 * a * 0.983
1.966a = 362404
a = 362404/1.966
a = 184335.7 m/s^2.
Thus, the acceleration of the bullet while in the barrel is 184335.7 m/s^2.
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Point Q is shown on the coordinate grid belowWhich statement correctly describes the relationship between the point (-3,2) and point G
The coordinate of Q is (-3,-2)
The relationship between (-3, -2) and (-3, 2)
(x,y) changes into (x,-y) which is the reflection along x axis
The point (-3, 2) is a reflection of point Q across the x-axis
Answer : The point (-3, 2) is a reflection of point Q across the x-axis
Marcus has his car insurance payment directly withdrawn from his savings account. One month after starting the payment, he had $915 in savings. Nine months after starting the payment, he had $235. Assume Marcus made no other deposits or withdrawals from the account. If the relationship between months and the amount of money in Marcus’s account is linear, what is the slope?
The slope of a line is given that passes through the points (x1,y1) and (x2,y2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case we know that:
After one month the account has $915, this can be represented by the point (1,915)
After nine months the account has $235, this can be represented by the point (9,235).
Plugging these two points in the expression for the slope we have:
[tex]\begin{gathered} m=\frac{235-915}{9-1} \\ m=\frac{-680}{8} \\ m=-85 \end{gathered}[/tex]Therefore, the slope is -85.
At its first meeting, the math club had 16 students attend. At its second meeting, 25 students attended. What was the percent of increase?
First, subtract 16 to 25:
25 - 16 = 9
next, calculate the associated percentage of 9 to 16, as follow:
(9/16)(100) = 56.25
Hence, the increase was of 56.25%
find the cost of building the new road
Question:
Solution:
Step 1: Applying the Pythagorean theorem, we find the length of the new path:
[tex]\text{new road = }\sqrt[]{(8000)^2+(15000)^2}\text{ = }17000[/tex]Step 2: Convert the above value to kilometers:
[tex]17000\text{ m (}\frac{1\operatorname{km}}{1000m})\text{ = 17 km}[/tex]Step 3: Multiply the price per kilometer by the above value:
[tex]17\text{ x }160000=\text{ 2720000}[/tex]so that, we can conclude that the correct answer is:
[tex]\text{2720000}[/tex]Find the third side in simplest radical form: 3 789
Apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c = hypotenuse (longest side )
a & b = the other 2 legs of the triangle
Replacing:
c^2 = 3^2 + (√89)^2
c^2 = 9 + 89
c ^2 = 98
c = √98 = √(49x2) = √49 √2 = 7 √2
Third side = 7 √2
I am supposed to give the reasons why these triangles are equal.
Statements Reasons.
1. NL bisects angles KNM and KLM. 1. Given.
2. KNL = MNL 2. Definition of angle bisector
KLN = MLN
3. NKL = NML 3. Parallelogram theorem.
4. Triangles NKL and NML are congruent. 4. AAA postulate.
The parallelogram theorem mentioned states that opposite interior angles are congruent.
The AAA postulate of congruence states that two triangles are congruent if all three interior angles are congruent correspondingly.
you are given the expression y+8=14 solve the equation by placing the steps in order (from top to bottom)
you are given the expression y+8=14 solve the equation by placing the steps in order (from top to bottom)
we have
y+8=14
step 1
subtract 8 both sides
so
y+8-8=14-8
simplify
y=6
the steps are
y+8=14
y+8-8=14-8
y+0=6
y=6
y = 2x - 9 y = -1/2x + 1Graph both equations to find the solutionfor this system.
To answer this question, we can graph both lines equations using the intercepts of both lines. The intercepts are the x- and the y-intercepts for both lines.
The x-intercept is the point where the line passes through the x-axis. At this point, y = 0. Likewise, the y-intercept is the point where the line passes through the y-axis. At this point, x = 0.
Therefore, we can proceed as follows:
1. Graphing the line y = 2x - 9First, we can find the x-intercept. For this, y = 0.
[tex]\begin{gathered} y=2x-9\Rightarrow y=0 \\ 0=2x-9 \\ 9=2x \\ \frac{9}{2}=\frac{2}{2}x \\ \frac{9}{2}=x\Rightarrow x=\frac{9}{2}=4.5 \end{gathered}[/tex]Therefore, the x-intercept is (4.5, 0).
The y-intercept is:
[tex]y=2(0)-9\Rightarrow y=-9[/tex]Therefore, the y-intercept is (0, -9).
With these two points (4.5, 0) and (0, -9) we can graph the line y = 2x - 9.
2. Graphing the line y = -(1/2)x +1We can proceed similarly here.
Finding the x-intercept:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \frac{1}{2}x=1 \\ 2\cdot\frac{1}{2}x=2\cdot1 \\ \frac{2}{2}x=2\Rightarrow x=2 \end{gathered}[/tex]Therefore, the x-intercept is (2, 0).
Finding the y-intercept:
[tex]\begin{gathered} y=-\frac{1}{2}(0)+1 \\ y=1 \end{gathered}[/tex]Then the y-intercept is (0, 1).
Now we can graph this line by using the points (2, 0) and (0, 1).
Graphing both linesTo graph the line y = 2x - 9, we have the following coordinates (4.5, 0) and (0, -9) ---> Red line.
To graph the line y = -(1/2)x + 1, we have the coordinates (2, 0) and (0, 1) ---> Blue line.
We graph both lines, and the point where the two lines intersect will be the solution of the system:
We can see that the point where the two lines intersect is the point (4, -1). Therefore, the solution for this system is (4, -1).
We can check this if we substitute the solution into the original equations as follows:
[tex]\begin{gathered} y=2x-9 \\ -2x+y=-9\Rightarrow x=4,y=-1 \\ -2(4)+(-1)=-9 \\ -8-1=-9 \\ -9=-9\Rightarrow This\text{ is True.} \end{gathered}[/tex]And
[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1\Rightarrow x=4,y=-1 \\ \frac{1}{2}(4)+(-1)=1 \\ 2-1=1 \\ 1=1\Rightarrow This\text{ is True.} \end{gathered}[/tex]In summary, we found the solution of the system:
[tex]\begin{gathered} \begin{cases}y=2x-9 \\ y=-\frac{1}{2}x+1\end{cases} \\ \end{gathered}[/tex]Using the intercepts of the lines, graphing the lines, and the point where the two lines intersect is the solution for the system. In this case, the solution is (4, -1) or x = 4, and y = -1.
Question 20 3 pts Find the derivative. 9 4 y = 36 4 dy dx O 23 + - 4x
we have the following:
[tex]y=\frac{9}{x^4}-\frac{4}{x}[/tex]derivate:
[tex]\begin{gathered} y^{\prime}=9\frac{d}{dx}(\frac{1}{x^4})-4\frac{d}{dx}(\frac{1}{x}) \\ y^{\prime}=9\cdot(\frac{-6}{x^5})-4(\frac{-1}{x^2}) \\ y^{\prime}=-\frac{36}{x^5}+\frac{4}{x^2} \end{gathered}[/tex]therefore, the correct answer is first option
What is the slope? y= x+2
The given equation is
[tex]y=x+2[/tex]It is important to know that the slope is the coefficient of x when it's expressed in slope-intercept form like this case.
Hence, the slope is 1.Write the translation of point P(2, -9) to point P'(0, -12). [A] (x, y) =(x-3, y – 2) [B] (x, y) = (x+3, y +2) [C] (x, y) = (x+ 2, y + 3) [D] (x, y) = (x-2, y-3)
Applying the transformation (x, y) → (x - 2, y - 3) to point P, we get:
P(2, -9) → (2 - 2, -9 - 3) → P'(0, -12)
Find the product of (x+3)^2
Find the product of (x+3)^2
Remember that
(x+a)^2=x^2+2xa+a^2
therefore
(x+3)^2=x^2+6x+9
answer is
x^2+6x+98340 x 58036 + x\y = 2
The variable y as the subject of the equation is y = x/-484020238
How to make the variable y the subject of the equation?The missing information from the complete question is added at the end of this solution
From the complete question, we have the following equation representing the given parameter
8340 x 58036 + x\y = 2
Evaluate the products in the above equation
So, we have the following representation
484020240 + x\y = 2
Solving further, we subtract 484020240 from both sides of the equation
So, we have the following representation
484020240 - 484020240 + x\y = 2 - 484020240
Solving further, we evaluate the difference
So, we have the following representation
x\y = -484020238
Cross multiply
-484020238y = x
Divide both sides by -484020238
y = x/-484020238
Hence, the solution is x/-484020238
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Complete question
Make y the subject in 8340 x 58036 + x\y = 2
here is an expression 2x + 3y Does the ordered pair 6,0 make the value of the expression less than, greater than, or equal to 12
2x + 3y
ordered pair = (x,y) = (6,0)
Replace in the expression:
2(6)+3(0)
12 +0
12
The ordered pair makes the expression equal to 12.
-3 (2x + 4) - (2x + 4) < -4(2x +3)
-3 (2x + 4) - (2x + 4) < -4(2x +3)
expand
-6x - 12 - 2x - 4 < -8x - 12
Collect like terms
-6x + 8x - 2x < 12 + 4 -12
The is no solution
Find the product of (x+4) (x+1)
Expanding:
[tex]\begin{gathered} x(x\text{ + 1) + 4 (x + 1)} \\ x^2\text{ + x + 4x + 4} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} x\text{ + 4x = 5x} \\ x^2\text{ }+\text{ 5x + 4} \end{gathered}[/tex]Use a rectangular array to write the product in standard form 3(4b + 12c + 11)
The given product is:
[tex]3(4b+12c+11)[/tex]It is required to use a rectangular array to write the product in standard form.
Draw the rectangular array as shown:
Partition the sum to give small rectangles as shown:
Calculate the area of each rectangle by multiplying the width and length, then find the sum to write the product in standard form:
Write the areas as a sum:
[tex]12b+36c+33[/tex]Hence, the required product in standard form is 12b+36c+33.
The required product in standard form is 12b+36c+33.
Line LM is the midsegment of trapezoid ABCD. AB = x + 8, LM = 4x + 3, and DC = 187. What is the value of x? (image attached)thank you ! :)
To solve that question we must remember that
Then
[tex]\text{ LM = }\frac{\text{ AB + DC}}{2}[/tex]Using the value the problem gives, we get the following equation
[tex]4x+3=\frac{(x+8)+187}{2}[/tex]Solving that equation for x
[tex]\begin{gathered} 4x+3=\frac{(x+8)+187}{2} \\ \\ 8x+6=(x+8)+187 \\ \\ 7x=2+187 \\ \\ 7x=189 \\ \\ x=\frac{189}{7} \\ \\ x=27 \end{gathered}[/tex]The value of x is 27.
Suppose that $2500 is invested at an interest rate of 7.2%. How much is the investment worth after 5 years if interest is compounded monthly? (Do not use the money sign and round to the hundredths place (2 spots))
The investment worth after 5 years if interest is compounded monthly is $3,579.47.
Calculation:-
FV = P (1+ r/m)^mt
= $2500 ( 1 + 7.2/12)¹²ˣ⁵
= $3,579.47.
The Future value is $3,579.47.
The total compound interest is $1,079.47.
FV - the future value of the investment, in our calculator it is the final stability
P - the preliminary stability (the fee of the funding)
r - the once-a-year interest charge (in decimal)
m - the variety of instances the interest is compounded in keeping with 12 months (compounding frequency)
t - the wide variety of years the cash is invested for 5 years
Compound interest, may be calculated with the use of the method FV = P*(1+R/N)^(N*T), wherein FV is the destiny price of the mortgage or investment, P is the initial important amount, R is the yearly interest charge, N represents the variety of times hobby is compounded in keeping with year, and T represents time in years.
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Write a rule for the nth term of the sequence, then find a_20. 7, 12, 17, 22, ...
Problem
To find the 20th term of the sequence: 7, 12, 17, 22.
The rule for the nth term of the sequence is addding 5 to the term before to get the next term.
Concept
This is an arithmetic sequence since there is a common difference between each term. In this case .
Common ratio = 5
The term to term rule of a sequence describes how to get from one term to the next.
Final answer
The first term is 7. The term to term rule is 'add 5'.
laura deon and ravi sent a total of 101 text messages during the weekend. ravi sent 2 times as many messages as deon laura sent 9 more messages than deon how many messages did they each send
Step 1: Represent laura, deon and ravi
[tex]\begin{gathered} \text{let l represents laura's sent messages} \\ \text{let d represents deon's sent messages} \\ \text{let r represents Ravi's sent messages} \end{gathered}[/tex]Step 2: Write the relationship between l, d, and r from the first statement
[tex]l+d+r=101[/tex]Step 3: Write the relationship from the second statements
[tex]\begin{gathered} r=2d \\ l=d+9 \end{gathered}[/tex]Step 4: Substitute the r and l in the first relationship
[tex]\begin{gathered} l+d+r=101 \\ d+9+d+2d=101 \\ d+d+2d=101-9_{} \\ 4d=92 \\ d=\frac{92}{4} \\ d=23 \end{gathered}[/tex]Step 5: Solve for r and l
[tex]\begin{gathered} r=2d \\ r=2\times23=46 \end{gathered}[/tex][tex]\begin{gathered} l=d+9 \\ l=23+9 \\ l=32 \end{gathered}[/tex]Hence, Ravi sent 46 messages, Deon sent 23 messages, and Laura sent 32 messages
What is the zero of function f?f(x)=3 square root of x+3 -6
Solution:
Given:
[tex]f(x)=3\sqrt{x+3}-6[/tex]The zeros of a function are the values of x when f(x) is equal to 0.
Hence,
[tex]\begin{gathered} 0=3\sqrt{x+3}-6 \\ \\ Collecting\text{ the like terms,} \\ 0+6=3\sqrt{x+3} \\ 6=3\sqrt{x+3} \\ \\ Divide\text{ both sides by 3;} \\ \frac{6}{3}=\sqrt{x+3} \\ 2=\sqrt{x+3} \\ \\ Taking\text{ the square of both sides;} \\ 2^2=x+3 \\ 4=x+3 \\ \\ Collecting\text{ the like terms;} \\ 4-3=x \\ 1=x \\ x=1 \end{gathered}[/tex]Therefore, x = 1
The correct answer is OPTION A.
When you have a figure like this how you find the slope
Hello there. To find the slope of the line, we have to figure out two points of the line and plug in the formula for the slope.
Given two points (x0, y0) and (x1, y1) from the line, the slope m can be found with the following formula:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]In this case, the image gave us two points from the line: (-4, -2) and (3, -4)
Plugging in the values, we have:
[tex]m=\frac{-4-(-2)}{3-(-4)}[/tex]Add the values
[tex]m=\frac{-4+2}{3+4}=\frac{-2}{7}[/tex]This is the slope of this line.