We are asked to solve a system of three linear equation in three unknowns (x, y, and z)
Eq 1) 5 x + 9 y + 10 z = -8
Eq 2) 6 x + y + z = 0
Eq 3) 6 x - y - z = 0
So we start by combining Eq 2 and 3 as they are. Adding term by term each side of the equal sign:
6 x + y + z + 6 x - y - z = 0+ 0
12 x + 0 + 0 = 0
12 x = 0
then x = 0/12 = 0
So x is zero
and then we can find y in terms of z using either Eq 2 or Eq 3:
6 (0) + y + z = 0
then
y = -z
Now we use the values : x = 0 and y = - z in Eq 1):
5 (0) + 9 (-z) + 10 z = -8
0 - 9 z + 10 z = -8
z = -8
So we found the three values:
x = 0, y = - z = -(-8) = 8, and z = -8
x = 0, y = 8 , and z = -8
6 Elliot planted h rows of corn in his garden. He later decided to plant 3 more rows for strawberries. Write an expression that represents the number of rows planted in Elliot's garden. 3h h : 3 © h+3 h - 3
Given
Elliot planted h rows of corn in his garden. He later decided to plant 3 more rows for strawberries.
Answer
Rows of corn planted = h
rows of strawberries planted = 3
Total rows planted = h +3
Identify the solid from its net. Choose the correct answer below. O square pyramid O rectangular pyramido triangular pyramid O rectangular prism
Answer:
Rectangular prism
Explanation:
The given net has 6 rectangular faces.
This corresponds with the net of a rectangular prism.
The solid is a rectangular prism.
The graph shows the function f(x). Which value is closest to the average rate of change from x = 1 to x = 4? A. −3.5B. −2.3C. −1.4D. −0.3A parabola is graphed on a coordinate plane. The horizontal x-axis ranges from negative 1 to 10 in increments of 1. The vertical y-axis ranges from negative 5 to 10 in increments of 1. The vertex is located at begin ordered pair 3.375 comma negative 4.188 end ordered pair. The parabola opens upward. It passes through the horizontal axis at begin ordered pair 1.603 comma 0 end ordered pair and begin ordered pair 5.147 comma 0 end ordered pair.
Answer:
B. −2.3
Explanation:
The average rate of change of f(x) from x = 1 to x = 4 is calculated using the formula below:
[tex]Rate\;of\;Change=\frac{f(4)-f(1)}{4-1}[/tex]From the graph:
• When x=4, the value of f(x)=-4 i.e. f(4)=-4
,• When x=1, the value of f(x)=3 i.e. f(1)=3
Therefore, the rate of change is:
[tex]Rate=\frac{-4-3}{3}=-\frac{7}{3}=-2.33[/tex]Therefore, the value that is closest to the average rate of change is -2.3.
Option B is correct.
A jet plane flies 3600 km in six hours. What would the average speed of the plane be in kilometers per hour
The average speed = distance/time
Since the jet flies 3600 km in 6 hours, then
The distance = 3600 km
The time = 6 hours
Divide them to find the average speed
[tex]\begin{gathered} A\mathrm{}S=\frac{3600}{6} \\ A\mathrm{}S=600\text{ km/h} \end{gathered}[/tex]The average speed of the jet is 600 km per hour
$1,000 at 14% for 2 yearswhat is the simple interest?what is the total amount?
Answer:
Simple Interest = $280
Amount = $1,280
Explanation:
Simple Interest = PRT/100
P is the Principal = $1000
R is the Rate = 14%
T is the Time = 2 years
Simple Interest = 1000 * 14 * 2/100
Simple Interest = 10 * 28
Simple Interest = $280
Amount = Principal + Interest
Amount = $1000 + $280
Amount = $1,280
Hence the required amount is $1,280
What is the Area of the base (B) for the rectangle prism?
We have the area of the base is given by
[tex]\begin{gathered} A=length\times width \\ A=7\times9 \\ A=63 \end{gathered}[/tex]Answer: 63 yd^2
CBiWhat is the value of Tti?02-61O2 + 603-310 3+31
If we multiply in numerator and denominator by the complex conjugate of 1+i, we have
[tex]\frac{6i}{1+i}\times\frac{1-i}{1-i}[/tex]which gives
[tex]\frac{6i+6}{2}[/tex]then, the answer is
[tex]3+3i[/tex]which corresponds to the last option
The temperature of dry ice is -109.3 degrees fahrenheit less than the outsidetemperature. Write and solve an equation to find the outside temperature.
Let's set x for the temperature of dry ice.
Let's set y to for outside temperature.
Now, we have the next statement "The temperature of dry ice is -109.3 degrees Fahrenheit less than the outside". Then, we can write the next equation:
x = -109.3 - y
To find the outside termperature, we need to solve the equation for y.
Then, the outside temperature is given by the next equation;
y=-109.3 - x
The marching band is learning a new formation. There are 22people in the first row, 33 people in the second row, 44 people inthe third row, and so on. How may people will be in the 7th row?If there are only 7 rows, how many people are in the band?
We can see that the number of people in each row has a linear relationship with the row number.
In the row 1 the number of people is 22, in the row 2 there are 33 people, 11 more than row 1. In the row 3, there are 44 people, 11 more than row 2.
So, the function is:
[tex]\begin{gathered} \text{people}=22+(n-1)\cdot11 \\ \text{people}=2\cdot11+(n-1)\cdot11 \\ \text{people}=11\cdot(n-1+2) \\ \text{people}=11\cdot(n+1) \\ \text{Where n is the number of row} \end{gathered}[/tex]We can use the equation above to find the number of people in row 7:
[tex]\text{people in row 7}=11\cdot(7+1)=11\cdot8=88[/tex]The number of people from row 1 to 7 is:
[tex]\begin{gathered} \text{Total}=\sum ^7_{n\mathop=1}11\cdot(n+1)=11\cdot(\sum ^7_{n\mathop=1}n+\sum ^7_{n\mathop=1}1)=11\cdot(\frac{7\cdot(7+1)}{2}+7) \\ \text{Total}=11\cdot(7\cdot\frac{8}{2}+7) \\ \text{Total}=11\cdot(7\cdot4+7) \\ \text{Total}=11\cdot35=385 \end{gathered}[/tex]The total number of people is 385
f(n) = n + 3 g(n) = n² + 4 Find f(4) x g(4)A. -20B. 10C. 140D. -6
Answer:
C. 140
Explanation:
Given f(n) and g(n) defined below:
[tex]\begin{gathered} f\mleft(n\mright)=n+3 \\ g\mleft(n\mright)=n^2+4 \end{gathered}[/tex]First, evaaluate f(4) and g(4):
[tex]\begin{gathered} f\mleft(4\mright)=4+3=7 \\ g\mleft(4\mright)=4^2+4=16+4=20 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} f(4)\cdot g(4)=7\times20 \\ =140 \end{gathered}[/tex]The correct choice is C.
What is the equation for the points (-3,1) and (-1,-1)
We need the equation for the line going through the points (-3, 1) and (-1, -1).
To do this we write the equation of the line as:
[tex]y=mx+b[/tex]The slope m can be calculated as the ratio of the difference of the y-coordinates and the difference of the x-coordinates:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{(-1)-1}{(-1)-(-3)}=\frac{-2}{2}=-1[/tex]Knowing the slope, we can calculate the y-intercept b using one of the points and replacing in the equation:
[tex]\begin{gathered} y=(-1)x+b \\ -1=(-1)(-1)+b \\ -1=1+b \\ b=-1-1=-2 \end{gathered}[/tex]The equation of the line is: y=-x-2
Use long division or synthetic division to find the quotient Q(x) and the remainder R(x)P(x)=x^3+3x^2-9x+5d(x)=(x+1)
Answer:
[tex]\begin{gathered} Quot\imaginaryI ent\text{Q}\operatorname{\lparen}\text{x}\operatorname{\rparen}=x^2+2x-11 \\ Remainder=16 \end{gathered}[/tex]Explanations:
Given the following functions expressed as:
[tex]\begin{gathered} P(x)=x^3+3x^2-9x+5 \\ d(x)=x+1 \end{gathered}[/tex]Using the synthesis division
From the synthetic division above, you can see that;
[tex]\begin{gathered} Quotient\text{ Q\lparen x\rparen}=x^2+2x-11 \\ Remainder\text{ R\lparen x\rparen}=16 \end{gathered}[/tex]Match each expression to the correct number of significant figures.27.65?1320-----?213.1 + 4.823200?4
Non-zero digits are always significant.
27.65 => 4 significant figure
13.1+4.8 = 17.9 => 3 significant figures
Trailing zeroes are not significant, except when there is a decimal point in the number.
320 => 2 significant figures
200 => 1 significant figure
Can you please check my answer? Use substitution to solve the system of equations:2y-4x=1818=3x+3yMy answer: (-1, 7)
x = -1
y = 7
Explanation:2y - 4x = 18 ...equation 1
18 = 3x+3y ...equation 2
Using substitution method:
We make y the subject of formula in equation 1:
2y - 4x = 18
2y = 18 + 4x
y = 1/2(18 + 4x)
y = 9 + 2x
substitute for y in equation 2:
18 = 3x + 3(9 + 2x)
18 = 3x + 27 + 6x
18 = 9x + 27
18 -27 = 9x
-9 = 9x
divide both sides by 9:
-9/9 = 9x/9
-1 = x
x = -1
substitute for x in equation 1:
2y - 4(-1) = 18
2y + 4 = 18
2y = 18-4
2y = 14
y = 14/2
y = 7
I have to write an equation for the line that passes through the given point and is perpendicular to the graph of the given equation
first, express the equation ins lope intercept form ( solve for y)
x-6y = -2
-6y = -x-2
y = (-x-2) /-6
y= 1/6x + 1/3
perpendicular line have negative inverse slopes:
slope = 1/6; negative inverse = -6
So far we have:
y= -6x +b
Replace (x,y) by the given point (-5,6) and solve for b (y intercept)
6 = -6(-5)+b
6 = 30+b
6-30= b
-24 = b
Final equation
y= -6x-24
9. Write an equation in standard form of an ellipse that is 10 units high and 8 units wide. The center of the ellipse is (0,0)..184 100
You know that the center of this ellipse is at this point:
[tex](0,0)[/tex]Therefore, it is centered at the Origin.
The Standard form of the equation of a ellipse centered at the Origin, is:
1. When it is horizontal:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]Where:
[tex]a>b[/tex]2. When it is vertical:
[tex]\frac{x^2}{b^2^{}}+\frac{y^2}{a^2^{}}=1[/tex]Where:
[tex]a>b[/tex]It is important to know that the coordinates of the vertices, when it is horizontal, is given by:
[tex](\pm a,0)[/tex]And the coordinates of the co-vertices are:
[tex](0,\pm b)[/tex]When it is vertical, the vertices are:
[tex](0,\pm a)[/tex]And the co-vertices:
[tex](\pm b,0)[/tex]You know that, in this case, the ellipse is 10 units high and 8 units wide, then you can identify that it is vertical.
Therefore, you can find "a" and "b" as following:
[tex]\begin{gathered} a=\frac{10}{2}=5 \\ \\ b=\frac{8}{2}=4 \end{gathered}[/tex]Then, its equation in Standard form is:
[tex]\begin{gathered} \\ \\ \frac{x^2}{16^{}}+\frac{y^2}{25^{}}=1 \end{gathered}[/tex]The answer is: Second option.
Solve the following using substitutionY = 2X - 34X -3Y = 31
In order to solve the given substitution we just have to replace 2X - 3 for y into 4X - 3Y = 31, like this:
4X - 3Y = 31
4x - 3(2x - 3) = 31
4x - 6x + 9 = 31
-2x + 9 = 31
-2x + 9 - 9 = 31 - 9
-2x = 22
-2x/-2 = 22/-2
x = -11
Then, x equals -11. By replacing -11 for x into Y = 2X - 3, we get:
Y = 2X - 3
Y = 2(-11) - 3
Y = -22 - 3
y = -25
Then, the solution is (-11, -25) x equals -11 and Y equals -25
ANALYZING RELATIONSHIPS A baker orders 162 eggs.Each carton contains 18 eggs. Which equation canyou use to find the number x of cartons? Explain yourreasoning and solve the equation.a. In words what is the problem asking you to solve?b. What variable are you going to use to represent what you are trying tofind?c. Create an equation that used the variable and will help you solve theproblem.d. What is the answer to the word problem?
Total number of eggs ordered = 162
Let "x" represent the number of cartons
Since each carton can contain 18 eggs , we have that
[tex]\begin{gathered} \text{number of cartons, }x\text{ = }\frac{162}{18}\text{ } \\ \text{Thus, 18x = 162} \end{gathered}[/tex](a) In words what is the problem asking you to solve?
The problem is asking us to find the number of cartons that will contain all 162 eggs if each carton can contain 18 eggs
(b) What variable are you going to use to represent what you are trying to
find?
Let "x" represent the number of cartons
(c) Create an equation that used the variable and will help you solve the
problem
Using the same equation derived above, we have that
18x = 162
(d) What is the answer to the word problem?
To obtain the answer to the word problem, we will solve the equation and get the value of "x"
[tex]\begin{gathered} 18x\text{ = 162} \\ x\text{ = }\frac{162}{18}\text{ = 9} \end{gathered}[/tex]Hence, the number of cartons that will completely accomodate all 162 eggs if each carton can contain 18 eggs is 9 cartons
Enter an equation in point-slope form for the line.(7,6) and (8,3) is on the line.
First, we will calculate the slope of the line
[tex]m=\frac{3-6}{8-7}[/tex][tex]m=\frac{3}{1}\rightarrow m=-3[/tex]Now let's calculate the y-axis crossing
[tex]b=y-mx[/tex][tex]b=6+3\cdot7[/tex][tex]b=6+21[/tex][tex]b=27[/tex]The equation would be: y = 3x - 15
[tex]b=y-mx[/tex][tex]b=3+3\cdot8[/tex][tex]b=27[/tex][tex]y=-3x+27[/tex]Create three function equations - one linear function, one quadratic function, and one cubicfunction — that all have a solution at (-5, 32).
Given point : (-5, 32)
A linear function would take the form:
[tex]y\text{ = ax + b}[/tex]Substituting the given point:
[tex]-5a\text{ + b = 32}[/tex]Our goal is to find the constants a and b.
set a = -5
[tex]\begin{gathered} -5(-5)\text{ + b = 32} \\ 25\text{ + b = 32} \end{gathered}[/tex]Solving for b:
[tex]\begin{gathered} b\text{ = 32 - 25} \\ =\text{ 7} \end{gathered}[/tex]Hence, the linear equation:
[tex]y\text{ = -5x + 7}[/tex]A quadratic function would take the form:
[tex]y=ax^2+bx\text{ + c}[/tex]Substituting the given point:
[tex]\begin{gathered} (-5)^2a\text{ -5b + c = 32} \\ 25a\text{ -5b + c = 32} \end{gathered}[/tex]Set a = 1 and b = -1:
[tex]\begin{gathered} 25(1)\text{ -5(-1) + c = 32} \\ 25\text{ + 5 + c = 32} \\ 30\text{ + c = 32} \\ Collect\text{ like terms:} \\ c\text{ = 32 - 30} \\ c\text{ = 2} \end{gathered}[/tex]Hence, the quadratic equation is:
[tex]y=x^2\text{ -x + 2 }[/tex]A cubic equation would take the form:
[tex]y=ax^3+bx^2\text{ + cx + d}[/tex]Substituting the given point:
[tex]\begin{gathered} (-5)^3a+(-5)^2b\text{ -5c + d = 32} \\ -125a\text{ + 25b -5c + d = 32} \end{gathered}[/tex]Set a = 1, b = 6, c = 1 :
[tex]\begin{gathered} -125(1)\text{ + 25(6) - 5(1) + d = 32} \\ d\text{ = 32 -20} \\ d\text{ = 12} \end{gathered}[/tex]Hence, the cubic equation would be:
[tex]y=x^3+6x^2\text{ + x + 12}[/tex]6. Figure ABC has vertices A (4,2), B(2,6), and C(6, 6). Sketch ABC and draw its image after the translation (x,y) → (x-6,y-3). 1 2
Locate the vertices on the plane and draw the figure:
Now, apply the translation to find the coordinates of the new figure.
[tex]\begin{gathered} A\colon(4-6,2-3) \\ A\colon(-2,-1) \\ B\colon(2-6,6-3) \\ B\colon(-4,3) \\ C\colon(6-6,6-3) \\ C\colon(0,3) \end{gathered}[/tex]Draw the new figure with coordinates D(-2,-1) E(-4,3) F(0,3):
This is a picture of the pre image ABC and the image DEF after the translation.
An Australian Shepherd breeder has had three litters of puppies from the same set of parents. The following table shows the results from the three litters. In the next litter, what is the probability of a puppy having no spots? Enter a fraction or round your answer to 4 decimal places, if necessary. Number of Puppies Black and White Red and white Black with Spots Red with Spots 8 6 9 4
The total number of puppies can be gotten to be:
[tex]\Rightarrow8+6+9+4=27[/tex]The number of puppies without spots will be:
[tex]\Rightarrow8+6=14[/tex]Recall the probability definition and formula: A probability is the number of desired outcomes (D) divided by the number of total outcomes (T), that is:
[tex]P=\frac{D}{T}[/tex]From what we have calculated earlier, we have that:
[tex]\begin{gathered} D=14 \\ T=27 \end{gathered}[/tex]Therefore, the probability will be:
[tex]P=\frac{14}{27}=0.5185[/tex]The probability is 14/27 or 0.5185.
The figure below is a trapezoid. If m
Given:
[tex]\begin{gathered} m\angle C+m\angle F=180\degree \\ m\angle C+77=180\degree \\ m\angle C=180\degree-77\degree \\ m\angle C=103\degree \end{gathered}[/tex][tex]\begin{gathered} m\angle D+m\angle E=180\degree \\ 121+m\angle E=180 \\ m\angle E=180-121 \\ m\angle E=59\degree \end{gathered}[/tex]a flagpole stands on level ground. Two cables R & S are attached. The combined length of the two cables is 50 ft. To the nearest degree, what is the measure of x
The combined length of cables is,
[tex]r+s=50[/tex]Determine the measure of cable r by using pythagoras theorem.
[tex]\begin{gathered} r^2=(16)^2+(12)^2 \\ =256+144 \\ =400 \\ r=\sqrt[]{400} \\ =20 \end{gathered}[/tex]Determine the measure of cable s.
[tex]\begin{gathered} 20+s=50 \\ s=50-20 \\ =30 \end{gathered}[/tex]For angle x, perpendicular is 16 and hypotenuse is 30.
Determine the measure of angle x.
[tex]\begin{gathered} \sin x=\frac{16}{30} \\ x=\sin ^{-1}(0.533) \\ =32.208^{\circ} \\ =32^{\circ} \end{gathered}[/tex]Thus, measure of angle x is 32 degree.
please help me ASAP!!!
we have
[tex]64^{(\frac{2}{3})}=\sqrt[3]{64^2}[/tex]Remember that
64=2^6
and
(2^6)^2=2^12
so
substitute
[tex]\sqrt[3]{64^2}=\sqrt[3]{2^{(12)}}=2^4=16[/tex]therefore
the answer is
option B and option DPlease solve and find the equation and put the equation in quadratic form
To find the solution to the question we would use the general representation of a quadratic equation below:
[tex]ax^2+bx+c=y[/tex]We then pick a suitable point
When x=0 and y =16
[tex]\begin{gathered} a(0)^2+b(0)+c=16 \\ c=16 \end{gathered}[/tex]We then pick two more suitable points, then solve the resulting simultaneous equation
When x= 3 and y= 0
we have
[tex]\begin{gathered} a(3)^2+b(3)+16=0 \\ 9a+3b=-16 \end{gathered}[/tex]Also, when x=-5 and y =0
we have
[tex]\begin{gathered} a(-5)^2+b(-5)+16=0 \\ 25a-5b=-16 \\ \end{gathered}[/tex]We have gotten two equations, we will solve them simultaneously using the elimination method.
We will multiply equation one by 5 and equation two by 3
[tex]\begin{gathered} 5(9a+3b=-16)_{} \\ 3(25a-5b=-16) \end{gathered}[/tex][tex]\begin{gathered} 45a+15b=-80 \\ 75a-15b=-48 \\ Add\text{ equation 2 from 1} \\ 120a=-128 \\ a=-\frac{128}{120} \\ a=\frac{-16}{15} \end{gathered}[/tex]Substitute the value of a in equation 1
[tex]\begin{gathered} 45(-\frac{16}{15})+15b=-80 \\ 3\times(-16)+15b=-80 \\ -48+15b=-80 \\ 15b=-80+48 \\ 15b=-32 \\ b=-\frac{32}{15} \end{gathered}[/tex]We will then substitute a and b and c in the representation of the quadratic equation.
[tex]\begin{gathered} -\frac{16}{15}x^2-\frac{32}{15}x+16=0 \\ Multiply\text{ through by 15} \\ -16x^2-32x+240=0 \\ therefore\text{ we have} \\ -x^2-2x+15=0 \end{gathered}[/tex]A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.8 MB. Yesterday, there were 1400 downloads of the song, for a total download size of 5523 MB. How many downloads of the standard version were there? Number of standard version downloads:
Given:
[tex]\begin{gathered} Standard-version-size=2.7MB \\ High-quality-version-size=4.8MB \end{gathered}[/tex]To Determine: The number of standard version downloads
Solution
Let the number of downloads for standard version be x and the number of downloads for high-quality version be y
Therefore
[tex]\begin{gathered} x+y=1400===equation1 \\ 2.7x+4.8y=5523===equation2 \end{gathered}[/tex]Combine the two equations together
[tex]\begin{gathered} From\text{ equation 1} \\ y=1400-x \\ Substitute\text{ for y in equation 2} \\ 2.7x+4.8(1400-x)=5523 \\ 2.7x+6720-4.8x=5523 \\ 2.7x-4.8x=5523-6720 \\ -2.1x=-1197 \\ x=\frac{-1197}{-2.1} \\ x=570 \end{gathered}[/tex]Substitute for x in equation 1
[tex]\begin{gathered} 570+y=1400 \\ y=1400-570 \\ y=830 \end{gathered}[/tex]Hence, the number of standard version downloads is 570
If Zach buys a footstool during the sale for 75% off but the original price is 36$ How much does Zach pay?
Amount Zach pays = $9
Explanation:original price = $36
75% off = discount of 75%
Amount he pays = original price - discount
discount = 75% of original price = 75/100 × 36
discount = $27
Amount he pays = $36 - $27
Amount Zach pays = $9
Christine ordered a belt from an online dealer for $47.92, before shipping costs. If Christine paid $51.06, what was the cost of shipping?
Assley, this is the solution:
Price Christine paid = $ 51.06
Price of the belt = $ 47.92
Cost of the shipping = 51.06 - 47.92
Cost of the shipping = $ 3.14
2(4z – 2) = 44 Submit
Answer: z = 6