Answers
Multiplying 9/8 and the first equation we get:
[tex]-\frac{63}{8}x-9y=\frac{81}{8}\text{.}[/tex]Adding the above equation and the second equation of the system we get:
[tex]-\frac{63}{8}x-4x=\frac{81}{8}-22.[/tex]Adding like terms, we get:
[tex]-\frac{95}{8}x=-\frac{95}{8}\text{.}[/tex]Therefore:
[tex]x=1.[/tex]Subtituting x=1 in the first equation, we get:
[tex]-7-8y=9.[/tex]Solving the above equation for y, we get:
[tex]\begin{gathered} -8y=9+7, \\ -8y=16, \\ y=-2. \end{gathered}[/tex]Answer:
[tex]x=1,\text{ y=-2.}[/tex]Related Questions
Claire is ordering trophies for her school. Company A charges $4.50 for each trophy and a one-time engraving fee of $26. Company B charges $8.50 for each tu trophy and a one-time engraving fee of $18. Which inequality can be used to find x, the minimum number of trophies than can be ordered so that the total charge at Company A is less than the total charge at Company BA. 4.5 + 26x < 8.5 + 18xB. 4.5 + 26x > 8.5 + 18xC. 4.5x + 26 > 8.5x + 18D. 4.5x + 26 < 8.5x + 18
Answers
It charges $4.50 per trophy and a one-time fee of $26.
Company B.It charges $8.50 per trophy and a one-time fee of $18.
To find x where Company A is less than Company B, we form the following inequality.
[tex]4.50x+26<8.50x+18[/tex]Now, we solve for x, first, we have to subtract 8.50 on each side.-
[tex]\begin{gathered} 4.50x+26-8.50x<8.50x+18-8.50x \\ -4x+26<18 \end{gathered}[/tex]Then, we subtract 26 on each side
[tex]\begin{gathered} -4x+26-26<18-26 \\ -4x<-8 \end{gathered}[/tex]At last, we divide the inequality by -4.
[tex]\begin{gathered} -\frac{4x}{-4}>-\frac{8}{-4} \\ x>2 \end{gathered}[/tex]Therefore, the minimum number of trophies that can be ordered so Company A charges less is 3.The right answer is D.Find the perimeter of the following rectangle. Write your answer as a mixed number in simplest form. Be sure to include the correct unit in your answer.
Answers
we add the four sides to get the perimeter
[tex]\begin{gathered} \frac{2}{3}+\frac{2}{3}+2\frac{1}{4}+2\frac{1}{4} \\ \\ \frac{4}{3}+4\frac{2}{4} \\ \\ 1\frac{1}{3}+4\frac{1}{2} \end{gathered}[/tex]add the integer part and the fraction
[tex]\begin{gathered} (4+1)(\frac{1}{3}+\frac{1}{2}) \\ \\ 5(\frac{(2\times1)+(3\times1)}{3\times2}) \\ \\ 5(\frac{5}{6}) \\ \\ 5\frac{5}{6} \end{gathered}[/tex]the perimeter is 5 5/6 yd because is a measure on one dimesion
Solve the system of linear equations by the elimination method.2x + 10y = 23x - 5y = -17
Answers
We will have the following:
2x + 10y = 2
2(3x - 5y = -17)
-----------------------
2x + 10y = 2
6x - 10y = -34
------------------------
8x + 0y = -32 => x = -4
Now, we replace in one of the expressions and solve for y:
2(-4) + 10y = 2 => -8 + 10y = 2
=> 10y = 10
=> y = 1
So, the solution of the system is (-4, 1).
Triangle LMN has the vertices shown on the coordinate grid
Answers
For this question we will use the following formula to compute the distance between two given points (x,y) and (v,w):
[tex]d_{(x,y),(v,w)}=\sqrt[]{(x-v)^2+(y-w)^2}.[/tex]Now, the length of segment MN is the distance between M(0,4) and N(3,-2):
[tex]\begin{gathered} d_{(3,-2),(0,4)}=\sqrt[]{(3-0)^2+(-2-4)^2}=\sqrt[]{3^2+6^2} \\ =\sqrt[]{9+36}=\sqrt[]{45}=3\sqrt[]{5}. \end{gathered}[/tex]Answer: The length of MN is:
[tex]3\sqrt[]{5}.[/tex]Find the area of a circle If the radius is 6 cmEXPLAIN HOW TO DO THE PROBELM IN THE ANSWER PLEASE
Answers
We would apply the formula for determining the area which is expressed as
Area = pi x radius^2
From the information given,
radius = 6
pi = 3.14
Area = 3.14 x 6^2
Area = 113.04 cm^2
Solve the equation for the specified variable.w=zh - 4zc3 for zPLEASE HELP
Answers
z = w/(h-4c^3)
The given equation:
w = zh - 4zc^3
Let's make z the subject of the formula:
[tex]\begin{gathered} w=zh-4zc^3 \\ \text{Let's factor out z} \\ w=z(h-4c^3) \end{gathered}[/tex]Divide through by the expression in the brackect in order to make z stand alone:
[tex]\begin{gathered} \frac{w}{h-4c^3}\text{ = }\frac{z(h-4c^3)}{h-4c^3} \\ \frac{w}{h-4c^3}\text{ = z} \end{gathered}[/tex]Therefore:
[tex]z\text{ = }\frac{w}{h-4c^3}[/tex]For each line find the Slope between the 2 points given - simplify each fraction to prove that the lines have a CONSTANT rate of change : 1) Point T : 2) Point R : 3) Point S : 4) Slope of TR : 5) Slope of RS :6) Slopw of TS : 7) Describe the Slope of the line : 8) Therefore the CONSTANT RATE OF CHANGE is ....?
Answers
For each line find the Slope between the 2 points given - simplify each fraction to prove that the lines have a CONSTANT rate of change :
1) Point T :
2) Point R :
3) Point S :
4) Slope of TR :
5) Slope of RS :
6) Slopw of TS :
7) Describe the Slope of the line :
8) Therefore the CONSTANT RATE OF CHANGE is ....?
Part 1) Point T(-7,6)
Part 2) Point R(-3,0)
Part 3) Point S(1,-6)
part 4) Find the slope TR
m=(0-6)/(-3+7)
m=-6/4
m=-3/2
Part 5) Find the slope RS
m=(-6-0)/(1+3)
m=-6/4
m=-3/2
Part 6) Find teh slope TS
m=(-6-6)/(1+7)
m=-12/8
m=-6/4
m=-3/2
Part 7) Describe the Slope of the line
the slope of the line is negative and its value is -3/2 and is constant
Part 8) Therefore the CONSTANT RATE OF CHANGE is ....?
REmember that the slope of the linear equation is the same that the rate of change, is a constant value equal to -3/2
Solve e 3t = 900 for t. (Round to three decimal places as needed.)
Answers
Answer
t = 2.267
Explanation
The questio to be solved is
e³ᵗ = 900
[tex]e^{3t}=900[/tex]To solve this, we take the natural logarithms of both sides
In e³ᵗ = In 900
3t (In e) = In 900
Note that In e = 1 and In 900 = 6.8024
3t (1) = 6.8024
3t = 6.8024
Divide both sides by 3
(3t/3) = (6.8024/3)
t = 2.267 to 3 decimal places.
Hope this Helps!!!
The pattern below follows the rule, "starting with a value of 3, everyconsecutive row has a value that is 2 less than twice the value of the previousrow."ValueRow 13Row 24Row 36What is the value for the 5th row?O A. 66B. 34O C. 18OD. 12
Answers
Given,
The data of the three rows is 3, 4, 6.
The formula for the insertion of data in successive row is,
[tex]\text{ }successive\text{ = 2 previous term -2}[/tex]The number at row 4 is,
[tex]\text{ forth row value = 2}\times6\text{ -2}=10[/tex]The number at row 5 is,
[tex]\text{ fifth row value = 2}\times10\text{ -2}=18[/tex]Hence, the value at fifth row is 18.
Find the area of the shaded figure. 6 1 1 2 3 4 5 6 7 8 9 10 11 12 ( ? ) square units Enter
Answers
The figure appears to be a rectangle with a part being cut off in a rectangular shape as well.
To be able to get the area of the shaded figure, we subtract the area of the big rectangle as a whole by the area of the rectangular cut part.
Given:
Dimension of the shaded rectangle (Whole),
Length = Dx = 12 - 2 = 10 Units
Width = Dy = 8 - 1 = 7 Units
Dimension of the unshaded part,
Length = Dx = 10 - 4 = 6 Units
Width = Dy = 3 - 1 = 2 Units
Let's now determine the area of the shaded part:
[tex]\text{ Area}_{SHADED}\text{ = (10 x 7) - (6 x 2)}[/tex][tex]\text{ = 70 - 12}[/tex][tex]\text{ Area}_{SHADED}\text{ = 58 Units}^2[/tex]Therefore, the area of the shaded figure is 58 squared units.
The sum of the ages of David and Whitney is 69 years. 6 years ago, David's age was 2 timesWhitney's age. How old is David now?
Answers
The sum of the ages of David (D) and Whitney (W) is 69 years:
[tex]D+W=69[/tex]6 years ago, David's age was 2 times Whitney's age.
The age of David 6 years ago was (D-6) and the age of Whitney was (W-6).
At that time the age of David was twice the age of Whitney:
[tex]D-6=2(W-6)=2W-12[/tex]Now we can replace the information of the first equation in the second one:
[tex]\begin{gathered} W=69-D \\ D-6=2W-12 \\ D-6=2\mleft(69-D\mright)-12 \\ D-6=138-2D-12 \\ D-6=126-2D \\ D+2D=126+6 \\ 3D=132 \\ D=\frac{132}{3} \\ D=44 \end{gathered}[/tex]David is 44 years old.
The perimeter of a rectangle field is 306 yards. If the width of the field is 59 yards, what is its length?
Answers
For the perimeter of a rectangle, the formula is;
[tex]\text{Per}=2(l+w)[/tex]In this instance, the perimeter is 306 yards while the width is 59 yards. Substituting the given values we would have;
[tex]\begin{gathered} 306=2(l+59) \\ 306=2l+118 \\ \text{Subtract 118 from both sides;} \\ 188=2l \\ We\text{ now divide both sides by 2} \\ \frac{188}{2}=\frac{2l}{2} \\ 94=l \end{gathered}[/tex]ANSWER:
The length of the rectangular field is 94 yards
What is the average rate of change of the function (x) = 3/7x-2 over the interval x= I4 to x=35?
Answers
SOLUTION
In this question, we need to get the average rate of change of the function.
f ( x ) = 3/ 7 x - 2
First , we need to get
f ( 14 ) = 3/ 7 ( 14 ) - 2 = 6 -2 = 4
f ( 35 ) = 3/ 7 ( 35 ) - 2 = 15 - 2 = 13
For the average rate of the function: f ( 35 ) - f ( 14 ) / 35 - 14
= 13 - 4 / 21
= 9 / 21
ion #3: On the same set of aces, graph and label triangle Q'R'S', the image of QRS after a dilation with a scale factor of 3/2 centered at the origin. am
Answers
The scale factor of (3/2) means that we multiply each coordinate of each point by (3/2). Let's write the coordinates of the Triangle already drawn.
[tex]\begin{gathered} Q=(-2,2) \\ R=(2,0) \\ S=(4,6) \end{gathered}[/tex]Let's find Q'R'S' by multiplying each coordinate with (3/2). So,
[tex]\begin{gathered} Q^{\prime}=(-2\times\frac{3}{2},2\times\frac{3}{2})=(-3,3) \\ R^{\prime}=(2\times\frac{3}{2},0\times\frac{3}{2})=(3,0) \\ S^{\prime}=(4\times\frac{3}{2},6\times\frac{3}{2})=(6,9) \end{gathered}[/tex]Let's draw the transformed triangle:
The red is QRS and the blue one is Q'R'S'
Vertical lines are parallel to the y axis, and horizontal lines are parallel to the x axis.....
Answers
Horizontal lines have a slope of zero, since the "rise" is zero.
Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed. ... If the slope has a value of zero, the line is horizontal, that is, it neither increases nor decreases.
• L1, and ,L2, are horizontal lines. Their slope is ,ZERO
,• L3, and ,L4, are vertical lines. Their slope is ,UNDEFINED
The equations for the horizontal and vertical lines it is enough to equal the value of x and y to the value where we want to put our line parallel to the axis
Horizontals like L1 and L2, take a single value of y and can take any value of x
[tex]\begin{gathered} L1 \\ y=3 \end{gathered}[/tex][tex]\begin{gathered} L2 \\ y=5 \end{gathered}[/tex][tex]\begin{gathered} L3 \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} L4 \\ x=6 \end{gathered}[/tex]In summary:Horizontal lines always have an equation of the form y = aVertical lines always have an equation of the form x = bTonia is saving $15.00 each week to buy a bicycle. The bicycle costs $129.99. Which inequality can be used to determine the number of weeks, w, in which Tonia must save money so that she has more than enough money to buy the bicycle? a 15.00w < 129.99 b 15.00w > 129.99 C W + 15.00 < 129.99 d W + 15.00 > 129.99
Answers
Problem given
Tonia is saving $15.00 each week to buy a bicycle. The bicycle costs $129.99. Which inequality can be used to determine the number of weeks, w, in which Tonia must save money so that she has more than enough money to buy the bicycle?
Solution
For this problem we know that w represent the number of weeks. The bycle cosys $129.99 and taking in count the info given the best answer would be:
15w > 129.99
Becuase after 129.99/15 weeks Tonia will ahve enough money to buy the bicycle
Ohh
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.12² - 27/6x² +33x + 36Rational expression in lowest terms:Variable restrictions for the original expression: x
Answers
Explanation:
The expression is given below as
[tex]\frac{12x^2-27}{6x^2+33x+36}[/tex]Step 1:
Simplify both the numerator and denominator
[tex]\begin{gathered} \frac{12x^{2}-27}{6x^{2}+33x+36} \\ 12x^2-27=3(4x^2-9)=3(2x-3)(2x+3) \\ 6x^2+33x+36=3(2x^2+11x+12) \\ 3(2x^2+11x+12)=3(2x^2+8x+3x+12) \\ 3(2x^2+11x+12)=3(2x(x+4)+3(x+4) \\ 3(2x^2+11x+12)=3(2x+3)(x+4) \end{gathered}[/tex]By rewritng the expression , we will have
[tex]\begin{gathered} \frac{12x^{2}-27}{6x^{2}+33x+36}=\frac{3(2x+3)(2x-3)}{3(x+4)(2x+3)} \\ \frac{12x^{2}-27}{6x^{2}+33x+36}=\frac{2x-3}{x+4} \end{gathered}[/tex]Hence,
The simplified expression will be
[tex]\frac{2x-3}{x+4}[/tex]The variable restriction of the original expression will be
[tex]\begin{gathered} 3(2x+3)(x+4)=0 \\ 2x+3=0,x+4=0 \\ 2x=-3,x=-4 \\ x=-\frac{3}{2},x=-4 \end{gathered}[/tex]Hence,
The variable restriction for the original expression will be
[tex]x\ne-\frac{3}{2},-4[/tex]D. One angle measures 6° more than twice another. If the two angles are complementary, find the measures of the angles.
Answers
if x is one of the angles, then, the other angle is 2x + 6. The two angles are complementary, that is, they add up 90 degrees.
Then, you can write:
x + 2x+ 6 = 90
by solving for x the previous equation, you obtain:
x + 2x + 6 = 90
3x + 6 = 90
3x = 90 - 6
3x = 84
x = 84/3
x = 28
and the value of the measure of other angle is:
2x + 6 = 2(28) + 6 = 62
Hence, the measures of the two angles are 28° and 62°
5 is the GCF for which pair of numbers...1) 15, 252) 13, 503) 12 52
Answers
the right option is 15 ,25, the first option
ebcause 15 and 25 are multiples of 5
2x - y = 76x – 3y = 14
Answers
You have the following system of equations:
2x - y = 7
6x - 3y = 14
In order to solve the previous system of equations you can use different methods. Here, you can use susbtitution. You proceed as follow:
solve the first equation for y:
2x - y = 7
-y = 7 - 2x
y = -7 + 2x
Next, this expression for y is replaced in the second equation:
6x - y = 7
6x - (-7 + 2x) =7
6x + 7 + 2x = 7
4x = 0
x = 0
The solution is the trivial solution, hence, the system has INFINITE SOLUTIONS
Use the elimination method to solve the system of equations.2x + 3y = 183x - 3y = 12A. (2,4)B. (2,6)C. (6,2)D. (6, 10)
Answers
2x + 3y = 18
3x - 3y = 12
first, add both equations to eliminate y:
2x +3y = 18
+
3x-3y = 12
_________
5x = 30
Solve for x:
x=30/5
x= 6
Replace x on any initial equation and solve for y:
2(6)+3y=18
12+3y=18
3y=18-12
3y= 6
y=6/3
y=2
Suppose a normal distribution has a mean of 62 and a standard deviation of4. What is the probability that a data value is between 58 and 64? Round youranswer to the nearest tenth of a percent.
Answers
the mean is 62
the standard deviation is 4
probability of between 58 and 64
z = (x - mean) / SD
z = (58 - 62)/4
z = 0.5
P(-1 < z < 0.5) = 0.5328
0.5328
53.3
Name the coordinates of point H after it is reflected over the x-axis and then the y-axis. The initial directions are in the pic below.
Answers
We have a point H = (x, y):
0. after H is reflected over the x-axis, we have H' = (x, -y),
,1. after H' is reflected over the y-axis, we have H'' = (-x, -y).
In this case, we have the point:
[tex]H=(x,y)=(-6,4).[/tex]After the two reflections, we get the point:
[tex]H^{\prime\prime}=(x^{\prime}^{\prime},y^{\prime}^{\prime})=(-x,-y)=(-(-6),-4)=(6,-4)\text{.}[/tex]Answer
The coordinates of point H after it is reflected over the x-axis and then the y-axis are:
[tex](6,-4)[/tex]choose the statement that correctly describes the pair <1 and <2a. alternate interior angles b. same – side interior angles c. corresponding angles d. alternate exterior angles
Answers
Given:
The line t1 and intersection lines l1, l2 and l3
As shown in the figure:
The angles 1 and 2 are supplementary angles, the sum of them = 180
so, the correct statemnt will be:
b. same – side interior angles
8 yd10 yd|Which is the lateral area for the cylinder?48760719671207
Answers
We must compute the lateral area of the cylinder of the figure.
From the figure we see that the cylinder has:
• a height h = 8 yd,
,• the inner right triangle with hypotenuse H = 10 yd.
To find the lateral area we need the diameter d of the cylinder. From the picture we see that the diameter of the cylinder is one of the cathetus of the inner right triangle:
Using Pythagoras Theorem we compute the diameter of the cylinder:
[tex]\begin{gathered} H^2=d^2+h^2 \\ d^2=H^2-h^2 \\ d=\sqrt[]{H^2-h^2} \\ d=\sqrt[]{(10yd)^2-(8yd)^2} \\ d=\sqrt[]{36yd^2} \\ d=6yd \end{gathered}[/tex]Now, the lateral area of the cylinder can be computed by multiplying the longitude of the circumference of the cylinder (which is π*d) and the height (h). We find that the lateral area of the cylinder is:
[tex]\begin{gathered} A=(\pi\cdot d)\cdot h \\ A=(\pi\cdot6yd)\cdot8yd \\ A=48\pi\cdot yd^2 \end{gathered}[/tex]Answer
48π
solve using elimination-8x-4y=-4-5x-4y=2
Answers
Given the system of equations :
[tex]\begin{gathered} -8x-4y=-4 \\ -5x-4y=2 \end{gathered}[/tex]Subtract the first equation from the second equation :
So,
[tex]\begin{gathered} -5x-4y-(-8x-4y)=2-(-4) \\ \\ -5x-4y+8x+4y=6 \\ 3x=6 \\ \\ x=\frac{6}{3}=2 \end{gathered}[/tex]substitute at the first equation to find y :
So
[tex]\begin{gathered} -8\cdot2-4y=-4 \\ -16-4y=-4 \\ -4y=-4+16 \\ -4y=12 \\ \\ y=\frac{12}{-4}=-3 \end{gathered}[/tex]So, the solution of the system is:
[tex]\begin{gathered} x=2 \\ y=-3 \end{gathered}[/tex]metry Precalculus Honors S1Understanding the Inverse Relationshiphe table shows the inputs and corresponding outputsor the function f(x) = (1)(2)*.026x84.Find the following values of the function.ƒ^¹ (3)=[f-¹ (8) =
Answers
...
SOLUTION
[tex]\begin{gathered} f(x)=(\frac{1}{8})2^x \\ f^{-1}(x)=? \end{gathered}[/tex]To determine the inverse function;
[tex]Solve\text{ the equation for x, then interchange x for y.}[/tex][tex]Let\text{ y=f\lparen x\rparen}[/tex][tex]\begin{gathered} y=\frac{1}{8}(2)^x \\ 8y=2^x \\ ln(8y)=ln2^x \\ ln(8y)=xln2 \\ x=\frac{ln(8y)}{ln2}\text{ ie y=}\frac{ln(8x)}{ln2} \\ \therefore f^{-1}(x)=\frac{ln(8x)}{ln(2)} \end{gathered}[/tex]Now,
[tex]f^{-1}(\frac{1}{2})=\frac{ln(8\times\frac{1}{2})}{ln2}=\frac{ln4}{ln2}=2[/tex][tex]f^{-1}(8)=\frac{ln(8\times8)}{ln2}=\frac{ln(64)}{ln2}=6[/tex]
Use the drawing tool(s) to form the correct answer on the provided number line.Cindy has $20 to spend at the store. She buys a pack of colored pencils that cost $4 and jelly beans that cost $2 per pound. If she spends more than $8 at the store, graph a compound inequality that shows the possible number of pounds of jelly beans she could have purchased.
Answers
We are given the following information.
Cindy has $20 to spend at the store.
She buys a pack of colored pencils that cost $4 and jelly beans that cost $2 per pound.
Let x be the number of pounds of jelly beans.
With the above information, we can set up the following inequality
[tex]4+2x\leq20[/tex]Less than or equal to sign is used because Cindy can only spend equal to or less than $20.
We are also given that she spends more than $8 at the store.
We can set up the following inequality
[tex]4+2x>8[/tex]Now, let us solve these two inequalities one by one.
[tex]\begin{gathered} 4+2x\leq20 \\ 2x\leq20-4 \\ 2x\leq16 \\ \frac{2x}{2}\leq\frac{16}{2} \\ x\leq8 \end{gathered}[/tex][tex]\begin{gathered} 4+2x>8 \\ 2x>8-4 \\ 2x>4 \\ \frac{2x}{2}>\frac{4}{2} \\ x>2 \end{gathered}[/tex]So, the compound inequality is
[tex]2The above compound inequality means that the number of pounds of jelly beans Cindy can purchase is greater than 2 and equal to or less than 8.Finally, let us graph the inequality on the number line.
Use an open point at 2 and a closed point at 8.
Round the final answer to the nearest foot as needed
Answers
As given by the question
There are given that the value of slope and run in the right angle triangle.
Now,
According to the statement, the figure of the right-angle triangle is shown below:
So from the right-angle triangle, find the value of x
Then,
From the formula of tan function
[tex]\text{tan}3^{\circ}25^{\prime}=\frac{x}{6300}[/tex]Then,
[tex]\begin{gathered} \text{tan}3^{\circ}25^{\prime}=\frac{x}{6300} \\ 0.0597=\frac{x}{6300} \\ x=6300\times0.0597 \\ x=376.11 \end{gathered}[/tex]Hence, the value of rising is 376 ft
write as a product: 2xy^2-y-2x+y^3
Answers
Given
[tex]2xy^2-y-2x+y^3[/tex]To write as a product.
Explanation:
It is given that,
[tex]2xy^2-y-2x+y^3[/tex]Regroup the terms in the above expression as,
[tex]\begin{gathered} 2xy^2-y-2x+y^3=2xy^2-2x-y+y^3 \\ =2x(y^2-1)+y(-1+y^2)_{} \\ =(2x+y)(y^2-1) \\ =(2x+y)(y-1)(y+1) \end{gathered}[/tex]Hence, the expression is written as, x=(2x+y)(y-1)(y+1).