The amounts that she has to spend are of $2000 in Country A and $500 in Country B, using a system of equations.
What is the system of equations?
The first step in building the system of equations is identifying the variables, as follows:
Considering the total amount of $3400 that she has to spend, and the rates of each country, the following equation is established:
1.3x + 1.6y = 3400.
She wants to have four times as much of currency A as she wants of currency B, hence the second equation of the system is presented as follows:
x = 4y.
Then the amount that she will have to spend in Country B is calculated replacing x = 4y on the first equation as follows:
1.3(4y) + 1.6y = 3400
6.8y = 3400
y = 3400/6.8
y = $500.
The amount that she has to spend in Country A is given as follows:
x = 4y = 4 x 500 = $2000.
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What number must you add to complete the square?2++ 24x = 50Answer here
we have
x^2+24x=50
complete the square
(x^2+24x+12^2-12^2)=50
x^2+24x+144=50+144
(x+12)^2=194
therefore
you must add 144 both sidesI don’t understand how to do inequality equation and how to put it on the line graph
Given,
The expression of inequality is:
[tex]2x-2\leq3x+1[/tex]Required:
The graph of the inequality expression.
Simplifying the inequality expression,
[tex]\begin{gathered} 2x-2\leq3x+1 \\ 2x-2-1\leqslant3x+1-1 \\ 2x-3\leq3x \\ 2x-2x-3\leq3x-2x \\ -3\leq x \\ x\ge-3 \end{gathered}[/tex]The graph of inequality expression is:
Hence, the graph of the equation obtained.
Caleb cut a rope into 4 pieces. The lengths of the pieces of rope are 5 2/8 inches, 7 7/8 inches, 4 1/8 inches, and 3 3/8 inches. Which choice is the closest estimate of the length of the original rope? A. 1 foot 7 inches B 1 foot 9 inches C. 1 foot 11 inches D. 2 feet 2 inches
SOLUTION:
Step 1:
In this question, we are given the following:
Caleb cut a rope into 4 pieces.
The lengths of the pieces of rope are 5 2/8 inches, 7 7/8 inches, 4 1/8 inches, and 3 3/8 inches.
Which choice is the closest estimate of the length of the original rope?
A. 1 foot 7 inches B 1 foot 9 inches C. 1 foot 11 inches D. 2 feet 2 inches
Step 2:
The details of the solution are as follows:
We need to add up the individual pieces of rope:
[tex]\begin{gathered} 5\frac{2}{8}\text{ inches + 7}\frac{7}{8}\text{ inches + 4}\frac{1}{8}\text{ inches + 3}\frac{3}{8}\text{ inches = 20}\frac{5}{8}\text{ inches} \\ \end{gathered}[/tex]Next:
Converting
[tex]20\frac{5}{8}\text{ inches to feet, we have that:}[/tex][tex]\begin{gathered} 1\text{ inch = 0.0833333 foot} \\ 20\frac{5}{8}\text{ inches = 20}\frac{5}{8}\text{ x 0.0833333 = 1.718749313 foot \lparen1 feet 9 inches \rparen} \\ \approx\text{ 1 foot 9 inches \lparen OPTION B \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
1 foot 7 inches ( OPTION B )
Audrey runs a farm stand that sells apples and raspberries. Each pound of apples sells for $1.75 and each pound of raspberries sells for $1.25. Audrey made $124.50 from selling a total of 80 pounds of apples and raspberries. Write a system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of raspberries sold. Define the variables that you use to write the system.
A system of linear equation in two variables can be solved for at least two equations. The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of raspberries sold are x + y = 180 and 1.75x + 1.25y = 124.50.
What is a system of linear equations?
A system of linear equation can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.
Given,
Rate of Apple is $1.75/pound.
Rate of raspberries is $1.25/pound.
Suppose the amount of apple be x pound.
And, the amount of raspberries be y pound.
As per the question total amount of apple and raspberries is 180 pound,
And, the total earning is $124.50.
Then, the system of equations can be written as,
x + y = 180
1.75x + 1.25y = 124.50.
Hence, two equations can be derived for the given situations which are x + y = 180 and 1.75x + 1.25y = 124.50.
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Answer: x + y = 180
1.75x + 1.25y = 124.50.
Hence, two equations can be derived for the given situations which are x + y = 180 and 1.75x + 1.25y = 124.50.
Step-by-step explanation:
hi, how do i find the domain and range and determine if they are both all real numbers?
We want to obtain the domain and range of the graphed function.
The function graphed is defined on the interval from x = -6 to +2 .
Therefore, the domain of the function is;
[tex]\lbrack-6,2\rbrack[/tex]The y-values of the function is on the interval from y = -2 to +2
Therefore, the range of the function is;
[tex]\lbrack-2,2\rbrack[/tex]Traingle A(1,8), M(6,8). P(2,3), is reflected over the x axis and then rotated 90degrees clockwise. What are the coordinates of its image A'M'P'?
Reflection over the x-axis transforms the point (x,y) into (x, -y), then
A(1,8) → A''(1, -8)
M(6,8) → M''(6, -8)
P(2,3) → P''(2, -3)
Rotation 90° clockwise transform the point (x, y) into (y, -x), then
A''(1, -8) → A'(-8, -1)
M''(6, -8) → M'(-8, -6)
P''(2, -3) → P'(-3, -2)
In triangle ABC, if a = 16, c = 22....
Let's first draw the triangle being described to better understand the scenario:
Step 1: Applying the Sine Law, let's first determine the measure of Angle C represented by x.
[tex]\text{ }\frac{\text{ a}}{\text{ Sine A}}\text{ = }\frac{\text{ c}}{\text{ Sine C}}[/tex][tex]\text{ }\frac{\text{ 16}}{Sine(32^{\circ})}\text{ = }\frac{\text{ 22}}{\text{ Sine (x)}}[/tex][tex]\text{ Sine(x) = }\frac{22\text{ }\cdot Sine(32^{\circ})}{16}\text{ = 0.72863898832}[/tex][tex]\text{ x = Sine}^{-1}(\text{0.72863898832)}[/tex][tex]\text{ x = }\angle C=\text{ 46.77}^{\circ}[/tex]Step 2: The sum of all interior angles of a triangle is equal to 180°, let's use this property to find the measure of Angle B represented by y.
[tex]\angle A\text{ + }\angle B\text{ + }\angle C=180^{\circ}[/tex][tex]\text{ 32 + }\angle B+46.77=180^{\circ}[/tex][tex]\angle B+78.77^{\circ}=180^{\circ}[/tex][tex]\angle B^{}=180^{\circ}\text{ - }78.77^{\circ}[/tex][tex]\angle B^{}=101.23^{\circ}[/tex]Therefore, the answer is letter C : 101.23° or 14.77°
hellppppwhat's the missing number? 7/16 = ?/64a) 4b) 21c) 28d) 55
Let x represent the missing number, and you'll now have;
[tex]\begin{gathered} \frac{7}{16}=\frac{x}{64} \\ \text{Cross multiply and you have;} \\ 7\times64=16x \\ \text{Divide both sides by 16} \\ \frac{7\times64}{16}=\frac{16x}{16} \\ 7\times4=x \\ 28=x \end{gathered}[/tex]Therefore, the missing number is 28
Make the following conversions.5 pounds 16 ounces toa. Ounces: ozb. Pounds: lb
Solution:
Note that 1 pound is equivalent to 16 ounces. So the conversion factors that we can use, are the following:
To convert from ounces to pounds, we multiply the number of ounces by the following conversion factor:
[tex](\frac{1\text{ lb}}{16\text{ oz}})[/tex]thus, to convert 16 ounces to pounds, we carry out the following operation:
[tex](\frac{1\text{ lb}}{16\text{ oz}})\text{ 16 oz = 1 lb}[/tex]now, to convert from pounds to ounces, we multiply the number of pounds by the following conversion factor:
[tex](\frac{16\text{ oz}}{1\text{ lb}})[/tex]thus, to convert 5 pounds to ounces, we carry out the following operation:
[tex](\frac{16\text{ oz}}{1\text{ lb}})5\text{ lb= 80 oz}[/tex]
so that, we can conclude that the correct answer is:
5 pounds are 80 ounces
16 ounces are 1 pound
Find the solution of the system of equations. 4x - y = 11 2.r – 4y = –26
Explanation:
We can use the substitution method to solve this system.
First we clear y from the first equation:
[tex]\begin{gathered} 4x-y=11 \\ 4x-11=y \\ y=4x-11 \end{gathered}[/tex]Then we replace this expression into the second equation:
[tex]\begin{gathered} 2x-4y=-26 \\ 2x-4(4x-11)=-26 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 2x-16x+44=-26 \\ -14x=-26-44 \\ x=\frac{-26-44}{-14}=\frac{-70}{-14}=5 \end{gathered}[/tex]And with x = 5 we replace it into the first equation and solve for y:
[tex]y=4x-11=4\cdot5-11=20-11=9[/tex]Answer:
The solution is (5, 9)
The greatest rectangular area that the farmer can enclose with 100 m of fencing is
m2.
Considering the vertex of a quadratic equation, the greatest rectangular area that the farmer can enclose with 100 m is of 625 m².
What is the vertex of a quadratic equation?A quadratic equation is modeled by the rule presented as follows:
y = ax^2 + bx + c
The vertex has these following coordinates.
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point in the function, as follows::
If a < 0, the vertex is a maximum point of the function.If a > 0, the vertex is a minimum point of the function.In this problem, the coefficients of the quadratic equation representing the area are given as follows:
a = -1, b = 50.
The greatest rectangular area that the farmer can enclose with 100 m is the y-coordinate of the vertex of the quadratic equation, hence:
[tex]y_v = -\frac{50^2 - 4(-1)(0)}{4(-1)} = 625[/tex]
The area is of 625 m².
Missing informationThe quadratic equation for the area is:
A(w) = -w² + 50w
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Answer:
625
explanation:
trust
VOCABULARY In the Quadratic Formula, what is the expression for the discriminant?
Answer: b^2-4ac
Step-by-step explanation:
For each of the following transformations on image A, resulting in image B, label it as a rotation, a reflection, a translation, or a dilation.
To be able to understand this question, we need to understand what each of the terms we are using mean.
Rotation is simply turning the figure using a specific point. For example , a case of doing a 360 turn around of a vehicle.
Dilation is simply increasing the dimension of the said object. In simpler terms, we are magnifying the dimensions
Reflection simply works with a mirror. When we get a mirror image, then we are reflecting
and Lastly translation. We are simply moving the given object in its entirety(no sides get left out) a particular distance without a change in size or dimension of the object.
Now let us take on the individual options
1. This is a reflection
We can see that the shape of the Deer appears to be in front of an object (mirror) which has helped to change the way it looked
2. This is a Dilation
We can see that the dimenion of the object was increased. In simpler terms, we can see that it was zoomed
3. This is a Rotation
The Bicycle in this case simply moved from a specific position to another at a certain angle (like moving around a ring road junction)
4. This is Translation
The Panda was simply moved in its entirety from one point to the other.
Summarily, we have the following for each of the images;
1. Reflection
2. Dilation
3. Rotation
4. Translation
IN ONE REGION 40% OF ALL RESIDENTIAL TELEPHONE NUMBERS ARE UNLISTED. IF 5 RESIDENTIAL HOUSING UNITS ARE RANDOMLY SELECTED FIND THE PROBABILITY THAT ALL OF THEM HAVE UNLISTED NUMBERS
Given:
Percentage of numbers unlisted = 40% = 0.40
Sample size, n = 5
Let's find the probability that all 5 of the selected houses have unlisted numbers.
To find the probability, we have:
p(numbers unlisted) = 0.40
Hence, we have:
q = 1 - p = 1 - 0.40 = 0.60
For the probability, apply the binomial probability:
0 .
[tex]P(x=5)=(^5C_5)(0.40)^5(0.60)^{5-5}[/tex]Solving further:
[tex]\begin{gathered} P(x=5)=(\frac{5!}{5!(5-5)!})(0.01024)(0.60)^0 \\ \\ P(x=5)=(\frac{5!}{5!(0)!})(0.01024)(1) \\ \\ p(x=5)=1*0.01024*1 \\ \\ p(x=5)=0.01024 \end{gathered}[/tex]Therefore, the probability that all 5 numbers have unlisted numbers is 0.01024
• ANSWER:
0.01024
Hello, this is a homework assignment, will you be able to help me?
answer: E
Remote Assignment 1-5 Score: 37/100 3/8 answered Progress saved Done Question 4 < > B0/13 pts 10 A BX bisects ZABC. If m ZABC = 9 x + 18 and mZCBX = 5 x + 7, find the value of mZABX. Submit Question
When a ray bisects an angle, it divides said angle in half. This means that the two new created angles will have the same measurement and when added they should be equal to the larger one. With this in mind we can find mABX as shown below:
[tex]\begin{gathered} \measuredangle ABC=\measuredangle ABX+\measuredangle CBX \\ \measuredangle ABX=\measuredangle ABC-\measuredangle CBX \end{gathered}[/tex]We were given the values for mABC and mCBX, so we use those in the expression above and solve for the value of mABX. We have:
[tex]\begin{gathered} \measuredangle ABX=9x+18-(5x+7) \\ \measuredangle ABX=9x-5x+18-7 \\ \measuredangle ABX=4x+11 \end{gathered}[/tex]The value of mABX is "4x + 11".
Patrick is manipulating the expression: 5(2x-3). He does the following steps.
Step #1: 5(2x)-5(3)
Step #2: (5.2)x-5 (3)
Step # 3: 10x15
(a) Write the properties that Patrick uses in Step #1 and Step #2
(b) Test the equivalency of these two expressions for x=4. show fhs substitution for both.
5 (2x - 3)
10x - 15
In linear equation, x = -1 is the value of x in equation .
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.a) 5( 2x - 3 ) -3( 3x - 7 ) = 5
10x - 15 -9x + 21 = 5
x + 6 = 5
x = 5 - 6
x = -1
b) x= 4
5 (2x - 3) = 5 ( 2 * 4 - 3 )
= 5 ( 8 - 3 ) ⇒ 5 * 5 = 25
10x - 15 = 10 * 4 - 15
= 40 - 15 ⇒ 25
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5×65= 9 is this correct
For this problem we have the following expression given:
[tex]5\cdot65=9[/tex]And we can conclude that it's incorrect since:
[tex]5\cdot65=325[/tex]And 325 is not equal to 9
use the circle unit to evaluate cos(23/6)
Given
[tex]\begin{gathered} \cos \text{ }\frac{23\pi}{6} \\ A\text{ complete revolution in a circle is 2}\pi \\ We\text{ have to re-write }\frac{23\pi}{6}\text{ in such a way that it will not be more than 2}\pi\text{ } \\ \text{Hence, } \\ cos\frac{23\pi}{6}\text{ = cos(}\frac{23\pi}{6}-\frac{24\pi}{6}) \\ \cos \text{(}\frac{23\pi}{6})\text{ = cos(}\frac{-\pi}{6}) \end{gathered}[/tex]The representation on the unit circle is shown below
Going round the circle in the negative direction, we realize
[tex]\cos (\frac{-\pi}{6})\text{ = cos(}\frac{11\pi}{6})\text{ = }\frac{\sqrt[]{3}}{2}[/tex][tex]\text{The answer is }\frac{\sqrt[]{3}}{2}[/tex]State if the triangles are similar and how do you know
Given the side lengths of the triangles:
AB = 27 + 15 = 42
AC = 24
AW = 16
AV = 27
Let's state if triangle ABC and triangle AVW are similar triangles.
The corresponding sides of similar triangles are in proportion.
Thus, to determine the the triangles are similar, the corresponding sides must be in the same ratio.
Apply the proportionality equation;
[tex]\frac{AC}{AW}=\frac{AB}{AV}[/tex]Let's determine in the equation is true.
Input values into the equation:
[tex]\begin{gathered} \frac{24}{16}=\frac{42}{27} \\ \\ 1.5=1.6 \end{gathered}[/tex]This equation is not true.
Therefore, we can say that
determine x so that the three points (x,-3),(9,1), and (13,2) will lie on a straight line.
Answer:
Explanation:
Let:
First, we use the slope formula:
Next, we find the slope from point 1 to point 2. So,
Then, we solve for x using the slope and points 2 and 3.
We can double check it by using all points:
Therefore, the answer is x = -7.
−5(x−1)−x+1=−18
This is a very hard question for me
Answer:
x=-2
Step-by-step explanation:
-5(x-1)-x+1=-18
subtraction and addition is left to right so ...
-5x+5-x+1=-18
-6x+6=18
divide both sides by 6...
-x+1=3
x=-2
Bamboo plants grow rapidy. A bamboo plant is 120 inches tailTomorrow it will be 134.2 inches tall, the next day it will be 148.4 inches tall, and on the next day it will be1626 inches tall. Which of the following models best illustrates this situation?
From the question
The Bamboo plant growth can be shown bellow
[tex]120,134.2,148.4,162.6[/tex]We are to find an equation that models the grwoth
The growth can be simplified as follows
[tex]\begin{gathered} Day1=120\text{ inches tall} \\ \text{Day 2 = 134.2 = (120 + 14.2) inches tall} \end{gathered}[/tex]also
[tex]\begin{gathered} \text{Day 3 = 148.4 = 120 + 28.4 = 120 +2(14.2)} \\ \text{Day 4 = 162.6 = 120 + 42.6 =120 + 3(14.2)} \end{gathered}[/tex]Therefore we can conclude that the function is
[tex]f(x)=120+14.2x[/tex]Where x is number of days
circumfrene=what when the diamter is 17
Answer:
[tex]17\pi[/tex]
Step-by-step explanation:
Circumference = diameter x pi
Diameter = 17
So the Circumference is [tex]17\pi[/tex]
Hope this helps :)
Have a nice day!
Graph the solution to the following inequality on the number line.(x+2)(x-7) greater than or equal to 0
Solve the inequality:
(x + 2)(x - 7) ≥ 0
The product of x + 2 and x - 7 can only be 0 if any (or both) of the factors is 0.
The product can only be positive if both are positive or both are negative. These conditions can be expressed as:
x + 2 ≥ 0 and x - 7 ≥ 0
OR
x + 2 ≤ 0 and x - 7 ≤ 0
The first pair of conditions lead to:
x ≥ -2 and x ≥ 7
The combination of both conditions produces a single solution:
x ≥ 7
The second pair of conditions lead to:
x ≤ -2 and x ≤ 7
The combination of both conditions produces a single solution:
x ≤ -2
The total solution to the inequality is:
x ≤ -2 U x ≥ 7
U = Union
The graph of the solution is:
A circle was inserted into a trapezoid. What is the area of the shaded region? Round your answer to the nearest tenth of a foot. 23 ft ft 10 ft 15 ft a 101.7ft2 202.3ft? x 152 ft? 4.50.3ft2 assessments
We can calculate the shaded area as the area of the trapezoid less the area of the circle.
The area of the trapezoid is:
[tex]\begin{gathered} A_t=\frac{b_1+b_2}{2}\cdot h \\ A_t=\frac{23+15}{2}\cdot8 \\ A_t=\frac{38}{2}\cdot8 \\ A_t=19\cdot8 \\ A_t=152 \end{gathered}[/tex]The area of the circle of radius r=8/2=4 ft is:
[tex]\begin{gathered} A_c=\pi r^2 \\ A_c=\pi\cdot4^2 \\ A_c\approx3.14\cdot16 \\ A_c\approx50.3 \end{gathered}[/tex]Then, the shaded area is the difference between the area of the trapezoid and the area of the circle:
[tex]\begin{gathered} A=A_t-A_c \\ A=152-50.3 \\ A=101.7\text{ ft}^2 \end{gathered}[/tex]Answer: 101.7 ft^2
On Giana's map of Texas, there is a close up view of the Dallas/Fort Worth area. She sees that from Dallas to Fort Worth is 4 centimeters. If 1 centimeter represents 9.7 miles, what is true distance between the cities?
On Giana's map of Texas, the close up view of the Dallas/Fort Worth area has 38.8 miles in actual
In the above question, it is given that
On Giana's map of Texas, there is a close up view of the Dallas/Fort Worth area, she sees the distances between Dallas to Fort Worth
Here are Giana's observations, she found
The distance from Dallas to Fort Worth = 4 centimeters
Also, 1 centimeters = 9.7 miles
Then we need to find the distance 4 centimeters will cover in actual
So, the distance from Dallas to Fort Worth in actual will be = 4 x 9.7 = 38.8 miles
Hence, On Giana's map of Texas, the close up view of the Dallas/Fort Worth area has 38.8 miles in actual
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Evaluate -b with exponent of 2 - 2bx with exponent of 2 on the x - x = -2
To solve the exercise, we replace x by -2 in the given expression:
[tex]\begin{gathered} -b^2-2bx^2-x \\ -b^2-2b(-2)^2-(-2) \end{gathered}[/tex]Now, we operate:
[tex]\begin{gathered} -b^2-2b(-2)^2-(-2)=-b^2-2b(-2)\cdot(-2)^{}-(-2) \\ -b^2-2b(-2)^2-(-2)=-b^2-2b\cdot4+2 \\ -b^2-2b\mleft(-2\mright)^2-\mleft(-2\mright)=-b^2-8b+2 \\ \text{ Because} \\ (-2)\cdot(-2)=2\cdot2=4 \\ \text{ and} \\ ^{}-(-2)=2 \end{gathered}[/tex]Therefore, the result of evaluate the given expression when x = -2 is:
[tex]$$\boldsymbol{-b}^{\boldsymbol{2}}\boldsymbol{-8b+2}$$[/tex]What is the inverse of the function h(x) = 5 over 2 x + 4
The given function is
h(x) = 5x/2 + 4
The first step is to replace h(x) with y. We have
y = 5x/2 + 4
The next step is to interchange x and y and solve for y. We have
x = 5y/2 + 4
Subtracting 4 from both sides of the equation, we have
x - 4 = 5y/2 + 4 - 4
x - 4 = 5y/2
Multiplying both sides of the equation by 2, we have
2(x - 4) = 5y/2 * 2
2(x - 4) = 5y
Dividing both sides of the equation by 5, we have
2(x - 4)/5 = 5y/5
y = 2(x - 4)/5
The next step is to replace y with h^-1(x). Thus,
h^-1(x) = 2(x - 4)/5
Use linear approximation, i.e. the tangent line, to approximate as follows: Let f(x) = and find the equation of the tangent line to f(x) at a nice" point near 0.202. Then use this to 1/0.202 approximate 1/0.202
ANSWER
[tex]\begin{equation*} 4.95 \end{equation*}[/tex]EXPLANATION
Given;
[tex]f\mleft(x\mright)=\frac{1}{x}[/tex]Now, evaluate its first derivative;
[tex]f^{\prime}(x)=-\frac{1}{x^2}[/tex]Now;
[tex]\begin{gathered} x=0.2=\frac{1}{5} \\ f(x)=5,f^{\prime}(x)=-25 \end{gathered}[/tex]Hence, we have;
[tex]l(x)=5-25(x-0.2)=5-25x+5[/tex]by substitution;
[tex]\begin{gathered} \frac{1}{0.202}=5.25(0.202-0.2) \\ =5-0.05 \\ \cong4.95 \end{gathered}[/tex]