the given series is 4 -16 64 -256
that is
4 x -4 = -16 = -4^2
-16 x -4 = 64 = 4^3
64 x -4 = -256 = -4^4
so we can say that is every time the number is multiplied with -4,
for a7, as 7 is an odd number so the negative sign will be there from the above observations
-4^7 = -16384
the recursive rule will be'
[tex]a_n=a_{n-1}\times-4[/tex]v+1.6>-5.5
nnnnnnnnnnnn
Answer:
v > -7.1
Step-by-step explanation:
4 ft 12 ft The pitch of the roof is
As shown : in the figure
The pitch of the roof is the angle between the roof and the horizontal line
As shown we have a right angle triangle
The opposite side to the angle = 4 ft
And the adjacent side to the angle = 12 ft
According to the given sides, we will calculate the angle using tan function
So, let the angle = x
So,
[tex]\begin{gathered} \tan x=\frac{opposite}{adjacent} \\ \\ \tan x=\frac{4}{12}=\frac{1}{3} \\ \\ x=\tan ^{-1}\frac{1}{3}\approx18.435^o \end{gathered}[/tex]So, the pitch angle of the roof = 18.435
instead of writing the angle , just we will write the slope = rise/run
So, the pitch of the roof = 1/3
Recipe A calls for 2 cups of sugar and makes 48 cookles. Recipe B calls for 3 cups of sugar and makes 54 of the same sized cookies. Determine which recipe contains more sugar in each cookle. Use complete sentences to explain your reasoning.
we are given two recipes for cookies and we are asked which of the two contains more sugar. To do that we need to find the amount of sugar per cookie for each recipe.
For recipe A we have:
[tex]2cups\rightarrow48cookies[/tex]This means:
[tex]\frac{2cups}{48cookies}=\frac{1}{24}\frac{cups}{cookies}[/tex]For recipe B we have:
[tex]3cups\rightarrow54\text{cookies}[/tex]This means:
[tex]\frac{3\text{cups}}{54\text{cookies}}=\frac{1}{18}(\frac{cups}{cookies})[/tex]Since 1/18 is greater than 1/24, this means that there is more sugar per cookie in recipe B than in recipe A.
Segment RS is translated by (x+1, y-2) and then reflected over the x-axis. The resulting segment R" S" has coordinates R" (7,3) and
S" (2,7). What are the coordinates of the segment RS?
can someone pls help meee
Answers:
R = (6, -1)
S = (1, -5)
==========================================================
Explanation:
R'' is located at (7,3)
Reflect this over the x axis to get R'(7,-3). We flip the sign of the y coordinate while keeping the x coordinate the same. The rule is [tex](x,y) \to (x,-y)[/tex]
Then we apply the inverse of (x+1, y-2) which is (x-1, y+2). Notice the sign flips.
Let's apply this inverse transformation to determine the coordinates of point R.
[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(7,-3)\to(7-1,-3+2)\\\\(7,-3)\to(6,-1)\\\\[/tex]
Therefore, point R is located at (6, -1)
-------------------
Point S'' is at (2,7)
It reflects over the x axis to get to (2,-7)
Then we apply that inverse transformation to get
[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(2,-7)\to(2-1,-7+2)\\\\(2,-7)\to(1,-5)\\\\[/tex]
Point S would be located at (1, -5)
A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Four white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 8 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $50.00, how much was each dark chocolate truffle?2.422.343.13
SOLUTION
Given the information on the question tab;
[tex]Let\text{ the price for a white chocolate truffle be W, and the price for a dark chocolate truffle be D;}[/tex][tex]\begin{gathered} From\text{ the statements made in the question;} \\ 4W=3D-----(1) \\ 8W+10D=50----(2) \end{gathered}[/tex][tex]\begin{gathered} From\text{ equation \lparen1\rparen;} \\ W=\frac{3D}{4}-----(3) \\ substituting\text{ W=}\frac{3D}{4}\text{ into equation \lparen2\rparen} \end{gathered}[/tex][tex]\begin{gathered} 8\times\frac{3D}{4}+10D=50 \\ 6D+10D=50 \\ 16D=50 \\ D=\frac{50}{16} \\ D=3.125\approx3.13 \end{gathered}[/tex]Final answer:
Each dark chocolate truffle costs $3.13
Bryce drew a rectangle and labeled five of the angles, as shown. He knew these factsWHOabout the angles:• The measurements of angles 1 and 3 are the same.The measurement of angle 2 equals 110°.• The measurements of angles 3 and 5 are the same.Part A Based on these facts, what is the sum of the measurements of angle 1and angle 2? Show your work or explain your answer.Part B What is the measurement of angle 4? Show your work or explain your answer.
The given figure is;
It is given that :
The measurements of angles 1 and 3 are the same.
The measurement of angle 2 equals 110°.
PART A:
Since, angle 1 , 2 and 3 are lie at the same point on the same line
Thus, from the property of angle on a line
Sum of all angles on a strainght line at a point is equal to 180 degree
thus;
Angle1 + Angle2 + Angle 3 = 180
Angle 1 + Angle 2 + Angle1 = 180 {Angle1 = Angle 3, given}
2(Angle 1) + Angle 2 = 180
2 (angle 1) + 110 = 180 {Angle 2 = 110, given}
2(Angle 1) = 180 -110
2(Angle 1) = 70
Angle 1 = 70/2
Angle 1 = 35
Since, angle 2 = 110
The sum of angle 1 and 2 is 110 + 35
Sum of angle 1 and 2 = 145
PART B:
From the properties of the rectangle;
All the angles of a rectangle are 90°
In the given rectangle;
Thus, in the triangle form by the angle3, 4 and the right angle
Sum of all angles in a triangle is equal to 180
Angle 3 + Angle 4 + 90 = 180
35 + Angle 4 + 90 = 180
Angle 4 + 125 = 180
Angle 4 = 180 - 125
Angle 4 = 55
.....
Silvergrove Hardware kept an inventory of 517,110 lawnmowers in the past. With a change inmanagement, the hardware store now keeps an inventory of 70% more lawnmowers. Howmany lawnmowers is that?
879,087.
EXPLANATION
To find the number of lawnmowers, we need to first find 70% of the number of lawnmowers that was kept in the past. Then add the to the number of lawnmowers kept in the past.
From the given question;
Number of lawnmowers kept in the past = 517, 110.
70% of lawnmowers kept in the past = 70% of 517 110
[tex]\begin{gathered} =\frac{70}{100}\times517\text{ 110} \\ \\ =361\text{ 977} \end{gathered}[/tex]Number of lawnmowers now kept in store = number of lawnmowers kept in the past + 70% of lawnmowers kept in the past
= 517 110 + 361 977
= 879,087.
the width of a rectangle is 8 inches less than its length, and the area is 9 square inches. what are the length and width of the rectangle?
The given situation can be written in an algebraic way:
Say x the width of the rectangle and y its height.
- The width of a rectangle is 8 inches less than its length:
x = y - 8
- The area of the rectangle is 9 square inches:
xy = 9
In order to find the values of y and x, you first replace the expression
x = y - 8 into the expression xy = 9, just as follow:
[tex]\begin{gathered} xy=9 \\ (y-8)y=9 \end{gathered}[/tex]you apply distribution property, and order the equation in such a way that you obtain the general form of a quadratic equation:
[tex]\begin{gathered} (y-8)y=9 \\ y^2-8y=9 \\ y^2-8y-9=0 \end{gathered}[/tex]Next, you use the quadratic formula to solve the previous equation for y:
[tex]y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]here you have a = 1, b = -8 and c = 9. By replacing these values you obtain:
[tex]\begin{gathered} y=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-9)}}{2(1)}=\frac{8\pm\sqrt[]{64+36}}{2} \\ y=\frac{8\pm\sqrt[]{100}}{2}=\frac{8\pm10}{2}=\frac{8}{2}\pm\frac{10}{2}=4\pm5 \end{gathered}[/tex]Hence, you have two solutions for y:
y1 = 4 + 5 = 9
y2 = 4 - 5 = -1
You select only the positive solution, because negative lengths do not exist in real life. Hence, you have y = 9.
Finally, you replace the value of y into the expression x = y - 8 to obtain x:
[tex]\begin{gathered} x=y-8 \\ x=9-8 \\ x=1 \end{gathered}[/tex]Hence, the width and length of the given recgtangle are:
width = 1 in
length = 9 in
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? N O svē units O 4/3 units 10,5 units O 165 units M
The all the sided of the equlatral triangle have the same lentgth. All the angles of the triangles are 60 degrees.
The expression for the hight of a equlatral triangle is,
[tex]\sin (60^0)=\frac{h}{l}_{}[/tex]Here, ''
Quadrilateral OPQR is dilated by a scale factor of 2/3 to form quadrilateral O'P'Q'R'. What is the measure of side RO?
Divide side R'O' (8) by th scale factor (2/3)
8 : 2/3= 12
How many -digit even numbers are possible the digit cannot be zero?
Answer:
45,000
Step-by-step explanation:
Hey! Let's help you with your question here!
So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).
First Digit:
Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.
Second, Third, Fourth Digit:
Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.
Fifth (Last) Digit:
For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.
Answer Explanation:
Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:
[tex]9*10*10*10*5[/tex]
[tex]=45,000[/tex]
Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.
PR and SU are parallel lines. Which angles are corresponding angles?
Given
PR and SU are parallel lines.
To find the pair of corressponding angles.
Explanation:
From, the figure,
Since PR and SU are parallel and the corressponding angles lie in the same corner.
Then,
[tex]\begin{gathered} \angle PQO,\angle STQ \\ \text{are corressponding angles.} \end{gathered}[/tex]Hence, the answer is Option c).
how the position of the decimal point changes in a q u o t i e n t as you divide by Precinct power of 10.
When we divide a number by a power of 10, the decimal point changes its position. Specifically, the decimal points will move to the left according to the exponent of the power. For example, let's say we have the following division.
[tex]\frac{542}{10^3}[/tex]As we said before, we just have to move the decimal point to the left. In this case, we have to move it to 3 spots.
[tex]\frac{542}{10^3}=0.542[/tex]Hence, the division is equivalent to 0.542.
That's how the division works when you divide by a power of 10.
30-28-25-21-16 next number
Answer:
10
Step-by-step explanation:
30 -2
28 -3
25 -4
21 -5
16 -6
= 10
Answer:
10
Step-by-step explanation:
Given the sequence 30, 28, 25, 21, 16, you want to know the next number.
DifferencesFirst differences between successive terms are ...
28 -30 = -2
25 -28 = -3
21 -25 = -4
16 -21 = -5
These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:
-3 -(-2) = -1
-4 -(-3) = -1
-5 -(-4) = -1
ApplicationThis observation tells us the next second difference is ...
-5 +(-1) = -6
And the next number in sequence is ...
16 +(-6) = 10
The next number is 10.
__
Additional comment
When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.
Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...
a(n) = 31 -(n)(n+1)/2
A parallelogram has an 9 inch base. if the parallelogram has an area of 54 square inches, find the height of the parallelogram.
In order to find the height of the parallelogram, we can use the following formula for its area:
[tex]A=b\cdot h[/tex]Where A is the area, b is the base and h is the height of the parallelogram.
Using A = 54 and b = 9, we can solve the equation for h:
[tex]\begin{gathered} 54=9\cdot h \\ h=\frac{54}{9} \\ h=6 \end{gathered}[/tex]So the height of the parallelogram is 6 inches.
Circumference of a circleThe radius of a circle measures 16 m. What is the circumference of the circle?Use 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
Solution:
Given:
[tex]\text{radius of a circle, r = 16m}[/tex]The circumference (C) of a circle is given by;
[tex]\begin{gathered} C=2\pi r \\ \text{where;} \\ C\text{ is the circumference of the circle} \\ r\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r=16m \\ \pi=3.14 \\ C=\text{?} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times16 \\ C=100.48m \end{gathered}[/tex]Therefore, the circumference of the circle is 100.48m
PLEASE HURRY!!!!!
Here is a hanger diagram. With a hanger diagram, when the diagram is balanced, there is equal weight on each side. Write an equation to represent the hanger. (Do NOT put spaces in your answer.)
Answer:
x = 8
x = 3
x = 2
x = 1
x = 1
x = 2
x + x+ x+ x+ x+ 2 = 17
try any number
You got 84 of 100 questions on the test correct. What percent did you get correct?Answer: 84%100%16%8.4%11/100 is equal to what percent?Answer: 110%10%89%11%3 out of 4 students in your class are girls. What percent of the class are girls?Answer: 3%4%75%25%
Divide the polynomial by the monomial (63xy^3+ 56x^2y^4)/(7xy)
ANSWER
9y² + 8xy³
EXPLANATION
To divide this polynomial by the given monomial, we can distribute the denominator into the sum,
[tex]\frac{63xy^3+56x^2y^4}{7xy}=\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}[/tex]Then, each coefficient simplifies with the coefficient of the monomial, since both are multiples of 7. Also, in the first term, x cancels out, and we have to subtract 1 from the exponent of y. In the second term, we subtract 1 from both the exponents of x and y,
[tex]\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}=9y^2+8xy^3[/tex]Hence, the result is 9y² + 8xy³.
What is lim (2x² - x + 3)/(3x² + 5) as x approaches + ∞?
Given:
lim (2x² - x + 3)/(3x² + 5)
We are to
Solve the triangle for the missing sides and angles. Round all side lengths to the nearest hundredth. (Triangle not to scale.)
The Law of Cosines
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]The triangle shown in the figure has two side lengths of a=4 and b=5. The included angle between them is x=100°. We can find the side length c by substituting the given values in the formula:
[tex]c^2=4^2+5^2-2\cdot4\cdot5\cos 100^o[/tex]Calculating:
[tex]c^2=16+25-40\cdot(-0.17365)[/tex][tex]\begin{gathered} c^2=47.946 \\ c=\sqrt[]{47.946}=6.92 \end{gathered}[/tex]Now we can apply the law of the sines:
[tex]\frac{4}{\sin A}=\frac{5}{\sin B}=\frac{c}{\sin 100^o}[/tex]Combining the first and the last part of the expression above:
[tex]\begin{gathered} \frac{4}{\sin A}=\frac{c}{\sin100^o} \\ \text{Solving for sin A:} \\ \sin A=\frac{4\sin100^o}{c} \end{gathered}[/tex]Substituting the known values:
[tex]\begin{gathered} \sin A=0.57 \\ A=\arcsin 0.57=34.7^o \end{gathered}[/tex]The last angle can be ob
in the diagram segment AD and AB are tangent to circle C solve for x
A property ostates that if two lines that are tangent to the circle intersect in an external point, they are congruent, i.e. they have the same length.
[tex]\begin{gathered} AD=AB \\ x^2+2=11 \end{gathered}[/tex]From this expression we can determine the possible values of x. The first step is to equal the expression to zero
[tex]\begin{gathered} x^2+2-11=11-11 \\ x^2+2-11=0 \\ x^2-9 \end{gathered}[/tex]The expression obtained is a quadratic equation, using the queadratic formula we can determine the possible values of x:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]For our expression
[tex]x^2+0x+-9[/tex]The coefficients are
a=1
b=0
c=-9
Replace them in the formula
[tex]\begin{gathered} x=\frac{-0\pm\sqrt[]{0^2-4\cdot1\cdot(-9)}}{2\cdot1} \\ x=\frac{0\pm\sqrt[]{36}}{2} \\ x=\frac{0\pm6}{2} \end{gathered}[/tex]Now calculate both possible values:
Positive:
[tex]\begin{gathered} x=\frac{+6}{2} \\ x=3 \end{gathered}[/tex]Negative:
[tex]\begin{gathered} x=\frac{-6}{2} \\ x=-3 \end{gathered}[/tex]The possible values of x are 3 and -3
I need help with this question involving the Cartesian plane will post pic
The graph of f(x) is a parabola with "arms up"
The vertex of the parabola is (0,-3)
Then we can know all the problem ask us:
increasing: (-3, infinity)
decreasing: (minus infinty, -3)
DNE maximum, beacuase it's arbitrarily large.
The minimum is the vertex: minimum of -3 at x = 0
The domain is all real numbers
The range is [-3, infinity)
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To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:
[tex]f(x)=ax^2+b[/tex]We focus on a and b. Always will be a squared x, but a and b vary. a lot
A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.
Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.
Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"
When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.
All the information the problem ask, you can get it by those numbers.
To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100
Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:
[tex]2x^2\text{ at x =1 }\Rightarrow f(1)=2\cdot1^2=2[/tex]For the same value of x, the first function is 100 and the second 2
i need help with this question... it's about special right triangles. The answer should not be a decimal.
4) The given triangle is a right angle triangle. Taking 30 degrees as the reference angle,
hypotenuse = 34
adjacent side = x
opposite side = y
We would find x by applying the Cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Cos 30 = x/34
Recall,
[tex]\begin{gathered} \cos 30\text{ = }\frac{\sqrt[]{3}}{2} \\ \text{Thus, } \\ \frac{\sqrt[]{3}}{2}\text{ =}\frac{x}{34} \\ 2x=34\sqrt[]{3} \\ x\text{ = }\frac{34\sqrt[]{3}}{2} \\ x\text{ = 17}\sqrt[]{3} \end{gathered}[/tex]To find y, we would apply the Sine trigonometric ratio. It is expressed as
Sin# = opposite side/hypotenuse
Sin30 y/34
Recall, Sin30 = 0.5. Thus
0.5 = y/34
y = 0.5 * 34
y = 17
Gina want to estimate the total of three bills she has to pay. the bills are for $125,$115,and $138. Gina wants to make sure that she has enough money. she wants the estimate to be greater than the total of the bills. should she round to the nearest ten or hundred
The bills are:
125
115
138
Since she wants an estimate that is greater than the actual total, she can round these numbers to the nearest ten.
125 will be rounded to the next tens, which is 130
115 will also be rounded to the next tens, which is 120
138 gets bumped to the next tens, that is 140
The total estimate is the sum of the 3 estimates we just made. That is:
130 + 120 + 140 = $390
You need a quarter of a pumpkin
to make a pie. How many pies
can you make with three and a
half pumpkins?
Answer: 14
Step-by-step explanation:
1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.
1 pumpkin = 4/4
3.5 pumpkins = 14/4
If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.
At an appliance store, if 63 stereos were sold during a one-month period, which of the following must be true?A. At least one stereo was sold on each day of the monthB. Exactly two stereos were sold on the same day during the monthC. At least one stereo was sold on either Monday, Wednesday, or Friday during the monthD. At least three stereos were sold on one day of the month.
Answer:
Alternative D. At least three stereos were sold on one day of the month.
Explanation:
Now, let's evaluate the options:
A. At least one stereo was sold on each day of the month
It is false.
We can not affirm that. For example, all the stereos can be sold on only one day of the month
B. Exactly two stereos were sold on the same day during the month
It is false.
Same explanation as A.
C. At least one stereo was sold on either Monday, Wednesday, or Friday during the month
It is false.
We can not affirm that too. The explanation is the same as for alternative A.
D. At least three stereos were sold on one day of the month.
It is true.
If two stereos are sold every day, for a month of 30 days, 60 stereos are sold. So, on some days 3 or more stereos are sold.
Also, if all the stereos are sold on the same day, more than 3 stereos were also sold.
So, alternative D is correct.
Is 7.787887888... a rational number?Highlight the correct answer below.a) Yes; it has a pattern which is repeatingb) Yes; it has a pattern which isterminatingc) No; it has a pattern which isterminatingd) No; it has a pattern which is repeating
A)
If This number 7.787887888... could be written as a ratio
[tex]\frac{a}{b}[/tex]Then it is called rational.
Since it has 7.78788788788... is an infinite number, with a repeating pattern notice it in bold. Then the only possible answer is:
Yes, it as a rational number, with a repeating pattern.
A.
Solve equation for x. 5x^2 - 4x =6
Answer:
Step-by-step explanation:
use the quadratic formula
5x^2-4x-6
4+-[tex]\sqrt{16+120}[/tex] all over 10
4+-[tex]2\sqrt{34}[/tex]/10
2+-[tex]\sqrt{34}[/tex]/5
D
Victoria and her children went into a grocery store and she bought $9 worth of applesand bananas. Each apple costs $1.50 and each banana costs $0.50. She bought a totalof 8 apples and bananas altogether. Determine the number of apples, x, and thenumber of bananas, y, that Victoria bought.Victoria boughtapples andbananas.
We will determine the solution as follows:
*First: From the text, we have the following expressions:
[tex]x+y=8[/tex]&
[tex]1.50x+0.5y=9[/tex]Here x represents apples and y represents bananas.
*Second: From the first expression, we solve for either x or y, that is [I will solve for ]:
[tex]x+y=8\Rightarrow x=8-y[/tex]*Third: Now, using the value for x, we replace in the second expression and solve for y, that is:
[tex]1.50x+0.5y=9\Rightarrow1.50(8-y)+0.5y=9[/tex][tex]\Rightarrow12-1.50y+0.5y=9\Rightarrow-y=-3[/tex][tex]\Rightarrow y=3[/tex]*Fourth: We replace the found value of y on the first expression and solve for x:
[tex]x+y=8\Rightarrow x+3=8[/tex][tex]\Rightarrow x=5[/tex]So, the number of apples was 5 and the number of bananas was 3.
