The table below shows the students in an Algebra class.GirlsBoysTotalOwn a graphing Do not own a graphingcalculatorcalculator125176713Total181230What is the probability that a randomly chosen student will be a girl and own a graphingcalculator?
Answers
Explanation:
The total number of students in the algebra class is given below as
[tex]n(S)=30[/tex]The number of girsl who won a graphing calculator is given below as
[tex]\begin{gathered} n(G_h\cap G_n)=12 \\ where, \\ G_h=have\text{ }graphing\text{ }calculator \\ G_n=does\text{ }not\text{ }have\text{ }graphing \end{gathered}[/tex]Concept:
To figure out the probabaility that a randomly chosen student will be a girl and own a graphing calculator, we will use the formula below
[tex]Pr(G_h\cap G_n)=\frac{n(G_h\cap G_n)}{n(S)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} Pr(G_{h}\operatorname{\cap}G_{n})=\frac{n(G_{h}\operatorname{\cap}G_{n})}{n(S)} \\ Pr(G_h\operatorname{\cap}G_n)=\frac{12}{30} \\ Pr(G_h\operatorname{\cap}G_n)=\frac{2}{5} \end{gathered}[/tex]Hence,
The final answer is
[tex]\frac{2}{5}[/tex]The FOUTH OPTION is the correct answer
Related Questions
The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?
Answers
Answer:
1/4
Step-by-step explanation:
I'm 95% sure that this is the answer. if im not correct, im sorry for wasting your time having to read all of this, and im sorry i couldnt help.
Solve the following system of equations using elimination. 2x + 5y = 12 -2x + 3y = 4
Answers
To solve a system of equation using elimination:
1. If it is necesary multyiply one of both equations for a number that makes each equation have an opposite term to the other equation.
In this case the equations already have opposite terms (2x and -2x)
2. Add equations:
3. Solve the variable in the result of substraction:
[tex]\begin{gathered} 8y=16 \\ y=\frac{16}{8} \\ \\ y=2 \end{gathered}[/tex]4. Use the value of the variable you get in the previus step to solve the other variable:
[tex]\begin{gathered} 2x+5y=12 \\ y=2 \\ \\ 2x+5(2)=12 \\ 2x+10=12 \\ 2x=12-10 \\ 2x=2 \\ x=\frac{2}{2} \\ \\ x=1 \end{gathered}[/tex]Then, the solution for the system of equations is x=1 and y=2A grocery store sells a bag of 3 oranges for $2.16. What is the cost of oranges, in dollars per orange?
Answers
Answer:
0.72
Step-by-step explanation:
The answer is that because all you have to do is just 2.16 divided by 3. Equalling to 0.72. Now we just have to do 0.72 + 0.72 + 0.72 and that would equal $2.16.
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simplify 3y-5y+10y-4y
Answers
To simplify 3y-5y+10y-4y, just add and subtract the coefficients of each term. That is, 3 - 5 + 10 - 4 = 4, which means that the final expression is 4y.
The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Answers
Answer:x=3
Step-by-step explanation: if they are similar lets say for instance BD is congruent to QS.
so TP is congruent to AE and AE is three so TP has to be three.
hope this helps!
please help me solve. I have 81 for blank 1 and 9 for blank 2. it is incorrect
Answers
We can further simplify
[tex]\sqrt[]{27}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3\text{ x 9}} \\ \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x }\sqrt[]{9} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x 3 = 3 x }\sqrt[]{3} \\ \sqrt[]{27}\text{ = 3 }\sqrt[]{3} \end{gathered}[/tex][tex]\sqrt[]{3}\text{ x }\sqrt[]{27\text{ }}\text{ = }\sqrt[]{3}\text{ x 3}\sqrt[]{3}[/tex]The answers for the blank spaces are
[tex]\sqrt[]{3}\text{ and 3}\sqrt[]{3}[/tex]What is the value of this expression: (−2)3 x 30 x (−4)−2
0
-3/2
-3/4
-1/2
3/2
3/4
1/2
Answers
The given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
In the above question, the following mathematical expression is given :
(−2)3 x 30 x (−4)(−20)
We need to find the value of the given expression by solving it using the BODMAS rule
According to the rule, first we'll solve the multiplication then subtraction
Therefore, we get
(−2)3 x 30 x (−4)(−20)
(-6) x 30 x (-)(-)80
We know, that (-) x (-) = +
and (-) x (+) = (-)
Therefore, we get
(-6) x 30 x (-)(-)80
(-6) x 30 x 80
-6 x 2400
- 14400
Hence, the given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
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find the remainder for the given division. (z^2+3z+1)/(z-2)
Answers
Explanation
Given the expression
[tex]\frac{z^{2}+3z+1}{z-2}[/tex]We are asked to find the remainder. We can use the remainder theorem. This can be seen below.
According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.
Therefore, we will have;
[tex]\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}[/tex]
Identify the graph of the ellipse given by the equation below.
Answer options are also attached :)
Answers
The required graph below which represents the given equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1. Which is the correct answer would be option (C).
What is an ellipse?An ellipse can be defined as a shape that looks like an oval circle.
The equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1 which is given in the question.
An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.
Center of the ellipse : (−7,5)
Vertex 1: (0,5)
Vertex 2: (−14,5)
We have attached the required graph below which represents the given
equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1.
Hence, the correct answer would be an option (C).
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How many solutions does the equation 6z − 3z − 7 = −2 + 3 have? (5 points)TwoNoneInfinitely manyOne
Answers
Answer:
One solution.
Explanation:
Let us try to solve the equation and see how many solutions it has.
The first step in solving the equation is to first simplify both the right-hand and the left-hand sides. This means adding all the like terms.
[tex]\begin{gathered} 6z−3z−7=−2+3 \\ \Rightarrow3z-7=1 \end{gathered}[/tex]Next, we add 7 to both sides. This gives
[tex]3x-7+7=1+7[/tex][tex]3x=8[/tex]dividing both sides by 3 gives
[tex]\boxed{z=8/3.}[/tex]which is exactly one solution!
Therefore, our equation had one solution.
three fifths of thr tshirts in a tshirt shop are on sale. five eighths of those tshirts are on sale. one third of those blue tshirts that are on sale are size medium. what fraction of the shops tshirts are blue tshirts that are on sale and are size medium? explain
Answers
3/5 of the T-shirts of the shop are on sale
5/8 of those on sale are blue
1/3 of the blue shirts on sale are medium size.
First calculate how many of the shirts on sale are blue:
[tex]\frac{5}{8}\frac{\div3}{5}=\frac{5}{8}\cdot\frac{5}{3}=\frac{25}{24}[/tex]25/24 of the shirts on sale are blue
Then divide that number by three to know how many are medium size:
[tex]\frac{25}{24}\div3=\frac{25}{72}[/tex]25/72 are blue and medium size
Box A weighs 212.04 kilograms. Box B weighs 212 1/4 kilograms Which statement is true?A) the box weigh the same amountB) Box B weighs 0.10 of a kilogram more than Box AC) Box A weighs 0.15 of a kilogram more than box BD) Vox b weighs 0.21 of a kilogram more than Box A
Answers
To be able to compare the weight of the boxes, we need to have their weight in decimal form:
Box A --> 212.04 kilograms
Box B --> 212 1/4 kilograms
Convert 212 1/4 to decimal:
[tex]\begin{gathered} \text{SINCE }\frac{1}{4}=0.25 \\ 212\frac{1}{4}=212.25 \end{gathered}[/tex]Box B --> 212.25
We can see that the weight of box B is more than the weight of box A, so we discard options A and C.
To find how much more is the weight of box B, we subtract the quantities:
[tex]212.25-212.04=0.21[/tex]Answer: Box B weighs 0.21 of a kilogram more than box A
Ellie wants to save her weekly allowance to go to Disneyland, In 3
weeks she has $40. In 7 weeks, she has $60. Let x represent the
number of weeks and let y represent the total amount saved. Write
an equation in slope intercept form that represents this situation
Answers
The equation in slope-intercept form that represents the situation is y = 5x + 25.
In 3 weeks Ellie she saved $40 and $60 in 7 weeks.
Let x and y represent the number of weeks and the total amount saved respectively.
The equation of a line in slope intercept form is given as:
y = mx + b where m is the slope and b is the y-intercept.
Now when x = 3, y = $40.
Therefore,
y = mx + b
40 = 3m + b --------------(1)
When x = 7, y = $60
y = mx + b
60 = 7m + b -------------(2)
Subtracting (1) from (2),
7m + b - 3m - b = 60 - 40
4m = 20
m = 5
So,
3m + b = 40
3(5) + b = 40
15 + b = 40
b = 25
Hence, the equation of the line in slope intercept form is y = 5x + 25.
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Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram.
Triangles L M N and P Q R are shown. The length of side L M is 11 and the length of P Q is 22. The length of M N is 7 and the length of Q R is 12. The length of N L is 6 and the length of R P is 12.
Which statement is true?
Answers
The statement that is true about the triangle is that D. The triangles are similar by the SSS similarity theorem.
How to illustrate the information?It should be noted that congruence simply refers to a scenario where there are the same triangles.
The SSS Similarity Theorem states that two triangles are similar if all three pairs of matching sides are proportionate.
Compare the shortest sides first, followed by the longest sides, when applying the SSS Similarity Theorem. Two triangles are similar if their corresponding side lengths are proportionate to one another.
Therefore, triangle LMN and PQR are the same.
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The triangles are not similar, but they are congruent.
The triangles are neither similar nor congruent.
The triangles are similar by the SAS similarity theorem.
The triangles are similar by the SSS similarity theorem.
Answer:
d) The triangles are similar by the SSS similarity theorem.
Find Sin A, Cos A, Sin B, and Cos B for the following. Enter answers as fractions in simplest form, not decimals.
Answers
Answer:
[tex]\begin{gathered} \sin A=\frac{\sqrt[]{6}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Explanation:
Let x represent unknown side length
We can go ahead and find x using the Pythagorean Theorem as seen below;
[tex]\begin{gathered} (5\sqrt[]{3})^2=5^2+x^2 \\ (25\times3)=25+x^2 \\ 75-25=x^2 \\ 50=x^2 \\ x=\sqrt[]{50}=\sqrt[]{25\times2}=\sqrt[]{25}\times\sqrt[]{2}=5\sqrt[]{2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]Let's find sin A as seen below;
[tex]\begin{gathered} \sin A=\frac{opposite}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \sin A=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \sin A=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Let's find cos A as seen below;
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \cos A=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find sin B as seen below;
[tex]\begin{gathered} \sin B=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \sin B=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find cos B as seen below;
[tex]\begin{gathered} \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \cos B=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Please help me with this question
Answers
Answer:
The cost of a card is 4 dollars
The cost of a baseball is 18 dollars
Step-by-step explanation:
13c + 9b = 214
3c + 8b = 156
(13c + 9b = 214) × -8
( 3c + 8b = 156) × 9
-104c - 72b = -1712
27c + 72b = 1404
-------------------------------
-77c = -308
÷-77 ÷-77
--------------------
c = 4
3c + 8b = 156
3(4) + 8b = 156
12 + 8b = 156
-12 -12
----------------------
8b = 144
÷8 ÷8
------------------
b = 18
I hope this helps!
a Is it possible to construct a triangle with lengths of 7, 54, and 45? EXPLAIN why or why not?
Answers
For a, b, and c to be the lengths of a triangle they must satisfy the following system of inequalities:
[tex]\begin{gathered} a+b>c, \\ a+c>b, \\ b+c>a\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\begin{gathered} 7+54>45, \\ 45+54>7,\text{ } \\ 45+7=52<54. \end{gathered}[/tex]Since the given numbers do not satisfy the last inequality, then they cannot be the lengths of a triangle.
Answer: No it is not possible to construct a triangle with lengths 7, 54 and 45, because:
[tex]45+7<54.[/tex]Solve the equation _(4t+_) =6t+15
Answers
The given expression is : _( 4t + _ ) = 6t + 15
In the 6t + 15,
The result obtained from measuring length is called a/an __________ measurement and is stated in __________ units.
Answers
The result obtained from measuring length is called a linear measurement and is stated in linear units.
The linear measurement is the distance between the two objects or points. The linear measurement is a single dimension measurement
The unit of the measurement of the length is called linear units. In US system of measurements the linear units are feet, yard and inch etc..,In metric system the linear units are meter, centimeter, decimeter etc..
Therefore the result obtained from measuring length is called a linear measurement and is stated in linear units.
Hence, the result obtained from measuring length is called a linear measurement and is stated in linear units.
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2. (04.01) Which point could be removed in order to make the relation a function? (4 points) {(-9, -8), (-8, 4), (0, -2), (4,8), (0, 8), (1, 2)} (4,8) (0,8) (-9, -8) (1, 2)
Answers
Answer:
(0,8)
Step-by-step explanation:
What is needed in order to be a function?
A value of x cannot have more than one value of y. In this question, we have that for x = 0, there are 2 values of y: -2 and 8. So one of those can be removed.
Among the options, we have: (0,8), which is the correct answer
Koharu pie dough recipe uses 6 oz of flour, 4 oz of butter, and 2 oz of water. Complete the sentences to describe the ratios in her recipe. The ratio of ____ to ____ is 3:2
Answers
Answer:
The ratio of flour to butter is 3:2
Step-by-step explanation:
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2 The model shown below is a composite of tworectangular prisms.What is the volume of the model in cubic units?F 640 H 960G 512 J 1,280
Answers
Answer
Volume of the prism = 960 cubic units
Explanaion:
Step 1: Divide the two prism
Volume of a rectangular prism is
l x w x h
Where l = length, w= width, and h = height
The volume = full prism - cut prism
Full prism = 16 * 10 * 8
Full prism = 1280 cubic units
Cut prism = 8 * 10 * 4
Cut prism = 320 cubic units
Volume = 1280 - 320
Volume = 960 cubic units
Find the slope of the linear regression line for the given data below. Round your
answer to two decimal places.
x y
2 25
3 19
48
5 11
6 15
7 14
Round your final result to two decimal places.
Answers
Answer:
hey bro listen
Step-by-step explanation:
you can't always
get the answers
here try to
do yourself and
see your potential.
Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.figure 1: 9 cubesfigure 2: 13 cubesfigure 3: (blank)figure 4: (blank)figure 5: (blank)
Answers
Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.
figure 1: 9 cubes
figure 2: 13 cubes
figure 3: (blank)
figure 4: (blank)
figure 5: (blank)
Let
f(0)=5
so
For n=0
f(1)=5+4=9
f(1)=9
For n=1
f(2)=9+4=13
f(2)=13
For n=2
f(3)=13+4=17
For n=3
f(4)=17+4=21
For n=4
f(5)=21+4=25
For n=5
f(6)=25+4=29
therefore
theanswer is
figure 3: 17figure 4: 21figure 5: 25Evaluate the polynomial function for the given values of the variable
Answers
ANSWERS
• P(2) = 11
,• P(-1) = 14
,• P(0) = 7
EXPLANATION
Every time we have to evaluate a function, what we have to do is replace the variable with the value and solve the operations.
Let's solve P(2),
[tex]P(2)=3(2)^2-4(2)+7[/tex]Solve the powers first,
[tex]P(2)=3\cdot4-4\cdot2+7[/tex]Then the products,
[tex]P(2)=12-8+7[/tex]And then the additions/subtractions,
[tex]P(2)=11[/tex]The process is the same for the other two values,
[tex]P(-1)=3(-1)^2-4(-1)+7=3\cdot1-4(-1)+7=3+4+7=14[/tex]And,
[tex]P(0)=3(0)^2-4(0)+7=3\cdot0-4\cdot0+7=0+0+7=7[/tex]Hence, P(2) = 11, P(-1) = 14 and P(0) = 7.
factorize the following if possible 5z^2+35z-90
Answers
Answer:
5z² + 35z - 90 = 0
5(z² + 7z - 18) = 0
z² + 7z - 18 = 0
(z - 2)(z + 9) = 0
r=−9, s=2
STEPS USING THE DIRECT FACTORING METHOD
5z²+35z−90
This quadratic equation can be resolved using a revolutionary direct factoring technique that does not rely on guesswork. The equation must have the form x2+Bx+C=0 to be solved using the direct factoring approach. To do this, multiply both sides of the equation by 5.
x²+7x−18=0
Let r and s be the factors for the quadratic equation such that x²+Bx+C=(x−r)(x−s) where the sum of factors (r+s)=−B and the product of factors rs=C
r+s=−7
rs=−18
When the average of the two integers is 1/2*-7=-7 /2, the sum of the two numbers r and s are exactly 7. You can also observe that the parabola symbolized by the quadratic equation y=x2+Bx+C has its axis of symmetry in the middle of r and s. An unknown quantity u separates the values of r and s from the center at an equal distance. Describe r and s about the variable u.
r=−7/2−u
s=−7/2+u
Put these in the product equation rs=-18 to solve for the unknown quantity u.
(−27−u)(−27+u)=−18
Simplify by expanding (a−b)(a+b)=a2–b2
49/4−u²=−18
Simplify the expression by subtracting 49/4 on both sides
−u2=−18−49/4=−121/4
To find the value of the unknowable variable u, simplify the expression by multiplying by 1 on both sides and taking the square root.
u2=121/4
u=±√121/4=±11/2
The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.
r=−7/2−11/2=−9
s=−7/2+11/2=2
Therefore, r=−9, s=2
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what is 576.984 round in to the nearest tenths
Answers
Answer: 577
Step-by-step explanation:
Answer:
577.0
Rounded to the nearest 0.1 or
the Tenths Place.
Step-by-step explanation:
576.984
You rounded to the nearest tenths place. The 9 in the tenths place rounds up to 10 because the digit to the right in the hundredths place is 8.
Because the tenths place was rounded up from 9 to 10, the tenths place becomes 0 and the ones place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0 and we add 1 to the previous place value.
577.0
When the digit to the right is 5 or greater we round away from 0.
576.984 was rounded up and away from zero to 577.0
Find the least common denominator of
8/x²+11x+28
and
-2/x^2+4x
Answers
The least common denominator of 8/( x²+11x+28 ) and -2/ (x^2+4x) is (x+4).
We have to find the least common denominator of 8/x²+11x+28 and -2/x^2+4x. We can solve this problem by following a few steps.
The denominator of both terms is, x²+11x+28 and x²+4x.
First of all, we have to find the factors of these two terms.
Let's find the factors of x²+11x+28.
x²+11x+28 = x²+11x+28
Or, x²+11x+28 = x²+ 4x+ 7x+ 28 [ we have to break the middle term in such a way as the product of consecutive terms must be 28 ]
Or, x²+11x+28 = x (x+4) +7 (x-4) [ we have to take ( x+ 4) as acommon ]
Or, x²+11x+28 = ( x+4 )( x+7 ).................(1)
Now find the factors of x²+4x.
x²+4x = x (x+4)..................(2) [ We have to take x as a common ]
Therefore, the common term between (1) and (2) is ( x+4 ). So, the least common denominator is ( x+4 ).
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What must x equal if a ∥ b? Explain.
Answers
The value of x should be equal to 23
Given
Angle at the top is 86
also equation 3x + 17
The lines are parallel
We know if a transverse line is drawn across two parallel lines then 3 types of angles would form namely Corresponding angle, alternate angle, Opposite angle.
From the geometry the angle 86 and the equations 3x + 17 are alternative angles.
Since alternative angles are equal 86 will be equal to 3x + 17
Now equating both
86 = 3x + 17
86 - 17 = 3x
69 = 3x
x = 23
Hence the value of x is equal to 23
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Answer: x=23
Step-by-step explanation:
Im not going to bore you with long algebra but basically 86-17=3x
69=3x inverse you get 23
Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets ofcardboard from which she cuts out 2-in squares from eachPLEASE CHECK PHOTO
Answers
Solution:
Given:
When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;
[tex]\begin{gathered} l=(x+4)-2-2=x+4-4=x \\ w=x-2-2=x-4 \\ h=2 \\ \\ The\text{ volume }V=792in^3 \end{gathered}[/tex]The volume of a cuboid is given by;
[tex]\begin{gathered} V=lwh \\ 792=(x)(x-4)(2) \\ Dividing\text{ both sides by 2;} \\ \frac{792}{2}=x(x-4) \\ 396=x^2-4x \\ \\ Collecting\text{ all sides to one side to form a quadratic equation;} \\ 0=x^2-4x-396 \\ x^2-4x-396=0 \end{gathered}[/tex]Solve the quadratic equation by factorization;
[tex]\begin{gathered} x^2-4x-396=0 \\ x^2+18x-22x-396=0 \\ x(x+18)-22(x+18)=0 \\ (x-22)(x+18)=0 \\ x=22,x=-18 \\ \\ Since\text{ the dimension of a box can not be negative, then;} \\ x=22in \end{gathered}[/tex]Hence, the dimension of the original piece of cardboard is;
[tex]\begin{gathered} (x+4)\text{ by }x \\ \\ Substitute\text{ the value of x, the dimension of the cardboard is;} \\ (22+4)\text{ by }22 \\ 26in\text{ by }22in \end{gathered}[/tex]Therefore, the dimensions of the original piece of cardboard are 26 in by 22in