Given,
The mathematical expressions are
1+4=5
2+5=12
3+6=21
8+11=?
The pattern of the expression is,
[tex]\begin{gathered} 1+1\times4=5 \\ 2+2\times5=12 \\ 3+3\times6=21 \end{gathered}[/tex]Similarly,
[tex]8+8\times11=96[/tex]Hence, the value is 96.
Completing the square to find the zeros3. a^2+2a-3=0
Answer:
1 and -3.
Explanation:
Given the quadratic polynomial:
[tex]a^2+2a-3=0[/tex]To use the completing the square method to find the zeros, follow the steps below:
Step 1: Take the constant to the right-hand side.
[tex]a^2+2a=3[/tex]Step 2: Divide the coefficient of a by 2, square it and add it to both sides.
[tex]a^2+2a+(1)^2=3+(1)^2[/tex]Step 3: Write the left-hand side as a perfect square.
[tex](a+1)^2=4[/tex]Step 4: Take the square root of both sides.
[tex]a+1=\pm\sqrt[]{4}[/tex]Step 5: Solve for a.
[tex]\begin{gathered} a=-1\pm\sqrt[]{4} \\ a=-1\pm2 \\ a=-1+2\text{ or }a=-1-2 \\ a=1\text{ or }a=-3 \end{gathered}[/tex]The zeros of the quadratic equation are 1 and -3.
find the area of a regular 18-gon with radius of 14 mmA≈ __ mm squared do not found until the final answer, then round to the nearest tenth as needed.
ANSWER
EXPLANATION:
Given that;
The radius of the 18-gon is 14mm
Follow the steps below
Step 1; Calculate the interior angle by using the below formula
[tex]\text{ }\theta\text{ = }\frac{\text{ 180 \lparen n - 2\rparen}}{n}[/tex]Since the polygon has 18 sides, then n = 8
[tex]\begin{gathered} \text{ }\theta\text{ }=\text{ }\frac{180\text{ \lparen18 - 2\rparen}}{18} \\ \\ \theta\text{ }=\text{ }\frac{180\text{ }\times\text{ 16}}{18} \\ \\ \theta\text{ }=\text{ }\frac{2880}{18} \\ \theta\text{ }=\text{ 160}\degree \end{gathered}[/tex]Step 2; Find the base angle of the triangle
Recall, that all regular polygon can be divided into isosceles triangle by joining the vertices to the center. Hence, the base angle can be calculated below as
[tex]\begin{gathered} \text{ Base angle = }\frac{160}{2} \\ \text{ Base angle = 80}\degree \end{gathered}[/tex]Step 3; Find the height of triangle using trigonometric
[tex]\begin{gathered} \text{ tan }\theta\text{ }=\text{ }\frac{\text{ opposite}}{\text{ adjacent}} \\ \text{ } \end{gathered}[/tex]Since the radius of the polygon is 14mm, therefore, the base length is
[tex]\begin{gathered} \text{ Base length = }\frac{14}{2} \\ \text{ Base length = 7mm} \end{gathered}[/tex][tex]\begin{gathered} \text{ Tan 80 = }\frac{h}{7} \\ \text{ cross multiply} \\ \text{ h = tan 80 }\times\text{ 7} \\ \text{ h = 7tan 80} \\ \text{ tan 80 = 5.671} \\ \text{ h = 7 }\times\text{ 5.671} \\ \text{ h = 39.697 mm} \end{gathered}[/tex]Step 4; Find the area of the triangle
[tex]\begin{gathered} \text{ Area of a triangle = }\frac{1}{2}bh \\ \text{ Area of a trianlge = }\frac{1}{2}\times7\times39.697 \\ \text{ Area of a triangle = }\frac{277.879}{2} \\ \text{ Area of a triangle = 138.94 mm}^2 \end{gathered}[/tex]Step 5; Find the area of the polygon
Since there are 18 triangles in the polygon, then calculate the area of the 18-gon
Area of 18-gon = 18 x 138.94
Area of 18-gon = 2500.9 mm^2
Therefore, the area of the 18-gon is 2500.
7 thirds x 3 eighths
Answer: 0.875
Step-by-step explanation:
7/3 x 3/8 -> 21/24 -> 7/8
7/8 converted to decimal: 0.875
Circle C and circle J are congruent, what is NM?
Ok, so
We know that two circles are congruent. This makes that the triangles there, are cogruent.
Let me draw the situation here below:
If both triangles are congruent, that means that their sides and angles are equal.
Now if we notice, we realize that side DG and side NM will be equal.
So, DG = NM
Which is the same that
14t - 26 = 5t + 1
If we solve the equation for t:
14t - 5t = 26 + 1
9t = 27
And t = 3
Now, we want to find NM measure.
And we just have to replace t=3 in the expression 5t+1
This will be 5(3) + 1, which is 16.
Therefore, NM measures 16.
33. A coin is tossed and a die with numbers 1-6 is rolled. What is P(head and 3)a. 1/12b. 1/4C.1/3d. 2/334. Two cards are selected from a deck of cards numbered 1 - 10. Once a card isselected, it is replaced. What is P(two even numbers)?a. 1/4b. 2/9c. 1/2d. 135. Which of the following in NOT an example of independent events?a. rolling a die and spinning a spinnerb. tossing a coin two timesc. picking two cards from a deck with replacement of first cardd. selecting two marbles one at a time without replacement36. A club has 25 members, 20 boys and 5 girls. Two members are selected atrandom to serve as president and vice president. What is the probability that bothwill be girls?b. 1/25c. 1/30d. *a. 1/537. One marble is randomly drawn and then replaced from a jar containing twowhite marbles and one black marble. A second marble is drawn. What is theprobability of drawing a white and then a black?b. 2/9c. 3/8a. 1/3d. 1/638. Maria rolls a pair of dice. What is the probability that she obtains a sum that iseither a multiple of 3 OR a multiple of 4?a. 5/9b. 7/12c. 1/36d. 7/3639. Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What isP(A and B)?c. 4/15d. 2/15b. 1/5a. 2/5
SOLUTION
(33) The question says a coin is tossed and a die with 6 faces is rolled, what is the probability of getting a head and a 3.
Probability is given as
[tex]Probability=\frac{expected\text{ outcome}}{total\text{ outcome }}[/tex]Now, a coin has two faces, a head and a tail. So, total outcome is 2 faces.
We want to get the probability of getting a head. This becomes
[tex]\begin{gathered} Probability\text{ of head = }\frac{expected\text{ outcome}}{total\text{ outcome}}=\frac{1\text{ head}}{2\text{ faces}} \\ =\frac{1}{2} \\ P(head)=\frac{1}{2} \end{gathered}[/tex]So, probability of getting a head is 1/2
A die has 6 faces labelled 1, 2, 3, 4, 5 and 6
Probability of getting a 3 should be
[tex]\begin{gathered} Probability\text{ of getting 3 = }\frac{one\text{ face showing 3}}{6\text{ faces}} \\ that\text{ is }\frac{1}{6} \end{gathered}[/tex]So, probability of getting a 3 is 1/6
Now probability of getting a head and a 3, that is P(head and 3), means we multiply both probabilities, we have
[tex]\begin{gathered} P(head\text{ and 3\rparen = }\frac{1}{2}\times\frac{1}{6} \\ =\frac{1}{12} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{12}[/tex]To show that you can identify implied mul-tiplication, rewrite this algebraic equationusing the times symbol wherever multipli-cation is implied.
In general, if a and b are two numbers,
[tex]\begin{gathered} ab=a*b \\ and \\ a(b)=a*b \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} bc=b*c \\ \Rightarrow3(bc)=3*(b*c)=3*b*c \\ and \\ 2d=2*d \end{gathered}[/tex]Thus, the answer is[tex]3*b*c=2*d[/tex]3*b*c=2*dCan decimals be constants?
Constants refer to a number and a decimal is a number expressed in decimal notation, therefore, decimals can be constants.
What is a decimal?A decimal number is the expression of a fraction in terms of the quotient of the fraction, for example, 1/4 in decimal form is 0.25.
The standard form or system for representing numbers that are integers and numbers that are non integers is the decimal number system which is based on the Hindu-Arabic number system.
When numbers (integers and non integers) are expressed as decimals, the numbers are cited as being in decimal notation.
The location of a number in decimal notation is between the ones and tenth place of the number.
A constant is a value in an expression or equation that remains the same in an equation.
A constant is therefore expressed quantitatively as a number.
Therefore, decimals, which are also numbers can be constants.
Learn more about decimals and fractions here:
https://brainly.com/question/26231115
#SPJ1
SI unit conversion Could you please help me with exercise number 12 please and explain the process? I copied exercise 11 from the board and trued to solve #13 but not sure if it’s correct
Given:-
[tex]9468mg=\ldots kg[/tex]To find the required solution.
So we use the formula,
[tex]1\operatorname{kg}=1000000mg[/tex]So now we substitute,
[tex]\frac{9468}{1000000}=0.009468[/tex]So the required solution is 0.009468 kg.
264 milligrams is how many grams
SOLUTION
Milligrams is a unit of measurement for mass in which a unit is a thousandth gram.
Hence
[tex]1000mg=1g[/tex]Then
[tex]264mg=xg[/tex]Therefore
[tex]x=\frac{264}{1000}=0.264g[/tex]Hence
[tex]264mg=0.264g[/tex]Therefore we conclude that
264 milligrams is 0.264g
A plane has a speed of 400mi/h. On a windy day, theplane could fly 75 mi with thewind in the same time it tookto fly 65mi against the samewind. What is the rate of thewind?
The plane has a top speed of 400 miles per hour. That means if it travelled at this same speed on a windy day, it would cover
[tex]undefined[/tex]I need help to find X for my warm up paper. I'll include the photo as it doesnt fit:) 2 brainly tutors tried to help but they just told me they couldnt and I really need help:/
The inscribed angle SKQ intercepts the arc SQ. The next equation relates their measures:
[tex]\begin{gathered} \angle SKQ=\frac{1}{2}\hat{SQ} \\ 75=\frac{1}{2}\hat{SQ} \\ 75\cdot2=\hat{SQ} \\ 150\text{ \degree}=\hat{SQ} \end{gathered}[/tex]Arc SQ can be expressed as the addition of arcs SR and RQ.
[tex]\begin{gathered} \hat{SQ}=\hat{SR}+\hat{RQ} \\ 150=\hat{SR}+60 \\ 150-60=\hat{SR} \\ 90\text{ \degree}=\hat{SR} \end{gathered}[/tex]The inscribed angle KQR intercepts the arc KR. The next equation relates their measures:
[tex]\begin{gathered} \angle KQR=\frac{1}{2}\hat{KR} \\ 78=\frac{1}{2}\hat{KR} \\ 78\cdot2=\hat{KR} \\ 156\text{ \degree}=\hat{KR} \end{gathered}[/tex]Arc KR can be expressed as the addition of arcs KS and SR.
[tex]\begin{gathered} \hat{KR}=\hat{KS}+\hat{SR} \\ 156=\hat{KS}+90 \\ 156-90=\hat{KS} \\ 66\text{ \degree}=\hat{KS} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} \hat{KS}=11x \\ 66=11x \\ \frac{66}{11}=x \\ 6=x \end{gathered}[/tex]in the diagram ,EF and AB are parallel .Line CD is a transversal PartA:Describe the transformation that will take
The described transformation is a translation and a reflection that is dilation.
By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made.
The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation. A function can be moved in one direction or another by translation, rotated around a point by rotation, reflected in its mirror image by reflection, and scaled by dilation.
The dilation is the transformation that causes the 2-d shape to stretch or contract vertically or horizontally by a fixed amount. The equation y = a.f. yields the vertical stretch (x). The function stretches in relation to the y-axis if a > 1.
Hence we get the required answer.
Learn more about Transformations here:
brainly.com/question/4289712
#SPJ9
Find the surface area of the isosceles trapezoid prism , Do not round answer
From the question;
The Area formula for a trapezoid is;
[tex]\begin{gathered} B=\frac{1}{2}h(b_1+b_2) \\ Where\text{ B=Area} \\ h=\text{height of the trapezoid} \\ b_1,b_2=bases_{} \end{gathered}[/tex][tex]\begin{gathered} B=\frac{1}{2}(3)(4+8) \\ B=18\operatorname{cm} \end{gathered}[/tex]So, we have the surface area as;
[tex]\begin{gathered} SA=ph+2B \\ \text{Where SA= surface area} \\ p=\text{perimeter of the trapezoid} \\ h=\text{height of the prism} \end{gathered}[/tex]But the perimeter p of the trapezoid is;
[tex]\begin{gathered} p=3.7\operatorname{cm}+4\operatorname{cm}+8\operatorname{cm}+3.7\operatorname{cm} \\ p=19.4\operatorname{cm} \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} SA=19.4(9)+2(18) \\ SA=174.6+36 \\ SA=210.6\operatorname{cm} \end{gathered}[/tex]What is a discrete set?Is option d and e and possibly c?
Discrete sets are sets which members are countable and distinct.
That is, they are separable and can only have a certain value.
For example, the number of players in a rugby team is discrete because they are countable.
Hence, options C, Dare applicable.
Tina babysits and cuts lawns to earn money. For one week, she babysits for 5 hours. She earns $8.25 per hour babysitting If Tina earns $92 this week, how much does tina earn cutting lawns? 1) $10.152) $16.753) $41.254( $50.75
Answer:
[tex]\text{ \$50.75}[/tex]Explanation:
Here, we want to calculate how much Tina earns cutting lawns
From the question, she earns $8.25 per hour for 5 hours cutting lawns
What she earned in totality that week would be:
[tex]\text{ 5 }\times\text{ \$8.25 = \$41.25}[/tex]What she earned cutting lawns would be the total earned minus what she earned cutting lawns
Mathematically, we have that as:
[tex]\text{ \$92 - \$41.25 = \$50.75}[/tex]Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.
Answer:
[tex]84.3\text{ cm}^2[/tex]Explanation:
Here, we want to calculate the area of the regular heptagon
Mathematically, we use the formula below:
[tex]A\text{ = a}^2n\text{ tan\lparen}\frac{180}{n})[/tex]where:
a is the length of the apothem which is 5 cm
n is the number of sides of the polygon which is 7 (heptagon is a 7-sides polygon)
Substituting the values, we have it that:
[tex]\begin{gathered} A\text{ = 5}^2\times7\text{ }\times\text{ tan }\frac{180}{7} \\ \\ A\text{ = 84.3 cm}^2 \end{gathered}[/tex]How do you write 1.9 x 102 in standard form?
We are given the following number in scientific notation.
[tex]1.9\times10^2[/tex]We are asked to write this number in standard form.
Method 1:
Simply multiply 1.9 by 10²
[tex]1.9\times10^2=1.9\times(10\times10)=1.9\times100=190[/tex]Method 2:
Simply move the decimal point to the right by 2 places (since the exponent is 2
which ordered pair below would prevent this table from being a function?
We have the following:
A relation is a correspondence of elements between two sets.
A function is a relation where each element of a set (A) corresponds to one and only one element of another set (B).
Therefore, the only value in x that is repeated is -2, therefore the answer (-2, 0)
What is the simplified value of 3/4 5/12 fraction
Thus, the final value is 5/16.
If a set of grades for a class has a large range and a small standard deviation,what can you say about the class? Include an interpretation that is specific togrades in a class.
A large ranges indicates that there is a large difference between the highest and lowest grade scores. A smaller deviation indicates that the grades scores are less varied amom themselves.
An example is when the highest grade is 100 and the lowest grade is 5. In this case the range is larger than the case when the highest is 100 and the lowest 60.
A smaller standard deviation means that the data set of grades are close to the mean of the data set. The behavior is the following
Justin’s shop sells 6 1/2 quarts of ice cream each day. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form.Include the correct unit in your answer.
1) In this question we need to remind ourselves that there is one equivalence between quarts and pints, namely:
[tex]1\:quart--->2\:pint[/tex]2) Based on that, we can write out the following set of ratios:
[tex]\begin{gathered} \frac{1}{6\frac{1}{2}}=\frac{2}{x} \\ \\ x=2\times6\frac{1}{2} \\ \\ x=13 \end{gathered}[/tex]Note that there is a proportional relationship between them.
3) Thus, this is the answer.
An investment of R2000 is made at 10 %per year simple interest for 3 years. The amount earned is there invested for 5 years at 16 %simple interest calculator the value of the investment at the end of 8 year
Explanation
We are asked to calculate the value of the investment at the end of 8 years
For the first part, we will find how much R2000 will yield after 3 years
[tex]\begin{gathered} A=P(1+rt) \\ P=2000 \\ r=10\text{ \% =0.1} \\ t=3 \\ \\ A=2000(1+0.1\times3) \\ A=2000(1+0.3) \\ A=2000(1.3) \\ \\ A=R2600 \end{gathered}[/tex]For the second part, we will have to know how much R2600 will yield after 5 years
[tex]\begin{gathered} P=2600 \\ t=5\text{ years} \\ r=16\text{ \%=0.16} \\ \\ A=2600(1+0.16(5)) \\ A=2600(1+0.8) \\ A=R4680 \\ \end{gathered}[/tex]At the end of the 8 years, the value of the investment will be R4680
Write an equation for the conic in the xy-plane for
Given:
[tex]\frac{(x^{\prime})^2}{15}-\frac{(y^{\prime})^2}{6}=1\text{ at }\theta=30^o[/tex]To find:
We need to find an equation for the conic in the xy-plane.
Explanation:
We can find the conic equation by using the following equation.
[tex]x^{\prime}=x\cos \theta+y\sin \theta\text{ and }y^{\prime}=y\cos \theta-x\sin \theta[/tex][tex]\text{Substitute }\theta=30^o\text{ in the eqatuions.}[/tex][tex]x^{\prime}=x\cos 30^o+y\sin 30^o\text{ and }y^{\prime}=y\cos 30^o-x\sin 30^o\text{.}[/tex][tex]\text{Use }\cos 30^o=\frac{\sqrt[]{3}}{2}\text{ and }\sin 30^o=\frac{1}{2}\text{.}[/tex][tex]x^{\prime}=x(\frac{\sqrt[]{3}}{2})+y(\frac{1}{2})\text{ and }y^{\prime}=y(\frac{\sqrt[]{3}}{2})-x(\frac{1}{2})[/tex][tex]x^{\prime}=\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y\text{ and }y^{\prime}=\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x[/tex][tex]\text{ Substitute }x^{\prime}=\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y\text{ and }y^{\prime}=\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x\text{ in the given equation.}[/tex][tex]\frac{(\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y)^2}{15}-\frac{(\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x)^2}{6}=1[/tex][tex]\frac{1}{15}(\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y)^2-\frac{1}{6}(\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x)^2=1[/tex][tex]\frac{1}{15}\mleft\lbrace(\frac{\sqrt[]{3}x}{2})^2+(2\times\frac{\sqrt[]{3}x}{2}\times\frac{y}{2})+(\frac{y}{2})^2\mright\rbrace-\frac{1}{6}\mleft\lbrace(\frac{\sqrt[]{3}y}{2})^2-2\times\frac{\sqrt[]{3}y}{2}\times\frac{x}{2}+(\frac{x}{2})^2\mright\rbrace=1[/tex][tex]\frac{1}{15}\mleft\lbrace\frac{3x}{4}^2+\frac{\sqrt[]{3}xy}{2}+\frac{y^2}{4}^{}\mright\rbrace-\frac{1}{6}\mleft\lbrace\frac{3y}{4}^2-\frac{\sqrt[]{3}xy}{2}+\frac{x}{4}^2\mright\rbrace=1[/tex][tex]\frac{3x^2}{15\times4}^{}+\frac{\sqrt[]{3}xy}{15\times2}+\frac{y^2}{15\times4}^{}-\frac{3y^2}{6\times4}^{}+\frac{\sqrt[]{3}xy}{6\times2}-\frac{x}{6\times4}^2=1[/tex][tex]\frac{x^2}{20}^{}+\frac{\sqrt[]{3}xy}{30}+\frac{y^2}{60}^{}-\frac{y^2}{8}^{}+\frac{\sqrt[]{3}xy}{12}-\frac{x^2}{24}^{}=1[/tex]Here LCM is 360, making the denominator 360.
[tex]18x^2+12\sqrt[]{3}xy+6y^2-45y^2+30\sqrt[]{3}xy-15x^2=360[/tex][tex]3x^2+42\sqrt[]{3}xy-39y^2-360=0[/tex]Final answer:
The equation for the conic in the xy-plane is
[tex]3x^2+42\sqrt[]{3}xy-39y^2-360=0[/tex]Which expression is undefined? -8÷(-8) -8÷80÷88÷0
The expressions where a number is divided by 0 are undefined, as the result would became indefinitely big (infinity).
The expression -8÷80÷88÷0 has a division by 0, so it is undefined.
Can you please show me how to do this so I can teach it to my boys? They need to Express percents as fractions or mixed numbers, and to express each percent as a decimal.
A. Let's convert the following percents into a fraction or a mixed number in the simplest form.
1.) 24%
4.) 150%
To be able to convert percentage into a fraction, we just apply the following formula:
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex]We get,
1.) 24%
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex][tex]\text{ = }\frac{24}{100}[/tex][tex]\text{ = }\frac{\frac{24}{4}}{\frac{100}{4}}\text{ = }\frac{6}{25}[/tex]Therefore, the fractional form of 24% is 6/25.
4.) 150%
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex][tex]\text{ = }\frac{150}{100}[/tex][tex]\text{ = 1 }\frac{50}{100}\text{ = 1}\frac{1}{2}[/tex]Therefore, the fractional form of 150% is 1 1/2.
B. Express each percent as a decimal.
9.) 8%
14.) 568%
To be able to convert a percentage to a decimal, we just divide all percentages by 100.
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex]9.) 8%
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex][tex]\text{ = 8 }\div\text{ 100}[/tex][tex]\text{ Decimal Equivalent = 0.08}[/tex]14.) 568%
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex][tex]\text{ = 568 }\div\text{ 100}[/tex][tex]\text{ Decimal Equivalent = 5.68}[/tex]Therefore, the decimal equivalent of 568% is 5.68.
convert the following from degrees to radians (use × 180/pi)(-2pi)/7
Use the conversion 180/pi
[tex]-\frac{2\pi}{7}\cdot\frac{180}{\pi}=-\frac{360}{7}=-51.43[/tex]which inequality best represents that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C
that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C:
[tex]-3C^{\circ}<1C^{\circ}[/tex]18/10 [blank] x/12 x =
18/10 = x/12
(18/10)* 12 = (x/12)* 12
18*12/ 10 = x (12/12)
216/ 10 = x
x= 108/5
x = 21.6
Suppose that y varies jointly with w and x and inversely with z and y = 24 when w = 8, X= 9 and z = 6. Write the equation that models the relationship. Then find y when w = 2, X= 20 and z = 8.
We would have the following:
[tex]24=\frac{8\cdot9}{6}\cdot2[/tex]From this, we will have the following expression:
[tex]z=2\cdot\frac{w\cdot x}{y}[/tex]Now, we determine the values after replacing the ones given:
[tex]8=2\cdot\frac{2\cdot20}{y}\Rightarrow y=\frac{4\cdot20}{8}\Rightarrow y=10[/tex]The value of y is 10.
Wyatt's eraser box is shaped as a rectangular prism. His erasers are cubes with 1-centimeter sides. The
bottom of the box can hold 14 erasers, and the box is 6 centimeters tall. How many erasers can Wyatt fit
in his box?
Each eraser has the shape of a cube with a side length of 1 cm.
The eraser box is a rectangular prism (a rectangular box).
We know the bottom of the box can hold 14 erasers. If we lay 14 more erasers on top of it, we would have used 2 cm of the box's height.
We can do it a total of 6 times until we top up the box, thus the total number of erasers that fit the box is 6*14 = 84 erasers