Two matrices can always be multiplied if the have the same dimensions. True False
Answers
SOLUTION:
Case: Matrices multiplication
Given:
Two matrices can always be multiplied if they have the same dimensions.
Method:
From the image above, if and only if the number of items of columns matches the number of items of the columns, then it is possible to multiply.
Final answer:
True,
Two matrices can always be multiplied if they have the same dimensions
Related Questions
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.
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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
Write an equation for the conic in the xy-plane for
Answers
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]>>Хx = [?](Enter the number that belongs in the green box.
Answers
Answer: x = 90 degrees
Explanation:
In the given figure, the opposite sides are parallel. This means that the vertices are right angles. A right angle is 90 degrees. Thus,
x = 90 degrees
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.
Answers
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.
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.
Answers
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.
What is a discrete set?Is option d and e and possibly c?
Answers
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.
7 thirds x 3 eighths
Answers
Answer: 0.875
Step-by-step explanation:
7/3 x 3/8 -> 21/24 -> 7/8
7/8 converted to decimal: 0.875
Find the surface area of the isosceles trapezoid prism , Do not round answer
Answers
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]How do you write 1.9 x 102 in standard form?
Answers
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
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?
Answers
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]which ordered pair below would prevent this table from being a function?
Answers
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
Answers
Thus, the final value is 5/16.
I have a practice question that I need explained and answered. Thank you - Rose
Answers
To determine the x - coordinate of the distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The distance between the two points is estimated using the above formular
[tex]\begin{gathered} x_2=4 \\ x_1=?_{} \\ y_1=-1 \\ y_2=9 \\ d=6\sqrt[]{6} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ 6\sqrt[]{6}=\sqrt[]{(x-4)^2+(9--1)^2} \\ \text{square both side } \\ (6\sqrt[]{6)^2}=(\sqrt[]{(x-4)^2+10^2})^2 \\ 216=(x-4)^2+100 \\ 216-100=(x-4)^2 \end{gathered}[/tex][tex]\begin{gathered} 116=(x-4)(x-4) \\ 116=x^2-8x+16 \\ 100=x^2-8x \\ x^2-8x-100=0 \end{gathered}[/tex]Solve using quadratic formular
[tex]\frac{-b\pm\sqrt[]{b^2}-4ac}{2a}[/tex][tex]\begin{gathered} \frac{-b\pm\sqrt[]{b^2}-4ac}{2a}\ldots..\text{ a= 1 , b = -8 , c = -100} \\ \frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-100)}}{2(1)} \\ \frac{8\pm\sqrt[]{64+400}}{2} \\ \frac{8\pm\sqrt[]{464}}{2}=\frac{8\pm4\sqrt[]{29}}{2} \\ \frac{2(4\pm2\sqrt[]{29)}}{2}=4\pm2\sqrt[]{29} \end{gathered}[/tex]Therefore the correct answer for the x - coordinates are:
[tex]\begin{gathered} x=4+2\sqrt[]{29}\text{ and } \\ x_{}=4-2\sqrt[]{29} \end{gathered}[/tex]18/10 [blank] x/12 x =
Answers
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
slove two-step liner equations 19=s/2+15
Answers
s = 8
Explanation:
19=s/2+15
collect like terms:
19 - 15 = s/2
4 = s/2
[tex]\begin{gathered} 4\text{ =}\frac{s}{2} \\ \text{cross multiply} \\ s\text{ = 4}\times2 \\ s\text{ = 8} \end{gathered}[/tex]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
Answers
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]Can decimals be constants?
Answers
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
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-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 Which of the following inequalities is represented by the number line?
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Here, we want to select the inequality that is represented by the plot
The first thing we will do here is to get the type of circle given, whether shaded or unshaded
As we can see, the circle on the number -3 is unshaded
What this mean is that the type of inequality we shall be considering is the one without equal to
Hence, option A and C is out of it
To get the correct one between B and D, we have to look at the direction of the black line beside the circle
The direction of the black line as we can see is towards the right hand side
What this mean is that the inequality in question is greater than the value on which we have the circle
Conclusively, this mean that our answer is the second option
how much higher is 1,774 than -118(adding and subtracting integers)
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To find the difference between two numbers, we substract the smaller one from the bigger one. In this case, the smaller one is -118 and the bigger one is 1,774. Then:
[tex]1774-(-118)=1774+118=1892[/tex]Then 1774 is higher than -118 by 1892
To show that you can identify implied mul-tiplication, rewrite this algebraic equationusing the times symbol wherever multipli-cation is implied.
Answers
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 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.
Answers
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.
Which expression is undefined? -8÷(-8) -8÷80÷88÷0
Answers
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.
what is the answer to the equation-2n+3=8
Answers
-2n + 3 = 8
-2n = 8 - 3
-2n = 5
n = -5/2
Circle C and circle J are congruent, what is NM?
Answers
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.
264 milligrams is how many grams
Answers
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
How do you solve literal equation:u=x-k, solve for x12am=4, solve for aa-c=d-r, solve for a
Answers
In order to solve a literal equation, we just need to isolate the chosen variable in one side of the equation. So we have:
[tex]\begin{gathered} u=x-k \\ u+k=x \\ x=u+k \\ \\ 12am=4 \\ a=\frac{4}{12m} \\ a=\frac{1}{3m} \\ \\ a-c=d-r \\ a=d-r+c \end{gathered}[/tex]convert the following from degrees to radians (use × 180/pi)(-2pi)/7
Answers
Use the conversion 180/pi
[tex]-\frac{2\pi}{7}\cdot\frac{180}{\pi}=-\frac{360}{7}=-51.43[/tex]Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.
Answers
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]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:/
Answers
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]Completing the square to find the zeros3. a^2+2a-3=0
Answers
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.