You can use decimal numbers (those numbers that have a comma after an interger part and before the decimal part)
You can use decimal numbers in real life in measures as:
Examples:
weight (you can weight 132,27 lb)
volumen of soda (you can drink a glass of soda of 8,45 oz = 0,25 L)
The temperature ( the temperature can be 89,9 F)
All the examples above have decimal number that can be useful in every-day life.
Factor 12x² + 19x - 21.O (6x + 7)(2x − 3)—O (4x - 3)(3x + 7)O(6x-7)(2x + 3)(4x + 3)(3x7)
given the expression
[tex]12x^2+19x-21[/tex]we are loking 2 numbers whose multiplication is equal to 12
and other 2 number whose multiplication is equal to 21
the sum of the cross multiplication is equal of 19, as follows
[tex](4x*3x)+((4x*7)+(3x*-3))+(-3*7)[/tex]factor is
[tex]\left(4x-3\right)\left(3x+7\right)[/tex]correct answer option B
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
Answer:
29 units
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/sqrt2
If In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Then BC is 29 units
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units.
We need to find BC
In triangle ACD,
tan 45° = CD/AD
CD = tan 45° x AD
= 1 x 20= 20 units
In triangle CDB,
tanФ = CD/BD
Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
BC = CD/sin 43.6°
= 20/0.689
= 29 units
Hence the length of BC will be 29 units.
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What are all the factors of 54?
To find the factors of a number, we can look for factors to divide it by subsequently.
It is easier to start with lower factors.
Let's start by "2".
Since "54" is even, it is divisable by "2":
[tex]\frac{54}{2}=27[/tex]So "2" is one of the factors.
Now, we have got 27. It is not even anymore, but it is divisable by "3":
[tex]\frac{27}{3}=9[/tex]So "3" is another factor.
Now we have got "9" and it is also divisable by "3":
[tex]\frac{9}{3}=3[/tex]So there is another "3" factor.
And since we have got now another "3", we know it is divisable by "3":
[tex]\frac{3}{3}=1[/tex]Now we have got to "1", so we found all the prime factors:
[tex]54=2\cdot3\cdot3\cdot3[/tex]Now,, we need to combine them to find all possible combinations.
We will start from low to high.
"1" is always a factor.
There is "2" there, so it is also a factor.
Then we have "3" as another factor.
There is no need to combine "1" with another factor, so we will start b combining 2 and 3:
[tex]2\cdot3=6[/tex]So, "6" is another factor.
We can combine 3 with 3:
[tex]3\cdot3=9[/tex]"9" is another factor.
Now we start combining three of them:
[tex]\begin{gathered} 2\cdot3\cdot3=6\cdot3=18 \\ 3\cdot3\cdot3=9\cdot3=27 \end{gathered}[/tex]So, "18" and "27" are factors.
And now we combine 4 of them, but this is get us back to "54" which is the last factor.
So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.
Answer:
Step-by-step explanation:
1 × 54 = 54, (1, 54) is a pair factor of 54.
2 × 27 = 54, (2, 27) is a pair factor of 54
3 × 18 = 54, (3, 18) is a pair factor of 54
6 × 9 = 54, (6, 9) is a pair factor of 54
Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).
I absolutely dont understand Division Property of Equality please help
We have the following equation.
[tex]20,000-1.8939m=10,000[/tex]Where m is the number of feet in a mile.
Let us subtract 20,000 from both sides of the equation then simplify
[tex]\begin{gathered} -20,000+20,000-1.8939m=10,000-20,000 \\ -1.8939m=-10,000 \end{gathered}[/tex]The negative sign cancels out and the equation becomes
[tex]\text{1}.8939m=10,000[/tex]Finally, we can apply the Division Property of Equality which states that when we divide both sides of the equation with same number then the equation remains valid.
Let us divide both sides of the equation by 1.8939 then simplify
[tex]\begin{gathered} \frac{1.8939m}{1.8939}=\frac{10,000}{1.8939} \\ m=\frac{10,000}{1.8939} \\ m\approx5280 \end{gathered}[/tex]Therefore, there are 5280 feet in a mile (rounded to nearest whole number)
This relation map is the musician to the instrument they play. is this relation a function?
I need answer for this word problems you have to shown that you can make several lattes then you add milk and begin to stirring. you use a total of 30 ounces of liquid. write an equation that represents the situation and explain what the variable represents.
hello
the question here is a word problem and we can either use alphabhets to represent the variables.
let lattes be represented by x and milk be represented by y
[tex]x+y=30[/tex]since the total ounce of liquid is equals to 30, we equate the whole sentence to 30.
Basically, the question is asking to solve a problem about rectangular prisms. It says the the shape of one box, with (h) height in feet, has a volume defined by the function:V(h) = h (h-5)(h-6)It says to graph the function. What is the maximum volume for the domain 0
The function representing the volume of the rectangular prism is given to be:
[tex]V(h)=h(h-5)(h-6)[/tex]Since we are expected to find the volume using the graph, we can prepare a table of values for the function using values of h as integers from 1 - 5, such that:
[tex]\begin{gathered} At\text{ }h=1 \\ V(1)=1(1-5)(1-6)=-4\times-5=20 \end{gathered}[/tex]The completed table is shown below:
Hence, we can plot these points on a graph using a graphing calculator for ease of work. This is shown below:
The maximum volume of the prism is represented by the highest point on the graph. The graph's highest point is at:
[tex]h=1.811[/tex]The corresponding value for the volume as can be seen on the graph is:
[tex]V=24.193[/tex]This is the maximum volume of the prism.
To the nearest cubic foot, the maximum volume of the rectangular prism is 24 cubic feet.
Can you please help with 44For the following exercise, sketch a graph of the hyperbola, labeling vertices and foci
We have the following equation of a hyperbola:
[tex]4x^2+16x-4y^2+16y+16=0[/tex]Let's divide all the equations by 4, just to simplify it
[tex]x^2+4x-y^2+4y+4=0[/tex]Just to make it easier, let's put the term if "x" isolated
[tex]x^2+4x=y^2-4y-4[/tex]Now we can complete squares on both sides, just remember that
[tex]\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}[/tex]Now let's complete it!
[tex]\begin{gathered} x^2+4x=y^2-4y-4\text{ complete adding 4 on both sides} \\ \\ x^2+4x+4=y^2-4y-4+4 \\ \\ (x+2)^2=y^2-4y \\ \end{gathered}[/tex]We already completed one side, now let's complete the side with y^2, see that we will add 4 again, then
[tex]\begin{gathered} (x+2)^2=y^2-4y \\ \\ (x+2)^2+4=y^2-4y+4 \\ \\ (x+2)^2+4=(y-2)^2 \end{gathered}[/tex]And now we can write it using the standard equation!
[tex]\begin{gathered} (y-2)^2-(x+2)^2=4 \\ \\ (y-2)^2-(x+2)^2=4 \\ \\ \frac{(y-2)^2}{4}-\frac{(x+2)^2}{4}=1 \end{gathered}[/tex]And now we can graph it like all other hyperbolas, the vertices will be:
[tex](-2,4)\text{ and }(-2,0)[/tex]And the foci
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ c^2=2^2+2^2 \\ \\ c^2=2\cdot2^2 \\ \\ c^{}=2\, \sqrt[]{2} \end{gathered}[/tex]Then the foci are
[tex](-2,2+2\, \sqrt[]{2})\text{ and }(-2,2-2\, \sqrt[]{2})[/tex]Now we can plot the hyperbola!
Hello everybody! I would really appreciate it if Somebody could give me the answer for this question and give a brief explanation on how they got it. Look at the photo for instructions!
Recall that the constant of variation of a straight line is the slope of the line.
To compute the slope we will use the following formula for the slope of a line:
[tex]s=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]Now, notice that points (-1,3) and (1,-3) are on the line, then substituting these points in the above formula we get:
[tex]s=\frac{3-(-3)}{-1-1}=\frac{6}{-2}=-3.[/tex]Answer: -3.
Picture explains it all
Answer: .1$ so 10cents
Step-by-step explanation:
The Wong family and the Nguyen family each used their sprinklers last summer. The water output rate for the Wong familys sprinkler was 35 L per hour. The water output for the Nguyen familys sprinkler was 20 L per hour. The families used their spirit for a combined total of 75 hours, resulting in a total water output of 2100 L. How long was each sprinkler used?
Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:
[tex]35W+20N=2100,(1)[/tex]Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:
[tex]W+N=75,(2)[/tex]We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:
[tex]W=75-N[/tex]Now we can replace this value in equation (1):
[tex]35(75-N)+20N=2100[/tex]Now we apply the distributive property:
[tex]2625-35N+20N=2100[/tex]Now we add like terms;
[tex]2625-15N=2100[/tex]Now we subtract 2625 from both sides:
[tex]\begin{gathered} -15N=2100-2625 \\ -15N=-525 \end{gathered}[/tex]Now we divide both sides by 15:
[tex]N=-\frac{525}{-15}=35[/tex]Now we replace this value in equation (2) where we already solved for W:
[tex]\begin{gathered} W=75-35 \\ W=40 \end{gathered}[/tex]Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.
How would you use the Pythagorean Theorem to find the missing length in the triangle shown? Find the missing length.
The given triangle is a right angle triangle. The pythagorean theorem is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = AB = c
one leg = BC = 9
other leg = AC = 12
By applying the pythagorean theorem, we have
[tex]\begin{gathered} c^2=9^2+12^2\text{ = 81 + 144} \\ c^2\text{ = 225} \\ c\text{ = }\sqrt[]{225} \\ c\text{ = 15} \end{gathered}[/tex]The missing length is 15 cm
it snowed 20 inches in 10 days in Montreal. Find the unit rate.
the expression is
[tex]\frac{20}{10}[/tex]We must divide each value by the value of the denominator to obtain the unit ratio
so
[tex]\frac{\frac{20}{10}}{\frac{10}{10}}=\frac{2}{1}=2[/tex]the unit ratio is 2 inches per day
Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.See image
Statement Problem: Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.
Solution;
We observe that as the value of x is increasing, the value of y is decreasing. Hence, it has a feature of an inverse variation.
When two variables are inversely related;
[tex]\begin{gathered} x\propto\frac{1}{y} \\ x=\frac{k}{y} \end{gathered}[/tex]But;
[tex]x=5,y=2[/tex]Thus, we have;
[tex]\begin{gathered} x=\frac{k}{y} \\ 5=\frac{k}{2} \\ k=5\times2 \\ k=10 \end{gathered}[/tex]Thus, the equation to represent the information is;
[tex]\begin{gathered} x=\frac{k}{y} \\ \text{Put the value of k in the equation;} \\ x=\frac{10}{y} \end{gathered}[/tex]The equation to represent the information is;
[tex]x=\frac{10}{y}[/tex]Find the perimeter of LMNPQ if the perimeter of ABCDE = 25.2 cm and ABCDE = LMNPQ
If two polygons are similar with the lengths of corresponding sides, we need to find the ratio between both figures:
Then:
[tex]\frac{SIDE\text{ PQ}}{\text{SIDE DE}}=\frac{25}{15}=\frac{5}{3}=\text{ 1,666}[/tex]So, the ratio is 5:3
The perimeter of LMNPQ is the same to say :
P of ABCDE = 25.2cm
Use the ratio
P of LMNPQ = 25.2 (5/3) cm
Then P = 42 cm
You have 4/5 of a pizza left over from your pool party. If you sent 4/9 of the leftover pizza home with your friends how much of the pizza do you have left in the box
If I sent 4/9 of the leftover pizza home with your friends the pizza do I have left in the box is 16/45.
What is pizza?
Pizza is an Italian food consisting of a typically flat, spherical foundation composed of leavened wheat dough that is topped with cheese, tomatoes, and frequently a number of additional toppings. Following that, the pizza is baked at a high temperature, typically in a wood-fired oven. A small pizza is also known as a pizzetta. A pizza maker is referred to as a pizzaiolo.
To get the quantity of the leftover pizza, we need to subtract the pizza sent by me to home from the total pizza I had in my lunch box.
So,
Pizza I have left = Pizza in lunch box - Pizza I have sent
Pizza I have left = 4/5 - 4/9
Pizza I have left = (4(9) - 4(5))/45
Therefore, Pizza I have left is 16/45.
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Estimate the time it would take you to drive 278 miles at38 miles per hour. Round to the nearest hour
Speed formula:
[tex]s=\frac{d}{t}[/tex]d is the distance
t is the time
As you need to find a time having the distance and speed, solve the equation above for t:
[tex]\begin{gathered} t\cdot s=d \\ t=\frac{d}{s} \end{gathered}[/tex]Use the given data to find the time:
[tex]\begin{gathered} t=\frac{278mi}{38mi/h} \\ \\ t=7.31h \\ \\ t=7h \end{gathered}[/tex]Then, it would take you 7 hours to drive 278 mi at 38mi/hon a horizontal line segment, point A is located at 21, point b is located at 66. point p is a point that divides segment ab in a ratio of 3:2 from a to b where is point p located
We have a one-dimensional horizontal line segment. Three points are indicated on the line as follows:
In the above sketch we have first denoted a reference point at the extreme left hand as ( Ref = 0 ). This is classified as the origin. The point ( A ) is located on the same line and is at a distance of ( 21 units ) from Reference ( Ref ). The point ( B ) is located on the same line and is at a distance of ( 66 units ) from Reference ( Ref ).
The point is located on the line segment ( AB ) in such a way that it given as ratio of length of line segment ( AB ). The ratio of point ( P ) from point ( A ) and from ( P ) to ( B ) is given as:
[tex]\textcolor{#FF7968}{\frac{AP}{PB}}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{3}{2}\ldots}\text{\textcolor{#FF7968}{ Eq1}}[/tex]The length of line segment ( AB ) can be calculated as follows:
[tex]\begin{gathered} AB\text{ = OB - OA } \\ AB\text{ = ( 66 ) - ( 21 ) } \\ \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = 45 units}} \end{gathered}[/tex]We can form a relation for the line segment ( AB ) in terms of segments related to point ( P ) as follows:
[tex]\begin{gathered} \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = AP + PB }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq2}} \\ \end{gathered}[/tex]We were given a ratio of line segments as ( Eq1 ) and we developed an equation relating the entire line segment ( AB ) in terms two smaller line segments as ( Eq2 ).
We have two equation that we can solve simultaneously:
[tex]\begin{gathered} \textcolor{#FF7968}{\frac{AP}{PB}}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{3}{2\text{ }}\ldots}\text{\textcolor{#FF7968}{ Eq1}} \\ \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = AP + PB }}\textcolor{#FF7968}{\ldots Eq2} \end{gathered}[/tex]Step 1: Use Eq1 and express AP in terms of PB.
[tex]AP\text{ = }\frac{3}{2}\cdot PB[/tex]Step 2: Substitute ( AP ) in terms of ( PB ) into Eq2
[tex]AB\text{ = }\frac{3}{2}\cdot PB\text{ + PB}[/tex]We already determined the length of the line segment ( AB ). Substitute the value in the above expression and solve for ( PB ).
Step 3: Solve for PB
[tex]\begin{gathered} 45\text{ = }\frac{5}{2}\cdot PB \\ \textcolor{#FF7968}{PB}\text{\textcolor{#FF7968}{ = 18 units}} \end{gathered}[/tex]Step 4: Solve for AP
[tex]\begin{gathered} AP\text{ = }\frac{3}{2}\cdot\text{ ( 18 )} \\ \textcolor{#FF7968}{AP}\text{\textcolor{#FF7968}{ = 27 units}} \end{gathered}[/tex]Step 5: Locate the point ( P )
All the points on the line segment are located with respect to the Reference of origin ( Ref = 0 ). We will also express the position of point ( P ).
Taking a look at point ( P ) in the diagram given initially we can augment two line segments ( OA and AP ) as follows:
[tex]\begin{gathered} OP\text{ = OA + AP} \\ OP\text{ = 21 + 27} \\ \textcolor{#FF7968}{OP}\text{\textcolor{#FF7968}{ = 48 units}} \end{gathered}[/tex]The point ( P ) is located at.
Answer:
[tex]\textcolor{#FF7968}{48}\text{\textcolor{#FF7968}{ }}[/tex]
If triangular pyramid P and triangular pyramid D are similar, which of the following statements must be true?
When two figures are similar, the relation or proportion between same measures is the same. So answer is option d.
Finding a final amount in a word problem on exponential growth or decay
Answer:
19g
Explanation:
Given the starting amount as 155grams, the below amount will be left after the 1st half life;
[tex]\frac{155g}{2}=77.5g[/tex]After the 2nd half-life, the below amount will remain;
[tex]\frac{77.5g}{2}=38.75g[/tex]After the 3rd half-life, the below amount will remain;
[tex]\begin{gathered} \frac{38.75}{2}=19.375g\approx19g\text{ (rounding to the nearest gram)} \\ \end{gathered}[/tex]Which graph represents an exponential function
This is algebra two graphing exponential functions
Answer: The Curved Line on Top
Step-by-step explanation: A positive-valued function of a real variable. So the top one
Just learned about this in Algebra 1 about 4 days ago.
4j+2=h solve for j please help
To solve for j'
4j + 2 = h
subtract 2 from both-side of the equation
4j + 2-2 = h -2
4j = h-2
divide both-side of the equation by 4
4j/4 = h-2/4
[tex]j=\frac{h-2}{4}[/tex]Factoring
64v^4-225w^10
I come up with
(8v^2+15w^2)(8v^2-15w^5) can I simplify it?
Your answer can't be simplified but it's also slightly incorrect. No worries!
You can simplify (64v^4 - 225w^10) by applying the difference of squares --> a^2 - b^2 = (a + b)(a - b)
Here, (64v^4) is a^2, and (225w^10) is b^2.
[tex]\sqrt{64v^4 }[/tex] = a = 8v^2
[tex]\sqrt{225w^{10} }[/tex] = b = 15w^5
Substitute the values:
(8v^2 + 15w^5)(8v^2 - 15w^5)
Therefore, the factorization of [tex]64x^{4} -225w^{10}[/tex] is:
[tex](8v^{2} + 15w^5)(8v^2-15w^5)[/tex]
The factorization is already the simplest. It can't be simplified further.
Picture of question linked. The choices for the answer are -infinity, infinity, and 0
The behavior of any polynomial function is determined by the exponent and the signal of the first term of the function.
In the case of f(x), the leading term is negative, and its expoent is odd. Therefore, when x is negative, the leading term will be positive and, when x is positive, the leading term is negative.
Therefore, we have:
[tex]\begin{gathered} As\text{ }x\rightarrow-\infty,\text{ }f(x)\rightarrow\infty \\ As\text{ }x\rightarrow\infty,\text{ }f(x)\rightarrow-\infty \end{gathered}[/tex]Could you help me with this please is from apex
Answer:
Completing the table we have;
Explanation:
Given the table in the attached image, we want to complete the table;
[tex]\text{Interest is 1\% compounded monthly}[/tex]For period 1;
simple interest;
[tex]i_1=Prt=100\times0.01\times1=\text{ \$1.00}[/tex]Compound interest;
[tex]\begin{gathered} f_1=P(1+\frac{r}{n})^{nt}=100(1+\frac{1}{12})^{1(12)}=\text{ \$}101.00 \\ \text{ Interest = }101.00-100=\text{ \$1.00} \end{gathered}[/tex]For period 2;
simple interest;
[tex]i_2=Prt=100\times0.01\times1=\text{ \$1.00}[/tex]compound interest;
[tex]\begin{gathered} f_2=P(1+\frac{r}{n})^{nt} \\ P=f_1=101.00 \\ =101(1+\frac{1}{12})^{1(12)}=\text{ \$}102.01 \\ \text{Interest}=102.01-101=\text{ \$}1.01 \end{gathered}[/tex]Total interest
simple interest;
[tex]i_t=i_1+i_2=1+1=\text{ \$2.00}[/tex]Compound Interest;
[tex]\text{ Total interest}=1.00+1.01=\text{ \$2.01}[/tex]Therefore, completing the table we have;
The height of the Empire State Building is 1250 feet tall. Your friend, who is 75 inches tall, is standing nearby and casts a shadow that is 33 inches long. What is the length of the shadow of the Empire State Building? Please help me draw triangles
The length of the building's shadow = 550.66 ft
Explanations:The height of the Empie State Building = 1250 feet
The friend's height = 75 inches
The length of the friend's shadow = 33 inches
[tex]\frac{Actual\text{ height of the friend}}{\text{Length of the friend's shadow}}=\text{ }\frac{Height\text{ of the building}}{\text{Length of the building's shadow}}[/tex][tex]\begin{gathered} \frac{75}{33}=\text{ }\frac{1250}{\text{Length of the building's shadow}} \\ 2.27\text{ = }\frac{1250}{\text{Length of the building's shadow}} \\ \text{Length of the building's shadow = }\frac{1250}{2.27} \\ \text{Length of the building's shadow = }550.66\text{ f}et \end{gathered}[/tex]Not sure on how to do this. Could really use some help.
We will have the following:
We will recall that the surface area of a sphere is given by:
[tex]A_s=4\pi r^2[/tex]So, the surface area of the given sphere will be:
[tex]\begin{gathered} A_s=4\pi(\sqrt{\frac{7}{3.14}})^2\Rightarrow A_s=4(3.14)\ast\frac{7}{3.14} \\ \\ \Rightarrow A_s=4\ast7\Rightarrow A=28 \end{gathered}[/tex]So, the surface area of the sphere will be 28 yd^2.
*The reason we can use "mental math" is that we are using an approximation of pi, which makes it so it cancels with the 3.14 in the denominator after a point; leaving a simple multiplication at the very end.
What is 16.02+8.5+14 ?? i want to know for a home work
Given:
[tex]16.02\text{ + 8.5 + 14}[/tex]To solve,
Step 1:
Express each value to a common decimal place.
We can express each value to two decimal places.
Thus, we have
[tex]16.02+8.50+14.00[/tex]Step 2:
Sum up the values.
Hence, 16.02 + 8.5 + 14 gives 38.52.
(06.03 MC) Use the expression 5(6 + 4x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: How many terms are in each factor of this expression? Part C: What is the coefficient of the variable term? (2 points)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Expression:
5(6 + 4x)
Step 02:
5(6 + 4x)
A.
5 = factor 1
(6 + 4x) = factor 2
B.
5 = factor 1 ( 1 term)
(6 + 4x) = factor 2 (2 terms)
C.
variable term: 4x
coefficient = 4
That is the full solution.
Abby scored 88, 91, 95, and 89 on her first four history quizzes. What score does Abby need to get on her fifth quiz to have an average of exactly 90 on her history quizzes? a.85b.86c.87a.88
Solution
For this case we can use the definition of average given by:
[tex]\text{Mean}=\frac{x_1+x_2+x_3+x_4+x_5}{5}[/tex]The final score needs to be 90 so we can do this:
[tex]90=\frac{88+91+95+89+x_5}{5}[/tex]And solving for x5 we got:
5*90 = 88+91+95+89+ x5
x5= 450 - 88- 91- 95 -89 = 87
Final answer:
c.87