We have the following:
[tex]7x+10-5x+3[/tex]We must group like terms and then simplify
[tex]\begin{gathered} (7x-5x)+(10+3) \\ 2x+13 \end{gathered}[/tex]Find the sum of the first three terms of the geometric series represented by the formula.
The easiest way to get the sum is to determine the first three terms using the given formula:
[tex]\text{ A}_n\text{ = }(\frac{8}{25})(\frac{5}{2})^{n\text{ - 1}}[/tex]We get,
First term, n = 1
[tex]\text{ A}_1\text{ = }(\frac{8}{25})(\frac{5}{2})^{n\text{ - 1}}\text{ = }(\frac{8}{25})(\frac{5}{2})^{1\text{ - 1}}\text{ = }(\frac{8}{25})(\frac{5}{2})^0[/tex][tex]\text{ A}_1\text{ = (}\frac{8}{25})(1)\text{ = }\frac{8}{25}[/tex]Second term, n = 2
[tex]\text{ A}_2\text{ = }(\frac{8}{25})(\frac{5}{2})^{2\text{ - 1}}\text{ = }(\frac{8}{25})(\frac{5}{2})^1[/tex][tex]\text{ A}_2\text{ = }(\frac{8}{25})(\frac{5}{2})^{}\text{ = }\frac{40}{50}\text{ = }\frac{20}{25}[/tex]Third term, n = 3
[tex]\text{ A}_3\text{ = }(\frac{8}{25})(\frac{5}{2})^{3\text{ - 1}}\text{ = }(\frac{8}{25})(\frac{5}{2})^2[/tex][tex]\text{ A}_3\text{ = }(\frac{8}{25})(\frac{25}{4})\text{ = }\frac{200}{100}\text{ = }\frac{50}{25}[/tex]Since the first three terms are already like terms (the same denominator), let's proceed on adding them.
[tex]\text{ Sum = }A_1+A_2+A_3_{}[/tex][tex]\text{ Sum = }\frac{8}{25}\text{ + }\frac{20}{25}\text{ + }\frac{50}{25}\text{ = }\frac{8\text{ + 20 + 50}}{25}\text{ = }\frac{78}{25}[/tex]Therefore, the sum of the first three terms is 78/25.
that's the expression with the property used to generate 5 y + 2 y + 6 + 2. is 5 y + 2 + 6 + 2y communtive property combining like terms or distributive property
If we compare the expression, we would notice that the difference between them is that the terms 2y, 6, and 2 are commuted.
[tex]5y+2+6+2y=5y+2y+2+6=5y+2y+6+2[/tex]Therefore, the answer is the commutative property.
RS2. Given: ZP ZQ andProve: PR=QRSupply the missing reason in Statement 1 of the proof of the the Converse of the Isosceles Triangle Theorem.Begin with isosceles APRQ with ZP ZQ. Construct RS, a bisector of ZPRQ.bisects ZPQR.R
We are given the following triangle:
We are given that:
[tex]\angle P=\angle Q[/tex]Since RS is a bisector this means that:
[tex]\angle PRS=\angle SRQ[/tex]Also, since S is a midpoint of PQ:
[tex]PS=SQ[/tex]By the reflexive property we have:
[tex]RS=RS[/tex]Since we have two pairs of congruent angles this means that:
[tex]\angle PSR=\angle QSR[/tex]Therefore, by SAS theorem of congruency:
[tex]\Delta PSR\cong\Delta QSR[/tex]Since the triangles are congruent this means that all of its sides are congruent too, therefore:
[tex]PR=QR[/tex]And thus we have concluded the proof.
Identify the sides or angles that need to be congruent in order to make the given triangles congruent by AAS
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Triangles
missing angle or side = ?
Step 02:
AAS = angle - angle - side
a. ΔABC Δ DEF
side AB side DE
b. ΔABC Δ DEF
∠A ∠ D
That is the full solution.
Use the Venn diagram to list the set A ∩ B inroster form.
Answer:
B
[tex]A\cap B=\lbrace b,h\rbrace[/tex]Explanation:
The set A n B, read as 'A intersection B', is the set of all the elements which belong to both set A and set B. It is a set of all the elements that are common in sets A and B.
Looking at the given Venn diagram, we can see that the elements that belong to both set A and set B are b and h. This can be written in roster form as seen below;
[tex]A\cap B=\mleft\lbrace b,h\mright\rbrace[/tex]Question 5: continuously.a. 543, 426, 940b. 16, 246, 789c. 7, 447, 626d. 222, 661Please Help! me with this question.
The exponential model for decay/decline is given by the formula:
[tex]F=P(1-r)^t[/tex]Where
P is the present value
r is the rate of decline per time period
t is the time period
F is the future value
Given,
initial population is 11 million (P = 11)
declining rate of 2.6% [in decimal, 2.6/100 = 0.026, r = 0.026]
time is 15 years [t = 15]
Substituting the given values into the formula, let's find "F", population after 15 years:
[tex]\begin{gathered} F=P(1-r)^t \\ F=11(1-0.026)^{15} \\ F=11(0.974)^{15} \\ F=7.409 \end{gathered}[/tex]Rounded to 2 decimal place, the population after 15 years would approximately be equal to
7.41 millionFind the geometric mean of 36 and 64.
Given the numbers:
36 and 64
Let's find the geometric mean of both numbers.
To find the geometric mean, apply the formula:
[tex]\sqrt[]{a\ast b}[/tex]Evaluate m2-n, if m= 6 and n=2
In order to solve the problem we need to evaluate it for m = 6 and n =2, so we need to use these on the expression.
[tex]m^2-n[/tex]Applying the points:
[tex](6)^2-2\text{ = 36 - 2 = 34}[/tex]The value of the expression is 34.
6) What is the probability of rolling a standard die and getting an oddnumber and a number less than or equal to 37
The probability of being born in May or on the 30th of any month
We have 12 months in a year
Probability of being born in may is 1/12
It is 1/12 because we only have one May in a year
OR 30th of every month
Out of all the months, only 11 months are upto 30 except February
The probability of being born on the 30th of any month is 11/12
In probability, or means addition
Therefore, we have
1/12 + 11/12
0.083 + 0.9166
= 0.9996
The answer is 0.9996 or approximately 1
1.2 pointsDavid's teacher asked him to solve the problemshown below.(-125 + 175) + (-125 + 165) + 110David's answer of 190 is incorrect. What is thecorrect answer?A.150B.160C.200D. 210Your answer
Use the order of operations to find the value of the given expression:
[tex](-125+175)+(-125+165)+110[/tex]Solve the expression inside the parenthesis first.
Since -125+175=50 and -125+165=40, then:
[tex](-125+175)+(-125+165)+110=50+40+110[/tex]Add the numbers from left to right:
[tex]50+40+110=90+110=200[/tex]Then:
[tex](-125+175)+(-125+165)+110=200[/tex]Therefore, the answer is:
[tex]C\text{. }200[/tex]for each Arithmetic sequence identify the next 3 terms of the sequence 5, 7.5,.....
Answer:
10, 12.5 and 15.
Explanation:
First, we determine the term which was added to 5.
[tex]\begin{gathered} 5+x=7.5 \\ x=7.5-5 \\ x=2.5 \end{gathered}[/tex]Therefore, the term that was added to 5 to get 7.5 is 2.5.
Next:
[tex]\begin{gathered} 7.5+2.5=10 \\ 10+2.5=12.5 \\ 12.5+2.5=15 \end{gathered}[/tex]Therefore, the next three terms of the arithmetic sequence are:
10, 12.5 and 15.
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. For how many minutes has the water been draining when Tank B contains x liters of water (answer as an expression)?
x=water in the tank in liters
t=time in minutes
start by writing the expression of the draining in the tank
[tex]x=80-2.5t[/tex]being 80 the initial value and 2.5 the rate at which is draining
to see how many minutes the tank has been draining when containing x liters clear the equation for t
[tex]\begin{gathered} x=80-2.5t \\ x-80=-2.5t \\ 2.5t=80-x \\ t=\frac{80-x}{2.5} \\ t=\frac{80}{2.5}-\frac{x}{2.5} \\ t=32-\frac{x}{2.5} \end{gathered}[/tex]hi I was having some trouble doing my project. I had trouble graphing Show Street, Carasoul Way, and Market Street. I would really love it if you would help me graph them.
Show street
* Must be parallel race car way.
* must run through -4,14
*must intersect with main drag at (-10,3)
Translate the word phrase into an algebraic equation and solve: the difference of x and fourteen is three.Provide your answer below:x=2
The statement "the difference of x and fourteen is three" can be written mathematically as:
[tex]x-14=3[/tex]To solve the equation, we add 14 to both sides of the equation:
[tex]\begin{gathered} x-14+14=3+14 \\ x=17 \end{gathered}[/tex]The value o
find the area of each figure. show all equations and work. round to the nearest tenth, if necessary.
Given the figure of a parallelogram shown in problem 5
We will find the area as follows:
The height = 4 m
The base = 10 m
Equation: Area = base x height
Area = 10 x 4 = 40 m²
Simplify.-2V/24y2 + 5V 96y?
The first step is to simplify the terms containing square roots. Thus, we have
[tex]\begin{gathered} \sqrt[]{24y^2}\text{ = 2y}\sqrt[]{6} \\ \text{Thus, } \\ -\text{ 2}\sqrt[]{24y^2}\text{ = - 2 }\times2\sqrt[]{6} \\ =\text{ - 4}\sqrt[]{6} \\ \text{Also, } \\ \sqrt[]{96y^2}\text{ = 4y}\sqrt[]{6} \\ \text{Thus, } \\ 5\sqrt[]{96y^2}^{}\text{ = 5 }\times4y\sqrt[]{6} \\ =\text{ 20y}\sqrt[]{6} \\ We\text{ would add both terms. Thus, we have} \\ -\text{ 4y}\sqrt[]{6}\text{ + 20y}\sqrt[]{6} \\ =\text{ 16y}\sqrt[]{6} \end{gathered}[/tex]We expressed both terms in surd form. The square root
Could you please tell me the answers and explain how to find them?
Answer:
[tex]x=2,x=3+i\sqrt{2},x=3-i\sqrt{2}[/tex]Explanation:
Given the function:
[tex]y=x^3-8x^2+23x-22[/tex]As seen on the graph, from the point (2,0) one of the roots of the function:
[tex]x=2[/tex]This means that x-2 is a factor of the polynomial y.
To get the other roots, first, divide y by x-2:
So, we have that:
[tex]\begin{gathered} y=x^{3}-8x^{2}+23x-22 \\ =(x-2)(x^2-6x+11) \end{gathered}[/tex]We then solve the quadratic equation for the other roots of y:
[tex]\begin{gathered} x^2-6x+11=0 \\ x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a},a=1,b=-6,c=11 \\ \\ x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(1)(11)}}{2\times1} \\ =\dfrac{6\pm\sqrt{36-44}}{2} \\ =\dfrac{6\pm\sqrt{-8}}{2} \\ =\frac{6}{2}\pm\frac{i\sqrt{8}}{2} \\ =3\pm\frac{i2\sqrt{2}}{2} \\ x=3\pm i\sqrt{2} \end{gathered}[/tex]The other two roots of y are:
[tex]\begin{gathered} x=3+i\sqrt{2} \\ \begin{equation*} x=3-\mathrm{i}\sqrt{2} \end{equation*} \end{gathered}[/tex]Thus, the exact roots of y are:
[tex]\begin{gathered} x=3+i\sqrt{2} \\ \begin{equation*} x=3-\mathrm{i}\sqrt{2} \end{equation*} \\ x=2 \end{gathered}[/tex]
Determine if the statement below is true or false. If it is false, rewrite the statement so it is true.The equation f (hg) = (fh)g is an example of applying the Associative Property of Multiplication.(1 point)This statement is false. The equation f (hg) = f (gh) is an example of applying the Associative Property ofMultiplicationThis statement is false. The equation f (hg) = (fh) g is an example of applying the Commutative Property ofMultiplicationThis statement is false. The equation f (hg) = (fh)g is an example of applying the Distributive Property ofMultiplicationThis statement is true.
Associative multiplication:
(x*y)*z = x*(y*z)
f (hg) = (fh)g is an example of applying the Associative Property of Multiplication?
From the previous definion we can conclude that the statement is true
5(9*4) + 7 + (3+1)
Using Associative property and commutative property:
1 + (3+7) + 4*(5*9)
4) A company that makes hair-care products had 3,000 people try a new shampoo. Of the3,000 people, 6 had a mild allergic reaction. What percent of the people had a mild allergicreaction?
To find the percentage of people who had a mild allergic reaction we just need to find the fraction by dividing the number of people with the allergic reaction by the total number of people who tried the product:
[tex]\frac{6}{3000}=0.002[/tex]Then, 0.002 of the total people experienced an allergic reaction. To convert the fraction into a percentage, we just need to multiply it by 100:
[tex]0.002\cdot100=0.2\text{ \%}[/tex]Answer: 0.2% of the people who tried the product had a mild allergic reaction.
What is the system of inequalities associated with the following graph?A. x+y≤2B. x+y<2C.x+yD.x+y>2
From the figure, to find the system of inequalities associated with it:
Since the intercepts x and y are, (2,0) and (0,2)
So, the equation of the line is,
[tex]x+y=2[/tex]Since the shaded area is located above the solid line,
Therefore, the inequality is
[tex]x+y\ge2[/tex]Hence, the correct option is C.
On At a snack bar, each medium drink costs $1.85 andeach large drink costs c more dollars than a mediumdrink. If 5 medium drinks and 5 large drinks cost atotal of $20.50, what is the value of c ?A) 0.45B) 0.40C) 0.30D) 0.25UniM esimi ornit2S-a anoita90D. 6 LỚP2196216 TUOY 16M
If x is the value of the large drink, then:
[tex]x=1.85+c\text{.}[/tex]With the given information we can set the following equation:
[tex]5\cdot1.85+5x=20.50.[/tex]Substituting the first equation on the board in the above equation we get:
[tex]5\cdot1.85+5(1.85+c)=20.50.[/tex]Solving for c we get:
[tex]\begin{gathered} 9.25+9.25+5c=20.50, \\ 5c=20.50-18.50, \\ c=\frac{2.00}{5}=0.40. \end{gathered}[/tex]Answer: Option B.
The length of a room is equal to 15 tiles. If the length of one tile is 4.5 cm, then findthe length of the room in cm
Given:
The length of a room is equal to 15 tiles.
The length of one tile is 4.5 cm.
Hence, the length of the room will be
[tex]4.5cm\times15=67.5cm[/tex]Therefore, the answer is 67.5cm.
John has walked 15% of the way home from school.if he has walked 300 meters so far how far does he walk home from school
Answer:
The way from home to school:
L = 2 000 m or L = 2 km
Step-by-step explanation:
Let's make a proportion:
300 m - 15%
X m - 100%
[tex]X=\frac{300*100}{15} = 2 000 m[/tex]
If < 1 and < 2 are supplementary angles in a ratio of 4:5.What is the measure of the smaller angle?
If < 1 and < 2 are supplementary angles in a ratio of 4:5.
What is the measure of the smaller angle?
we have that
<1+<2=180 ------> equation A
<1/<2=4/5
<1=(4/5)<2 ------> equation B'
substitute equation B in equation A
(4/5)<2+<2=180
solve for <2
(9/5)<2=180
<2=180(5/9)
<2=100 degrees
that means
<1=80 degrees
therefore
the measure of the smaller angle is 80 degreesYou are shown a scatter plot where the variables have a negative correlation but there are no labels on the axes.Which of the following options could be used to label the axes? Select all that apply.A)The height of plants after each month.B)The age of tadpole and length of its tail.C)The number of television sets sold each week during football season.D)The number of toys bought each week bought by grandparents.E)The amount of energy from solar panels and the amount of energy from other sources used in a house.
Lets say, for example, that the following scatter plot represents a negative correlation:
When a correlation is negative, this means that when the variable in the x-axis increases, the variable in the y-axis will decrease.
For the first example:
A)The height of plants after each month.
When time passes by, is logical to think that the height of the plats will increase, since plants
77(-2,-2)A(2, 2)The distance of AB = [? ]Round to the nearest tenth.Hint: d = √(x₂-x₁)² + (y2 - Y₁)²
Given the points:
( x1 , y1) = (-2, - 2 )
(x2, y2 ) = (2 , 2 )
Apply:
[tex]d=\sqrt[\placeholder{⬚}]{(x2-x1)^{^2}+(y2-y1)^{^2}}[/tex]Replacing:
[tex]d=\sqrt[\placeholder{⬚}]{(2-(-2))^{^2}+(2-(-2)^{^2}}[/tex][tex]d=\sqrt[\placeholder{⬚}]{(2+2)^{^2}+(2+2)^{^2}}[/tex][tex]d=\sqrt[\placeholder{⬚}]{4^{^2}+4^{^2}}=\sqrt[\placeholder{⬚}]{16+16}=\sqrt[]{32}=5.7[/tex]Answer:
5.7
Solve the equation for x, and enter your answer in the box below. X - 12 = -5
We are given the following equation
[tex]x-12=-5[/tex]Let us solve the equation for x.
Step 1:
Add 12 to both sides of the equation to eliminate 12 on the left side of the equation.
[tex]\begin{gathered} x-12+12=-5+12 \\ x=7 \end{gathered}[/tex]Therefore, the value of x is 7
[tex]x=7[/tex]What’s the correct answer answer asap for brainlist
The main goal of the Federal Reserve Banking System to Help and protect and consumers.
What is Federal Reserve Banking System?The Federal Reserve System which is often referred to as the Federal Reserve or "the Fed," is the central bank of the United States. It was created on December 23, 1913, with the enactment of the Federal Reserve Act, after a series of financial panics (particularly the panic of 1907) that led to the desire for central control of the monetary system in order to alleviate the financial crises that were occurring. Events such as the Great Depression in the 1930s, Great Recession during the 2000s,etc have led to the expansion of the roles and responsibilities of the Federal Reserve System. Federal Reserve Banking System was created to provide the nation with a safer, more flexible, and more stable monetary and financial system. It has specifically three goals : maximum employment, stable prices, and moderate long-term interest rates in the United States
To know more about Federal Reserve Banking System, visit:
https://brainly.com/question/1984442
#SPJ13
In a Toy store, the ration of dolls to teddy bears is 9:3. If the store has 240 dolls, how many teddy bears are in the store
9:3 = 3:1
240/3 =
80
There are 80 teddy bears in the store.
I need help with this practice It asks to graph the function*if you can, use Desmos to graph
explanation:
We are told to graph the function:
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]Using Desmos, we have
