By solving a simple linear equation we will see that the number is -29.
How to find the number?Let's define x as the number, then the sentence:
"If the sum of a number and nine is tripled , the result is two less than twice the number"
Can be written as the equation:
3*(x + 9) = 2x - 2
This is a linear equation that we can solve for x:
3*(x + 9) = 2x - 2
3x + 27 = 2x - 2
3x - 2x = -2 - 27
x = -29
The number is -29.
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How many terms are in 6b+b2+5+2b-3f
In that polynomial there are 5 terms, they are separated by signs.
If we simplify the new number of terms is 4
6b + b^2 + 5 + 2b - 3f
8b + b^2 + 5 - 3f
Simplify the expression below. Share all work/thinking/calculations to earn full credit. You may want to do the work on paper and then upload an image of your written work rather than try and type your work. \sqrt[4]{ \frac{162x^6}{16x^4} }
Lucy sold some items at a garage sale. She spent 7/12 of her earnings on a new bike. She uses 3/5 of the remainder to purchase a gift for her mom. What fraction of her total earnings was spent on her mom's gift?
First we have to find what fraction remained after buying the bike.
Subtracting 7/12 from 12/12 ( which represents the total)
The result is 5/12
Then, we are going to multiply 3/5 by 5/12 ( the remainder) to find our final answer.
[tex]\begin{gathered} \frac{3}{5}\cdot\frac{5}{12}=\frac{15}{60} \\ \frac{15}{60}=\frac{5}{20}=\frac{1}{4}\text{ Simplifying our fraction} \end{gathered}[/tex]The fraction of her total earnings spent on her mom's gift was 1/4
The population P of a city is given by P = 115600e^0.024t, where t is the time in years. According to this model, after how many years will the population be 130,000?4.29 years4.89 years5.19 years4.49 years
Given:
The population P of a city is given by,
[tex]P=115600e^{0.024t,}[/tex]To find:
The time taken for the population to reach 130,000.
Explanation:
Substituting P = 130,000 in the given function, we get
[tex]\begin{gathered} 130000=115600 \\ e^{0.024t}=\frac{130000}{115600} \\ e^{0.024t}=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}[/tex]Therefore, the number of years required for the population to reach 130,000 is 4.89years.
Final answer:
The number of years required is 4.89years.
Use the long division method to find the result when 8x3 + 30x2 + 3x – 1 is divided by 4x + 1. If there is a remainder, express the result in the form q(x) + r(3) b(x)
Answer:
[tex]2x^2+7x-1[/tex]Explanation:
Given the polynomial division:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}[/tex]The long division table is attached below:
Therefore, we have that:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}=2x^2+7x-1[/tex]9+7d=16 how do i slove it
9 + 7d = 16
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9 + 7 d = 16
1. we subtract 9 from the two sides
9 - 9 + 7 d = 16 -9
0 + 7 d = 7
2. We divide by 7 both sides
(7 d)/ 7 = 7/ /7
7/7= 1
d= 1
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Answer
9 + 7d = 16
7d= 16 - 9
d= 7/ 7= 1
d= 1
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16What exactly are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal. A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, equations true for x = 2 and x = -2 are:
Roots of x = -2:
x² = 4x² - 4 = 0Roots of x = 2:
x² = 4Now, multiply 4 on both sides as follows:
4x² = 16Therefore, equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16Know more about equations here:
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Correct question:
Which equations are true for x = –2 and x = 2? Select two options
A. x2 – 4 = 0
B. x2 = –4 3
C. x2 + 12 = 0
D. 4x2 = 16
E. 2(x – 2)2 = 0
-5 > 5 + x/3 I am so confused on these things
Let's solve the inequality:
[tex]\begin{gathered} -5>5+\frac{x}{3} \\ -5-5>\frac{x}{3} \\ -10>\frac{x}{3} \\ -10\cdot3>x \\ -30>x \\ x<-30 \end{gathered}[/tex]Therefore the solution for the inequality is:
[tex]x<-30[/tex]In interval form this solution is written as:
[tex](-\infty,-30)[/tex]This means that x has to be less than -30 for the inequality to be true.
how to write the indicated expression for[tex] \frac{1}{2} m \: inches \: in \: feet[/tex]
Answer:
Rewriting the given expression in feet gives:
[tex]\frac{1}{24}m\text{ feet}[/tex]Explanation:
We want to write the expression below in feet.
[tex]\frac{1}{2}m\text{ inches in f}eet[/tex]Recall that;
[tex]\begin{gathered} 1\text{ foot = 12 inches} \\ 1\text{ inch = }\frac{1}{12}foot \end{gathered}[/tex]so, converting the expression to feet we have;
[tex]\begin{gathered} \frac{1}{2}m\text{ inches =}\frac{1}{2}m\times\frac{1}{12}feet \\ =\frac{1}{2}\times\frac{1}{12}\times m\text{ f}eet \\ =\frac{1}{24}m\text{ f}eet \end{gathered}[/tex]Therefore, rewriting the given expression in feet we have;
[tex]\frac{1}{24}m\text{ feet}[/tex]1. If triangle ABC is congruent to triangle DEF, DE=17, EF =13, DF =9, and BC = 2x-5, then which of the following is the correctvalue of x?(1) 5(3) 9(2) 7(4) 11
If both trianlges are congruent, we get that:
[tex]BC=DE[/tex]This way,
[tex]2x-5=17[/tex]Solving for x :
[tex]\begin{gathered} 2x-5=17 \\ \rightarrow2x=17+5 \\ \rightarrow2x=22 \\ \Rightarrow x=11 \end{gathered}[/tex]This way, we get that x = 11
Answer: Option 4
The student Fun Club plans to go to the movies. At the matinee, tickets cost $6 and popcorn is $3. At evening shows, tickets cost $9 and popcorn is $4. The Fun Club attends a matinee and spends less than $60, and then attends an evening show and spends more than $36. If they purchased the same number of tickets and popcorns at each show, which of the following is a possible solution for the number of tickets and popcorns purchased?
Matinee
Cost of each ticket: $6
Cost of popcorn: $3
Evening:
Ticket: $9
Popcorn: $4
Number of tickets: x
Number of popcorns : y
The Fun Club attends a matinee and spends less than $60
6x + 3y < 60
Then attends an evening show and spends more than $36
9x+ 4y < 36
We have the system:
6x + 3y < 60 (a)
9x+ 4y >36 (b)
Graph each inequality:
The intersection of red and blue is the solution.
7 tickets and 5 popcorns (7,5) is inside the intersection, So, it is the solution.
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 18 people took the trip. She was able to purchase coach tickets for $170 and first class tickets for $1010. She used her total budget for airfare for the trip, which was $10620. How many first class tickets did she buy? How many coach tickets did she buy:
Explanation
Let the number of people with coach tickets be x and the number of people with first class tickets be y. Since the trip goers contained a total of 18 people we will have;
[tex]x+y=18[/tex]A coach ticket cost $170 dollars and the first class tickets cost $1010. Also, Sarah spent a total of $10620 to buy the tickets. This would give us;
[tex]170x+1010y=10620[/tex]We will now solve the equation simultaneously.
[tex]\begin{gathered} \begin{bmatrix}x+y=18\\ 170x+1010y=10620\end{bmatrix} \\ isolate\text{ for x in equation 1}\Rightarrow x=18-y \\ \mathrm{Substitute\:}x=18-y\text{ in equation 2} \\ 170\left(18-y\right)+1010y=10620 \\ 3060+840y=10620 \\ 840y=10620-3060 \\ 840y=7560 \\ y=\frac{7560}{840} \\ y=9 \\ \end{gathered}[/tex]We will substiuite y =9 in x=18-y. Therefore;
[tex]\begin{gathered} x=18-9=9 \\ x=9 \end{gathered}[/tex]Answer: From the above, Sarah bought 9 coach tickets and 9 first-class tickets.
In the function rule for simple interest A(t)=P(1+rt), is P a variable? Explain.
P is a variable in the function rule for simple interest A(t)=P(1+rt).
What is a variable?Mathematically, a variable is any number, vector, matrix, function, argument of a function, set, or element of a set.
A variable assumes any possible values in a mathematical expression, problem, or experiment.
A simple interest function showing the amount after some periods is given as A(t)=P(1+rt). In this function, P represents a variable (the principal amount) because it can change depending on the amount invested or borrowed.
Thus, P is a variable in the simple interest function because it can assume any value.
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Answer:
when buying a house
Step-by-step explanation:
Given: D is the midpoint of segment AC, angle AED is congruent to angle CFD and angle EDA is congruent to angle FDCProve: triangle AED is congruent to triangle CFD
Since Angle AED is congruent to angle CFD and angle EDA is congruent to angle FDS, we can use the midpoint theorem to get the following:
[tex]\begin{gathered} D\text{ is midpoint of AC} \\ \Rightarrow AD\cong AC \end{gathered}[/tex]therefore, by the ASA postulate (angle,side,angle), we have that triangle AED is congruent to triangle CFD
step by step guide I am stuck at the part where you have to divide, I have split them up into 2 and got GCF for p on first term and 6 on second term
We have the next expression:
[tex]pq\text{ - pr + 6q-6r}[/tex]Factorize using factor by grouping.
First, let's find the common terms. The one who is in all terms or majority terms.
In this case, let's use p:
[tex]p(q-r)+6q-6r[/tex]Factorize the common term 6.
[tex]p(q-r)+6(q-r)[/tex]Look at the expressions, both are multiply by (q-r), so we can rewrite the expression like this:
Factorize the common term (q-r)
[tex](q-r)(p+6)[/tex]complete the Pattern 444 4440 44,400 there are three empty lines I need to finish the pattern
Given:
d. 444 4,440 44,400
e. 9.5 950 9500
The pattern for d as you can see all numbers have 444 but they keep adding extra 0's to each number.
So the next number should have another extra 0 after 44400.
The pattern for all parts a to e seem to be multiplying each number by 10 or dividing by 10 that is why for d. 444 has no 0's but then if you multiply by 10 you get 4440.
If you do 4440*10 you get 44400.
Answer:
The same pattern applies to e.
For the first blank divide 9.5 by 10 so then 9.5 ÷ 10 = 0.95
For the 2nd blank. Multiply by 10 to 95,000 so you get 950,000. Notice how 950,000 has an extra 0.
3rd blank should be 9500000
Drag each expression to the correct location on the model. Not all expressions will be used.552 + 25r + 2071
Given
[tex]\frac{5x^2+25x+20}{7x}[/tex]To find: The equivalent rational expression.
Explanation:
It is given that,
[tex]\frac{5x^2+25x+20}{7x}[/tex]That implies,
[tex]\frac{5x^2+25x+20}{7x}[/tex]find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there is more than one zero, separate them with commas.)edit: if possible please double check answers would high appreciate it.
Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):
[tex]\begin{gathered} x=1-3i \\ x=1+3i \end{gathered}[/tex]also, notice that if we evaluate -1 on p(x), we get:
[tex]\begin{gathered} p(-1)=(-1)^3-(-1)^2+8(-1)+10=-1-1-8+10 \\ =-10+10=0 \end{gathered}[/tex]therefore, the zeros of p(x) are:
x = 1-3i
x = 1+3i
x = -1
Toy It Examine the worked problem and solve the equation. 4 4 1 (x) 1 = 9 3 3 1 1 + 3 3 4 3 :9+ 3 3 28 The solution is x=
Given:
[tex]\frac{4}{3}(x)-\frac{1}{3}=9[/tex]Let's evaluate and solve for x.
First step:
Add 1/3 to both sides of the equation
[tex]\begin{gathered} \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3}=9+\frac{1}{3} \\ \\ \frac{4}{3}(x)=\frac{28}{3} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} 4x(3)\text{ = 28(3)} \\ \\ 12x\text{ = }84 \end{gathered}[/tex]Divide both sides by 12:
[tex]\begin{gathered} \frac{12x}{12}=\frac{84}{12} \\ \\ x=7 \end{gathered}[/tex]ANSWER:
x = 7
10x + 50 + 6x = 58 if x is the solution to the given equation, what is the value of 32x
The solution to the given equation is;
[tex]\begin{gathered} 10x+50+6x=58 \\ \text{Collect all like terms,} \\ 10x+6x=58-50 \\ 16x=8 \\ \text{Divide both sides by 16} \\ \frac{16x}{16}=\frac{8}{16} \\ x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of 32x shall be;
[tex]\begin{gathered} 32x \\ =32(\frac{1}{2}) \\ =\frac{32}{2} \\ =16 \end{gathered}[/tex]The answer is 16
Becca wants to make a giant apple pie to try and break the world record. If she succeeds in making a pie with 20 foot diameter, what will the size of the crust covering the pie be?
ANSWER :
62.83 feet
EXPLANATION :
The pie has a diameter of 20 feet.
The size of the crust covering is the circumference of the pie.
The circumference formula is :
[tex]C=2\pi r[/tex]We know that the radius is half of diameter.
So the radius is 20/2 = 10 feet.
Using the formula above :
[tex]\begin{gathered} C=2\pi(10) \\ C=62.83 \end{gathered}[/tex]Ramesh leaves 2/3 of his property for his wife and 1/4 for his son and remaining for his daughter what part does his daughter receive Help me fast
x[tex] {x}^{3} {y}^{8} term(x + y) ^{11} [/tex]find the coefficient of the given term in the binomial expansion
Using the binomial theorem, we have that the expansion of (x+y)^11 is:
[tex]\begin{gathered} (x+y)^{11}= \\ x^{11}+11x^{10}y+55x^9y^2+165x^8y^3+330x^7y^4+462x^6y^5+462x^5y^6+330x^4y^7+165x^3y^8+55x^2y^9+11xy^{10}+y^{11} \end{gathered}[/tex]notice that the coefficient of the term x^3 y^8 is 165
012Explanation34BCheck5Use the figure and the table to answer the parts below.67(a) Find the probability that a real number between 4 and 6 is picked.08(b) Find the probability that a real number between 4 and 7 is picked.0RegionABCXArea0.320.560.12 I need help with this math problem
Given:
The graph is:
Find-:
(a)
Find the probability that a real number between 4 and 6 is picked.
(b)
Find the probability that a real number between 4 and 7 is picked.
Explanation-:
The area of the region
[tex]\begin{gathered} \text{ Region }\rightarrow\text{ Area} \\ \\ A\rightarrow0.32 \\ \\ B\rightarrow0.56 \\ \\ C\rightarrow0.12 \end{gathered}[/tex]The probability is:
[tex]P(A)=\frac{\text{ Favorable outcome}}{\text{ Total outcome}}[/tex]The total outcomes is:
[tex]\begin{gathered} =0.32+0.56+0.12 \\ \\ =1 \end{gathered}[/tex](a)
Probability to the 4 and 6
The 4 to 6v region is B
[tex]\begin{gathered} P(B)=\frac{\text{ favorable outcomes for B}}{\text{ Total outcomes}} \\ \\ P(B)=\frac{0.56}{1} \\ \\ P(B)=0.56 \end{gathered}[/tex](B)
Probability for 4 to 7
The region B and C
[tex]\begin{gathered} 1. \\ \\ P(B\text{ and }C)=\frac{0.56+0.12}{1} \\ \\ =0.68 \end{gathered}[/tex]Use the substitution property of equality to complete the following statement.
Given:-
[tex]8x+y=12[/tex]To find x when y is 3.
So now we substitute,
[tex]\begin{gathered} 8x+y=12 \\ 8x+3=12 \\ 8x=12-3 \\ 8x=9 \\ x=\frac{9}{8} \end{gathered}[/tex]So the value is,
[tex]\frac{9}{8}[/tex]what is the scale factor from triangle PQR to triangle STU
To find the scale factor from one triangle to another we need to divide the measurements of the second triangle by the corresponding measurements of the first triangle.
Since we need the scale factor from triangle PQR to triengle STU we need to divide the measurements of STU by the corresponding measurements of triangle PQR.
Sides PR and SU are corresponding sides, so we sivide 12 by 8:
[tex]\frac{12}{8}=\frac{3}{2}[/tex]To confirm, we also divide the measurements of sides UT and RQ:
[tex]\frac{9}{6}=\frac{3}{2}[/tex]Thus, the scale factor is: 3/2 = 1.5
For questions 5-6, g(x) is a transformation of f(x) = x2. What is the function g(x) that is represented by the graph? QUESTION 5
The transformation in question 5 shows a shift to the left by 3 units.
A shift to the left by b units has the rule:
[tex]f(x)\to f(x+b)[/tex]Therefore, the shift to the left by 3 units will yield the function:
[tex]x^2\to(x+3)^2[/tex]Hence, the function g(x) will be:
[tex]g(x)=(x+3)^2[/tex]You have a $250 gift card to use at a sporting goods store. a) Write an inequality that represents the possible numbers x of pairs of socks you can buy when you buy 2 pairs of sneakers. PRIO *12 SALE PRICE $80 b) Can you buy 8 pairs of socks? Explain.
Sale price 12
number of socks =X
Sneakers sprice 80
Amount disposable 250
Then
Part a)
250 - 2•80 = 12X
250 - 160 = 12X
90 ≥ 12 X
Part b)Can buy 8 pairs?
Answer NO , because 90 < 12•8
find the value of x,y,z
Answer: x =116 degrees
y = 88 degrees
Explanation:
[tex]\begin{gathered} \text{ Find the value of x, y, and z} \\ To\text{ find z} \\ \text{Opposite angles are supplementary in a cyclic quadrilateral} \\ 101\text{ + z = 180} \\ \text{Isolate z} \\ \text{z = 180 - 101} \\ \text{z = 79 degre}es \\ To\text{ find x} \\ 2(101)\text{ = x + 86} \\ 202\text{ = x + 86} \\ \text{Collect the like terms} \\ \text{x = 202 - 86} \\ \text{x = 116 degr}ees \\ \text{ find y} \\ 2z\text{ = y + 70} \\ z=\text{ 79} \\ 2(79)\text{ = y + 70} \\ 158\text{ = y + 70} \\ \text{y = 158 - 70} \\ \text{y = 88 degre}es \end{gathered}[/tex]Therefore, x = 116 degrees, y = 88 degrees, and z = 79 degrees
If f(x) = -2x + 8 and g(x) = v* + 9, which statement is true?
We have the function;
[tex]f(x)=-2x+8[/tex]and
[tex]g(x)=\sqrt[]{x+9}[/tex]Let's obtain f(g(x) before we make conclusions on the statements.
[tex]f^og=-2(\sqrt[]{x+9})+8[/tex]The domain of f(g(x) starts from x= - 9, this is where the function starts on the real line.
But - 6 < -9 , and thus,
The answer is - 6 is in the domain of the function.