The equivalent equations to 1/2(6x + 8) = x − 8 include:
A. 4 = -2x - 8
E. 2x + 4 = -8
What is an equation?It should be noted that an equation shows the relationship between the variables. This usually illustrated by having and equal to sign.
In this case, 1/2(6x + 8) = x − 8 will be:
3x + 4 = x - 8
Collect like terms
3x - x = -8 - 4.
2x = -12
Divide
x = -12/2
x = -6
Therefore, 4 = -2x - 8
2x = -8 - 4
2x = -12
x = -12/2 = -6
Therefore, A is correct.
E. 2x + 4 = -8
2x = -8 - 4
2x = -12
x = -12/2
x = -6
E is also correct.
The correct options are A and E.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Question
Ben takes out a loan of $2,500 with a 5.5% interest rate that is compounded semi-annually.
If he pays off the loan in 5 years, how much will he end up paying? Round your answer to the nearest dollar.
Ben end up paying $3279.12 over the course of five years with rate of interest 5.5% for a principal of $2500.
Explanation:Compounding interest semiannually means that at the start of the compounding period, in this case, every six months, the principal of a loan or investment includes the total interest from the previous period.
In the question, we are given the following information:
P = $2500
r = 5.5% = 0.055
t = 5 years
n = 2
The compound interest is calculated as follows:
A = [tex]P(1 + r/n)^{nt}[/tex]
where A denotes the amount, p denotes the principal, r denotes the interest rate, t denotes the time in years, and n denotes the type of compound interest.
A= 2500( 1 + 0.055/2)¹⁰
= 3279.12 ≈ $3279
A = $3279.12
Ben will end up paying $3279.12 at the end of 5 years for n = 2.
To learn more about compound interest refer to :
https://brainly.com/question/28020457
#SPJ13
eight Row in the table below gives you a number x a number Y and either a third number Z or the average pay of the three numbers that have which of the three numbers is given by a equals x + y + z / 3 fill in the missing numbers
Given three numbers x, y and z
The average of the numbers = A
[tex]A=\frac{x+y+z}{3}[/tex]We will complete the given table
When : x = 7 , y = 12 , z = 8
[tex]A=\frac{7+12+8}{3}=\frac{27}{3}=9[/tex]When x = 23 , y = 17 , z = 2
[tex]A=\frac{23+17+2}{3}=\frac{42}{3}=14[/tex]For the last case,
x = 4 , y = 11 , A = 6
[tex]6=\frac{4+11+z}{3}[/tex]Solve for z, multiply both sides by 3
[tex]\begin{gathered} 6\cdot3=\frac{4+11+z}{3}\cdot3 \\ 18=4+11+z \\ 18=15+z \\ \\ z=18-15=3 \end{gathered}[/tex]A TV has a listed price of $510.99 before tax. If the sales tax rate is 8.25%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
The most appropriate choice for sales tax will be given by-
Total cost of the TV with sales tax included is $553.15
What is sales tax?
Sales tax is a tax imposed by the government on the price of a commodity for the sale of that commodity. Imposing sales tax on a product increases the price of the product. Nowadays, sales tax has been replaced by Goods and Service Tax (GST).
Here,
Listed price of television = $510.99
Rate of sales tax = 8.25%
Sales tax to be added = [tex]\frac{8.25}{100}\times 510.99[/tex]
= $[tex]42.16[/tex]
Total cost of the TV with sales tax included = $(510.99 + 42.16)
= $553.15
To learn more about sales tax, refer to the link:
https://brainly.com/question/9437038
#SPJ13
Your answer is incorrect. A house has increased in value by 24% since it was purchased. If the current value is $527,000, what was the value when it was purchased? $102.000
We are given the final value of the house after its price was increased by 24%
We must go back to the original price knowing the final price. It's called inverse percentage calculation
To calculate the 24% of the value, we multiply by 24 and divide by 100, that is
value * 24 / 100 = 0.24 * value
The original price of the house is 100%, the increase is 24%, thus the final value of the house is 100% + 24% = 124%
What we were given as data is 124% of the original price of the house
As we did above, to compute 124% of a value, we multiply by 124 and divide by 100. Being P the original price of the house, then the final value is
P * 124% = P * 124 / 100 = 1.24 * P
We know this value:
1.24 * P = $527,000
Divide by 1.24 both sides of the equation
P = $527,000 / 1.24 = $425,000
The original price of the house was $425,000
Let's check it out:
Original price: $425.000
Increase: 0.24 * 425,000 = $102,000
Final Price: $425,000 + $102,000 = $527,000
The condition is met and the question is answered
help me please
thank you
Answer:
Domain: A, [1, 7]
Range: A, [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimetersand the ratio of the areas.
SOLUTION
Since the rectangles are similar,
The ratio of their perimeter is thus
[tex]\begin{gathered} \frac{P1}{P2}=\frac{l1}{l2} \\ \\ \frac{P1}{P2}=\frac{10}{25} \\ \\ P1\colon P2=\frac{2}{5} \\ \\ P1\colon P2=2\colon5 \end{gathered}[/tex]Ratio of their areas become
[tex]\begin{gathered} \frac{A1}{A2}=\lbrack\frac{l1}{l2}\rbrack^2 \\ \\ \frac{A1}{A2}=\lbrack\frac{10}{25}\rbrack^2 \\ \\ \frac{A1}{A2}=\frac{100}{625} \\ \\ \frac{A1}{A2}=\frac{4}{25} \\ \\ A1\colon A2=4\colon25 \end{gathered}[/tex]A pediatric nurse earns $45 per hour in Washington State. Apediatric nurse earns $55 per hour in California. What percent of theWashington State nurse's pay did the California nurse earn? Roundyour answer to the nearest tenth of a percent.
In order to calculate the percent of one nurse over the other, we can divide both payments and then convert the result to a percentage value.
So we have:
[tex]\frac{55}{45}=1.2222=122.22\text{\%}[/tex]Therefore the California nurse earns 122.22% of the Washington State nurse's pay.
Anthony, an aspiring meteorologist, spent the past few weekends studying the clouds. He took detailed notes on the types of clouds observed and the time of day they were observed. Stratocumulus Stratus Morning 4 1 Afternoon 3 7. 8 4 Evening What is the probability that a randomly selected cloud was observed in the afternoon or morning? Simplify any fractions.
The searched probability is
[tex]P(\text{AFTERNOON }\cup\text{ MORNING)}[/tex]is given by
[tex]P(\text{AFTERNOON }\cup\text{ MORNING)}=\text{ }P(\text{AFTERNOON )}+P(\text{ MORNING)-}P(\text{AFTERNOON }\cap\text{ MORNING)}[/tex]which gives
[tex]P(\text{AFTERNOON }\cup\text{ MORNING)}=P(\text{AFTERNOON )}+P(\text{ MORNING)}[/tex]because the events "afternoon" and "morning" are mutually exclusive. Then, we get
[tex]\begin{gathered} P(\text{AFTERNOON }\cup\text{ MORNING)}=\frac{5}{27}+\frac{10}{27} \\ P(\text{AFTERNOON }\cup\text{ MORNING)}=\frac{15}{27} \end{gathered}[/tex]then, the answer is 15/27
Write a system of equations to describe the situation below solve using illumination and fill in the blanks
Solution:
Let the cost of a tray of club sandwiches be s, and the cost of a tray of vegetarian sandwiches be v.
Then, the first order was for 6 trays of club sandwiches and 3 trays of vegetarian sandwiches at a cost of $75. We have;
[tex]6s+3v=75\ldots\ldots.\ldots\ldots.\text{equation}1[/tex]Also, the second order was for 9 trays of club sandwiches and 9 trays of vegetarian sandwiches at a cost of $144. We have;
[tex]9s+9v=144\ldots.\ldots\ldots\ldots....\ldots\text{equation}2[/tex]We would solve the two equation simultaneously, using elimination method.
Multiply equation 1 by 9 and equation 2 by 3.
[tex]\begin{gathered} (6s+3v=75)\times9 \\ 54s+27v=675\ldots.\ldots..\ldots..equation4 \\ (9s+9v=144)\times3 \\ 27s+27v=432\ldots\ldots..\ldots equation5 \end{gathered}[/tex]Subtract equation 5 from equation 4. We have;
[tex]\begin{gathered} 54s-27s+27v-27v=675-432 \\ 27s=241 \\ s=\frac{243}{27} \\ s=9 \end{gathered}[/tex]Substitute the value of s in equation 1. We have;
[tex]\begin{gathered} 6s+3v=75 \\ 6(9)+3v=75 \\ 54+3v=75 \\ \text{Subtract 54 from both sides;} \\ 54-54+3v=75-54 \\ 3v=21 \\ \text{Divide both sides by 3;} \\ \frac{3v}{3}=\frac{21}{3} \\ v=7 \end{gathered}[/tex]Thus;
FINAL ANSWER: A tray of club sandwiches costs $9, and a tray of vegetarian sandwiches costs $7
31. If Alain Junev and Parc Lafontaine together to do a job in 6 hours and Alainalone does the job in 10 hours, how long does it take Parc alone to do thejob?a. 12 hr b. 20 hr c. 15 hr d. 9 hr
They both together do the job is 6 hours.
It is given that Alain did the job in 10 hours.
We have to determined that how much time is take for Parc alone to do the job.
The height of a soccer ball that is kicked from the ground canbe approximated by the function:y = -18x2 + 36xwhere y is the height of the soccer ball in feet x seconds after it is kicked.What is the soccer ball's maximum height in feet?
For this problem you have to derive the equation given:
[tex]\begin{gathered} y^{\prime}=(-18x^2+36x)^{\prime}\text{ = -36x+}36 \\ \text{Now we equal to zero} \\ -36x+36=0 \\ \text{and we solve for x} \\ x=1 \end{gathered}[/tex]If we derive y again we notice that y''=-36 that means that a maximum is reached for x=1, then the maximum height of the ball is
[tex]y=-18(1^2)+36(1)=18[/tex]y= 18 feet
Find the area of the shaded portion of the figures below . Use straight pi= 3.
The area of a circle is given by the following formula:
[tex]A_C=\pi\cdot r^2[/tex]where r is the lenght of the circle's radius.
In this case, we have a radius of 12 units, so the area will be
[tex]A_C=\pi\cdot12^2=3.14\cdot144=452.16[/tex]We are however, asked to find the area of the shaded region, which is encased within a square. From the image we can see that the circle's radius is half the length of a side of the square. In other words, the square's sides measure 24 units.
The area of a square is given by
[tex]A_S=s^2[/tex]where s is the lenght of the sides of the square. In this case,
[tex]A_S=24^2=576[/tex]Now, in order to determine the area of the shaded region, we subtract the area of the circle from the area of the square:
[tex]A_R=A_S-A_C=576-452.16=123.84[/tex]So the area of the shaded region is 123.84 square units.
Evelyn's friend, Natalie needs 40 yards of yarn to make 10 quilts. How many yards of yarn does she need to make 12 quilts?
Answer:
48
Step-by-step explanation:
40 yards / 10 quilts = 4 yards per quilt
12 * 4 = 48
Hope this helps.
Answer:
48 yards
Step-by-step explanation:
Hey there!
To find the answer, we must first find how much yards of yarn she needs for 1 quilt
we do, 40/10 which is 4
Meaning, she needs 4 yards of yarn to make 1 quilt
Now we multiply 4 by 12 since we are making 12 quilts
4 x 12 = 48
So, Natalie needs 48 yards of yarn to make 12 quilts
Find the period in degrees of F(x)= –2 sin(4x)
Answer:
Explanation:
We were given that:
52. 3×16 I’ve been on this question for a while I don’t know what homework they give kids now days and they do it so different
Answer: 3x16=48
Step-by-step explanation: Multiplying is just like adding multiple times, so this is 16x3, or adding 16 three times. 16+16+16=48 I hope this helps!
Victoria wants to put at least one circular window in her basement. Victoria is trying to decide whether to put in three small windows, each with a 2 ft radius, or one large window with a 4 ft radius. Since Victoria wants to let in as much light as possible, she wants to use the option with the greater area. Should she install three small windows or one large window? What is the difference in the areas of the three small windows and one large window?
The following are the options Victoria's been thinking of in installing a circular window in her basement.
a.) Three small windows, each with a 2 ft radius.
b.) One large window with a 4 ft radius.
Since Victoria wants to let in as much light as possible, she wants to use the option with the greater area.
We must determine which options have the greater area.
Let's
May u please help me with Geometry. The last one question.
Beacuse to both sides of the equation you distribute the number that is outside the parentheses when making the product.
Then, you operate on both sides of the equation -7x, that is, you use the additive inverse of 7x
[tex]\begin{gathered} 7x-7-7x=6x-4-7x \\ -7=-1x-4\text{ }\rightarrow\text{ additive inverse property} \\ \end{gathered}[/tex]Then, you operate on both sides of the equation 4, that is, you use the add inverse of -4
[tex]\begin{gathered} -7=-1x-4 \\ -7+4=-1x-4+4 \\ -3=-1x\text{ }\rightarrow\text{ additive inverse property} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} -3=-1x \\ \frac{-3}{-1}=x\text{ }\rightarrow\text{ Division property} \\ 3=x\text{ }\rightarrow\text{ Reflexive property} \end{gathered}[/tex]12 < 2x - 8 or 16 ≥ 2x - 8
can someone help
X E (10,12]
Isolate the Variable by dividing each side by factors i.e 2 that don't contain the variable.
12<2x-8
6<x-4
10<x
Inequality Form:
x>10
Interval Notation:
(10,∞)
Isolate the variable by dividing each side by factors i.e 2 that don't contain the variable.
16>=2x-8
8>=x-4
12>=x
Inequality Form:
x≤12
Interval Notation:
(−∞,12]
Combining Both : X E (10,12]
To learn more about Steps to solve Linear Equations:https://brainly.com/question/28898641?answeringSource=feedPublic%2FhomePage%2F20
Write an equation using four numbers that multiply to , none of which are opposites.
An equation using four numbers that add to 0 none of which are opposites is 15 + (-10) + 1 + 4
What is an equation?It should be noted that an equation is simply used to show the relationship between the variables.
Based on the information given, the appropriate equation will be:
= 15 + (-10) + 1 + 4
= 15 - 10 + 1 + 4
= 0
Learn more about equations on
brainly.com/question/2972832
#SPJ1
Write an equation using four numbers that as
add to 0 none of which are opposites.
Three students attempt to define the geometric object called an angle.
Can you match the teacher's comments to the definitions?
The explanation of the geometric shape known as an angle is made by three students. The matching answer is 1-1, 2-2,3-3.
Given that,
The explanation of the geometric shape known as an angle is made by three students.
We have to match the definitions to the teacher's comments.
Step1: definition of angle
Step2: teachers comments
1- Ruby's definition: The amount of turn between two straight lines that have a common vertex.
1-Bingo! you got it.
2-Shriya's definition: Two lines that come together.
2- Were you thinking of intersecting lines?
3- Abhishek's definition: A figure composed of two rays sharing a common endpoint. The common endpoint is known as vertex.
3-You seem to be getting at the idea of the measure of an angle,
not the definition of the angle itself.
Therefore, The matching answer is 1-1, 2-2,3-3.
To learn more about matching visit: https://brainly.com/question/14275644
#SPJ1
I need help with this practice problem.It’s from my trig prep guide. It asks to answer (a) & (b).
The general binomial theorem can be expressed as:
[tex](a+b)^n=\sum ^n_{k\mathop=0}C^n_k\cdot a^{n-k}\cdot b^k[/tex]Now, for this problem we identify:
[tex]\begin{gathered} a=3x^5 \\ b=-\frac{1}{9}y^3 \\ n=4 \end{gathered}[/tex](a)
Then, using the general form:
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}C^4_k\cdot(3x^5)^{4-k}\cdot(-\frac{1}{9}y^3)^k[/tex](b)
The combination operator for this sum:
[tex]\begin{gathered} C^4_0=C^4_4=1 \\ C^4_1=C^4_3=4 \\ C^4_2=6 \end{gathered}[/tex]Then, the simplified terms of the expansion are:
[tex]\begin{gathered} C^4_0\cdot(3x^5)^4\cdot(-\frac{1}{9}y^3)^0=81x^{20} \\ C^4_1\cdot(3x^5)^3\cdot(-\frac{1}{9}y^3)^1=4\cdot(27x^{15})\cdot(-\frac{1}{9}y^3)=-12x^{15}y^3 \\ C^4_2\cdot(3x^5)^2\cdot(-\frac{1}{9}y^3)^2=6\cdot(9x^{10})\cdot(\frac{1}{81}y^6)=\frac{2}{3}x^{10}y^6 \\ C^4_3\cdot(3x^5)^1\cdot(-\frac{1}{9}y^3)^3=4\cdot(3x^5)\cdot(-\frac{1}{729}y^9)=-\frac{4}{243}x^5y^9 \\ C^4_4\cdot(3x^5)^0\cdot(-\frac{1}{9}y^3)^4=\frac{1}{6561}y^{12} \end{gathered}[/tex]If they had 15 oranges,9 peaches and 18 pears to distribute into the baskets.How many baskets can they make with the SAME number of pieces of fruit in each one?? How many pieces of each type of fruit will be in each basket?
what is the outlier, if any 5,12,14,19,19,21,25,29,33
We are given a set of data, 5, 12, 14, 19, 19, 21, 25, 29, 33
Firstly, we need to find the mean of the data
[tex]undefined[/tex]Looking for help on this problem. Help is appreciated a lot!
/
[tex]t^3=-\cfrac{27}{343}\implies t^3=-\cfrac{3^3}{7^3}\implies t^3=-\left( \cfrac{3}{7} \right)^3\implies t^3=-\left( \cfrac{3}{7} \right)\left( \cfrac{3}{7} \right)\left( \cfrac{3}{7} \right) \\\\\\ t^3=+\left( -\cfrac{3}{7} \right)\left( -\cfrac{3}{7} \right)\left( -\cfrac{3}{7} \right) \implies t^3=+\left( -\cfrac{3}{7} \right)^3 \\\\\\ t^3=\left( -\cfrac{3}{7} \right)^3\implies t=-\cfrac{3}{7}[/tex]
help me pleaseee!!!
thank you
The cost C(x) for printing any amount of copies is C(x) = 0.25x + 75.
What is an expression?An expression is in the form of variables and constants separated by the operation of addition and subtraction.
Given the initial cost of producing a newsletter has an initial charge of 75 dollars for formatting and editing and 0.25 dollars for printing each copy.
Here the initial cost is a constant and now of. of copies is a variable in x.
∴ Our equation for expressing the cost C(x) for printing any amount of copies is,
C(x) = 0.25x + 75.
learn more about expression here :
https://brainly.com/question/13947055
#SPJ1
11/12 divided by 4/5
Given the general rule for the division of fractions:
[tex]\begin{gathered} \frac{a}{b}\frac{\cdot}{\cdot}\frac{c}{d}=\frac{a\cdot d}{b\cdot c} \\ b,d\ne0 \end{gathered}[/tex]in this case, we can use the formula in the following way:
[tex]\frac{11}{12}\frac{\cdot}{\cdot}\frac{4}{5}=\frac{11\cdot5}{12\cdot4}=\frac{55}{48}[/tex]therefore, the answer is 55/48
Please help me figure out which property goes with each equation
step 3 ------> distributive property of multiplication
step 5 ----> subtraction property of equality
step 2 ----> addition property of equality
step 1 ----> multiplication property of equality
step 4 ---> division property of equality
The correct order is
3-5-2-1-4
Out of the 50 people interviewed 6 people said Spider-Man was their favorite super hero. What percent of people said that Spider-Man was their favorite superhero?
To solve find the percentage of people that said Spider-Man was their favorite superhero
We will simply write
[tex]\frac{6}{50}\times\text{ 100\%}[/tex][tex]=\frac{600}{50}percent[/tex]=12%
Therefore; 12% of the people said Spider-Man was their favorite superhero
riRick is creating I love version for Morty to make the potion Rick needs 51 mL of a mixture solution where 40% is carbonated water after checking around his job grapevines to Solutions he could use the first solution he found is 65% green tea and 15% carbonated water and 20% whole milk the second solution is 17% orange juice 38% lemonade and 45% carbonated water how much of the first solution in the second solution does Rick need to mix together to create the Love Potion round your final answer to one decimal place you may solve this problem using any method .
Answer:
First Solution: 8.5mL
Second Solution: 42.5 mL
Explanation:
Let us call x the number of mL of the first solution and y the number of mL of the second solution.
Now, from the fact that the final solution is 51 mL, we know that
[tex]x+y=51[/tex]Furthermore, from the fact that the final solution 40% carbonated water, meaning there are in total
[tex]51\times\frac{40}{100}=20.4mL[/tex]of carbonated water in the love potion.
Now, the first solution contributes 15/100 * x mL of carbonated water in the solution whereas the second solution contributes 45/100 * y mL. Since all 20.4 mL of carbonated water in the solution is coming from solution 1 and 2, then it must be that
[tex]\frac{15}{100}x+\frac{45}{100}y=20.4[/tex][tex]0.15x+0.45y=20.4[/tex]Thus we have two equations and two unknowns
[tex]\begin{gathered} 0.15x+0.45y=20.4 \\ x+y=51 \end{gathered}[/tex]We solve the above system by elimination.
First multiplying the second equation by 0.15 gives
[tex]\begin{gathered} 0.15x+0.45y=20.4 \\ 0.15x+0.15y=51\cdot0.15 \end{gathered}[/tex]which simplifies to give
[tex]\begin{gathered} 0.15x+0.45y=20.4 \\ 0.15x+0.15y=7.65 \end{gathered}[/tex]Subtracting the first equation from the second gives
[tex]0.30y=12.75[/tex]Finally, dividing both sides by 0.30 gives
[tex]\boxed{y=42.5.}[/tex]With the value of y in hand, we now put it into x+ y = 51 and solve to x to get
[tex]x+42.5=51[/tex]subtracting 42.5 from both sides gives
[tex]\boxed{x=8.5.}[/tex]Hence, to conclude the needed amounts of the solution are:
First Solution: 8.5mL
Second Solution: 42.5 mL
Please help!!
Solve for angle FGD
Answer:
m∠FGD = 132°
Step-by-step explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Therefore, as AB is parallel to CD, and line EH intersects them:
⇒ m∠EFB = m∠FGD
Substitute the given expressions for the angles and solve for x:
⇒ (3x - 120)° = (x + 48)°
⇒ 3x - 120 = x + 48
⇒ 3x - 120 - x = x + 48 - x
⇒ 2x - 120 = 48
⇒ 2x - 120 + 120 = 48 + 120
⇒ 2x = 168
⇒ 2x ÷ 2 = 168 ÷ 2
⇒ x = 84
Substitute the found value of x into the expression for m∠FGD:
⇒ m∠FGD = (84 + 48)°
⇒ m∠FGD = 132°
