The given expression is - 7(2x - 3)
The first step is to open the bracket by multiplying each term inside the bracket by the term outside. Then we would add or subtract where necessary.
It becomes
- 7 * 2x + - 7 * - 3
Recall, - * - = +
The simplified expression would be
- 14x + 21
The correct option is A
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]
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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
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]Simplify: x + (7 + 14x)Options:15 x + 721 x22 x21 x + 1
Step 1
Given;
[tex]x+(7+14x)[/tex]Required; To simplify the question.
Step 2
[tex]\begin{gathered} Bring\text{ like terms together} \\ x+14x+7 \\ Simplify \\ 15x+7 \end{gathered}[/tex]Answer;
[tex]15x+7[/tex]Which of the following is the correct representation of (-5,6) as a linear combination of unit vectors?05i - 6j0 -5i + 6jO 6i - 5j0 -6i + 5j
The correct combination of vectors is:
[tex]-5i+6j[/tex]This comes from the fact that we need to multiply the x component by i and the y component by j.
On a camping trip, Nina kept a log of the types of snakes she saw. She noted their colors and approximate lengths. Red Bright orange 1 foot long 3 3 2 feet long 3 1 3 feet long 2 2 What is the probability that a randomly selected snake is 3 feet long or bright orange? Simplify any fractions. S
we make a ratio between the number of the selected snakes and the total of snakes
selected snakes
are 3 feet long or bright orange
4 are 3 feet long and 6 are orange, but 2 oranges are 3feet long too, then we count
The volume of a cube is 64 feet, and hat is the length of the cube?
So the volume of a cube is given by:
[tex]r^3=64[/tex]Where r is the length of its sides. By finding r we can find the length of the cube:
[tex]\begin{gathered} r^3=64 \\ r=\sqrt[3]{64}=4 \end{gathered}[/tex]So the cube is 4 feet long.
Answer:
B,C,D:)
Step-by-step explanation:
i got 100%
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?
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.
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]
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]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.
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
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.
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90 times by x = 9,000
The value of x based on the multiplication in 90 × x = 9000 is 100.
What is multiplication?Multiplication simply means the product of numbers given. This is illustrated with the sign given as ×.
In this case, 90 × x = 9000
Multiply 90 by x which equates to 9000
90x = 9000
Divide by 90
90x / 90 = 9000 / 90
x = 100
The value of x is 100.
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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
A 6-foot hiker casts a 11-foot shadow, and a nearby tree casts a 34-foot shadow. Find the height of the tree
(round to the nearest tenth).
feet
Answer: 62.33
The ratio of the real length to the shadow is 6:11. to make the first ratio 34 then I could multiply both sides by 34/6 which would make 34:374/6. When 374 is divided by 6 it equals 62 1/3 which also equals 62.33333... Then I would round it to 62.33.
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.
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]Given a line with slope of -1 and y-intercept of 8, which of the ordered pairs given below would NOT be on the line?
We have a line with slope -1 and y-intercept of 8.
We can write the equation of this line as:
[tex]\begin{gathered} y=mx+b \\ y=-x+8 \end{gathered}[/tex]Then, we can test the values for each x-coordinate and see if it matches the y-coordinate indicated by the point:
Point (3,5)
[tex]y(3)=-3+8=5\longrightarrow\text{ is on the line}[/tex]Point (2,10)
[tex]y(2)=-2+8=6\ne10\longrightarrow\text{ is NOT on the line}[/tex]Answer: the point (2,10) is not on the line.
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
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]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
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°
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 period in degrees of F(x)= –2 sin(4x)
Answer:
Explanation:
We were given that:
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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2 a+6 divided by 2a²-18
[tex] \frac{2a + 6}{ 2{a}^{2} - 18} \\ = \frac{2(a + 3)}{2( {a}^{2} - 9)} \\ = \frac{a + 3}{(a + 3)(a - 3)} \\ = \frac{1}{a + 3} [/tex]
ATTACHED IS THE SOLUTION
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.
