Given the equation;
[tex]-2y-15\text{ = 4y+15}[/tex]You are to calculate the value of y. This is as shown below;
First collect the like terms;
[tex]\begin{gathered} -2y\text{ - 4y = 15+15} \\ \end{gathered}[/tex]Evaaluate the expression an find y;
[tex]\begin{gathered} -6y=30 \\ \end{gathered}[/tex]Divide both sides by -6;
[tex]\begin{gathered} \frac{-6y}{-6}=\frac{30}{-6} \\ y\text{ = -5} \end{gathered}[/tex]Hence the value of y is -5
Hello, I need some assistance with this homework question please for precalculusHW Q32
What is the correct answer to 9+(-3)= ?
To solve the question given, we will follow the steps below:
Open the parenthesis
9+(-3)
= 9 - 3
=6
The correct answer is 6
resultado de w+2 1/2=3 1/2
We need to solve the following expression:
[tex]w+2\frac{1}{2}=3\frac{1}{2}[/tex]To do that we have to isolate the w variable on the left side of the equal sign, this is done by changing the signal of the constant number as shown below:
[tex]w=3\frac{1}{2}-2\frac{1}{2}[/tex]We can now subtract the two mixed fractions to determine the value of w.
[tex]\begin{gathered} w=3\text{ + }\frac{1}{2}-(2+\frac{1}{2}) \\ w=3-2+\frac{1}{2}-\frac{1}{2}=1 \end{gathered}[/tex]The value of w is 1.
15 is 20% of what numberOA 3O B. 60O C 75O D. 300
c)75
Explanation
to figure out this, we can use a rule of three
so,
let x represents the unknown value(
[tex]\begin{gathered} if \\ 15\Rightarrow20\text{ \%} \\ \text{then} \\ x\Rightarrow100\text{ \%} \end{gathered}[/tex]make the proportion and solve for x
[tex]\begin{gathered} \frac{15}{20}=\frac{x}{100} \\ \text{cross multiply} \\ 15\cdot100=20\cdot x \\ 1500=20x \\ \frac{1500}{20}=x \\ 75=x \end{gathered}[/tex]so, the answer is
C)75
I hope this helps you
41. Supermarket discount stores, and drugstores use a measure called sales per linear foot in deciding how much shelf space to allot for different items. To calculate this measure, divide the gross sales of an item by the number of linear feet of shelf space that the item occupies. Consider the following figures for two brands of vitamins: 
A box of pencils weighed 2.81 grams. If a principal ordered 38 boxes, how much would they weigh?
Answer:106.78
(If this answer is wrong, please message me and I will try to fix it)
Step-by-step explanation: let's take 2.81 grams, if you times that by 38 boxes, you will get 106.78 grams.
at 3:00 the temperature is 8°C the temperature increases 2 degrees each hour for the next 3 hours. what is the temperature at 6:00?
We know that at 3:00 the temperature is 8°C, and the temperature increases 2°C each hour for the next 3 hours.
This means that after 3 hours, the temperature will increase:
[tex]2^{\circ}C+2^{\circ}C+2^{\circ}C=6^{\circ}C[/tex]Thus, the temperature at 6:00 will be:
[tex]8^{\circ}C+6^{\circ}C=14^{\circ}C[/tex]Sally can paint a room in 4 hours while it takes Steve 8 hours to paint the same room. How long would it take them to paint the room if they worked together?
Sally paints a room in 4 hours, so in 1 hour she paints 1/4 of a room.
Steve paints a room in 8 hours, so in 1 hour she paints 1/8 of a room.
So,
1 hour -----> 1/4 + 1/8 of a room
x hour -----> 1 of a room
Are The Ratios 1:2 and 18:16 equivalent?
The ratios given are;
1: 2 and 18: 16
To know it the ratios are equivalent , simplify the second pair until you can nologer express it in its simplest form then compare it with the he
solving a tax rate or interest rate problem using a system ofDonna bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $150 more than the desktop. She paid for the computersusing two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges forone year were S303. How much did each computer cost before finance charges?Note that the ALEKS graphing calculator can be used to make computations easier.
Answer
Cost of desktop = $1750
Cost of laptop = $1900
Explanation:
Let the price of the desktop computer be x
Let the price of laptop computer be y
Laptop cost $150 more than desktop
Therefore, the cost of laptop y is given mathematically below
y= x + 150 ------------ equation 1
The interest rate of laptop is 9.5%
The interest rate of desktop is 7%
A sum of $303 was paid for the total financial charges
This statement can be represented mathematically as
0.07x + 0.095y = 303 ------------------ equation 2
Combine the two system of equations together and solve simultaneously
y = x + 150 ------------ equation 1
0.07x + 0.095y = 303 ---equation 2
Substitute the value of y in equation 2
0.07x + 0.095(x + 150 ) = 303
Open the parentheses
0.07x + 0.095x + 14.25 = 303
Collect the like terms
0.07x + 0.095x = 303 - 14.25
0.165x = 288.75
Divide both sides by 0.165
0.165x / 0.165 = 288.75 / 0.165
x = $1750
Find y
Since y = x + 150
x = 1750
y = 1750 + 150
y = $1900
Therefore, the cost of a desktop is $1750 and the cost of a laptop is $1900Answer
Parker offers to pay for 5 of his friends to play laser tag, but 3 of them don't want to play. If laser tag costs $6 per person, how much will Parker spend on his friends? Choose the correct expression and solution to this problem. O A. The expression is 5(6 - 3). Parker will spend $10. B. The expression is 6.5 - 3. Parker will spend $27
Expression: 6 (5-3) (option C)
Parker will spend $12
Explanation:
number of friends = 5
number of friends that don't play laser tag = 3
The cost of laser tag per person = $6
Amount Parker spend on his friends = 6 (5-3)
Expression: 6 (5-3)
Amount Parker spend on his friends = 6 (5-3) = 6(2)
Parker will spend $12
11. Write ____ as a single radical using the smallest possible root.
Answer:
[tex]\sqrt[6]{n^{23}}[/tex]Explanation:
The given expression is
[tex]\sqrt{n^5}\sqrt[3]{n^4}[/tex]To simplify, we first need to write them in exponent form
[tex]n^{\frac{5}{2}}\cdot n^{\frac{4}{3}}[/tex]Now, we can add the exponents
[tex]\begin{gathered} n^{\frac{5}{2}}\cdot n^{\frac{4}{3}}=n^{\frac{5}{2}+\frac{4}{3}}=n^{\frac{23}{6}} \\ \\ Because \\ \frac{5}{2}+\frac{4}{3}=\frac{5(3)+2(4)}{2(3)}=\frac{15+8}{6}=\frac{23}{6} \end{gathered}[/tex]Finally, we can write the expression in radical form
[tex]n^{\frac{23}{6}}=\sqrt[6]{n^{23}}[/tex]Therefore, the answer is
[tex]\sqrt[6]{n^{23}}[/tex]A store sells packages of candy for $52. Each packet cost $4 to make and contains $48 flavored gum and candy.Rolando knows how much each candy cost per pound and knows how many pounds of each candy are packed in each package. Let x represent the amount of gum per pound in each package and y represent the amount of candy per pound in each package.Use the following equation to complete the questions: x+y=180.75x+5.25y+4=52how many pounds of candy are in a box?what is the price per pound for a piece of candy?what does the term 0.75x represents in the second equation?
Let:
x be the amount of gum in pounds in each package.
y be the amount of candy in pounds in each package.
Each box or package cost $52: a packaging that cost $4 and $48 in gum and candy.
The amount of candy (in pounds) in each package is shown in the equation:
[tex]x+y=18[/tex]As this is the sum of the amount of gum x and the amount of candy y, we can say that each package has 18 pounds of candy and gum.
Then, the following equation,
[tex]0.75x+5.25y+4=52[/tex]seems to be the total cost, as it results in 52, that is the total cost of the box. There is also a term with value 4, that corresponds to the packaginf cost.
The other terms represent the cost of the gum (0.75 * x) and the candy (5.25 * y).
We can read from this equation that the price per pound of the gum is 0.75, because it is the factor that multiply the amount x to calculate the cost.
In the same way, we can say that 5.25 is the price per pound of the candy, as it is the factor that multiplies y.
Answers
How many pounds of candy are in a box? 18 pounds
What is the price per pound for a piece of candy? 5.25 $/lb
What does the term 0.75x represents in the second equation? The second equation represents the sum of all the costs (gum, candy and packaging cost). The term 0.75x represents the cost of the gum, as it multiplies the price of the gum per pound (0.74 $/lb) and the amount of gum (x, in lb/package).
for a science project Miranda will monitor the growth of two different plants, plant 1 and plant 2. at the start of the project plant 1 is 18 I'm tall and plant 2 is 4cm tall. plant 1 is expected to grow at a rate of 3 I'm per week.part a: what is the solution to the systems of equations in Mirandas graph? part b: what is the meaning of the solution to the systems of equations in the context of Miranda plant growth?part c: give a description of what the graph shows should happen with the plants growth before and after the point of intersection.
The lines in the graph represent the growth rate of two plants, the height is on the y-axis and the time is on the x-axis.
a)
If the plants growth represent an equation system, the solution of said system will be the point where both lines intersect. This point is arround x=7 weeks and y=39 centimeters, you can expres it as a ordered pair (7,39)
b)
This means that by the 7nth week both plants were 39 centimeters tall.
c)
Looking at the graph, the line corresponding to plant 2 is more inclined than the line of plant 1, this means that the growth rate (slope) of plant 2 is greater than the growth rate of plant 1.
The second plant grows faster than the first one.
a sphere has radius 3xcm. write down an expression for the surface area of the sphere in terms of x.give your answer in the simplest form
The expression to obtain the surface area of a sphere is
[tex]A=4\cdot\pi\cdot r^2[/tex]If the radius is equal to 3x cm then the expression is
[tex]A=4\cdot\pi\cdot(3x)^2[/tex]square the 3x
[tex]\begin{gathered} A=4\cdot\pi\cdot(3^2)\cdot x^2 \\ A=4\cdot\pi\cdot9\cdot x^2 \end{gathered}[/tex]Simplify the expression
[tex]A=36\pi\cdot x^2[/tex]The expression for the surface area of a sphere of radius 3x cm is:
[tex]A=36\cdot\pi\cdot x^2[/tex]latethe average rate of change from x = -21 of the function below.x2²+5x-12find the change in y by evaluating theon at-2 and 1:✓mange in y isREF
The given function is:
[tex]f(x)=x^2+5x-12[/tex]At x = -2:
f(-2) = (-2)² + 5(-2) - 12
f(-2) = 4 - 10 - 12
f(-2) = -18
At x = 1
f(1) = (1)² + 5(1) - 12
f(1) = 1 + 5 - 12
f(1) = -6
The change in y = f(1) - f(-2)
The change in y = -6 - (-18)
The change in y = -6 + 18
The change in y = 12
The sum of two numbers is 35. The larger number is one less than three times the smaller number. Let represent the larger number. Let represent the smaller number. Write a system of equations to represent this situation. What are the two numbers?
Explanation
To solve the question we will have to set up a simultaneous equation
If x represents the larger number
y represents the smaller number, then
The sum of the two numbers is 35
[tex]Equation\text{ 1: x+y=35}[/tex]The larger number is one less than three times the smaller number.
[tex]Equation\text{ 2: }x=3y-1[/tex]So, we will solve the equation using the substitution method
Thus, we will substitute x = 3y -1 into equation 1
[tex]\begin{gathered} 3y-1+y=35 \\ 3y+y-1=35 \\ 4y-1=35 \\ 4y=35+1 \\ 4y=36 \\ \\ y=\frac{36}{4} \\ \\ y=9 \end{gathered}[/tex]The smaller number is 9
The larger number will be
[tex]\begin{gathered} x+y=35 \\ x=35-y \\ x=35-9 \\ x=26 \end{gathered}[/tex]The larger number is 26
The answers are 9 and 26
If a board 9 feet 6 inches in length is cut into 2 equal parts, what will be the length of each part?
5 feet 2 inches
4 feet 8 inches
4 feet 5 inches
4 feet 9 inches
3 feet 8 inches
Answer:
4 feet and 9 inches
Step-by-step explanation:
First, we shall convert 9 feet and 6 inches into just inches.
9 x 12 = 108
108 + 6 = 114 inches.
114 divided by 2 = 57 inches.
Then, we divide 57 by 12:
57 divided by 12 = 4.75.
So, we have 4 feet.
0.75 x 12 = 9 inches.
In conclusion, we have 4 feet and 9 inches.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
could I get an explanation on what the answers are and why?
a) Given:
[tex]k(x)=-x-3[/tex]It is of the form, y=mx+c.
Comparing we get, m=-1. That is a negative slope.
So, the answer is
Line with a negative slope.
b) Given:
[tex]g(x)=-4x^2+1[/tex]Since the quadratic function and its sign of the leading term is negative.
So, the answer is,
Parabola oppening down.
C) Given:
[tex]f(x)=3[/tex]It is of the form, y=c.
Comparing we get, the y-intercept is c=3. It is parallel to the x-axis.
So, the answer is,
Horizontal line.
The point (7,-2) is a point on the graph of y=f(x)B) write the function that would shift (7,-2) right 3 then up 4
B) We have to find a function that would shift (7,-2) 3 units to the right and 4 units up.
To move a function in the horizontal axis, we have to add or substract the numbers of units in the argument:
f(x-k) will translate f(x) "k" units to the right. If "k" is negative, the function will be translated "k" units to the left.
Then, if we need to translate the point 3 units to the right, f(x) should have an argument of (x-3).
If we have to translate it in the vertical axis, we just add or substract outside f(x).
For example, f(x)+h will translate f(x) "h" units up. If "h" is negative, it will be translated down.
In this case, as we have to translate the function 4 units up, we add 4 outside of f(x).
Combining the two translations, we get:
[tex]y=f(x-3)+4[/tex]Answer:
B) The function that translates the function 3 units right and 4 units up is y = f(x-3)+4.
Label each point on the number line with the correct value
By converting fraction to decimal, it is obtained that
a = [tex]-\frac{7}{3}[/tex]
b = [tex]-2\frac{5}{8}[/tex]
c = -2.9
What is decimal and fraction?
Suppose there is a collection and a part of collection has to be taken. The part which is taken is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
Decimal numbers are those numbers which consist of an integer part and a fractional part.
Decimal are of two types-
Terminating decimals are those decimals which has finite number of figures after decimal point
Non terminating decimals are those decimals which has infinite number of figures after decimal point.
Here, the fraction needs to be converted to decimal
[tex]-\frac{7}{3} =[/tex] -2.33 which lies between -2 and -2.5. So Point c is [tex]-\frac{7}{3}[/tex]
[tex]-2\frac{5}{8} =[/tex] -2.625 which lies between -2.5 and -2.9. So point b is [tex]-2\frac{5}{8}[/tex]
Point a is -2.9
To learn more about decimal and fraction, refer to the link -
https://brainly.com/question/23038
#SPJ1
7. Triangle MNQ is similar to triangle MOP. N 30 cm 9 cm M 0 12 cm P M M 24 cm Find the length of NQ. O A. 9.6 cm O B. 15 cm O C. 60 cm O D. 22.5 cm Please help!!! :( It is due today !!!
If the triangles MNQ and MOP are similar, then you know that the corresponding sides are at the same ratio. Because of this property, we can determine that:
[tex]\frac{MN}{MO}=\frac{MQ}{MP}=\frac{NQ}{OP}[/tex]We know the measure of the corresponding sides MQ=12cm and MO=24cm, and the measure of the corresponding side to NQ, using these measures we can calculate NQ as follows:
[tex]\begin{gathered} \frac{MQ}{MO}=\frac{NQ}{OP} \\ \frac{12}{24}=\frac{x}{30} \\ 30(\frac{12}{24})=x \\ x=15 \end{gathered}[/tex]Side NQ measures 15 cm
The correct option is B.
Beth had 1/3 hour to get ready for work.She spent 1/5 hour putting on makeup.How much time does Beth have left?Give your answer in simplest form.1 hourEnter
To find how much time Beth has left, substract the time she spends on make up to the time she had to get ready.
This means that you have to substract 1/5 hour, which is the time she spends in make up, to 1/3 hour which is the time she has to get ready. This is: 1/3-1/5.
Imagine that you spent certain time on doing any activity, then you have to substract that time you spent from the time you had to do all your activities and duties. That is exactly what happened with Beth, she had 1/3 hour, but she spent 1/5 on make up, she needs to substract that 1/5 hour spent to the total time she had to know how much time she has left.
This will be a substraction of not similar fractions, you solve it this way:
[tex]\begin{gathered} \frac{1}{3}-\frac{1}{5} \\ =\frac{1\cdot5-1\cdot3}{3\cdot5} \\ =\frac{5-3}{15} \\ =\frac{2}{15} \end{gathered}[/tex]Now, she has 2/15 hours left.
Select the correct answer.What is the domain of the function f(x) = x + 3x + 5?A. all whole numbersB. all positive real numbersC. all integersD. all real numbersRasatWats the answer
The given function is:
[tex]f(x)=x+3x+5[/tex]The domain is the set of all x-values for which the function is defined.
We can observe in this function, we don't have any restrictions on the domain, since the function is defined for any real number.
So, the domain is all real numbers.
Answer: D.
IF LA = LB and LB = LC, then LA = LC. What property has been illustrated? a. Transitive b. Substitutionc. Distributived. Reflexive
The transitive property states that if x = y and y = z, then x = z
Considering the given scenario, IF LA = LB and LB = LC, then LA = LC, by comparing this statement with the earlier statement, we can see that
LA = x
LB = y
LC = z
Thus, the property being illustrated is
a. Transitive
Keishas teacher gives her the following information: • m,n,p, and q are all integers and p =/ 0 and q =/ 0 • A= m/q and B = n/pAnswer: A+B = mp + nq / pq, so the sum of a rational number and an irrational number is an irrational number A•B = mp + nq / pq, so the product of two rational number is a rational number A + B = mp + nq / pq, so the sum of two rational number is a rational number. A•B = mp + nq / pq , so the product of two irrational number is an irrational number
Let A and B be the following fractions:
[tex]\begin{gathered} A=\frac{m}{q} \\ B=\frac{n}{p} \\ p,q\ne0 \end{gathered}[/tex]if we add A and B, we get:
[tex]A+B=\frac{m}{q}+\frac{n}{p}=\frac{mp+nq}{pq}[/tex]therefore, the sum of two rational numbers is a rational number
What would be the angles for K, J, and L?
The given is a triangle. As we know that the sum of all the interior angles in a triangle is 180 degrees, we have,
[tex]\begin{gathered} 6x-5+x+8+2x-3=180 \\ 9x=180 \\ x=\frac{180}{9}=20 \end{gathered}[/tex]Therefore, the angles can be calculated as,
[tex]\begin{gathered} K=6\times20-5=115 \\ J=20+8=28 \\ L=2\times20-3=37 \end{gathered}[/tex]Solve the equation. -2/3 (x - 7) = 1/6 (x + 1) - 3
Given:
[tex]\frac{-2}{3}(x-7)=\frac{1}{6}(x+1)-3[/tex]Solving it,
[tex]\begin{gathered} \frac{-2}{3}x+\frac{14}{3}=\frac{x}{6}+\frac{1}{6}-3 \\ \end{gathered}[/tex]Solving further,
[tex]\begin{gathered} \frac{-2}{3}x-\frac{x}{6}=\frac{1}{6}-3-\frac{14}{3} \\ \frac{-4x-x}{6}=\frac{1-18-28}{6} \\ \frac{-5x}{6}=\frac{-45}{6} \\ -5x=-45 \\ x=\frac{45}{5} \\ x=9 \end{gathered}[/tex]Therefore, the value of x = 9
What are the intercepts of the equation 18x - 9y + 3z = 18?1. (1, 0, 0), (0, 2, 0), (0, 0, 6)2.(1, 0, 0), (0, -2, 0), (0, 0, 6)3.(6, 0, 0), (0, 3, 0), (0, 0, 1)4.(6, 0, 0), (0, -3, 0), (0, 0, 1)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]18x-9y+3z=18[/tex]To get the intercepts, we pick a point and equate the others to zero and then solve for the point.
STEP 2: Get the values of x when y and z are zeroes
[tex]\begin{gathered} 18x-9y+3z=1,z) \\ 18x-9(0)+3(0)=18 \\ 18x-0+0=18,18x=18 \\ Divide\text{ both sides by 18} \\ \frac{18x}{18}=\frac{18}{18} \\ x=1 \\ (x,y,z)\Rightarrow(1,0,0) \end{gathered}[/tex]STEP 3: Get the values of y when x and z are zeroes
[tex]\begin{gathered} 18x-9y+3z=18_{} \\ \text{Let x and z be 0} \\ 18(0)-9y+3(0)=18 \\ 0-9y+0=18 \\ -9y=18 \\ Divide\text{ both sides by -9} \\ \frac{-9y}{-9}=\frac{18}{-9} \\ y=-2 \\ (x,y,z)\Rightarrow(0,-2,0) \end{gathered}[/tex]STEP 4: Get the value of z when x and y are zeroes
[tex]\begin{gathered} 18x-9y+3z=18_{} \\ \text{Let x and y be 0} \\ 18(0)-9(0)+3z=18 \\ 3z=18 \\ Divide\text{ both sides by 3} \\ \frac{3z}{3}=\frac{18}{3} \\ z=6 \\ (x,y,z)\Rightarrow(0,0,6) \end{gathered}[/tex]Hence, the intercepts are:
[tex](1,0,0),(0,-2,0),(0,0,6)[/tex]x - y + z = - 3x - y - z = - 35x - 5y + z = - 15Solution: _, _, _
Given -
x - y + z = -3
x - y - z = -3
5x - 5y + z = -15
To Find -
Solution =?
Step-by-Step Explanation -
x - y + z = -3 ........(1)
x - y - z = -3 ..........(2)
5x - 5y + z = -15 .........(3)
So, from equation 1:
z = -3 -x + y
Now, put the value of z in equation 2 and 3:
x - y - (-3 -x + y) = -3
2x - 2y = -6
x - y = -3 ........(4)
5x - 5y + (-3 -x + y) = -15
4x - 4y = -12
x - y = -3 ......(5)
Now, on subtracting equations (5) and (6):
x - y -(x - y) = -3 - (-3)
x - x + y - y = 3 - 3
0 = 0
So, The System of equations has infinitely many solutions
Final Answer -
Solution: infinitely many solutions