Given:
Given the inequalities:4
[tex]\begin{gathered} 4x+3>0 \\ 9x-5<100 \\ x+4\leq10 \\ 72\div x\ge4 \end{gathered}[/tex]Required: Identify the inequality in which x = 8 is a solution.
Explanation:
Substitute 8 for x in each inequality and check whether it satisfies the inequality.
Consider 4x + 3 > 0.
[tex]4\cdot8+3=35>0[/tex]So, x = 8 satisfies the inequality 4x + 3 > 0.
Consider 9x - 5 < 100.
[tex]9\cdot8-5=67<100[/tex]So, x = 8 satisfies the inequality 9x - 5 < 100.
Consider x + 4 ≤ 10.
[tex]8+4=12>10[/tex]So, x = 8 not satisfies the inequality.
Consider 72 ÷ x ≥ 4.
[tex]72\div8=9\ge4[/tex]So, x = 8 satisfies the inequality.
Final Answer: The inequality in which x = 8 is not a solution is x + 4 ≤ 10.
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
1.Find the quotient of 1/2and 3/4.2. Divide 4by2/33.If 5/9is divided by3, what is the quotient4. Mrs. Dolentebuys 5 1/2kilograms of rice. If she cooks 1/4kilogram for every meal, how many meals will it last?5.Marita needs 2/3meter of lace for each pillowcaseshe makes. How many pillowcasescan she make with 7 1 3meters of lace
1) We can find the quotient between two fractions by multiplying the first one by the reciprocal of the second one this way:
[tex]\frac{\frac{1}{2}}{\frac{3}{4}}=\frac{1}{2}\times\frac{4}{3}=\frac{4}{6}=\frac{2}{3}[/tex]2) Let's now divide 4 by 2/3 following the same principle:
[tex]\frac{4}{\frac{2}{3}}=4\times\frac{3}{2}=\frac{12}{2}=6[/tex]Notice that we have simplified as well as the previous item (1).
3) Proceeding with that we have:
[tex]\frac{\frac{5}{9}}{3}=\frac{5}{9}\times\frac{1}{3}=\frac{5}{27}[/tex]4) To find this out, we need to convert that Mixed Number to Improper Fraction:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{2\times5+1}{2}=\frac{11}{2} \\ \frac{\frac{11}{2}}{\frac{1}{4}}=\frac{11}{2}\times4=\frac{44}{2}=22 \end{gathered}[/tex]We kept the denominator then multiplied it by the whole number and added it to 1. So it will last 22 meals.
5) To find it out we are going to divide 7 1/3 by 2/3 meter, after converting that Mixe Number into an Improper Fraction:
[tex]\begin{gathered} 7\frac{1}{3}=\frac{3\times7+1}{3}=\frac{22}{3} \\ \frac{\frac{22}{3}}{\frac{2}{3}}=\frac{22}{3}\times\frac{3}{2}=\frac{66}{6}=11 \end{gathered}[/tex]Notice, that we have used the same procedure to convert from Mixed Numbers to an Improper fraction. Marita can make 11 pillowcases.
And those are the answers.
The Reyes family is going to the mall. When they leave home,
What is the problem about?
Average speed
What information is given?
Starting odometer reading, ending odometer reading, time taken
What do you need to find?
The average speed of the car
An odometer measures the distance traveled by a wheeled vehicle
The starting odometer reading was 54,362 miles
The ending odometer reading was 54,372 miles
It took 15 minutes to get to the mall
Step 1: Find how far Reyes traveled in 15 minutes
54372 - 54362 = 10 miles
At this speed, the car will travel 10 miles in 15 minutes
Step 2: How far the Reyes would travel in 60 minutes?
The Reyes would travel 40 miles in 60 minutes
Hello, I need some assistance with this homework question please for precalculusHW Q32
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]Find the number of distinct arrangements of 12 letters in REENGINEERED. Two of the same letter are considered identical
We have to find the number of distinct arrangements of 12 letters in REENGINEERED.
First, we list the number of unique letters we have and its frequency. We have:
• R: 2
,• E: 5
,• N: 2
,• G: 1
,• I: 1
,• D: 1
for a total of 12 letters.
We can then calculate the number of distinct arrangements as the the total number of arrangements divided by the permutations that are repeated.
This can be expressed as the factorial of 12 divided by the product of the factorial of the frequencies of each letter (the letters that have a frequency of 1 will not affect the result so they are ignored for the denominator):
[tex]n=\frac{12!}{2!5!2!}=\frac{479001600}{2*120*2}=\frac{479001600}{480}=997920[/tex]Answer: there are 997,920 distinct arrangements.
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
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]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
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
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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.
Clara likes the buffet option of chicken, swordfish, roasted potatoes, and brussels sprouts
for $23 per person. She does not think everyone will eat the swordfish, so she decides to
only do a half portion of swordfish per guest, which means half the price. If the original
price of the swordfish was $7 per guest, what will the new overall price of the buffet be
per person?
The unitary method is used to find the unit value of the quantity. The price for the buffet after taking half portion of swordfish will be $19.5.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The price for complete buffet is $23 per person.
The price for swordfish per guest is $7.
Then, the price for half portion swordfish is $7 / 2 = $3.5.
Now, the price of buffet without swordfish is $23 - $7 = $16.
Thus, after taking only half portion of swordfish the new price becomes,
$16 + $3.5 = $19.5
Hence, the new price of the buffet for each person will be $19.5.
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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
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.
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.
I need help solving this problem. My answer isn’t coming out right. I have to find the missing length.
From the given diagram we get that the lines marked with the arrow are parallel, then the two triangles are similar.
To answer this question we will use the following diagram as a reference:
Therefore:
[tex]\frac{?}{18}=\frac{9-4}{9}.[/tex]Simplifying the above result we get:
[tex]\frac{?}{18}=\frac{5}{9}.[/tex]Multiplying the above result by 18 we get:
[tex]\frac{?}{18}\times18=\frac{5}{9}\times18.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} ?=\frac{90}{9}, \\ ?=10. \end{gathered}[/tex]Answer:
[tex]?=10.[/tex]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: 
what is the area of a triangle with a base of 5ft and a height of 8.4ft?
To answer this question, we need to remember the formula for finding the area of a triangle:
[tex]A_{\text{triangle}}=\frac{b\cdot h}{2}[/tex]Where
• b is the base of the triangle
,• h is the height of the triangle
Then, we have that:
b = 5ft
h = 8.4ft
Then, we have:
[tex]A_{\text{triangle}}=\frac{5ft\cdot8.4ft}{2}=\frac{42ft^2}{2}\Rightarrow A_{triangle}=21ft^2[/tex]Therefore, the area of this triangle is equal to 21 sq. feet.
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.
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
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
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.
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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.
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.
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.
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
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.