Answer:
[tex]x\leq 36[/tex]
The solution for [tex]x[/tex] is all real numbers less that or equal to 36.
Step-by-step explanation:
Given expression:
[tex]\frac{1}{2}x\leq18[/tex]
To find the solution for [tex]x[/tex]
Solution:
In order to solve for [tex]x[/tex] , we will make sure to isolate the unknown variable [tex]x[/tex] on left side alone by doing math operations on both sides of the inequality.
We have:
[tex]\frac{1}{2}x\leq18[/tex]
Multiplying both sides by 2.
[tex]2.\frac{1}{2}x\leq18\times 2[/tex]
The 2 on left side will cancel each other leaving [tex]x[/tex] alone.
Thus, we have:
[tex]x\leq 36[/tex]
Thus, solution for [tex]x[/tex] is all real numbers less that or equal to 36.
Answer:
D
Step-by-step explanation:
My sister is 19 years old. My brother says that his age minus eighteen is equal to my sister's age. How old is my brother? Enter an equation, using b as your variable, to find how old my brother is. The equation is My brother is years old.
Step-by-step explanation:
If you find my answer helpful...mark it as brainliest.
An equation is created to solve for the brother's age: b - 18 = 19. By adding 18 to both sides, we determine the brother is 37 years old.
To solve for the brother's age, you need to create an equation based on the information given. Since the sister is 19 years old, and the brother says his age minus eighteen is equal to the sister's age, the equation is: b - 18 = 19.
Now, solve for b (the brother's age) by adding 18 to both sides of the equation:
b - 18 + 18 = 19 + 18b = 37Therefore, the brother is 37 years old.
john traveled 150km in 6 hours and alice traveled 180km in 4 hours. what is the ratio of the average speed of john to average speed of alice?
a. 3:2
b. 2:3
c. 5:9
d. 5:6
The average speed of John and Alice are determined first by dividing the total distance by the total time taken. The ratio of the average speeds is 25:45 or in simplified form, 5:9. Therefore, the correct answer to the question is (c) 5:9.
Explanation:To find the ratio of the average speed of John to Alice, we first need to calculate their average speed individually. The average speed is obtained by dividing the total distance covered by the total time taken.
For John, his average speed would be 150km/6 hours = 25km/h. For Alice, her average speed would be 180km/4 hours = 45km/h.
So, the ratio of the average speed of John to Alice would be 25 : 45. In simplest form, this ratio becomes 5 : 9 (divided both numbers by 5).
Therefore, the answer is (c) 5:9.
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A person standing close to the edge on the top of a 400-ft building drops a baseball. The quadratic function h left parenthesis t right parenthesis equals negative 16 t squared plus 400 models the ball’s height above the ground, h left parenthesis t right parenthesis, in feet, t seconds after it was dropped.
Find h left parenthesis 0 right parenthesis AND interpret the meaning of the function value in the context of the problem.
Answer:
[tex]h(0)=400[/tex]
The above function value for [tex]h(0)[/tex] shows that height of the ball before it was dropped i.e. at time = 0 seconds.
The height of the ball above the ground before it was dropped = 400 ft.
Step-by-step explanation:
Given:
The quadratic function that models the height of the baseball above the ground in feet , [tex]t[/tex] seconds after it was dropped is given as:
[tex]h(t)=-16t^2+400[/tex]
To find [tex]h(0)[/tex] and interpret the meaning of the function value in contect of the problem.
Solution:
In order to find [tex]h(0)[/tex], we will replace [tex]t=0[/tex] in the given function as [tex]h(t)[/tex] is a function of time [tex]t[/tex].
Thus, we have:
[tex]h(0)=-16(0)^2+400[/tex]
[tex]h(0)=16(0)+400[/tex]
[tex]h(0)=0+400[/tex]
[tex]h(0)=400[/tex] (Answer)
The above function value for [tex]h(0)[/tex] shows that height of the ball before it was dropped i.e. at time = 0 seconds.
The height of the ball above the ground before it was dropped = 400 ft.
Fraction equivalents
7/15 = ?/45
Answer:
21/45
Step-by-step explanation:
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There are 10 cranberry and 15 strawberry juices. You randomly pick two juices. What's the probability you'll get two strawberry juices.
Answer:
7/20Explanation:
The theoretical probability, P (A), of an event, A, is:
P(A) = number of outcomes of event A / total number of possible outcomesFor 10 cranberry and 15 strawberry juices, the number of outcomes for two strawberry juices are:
Combination of 15 strawberry juices chosen in two:[tex]C^{15}_{2}=\frac{15!}{(15-2)!(2!)}=\frac{15!}{13!2!}=\frac{15\times 14}{2}=105[/tex]
The total number of possible outcomes is:
Combination of 25 juices chosen in two:[tex]C^{25}_{2}=\frac{25!}{(25-2)!(2!)}=\frac{25!}{23!2!}=\frac{25\times 24}{2}=300[/tex]
Thus, the probability of randomly picking two strawberry juices is:
P (two strawberry juices) = 105/300 = 7/20Note that you can obtain it as the product of the probabilities that the first juice is a strawberry juice and the second juice is also strawberry juice:
[tex]15/25\times 14/24=(15\times 25)/(14\times 24)=210/600=7/20[/tex]
Write 8 x 8 x 8 x 8 using exponents.
Step-by-step explanation:
The exponent form of the given product is given by 8³
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here: The product of 8×8×8
We know by the law of exponents that
a×a×a=a³
Thus 8×8×8=8³
Hence, The exponent form of the given product is given by 8³
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$650 is invested in an account at 3%
simple interest per year. Write the
first 5 terms of the sequence that
shows the value of the account at
yearly intervals.
Answer:
Step-by-step explanation:
Simple interest = [tex]650*\frac{3}{100}=$19.5[/tex]
End of first year = 650+19.5 = $669.50
End of second year = 669.50+19.5 = $ 689
End of third year = 689+19.5 = $708.50
End of fourth year = 708.50 +19.5 = $ 728
End of fifth year = 728 +19.5 = $747.50
What value correctly fills in the blank so that the expressions are equivalent?
32 + 72 = _x(4 + 9)
Answer:
8
Step-by-step explanation:
Notice:
32 = (8 x 4)
72 = (8 x 9)
Hence,
32 + 72
= (8 x 4) + (8 x 9) (factorize out the 8)
= 8 x (4 + 9)
therefore the musing number is 8
Answer:
Step-by-step explanation:
32 + 72 = 8*4 + 8* 9
= 8* (4 + 9)
So 8 will come in the blank
what is the definition of median
Answer:
the middle sequentially in a list of numbers (sorted from lowest to highest)
Step-by-step explanation:
for example, in the dataset 2, 4, 6, 8, 10, 6 would be the median because it is in the middle when sorted properly
Answer: The median is the middle value in the list of numbers
Step-by-step explanation:
For example: 5,3,7,10,22,12,15,100,98
The median is 22 because it is in the middle of all the number displayed
If Sue can read 25 pages in ten minutes, how long will it take her to read 250 pages?
Answer:
100 minutes
Step-by-step explanation:
25 x 10 = 250
10×10=100
Solve for x. Then find the measure of each identified angle. Check your solution
Answer:
put a pic of the question
Step-by-step explanation:
plz
2x+3y=4 4x+6y=9 what is the value of x and y
Answer:
No Solution.
Step-by-step explanation:
2x+3y=4
4x+6y=9
-------------
-2(2x+3y)=-2(4)
4x+6y=9
----------------------
-4x-6y=-8
4x+6y=9
-------------------
0=1
no solution
Answer:
No solution.
Step-by-step explanation:
2x + 3y = 4
4x + 6y = 9
Multiply both sides of the first equation by -2. Then write the second equation below it and add them.
-4x - 6y = -8
+ 4x + 6y = 9
-------------------------
0 + 0 = 1
Since the statement 0 = 1 is false, there is no solution to this system of equation.
F(7) if f(x)=5x
Answer_______
Answer:
35
Step-by-step explanation:
put 7 instead x and it will be 5*7 that is 35
What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches. Explain
448 square inches.
The surface area of the box is 448 square inches so that is the least amount of paper needed to cover the box.
Answer:204
Step-by-step explanation: Just that good.
What is the slope of the line represented by the equation y =
x - 3?
Answer:
The slope of the line is: 1
The y-intercept is: -3
You can graph the line using the slope and y-intercept, or two points.
Answer:
1.
Step-by-step explanation:
The general form of a line is y = mx + c where m = the slope.
y = x - 3
or we can write it as y = 1x - 3
- so the slope is 1.
Mrs McCarr buys 9 packages of markers for an art project. Each packages has 10 markers. How many markers does Mrs McCarr buy?
Answer:
Mrs. McCarr buys 90 markers
Step-by-step explanation:
10 markers per package × 9 packages of markers = 90 markers in total
90 markers because 10 times 9 equals 90
Aguy wire for a tree is 20 ft. long, making a 21oangle with the ground. How far is the base of the tree from a stake anchoring the wire?
Answer:
The base of the tree from a stake anchoring the wire is 18.67 feet far.
Step-by-step explanation:
Given:
the length of the wire = 20 feet
Angle that the wire makes with the ground = 21 degrees
To Find:
The Distance from the base of the tree from the stake anchoring wire = ?
Solution:
We we construct a figure using the given data we end up with the right triangle as shown below
So now we can use the cosine ratio to find the distance from the base of the tree to the anchoring wire
Let d be the distance of base of the tree from a stake anchoring the wire
[tex]Cos(angle) =\frac{\text{Adjacent side}}{Hypotenuse}[/tex]
On substituting the values we get
[tex]cos(21^{\circ}) =\frac{d}{20}[/tex]
[tex]d = cos(21^{\circ}) \times 20[/tex]
d = [tex]0.9335 \times 20[/tex]
d = 18.67 feet
A child grew 3 1/4 inches one year and 4 3/4 inches the next year. How many inches did the child grow over the two years?
BRAINLIEST GETS 15 POINTS
Answer:
4 inches
Step-by-step explanation:
express the mixed fraction in improper form
3 1/4 = 13/4
4 3/4 = 19/4
hence total growth
= 3 1/4 + 4 3/4
= 13/4 + 19/4
= (13+19)/4
= 32/4
= 4 inches
Answer:
8 inches.
Step-by-step explanation:
3 1/4 + 4 3/4
= 3 + 4 + 1/4 + 3/4
= 7 + 4/4
= 7 + 1 = 8 inches.
last week, the price, in dollars, of a gallon of gasoline was g. This week the price of gasoline per gallon increased by 5%. Which expressions represent this weeks price, in dollars, of a gallon of gasoline?
A. g+0.05
B. g+0.05g
C. 1.05g
D. 0.05g
E. (1+0.05)g
The price of gasoline in this week is 1.05g. Option C
Step-by-step explanation:
Given,
The price of a gallon of gasoline = g in last week.
The price of gasoline increased by 5% this week.
To find the price of gasoline this week.
Formula
If an original price of an object a increased by b% the final price will be = a×[tex]\frac{100+b}{100}[/tex]
So,
The price of gasoline in this week = g×1.05 = 1.05g
[ Please note: Here option C and E have same value. So, both are correct].
The expressions represent this week's price, in dollars, of a gallon of gasoline, is 1.05g.
Given that,
Last week the price, in dollars, of a gallon of gasoline was g.
This week the price of gasoline per gallon increased by 5%.
We have to determine,
Which expressions represent this week's price, in dollars, of a gallon of gasoline?
According to the question,
The price of a gallon of gasoline = g in last week.
The price of gasoline increased = 5% = 0.05
The expressions represent this week's price, in dollars, of a gallon of gasoline is,
= Price of gallon last week + Price of gallon increased this week
= g + 0.05g
= (1 + 0.05)g
= 1.05g
Hence, The expressions represent this week's price, in dollars, of a gallon of gasoline, is 1.05g.
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A cow produces 20000lbs of milk in a year. A gallon of milk weighs 8.6lbs. How many gallons did the cow produce?
Answer:
2,325.58 Gallons
Step-by-step explanation:
20,000÷8.6=2,325.58
What property is it when Segment AB is Congruent to AB
Answer:
Therefore,
[tex]Segment\ AB \cong Segment\ AB[/tex] ....Reflexive Property.
Step-by-step explanation:
Reflexive Property :
The reflexive property of equality means that anything is equal to itself. The formula for this property is a = a. This property tells us that any number is equal to itself. For example, 3 is equal to 3.Here it is given When
[tex]Segment\ AB \cong Segment\ AB[/tex]
AB is Equal to itself, Hence it is the Reflexive Property.
Therefore,
[tex]Segment\ AB \cong Segment\ AB[/tex] ....Reflexive Property.
f(2/9) if f(x)=3x+1/3
Answer:
1
Step-by-step explanation:
Jerry and Phil took a math test on Wednesday they scored 178 points altogether Jerry scored 10 points higher than fill what is each students score
Answer:
Step-by-step explanation:
j + p = 178
j = p + 10
p + 10 + p = 178
2p + 10 = 178
2p = 178 - 10
2p = 168
p = 168/2
p = 84 <==== Phil's score
j = p + 10
j = 84 + 10
j = 94 <====Jerry's score
Final answer:
Jerry scored 94 and Phil scored 84.
Explanation:
To find Jerry and Phil's scores, we'll set up two equations based on the given information. Let's say Jerry's score is represented by 'J' and Phil's score is represented by 'P'. We know that Jerry scored 10 points higher than Phil, so J = P + 10. We also know that their scores combined equal 178, so J + P = 178. Now we can solve these two equations to find each student's score. Substituting the first equation into the second equation, we get (P + 10) + P = 178. Simplifying this equation gives us 2P + 10 = 178. Subtracting 10 from both sides gives us 2P = 168. Finally, dividing both sides by 2 gives us P = 84. So Phil's score is 84. Substituting this value back into the first equation, we get J = 84 + 10 which gives us J = 94. Therefore, Jerry's score is 94.
3) The expression (x12)(y-13)(x-5)(y4
equivalent xmyn. What is the value of n
Answer:
Therefore the value of n is
[tex]n=-9[/tex]
Step-by-step explanation:
Given:
[tex]x^{12}y^{-13}x^{-5}y^{4}=x^{m}y^{n}[/tex]
To Find:
n = ?
Solution:
Using identity
[tex]1.\ x^{a}x^{b}=x^{a+b}[/tex]
[tex]2.\ x^{a}x^{-b}=x^{a-b}[/tex]
[tex]3.\ x^{-a}x^{b}=x^{-a+b}[/tex]
Therefore
[tex]x^{(12-5)}y^{(-13+4)}=x^{m}y^{n}[/tex]
[tex]x^{7}y^{-9}=x^{m}y^{n}[/tex]
Now on Comparing and Equality Property we get
[tex]m =7\\n=-9[/tex]
Therefore the value of n is
[tex]n=-9[/tex]
The final expression is [tex]x^{7}[/tex] [tex]y^{-9}[/tex] , making n = -9.
The given expression is([tex]x^{12}[/tex])([tex]y^{-13}[/tex])([tex]x^{-5}[/tex])([tex]y^4[/tex]). We want to find the equivalent expression in the form [tex]x^{m}[/tex] [tex]y^n[/tex], where m and n are exponents that we need to determine.
Here's how to simplify it step by step:
Combine the exponents of x:[tex]x^{12}[/tex] * [tex]x^{-5}[/tex] = [tex]x^{12-5}[/tex] = [tex]x^{7}[/tex]
2. Combine the exponents of y:
[tex]y^{-13}[/tex] *[tex]y^{4}[/tex] = [tex]y^{-13+4}[/tex] = [tex]y^{-9}[/tex]
Therefore, the expression simplifies to [tex]x^{7}[/tex] [tex]y^{-9}[/tex]. This means that m = 7 and n = -9. Thus, the value of n is -9.
Question-The expression ([tex]x^{12}[/tex])([tex]y^{-13}[/tex])([tex]x^{-5}[/tex])([tex]y^4[/tex]) is equivalent to [tex]x^m y^n[/tex].
What is the value of n?
Gorillas and chimpanzees can learn language to communicate with humans. By 2017 , a gorilla named Koko had learned 700 words. This was 50 fewer than 5 times as many as a chimp named Washoe knew a decade earlier. How many words did Washoe know?
Answer:
130
Step-by-step explanation:
700 - 50 = 650
650/5 = 130
Answer:
150 words
Step-by-step explanation:
k = 700....koko knows 70 words
k = 5c - 50....this is 50 fewer then 5 times the chimps(c)
5c - 50 = 700
5c = 700 + 50
5c = 750
c = 750/5
c = 150 <=== the chimp, Washoe, knew 150 words
In a vial containing 5/6 parts, you withdraw 1/12. How many parts remain?
A circus charges $2.50 for kids tickets and $6 for adult’s tickets. Last weekend, twice as many kids attended the circus than adults. If the ticket sales totaled $7,150, how many kids attended the circus?
The number of kids attending the circus is 1300.
Let's denote:
- ( K ) as the number of kids attending the circus.
- ( A ) as the number of adults attending the circus.
Given:
- The price of a kid's ticket is $2.50.
- The price of an adult's ticket is $6.
- The total ticket sales is $7,150.
- The number of kids attending the circus is twice the number of adults.
We can set up a system of equations based on the given information:
1. The total ticket sales:
[tex]\[ 2.50K + 6A = 7150 \][/tex]
2. The number of kids attending the circus is twice the number of adults:
[tex]\[ K = 2A \][/tex]
Now, we can solve this system of equations.
We can substitute the expression for ( K ) from equation 2 into equation 1:
[tex]\[ 2.50(2A) + 6A = 7150 \][/tex]
[tex]\[ 5A + 6A = 7150 \][/tex]
[tex]\[ 11A = 7150 \][/tex]
Now, solve for ( A ):
[tex]\[ A = \frac{7150}{11} \][/tex]
[tex]\[ A \approx 650 \][/tex]
So, the number of adults attending the circus is approximately 650.
Now, we can find the number of kids attending the circus using the expression we found for ( A ) in terms of ( K ):
[tex]\[ K = 2A \][/tex]
[tex]\[ K = 2 \times 650 \][/tex]
[tex]\[ K = 1300 \][/tex]
So, the number of kids attending the circus is 1300.
Find the value of x to the nearest tenth.
19.7 19.2 20.8 21.3
Answer:
x=20.8 units
Step-by-step explanation:
The picture of the question in the attached figure
we know that
In a circle, perpendicular bisector of a chord passes through the center of a circle
That means
x/2 is the base of the right triangle of the figure
Applying the Pythagorean Theorem in the right triangle
[tex]12^2=6^2+(\frac{x}{2})^2[/tex]
Solve for x
[tex]144=36+\frac{x^2}{4}\\\\\frac{x^2}{4}=144-36\\\\\frac{x^2}{4}=108\\\\x^2=432\\\\x=20.8\ units[/tex]
The sum of the first 46 postive and odd numbers is
The sum of first 46 positive and odd numbers is 2116
Solution:
Given that we have to find the sum of first 46 positive and odd numbers
The sum of first "n" natural odd numbers which are positive is given as:
[tex]Sum = n^2[/tex]
Here, n = 46
Therefore,
sum of first 46 positive and odd numbers = [tex]46^2[/tex]
sum of first 46 positive and odd numbers = [tex]46 \times 46 = 2116[/tex]
Thus the sum of first 46 positive and odd numbers is 2116
There are 6 buses going on a field trip. There are 30 students on each bus. When they get to the park 42 students when to the slides. 28 students went to the swings. 39 students went to the grassy area to eat lunch. How many students are left?
Answer:
There are 71 students that are left
Step-by-step explanation:
Let's calculate the number of students left this way:
Total students = 30 * 6 = 180
Students that went to the the slides = 42
Students that went to the the swings = 28
Students that went to the the swings = 39
Students left = Total students - Students that went to the the slides - Students that went to the the swings - Students that went to the the swings
Replacing with the real values, we have:
Students left = 180 - 42 - 28 - 39
Students left = 180 - 109
Students left = 71