There were 980 student desks originally before the purchase was made.
Step-by-step explanation:
Total desks purchased = 295
As 50 new desks are for teachers, therefore, we will subtract this amount from total;
Desks purchased for students = 295-50 = 245
Let,
x be the number of original student desks, therefore,
[tex]\frac{1}{4}\ of\ x=245\\\frac{x}{4}=245[/tex]
Multiplying both sides by 4
[tex]4*\frac{x}{4}=245*4\\x=980[/tex]
There were 980 student desks originally before the purchase was made.
Keywords: subtraction, fractions
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4 meals cost $23.00. You have a coupon for a 10% discount. How much will you pay per meal? HELLLLLPP
Answer:
$5175 per meal
Step-by-step explanation:
10% of $23.00 is $2.30, now you subtract $2.30 from $23.00 which makes $20.70. Now your getting four meals, so you split the money four ways which would be $20.70/4 which would equal $5.175 per meal
Evaluate each expression for g = -7 and h = 3 and match it to its value.
1. -4 g + h
2. 10 g - h
3. -10 h - g
4. -21 gh
5. 2 g + h2
6. 46 g2 - h
So you got to match the ones on the left to the right
The given expressions are solved and matched
Solution:To match the given expressions we need to solve the expressions with the given values of g and h and find their value.
Given that g = -7 and h = 3
[tex]\begin{array}{l}{\text { 1) } g+h=-7+3=-4} \\\\ {\text { 2) } g-h=-7-3=-10} \\\\ {\text { 3) } h-g=3+7=10} \\\\ {\text { 4) } g h=-7 \times 3=-21} \\\\ {\text { 5) } g+h^{2}=-7+3^{2}=-7+9=2} \\\\ {\text { 6) } g^{2}-h=(-7)^{2}-3=49-3=46}\end{array}[/tex]
The expressions are evaluated by substituting g = -7 and h = 3 into each one. After calculation, the matching values are found for each expression.
Explanation:To evaluate each expression for g = -7 and h = 3, we'll substitute these values into the equations and perform the operations step by step.
-4g + h : -4(-7) + 3 = 28 + 3 = 3110g - h : 10(-7) - 3 = -70 - 3 = -73-10h - g : -10(3) - (-7) = -30 + 7 = -23-21gh : -21(-7)(3) = -21 * 21 = -4412g + h^2 : 2(-7) + 3^2 = -14 + 9 = -546g^2 - h : 46(-7)^2 - 3 = 46 * 49 - 3 = 2254 - 3 = 2251Then, you can match each expression to its corresponding value that has been calculated:
Expression 1 matches with 31Expression 2 matches with -73Expression 3 matches with -23Expression 4 matches with -441Expression 5 matches with -5Expression 6 matches with 2251A ball is thrown directly upward from a height of 7 feet with an initial velocity of 50 ft./s use the quadratic formula to find the number of seconds it takes the ball to hit the ground
Answer:
The time taken by ball to hit the ground is 5.10 seconds .
Step-by-step explanation:
Given as :
The height cover by ball to move upward = 7 feet
The initial velocity = u = 50 feet per sec
Let the time taken by ball to hit the ground = t sec
Let the deacceleration rate = - 9.8 m/s²
The final velocity of the ball = v= 0 at the top
So, From equation
v = u + at
I.e v = u + a × t
Or, 0 = 50 + ( - 9.8) × t
Or, 9.8 t = 50
∴ t = [tex]\frac{50}{9.8}[/tex]
I.e t = 5.10 seconds
So, time taken = 5.10 sec
Hence The time taken by ball to hit the ground is 5.10 seconds . Answer
Which of the following expressions is equivalent to the one above? 42x + 21.
Please help ASAP
Answer:
21(2x+1)
Step-by-step explanation:
42x+21=21(2x+1)
Kelsey is writing a thank-you note to a friend. She has 9 kinds of cards and 7 kinds of envelopes that fit the cards. She has 3 designs of first-class stamps, although she only needs to use one. Finally, Kelsey has to pick a color of pen with which to write the note, and she has 2 to choose from. How many different ways can the thank-you note look?
Answer:
378
Step-by-step explanation:
Work 1:She has 9 kinds of cards out of which she has to chose only 1.
The number of ways of doing this is 9 (she can pick any one of them).
Work 2:She has 7 kinds of cards out of which she has to chose only 1.
The number of ways of doing this is 7 (she can pick any one of them).
Work 3:She has 3 designs of first-class stamps out of which she has to chose only 1.
The number of ways of doing this is 3 (she can pick any one of them).
Work 4:She has to pick the color of pen and she has 2 to choose from.
The number of ways of doing this is 2 (she can choose any one of them).
She has to do Work 1 and Work 2 and Work 3 and Work 4.
∴By the fundamental counting principle, the total number of different ways in which the thank-you note can look is 9×7×3×2 = 378
A restaurant sells tea for $1.50 plus $0.05 per refill a gas station store sells tea for $0.50 plus $0.50 per refill?
Answer:
Part a) [tex]y=0.05x+1.50[/tex]
Part b) [tex]y=0.50x+0.50[/tex]
Part c) The graph in the attached figure
Part d) see the explanation
Step-by-step explanation:
The complete question is
A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.
Part a) Write a linear function for the price of tea at restaurant
Part b) Write a linear function for the price of tea at gas station store
Part c) Graph both equations
Part c) Compare the lines in terms of slope and y-intercept
Let
y -----> the price of tea in dollars
x -----> the number of refills
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value (value of y when the value o x is equal to zero)
Part a)
At restaurant
we have that
The slope or unit rate is equal to
[tex]m=\$0.05\ per\ refill[/tex]
The initial value or y-intercept is equal to
[tex]b=\$1.50[/tex]
substitute
[tex]y=0.05x+1.50[/tex]
Part b)
At gas station store
we have that
The slope or unit rate is equal to
[tex]m=\$0.50\ per\ refill[/tex]
The initial value or y-intercept is equal to
[tex]b=\$0.50[/tex]
substitute
[tex]y=0.50x+0.50[/tex]
Part c) Graph both equations
we know that
The easiest way to graph a line is with two points
Find the intercepts of the line
At restaurant
[tex]y=0.05x+1.50[/tex]
The y-intercept is the point (0,1.50)
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=0.05x+1.50[/tex]
[tex]x=-30[/tex]
The x-intercept is the point (-30,0)
Plot the points and join to graph the line
see the attached figure
At gas station store
[tex]y=0.50x+0.50[/tex]
The y-intercept is the point (0,0.50)
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=0.50x+0.50[/tex]
[tex]x=-1[/tex]
The x-intercept is the point (-1,0)
Plot the points and join to graph the line
see the attached figure
Part c) Compare the lines in terms of slope and y-intercept
The slope or unit rate at the restaurant is less than the slope at the gas station store
[tex]\$0.05\ per\ refill < \$0.50\ per\ refill[/tex]
The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store
[tex]\$1.50 > \$0.50[/tex]
what is c
5c+16.5=13.5+10
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
c = 7/5
Decimal Form:
c = 1.4
Mixed Number Form:
c = 1/2/5
Edit: I answered this on Jan 7th, 2021.
Please help!!!!!!!!!!!!
Turn percentage into a decimal.
3% = 0.03
Multiply.
40,400 * 0.03 = 1,212
Subtract.
40,400 - 1,212 = $39,188
_______
Alice earned $39,188 last year.
_______
Best Regards,
Wolfyy :)
Answer:
The correct answer is 39,188.
Step-by-step explanation:
Alice Swanson's current earnings for this year are 40,400. Her earnings were 3% less than this last year. To find her earnings for last year, we will use the "Percent • Whole = Part" formula. But first, we must put 3% into a decimal form: 3 ÷ 100 = 0.03. Now let's solve:
40,400 • 0.03 = 1,212
1,212 is 3% of 40,400. To find Alice's earnings for last year, we will subtract her raise from her current earnings:
40,400 - 1,212 = 39,188
Hope this helps,
♥A.W.E.S.W.A.N.♥
60% of the work is done in 17 minutes, 40% of the same work, when is done (in minutes)?
Answer:
It would be 11.333 minutes
Step-by-step explanation:
I solved this by setting up a cross multiplication.
60%/17 so then 40/x.
Then here cross multiplying. 60x=680. divide by 60 and x would = 11.33
Danielle owes $47.25 for text messaging in the month of June. If her text messaging plan costs $6 for the first 600 messages and 25¢ for each additional text message.
how many text messages did she send that month?
Answer:
1002
Step-by-step explanation:
Answer:
165 additional messages
Step-by-step explanation:
$47.25 - $6.00 for 600 messages and 0.25/each additional message= $47.25-$6.00=41.25/0.25 per message =165 additional messages for a total of 765
Your school is located at (2, -1), which is 2 blocks east and
1 block south of the center of town. To get from your house to the school,
you walk 5 blocks west and 2 blocks north.
Let's begin by understanding your initial position, which is the school, located at coordinates (2, -1). The school is 2 blocks east and 1 block south of the center of town. This means that if you were to go to the center of town, you would travel 2 blocks west and 1 block north from the school. Now, to find out where your house is in relation to the school, we can reverse the steps you take to get from your house to the school. You’ve said you walk 5 blocks west and 2 blocks north to reach the school. Since you walk west to reach school, your house must be to the east of the school. Similarly, since you walk north to reach school, your house must be to the south of the school. To get back to your house from the school, then, you'd need to reverse both of these movements. To find the house’s position, we start with the school's position at (2, -1): 1. Since you walk 5 blocks west to get to school, let's go 5 blocks east from the school to get back to your house. Moving east means increasing the x-coordinate. So, starting from the x-coordinate of the school, which is 2, we add 5 to find the x-coordinate of your house. This gives us 2 + (-5) = -3. 2. Next, since you walk 2 blocks north to get to school, let's go 2 blocks south from the school to reach your house. Moving south means decreasing the y-coordinate. So, starting from the y-coordinate of the school, which is -1, we subtract 2 to find the y-coordinate of your house. This gives us -1 + 2 = 1. Therefore, the coordinates of your house are (-3, 1), which means your house is 3 blocks west and 1 block north of the center of town.
Final answer:
To locate the student's house on a grid, you need to reverse the movements made from the school to the house. By subtracting 5 blocks west and adding 2 blocks north from the school's coordinates (2, -1), the house's coordinates are determined to be (-3, 1).
Explanation:
The question involves a two-dimensional path on a grid, similar to the coordinates and movements given in the examples provided. To solve the problem, imagine that you start at the center of town, move 2 blocks east and 1 block south to reach the school at (2, -1), and then move from your house to the school by walking 5 blocks west and 2 blocks north.
To find your house's coordinates, you need to reverse the movements. Starting from the school's location at (2, -1), moving 5 blocks west means subtracting 5 from the x-coordinate, and moving 2 blocks north means adding 2 to the y-coordinate. Thus, the coordinates of your house would be (2 - 5, -1 + 2) which simplifies to (-3, 1).
Calculate 30days monthly dose for each prescription.
1. Order: Alprazolam 2 mg take 1 tab by mouth twice a day for 30days. How many total tablets will the patient take for 1 month (30days)
Give:
2. Order: Tramadol Hychloride 10mg take 1 tab by mouth 4 times a day before meal for 30days. How many total tablets will the patient take for 30days?
Give:
1. 60 tablets
2. 120 tablets
Step-by-step explanation:
1. Order: Alprazolam 2 mg take 1 tab by mouth twice a day for 30days. How many total tablets will the patient take for 1 month (30days)
As the patient has to take 1 tablet twice a day, that will be 2 tablets per day so the total number of tablets will be:
[tex]30*2 = 60\ tablets[/tex]
And
60*2 = 120 mg
2. Order: Tramadol Hychloride 10mg take 1 tab by mouth 4 times a day before meal for 30days. How many total tablets will the patient take for 30days?
As the patient has to take 4 tablets each day, that means the total tablets for one month or 30 days will be:
[tex]30* 4 = 120\ tablets[/tex]
And
120*10 = 1200 mg
Hence,
1. 60 tablets
2. 120 tablets
Keywords: Multiplication,
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A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. Find each temperature. Show your work.
If it continues to fall at this rate, what will the temperature be:
in 2 hours? _______ in 5 hours? _______ in half an hour? _______
Answer:
in 2hrs = -6°C
in 5hrs = -15°C
in half an hr = -1.5°C
Step-by-step explanation:
in an hr, the temperature falls by 3°C = 0 -3 = -3°C
in 2hrs = 2*-3°C = -6°C
in 5hrs = 5*-3°C = -15°C
in half an hr = 0.5 * -3°C = -1.5°C
The required continues to fall at this rate of the temperature in 2 hours -6°C ,5hours in -15°C and in half an hour -1.5°C.
Given that,
A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour.
We have to find,
If it continues to fall at this rate, what will the temperature be in 2 hours 5 hours and in half an hour.
According to the question,
A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour.
In an hour the temperature falls by 3°C = 0 - 3 = -3°C
The temperature fall in 2hrs = (2)(-3°C) = -6°C
The temperature fall in 5hrs = (5)(-3°C) = -15°C
The temperature fall in half an hour = (0.5)(-3°C) = -1.5°C
Hence, The required continues to fall at this rate of the temperature in 2 hours -6°C ,5hours in -15°C and in half an hour -1.5°C.
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Which set of rational numbers is arranged from least to greatest? 1 over 5, −1.4, negative 1 over 2, 3 3, negative 1 over 2, −1.4, 1 over 5 3, 1 over 5, −1.4, negative 1 over 2 −1.4, negative 1 over 2, 1 over 5, 3
Answer:
Option 4 - [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]
Step-by-step explanation:
To find : Which set of rational numbers is arranged from least to greatest?
Solution :
The set of rational numbers are
[tex]3,\ \frac{1}{5},\ -1.4,\ -\frac{1}{2}[/tex]
Writing all number in one form,
[tex]\frac{1}{5}=0.2[/tex]
[tex]-\frac{1}{2}=-0.5[/tex]
Now, -1.4<-0.5<0.2<3
From least to greatest the set of natural numbers are
[tex]-1.4<\ -\frac{1}{2}<\frac{1}{5}<\ 3[/tex]
So, [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]
Therefore, option 4 is correct.
Answer:
Option 4
Step-by-step explanation:
(2x + 1 ) (x - 3 ) = 2x² - 5x -3
Is it correct ? please I need all the way that allows us to have this answer
Answer:
It is.
Step-by-step explanation:
1. Multiply 2x *x and 2x* -3 ;
2. Multiply 1*x and 1*(-3) ;
You should get: 2x^2 -6x +x -3 = 2x^2 -5x -3;
3. Add -6x +x;
In the end you get : 2x^2 -5x -3=2x^2 -5x -3
Answer:
YES. It is correct.Step-by-step explanation:
Use FOIL:
(a + b)(c + d) = ac + ad+ bc+ bd
(2x + 1)(x - 3)
= (2x)(x) + (2x)(-3) + (1)(x) + (1)(-3)
= 2x² - 6x + x - 3 combine like terms
= 2x² + (-6x + x) - 3
= 2x² - 5x - 3
2x+4=8 what would the equation be and what does x equal
Answer:
x=2
Step-by-step explanation:
2x+4=8
2x=8-4
2x=4
x=4/2
x=2
Answer:
x = 2
Step-by-step explanation:
The equation shown is a perfectly good equation.
___
Look at what is being done to the variable. It is multiplied by 2, and 4 is added to the product.
To find the value of the variable, we reverse these operations, in reverse order. We undo the addition by adding the opposite of 4 (to both sides of the equation).
2x +4 -4 = 8 -4
2x = 4 . . . . . simplify
We undo the multiplication by multiplying by the inverse value, 1/2 (to both sides of the equation).
(1/2)(2x) = (1/2)(4)
x = 2 . . . . . simplify
_____
The rules of equations are pretty simple: whatever you do to one side, you must also do to the other side.
_____
Comment on this equation
You may notice that all of the numbers in this equation are divisible by 2. Another way to solve it is to start by dividing (both sides!) by 2:
x + 2 = 4
Now, you have a 2nd-grade problem in addition facts: what added to 2 gives 4? Since you know your addition facts, you know the answer is 2. In algebra, we solve this by subtracting 2 (from both sides!).
x = 2
A triangular courtyard has a perimeter of 120 meters. The lengths of two sides are 30 meters and 50 meters. How long is the third side?
Answer:
the third side is 40 m long
Step-by-step explanation:
The perimeter of the triangle is the sum of its three sides, and they give you what that value in meters is (120 m)
Your are given the length of two of them: 30 m and 50 m, and need to find the third one (let's call it "x" for this unknown side)
Now set the following equation:
Perimeter = side 1 + side 2 + side 3 --> replace these with the info you know
120 m = 30 m + 50 m + x --> add 30 m and 50 m obtaining 80 m
120 m = 80 m + x --> now solve for x (isolate the x on one side) by subtracting 80 m from both sides
120 m - 80 m = x --> perform the subtraction 120 m - 80 m = 40 m
40 m = x
Which tells us that the third unknown side has a length of 40 m
Answer:
The third side is 40 meters long
Step-by-step explanation:
From the question, we were told that a triangular courtyard has a perimeter of 120 meters, we are to find the length of the third side if the other two sides are 30 and 50 meters.
First, we need to know that perimeter is the distance around a polygon.
Let the third side = side c, let the two sides be side A and side B
Perimeter = side A + side B + side c
side A = 30 meters
side B = 50 meters
side C = ?
Perimeter = 120 meters
We can now proceed to insert the values in the equation above
Perimeter = side A + side B + side c
120 = 30 + 50 + side c
120 = 80 + side c
Subtract 80 from both-side of the equation
120 - 80 = 80 - 80 + side c
40 = side c
side c = 40 meters
Therefore, the third side is 40 meters long
30 POINTS!!! Calculate the percent increase or decrease between the starting and ending quantities below. Round your answer to one decimal place.
1) Start: 3 End: 10
2) Start: 9 End: 20
3) Start: 100 End: 85
1) There is 233.33% increase in the quantity.
2) There is 122.22% increase in the quantity.
3) There is 15% decrease in the quantity.
Step-by-step explanation:
1) Start: 3 End: 10
Change = End - Start
Change = [tex]10-3=7[/tex]
As the change is positive, therefore, it shows an increase
Percent increase = [tex]\frac{Change}{Start}*100[/tex]
Percent increase = [tex]\frac{7}{3}*100 = 233.33\%[/tex]
There is 233.33% increase in the quantity.
2) Start: 9 End: 20
Change = [tex]20-9=11[/tex]
As the change is positive, it shows an increase.
Percent increase = [tex]\frac{Change}{Start}*100[/tex]
Percent increase = [tex]\frac{11}{9}*100 = 122.22\%[/tex]
There is 122.22% increase in the quantity.
3) Start: 100 End: 85
Change = 85-100 = -15
Negative sign shows that it is a decrease in quantity.
Percent decrease = [tex]\frac{Change}{Start}*100[/tex]
Percent decrease = [tex]\frac{15}{100}*100 = 15\%[/tex]
There is 15% decrease in the quantity.
Keywords: Percentage, increase
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Answer:
1. 233.333%
2.122.2%
3.-12%
Step-by-step explanation: Hopes this helps you :)
7l+5.5d=6.75
L+d=4.5
Solve for l and d
Answer:
The solution of the given system is given as L = -12, d =16.5
Step-by-step explanation:
7 L+ 5.5 d = 6.75
L + d = 4.5
From (2), we get:
L + d = 4.5
⇒ d = 4.5 - L
Substitute the above value of d is the above first equation:
7 L+ 5.5 d = 6.75 ⇒ 7 L+ 5.5 (4.5 - L) = 6.75
⇒ 7 L + 24.75 - 5.5 L = 6.75
or, 1.5 L = 6.75 - 24.75 = -18
or, L = -18/1.5 = 12
or, L = -12
Now, d = 4.5 - L = 4.5 - (-12) = 16.5
or, d = 16.5
Hence, the solution of the given system is given as L = -12, d =16.5
Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. The number of cells in successive rings forms an arithmetic sequence..
A-Write a rule for the number of cells in the
ring.
b. How many cells are in the honeycomb after the ninth ring is formed?
Answer:
Part B is 271!!!
Step-by-step explanation:
a9=54
S9=9/2(6+54)=270
270+1
=271
By plugging in the ring number, 9, in the equation for the number of
cells in a ring, gives 54.
Response:
A. The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6
B. The number of cells in the ninth ring are 54 cells
How can the number of cells be expressed as an arithmetic sequence?Given;
The type of sequence = Arithmetic sequence
From the possible drawing of the question obtained from a similar question, we have;
Number of cells in the first ring that goes around the first cell = 6
Number of cells that go around the second ring = 12
A. The common difference of the arithmetic sequence = 12 - 6 = 6
We have that the nth term of an arithmetic sequence is; aₙ = a + (n - 1)·d
Taking the first ring as the first term, we have;
a = 6
Which gives;
The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6
Where;
n = The ring number
B. In the ninth ring, we have;
a₉ = 6 + (9 - 1) × 6 = 54
The number of cells in the ninth ring, a₉ = 6 + (9 - 1) × 6 = 54Learn more about arithmetic sequence here:
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Deena drove 585 miles in nine hours Kristen drove 605 miles in 11 hours who drove at A faster rate
The solution involves calculating the average speed for each driver (distance travelled divided by time). Deena's average speed was 65 mph and Kristen's was 55 mph, therefore, Deena drove at a faster rate.
Explanation:To solve this question, we need to compute each driver's average speed. Average speed is calculated by dividing the total distance traveled by the total time taken to cover that distance. Mathematically, average speed = total distance/total time.
For Deena, we calculate her average speed by dividing her total distance traveled (585 miles) by the time she took to cover this distance (9 hours). Doing the division, we find Deena's average speed to be about 65 mph.
Similarly, for Kristen, we divide her total distance traveled (605 miles) by the time she took to cover this distance (11 hours). Kristen's average speed comes out to be approximately 55 mph.
By comparing the average speeds, we find Deena drove at a faster rate than Kristen.
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2. Which of the following (a,b) pairs is
ollowing (a,b) pairs is the solution
the system of equations 2a + b = 3 and
a - 3b = 5?
F. (-2, 7)
G. (0, 3)
J. (2,-1)
K. (3,-3)
The pair (2, -1) is the solution the system of equations.
The given system equations are 2a+b = 3 and a - 3b = 5.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here,
2a+b = 3 --------(1) and a - 3b = 5 --------(2)
Multiply equation (1) by 3
6a+3b=9 --------(3)
Add equation (2) and (3), we get
a - 3b+6a+3b = 5+9
⇒ 7a = 14
⇒ a = 2
Put a=2 in the equation (1), that is
2(2)+b=3
⇒ b=-1
Therefore, the pair (2, -1) is the solution the system of equations.
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Final answer:
The correct pair (a,b) that solves the given system of equations 2a + b = 3 and a - 3b = 5 is (2, -1), which is option J.
Explanation:
To find which pair (a,b) is the solution to the system of equations 2a + b = 3 and a - 3b = 5, we can use substitution or elimination. Here's a step-by-step explanation using the elimination method:
Multiply the second equation by 2 to align the coefficients of a: 2(a - 3b) = 2(5) gives us 2a - 6b = 10.Add this new equation to the first equation: (2a + b) + (2a - 6b) = 3 + 10, simplifying to 4a - 5b = 13.Now we solve this new equation for a: a = (13 + 5b) / 4.Substitute this expression for a in one of the original equations: 2((13 + 5b) / 4) + b = 3.Simplify and solve for b: (13 + 5b)/2 + b = 3, which gives b = -1.Now that we have b, we can find a: 2a - 1 = 3 which gives a = 2.Therefore, the correct solution to the system of equations is (2, -1), which corresponds to option J.
Let f(x) = - 3x-1, h(x) = - X+3.
Find (f o h)(4).
To find (f o h)(4), substitute h(4) into f(x) and evaluate the expression.
Explanation:To find (f o h)(4), we need to first find h(4) and then substitute that value into f(x). Let's start by finding h(4).
h(x) = - x + 3
h(4) = -4 + 3 = -1
Now, we substitute h(4) into f(x).
f(x) = -3x - 1
f(h(4)) = f(-1) = -3(-1) - 1 = 2
Therefore, (f o h)(4) = 2.
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How many ml of 1:4 solution and how many ml of sterile water are needed to prepare 600 ml of 1:20 solution ?
Answer:
Approximately 143 mL of 1:4 solution and 457 mL of water
Step-by-step explanation:
A 1:4 solution has a concentration of 1/(1+4) = 1/5 or 20%.
Similarly, a 1:20 solution has a concentration of 1/(1+20) = 1/21 or 4.76%.
If x is the mL of 20% solution and y is the mL of water, then:
x + y = 600
1/5 x = 1/21 (600)
Solve:
x = 5/21 (600)
x ≈ 143
y ≈ 457
You need approximately 143 mL of 1:4 solution and 457 mL of water.
GETS BRAINILIST!!!A class has 6 boys and 14 girls. What is the ratio in simplest form that compares number of boys to total number of students? 6:14 6:20 3:7 3:10
Answer:
3:10
Step-by-step explanation:
1. Find the total number of students by doing
14 + 6= 20
2. Now make your ratio
6:20
3. To make it in simplest form, divide both sides by 2
6 divided by 2 is 3
20 divided by 2 is 10
4. Your answer is
3:10
Answer:
3:10
Step-by-step explanation:the answer would be 6:20, but that can be simplified by 2. 6 divided by 2 equals 3, 20 divided by 2 equals 10. 3:10
7 mm = _____ cm
0.7
7,000
700
70
Answer:
0.7
Step-by-step explanation:
7 millimiters equals 0.7 centimeters
Answer:
0.7 cm
Step-by-step explanation:
1 mm=0.1 cm
7 mm=0.1*7=0.7 cm
Find the solution(s) to 9x2 - 54x = 0. Check all that apply.
The solutions to the equation 9x^2 - 54x = 0 are x = 0 and x = 6, found by factoring and setting each factor equal to zero.
To find the solution(s) to the equation 9x2 - 54x = 0, we can start by factoring out the greatest common factor, which is 9x. This gives us:
9x(x - 6) = 0
Now, we set each factor equal to zero:
9x = 0x - 6 = 0From the first equation, we divide by 9 to isolate x:
x = 0
From the second equation, we add 6 to both sides:
x = 6
Thus, the solutions to the equation are:
x = 0x = 6The length of a rectangle is 1 units more than the width. The area of the rectangle is 56 units. What is the length, in units, of the rectangle?
Answer:
7 is width
Step-by-step explanation: i got it right
The length of the rectangle is 7 unit.
What is rectangle?A rectangle is a plane shape that has pair of opposite sides equal.
To calculate the length of the rectangle, we use the formula below
Formula:
A = LW............ Equation 1Where:
A = Area of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Assuming the width of the rectangle is y unit
A = 56 unitL = (y+1) unitW = y unitSubstitute these values into equation 1
56 = y(y+1)56 = y²+ySolving the quadratic equation,
y = +7 or y = -8Since length can not be negative,
y = 7 unit.Hence The length of the rectangle is 7 unit.
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If P(x)=6x^3=13x^2+x-2, and P(-2)=0, then the factorization of P(x) is
Answer:
Factorization of [tex]P(x)=(x+2)(2x+1)(3x-1)[/tex]
Step-by-step explanation:
Given:
The given polynomial is [tex]P(x)=6x^3+13x^2+x-2[/tex]
Also, [tex]P(-2)=0[/tex]
Since, for [tex]x=-2[/tex], [tex]P(x)[/tex] is 0, therefore, [tex]x+2[/tex] is a factor of the polynomial.
Now, let us divide the given polynomial by [tex]x+2[/tex] using long division method. Therefore,
[tex]\frac{6x^3+13x^2+x-2}{x+2}=6x^2+x-1[/tex]
The process of long division is shown below.
Now, factoring the quotient [tex]6x^2+x-1[/tex], we get
[tex]6x^2+x-1=6x^2+3x-2x-1=3x(2x+1)-1(2x+1)=(3x-1)(2x+1)[/tex]
Therefore, the factors of polynomial [tex]P(x)[/tex] are [tex](x+2),(2x+1),\ and\ (3x-1)[/tex]
Hence, the factorization of [tex]P(x)[/tex] is:
[tex]P(x)=(x+2)(2x+1)(3x-1)[/tex]
Which of these is the net of a cube?
Answer:
B
Step-by-step explanation: