Answer:
[tex]\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}[/tex]
Step-by-step explanation:
When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?
[tex]f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}[/tex]
Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’. What are the coordinates of the vertices of triangle A’B’C’?
A
A’ (1, 4), B’ (4, 1), C’ (1, 1)
B
A’ (-3, 4), B’ (0, 1), C’ (-3, 1)
C
A’ (-1, -4), B’ (-4, -1), C’ (-1, -1)
D
A’ (-5, -4), B’ (-8, -1), C’ (-5, -1)
Given:
Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.
To find:
The coordinates of the vertices of triangle A’B’C’.
Solution:
If triangle ABC reflected across y-axis, then
[tex](x,y)\to (-x,y)[/tex]
[tex]A(-1,4)\to A_1(1,4)[/tex]
[tex]B(-4,1)\to B_1(4,1)[/tex]
[tex]C(-1,1)\to C_1(1,1)[/tex]
Coordinates of image after reflection across y-axis are [tex]A_1(1,4),B_1(4,1),C_1(1,1).[/tex]
Then triangle translated 4 units to the left to form triangle A’B’C’.
[tex](x,y)\to (x-4,y)[/tex]
[tex]A_1(1,4)\to A'(-3,4)[/tex]
[tex]B_1(4,1)\to B'(0,1)[/tex]
[tex]C_1(1,1)\to C'(-3,1)[/tex]
Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).
Hence, the correct option is B.
Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of
1.2 gallons per minute,
Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of
0.8 gallon per minute.
After how many minutes will both aquariums contain the same amount of water?
Answer:
The Answer is B
Step-by-step explanation:
HDHSJSJSDVSV HELP ME
Answer:
let me see the drop box options !! it helps alot!
What is the slope of the line that passes through the points (-9, 2) and (1, 27)?
Answer:
The answer is
[tex] \huge \frac{5}{2} \\ [/tex]
Step-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]
From the question the points are
(-9, 2) and (1, 27)
We have
[tex]m = \frac{27 - 2}{1 - - 9} = \frac{25}{1 + 9} = \frac{25}{10} = \frac{5}{2} \\ [/tex]
We have the final answer as
[tex] \frac{5}{2} \\ [/tex]
Hope this helps you
The points D, E, F and G all lie on the same line segment, in that order, such that the ratio of DE:EF:FGDE:EF:FG is equal to 6:5:1.6:5:1. If DG=36,DG=36, find DF.DF.
Answer:
i
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
1 1/2 x 3/4 pls full aswer
Answer:
1.125 or 9/8
Step-by-step explanation:
guys can u help me put the answers with the graphs i will give 20 points
Answer:
a
f
L
v
o
r
t
e
Step-by-step explanation:
Answer:
Check explanation.
Step-by-step explanation:
y > 3x - 4 = F
y < - 1/2x + 9 = L
y > 3x + 2 = U
y > 5 = R
y < - 2/3x = I
y > 1/3x + 3 = T
These are all the ones I can find, call me back if you still need help.
please help thank you so much
Answer:
no solution
Step-by-step explanation:
A store plans to sell two different game consoles, the YuuMi and the ZBox. The store’s wholesale cost for a YuuMi is $250, and the store can sell one for $295. The ZBox’s wholesale price is $400, and the store can sell it for $450. The store’s marketing research indicates that the total monthly demand for game consoles will not exceed 250 units sold. The store’s financial manager does not want to invest more than $70,000 in inventory costs for game consoles. How many of each game console should the store stock in order to maximize their profits, and what is their maximum monthly profit?
Constraints:
Objective formula:
9514 1404 393
Answer:
Constraints: x + y ≤ 250; 250x +400y ≤ 70000; x ≥ 0; y ≥ 0Objective formula: p = 45x +50y200 YuuMi and 50 ZBox should be stockedmaximum profit is $11,500Step-by-step explanation:
Let x and y represent the numbers of YuuMi and ZBox consoles, respectively. The inventory cost must be at most 70,000, so that constraint is ...
250x +400y ≤ 70000
The number sold will be at most 250 units, so that constraint is ...
x + y ≤ 250
Additionally, we require x ≥ 0 and y ≥ 0.
__
A profit of 295-250 = 45 is made on each YuuMi, and a profit of 450-400 = 50 is made on each ZBox. So, if we want to maximize profit, our objective function is ...
profit = 45x +50y
__
A graph is shown in the attachment. The vertex of the feasible region that maximizes profit is (x, y) = (200, 50).
200 YuuMi and 50 ZBox consoles should be stocked to maximize profit. The maximum monthly profit is $11,500.
A solid right pyramid has a square base. The base
edge length is 2 cm longer than the height of the
pyramid.
If the height is 6 cm, what is the volume of the
pyramid?
20 m3
Answer:
128 cm^3
Step-by-step explanation:
Waters added or drain from a tank each day the first day 13/10 of a gallon is added to the empty tank the second day 11/10 of a gallon is drained from the tank the third day 12/10 of a gallon is added to the tank the fourth day 1 gallon is drained from the tank the amount of water in the tank after 15 days is given by
Answer:
2 gallons
Step-by-step explanation:
You have to find the pattern of adding and draining water for 15 days. To get there you need to subtract 2 and add 1 but keep the negative/positives the same i.e. (this is for the 10ths of gallons)
13-2=11
11+1=10
keeping the pattern for 15 days:
+13, 11,+12,-10,+11,-9,+10,-8,+9,-7,+8,-6,+7,-5,+6 = 20 (10ths of gallons)
20/10 = 2
Select the best answer for the question.
9. What is 36:39 in simplest form?
O A. 36:39
O B. 13:12
O C. 1.3
O D. 12:13
Answer:
d
Step-by-step explanation:
12*3=36 and 13*3=39
Please help as soon as u see this!
Answer:
c, or 8
Step-by-step explanation:
Answer:
D
It would be either C or D because anything greater than 5, you move the next number up 1 digit.
Step-by-step explanation:
Which angles are corresponding angles?
Picture in the question, please help on test that’s due soon!
Answer:
8 and 16
Step-by-step explanation:
Answer:
I have 8 and 16
How do you do this question?
Step-by-step explanation:
ln(n) is smaller than n for all n ≥ 1.
Therefore, ln(n) / n⁴ is smaller than n / n⁴ = 1 / n³.
1 / n³ converges (p series test). Therefore, the smaller function ln(n) / n⁴ also converges.
me pueden explicar las sumas y restas con punto decimal por favor
Answer:
Para sumar o restar decimales se colocan los números decimales uno debajo del otro, haciendo que coincidan las unidades en la misma columna. De esta manera, también tienen que coincidir las décimas, las centésimas… y la coma.
Step-by-step explanation:
At a farmer’s market, a basket of strawberries costs $20 and a basket of peaches costs $18. On Saturday, 23 baskets were sold and $430 collected. If x represents the number of baskets of strawberries and y represents the number of baskets of peaches, how many baskets of peaches were sold on Saturday?
Answer:
The number of basket of strawberries are 8 and number of basket of peaches are 15.
Step-by-step explanation:
As given
x = represents baskets of strawberries .
y = represents baskets of peaches .
As given
At a farmer’s market, a basket of strawberries costs $20 and a basket of peaches costs $18.
On Saturday, $430 worth of strawberries and peaches were sold, and a total of 23 baskets were sold.
Than the equations becomes
x + y = 23
20x + 18y = 430
Multiply x + y = 23 by 20 and subtracted from 20x + 18y = 430.
20x - 20x + 18y - 20y = 430 - 460
-2y = -30
2y = 30
y = 15
Put y = 15 in the equation x + y = 23
x + 15 = 23
x = 23 - 15
x = 8
Therefore the number of basket of strawberries are 8 and number of basket of peaches are 15.
Answer:
D 15 baskets of peaches
Step-by-step explanation:
took the test
Translate the algebraic expression into a verbal (word) phrase: 2(x + 5)
Answer:
a number plus five times two
Step-by-step explanation:
a number plus five times two
Explaining a Rule for Dividing Fractions
Explain the steps you would take to find the quotient of
1
3
÷ 4
3
Answer:
One rule for dividing fractions is the rule where instead of doing 13/43, you can do 13 times 1/43.
Step-by-step explanation:
Yeah
Answer:
1/4
Step-by-step explanation:
Sample response: First, rewrite the problem as a multiplication problem. Multiply 1/3 by the reciprocal of 4/3, which is 3/4. Then multiply to get 3/12. Simplifying gives the answer of 1/4.
What is the solution to 2x -8 > 12?
Answer:
x>10
Step-by-step explanation:
2x - 8 >12
2x>12 +8
2x >20
x >20 :2
x>10
order the numbers from least to greatest please help
Answer:
-2,-7/4, 1/2, square root of 5, 2.4
Step-by-step explanation:
Answer:
-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4
Step-by-step explanation:
1/2
-2
√5≈2.24
-1.75
2.4
-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4
Estimate. Then find the difference. 476-269
Answer: 207
Step-by-step explanation:
Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.
Step 1: Use the algorithm method.
Step 2: Therefore, 476 − 269 = 207.
207
~I hope I helped you! :)~
original amount : 30, new amount : 45 what is the percent change
Answer:
50%
Step-by-step explanation:
Percent change = {(New-Old)/(Old)}*100%
So,
{(45-30)/(40)}*100
=(15/30)*100
=50%
Replace "?" with ">", "<", or "=' to make the sentence true:
13+7?11
Describe the steps that you need to follow to reach the correct answer
___________________________________
Write an equality to represent the following statement:
"A number is greater than 4"
Describe the steps that you need to follow to reach the answer.
Answer:
[tex]>[/tex]
Step-by-step explanation:
[tex]13 + 7 = 20[/tex]
[tex]20 > 11[/tex]
I know this because if 13 + 7 is 20, thats bigger than 11.
Ex of greater than 4:
10 > 4
-BBBM
Answer:
Step-by-step explanation:
The first one is going to be a less than symbol and the steps you would need to take is add 13 and 7. the second problem, you could do 5=4 and your answer would be greater than four. The steps you would take is 5=4 which is 9 and 9 is greater than 4
A store owner paid $15 for a book. She marked up the price of the book by 20% to determine its selling price. What is the selling price, in dollars, of the
books?
Answer:
18
Step-by-step explanation:
.2x15=3
3+15=18
Answer:
18$
Step-by-step explanation:
I need help ASAP !
Please fast ! What mathematical term do we use for the first part of proof ?
Answer:
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference.
Its got to be in there.
A car travels at an average speed of 48 miles per hour. How long does it take to travel 180 miles?
Answer:
Step-by-step explanation:
It will take 3hr and 36 min to travel 180 miles
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]s = \frac{distance \: traveled}{time \: of \: the \: distance \: traveled} \\ [/tex]
[tex]48 = \frac{180}{t} \\ [/tex]
Multiply sides by t
[tex]48 \times t = \frac{180}{t} \times t \\ [/tex]
[tex]48t = 180[/tex]
Divided sides by 48
[tex] \frac{48}{48} t = \frac{180}{48} \\ [/tex]
[tex]t = \frac{4 \times 9 \times 5}{4 \times 3 \times 4} \\ [/tex]
[tex]t = \frac{3 \times 5}{4} \\ [/tex]
[tex]t = \frac{15}{4} \\ [/tex]
[tex]t = \frac{16 - 1}{4} \\ [/tex]
[tex]t = \frac{16}{4} - \frac{1}{4} \\ [/tex]
[tex]t = 4 - 0.25[/tex]
[tex]t = 3.75 \: \: \: \: hours[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
angle 1 and angle 4 are blank angles
Answer:
C. vertical angles
Step-by-step explanation:
A trail mix recipe includes granola, oats, and almonds. How many Calories are in 2 cups of trail mix?
Answer:
1,080 calories
Step-by-step explanation:
You can also use the method of direct proportion:
cups
calories
=
0.25
135
=
2
x
←
cross-multiply
0.25
x
=
135
×
2
x
=
135
×
2
0.25
x
=
1080
calories
Answer:
1,080 calories.
Step-by-step explanation:
135/1 ÷ 1/4
135/1 · 4/1
= 540/1 cup
540 calories · 2 = 1,080 calories
=1,080 calories in 2 cups of trail mix
What is The geometric series 24_8+8/3_8/9+8/27_8/81 usn siga notaton
Answer:
17
Step-by-step explanation:
Use BODMAS Method
B - Brackets
O - Power
D - Division
M - Multiplication
A - Addition
S - Subtraction
24 - 8 + 8/3 - 8/9 + 8/27 - 8/81
First division
8/3 = 2.66666666667
8/9 = 0.88888888888
8/27 = 0.29629629629
8/81 = 0.09876543209
Then Subtract
24 - 8 = 15
2.66666666667 - 0.88888888888 = 1.77777777779
0.29629629629 - 0.09876543209 = 0.1975308642
Then lastly add
15 + 1.77777777779 + 0.1975308642 = 16.975308642
In these type of questions, the answer have decimals, so we have to round it to near whole number.
So nearest whole number is 17
Answer = 17
Hope you understand
:-)