Answer:
a=3
b=1
Step-by-step explanation:
3=2a-3 => a=3
b=2*2-3 = 1
A caterer is agrranging 72 ham sandwiche and 48 pimento cheese sandwiches on serving trays. He would like to arrange the sandwiches so tht each tray has the same number of each kind of sandwich. The number of ham sandwiches on a tray does not need to equal the number of pimento cheese sandwiches on the tray. What is the maximum number of traysthe caterer can use? .
Answer:
24
Step-by-step explanation:
The greatest number of trays the caterer can split the 72 ham sandwiches and 48 pimento cheese sandwiches into can be determined by calculating the highest common factor and 48 and 72
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Factors of 72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
the highest common factor is 48 ad 72 is 24
Question 1 of 10 If f(x) = 5x and g(x) = x+1, find (f.g)(x).
Answer:
D
Step-by-step explanation:
(f • g)(x)
= f(x) × g(x)
= 5x³( x + 1) ← distribute parenthesis
= 5[tex]x^{4}[/tex] + 5x³ → D
POINTS!!
Draw a diagram of the archway modeled by the equation y = -x2 + 5x + 24. Find and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis.
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25.
ratio of 55 paise is to 1 rupees
Answer:
You have to equal the unit first,
as 1 Rupee = 100 paise,
so,
55paise: 100paise,
= 11:20
I hope it hepled : )
Please help!!-- What is the measure of arc AT in the circle O below?
Answer:
97
Step-by-step explanation:
Arc AT = angle at the center 97°
Increase £16470.45 by 13.5% Give your answer rounded to 2 DP. Someone help pls
Answer: £18693.96
Step-by-step explanation:
13.5% = 0.13516470.45 + 16470.45(0.135)
= 16470.45(1 + 0.135)
= 16470.45(1.135)
≈ 18693.96
Oof, someone please help asap! I don't recall ever seeing this type of question before!
Answer:
90
Step-by-step explanation:
You are looking for the highest common factor for 270 and 360.
Factor the 2 numbers
270 = 2 * 5 * 3 * 3 * 3
360 = 2 * 2 * 2 * 3 * 3 * 5
Each of the numbers has a 5
Each of the numbers has two threes
Each of the numbers has one 2
So the answer is 2 * 3*3 * 5
Identify the ethical issue(s) in each experiment. Beginning in the 1940s, the Department of Medicine at the University of Chicago tested anti-malaria medications on inmates at the Stateville Penitentiary. Inmates readily volunteered, as their parole would be reviewed upon completion of their sentence. Inmates who participated in the study reported that they were informed of the risks involved in participating in the study, including the possibility of death.
In the 1960s, Stanley Milgram studied the willingness of subjects to obey an authority figure, even at the risk of being harmed. The subjects believed they were taking part in a study on learning. They were assigned to the role of teacher and were ordered to administer electrical shocks with increasing voltage to the learner whenever the learner made an error. The learner was an actor who remained unharmed. The subjects were not initially told that it was a study of obedience, as this might affect the outcome, and they were not prepared for possible psychological distress.
In the 1950s and 60s, Saul Krugman infected mentally disabled children enrolled at the Willowbrook State School in New York with hepatitis in order to better understand how the disease spread and how it could be combatted. Parents agreed to enroll their children in the study in exchange for admission to the school.
Full question attached
Answer:
1. Subjects were not aware of the purpose of the experiment.
2. Subjects were not aware of all potential risks.
Subjects were not aware of the purpose of the experiment.
3. Subjects were coerced into participating
Explanation:
Ethics are the moral principles and codes that guide our daily decisions and actions. Ethical issues in conducting experiments or research aim at protecting the dignity of subjects or participants in the research. Major ethical issues in conducting research include: Respect for anonymity and confidentiality, beneficence(should not harm participants), and informed consent(independently volunteers after clear comprehensive information on research).
1. Experiment violates informed consent as participants were not aware of the purpose of research.
2. Experiment violates informed consent and beneficence as participants weren't fully informed and faced the risk of being harmed.
3. Experiment violates beneficence and informed consent as participants faced the risk of being harmed and did not independently volunteer for the research.
Zachary's art club ordered a giant sub sandwich for a party. It was 6 feet long! When the sandwich arrived, Zachary cut it into 16 equal pieces.
How long was each piece?
Write your answer as a proper fraction or mixed number.
Answer:
3/8 feet long
Step-by-step explanation:
Find how long each piece was by dividing 6 by 16:
6/16
Simplify this by dividing each number by 2:
6/16
= 3/8
So, each piece was 3/8 feet long
HI I really need help with this its in the picture
Explanation:
The blue rectangle has area of 4a^2*6a^2 = 24a^4
The red rectangle has area 4a^2*9a = 36a^3
The green rectangle has area 4a^2*3 = 12a^2
The total area is 24a^4 + 36a^3 + 12a^2
What is the equation of the line graphed below?
5
-5
5
(1, -3)
-5
O A. y = 3x
B. y=-3x
c. y=-5
D. y =
-X
Answer:
C: y=-3x
Step-by-step explanation:
Rise over run: in this case you go down so -3/1=-3
express 3 as a percent of 5
Answer:
0.15
Step-by-step explanation:
first get three percent:
3/100 = 3%
then use of operation:
3% of 5;
= (3/100) * 5
Answer:
60%
Step-by-step explanation:
To change a fraction to a percentage, multiply the fraction by 100% , then
[tex]\frac{3}{5}[/tex] × 100% = [tex]\frac{3(100)}{5}[/tex] = [tex]\frac{300}{5}[/tex] = 60%
What is the slope of the line shown in the graph?
A coordinate plane is shown. Points are graphed at −3 comma 2 and −1 comma −1. The points are connected by a line.
−3 over 2
−1 over 2
3 over 2
Undefined
Find the equation of a quadratic function in general form whose graph has points: (-2, 3) (0, 3) and (-4,-5).
Try your best to show complete work & explain your strategy.
Answer:
-x²-2x+3
Step-by-step explanation:
The first thing I noticed is that the first and second point has the same y intercept despite being only 2 x coordiantes away. This must mean that the vertex's x coordiante is probably (-1,4)
Because the vertex is probably (-1,4) the graph must also be concave down because the point (-4,-5) is below it
writing this in vertex form we get
-a(x+1)²+4
Where a is some constant
solve for a by plugging in (0,3)
3= -a(0+1)²+4
3= -a+4
-1= -a
a=1
therefore the equation looks like
-(x+1)²+4
expanding this so that it's in stantard form...
-(x²+x+x+1)+4
-x²-2x+3
which is the final answer
In right ΔDEF, DF = 20, m∠ F = 90˚, EF = 17. Which of the following is true? Does option 5 apply
Answer:
Step-by-step explanation:
From the picture attached,
ΔDEF is a right triangle with two sides,
EF = 17 units
DF = 20 units
By applying Pythagoras theorem in the given triangle,
DE² = DF² + EF²
(20)² = DF² + (17)²
DF² = 400 - 289
DF = √111
Trigonometric ratios for the ∠F,
sin(F) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}F=\frac{\sqrt{111}}{20}[/tex]
[tex]\text{cosF}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}F=\frac{17}{20}[/tex]
[tex]\text{tan}F=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
[tex]\text{tan}F=\frac{\sqrt{111}}{17}[/tex]
Choose the correct option.
This graph shows a proportional relationship.
What is the constant of proportionality?
Answer:
[tex]m = \frac{3}{4}[/tex]
Step-by-step explanation:
Given
See attachment
Required
The constant of proportionality
Select two points on the graph
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (4,3)[/tex]
So, the constant of proportionality (k) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{3-0}{4-0}[/tex]
[tex]m = \frac{3}{4}[/tex]
The interior angles of a hexagon are in the ratio 1:2:3:4:5:9 Find the angles. This is an example of a concave hexagon. Write in an equation.
Answer:hope this helps.. please mark as brainliest.....
9514 1404 393
Answer:
30°, 60°, 90°, 120°, 150°, 270°
Step-by-step explanation:
Let x represent the smallest angle. Then the sum of angles of the hexagon is ...
x + 2x + 3x + 4x + 5x + 9x = 720°
24x = 720°
x = 30°
The angles are ...
30°, 60°, 90°, 120°, 150°, 270°
Numbers are formed using the digits 1, 2, 3, 4, 5, 6. If no digit may be repeated, how many two-digit
numbers can be formed
A. 15
B. 20
C. 30
D. 6
I got 20.
I may have done it wrong so maybe wait until others have answered.
WOrth 10 pts ... pls help
Someone please tell me what the cube root of x to the power of 3 is?
Answer:
x
Step-by-step explanation:
The cube root of x to the power of 3 is
( [tex]\sqrt[3]{x}[/tex] )³ = ( [tex]x^{\frac{1}{3} }[/tex] )³ = x
or
[tex]\sqrt[3]{x^3}[/tex] = x
Write the equation of the line parallel to 4y - x = -20 that passes through the point (8,3).
Answer:
y= ¼x +1
Step-by-step explanation:
Rewriting the equation into the slope-intercept form (y= mx +c, where m is the gradient and c is the y- intercept):
4y -x= -20
4y= x -20 (+x on both sides)
y= ¼x -5 (÷4 throughout)
Thus, slope of given line is ¼.
Parallel lines have the same gradient.
Gradient of line= ¼
y= ¼x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= 3,
3= ¼(8) +c
3= 2 +c
c= 3 -2
c= 1
Hence the equation of the line is y= ¼x +1.
Rudy rode a bike at the speed of 32 2/3 miles per 3 1/2 minutes. What is his speed in terms of miles per hours?
HELPPP
Answer:
[tex]32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour[/tex]
560 miles per hourhelppppppppppppp plzzzzz
the answer is in the picture
find the area of the triangle
Answer:
Formula for area of a triangle= L*H/2
Step-by-step explanation:
Let's say your triangle has an A length of 15 and your B height is 12. You then multiply your length and height to get 180. Then you divide your answer by 2 and get 90.
Hope this helps!! :)
Jul 02, 10:37:22 AM
Drag the numbers below to put them in order from least to greatest:
9.58 9.558 9.62 9.7 9.691 9.592
Answer: 9.558, 9.58, 9.592, 9.62, 9.691, 9.7
Step-by-step explanation:
Answer:
9.7 9.58 9.62 9.558 9.592 9.691
On the last math test in Kenzie’s class, 17 out of 25 students scored an 80 or higher. Which percent is closest to the experimental probability that a student selected at random will score an 80 or higher on the next test?
Answer
There is a 68 percent that a student selected a random will score an 80 or higher on the next test.
Explanation
You just need to find the percentage of 17 out of 25, or 17/25.
You can do this by dividing 17 by 25.
17/25 equals 0.68, or 68 percent.
I need help with 7 and 8 please
Answer:
Can't See 7 clearly
8) (9,9)
Step-by-step explanation:
[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]
Add x's and divide by 2
Add y's and divide by 2
Like taking the average of the coordinates.
Simplify. 6x-2
A.6/x^2
B.x²/6
C.1/6x^2
D.1/36x^2
Answer:
Step-by-step explanation:
[tex]a^{-m}=\frac{1}{a^{m}}\\\\6x^{-2}=6*\frac{1}{x^{2}}=\frac{6}{x^{2}}[/tex]
The table shows the height of water in a pool as it is
being filled
The slope of the line through the points is 2. Which
statement describes how the slope relates to the
height of the water in the pool?
Height of Water in a Pool
Time
(min)
2
4
6
8
10
Height
(in.)
8
12
16
20
24
The height of the water increases 2 inches per
minute.
The height of the water decreases 2 inches per
minute.
The height of the water was 2 inches before any
water was added.
The height of the water will be 2 inches when the
pool is filled.
Answer:
Step-by-step explanation:
Slope is the rate of change. For us, this rate of change is inches of water per minute. If this rate of change is 2/1, that means that the rate is changing 2 inches every minute (aka The height of the water increases 2 inches per minute, first choice in your list of possibilities).
plz help ASAP with explanation
Answer:
(in image attached)
Step-by-step explanation:
A.
Left: 6×-3
Right: -3×-2
Bottom: 6×-2
B.
48÷6 = 8
-42÷6 = -7
-56÷8 = -7
-56÷-7= 8
