Answer:
The highest score is 91 and the lowest score is 53
Step-by-step explanation:
The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average is 72.
1. The method used to solve this question, is the use of absolute values.
2. Let x be the value that we can use to represent the lowest and highest scores. The equation using absolute values is given as:
| x - 72 | = 19.
Therefore:
x - 72 = 19 (highest score) or
- (x - 72) = 19 (lowest score)
3. We have to find the value of x for which it is the highest or lowest score.
The highest score is given as:
x - 72 = 19
x = 19 + 72
x = 91
For lowest score:
-(x - 72) = 19
-x + 72 = 19
x = 72 - 19
x = 53
The highest score is 91 and the lowest score is 53
given that a*b=2a-3b,then 2*(-3)=
Answer:
13
Step-by-step explanation:
Given: a*b=2a-3b
To find: 2*(-3)
Solution:
Numbers that are used for counting are known as natural numbers. Number along with the digit 0 are known as whole numbers.
In the question, [tex]*[/tex] is used to define relation between a and b as [tex]a*b=2a-3b[/tex]
To find 2*(-3), use the given condition: a*b=2a-3b
Put [tex]a=2,b=-3[/tex]
[tex]2*(-3)=2(2)-3(-3)=4+9=13[/tex]
Given that a*b = 2a-3b,then 2*(-3)= 13
The given binary operation is:
a*b = 2a - 3b
Applying this binary operation to 2*(-3), we are going to substitute a = 2 and b = -3 into the binary operation a*b = 2a - 3b
If a = 2 and b = -3:
2*(-3) = 2(2) - 3(-3)
2*(-3) = 4 + 9
2*(-3) = 13
Therefore, given that a*b = 2a-3b,then 2*(-3)= 13
Learn more here: https://brainly.com/question/16827196
What are the answers to these questions
Answer:
135°
Step-by-step explanation:
You want QRT. So if you look at it you have a straight line, which equals 180°. you already have an angle at 45° so all you do is 180-45 and that equals 135°
calculate the number in the middle of -8 and 31
Step-by-step explanation:
do you mean --8 plus 31
Solve the simultaneous equation
y=9-x
y= 2x^2+4x+6
Answer:
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The intersecting points of given two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given simultaneous equation
y = 9-x ...(i)
y = 2 x² +4 x+6 ..(ii)
Equating (i) and (ii) equations , we get
9 -x = 2 x² +4 x+6
⇒ 2 x² +4 x + 6- 9 +x =0
⇒ 2 x² + 5 x - 3 =0
⇒ 2 x² +6 x -x -3 =0
⇒ 2 x ( x +3) -1 ( x+3) =0
⇒ (2 x -1 ) ( x+3) =0
⇒ (2 x -1 ) = 0 and ( x +3 ) =0
[tex]2 x =1[/tex] and x = -3
x = 1/2 and x =3
Step(ii):-
x = 3 ⇒ y = 9 - 3 =6
A( 3 ,6)
[tex]x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}[/tex]
[tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Final answer:-
The intersecting points of two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)
From the question,
We are to solve the given simultaneous equations
The given equations are
y = 9-x ---------- (1)
y = 2x²+4x+6 ---------- (2)
Substitute equation (1) into equation (2)
y = 2x²+4x+6
That is
9-x = 2x²+4x+6
Simplifying, we get
0 = 2x² +4x +x +6 -9
0 = 2x² +5x -3
∴ 2x² +5x -3 = 0
Now, solving the quadratic equation
2x²+6x -x -3 = 0
Factorizing
2x(x+3) -1(x+3) = 0
Then, we get
(2x -1)(x+3) = 0
∴ 2x - 1 = 0 OR x + 3 = 0
2x = 1 OR x = -3
∴ x = 1/2 OR x = -3
Now, substitute the values of x into equation (1) to determine the values of y
y = 9-x
When x = 1/2
y = 9 - 1/2
y = 8 1/2
and when x = -3
y = 9 --3
y = 9+3
y = 12
Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)
Learn more here: https://brainly.com/question/24448700
Hannah babysits to earn money. She charges $6.50 to babysit for the first hour. She charges $5.75 for each additional hour. Let "n" equal the number of hours after the first hour. Which expression represents how much Hannah charges? *
Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?
y = −one fourthx2 + 5
y = −one fourthx2 − 5
y = one fourthx2 + 5
y = one fourthx2 − 5
Answer:
a) The equation of the parabola
[tex]y = \frac{-x^{2} }{4} +5[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the directrix of the parabola y = 6
Focus of the parabola S(0,4)
The standard equation of the parabola
( x- h)² = 4 a (y-k)
(h,k) is the vertex of the parabola
Axis of the parabola is parallel to y-axis
Given the directrix of the parabola y = 6
The directrix of the parabola y = k -a = 6
k-a =6 ...(i)
The focus of the parabola
S( h , K+a) = (0,4)
so h = 0 and K+a =4
K+a =4 ....(ii)
Step(ii):-
Solving (i) and (ii) equations , we get
Adding (i) and (ii) equations and we get
K-a + k+a = 6 +4
2 K = 10
K =5
Substitute K =5 in equation (i)
K -a =6
5 -a =6
5-6 =a
a = -1
Step(iii):-
we have (h,k) =( 0,5) and a = -1
The equation of the parabola
( x- h)² = 4 a (y-k)
( x- 0)² = 4 (-1) (y-5)
x² = -4 y + 20
-4 y = x² - 20
dividing '-4' on both sides, we get
[tex]y = \frac{x^{2} }{-4} +\frac{-20}{-4}[/tex]
[tex]y = \frac{-x^{2} }{4} +5[/tex]
Final answer:-
The equation of the parabola
[tex]y = \frac{-x^{2} }{4} +5[/tex]
the perimeter of a pickleball court is 128 feet. The width is represented by x and the length is represented by 2x + 4. What are the actual dimensions of the pickleball court (length and width)?
Answer:
x=62.
Step-by-step explanation:
2x +4=128
2x=128-4
2x=124
x= 62
Solve the system using elimination.
-9x - 4y = 1
3x + 3y = 3
([?], [])
Step-by-step explanation:
-9x-4y=1....eq1
3x+3y=3.....eq2
multiply eq2 by 3
to get
9x+9y=9....eq3
add eq1 and 3
0+5y=10
5y=10
divide both sides by 5
y=2
substitute y=2 in to eq1
-9x-4(2)=1
-9x-8=1
grouping of like terms
-9x=1+8
-9x=9
divide both sides by -9
x= -1
now the answer is
x= -1, y=2
What is the slope of the linear represents by the equation y = 4/5 x -3
Answer:
4/5
Step-by-step explanation:
y = mx + b
4/5 = m = slope
Answer:
The slope is 4/5.
Step-by-step explanation:
It's a linear equation. Which means that you can graph a "line" out of it.
The format is y=mx+b
mx=slope
b= y-intercept.
The slope is 4/5.
Carl wants to put up a glow-in-the-dark sticker display on his bedroom ceiling. He needs a gallon of black paint which costs $12. The stickers cost $18 per package and he wants to buy 2 packages. Which of the following is a good estimation of how much change Carl will get back if he gives the cashier $60?
Answer:3a ?
Step-by-step explanation:
Answer:
✈️?
Step-by-step explanation:
The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to model the same sequence?
Answer:
The explicit formula is Tn = 18[(2/3)^(n-1)]
Where n is the term we are looking for
Step-by-step explanation:
Here, we want to get an explicit formula to model the equation
Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12
F(3) = 2/3 * f(2) = 2/3 * 12 = 8
F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3
F(5) = 2/3 * 16/3 = 32/9
Thus, seeing how the equations are progressing, we can definitely see a pattern.
That is Tn = (2/3)^(n-1)(18)
Answer:
Answer in image.
Step-by-step explanation:
Which of these decimals in expanded form are less than 6.2? Check all that apply. 6 + 0.2 + 0.08 6 + 0.1 + 0.07 6 + 0.2 + 0.00 (6 × 1) + (1 × 0.1) + (5 × 0.01) (6 × 1) + (2 × 0.1) + (1 × 0.01) (6 × 1) + (3 × 0.1) + (9 × 0.01)
Answer:
6 plus .1 plus .007
6 times 1 plus 1 times .1 plus 5 times .01
Step-by-step explanation:
Hope this helps
Please help me answer.
Answer:
Slope-intercept: y=3/4x+1
Sorry idk how to do general form
Step-by-step explanation:
Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.
The slope of this graph is 3/4, and the y-intercept is 1.
Answer:
Slope-intercept form: [tex]y=\frac{3}{4}x+1[/tex]
General form: [tex]-3/4x+y-1[/tex]
Step-by-step explanation:
Firstly, to get the slope intercept form, we need to find the slope and the y-intercept. To find the slope, we can use the slope formula and calculate the "rise over run" for these two points. The coordinate of the first point is (0, 1) , and the coordinate of the second point is (4, 4). If x1 = 0, x2 = 4, y1 = 1, and y2 = 4, we can plug those values into the slope formula that I mentioned earlier, which is [tex]\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}}[/tex]. So, after we plug in those values we get in the two points, we can see that [tex]\frac{4-1}{4-0}[/tex], so the slope is [tex]\frac{3}{4}[/tex]. The x moves right 4 times and the y goes up 3 times. Finally, the y-intercept value is 1 because when x = 0, y is 1, and the point we used for the slope formula (0, 1) proves that. For the slope-intercept form, [tex]mx+b[/tex], where m is the slope and b is the y-intercept, m is [tex]\frac{3}{4}[/tex] and b is 1. So, our final answer for the slope-intercept form is [tex]y=\frac{3}{4}x+1[/tex]. Now we can find the general form. To do this, we must get one side of the equation to equal 0. Using our slope-intercept equation, [tex]y=\frac{3}{4}x+1[/tex], we can subtract y from both sides to get 0 on the left, like this: [tex]0=\frac{3}{4}x+1-y[/tex]. Then, we can rearrange the variables to general form: [tex]0=\frac{3}{4}x-y+1\\[/tex]. That is our general form answer. To recap, to find the slope, find the coordinates of the two points, and then plug in those points into the slope formula to find the steepness of the line. Then, add the y intercept that we can see on the graph. For general form, subtract y from both sides and rearrange the equation. Hope this helps!
Find the value of 4 + (27 - 12 ∙ 2) ÷ 2.
Step-by-step explanation:
4 + (27 - 12 * 2) / 2
4 + (27 - 24) / 2
4 + 3/2
5 1/2
Answer:
5 1/2
Step-by-step explanation:
4 + (27 - 12 ∙ 2) ÷ 2=
4 + (27 - 24) ÷ 2=
4 + 3/2= 5 1/2
Solve for x. Round your answer to the nearest thousandth. a. 8.691 c. 6.474 b. 6.252 d. 12.956
Answer:
The answer is B 6.252
Step-by-step explanation:
Quinn returned home one summer's day to find it sweat-inducingly hot! He turned the air conditioner on and fell asleep. The room's temperature decreased by 0.5^\circ0.5
∘
0, point, 5, degrees Celsius each minute, and Quinn woke up 606060 minutes later when it was 10^\circ10
∘
10, degrees Celsius.
Answer:
[tex]f(x)=-0.5x+40[/tex]
Step-by-step explanation:
To solve this problem, we need to find the linear function. We know that the constant rate of change is -0.5° Celsius per minute. Also, after 60 minutes the temperature was 10° Celsius. So, we have a one point and the slope of the linear function, let's use the point-slope formula
[tex]y-y_{1} =m(x-x_{1} )\\y-10=-0.5(x-60)\\y=-0.5x+30+10\\y=-0.5x+40[/tex]
Where the y-intercept is at (0, 40).
Now, we have two points to graph the relation between minutes and Celsius degrees.
Therefore, the room's temperature as a function of time is
[tex]f(x)=-0.5x+40[/tex]
Its graph is attached.
Answer:
Put one of the dots 2 spaces obove 60 and the other dot 3 spaces above 50.
Step-by-step explanation:
What is the number of sides of a regular polygon whose exterior and interior angles are in the ratio 1:5?
Answer:
12
Step-by-step explanation:
n*30=360
n=360/30
n=12
Which interval for the graphed function contains the local
minimum?
O f-1,1]
(1.2)
O(-3,-1)
O (-5, -3)
There are 15 students going on a field trip. If 3/5 of them pack there lunches, how many students pack their lunches?
Answer:
9 pack their lunches
Step-by-step explanation:
Take the number of students and multiply by the fraction that pack their lunches
15 *3/5 =
15/5 * 3
3*3
9
49 - 3 + 9 times 8 divided by 2
Answer:
82
Step-by-step explanation:
49 - 3 + 9 times 8 divided by 2
Answer:
82
Step-by-step explanation:
49 -3 + 9*8/2
PEMDAS
Multiply and divide from left to right
49 -3 + 72/2
49 -3 + 36
Add and subtract from left to right
46 +36
82
The cost of a large pizza is $10.99. Each additional topping costs $1.25. Write an expression that can be used to find the cost of a pizza when x toppings are included
Answer: 10.99 + 1.25x
Step-by-step explanation:
The cost of a large pizza is $10.99 and each additional topping costs $1.25. The expression that can be used to calculate the cost of a pizza when x toppings are added will be:
Cost of pizza + (number of additional toppings × 1.25)
Since x toppings are included, this will be:
= 10.99 + (1.25 × x)
= 10.99 + 1.25x
What numbers are not square or even?
Answer:
Search Results
Featured snippet from the web
Odd and even square numbers
As all even square numbers are divisible by 4, the even numbers of the form 4n + 2 are not square numbers. As all odd square numbers are of the form 4n + 1, the odd numbers of the form 4n + 3 are not square numbers.
Step-by-step explanation:
A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B. A coordinate plane with a circle drawn. The center of the circle is the origin, (0, 0). The circle has a diameter of 16 units. There is a line segment drawn from Point A at (8, 0), passing through (0, 4) to Point B at (negative 4, 6). Which equation represents Grant’s path? y = 2 – 4x y = 4 – y = 6 – y = 8 – 2x
Answer:
y = 4 - x/2
Step-by-step explanation:
Since the line passes through the points A(8,0) and B(4,6), we find that gradient of that lime m = (y₂ - y₁)/(x₂ - x₁) where (8,0) = (x₁, y₁) and (-4,6) = (x₂, y₂).
So, m = (6 - 0)/(-4 - 8) = 6/-12 = = -1/2.
Since the line passes through the point (0,4), the equation of the line is
m = (y - y₃)/(x - x₃) where (x₃, y₃) = (0,4)
So, -1/2 = (y - 4)/(x - 0)
= (y - 4)/x
-x/2 = y - 4
y = 4 - x/2
which is the equation of the line.
Answer:
B
Step-by-step explanation:
Pls help me with this questions
Step-by-step explanation:
6a
Sn = n/2 [2a + (n-1) d]
(2Sn)/ n = 2a + (n - 1) d
2a + (n-1) d = (2Sn)/n
(n-1) d = (2Sn - 2a)/n
[tex]d = \frac{2sn \: - 2a}{(n(n - 1))} [/tex]
[tex]d = \frac{2(sn - a)}{ {n}^{2} - n} [/tex]
6b
[tex]d = \frac{2(56 - 25)}{ {32}^{2} - 32} [/tex]
d = ¹/16
7a.
E = (mv²)/2 + mgh
E = m( v²/2 + gh)
E/m = v²/2 + gh
E/m - gh = v²/2
2(E/m - gh) = v²
so
[tex]v = \sqrt{2( \frac{e}{m} - gh)}[/tex]
7b.
[tex]v = \sqrt{2( \frac{4900}{20} - 9.8 \times 15)}[/tex]
v = 14 m/s
Solve the simultaneous equations
3a+2b+1
a+2b=5
a=
b=
Answer: a=-2, b=7/2
Step-by-step explanation:
To solve for a and b, we can use the elimination method for these system of equations.
3a+2b=1
a+2b=5
Since there is a 2b in both equations, we can subtrac the 2 equations.
2a=-4
a=-2
Now that we have found a, we can plug it into ay of the equations to find b.
-2+2b=5
2b=7
b=7/2
David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Answer:
4x^2+10x-2=0
Step-by-step explanation:
So the total area of mirror: 2*3 = 6 ft sq
8-6 = 2 ft sq is the area of the frame
x is the thickness of the frame
so we have (2*x)*2+(3*x)*2+x*x*4= 2
4x+6x+4x^2=2
-> 4x^2+10x-2=0
The volume of a cube is represented by the polynomial 8x³ - 60x² + 150x - 125. Determine the measure of the edge of that cube.
Answer:
Edge = 2.5
Step-by-step explanation:
please help with question below thank you
Answer:
44/51
Step-by-step explanation:
1 5/6 ÷ 2 1/8
Change to improper fractions
1 5/6 = (6*1+5)/6 = 11/6
2 1/8 = (8*2 +1) /8 = 17/8
11/6 ÷17/8
Copy dot flip
11/6 * 8/17
11/17 * 8/6
11/17 *4/3
44/51
A customer at a restaurant can choose a soup and a salad from the menu choices shown.
Which sample space represents all the possible ways to choose one soup and one salad?
OG, OC, OT, OV, TG, TC, TV, VG, VC, GC
OG, TC, VC
Soup
Salads
Onion (O) Garden (G)
Tomato (U) Chopped (C)
Vegetable (V)
OG, OC, TG, TC, VG, VC
OG, OC, TG, TC, VC
Answer:
OG, OC, TG, TC, VG, VC
Step-by-step explanation:
Soups: O, T, V
Salads: G, C
For each soup, he can choose 2 salads.
OG, OC, TG, TC, VG, VC
The sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.
What is sample space?Sample space is the set of all the possible values or the outcomes of a event.
Let suppose the coin are tossed two times. Then the set of possible outcome or sample space of it can be given as,
[tex]S=\{HH,HT,TH,TT\}[/tex]
Here, H denotes the head and T denotes the tail part of the coin.
A customer at a restaurant can choose a soup and a salad from the menu choices shown.
Soup SaladsOnion (O) Garden (G)Tomato (T) Chopped (C)Vegetable (V)For this menu the customer choose one onion as soup and one garden as salad which can be represented as (OG). Similarly, the sample space of his choice can be,
[tex]\{OG, OC, TG, TC, VG, VC\}[/tex]
Thus, the sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.
Learn more about the sample space here;
https://brainly.com/question/9222927
#SPJ2
Factor the expression completely. 1/4 +11/4
Answer:
3
Step-by-step explanation:
1/4 +11/4
(1+11)/4
12/4
3
Answer:
=3
Step-by-step explanation:
The correct answer to this question is =3. I added the steps down below. I also added a attachment that refer to a number line for this question.
1: =1/4+11/4
2: =1+11/4
3: 12/4
4: =3
Answer: =3
Number line attached.
Hope this helps.
