Answer:
(f-g)(x)= -x-4
(f.g)(x)= 2x^2 -2x-4
(f+g)(-1) = 3(-1) = -3
Step-by-step explanation:
Hi, to answer this question we have to solve the expressions:
(f-g)(x) = x-2 -(2x+2)
(f-g)(x)= x-2 -2x-2
(f-g)(x) = -2x+x-2-2
(f-g)(x)= -x-4
(f.g)(x) = x-2 (2x+2)
(f.g)(x)= 2x^2 +2x-4x-4
(f.g)(x)= 2x^2 -2x-4
(f+g)(x)= x-2 +2x+2
(f+g)(x) = x+2x-2+2
(f+g)(x)= 3x
(f+g)(-1) = 3(-1) = -3
Feel free to ask for more if needed or if you did not understand something.
4sinθ – 1 = - 3 for 0<θ< 360
Answer:
[tex] \theta = 210^\circ [/tex] or [tex] \theta = 330^\circ [/tex]
Step-by-step explanation:
[tex] 4 \sin \theta - 1 = -3 [/tex]
[tex] 4 \sin \theta = -2 [/tex]
[tex] \sin \theta = \dfrac{-2}{4} [/tex]
[tex] \sin \theta = -0.5 [/tex]
For sin θ = 0.5, the reference angle is θ = 30 deg.
[tex] \sin 30^\circ = 0.5 [/tex]
[tex] \theta = 210^\circ [/tex] or [tex] \theta = 330^\circ [/tex]
Thanks a lot... Plz answer with steps
24 and 16
Step-by-step explanation:
let's assume two part be x and (40 - x)
According to Question,
[tex] x\dfrac{1}{4} = (40 - x) \dfrac{3}{8} [/tex]
[tex] x= \dfrac{3(40 - x)}{2} [/tex]
[tex]2 \times x = 120 - 3x [/tex]
[tex]2x + 3x = 120[/tex]
[tex]5x = 120[/tex]
[tex] \cancel{5}x= \cancel{120}[/tex]
[tex]x = 24[/tex]
Hence one part is 24 and other is (40 - 24) = 16 .
Answer: 24 and 16
Step-by-step explanation:
A rope that is 245 cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2:3, and the ratio of the lengths of the second piece to the third piece is 4:5. What is the length of the longest of the three pieces?
Answer:
The length of longest piece is 105 cm.
Step-by-step explanation:
Given:
Rope is 245 cm long.
Ratio of lengths of first to second piece = 2:3.
Ratio of lengths of second to third piece = 4:5.
To find:
Length of longest piece = ?
Solution:
We are given the ratio of first and second pieces AND
ratio of second and third pieces.
Common link is second piece.
We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.
2:3
4:5
Multiply 1st ratio by 4 and 2nd ratio by 3:
Now, the ratio becomes:
8:12 and 12:15
And the ratio of three pieces can be represented as:
8: 12: 15, this ratio is the first piece: second piece: third piece
[tex]\Rightarrow 8x+12x+15x = 245\\\Rightarrow 35x = 245\\\Rightarrow x = \dfrac{245}{35}\\\Rightarrow x = 7[/tex]
So, the pieces lengths will be
First piece = [tex]8 \times 7 = 56[/tex] cm
Second piece = [tex]12 \times 7 = 84[/tex] cm
Third piece = [tex]15 \times 7 = 105[/tex] cm
So, the length of longest piece is 105 cm.
PLEASE HELP!! ASAP PLEASE!!
Answer:
option c is the right answer
Need help quick quick quico
Answer:
7 batches
Step-by-step explanation:
In solving the formula A = (1/2)bh, in solving for h, you could first multiply both side by 1/2. True or False?
Answer:
False.
Step-by-step explanation:
If you multiply both sides by 1/2, you will get 1/4 at the right side.
So the correct way, to solve h, you have to divide both sides by 1/2.
Construct a 99% confidthence interval for the population mean .Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth.
A) Determine the critical value ta/2 with n-the 1 degrees of freedom
B) Determine the lower and upper bound of the confidence interval
C) Interpret the confidence interval.
Confidence interval for mean, when population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom
We assume the population has a normal distribution.
Given, n= 19 , s= 3.8 , [tex]\overline{x}=22.4[/tex]
[tex]\alpha=1-0.99=0.01[/tex]
A) Critical t value for [tex]\alpha/2=0.005[/tex] and degree of 18 freedom
[tex]t_{\alpha/2}[/tex] = 2.8784
B) Required confidence interval:
[tex]22.4\pm ( 2.8744)\dfrac{3.8}{\sqrt{19}}\\\\=22.4\pm2.5058\\\\=(22.4-2.5058,\ 22.4+2.5058)=(19.8942,\ 24.9058)\approx(19.9,\ 24.9)[/tex]
Lower bound = 19.9 years
Uppen bound = 24.9 years
C) Interpretation: We are 99% confident that the true population mean of lies in (19.9, 24.9) .
What is the angle formed by the line y=2x−1 and x-axis?
Answer:
63.4°
Step-by-step explanation:
y = 2x - 1
dy/dx = 2
∴ The angle is arc tan(2) = tan^-1(2) = 63.4°
Last question! Having some trouble.
Answer:
C
Step-by-step explanation:
The abscissa is the value of the x- coordinate and the ordinate is the value of the y- coordinate.
Since the point is in the second quadrant then x- coordinate will be negative and the y- coordinate positive.
C is the only point which meets this condition and
- 3 = 2(1) - 5 = 2 - 5 = - 3 ( 5 less than twice the ordinate) → C
Please answer the following questions
Answer:
4a) 110 square centimetres
4b) 127 square centimetres
6) 292 square centimetres
8) 800 tiles
Step-by-step explanation:
4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:
a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:
A = 12 * 15 = 180 square centimetres
The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:
a = 10 * 7 = 70 square centimetres
Therefore, the area of the shaded part is:
A - a = 180 - 70 = 110 square centimetres
b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:
A = 13 * 11 = 143 square centimetres
The unshaded part has dimensions 8 cm by 2 cm. Its area is:
a = 8 * 2 = 16 square centimetres
Therefore, the area of the shaded part is:
A - a = 143 - 16 = 127 square centimetres
6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.
The frame has dimensions 24 cm by 18 cm. Therefore, its area is:
A = 24 * 18 = 432 square centimetres
The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:
a = 14 * 10 = 140 square centimetres
Therefore, the background area of the space not covered by the photograph is:
A - a = 432 - 140 = 292 square centimetres
8) The floor has dimensions 8 m by 4 m. The area of the floor is:
A = 8 * 4 = 32 square centimetres
Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:
a = 0.2 * 0.2 = 0.04 square metres
The number of tiles that are needed is the area of the floor divided by the area of each tile:
A / a = 32 / 0.04 = 800 tiles
Pls help. I rly don't understand it.
Answer:
You just need to demonstrate that the expression is not equivalent. To do that, we just need to evaluate the expression with a specific number.
[tex]\frac{3}{8}x+2 \neq \frac{3}{2}x+5[/tex]
For [tex]x=0[/tex], we have
[tex]\frac{3}{8}(0)+2 \neq \frac{3}{2}(0)+5\\2 \neq 5[/tex]
Notice that the answer is true because 2 is not equivalent to 5.
Therefore, the expression is actually non-equivalent.
Given that ACAB - ACED, lind the value of y to 1 dermal place
Answer:
y = 15
Step-by-step explanation:
The triangles CAB and CED are similar (Using the case AA), so we can write the following relations:
[tex]\frac{12}{28} =\frac{15}{x}=\frac{y}{35}[/tex]
Using the first two fractions, we can find the value of x:
[tex]\frac{12}{28} =\frac{15}{x}[/tex]
[tex]12x = 28*15[/tex]
[tex]12x = 504[/tex]
[tex]x = 504/12 = 42[/tex]
Using the first and last fractions, we can find the value of y:
[tex]\frac{12}{28} =\frac{y}{35}[/tex]
[tex]28y = 12*35[/tex]
[tex]28y = 420[/tex]
[tex]y = 420/28 = 15[/tex]
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 4.5%, and the tax in the second city was 3.5% . The total hotel tax paid for the two cities was $317.50. How much was the hotel charge in each city before tax? First city: Second city:
Answer:
$3750 and $4250
Step-by-step explanation:
x + 500 = y
.045x + .035y = 317.50
.045x + .035(x + 500) = 317.50
.045x + .035x + 17.5 = 317.50
.08x = 300.00
x = 3750
y = 4250
PLEASE HELP ME! I will mark you as BRAINLIEST if you answer this correctly.
Answer:
0.92
Step-by-step explanation:
Each year, the value declines. This eliminates choices A and D.
The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...
0.92 . . . . the third listed choice
if (x)= 2x square minus 1,then f(-3)
Answer:
17.
Step-by-step explanation:
f(x) = 2x^2 - 1
f(-3) = 2(-3)^2 - 1
= 2 * 9 - 1
= 18 - 1
= 17
Hope this helps!
Hope it will help u....
Hurry I need it now !
(04.01 MC)
Which characteristics will prove that ΔDEF is a right, scalene triangle?
Answer:
A right scalene triangle would have a 90 degree angle and 3 non congruent sides
Step-by-step explanation:
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2)
A. y + 2 = 2(x - 2)
B. y 4 20 + 1)
c. y + 1 = 2(3-4)
D. y 2 233 - 2)
Answer:
The answer is option BStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find an equation of a line given two points first find the slope / gradient
Slope of the line using points (-1,4) and (-2,2) is
[tex]m = \frac{2 - 4}{ - 2 + 1} = \frac{ - 2}{ - 1} = 2[/tex]
So the equation of the line using point (-1,4) is
y - 4 = 2( x + 1)Hope this helps you
In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture. A conical-shaped umbrella has a radius of 0.4 m and a height of 0.45 m. Calculate the amount of fabric needed to manufacture this umbrella. (Hint: an umbrella will have no base) A cone has a volume of 150 cm3 and a base with an area of 12 cm2. What is the height of the cone? Find the dimensions of a deck which will have railings on only three sides. There is 28 m of railing available and the deck must be as large as possible. A winter recreational rental company is fencing in a new storage area. They have two options. They can set it up at the back corner of the property and fence it in on four sides. Or, they can attach it to the back of their building and fence it in on three sides. The rental company has decided that the storage area needs to be 100 m2 if it is in the back corner or 98 m2 if it is attached to the back of the building. Determine the optimal design for each situation.
Answer:
1. The amount of ice needed = 18 m²
2. The amount of fabric needed to manufacture the umbrella is 0.76 m²
3. The height of the cone, is 3.75 cm
4. The dimensions of the deck are;
Width = 28/3 m, breadth = 28/3 m
The area be 87.11 m²
5. The dimensions of the optimal design for setting the storage area at the corner, we have;
Width = 10m
Breadth = 10 m
The dimensions of the optimal design for setting the storage area at the back of their building are;
Width = 7·√2 m
Breadth = 7·√2 m
Step-by-step explanation:
1. The amount of ice needed is given by the volume, V, of the pyramid given by V = 1/3 × Base area × Height
The base area = Base width × Base breadth = 3 × 5 = 15 m²
The pyramid height = 3.6 m
The volume of the pyramid = 1/3*15*3.6 = 18 m²
The amount of ice needed = 18 m²
2. The surface area of the umbrella = The surface area of a cone (without the base)
The surface area of a cone (without the base) = π×r×l
Where:
r = The radius of the cone = 0.4 m
l = The slant height = √(h² + r²)
h = The height of the cone = 0.45 m
l = √(0.45² + 0.4²) = 0.6021 m
The surface area = π×0.4×0.6021 = 0.76 m²
The surface area of a cone (without the base) = 0.76 m²
The surface area of the umbrella = 0.76 m²
The amount of fabric needed to manufacture the umbrella = The surface area of the umbrella = 0.76 m²
3. The volume, V, of the cone = 1/3×Base area, A, ×Height, h
The volume of the cone V = 150 cm³
The base area of the cone A = 120 cm²
Therefore we have;
V = 1/3×A×h
The height of the cone, h = 3×V/A = 3*150/120 = 3.75 cm
4. Given that the deck will have railings on three sides, we have;
Maximum dimension = The dimension of a square as it is the product of two equal maximum obtainable numbers
Therefore, since the deck will have only three sides, we have that the length of each side are equal and the fourth side can accommodate any dimension of the other sides giving the maximum dimension of each side as 28/3
The dimensions of the deck are width = 28/3 m, breadth = 28/3 m
The area will then be 28/3×28/3 = 784/9 = [tex]87\frac{1}{9}[/tex] =87.11 m²
5. The optimal design for setting the storage area at the corner of their property with four sides is having the dimensions to be that of of a square with equal sides of 10 m each as follows;
Width = 10m
Breadth = 10 m
The optimal design to have the storage area at the back of their building having a fence on only three sides, is given as follows;
Storage area specified = 98 m²
For optimal use of fencing, we have optimal side size of fencing = s = Side length of a square
s² = 98 m²
Therefore, s = √98 = 7·√2 m
Which gives the width = 7·√2 m and the breadth = 7·√2 m.
Linda sells cookies for $2 and hamburgers for $3. She sold 25 items and made $60. How many cookies did she sell ?
Answer:
10 cookies
Step-by-step explanation:
10 x 3 = 30
15 x 2 = 30
30 + 30 = $60
The number of cookies sold by Linda will be 10 cookies.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Linda sells cookies for $2 and hamburgers for $3. She sold 25 items and made $60.
The number of cookies sold by Linda will be calculated as below:-
10 x 3 = 30
15 x 2 = 30
30 + 30 = $60
Therefore, the number of cookies sold by Linda will be 10 cookies.
To know more about Expression follow
brainly.com/question/723406
#SPJ5
Which values for A and B will create infinitely many solutions for this system of equations?
4 x minus A y = 15. Negative 4 x + 6 y = B.
A = negative 6, B = 15
A = 6, B = 15
A = 6, B = negative 15
A = negative 6, B = negative 15
Answer: C) A = 6, B = -15
Step-by-step explanation:
In order to have infinitely many solutions, you must end up with 0 = 0 when adding the equations together.
4x - Ay = 15
-4x + 6y = B
(6 - A)y = 15 + B
↓ ↓
6 - A = 0 15 + B = 0
6 = A B = -15
Answer:
C
Step-by-step explanation:
TOOK THE TEST
a fraction is such that the numerator is 2 less than the denominator if you add 3 to the numerator and 5 to the denominator the resulting fraction is 3/5 find the fraction
Answer:
The required fraction is 3/5
Answer: 3/5
Step-by-Step Explanation:
Let x represent the denominator of the fraction, then we have [tex]\dfrac{x-2}{x}[/tex]
Now add 3 to the numerator and 5 to the denominator and set it equal to 3/5:
[tex]\dfrac{(x-2)+3}{(x)+5}=\dfrac{3}{5}\\\\\\\text{Simplify:}\\\dfrac{x+1}{x+5}=\dfrac{3}{5}\\\\\\\text{Cross Multiply and solve for x:}\\5(x+1)=3(x+5)\\5x+5=3x+15\\2x=10\\x=5[/tex]
Substitute x = 5 into the original fraction:
[tex]\dfrac{(5)-2}{(5)}\quad =\large\boxed{\dfrac{3}{5}}[/tex]
Identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized blockdesign, or matched pairs design.
A drug is designed to treat insomnia. In a clinical trial of the drug, amounts of sleep each night are measured before and after subjects have been treated with the drug.
The most appropriate is (randomized block, matched pairs, completly randomized) design.
Answer:
Matched pairs design
Step-by-step explanation:
Looking at the options;
-It's not a completely randomized design because a randomized design will assign all individuals to a group which in this case it doesn't.
- It's not a randomized block design because randomized block design will group the subjects in question into 2 or more blocks which have a common characteristic and will then randomly assign subjects in each of the blocks.
-It's a matched pair because every individual/subject undergoes measurements both before and after being treated with the drugs.
Thus, the correct option is matched pairs design.
lcm of b square and b cube is
Answer:
HCF is b since we take the least value. That's it. When the two numbers have same base, the LCM will be the base with greater power. So the answer is LCM = b^2
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
HCF is b since we take the least value. That's it. When the two numbers have same base, the LCM will be the base with greater power. So the answer is LCM = b^2.
What is the answer to 99,200 + 10(18/2)?
Answer:
99,290
Step-by-step explanation:
99,200 + 10(18/2)
= 99,200 + 10(9)
= 99,200 + 90
= 99,290
dentify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A researcher selects every 890 th social security number and researcher selects every 890th social security number and surveys surveys that the corresponding corresponding person.person. nothing nothing nothing Which type of sampling did the researcher researcher use
Complete Question:
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below;
A researcher selects every 890th social security number and surveys the corresponding person. Which type of sampling did the researcher use?
Answer:
Systematic sampling.
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Random sampling.
2. Convenience sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Systematic sampling.
A systematic sampling is a type of probability sampling method which involves the researcher selecting or collecting data from a larger population.
Under systematic sampling method, samples are selected from an ordered (fixed) sample population at periodic interval. Therefore, numbers are assigned to every member of the population and then, the "nth" member are selected by the researcher after choosing a fixed starting point.
In this scenario, the researcher selects every 890th social security number and surveys the corresponding person.
Hence, the type of sampling used by the researcher is systematic sampling.
Three triangles have sides of lengths 3, 4, and 5. Their respective perimeters are 6, 8 and 10. The triangles are similar to each other.
True or false
Answer:
'll tell you where the problem lies - it is IMPOSSIBLE to form triangles like this.
If the perimeter of the smallest triangle is 6 and one side is 3, then the sum of the other two sides can only be 6 - 3 = 3
One property to enable you to form a triangle is that NO ONE SIDE can be greater or equal to the sum of the other two sides. In the smallest triangle 1 side of length 3 equals the other two sides.
In the middle triangle one side of length "4" equals the sum of the other two sides and
In the large triangle one side of length "5" equals the other two sides.
Therefore when I say "triangle" above I am not actually correct because it is IMPOSSIBLE to form triangles with those dimensions of 1 side and with those perimeters
The shaded rectangle in the diagram consists ofthree squares. (Picture for full question)
Answer: 243 cm²
Step-by-step explanation: If the diameter is 18, the radius is 9. Each square is 9×9, so 81 cm² for each. Multiply: 81×3 = 243
Or take the length times width to get area 27×9= 243
Please help. First person to answer correctly with explanation will get brainiest!!!
Answer:
64° aka D
Step-by-step explanation:
∠J + ∠L + ∠LKJ = 180°
58° + 58° + ∠LKJ = 180°
116° + ∠LKJ = 180°
∠LKJ = 180° - 116°
= 64°
hope i helped
-lvr
PLEASE HELP!!!
Rectangle EFGH is reflected across the origin and then rotated 90° clockwise about the origin, forming rectangle E″F″G″H″. What are the coordinates of rectangle E″F″G″H″?
(A.) E″ (1, –5), F″ (1, –1), G″ (4, –1), H″ (4, –5)
(B.) E″ (–1, –5), F″ (–1, –1), G″ (–4, –1), H″ (–4, –5)
(C.) E″ (–1, 5), F″ (–1, 1), G″ (–4, 1), H″ (–4, 5)
(D). E″ (5, 1), F″ (1, 1), G″ (1, 4),
H″ (5, 4)
Answer:
c.
Step-by-step explanation:
90 degrees clockwise is (x,y)-(y,-x)
Answer:
The answer is A
Step-by-step explanation:
Took the test
Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving. * Round to one decimal place, if necessary.*
The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.
1) The ball starts (blank/answer) feet above the ground.
2)The ball reaches a maximum height of (Blank/answer) feet at a horizontal distance of (blank/answer) feet away from the golf club it was hit with.
3)The ball returns to the ground at about (blank/answer) feet away.
Answer:
1.) Zero ( 0 )
2.) 55.47 feet , 8.6 feet
3.) 17.2 feet
Step-by-step explanation:
The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.
1.) Since the equation has no intercept,
The ball will start zero feet above the ground.
2.) The distance of the ball at the maximum height will be achieved by using the formula
X = -b/2a
Where b = 4.3, a = -0.25
Substitutes both into the formula
X = -4.3 / 2( - 0.25 )
X = - 4.3 / - 0.5
X = 8.6 feet
Substitute X into the function to get the maximum height
h(x) = −.25(8.6)^2 + 4.3(8.6)
h(x) = 18.49 + 36.98
h(x) = 55.47 feet
3) As the ball returns to the ground, the height will be equal to zero, therefore,
0 = -0.25x^2 + 4.3x
0.25x^2 = 4.3x
X = 4.3/0.25
X = 17.2 feet
The ball returns to the ground at about 17.2 feet away