Answer: lock down
Step-by-step explanation: f(x)= 8x2 + 5=21--> f(x)=21
g(x)= -2x5 - 4=-14--> g(x)=-14
f(2)+g(5) = 7
Step-by-step explanation:
Given,
f(x) = 8x+5
g(x) = -2x-4
To find f(2)+g(5)
Now,
f(2) means putting the value of x = 2 in f(x)
g(5) means putting the value of x = 5 in g(x)
f(2) = 8(2)+5 = 21
g(5) = -2(5)-4 = -14
Hence,
f(2)+g(5) = 21-14 = 7
Prove that cos²(A-B)-sin²(A+B)=cos2Acos2B
Answer:
see below
Step-by-step explanation:
Prove : cos²(A-B)-sin²(A+B)=cos2Acos2B
LHS,
cos²(A-B) - sin²(A+B) (expand using double angle identities)
= [tex]\frac{1 + cos [2(A-B)]}{2} - \frac{1 - cos [2(A+B)]}{2}[/tex]
= [tex]\frac{1}{2} + \frac{1}{2} cos[2(A-B)] - \frac{1}{2} + \frac{1}{2} cos[2(A+B)][/tex]
= [tex]\frac{1}{2} cos[2(A-B)] + \frac{1}{2} cos[2(A+B)][/tex]
= [tex]\frac{1}{2} cos(2A-2B) + \frac{1}{2} cos(2A+2B)[/tex] (expand using sum/difference identities)
= [tex]\frac{1}{2} (cos2Acos2B + sin2Asin2B ) + \frac{1}{2} (cos2Acos2B - sin2Asin2B )[/tex]
= [tex]\frac{1}{2} cos2Acos2B + \frac{1}{2}sin2Asin2B + \frac{1}{2} cos2Acos2B - \frac{1}{2}sin2Asin2B[/tex]
= [tex]\frac{1}{2} cos2Acos2B + \frac{1}{2} cos2Acos2B[/tex]
= [tex]cos2Acos2B[/tex] (= RHS , Proven)
Combine like terms to create an eq
3.26d + 9.75d - 2.65
Answer:
13.01d-2.65
Step-by-step explanation:
Since there r numbers with the variable d, combine them.
(i) Calculate the mean and standard deviation for these weekly incomes.
221 248 251 255 259 263 264 272 291 297 374
Answer:
Mean = 272.3
sd = 37.7
Step-by-step explanation:
Mean = sum/n
(221+248+251+255+259+263+264+272+291+297+374) ÷ 11
= 2995/11
= 272.2727273
Variance = (sum of x²)/n - mean²
[(221²+248²+251²+255²+259²+263²+264²+272²+291²+297²+374²)/11] - (2740/11)²
= (831067/11) - (2995/11)²
= 1419.107438
sd² = variance
sd = sqrt(1419.107438)
sd = 37.67104243
Dr. Strauss has a bottle that contains 18 ounces of medicine. How many one-fourth ounce doses are
in 18 ounces?
There are doses.
Answer:72 IS THE ANSWER
Step-by-step explanation:
BRAINLIEST????? PLEASE
Number of one-fourth ounce doses are in 18 ounces is 72 doses
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is Division?Division is a simple operation in which a number is divided.
Given,
Bottle contains 18 ounces of medicine
Therefore
Number of one-fourth ounce doses are in 18 ounces = [tex]\frac{18}{0.25}=72[/tex] doses
Hence, Number of one-fourth ounce doses are in 18 ounces is 72 doses
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Sally paid the following bills rent $450.00 cell phone $37.50 and cable $69.99 how much money did she pay ?
Answer:
557.49
Step-by-step explanation:
Add the three bills together
450.00
37.50
69.99
--------------
557.49
A cylinder with height 10 inches and radius 4 inches is filled with water. The water is poured into a bowl
(hemisphere) with radius 5 inches. Sketch a cylinder and a hemisphere with dimensions labeled. If all the water
will fit, tell how much empty space remains in the bowl. If all the water will not fit, tell how much water is left in
the cylinder. (leave your answer in terms of pi)
Answer:
Volume of water left in the cylinder=[tex]76\frac{2}{3}\pi \:in^3[/tex]
Step-by-step explanation:
Height of the Cylinder=10 inches
Radius of the cylinder=4 Inches
Volume of the Cylinder
[tex]=\pi r^2h\\=4^2*10\pi\\=160\pi\:in^3[/tex]
Radius of the Hemisphere=5 Inches
[tex]\text{Volume of a Hemisphere}=\frac{2}{3}\pi r^3\\ =\frac{2}{3}\pi *5^3\\=\frac{250\pi}{3} in^3[/tex]
Since the Volume of the cylinder is greater than the Volume of the bowl, all the water will not fit.
[tex]\text{Therefore: volume of water left} =160\pi-\frac{250\pi}{3}\\=76\frac{2}{3}\pi \:in^3[/tex]
The data set below shows the weights of some puppies, in pounds, at a kennel:
10, 10, 10, 11, 12, 12, 14, 14, 15
Which histogram represents the data set?
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 2, the bar for the second range goes to 4, the bar for the third range goes to 3.
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 3, the bar for the second range goes to 4, the bar for the third range goes to 2.
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 2, the bar for the second range goes to 3, the bar for the third range goes to 4.
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 4, the bar for the second range goes to 2, the bar for the third range goes to 3.
Answer:
D. A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 4. The bar for the second range goes to 2, the bar for the third range goes to 3.
There are 3 less than twice as many cats than dogs in the local animal shelter. If there are 210 cats and
dogs combined, how many dogs are in the animal shelter?
There are 71 dogs in the local animal shelter.
To determine the number of dogs and cats in the shelter, let's denote the number of dogs by D and the number of cats by C. According to the problem statement, there are twice as many cats as dogs, minus three. Mathematically, this is represented as C = 2D - 3. We also know that the combined total of cats and dogs is 210, which can be expressed as C + D = 210. To find the number of dogs, we can solve these two equations simultaneously.
From the first equation, we solve for C in terms of D: C = 2D - 3.
Substitute C into the second equation: (2D - 3) + D = 210.
Combine like terms: 3D - 3 = 210.
Add 3 to both sides of the equation: 3D = 213.
Divide both sides by 3 to solve for D: D = 71.
Therefore, there are 71 dogs in the local animal shelter.
Write an equation for the line that has a slope of 1/2 and passes through the point (-2,5)
Answer:
y=0.5x+6
Step-by-step explanation:
6 is the y-intercept because you go up 1 over 2.
Answer: The equation of line is [tex]2y - x - 12 = 0[/tex]
Step-by-step explanation:
The formula for finding the equation of a line when slope and a point is gives is :
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]x_{1}=-2[/tex]
[tex]y_{1}=5[/tex]
[tex]m = 1/2[/tex]
substituting into the formula , we have :
[tex]y - 5 = 1/2 ( x-(-2) )[/tex]
multiply through by 2 , we have
[tex]2(y-5) = 1(x+2)[/tex]
[tex]2y - 10 = x + 2[/tex]
[tex]2y - x - 10 - 2 = 0[/tex]
[tex]2y - x - 12 = 0[/tex]
Therefore : the equation of line is [tex]2y - x - 12 = 0[/tex]
What is 6h-15 when h = 3
Answer:
H=3
Step-by-step explanation:
1. 6(3)-15
2.18-15
3. 3
4. Brainliest please
Solve this equation.
3.5(2.25 + x) = 14
Answer:
1.75
Step-by-step explanation:
Use the distributive property first.
(3.5 x 2.25) (3.5 x X) = 14
7.875 + 3.5x = 14 Now subtract 7.875 from both sides
3.5x = 6.125 Now divide 3.5 by both sides
x = 1.75
The equation 3.5(2.25 + x) = 14 is solved by first distributing 3.5 through the parentheses, then isolating x on one side, yielding a result of x = 1.75.
Explanation:In this mathematical equation, the first step is to distribute 3.5 to (2.25 + x). The result is 7.875 + 3.5x = 14. We then subtract 7.875 from both sides to isolate the term with x which gives 3.5x = 6.125. Finally, to solve for x, we divide both sides by 3.5. This gives us x = 1.75.
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Round your answer to the nearest whole. use Pie as 3.14
Find the volume of a cylinder with a radius of 3 cm and a height of 11 cm.
Anna is shopping for a new backpack. The probability that the backpack is pink is 0.7, and the probability that it is canvas is 0.7. The probability that it is pink and canvas is 0.5. What is the probability that it is pink or canvas. A) 0.3 B) 0.5 C) 0.9 D) 1.4
The probability that the backpack is pink or canvas is option (c) 0.9.
The probability that the backpack is pink or canvas can be calculated using the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B).
According to the question,
A represents: the event that the backpack is pink
B represents: the event that the backpack is the canvas
Substituting the given probabilities, we get:
P(pink or canvas) = 0.7 + 0.7 - 0.5 = 0.9.
So, the probability that the backpack is pink or canvas is option (c) 0.9.
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A guinea pig weighs 1,130 grams.
What does the guinea pig weigh measured in kilograms?
The weight of the guinea pig measured in kilograms is A = 1.130 kg
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the measurement of unit be represented as A
Now , the weight of the guinea pig = 1,130 grams
where from the unit conversion
1000 grams = 1 kg
So , weight of the guinea pig measured in kilograms A = 1,130 grams / 1000
On simplifying , we get
The weight of the guinea pig measured in kilograms A = 1.130 kilograms
Therefore , the value of A is 1.13 kg
Hence , the measurement is A = 1.13 kg
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The guinea pig weight measured in kilograms is 1.13kgs.
To convert the weight of a guinea pig from grams to kilograms, you need to understand the relationship between these units:
In the metric system, 1 kilogram (kg) is equal to 1,000 grams (g).
Start with the weight of the guinea pig: 1,130 grams.
Use the conversion factor: 1,000 grams = 1 kilogram.
Divide the weight in grams by the conversion factor to find the weight in kilograms.
1,130 grams ÷ 1,000 = 1.13 kilograms.
Ethan will subtract a 3-digit number
from 920. He says the difference could be a 1-digit
number, a 2-digit number, or a 3-digit numbens
Write three subtraction equations that show each
difference. Be sure you start with 920 and subtract a
3-digit number each time
Subtracting smaller 3-digit numbers from 920 results in 3-digit answers, subtracting larger 3-digit numbers gives 2-digit answers, and subtracting even larger 3-digit numbers results in 1-digit answers. Examples include: 920 - 120 = 800, 920 - 825 = 95, and 920 - 915 = 5.
Explanation:This question involves simple subtraction operations. Here are three subtraction equations that meet the conditions:
For a 3-digit result: 920 - 120 = 800. Here, subtracting a 3-digit number (120) from our original number (920) results in a 3-digit number (800). For a 2-digit result: 920 - 825 = 95. In this case, subtracting a bigger 3-digit number (825) leaves us with a 2-digit number (95). For a 1-digit result: 920 - 915 = 5. Subtraction of an even larger 3-digit number (915) results in a 1-digit number (5).
As we increase the 3-digit number that we subtract from 920, the result decreases in the number of digits,
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To subtract 3 digit numbers from 920 and end up with a 1-digit, 2-digit or 3-digit number, the following equations are provided: 920 - 911 = 9, 920 - 815 = 105 and 920 - 100 = 820.
Explanation:To find three subtraction equations that show the difference when subtracting a 3-digit number from 920, we need to consider all possible scenarios for the difference.
The smallest possible difference would be a 1-digit number.
To get a 1-digit number, 2-digit number, or a 3-digit number as the result while subtracting a 3-digit number from 920, here are three equations:
• The smallest possible difference would be a 1-digit number. 920 - 911 = 9
• The next possible difference would be a 2-digit number. 920 - 815 = 105
• The largest possible difference would be a 3-digit number. 920 - 100 = 820
In each equation, we started with 920 and subtracted a 3-digit number. Given that the numbers we subtract are less than 920, it becomes possible to get a 1-digit, 2-digit, or 3-digit result.
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For which values of x is the expression undefined?
X – 9
——————
X^2+9x + 18
Answer:
-3, -6
Step-by-step explanation:
Any number of x that makes the bottom 0 makes the expression undefined.
Factor the polynomial in the denominator:
(x+3)(x+6)
Values of x that makes the expression undefined are -3 and -6
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Which equation represents the line
3x - 2y = -8 in slope-intercept
form?
Answer:
The slope -intercept form of the equation is;
y = [tex]\frac{3}{2}[/tex] x + 4
Step-by-step explanation:
The slope-intercept form of an equation is;
y = mx + c
where m is the slope and c represent the intercept
To represent the equation given; 3x - 2y = -8 in its slope intercept form, we will follow the steps below:
3x - 2y = -8
subtract 3x from both-side of the equation
3x - 3x -2y = -3x - 8
-2y = -3x -8
Divide throught the equation by -2
-2y/-2 =-3x/-2 -8/-2
y = [tex]\frac{3}{2}[/tex] x + 4
The slope -intercept form of the equation is;
y = [tex]\frac{3}{2}[/tex] x + 4
Judy is baking a round cake for her niece's birthday and the recipe requires her to coat the bottom of the pan with flour. If the cake pan has an 8-inch diameter, what is the area that she will need to cover with flour on the bottom of the pan?
Answer:
A = 50.24
Step-by-step explanation:
Diameter = 8
8/2 = 4
4 is the radius
A = πr2
A = 3.14 x 42
4 x 4 = 16
A = 3.14 x 16
A = 50.24
Answer:
A = 50.24
Step-by-step explanation:
Diameter = 8
8/2 = 4
4 is the radius
A = πr2
A = 3.14 x 42
4 x 4 = 16
A = 3.14 x 16
A = 50.24
Write an algebraic expression that represents A less than 27.
Answer:
A=26
Step-by-step explanation:
well, A is less than 27 so A could be 26?
A frog sitting on a stump 3 feet high hops off and lands on the ground.
During its leap, its height h in feet is given by h= -0.5d^2 + 2d + 3, where d
is the distance from the base of the stump. How far is the frog from the
base of the stump when it landed on the ground? *
Answer: The distance of frog from the base of the stump is 5.16 feet ( approx)
Step-by-step explanation:
Given, A frog sitting on a stump 3 feet high hops off and lands on the ground.
During its leap, its height h in feet is given by [tex]h= -0.5d^2 + 2d + 3[/tex], where [tex]d[/tex] is the distance from the base of the stump.
When the stump landed on the ground, h= 0 .
So put h=0 in the given equation , we get
[tex]0=-0.5d^2 + 2d + 3\\\\\Rightarrow\ 0.5d^2-2d-3=0[/tex]
Multiply both sides by 2 , we get
[tex]d^2-4d-6=0\\\\\Rightarrow\ d=\dfrac{-(-4)\pm\sqrt{4^2-4(1)(-6)}}{2(1)}\\\\=\dfrac{4\pm\sqrt{16+24}}{2}\\\\=\dfrac{4\pm\sqrt{40}}{2}\\\\=\dfrac{4\pm2\sqrt{10}}{2}=2\pm\sqrt{10}[/tex]
[tex]i.e.\ d=2-\sqrt{10}\ \ or\ \ d=2+\sqrt{10}\\\\\ i.e. d=2-3.1622\ \ or\ \ d=2+3.1622\\\\ i.e. d= -1.1622\ \ or\ \ d=5.1622\approx5.16[/tex]
Since , distance cannot be negative.
Hence, the distance of frog from the base of the stump is 5.16 feet ( approx).
Help worth 10 points!!
Answer:
the answer is B
Step-by-step explanation:
the line is a negative slope so therefore the answer must be negative, use the simple rise over run method to find the slope like normal! :)
We can find 2 points on the graph to solve for the slope; (-2, 0) and (2, -3)
Slope formula: y2-y1/x2-x1
= -3-0/2-(-2)
= -3/4
Therefore, the answer is B.
Best of Luck!
A cash register contains $10 bills and $100 bills with a total value of $2010. If there are 30 bills total, then how many of each does the register contain? $10 bills
Answer:
there will be 19 $100 bills
and 11 $10 bills
Step-by-step explanation:
[tex]100*19=1900\\10*11=110\\1900+110=2010[/tex]
Answer:
11
Step-by-step explanation:
Let x be how many $10 bills there are.
Let y be how many $100 bills there are
x + y = 30
x = 30 - y
10x + 100y = 2010
10(30 - y) + 100y = 2010
300 - 10y + 100y = 2010
-10y + 100y = 2010 - 300
90y = 1710
y = 1710 / 90
y = 19
x = 30 - 19
x = 11
Q3. Express 984. 6080 correct to
a. 2 decimal places _______________
b. 4 significant figures _____________
c. 3 decimal places ________________
d. the nearest hundredth___________ help
Answer:
a) 984.6080 = 984.61 to 2 decimal places
b) 984.6080 = 984.6 to 4 significant figures
c) 984.6080 = 984.608 to 3 decimal places
d) 984.6080 = 984.61 to the nearest hundredth
Step-by-step explanation:
Answers to the approximation questions above are supplied below.
First, you needs to know approximation processes:
Step 1: Keep the required number of digits in question.
Step 2: Before rounding off the remaining digits, look at the next digit to the required number of accuracy, if it is 5 or more, increase the last digit of the number you're keeping by 1, otherwise leave it as it is and round down to zero all the unwanted digits.
Similarly, there is need know the meaning of each degree of accuracy.
1. Decimal places: These are the number of digits occurring after the decimal point. E.g. a set of figures in 1 decimal place has only one digit after decimal point, i.e. 65.4. In the case of the question above,
a) 984.6080 = 984.61 to 2 decimal places
c) 984.6080 = 984.608 to 3 decimal places
2. Significant figures: Basically, these are nonzero digits in a set of figures. However, when zero is in the middle of nonzero digits, i.e, 3045, such zero is a significant figure. In the question above,
b) 984.6080 = 984.6 to 4 significant figures
3. Hundredth: Under place value system, hundredth of a set of figures is located at two digits after the decimal point. In other words, hundredth is same as two decimal places so the same approach is required for the two. Thus;
d) 984.6080 = 984.61 to the nearest hundredth
You can see that the result for both 2 decimal places and nearest hundredth are the same, that is, 984.6080 = 984.61 to 2 decimal places and to the nearest hundredth respectively.
Therefore, the answers are summarized thus:
a) 984.6080 = 984.61 to 2 decimal places
b) 984.6080 = 984.6 to 4 significant figures
c) 984.6080 = 984.608 to 3 decimal places
d) 984.6080 = 984.61 to the nearest hundredth
Answer:
984.6080
a. 2 decimal places
984.61
b. 4 significant figures
984.6
c. 3 decimal places
984.608
d. the nearest hundredth
984.61
A rectangle has an area of 80cm² and a perimeter of 48cm.
Find the length and width of the rectangle.
Answer:
20,4
Step-by-step explanation:
Suppose that x, y are the the length and width
Area=x*y=80
Parameter=2(x+y)=48....x+y=24
Xy=80...x(24-x)=80...x=20,y=4
Answer:
20,4
Step-by-step explanation:
20+20+4+4=48
20*4=80
F(x)= (x-2)(x-3)(x-5) simplify the right side. What is the equation?
Answer:
x³ - 10x² + 31x - 30
Step-by-step explanation:
Given
(x - 2)(x - 3)(x - 5) ← expand the second pair of factors using FOIL
= (x - 2)(x² - 8x + 15) ← distribute
= x³ - 8x² + 15x - 2x² + 16x - 30 ← collect like terms
= x³ - 10x² + 31x - 30
What is the area of the triangle? 11 14 4
Answer:
616
Step-by-step explanation:
Quadrilateral PQRSis graphed in the coordinate plane.
To the nearest tenth, what is the perimeter of quadrilateral PQRS?
Answer:
33.6
Step-by-step explanation:
As we can see in the graph, the points:
P is located at (-2, 8)Q is located at ( 6, 8) R( is located at (6, 2) S is located at (-5, 0)To find a distance between two points or the length of the segment, we use the following formula:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
Because the two points P and Q are located at the same libe y = 8
=> the lenght of PQ = [tex]\sqrt{(6- (-2))^{2} } = \sqrt{8^{2} } = 8\\[/tex]
Because the two points R and Q are located at the same libe x = 6
=> the length of RQ = [tex]\sqrt{(8-2)^{2} } = \sqrt{6^{2} } = 6\\[/tex]
The lenght of RS is: [tex]\sqrt{(-5-6)^2+(0-2)^2} = \sqrt{-11^{2} +(-2)^{2} }[/tex] = [tex]\sqrt{125} = 11.1[/tex]
The lenght of SP is: [tex]\sqrt{(-5-(-2))^2+(0-8)^2} = \sqrt{-3^{2} +(-8)^{2} } = \sqrt{73}[/tex] = 8.5
=> the perimeter of quadrilateral PQRS = PQ+RQ+RS+SP
= 8+6+11.1+8.5
= 33.6
Answer:33.7
Step-by-step explanation:
8+8.5+6+11.2=33.7
Explore the properties of inscribed angles
by following these steps.
1. Move point C and observe how the
angle measures change.
When AC changes,
m ZABC and m ZADC____
and are _____
to each other.
Answer:they change and are always equal to each other
part 2. they do not change
part 3. 1/2
i just did it on edge 2020
When AC changes, angles ABC and ADC are also changes and are equal to each other.
Inscribed angle :An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of a circle.
This is different than the central angle, whose vertex is at the center of a circle.
From given figure, It is observed When AC changes, angles ABC and ADC are also change but equal to each other.
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Which expressions are equivalent to 4(9b+6)?
Answer:
4(9b+6) is equivalent to 4 x (9 x b + 6)
Antoine is designing a new, cylindrical drinking glass. If the glass has a diameter of 8 centimeters and a height of 12.8, what is it’s volume? Round to the nearest tenth
Answer:
643.4
Step-by-step explanation:
Answer:
The answer is: 643.4
Step-by-step explanation: