Answer:
4
Step-by-step explanation:
We know that [tex]a = 4[/tex] and [tex]b = -1[/tex], as they are given in the problem. All we have to do is plug them into the equation and solve it.
[tex]5 - 2(a + 3b)/2\\ = 5 - 2(4 -3)/2\\= 5 - 1\\= 4[/tex]
The graphs below have the same shapes. What is the equation for the red graph?
The equation of the red graphed function is: g(x) = 1 - x².
How to Find the Equation of a Graphed Function?Given the graph shown in the attachment below, the graphed function heads downwards, and the x - axis is intercepted at ( 1, 0 ) and (-1,0).
Thus, the x-intercepts, which is the zeros of the function, are: 1 and -1.
So, g(x) = (x + 1)(x -1)
Expand:
g(x) = 1 - x²
The equation of the red graph is: g(x) = 1 - x².
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14)
Given a circle with a radius of 5, which equation expresses it as the ratio of the circumference of a circle to its diameter?
A)
B)
C)
D)
sin
- 7
10
216
C
Answer: 10
Step-by-step explanation: The diameter is twice the radius
17, 18, 22, 31, 47 what is the next number
Answer:
the next number is 47+ 16 =63
The students in Mr. McIntyre’s class and the students in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results.
Mr. McIntyre’s Class
A dot plot titled Mister McIntyre's Class. A number line going from 0 to 5 is labeled Number of Pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Mrs. Ramos’s Class
A dot plot titled Misses Ramos's Class. A number line going from 0 to 5 is labeled Number of Pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
Which statement correctly compares the means of the data in the dot plots?
The correct statement compares the means of the data in the dot plots is option C; the mode is greater for Mrs. Ramos’s class.
What are the median and mode of the data?Median represents the middle value of the given data when arranged in a particular order.
Mode is that number that appears most frequently in the given set of data.
Given;
The Number of pets in Mr. McIntyre’s class ;
0,0,0,0,0,1, 1, 1, 1, 1, 4, 4, 4, 4, 1,
Median = 1
Mode = 0 and 1
The Number of pets in Mrs. Ramos’s Class;
0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3
Median = 3
Mode = 4 and 5
Hence, C; The mode is greater for Mrs. Ramos’s class.
The remaining part of the question is
"Which statement correctly compares the measures of center of the data in the dot plots?
The median is greater for Mr. McIntyre’s class.
The median is the same for both classes.
The mode is greater for Mrs. Ramos’s class.
The mode is the same for both classes."
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Another day, another math problem 2
Answer:
-7
Step-by-step explanation:
you can use power rule of derivatives for that.
PLEASE GIVE STEP BY STEP EXPLANATION !!
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The two types of transformations that can be used to transform f(x) to g(x). g (x) = f(x) + 16 and g (x) = f(x + 8)
ABC has vertices at A (12, 8), B (4, 8)
What is the equation about?f(x)= 0, -1 ,5,14
g(x)= -6, -1, -1, 14
g(x)=f(x)+k
-6= 0+k
k= -6
A) g (x) = f(x) + 16 and
g(x) = f(x + 8)
B) g(x)=f(x)+k
-1= -1+ k
k= -1+1=0
g(x)=f(x)+k
-1= 5+k
k= -1-5=-6
g(x)=f(x)+k
14= 14+k
k= 0
k= -6,0,-6,0
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A fingernail grows about 0.1 mm, day. How much does a fingermail grow in 45 days ? 90 days?
Answer:
- In 45 days = 4,5mm ; In 90 days = 9mm
Step-by-step explanation:
in 45 days = 0,1 * 45 = 4,5 mm ; in 90 days = 0,1 * 90 = 9mm
Please help I’m confused
Answer:
Step-by-step explanation:
A cylindrical can has a height of 19 cm and a radius of 6 cm. The volume of the cylindrical can is decreasing at a rate of 563 cubic cm per second, with the height being held constant. What is the rate of change of the radius, in cm per second, when the radius is 6 cm?
Round your answer to the nearest hundredth.
The rate of change of radius at radius 6cm is 0.79 cm/sec.
The rate of change of a function is simply the derivative of the function with respect to the changing parameter in the function i.e. variable in the function.
So for calculating the rate of change of radius, we calculate the rate of volume change as volume is the function of radius.
As we know volume of the cylinder is given by V=πr²h
where r is the radius and h is the height of the cyclinder.
Given that rate of change of volume = 563 cm/sec
⇒ dV/dt =563 cm/sec
⇒ d(πr²h)/dt =563
taking πh outside the derivative as π and h is constant term
⇒ πh dr²/dt =563
⇒ πh (dr²/dr)(dr/dt)= 563 (applying chain rule dy/dx = (dy/du)(du/dx))
⇒ πh(2r)(dr/dt) =563
⇒dr/dt= 563/(2πhr)
given height of the cylinder h= 19cm
rate of change of radius at radius r =6cm= dr/dt= 563/(2πhr)= 563/(2*π*19*6)= 0.79 cm/sec
Therefore rate of change of radius at radius 6cm is 0.79 cm/sec.
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The probability that the number of students who will take the mathematics exam is 40 out of 50. What is the expressed as a percentage
Answer:
I think it's 80%
Step-by-step explanation:
Method 1: (40/50)*100 = 80%
Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%
Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she gave, but she was penalized 1 point for every incorrect answer. In the end, Thalia had a total of 28 points. In order to determine the number of correct and incorrect answers that she gave, a viewer at home used the system of linear equations x + y = 20 and 2 x + y = 28, with x being the number of correct answers and y being the number of incorrect answers. The viewer solved the system by using the linear combination method as shown.
x + y = 20. + StartFraction Negative 2 x minus y = negative 28 over Negative x = negative 8 EndFraction. StartFraction negative x Over negative 1 EndFraction = StartFraction negative 8 Over negative 1 EndFraction. X = 8.
8 + y = 20. 8 + y minus 8 = 20 minus 8. y = 12.
The viewer calculated that the contestant answered 8 questions correctly and 12 questions incorrectly. What went wrong?
The viewer mistakenly determined that one of the equations in the system should be x + y = 20.Instead modifications should have been made before applying the equation.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
The viewer multiplied the equation 2 x + y = 28 by –1 incorrectly.
The viewer added the equations x + y = 20 and Negative 2 x minus y = negative 28 incorrectly.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
Total Questions = 20
Total Points = 28
Correct Answers = +2 points
Incorrect Answers = -1 point
The viewer represents the correct answers with x and the incorrect ones with y.
x+y = 20
for every correct answers 2 points;
and for every incorrect answers, -1 point
This can be written as
2x-y = 28
The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;
now
2x-y = 28
x+y = 20
On adding the equations
]3x = 48
x = 16
y = 4
This means that the contestant answered 16 questions correctly and 4 questions incorrectly
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.
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a farmer uses 1/6 of his land to plant pineapples, 5/9 to plant durians and the remaining 48.5 acres to plant vegetables. calculate the area of land used to plant pineapples and durians
Step-by-step explanation:
x = total area of land
x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6
6x - x - 30/9 × x = 291
5x - 30/9 × x = 291 | multitude both sides by 9
45x - 30x = 2,619
15x = 2,619
x = 174.6 acres
pineapples were planted on 174.6 × 1/6 = 29.1 acres.
durians were planted on 174.6 × 5/9 = 97 acres.
1) When the polynomial P(x) is divided by x+5, the remainder is 3. Which of the following is definitely true?
a) P(3) = 5
b) P(-5) = 3
c) P(5) = 3
d) P(-3) = 5
2) P is a degree 3 polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i. What is the other zero?
a) 4-3i
b) 4+3i
c) -5
d) 3-4i
1) The definitely true for the statement is b) P(-5) = 3.
2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
What is the remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
Given;
1) When the polynomial P(x) is divided by x+5, the remainder is 3.
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).
So, P(-5) = 3
Therefore, the definitely true for the statement is b) P(-5) = 3.
2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.
The complex roots always exist in conjugate pairs so,
3 + 4i and 3 - 4i
Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
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On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).
The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).
The domain is all real numbers.
The range is all real numbers.
If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.
The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).
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Answer:
A
Step-by-step explanation:
3. College Students (10 points)
In Fall 2019, there were approximately 16.6 million undergraduate students in degre
granting postsecondary institutions. This represents a 5% decrease from the Fall 200
number of students. How many undergraduate students were there in 2009?
Source: https://nces.ed.gov/fastfacts
The number of students is 33.2 million
What is percentage decrease?Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.
Given:
In 2019= 16.6 million
% decrease = 5%
So,
% decrease= x - 16.6/ x
5% = x- 16.6/x
0.05= (x-16.6)/x
0.05x = x-16.6
-0.05 x = -16.6
x= 16.6/0.05
x= 16600000/0.05
x= 332,000,000
x= 33.2 million.
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How do i find the domain of F and write in interval notation??? I completely confused
Answer:
898
Step-by-step explanation:
898999
Suntract (7x-3x)-(5x-6).
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]
[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]
[tex]\qquad \tt \rightarrow \: - x + 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:6-x
Step-by-step explanation:
The solution is in the image
The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. 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? 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. help me
Answer:
The height of the water increases 2 inches per minute.
Step-by-step explanation:
the slope is always the ratio of
y coordinate change / x coordinate change
in our case, x is the time (minutes), and y is the water height (inches).
we see, the longer the pool get filled, the higher the water gets. logical, right ?
by checking the data points we see :
with every 2 minutes passing the water height increases by 4 inches.
so, the slope is +4/+2 = 2/1 = 2
and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.
every 2 minutes 4 inches more.
so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.
and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.
If ( 3 y − 9 ) 2 + 7 = 43 , then what is(are) the values of y?
Answer:
y = 5 and y = 1
Step-by-step explanation:
[tex]\textsc {Subtract 7 from each side :}[/tex]
⇒ (3y - 2)² + 7 - 7 = 43 - 7
⇒ (3y - 2)² = 36
[tex]\textsc {take the square root on each side :}[/tex]
⇒ √(3y - 9)² = √36
⇒ 3y - 9 = ±6
[tex]\textsc {When equal to +6, add 9 on each side :}[/tex]
⇒ 3y - 9 + 9 = 6 + 9
⇒ 3y = 15
[tex]\textsc {Divide by 3 on each side :}[/tex]
⇒ 3y/3 = 15/3
⇒ y = 5
[tex]\textsc {When equal to -6, add 9 on each side :}[/tex]
⇒ 3y - 9 + 9 = -6 + 9
⇒ 3y = 3
[tex]\textsc {Divide by 3 on each side :}[/tex]
⇒ 3y/3 = 3/3
⇒ y = 1
What must be added to -31 to get 12
Answer:
43
Step-by-step explanation:
31+12=43
Therefore adding 43 to -31 should give the answer 12.
Hii!
____________________________________________________________
Answer:
43
Step-by-step explanation:
We can find an answer to this question by setting up an equation.
-31+x=12
x is the unknown amount we should add to -31 to obtain 12.
Now, to solve it for the variable, x, we need to add 31 to both sides.
Upon doing this we obtain.
x=43
∴, 43 should be added to -31 to get 12
--
Hope that this helped! Best wishes.
--
If anyone can help me to solve this.
Answer:
1) x + 96 = 90°
2) x + 89 = 80°
Step-by-step explanation:
Consecutive Interior Angles Theorem
When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line. Each pair of consecutive interior angles are supplementary (sum to 180°).
Question 1To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:
⇒ (x + 96)° + (x + 96)° = 180°
⇒ x + 96 + x + 96 = 180
⇒ 2x + 192 = 180
⇒ 2x + 192 - 192 = 180 - 192
⇒ 2x = -12
⇒ 2x ÷ 2 = -12 ÷ 2
⇒ x = -6
Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:
⇒ x + 96 = -6 + 96 = 90°
⇒ x + 96 = 90°
Question 2To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:
⇒ (x + 109)° + (x + 89)° = 180°
⇒ x + 109 + x + 89 = 180
⇒ 2x + 198 = 180
⇒ 2x + 198 - 198 = 180 - 198
⇒ 2x = -18
⇒ 2x ÷ 2 = -18 ÷ 2
⇒ x = -9
Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:
⇒ x + 89 = -9 + 89
⇒ x + 89 = 80°
Answer:
[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]
Step-by-step explanation:
Part 1 :
x + 96 + x + 96 = 180 (angle pairs of a line)2x + 192 = 1802x = -12x = -6∠ = -6 + 96∠ = 90°Part 2 :
x + 109 + x + 89 = 180 (same reason)2x + 198 = 1802x = -18x = -9∠ = -9 + 89∠ = 80°radical 5* radical 2
Answer:
[tex] \sqrt{10} [/tex]
Step-by-step explanation:
Rule: [tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]
[tex] \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} [/tex]
What is the solution to the following equation?
3( x - 4 ) - 5 = x - 3
A. x = 8
B. x = 3
C. x = 12
D. x = 7
Answer:
x = 7
Step-by-step explanation:
3(x - 4) - 5 = x - 3
3x - 12 - 5 = x - 3
2x = -3 + 12 + 5
2x = 14
x = 7
What is the solution to this system of equations y=3x-4 4y=12x-4 a no solution b (0,4) C Infinite solutions
Answer:
C
Step-by-step explanation:
y = 3x - 4
4y = 12x - 4
divide the bottom equation by 4
y = 3x - 4
y = 3x - 1
y = -3
3x - 1 = -3
3x = -2
x = -2/3
(-2/3, -3) is the answer. by this logic, there is a splution so can't be a, the answer is not (0, 4) so not b so it must be c
What are the rational roots of ? x = 1, x = -1 x = 1, x = 0 x = 1, x = 2 This polynomial has no rational roots.
A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked
at random. What is the probability that the counter is green or purple? Give
your answer as a fraction.
A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.
The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).
So the probability of selecting a green or purple counter is:
Probability = (Number of green counters + Number of purple counters) / Total number of counters
Probability = (7 + 1) / 11
Probability = 8/11
Therefore, the probability of selecting a green or purple counter is 8/11.
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A cab company charges a $5 boarding rate in addition to its meter which is $3
for every mile. What is the equation of the line that represents this cab
company's total charge?
Re
co
Answer:
m3+5
Step-by-step explanation:
m is miles
take the number of miles multiply by3
take that answer add 5
The equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
What is an Equation ?A statement that relate two expressions with an equal sign is called an Equation.
It is given that
A cab company charges a $5 boarding
Charges for every mile is $3 per mile
Let x be the mile travelled
The cab's total charge is represented by y
then y = 3x + 5
Therefore the equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
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What is the surface area of prism below?
Answer:
Aprism = 483.246 yd2
Step-by-step explanation:
The surface area is the sum of the 2 circles areas and the rectangle area.
Ac1 = PI*r2
Ac1 = (3.14)*(11.4/2)2
Ac1 = 102.0186 yd2
Ac1 = Ac2 then
Ac2 = 102.0186 yd2
Now the perimeter of the circle is one the sides of the rectangle:
Pc = 2PI*r
Pc = 2*3.14*(11.4/2)
Pc = 35.796 yd
Now the area of the rectangle is:
Ar = 7.8yd*35.796yd
Ar = 279.2088 yd2
Then, the surface area of prism is:
Aprism = Ac1 + Ac2 + ArAprism = 102.0186yd2 + 102.0186yd2 + 279.2088yd2Aprism = 483.246 yd2Describe the graph of a quadratic function below given in table form
A condominium is taxed based on its $78,584 value. The tax rate is $3.49 for every $100 of value. If the tax is paid before March 1, 4%
of the normal tax is given as a discount. How much tax is paid if the condominium owner takes advantage of the discount?
The tax paid by the condominium owner is $2,632.88.
What is the tax paid?
Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.
Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.
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