Answer:
21
Step-by-step explanation:
[tex]3t-7=5t[/tex]
subtract 3t from both sides
[tex]-7 = 2t[/tex]
multiply both sides by 3
[tex]-21 = 6t[/tex]
so 6t = -21
What are the rational roots of ? x = 1, x = -1 x = 1, x = 0 x = 1, x = 2 This polynomial has no rational roots.
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°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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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 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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Please help I’m confused
Answer:
Step-by-step explanation:
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
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.
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]
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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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.
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
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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solve the following inequality ( algebra 1 )
Answer:
m<1 OR m>7
Step-by-step explanation:
3m<5-2
3m<3
m<1
m+1>8
m>8-1
m>7
Answer:
m<1 or m>7
Step-by-step explanation:
3m + 2 < 5
3m + 2-2 < 5-2
3m < 3
[tex]\frac{3m}{3}[/tex] < [tex]\frac{3}{3}[/tex]
m < 1
[tex]\frac{m+1}{2}[/tex] > 4
[tex]\frac{m+1}{2}[/tex]*2 > 4*2
m +1 > 8
m +1 -1 > 8 -1
m > 7
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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Vikram drinks 6/10 of a litter of water after gym class and 33/100 of a litter of juice with his lunch Vikram says he drank a total of 39 hundredths of a litter. use the drop-down menus to explain why Vikram is not correct?
Answer: Vikram is not incorrect because he found the sum by adding the numerators and denominators
Step-by-step explanation: The first blank doesn't have a word so I answer it
Another day, another math problem 2
Answer:
-7
Step-by-step explanation:
you can use power rule of derivatives for that.
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
How do i find the domain of F and write in interval notation??? I completely confused
Answer:
898
Step-by-step explanation:
898999
Find the next number in the sequence: 10, 37, 82, 145, 226,
Answer:
325
Step-by-step explanation:
10 is 3^2 + 1
37 is 6^2 + 1
82 is 9^2 + 1
145 is 12^2 + 1
226 is 15^2 + 1
325 is 18^2 + 1
325 is the next number in the sequence and is also the answer.
Draw a
box-and-whisker plot for the set of data.
27, 35, 44, 51, 52, 54, 56, 69, 69, 79, 80, 100, 100
a.
b.
C.
d.
0510 15 20 25 30 35 40 45 50 55 60 65 70
05 10 15 20 25 30 35 40
45 50-55
HHH
05
#2
0 5 10 15 20 25 30 35 40 45 50 55
60 65 70
60 65 70
10 15 20 25 30 35 40 45 50 55 60 65 70
75 80 85 90
75 80 85 90
75
75
95 100
80 85 90
95 100
80 85 90 95 100
95 100
Answer: B
Step-by-step explanation:
The maximum is 100 and the minimum is 27.
The only option that shows this is B.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
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
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.
--
A new element with atomic number 116 was discovered in 2000. In 2012 it was named livermorium, Lv. Although Lv is radioactive and short-lived, its chemical properties and reactivity should follow periodic trends.
a. Determine the electron configuration for the valence electrons of Lv in the ground state. (2 pts)
Answer:
7s²7p⁴
Step-by-step explanation:
Livermorium is located in the seventh period and sixteenth column of the periodic table. The noble gas configuration for livermorium is [Rn]7s²5f¹⁴6d¹⁰7p⁴. The valence electrons are the ones in the orbitals with the highest quantum number (coefficient). Remember, there can be up to 8 valence electrons at one time. Therefore, the valence electron configuration is 7s²7p⁴.
Let's check
116 is the atomic noElectronic configuration
1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶4f¹⁴6s²5d¹⁰6p⁶7s²5f¹⁴6d¹⁰7p⁴Valence electrons
7s²7p⁴The 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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Describe the graph of a quadratic function below given in table form
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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Triangle P R Q is shown. Angle R P Q is 39 degrees. The length of P R is 6, the length of R Q is p, and the length of P Q is 8.
Law of cosines: a2 = b2 + c2 – 2bccos(A)
Which equation correctly uses the law of cosines to solve for the missing side length of TrianglePQR?
62 = p2 + 82 – 2(p)(8)cos(39°)
p2 = 62 + 82 – 2(6)(8)cos(39°)
82 = 62 + p2 – 2(6)(p)cos(39°)
p2 = 62 + 62 – 2(6)(6)cos(39°)
According to law of cosines the length of RQ can be written as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].
Given the length PR is 6 , the length of RQ is p, the length of PQ is 8 and the angle RPQ is 39 degrees.
A length of the triangle can be written as according to law of cosines if sides are given and one angle is [tex]a^{2} =b^{2} +c^{2} -2bccos(A)[/tex]
We have to just put the values in the above equation.
as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].
p is the side opposite to angle given , the length of other sides are 6 and 8 and angle is 39 degrees.
Hence the side can be written as according to law of cosines if the angle is 39 degrees is as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].
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Answer: OPTION B
Step-by-step explanation:
edge22
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:
