Answer:
Option 4.
Step-by-step explanation:
The information is that the points G and H are the midpoints of ED and EF.
For example G will be (5 + (-2))/ 2 , (4 - 0) / 2 which is (1.5, 2).
If we calculate H it is (6.5, -3).
The answer is option 4.
Write an expression for this phrase, the evaluate it: Seven plus the sum of five and three tenths and two and two tenths
7 + [3+ (3/10)] + [2 + (2/10)] is an expression for this phrase. , and the score is 14.5.
What is meant by expression?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the terms 4m and 5 are separated by the arithmetic sign + and m is the variable of the given expression.Therefore,
7 + [3+ (3/10) ] + [2 + (2/10)]
= 7 + ( 3 + 0.3 ) + (2 + 0.2 )
simplifying then we get,
=7 + 3.3 + 2.2
= 7 + 5.5
= 14.5
Hence, 7 + [3+ (3/10)] + [2 + (2/10)] is an expression for this phrase. , and the score is 14.5.
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The value of f(-2) is 2 while the equation f(x) = 4 has a solution of O
we have that
For x=2
the value of the function f(x) is equal to 2
while
f(x)=4 is when the value of x is equal to zero
Solve the system by substitution.5x - 2y + 3z =62x - 4y - 3z = - 23X + 6y - 8z = 1X =Y =Z =
X=1
Y=4
Z=3
Explanation
\(\begin{gathered} 5x-2y+3z=6\Rightarrow equation(1) \\ 2x-4y-3z=-23\Rightarrow equation(1) \\ x+6y-8z=1\Rightarrow equation(1) \end{gathered}\)
Step 1
b) isolate the x variable in equaiton (1) and equation(2)
so
\(\begin{gathered} 5x-2y+3z=6\Rightarrow equation(1) \\ \text{add 2y in both sides} \\ 5x-2y+3z+2y=6+2y \\ 5x+3z=6+2y \\ \text{subtract 3z in both sides} \\ 5x+3z-3z=6+2y-3z \\ 5x=6+2y-3z \\ \text{divide both sides by 5} \\ \frac{5x}{5}=\frac{6+2y-3z}{5} \\ x=\frac{6+2y-3z}{5}\Rightarrow equation(1A) \end{gathered}\)and
\(\begin{gathered} 2x-4y-3z=-23\Rightarrow equation(2) \\ 2x=-23+4y+3z \\ x=\frac{-23+4y+3z}{2} \end{gathered}\)b) now replace x value from equaton (1) into equation (3)
\(\begin{gathered} x+6y-8z=1 \\ \frac{6+2y-3z}{5}+6y-8z=1 \\ \frac{6+2y-3z}{5}=1-6y+8z \\ 6+2y-3z=5(1-6y+8z) \\ 6+2y-3z=5-30y+40z \\ 6-5+2y+30y-3z-40z=0 \\ 1+32y-43z=0 \\ 32y-43z=-1\Rightarrow equation(4) \end{gathered}\)c) now replace x value from equaton (2) into equation (3)
\(\begin{gathered} x+6y-8z=1 \\ \frac{-23+4y+3z}{2}+6y-8z=1 \\ \frac{-23+4y+3z}{2}=1-6y+8z \\ -23+4y+3z=2(1-6y+8z) \\ -23+4y+3z=2-12y+16z \\ -23+4y+3z-2+12y-16z=0 \\ -25+16y-13z=0 \\ 16y-13z=25\Rightarrow equation(5) \end{gathered}\)Step 2
now, use equation (4) and equation(5) to
\(\begin{gathered} 32y-43z=-1\Rightarrow equation(4) \\ 16y-13z=25\Rightarrow equation(5) \end{gathered}\)a) isolate the y value from equation(1) and substitute into equation(2)
z=
\(\begin{gathered} 32y-43z=-1\Rightarrow equation(4) \\ 32y=-1+43z \\ y=\frac{-1+43z}{32} \\ \text{replace in eq(5)} \\ 16y-13z=25\Rightarrow equation(5) \\ 16(\frac{-1+43z}{32})-13z=25 \\ (\frac{-1+43z}{2})-13z=25 \\ (\frac{-1+43z}{2})=25+13z \\ -1+43z=2(25+13z) \\ -1+43z=50+26z \\ 43z-26z=50+1 \\ 17z=51 \\ z=\frac{51}{17} \\ z=3 \end{gathered}\)so
Z= 3
b) replace the z value in equation (4) to find z
\(\begin{gathered} 32y-43z=-1\Rightarrow equation(4) \\ 32y-43(3)=-1 \\ 32y=-1+129 \\ 32y=128 \\ y=4 \\ \end{gathered}\)Y=4
c) finally,l replace the Z and Y value in equation (1A)
\(\begin{gathered} x=\frac{6+2y-3z}{5}\Rightarrow equation(1A) \\ x=\frac{6+2(4)-3(3)}{5} \\ x=\frac{6+8-9}{5}=\frac{5}{5}=1 \end{gathered}\)so
X=1
therefore, the answer is
X=1
Y=4
Z=3
I hope this helps you
Please helppppppppp!!!!!!!!
Answer:
1. f(12), 2. F(m)=2500, 3. F(v)>_3000, 4. 0.9f(30)
Step-by-step explanation:
1. Amtrak reduced its round-trip ticket from Sacramento to San Francisco by $49. The sale price was $140. What was the original price?
Therefore , the solution of the given problem of unitary method comes out to be the round-trip ticket's initial cost was $189.
What precisely is a unified method?To finish a job using a unitary method, multiply the result by two after calculating the dimension of this tiny subsection. The unit technique, put simply, removes a planned object from a specific set along with subsets of pixels. 40 pens, for instance, variable would cost Rs and kg ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. It is possible to respond and include (mathematics, algebra).
Here,
Let's name the round-trip ticket's initial cost "x". The sale price was: because we know Amtrak lowered the cost by $49, which was:
=> x - 49 = 140
We can add 49 to both sides of the calculation to find x:
=> x - 49 + 49 = 140 + 49
Simplifying:
=> x = 189
Consequently, the round-trip ticket's initial cost was $189.
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What kind of graph is this ?
A. Positive
B. Negative
C. Zero
D. Undefined
Answer:
B. Negative
Step-by-step explanation:
Line is going downwards
What is the slope of the line segment that passes through
points (1,3) and (5, 13)?
Answer: 5/2
Step-by-step explanation:
slope equation: (y2-y1)/(x2-x1)
13-3/5-1 = 10/4 or 5/2
Answer:
2.5
Step-by-step explanation:
Gradient (slope) =
\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)
y=9/4×2
sketch the graph of f and f on the same set of axes
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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i buy 5 metres of cloth at x per metre. How much change will i get from 7,000 NGN
Answer:
charge it 1400 per meter
Step-by-step explanation:
given data
rate = x per meter
cloth = 5 meter
price = 7000
solution
we get here change that i get is x
we get 5 meter at x rate so
5 × x = 7000 ...........1
x = \(\frac{7000}{5}\)
x =
so we charge it 1400 per meter
helpp!!!
A package of balloons contains 4 red, 6 blue, 3 yellow, and 5 orange balloons. Javier will randomly choose one balloon from the package to blow up. He then will randomly choose a second balloon to blow up. What is the probability that Javier chooses an orange balloon and then a yellow balloon?
A 5/108
В. 5/ 102
с. 1/15
D. 1/6
e. 4/9
Answer:
in my opinion the answer is 78
Step-by-step explanation:
you divide all of them then add akll tof them simple
A triangle. A ABC, has angle measures of 82*, 75, and 23' and no sides equal (congruent) in length. How would this triangle be
classified?
Equilateral right
Isosceles obtuse
O Scalene acute
Isosceles acute
The triangle given is a scalene acute triangle
Classification of TriangleA triangle can be classified based on the measures of its angles and the lengths of its sides.
In this case, the angle measures of the triangle are 82, 75, and 23 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can verify that these angles satisfy this condition: 82 + 75 + 23 = 180.
The triangle is not an equilateral triangle because all the sides are not of equal length.
The triangle also doesn't have one right angle so it can't be right triangle.
Now, as per the angle measures, none of the angles are right angles, but one angle is greater than 90 degree, so this triangle is not acute triangle.
So, this triangle is not an Obtuse triangle since it has no angle greater than 90 degrees.
As the triangle has no sides of equal length, it is also a Scalene triangle.
Therefore, the triangle would be classified as a Scalene acute triangle (c).
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The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
12 5/25 as a mixed number in simpllest t form
Answer:
305/25
Step-by-step explanation:
12*25 = 300
300 + 5 = 305
305/25 = 25.41
therefore 305/25 is simplest
I GIVE BRAINLIEST FOR ANSWERS AND EXPLANATION
-
Which expression is equivalent to (-11x² + 1.4x − 3) + (4x² - 2.7x+8)?
A. -7x²-1.3x+5
B. -7x2 +1.3x+5
C. 7x²-1.3x+5
D. 7x² +1.3x+5
Answer: the answer is A.
Max has three blue and two red shirts. On each day of the three days,Monday,Tuesday and Wednesday, he selects one shirt at random to wear. Max wears each shirt that he selects only once.
i)what is the probability that Maxwell will wear a blue shirt on Monday?
ii)what is the probability that Maxwell will wear a shirt of the same color on all three days?
iii)What is the probability that Maxwell will not wear a shirt of the same color on consecutive days?
Answer:
Step-by-step explanation:
i) 3/5 3blue shirts out of 5 possible options
ii) (3/5)(2/4)(1/3) = 6/60 = 1/10
this must be a blue shirt as there are not enough red shirts to complete the task.
iii) possible options brb or rbr
3/5(2/4)2/3 + 2/5(3/4)1/3 = 12/60 + 6/60 = 18/60 = 3/10
Solve the system of equations
3x-y=6
6x+y=21
Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation
Find domain
Range
Y-intercept
Xi intercept
Vertical asymptote
Horizontal asymptote
Pic attached below
The domain and range of the function f(x) = 3/x + 2 are (-∞, 0) ∪ (0, ∞) and (-∞, 2) ∪ (2, ∞). The vertical and horizontal asymptotes are x = 0 and y = 2 respectively
What is the domain and range of a functionIn mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.
To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.
The function f(x) = 3/x + 2
The domain of the function is (-∞, 0) ∪ (0, ∞)
The range of the function is (-∞, 2) ∪ (2, ∞)
The x - intercept is (-3/2, 0)
The y - intercept does not exist
The vertical asymptotes is x = 0
The horizontal asymptotes is y = 2
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Can you explain to me how did we get the answer
The end behavior of the polynomials are as follows;
(a) y = x³ - 9·x² + 8·x - 14
End behavior; y → ∞ as x → ∞
\({}\) y → -∞ as x → -∞
(b) y = -8·x⁴ + 13·x + 800
End behavior; y → -∞ as x → -∞
\({}\) y → -∞ as x → ∞
What is the end behavior of a a polynomial?The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.
The factors that effect the end behavior of a polynomial are;
The degree of the polynomial, (even or odd)
The sign of the leading coefficient of the polynomial (positive or negative)
The leading coefficient is the coefficient of the term with the highest degree.
(a) The polynomial, function, y = x³ - 9·x² + 8·x - 14
The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;
y tends to positive infinity as x tends to positive infinity
y tends to negative infinity as x tends to negative infinity
End behavior;
y → ∞ as x → ∞
y → -∞ as x → -∞
(b) The polynomial function can be expressed as follows;
y = -8·x⁴ + 13·x + 800
The above polynomial of degree 4 is an even degree polynomial
The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative
The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;
y-values approaches negative infinity as x approaches negative infinity
y-values approaches negative infinity as x approaches positive infinity
End behavior;
y → -∞ as x → -∞
y → -∞ as x → ∞
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PLEASE HELP ME ASAP!!
Answer:
Equation 8+4 12+4 16+4 M=8 B=20 Your welcome
Step-by-step explanation:
David has available 40 yards of fencing and wishes to enclose a rectangular area.
Answer:
5 units will be your width and 15 will be your length so it would look like side#1=5 side #2=15 side number3 is 5 and side number 4 is 15 assuming that side 1 and 3 are parallel.
Step-by-step explanation:
yes
A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
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A woman can invest some money at 10% simple interest or at 8% compound interest. If
she invests $8000 for 3 years, find which is the more profitable investment and by how much.
Answer:
3/12 percent
Step-by-step explanation:
Which sequence of transformations was applied to the parent tangent function to create the function m(x) = 2tan(3x+4)
The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.
To determine the sequence of transformations, let's break down the given function:
1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.
2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.
3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.
4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.
5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.
In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.
Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.
After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)
This example helps illustrate the effect of the transformations on the graph of the function.
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what is the product of 2.17 and 1.5
Answer:
3.255 or 3.67
Step-by-step explanation:
MATHS -_-
Answer:
The answer is 3.255
Step-by-step explanation:
When the word product is being used it means that the operation you will be doing is multiplication.So it would be 2.17 x 1.5 and when you multiply them you get 3.255
hope that helped buddy :)
Lily invested $60,000 in an account paying an interest rate of 6 1 2 6 2 1 % compounded continuously. Lydia invested $60,000 in an account paying an interest rate of 6 1 8 6 8 1 % compounded monthly. To the nearest hundredth of a year, how much longer would it take for Lydia's money to triple than for Lily's money to triple?
Using interest equations, it is found that it will take 1.08 year more for Lydia's money to triple than for Lily's.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.What is the amount in continuous compounding?It is given by:
\(A(t) = Pe^{rt}\)
For Lily, the parameters are as follows: r = 0.065, with continuous compounding. The time to triple is t for which A(t) = 3P, hence:
\(A(t) = Pe^{rt}\)
\(3P = Pe^{0.065t}\)
\(e^{0.065t} = 3\)
\(\ln{e^{0.065t}} = \ln{3}\)
\(0.065t = \ln{3}\)
\(t = \frac{\ln{3}}{0.065}\)
\(t = 16.90\).
For Lydia, using compound interest, the parameters are: r = 0.06125, n = 12, hence:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
\(3P = P\left(1 + \frac{0.06125}{12}\right)^{12t}\)
\((1.00510416667)^{12t} = 3\)
\(\log{(1.00510416667)^{12t}} = \log{3}\)
\(12t\log{(1.00510416667)} = \log{3}\)
\(t = \frac{\log{3}}{12\log{(1.00510416667)}}\)
\(t = 17.98\)
17.98 - 16.9 = 1.08, hence, it will take 1.08 year more for Lydia's money to triple than for Lily's.
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where is the point (0, –4) located
4 points below the origin
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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Find the exact length of the curve. x = 1/3√y(y - 3), 4 ≤ y ≤ 16.
The exact length of the given curve is 62/3
We can calculate the above answer by following the steps given below,
We have been given the following values,
x = 1/3 √y (y - 3), 4 ≤ y ≤ 16
The curve is of the length, x = f(y) from y =a to y = b is given by:
x = 1/3 √y (y - 3)
x = 1/3 (- 3)
dx/dy = 1/3 [(3/2)- (3/2)]
= 1/3 [(3/2) - (3/2)]
= 1/2 [ - 1/]
= (y-1)/2√y = f'(y)
Now we will calculate the length of the curve
= \(\int\limits^a_b {\sqrt{1+f'(y)^{2} } } \, dy\)
= \(\int\limits^a_b{\sqrt{1+ (\frac{y-1}{2\sqrt{y} } )^2} } \, dy\) (here a= 4, b=16)
= \(\int\limits^{16} _4 {\sqrt{1+ (\frac{y^2+2y-1}{4y} } )^} } \, dy\)
= \(\int\limits^{16} _4 {\sqrt{\frac{4y+ y^2+ 2y-1}{4y} } } \, dy\)
= \(\int\limits^{16}_4 {\frac{y+1}{2\sqrt{y} } } \, dy\)
= \(\int\limits^{16}_4 {\frac{1}{2}\sqrt{y} } \, dy+ \int\limits^{16}_4 {\frac{1}{2\sqrt{y} } } \, dy\)
= [1/3 (64-8)] +[4-2]
= (56/3)+2
= 62/3
Therefore the exact length of the curve that we get after solving the equation for curve is x = 1/3, 4 ≤ y ≤ 16, is 62/3.
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Which number is composite?
53, 81, 41, 47,31
O41
81
31
47
Pls hurry its a test
Answer:
81
Step-by-step explanation:
A composite number is a number that can be divisible by more than 1.
81 can be divisible by 1 and 9.
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