Answer:
The standard form of the equation is y = 2x^2 + 16x + 25
Step-by-step explanation:
To find the standard form, first square the parenthesis.
y = 2(x + 4)^2 - 7
y = 2(x^2 + -8x + 16) - 7
Now distribute the 2
y = 2(x^2 + 8x + 16) - 7
y = 2x^2 + 16x + 32 - 7
Now combine like terms
y = 2x^2 + 16x + 32 - 7
y = 2x^2 + 16x + 25
Answer:
y = 2x^2 + 16x + 25
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
A. (1,-1); maximum
B. (-1,1); minimum
C. (-1,1); maximum
D. (1,-1); minimum
The correct answer is d
The vertex of the graph is at minimum or maximum option (D) (1, -1); the minimum is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have shown a graph of a parabola in the picture.
As the graph opens up and has a vertex at (1, -1)
The minimum value of graph,
At x = 1
y = -1
Thus, the vertex of the graph is at minimum or maximum option (D) (1, -1); the minimum is correct.
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A square has a perimeter of 36 units. One vertex of the square is located at (3, 5) on the coordinate grid. What could be the x- and y-coordinates of another vertex of the square?
Answer:
(3,-5)
Step-by-step explanation:
Answer with explanation:
Perimeter of Square = 36 units
Also, Perimeter of Square =4 × Side
→4 × Side=36
Dividing both sides by ,4 we get
Side of Square = 9 units
Length of Diagonal of square having side a, =√2 a
Length of Diagonal of Square having side , 9 units =9 √2 units
One Vertex of the Square =(3,5)
As , All Interior Angles of Square measures 90°.
So, Other vertices of Square will be, (3,-4),(-6,-4) and (-6,5).
Find the area of the trapezoid by decomposing it into other shapes.
A)
25.5 cm2
B)
27.5 cm2
C)
32.5 cm 2
D)
35.5 cm2
The answer is A) 25.5 cm2.
x = 2t
y = t + 5, -2 ≤ t ≤ 3
Can you please graph this
Answer:
See attachment
Step-by-step explanation:
The given parametric equations are;
[tex]x=2t[/tex] and [tex]y=t+5[/tex], [tex]-2\le t\le 3[/tex].
We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.
Plotting points;
When [tex]t=-2[/tex],
[tex]x=2(-2)=4[/tex] and [tex]y=-2+5=3[/tex]
This gives the point (-4,3).
When [tex]t=0[/tex]
[tex]x=2(0)=0[/tex] and [tex]y=0+5=5[/tex]
This gives the point (0,5).
When [tex]t=3[/tex]
[tex]x=2(3)=6[/tex] and [tex]y=3+5=8[/tex]
This gives the point (6,8).
We plot these points and draw a straight line through them.
Eliminating the parameter.
[tex]x=2t[/tex]
[tex]y=t+5[/tex]
Make t the subject in the second equation;
[tex]t=y-5[/tex]
Substitute into the first equation;
[tex]x=2(y-5)[/tex]
This implies that;
[tex]x=2y-10[/tex]
[tex]y=\frac{1}{2}x+5[/tex]
This is an equation of a straight line with slope [tex]\frac{1}{2}[/tex] and y-intercept 5 on the interval
[tex]-4\le x \le 6[/tex]
Answer:
The answer is in attachment
Step-by-step explanation:
First step finde a function t(x) ⇒ t=x/2;
Now we need to finde the limits of that function:
if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6
Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6
Solve x^2+5x=-6 please solve this using quadratics
x2 + 5x + 6 = 0
(x + 2)(x + 3) = 0
x = -2 or -3
Answer:
x = - 3, x = - 2
Step-by-step explanation:
Given
x² + 5x = - 6 ( add 6 to both sides )
x² + 5x + 6 = 0 ← in standard form
(x + 3)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 2 = 0 ⇒ x = - 2
All possible solutions for -6k < -12
ANSWER
All possible solutions are
[tex]k \: > \: 2[/tex]
EXPLANATION
The given inequality is
[tex] - 6k \: < \: - 12[/tex]
Divide both sides by -6 and reverse the inequality sign.
[tex] k \: > \: \frac{ - 12}{ - 6} [/tex]
[tex]k \: > \: 2[/tex]
All real numbers greater than 2.
a) As x decreases within bound, f(x) increases without bound.
b) As x decreases without bound,f(x) approaches zero
c) as x increases without bound,f(x) approaches the line y = - 4
d) as x decreases without bound,f(x) approaches the line y = - 4
Answer:
a) As x decreases within bound, f(x) increases without bound.
c) as x increases without bound,f(x) approaches the line y = - 4
Step-by-step explanation:
From the graph, we can see, as x becomes more negative, y gets larger and larger.
As x→ -∞, y → ∞
As x decreases without bound, y increases without bound
We can also see as x gets larger and larger, y gets closer to -4
As x →∞, y → -4
As x increases without bound, y approaches -4
As x decreases within a limit, f(x) increases without bound.
Explanation:The correct statement in this question is a) As x decreases within bound, f(x) increases without bound.
To understand this concept better, we can look at the graph of the function y = 1/x. As x approaches zero (within the bound), the value of y increases without bound, meaning it becomes very large and approaches infinity.
Other functions can also exhibit similar behavior where as x decreases within a limit, the corresponding values of f(x) increase without bound.
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Find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°)
Answer:
-8i
Step-by-step explanation:
To multiply numbers is polar form
z1 = r1 ( cos theta 1 + i sin theta 1)
z2 = r2 ( cos theta 2 + i sin theta 2)
z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)
z1 = 2(cos 70° + i sin 70°)
z2 = 4(cos 200+ i sin 200)
z1z2 = 2*4 (cos (70+200) + i sin (70+200)
z1z2 = 8 (cos(270) + i sin (270))
= 8 (0 + i (-1))
=-8i
The product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), is found by multiplying the moduli and adding the angles, resulting in -8i.
To find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), we use the properties of complex numbers in trigonometric form. According to the properties, the product of two complex numbers in this form is given by multiplying their moduli (or absolute values) and adding their angles.
The product is: |z1||z2| e[tex]^{(i(angle1+angle2)),}[/tex] where |z1|, |z2| are the moduli of z1 and z2, and angle1, angle2 are the angles of z1 and z2 respectively.
For z1 and z2, we have:
|z1| = 2Angle1 = 70°|z2| = 4Angle2 = 200°The product is:
|z1||z2| = 2 * 4 = 8
Sum of the angles: angle1 + angle2 = 70° + 200° = 270°
Therefore, z1z2 = 8(cos 270° + i sin 270°), and since cos 270° = 0 and sin 270° = -1, the product simplifies to z1z2 = 8i(-1) = -8i.
The function table shows the rule y = 3x + 5. Which number correctly completes the table?
Answer:
the answer is 3
Step-by-step explanation:
11-8=3
17-11=6
6/2=3
Answer:the answer is 14 just took the test
Step-by-step explanation:
Is parallelogram a rectangle
Answer:
Sometimes, but not always.
Step-by-step explanation:
A parallelogram is a quadrilateral with two pairs of parallel sides, but there are no requirements for its interior angles. A rectangle, on the other hand, must have four interior 90 degree angles. So a rectangle is always a parallelogram, but a parallelogram is not always a rectangle.
A parallelogram is usually defined as a quadrilateral with 2 pairs of equal, opposite and parallel sides. It can also form right angles between adjacent sides. Therefore, not all rectangles are squares, not all parallelograms are rectangles.
Hope I could help! :)
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Solve the given system of equations.
4x-5y=10
-x-8=3y
To solve the system of equations, start by isolating one variable in one equation. Substitute the value of the variable into the other equation, and solve for the remaining variable. The solution to the system of equations is x = 118/17 and y = -42/17.
Explanation:To solve the given system of equations:
4x - 5y = 10
-x - 8 = 3y
Start by isolating one variable in one equation. Let's isolate x in the second equation.Add x to both sides: -x + x - 8 = 3y + x.Simplify: -8 = 3y + x.Rewrite the equation as x = -8 - 3y.Now substitute the value of x in the first equation.Replace x with -8 - 3y: 4(-8 - 3y) - 5y = 10.Distribute: -32 - 12y - 5y = 10.Combine like terms: -32 - 17y = 10.Add 32 to both sides: -17y = 42.Divide by -17: y = -42/17.Substitute the value of y back into x = -8 - 3y to find x.Replace y with -42/17: x = -8 - 3(-42/17).Simplify: x = -8 + 126/17.Find a common denominator for -8 and 126/17, which is 17.Convert -8 into a fraction over 17: -8/17.Add the fractions: x = (-8/17) + (126/17).Simplify: x = (118/17).Therefore, the solution to the system of equations is x = 118/17 and y = -42/17.
Final answer:
The solution to the system is x = -10/7 and y = -22/7.
Explanation:
To solve the given system of equations, 4x-5y=10 and -x-8=3y, we can use the method of substitution or elimination. Let's use the substitution method:
Step 1: Solve one equation for one variable in terms of the other. From the second equation, we can rearrange it to get x in terms of y: x = 3y + 8.
Step 2: Substitute the expression for x in terms of y into the other equation.
Substituting 3y + 8 for x in the first equation gives us 4(3y + 8) - 5y = 10.
Step 3: Simplify and solve for y.
Expanding the equation and solving for y gives us 12y + 32 - 5y = 10.
Combining like terms yields 7y + 32 = 10.
Subtracting 32 from both sides gives us 7y = -22.
Dividing both sides by 7 gives us y = -22/7.
Step 4: Substitute the found value of y back into the equation x = 3y + 8 to solve for x.
Substituting -22/7 for y gives us x = 3(-22/7) + 8.
Simplifying the expression gives us x = -66/7 + 56/7, which equals -10/7.
Therefore, the solution to the system of equations is x = -10/7 and y = -22/7.
what is the area of this figure enter your answer in the box.
PLEASE HELP ME!?
Answer:
its 18 inchs in diamatr
Step-by-step explanation:
The area of the figure is 400 in.
Find the sum of the finite geometric sequence
Answer:
45
Step-by-step explanation:
Use the geometric sum formula for in infinite sum. 20 terms of this basic formula is close enough The 20th term is 8.6 * 10^-10 which means this goes out to a number with 9 zeros after the decimal and before the 8.
Put another way, the tenth number of this series is the only one affected.
When you use a spreadsheet, it seems to know that the answer is 3/2 as the solution to the sum.
Solution.
Sum = a / (1 - r)
a = 1
r = 1/3
Sum = 1 / (1 - 1/3)
Sum = 1 // 2/3
sum = 3/2
Now you can worry about the 30.
30 * sum(1/3)^n = 30* 3/2 = 45
If there is something you want more information on, leave a note.
The sum of a finite geometric sequence can be calculated using the formula S = a1(1 - r^n) / (1 - r), where S is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.
Explanation:The student's question pertains to the summation of a finite geometric sequence. A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Considering the information provided doesn't match the exact question, we would educate the student on how to find the sum of a finite geometric sequence using the standard formula for such a sum, which is S = a1(1 - r^n) / (1 - r), where S is the sum of the sequence, a1 is the first term, r is the common ratio, and n is the number of terms.
Unfortunately, specific values were not provided in the question. Therefore, to calculate the sum, we'd need the initial term, the ratio, and the number of terms. This formula is only applicable if the common ratio r is not equal to 1. Essential to note is that if the common ratio is greater than 1, the terms in the sequence increase, and if the ratio is between 0 and 1, the terms decrease.
What is the answer to number 1
Solve the equation 2 cos ( x ) + 1 = 0 2 cos x + 1 = 0 , 0 ≤ x ≤ 2 π 0 ≤ x ≤ 2 π . Show all of your work
Answer:
2π/3, 4π/3
Step-by-step explanation:
I interpret your question as asking us to solve the equation
2cos(x) + 1 = 0
2cos(x) = -1
cos(x) = -½x
x = arccos(-½), 0 ≤ x ≤2π
Since the cosine is negative, x must be in the second or third quadrant.
Referring to the unit circle, we find that
x = 2π/3 (120°) or x = 4π/3 (240°)
A woman wants to make a 4 inch wide copy of a drawing that is 5 inch wide. On the photo copier, what percent setting should she use to make a copy this size
A 5%
B 80%
C 90%
D 125%
Answer:
B 80 %
Step-by-step explanation:
She wants to reduce the size of the drawing, so the setting should be a proper fraction.
Setting = 4/5
Multiply numerator and denominator by 20 = 80/100
Convert to percent = 80 %
The setting should be 80 %.
Answer:
80%
Step-by-step explanation:
4/5 multiply them together and it equals 20
then multiply 4 and 5 by 20 which will get you
80/100 so.. convert it to percentage and you get...
80%
what is the value of the expression
2 1/4 divided by 1 2/5
Answer:
Step-by-step explanation:
2 1/4 divided by 1 2/5
8/4 + 1/4 divded by 5/5 +2/5
9/4 divided by 7/5
9/4 times 5/7
9 times 5 over 4 times 7
45 over 28
which equation is represented by the graph below ?
Answer:
C) y = ln(x) + 4
Step-by-step explanation:
The equation can't be A or B, because they are exponential functions, and they can have negative x-values.
It must be one of the two ln functions, because they can't have negative values of x.
To decide between C and D, insert a value of x that makes it easy to calculate the value of y.
Let x = 1.
For Equation C,
y = ln(1) + 4 = 0 + 4 = 4
For Equation D,
y = ln(1) + 5 = 0 + 5 = 5
We draw a vertical line from x = 1 and see where it intersects the graph.
The intersection is at (1, 4), so the correct equation is
y = ln(x) + 4
Four brothers and their sister have the average age 7. Four brothers have the average age 6. How old is the sister?
Answer:
11 years old
Step-by-step explanation:
If four brothers have the average age 6, then the sum of their ages is
[tex]4\cdot 6=24[/tex]
years.
Let x years be the age of sister. If four brothers and their sister have the average age 7, then
[tex]\dfrac{24+x}{5}=7.[/tex]
Multiply this equation by 5:
[tex]24+x=35\Rightarrow x=35-24=11.[/tex]
The sister is 11 years old.
Which of the following is not a measure of central tendency?
A. Mean
B. Median
C. Range
D. Mode
Answer:
Range
Step-by-step explanation:
suppose the linear regression line y= 2.4x + 3.1 predicts the time,in minutes it takes you to be served at a food stand if there are x people in line ahead of you. About how much time would it take you to be served if there are 3 people in line ahead of you?
Using the linear regression equation y = 2.4x + 3.1, substituting '3' for 'x' results in a predicted wait time of approximately 10.3 minutes when there are 3 people in line ahead of you.
Explanation:To calculate the time it would take to be served at a food stand if there are 3 people in line ahead of you, we will use the given linear regression equation y = 2.4x + 3.1.
Plugging in the value of 3 for x (which represents the number of people in line), we get the result as:
y = (2.4 * 3) + 3.1
y = 7.2 + 3.1
y = 10.3 minutes
Therefore, according to the regression line, it will take approximately 10.3 minutes for you to be served if there are 3 people in line ahead of you.
Final answer:
To determine the service time with 3 people in line, substitute 3 into the regression equation y = 2.4x + 3.1 to get y = 2.4(3) + 3.1, which calculates to approximately 10.3 minutes.
Explanation:
The question involves using a linear regression line to predict the time it would take to be served at a food stand based on the number of people in line ahead. The given linear regression equation is y = 2.4x + 3.1, where y represents the time to be served in minutes and x represents the number of people in line. To find the time it would take to be served when there are 3 people in line ahead, simply substitute 3 for x in the equation:
y = 2.4(3) + 3.1
= 7.2 + 3.1
= 10.3 minutes.
So, it would take approximately 10.3 minutes to be served if there are 3 people in line ahead of you.
A living room has a circular rug. According to a small tag, the rug has a circumference of 6.28 yards. What is the rug's radius? Use 3.14 for .
To find the radius of the circular rug with a circumference of 6.28 yards, the formula r = C / (2π) is used, where π is approximated as 3.14. By substituting the given circumference into the formula, the radius is calculated to be 1 yard.
Explanation:The question is asking to calculate the radius of a circular rug given its circumference. The formula for the circumference of a circle is C = 2πr, where C is the circumference, π (pi) generally approximated as 3.14, and r is the radius of the circle. To find the radius, we rearrange the formula to solve for r: r = C / (2π).
In this case, the circumference is given as 6.28 yards. Using the formula:
r = 6.28 yards / (2 × 3.14)
r = 6.28 / 6.28
r = 1 yard
Therefore, the radius of the circular rug is 1 yard.
the area of a parallelogram is 36x^6y^5. if the base of the parallelogram is 3xy^2 units,what is the height of the parallelogram
Answer:
h = 12x^5y^3
Step-by-step explanation:
The area of a parallelogram is found using A = b*h. Substitute the values given and solve for h.
A = b*h
36x^6 y^5 = 3xy^2 * h
36x^6 y^5 ÷ 3xy^2 = h
12x^5y^3 = h
what does this number represent
answer is: a number to the third power divided by ten. pls mark brainliest!!
Graph this line using the slope and y
-intercept:
y
=
-
1
7
x
+
8
Click to select points on the graph.
Answer:
The expression is
y = -17*x + 8
Which is already in the slope intercept form
y = m*x + b
Where m is the slope and b is the y-intercept.
The slope
m = -17
The intercept
b = 8
Please see attached picture for graph
Select all the correct locations on the table
Answer:
(i) Exponential Decay
(ii)linear
(iii)Exponential Growth
Step-by-step explanation:
(i)
Cost of the van=$25,000.
After 2 years, value of van=$17,500.
After 4 years, value of van = $12,250.
Its a decay but to be a exponential decay it must have constant rate.
As its known the exponential decay formula is [tex]C=C_{0} e^{-kt}[/tex]
Now substitute the values in the above formula
[tex]17500=25000 e^{-k*2}[/tex]
Now on simplification, we get
[tex]k=0.1783[/tex]
Now again apply the same formula for the next time interval
[tex]12250=25000 e^{-k*4}[/tex]
Now on simplification, we get
[tex]k=0.1783[/tex]
Since the value of k is constant for both the time interval. Hence the decays is exponential.
(ii)
At the beginning, battery life=100%.
After 3 Hours, battery life=60%.
After 6 Hours, battery life = 20%.
Since the value of battery life decreases by 40% in each interval. Hence the decay of battery life is linear.
(iii)
Initial population=20.
After 5 years, population=30.
After 10 years, population = 45.
Its a growth but to be a exponential growth it must have constant rate.
As its known the exponential growth formula is [tex]P=P_{0} e^{kt}[/tex]
Now substitute the values in the above formula
[tex]30=20 e^{-k*5}[/tex]
Now on simplification, we get
[tex]k=-0.081[/tex]
Now again apply the same formula for the next time interval
[tex]45=20 e^{-k*10}[/tex]
Now on simplification, we get
[tex]k=-0.081[/tex]
Since the value of k is constant for both the time interval. Hence the decays is exponential.
help me with this I really need help
Answer:
i think it is 19 is the whole number 9/40 is the remainder
Step-by-step explanation:
Probability 0.1 0.3 0.2 0.2 0.1 0.1 Which is the expected value of the random variable with the given probability distribution? a. 17 c. 17.8 b. 17.2
Answer:
it is going to be a
Step-by-step explanation:
but u have to add the number and move your demical
Answer:
Option b 17.2
Step-by-step explanation:
Given is a probability distribution of a random variable say x in table form.We have to find the mean.
All probabilities lie between 0 and 1 and add to 1.
Hence this is a valid prob distribution.
To find mean we multiply the random variable x value with probability and add.
Mean = E(X) = [tex]\Sigma p_i x_i = 15(0.1)+16(0.3)+17(0.2)+18(0.2)+19(0.1)+20(0.1)\\=1.5+4.8+3.4+3.6+1.9+2\\= 17.2[/tex]
Hence option b is right answer.
3v/7=6, then v=
a) 1-2/3
b) 2-4/7
c) 14
d) 42
Answer:
c) 14
Step-by-step explanation:
The given equation is [tex]\frac{3v}{7}=6[/tex].
We need to solve this equation for v, so we multiply both sides of the equation by the multiplicative inverse of [tex]\frac{3}{7}[/tex] which is [tex]\frac{7}{3}[/tex] to obtain;
[tex]\frac{7}{3} \times \frac{3v}{7}=6\times \frac{7}{3}[/tex].
We simplify to obtain;
[tex]v=2\times 7[/tex]
[tex]v=14[/tex]
The correct choice is C.
Answer: option c
Step-by-step explanation:
To solve this problem you must apply the following proccedure:
- Multiply both sides of the equation by 7.
- Divide both sides of the equation by 3.
Therefore, keeping the steps above on mind, you obtain the result shown below:
[tex]\frac{3v}{7}=6\\\\(7)\frac{3v}{7}=6(7)\\\\3v=42\\\\\frac{3v}{3}=\frac{42}{3}\\ v=14[/tex]
Which of the following are solutions to the equation below? 6x 2 - 2x + 36 = 5x 2 + 10x
6, 6 are the solutions of the given equation.
What is equation ?
It is a mathematical statement which contains two algebraic expressions on both sides of an ' = ' sign.
Equation shows the equality between the expressions in left hand and right hand side.
What is the solution of given equation ?The given equation is [tex]6x^{2} -2x+36=5x^{2} +10x[/tex]
Solving the equation, [tex]6x^{2} -5x^{2} -2x-10x+36=0[/tex]
⇒ [tex]x^{2} -12x+36=0[/tex]
⇒ [tex](x-6)^{2} =0[/tex]
∴ The equation have double root, the values of x are 6, 6
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