a bike path is 6 3/4 miles long. what whole number is closest to 6 3/4
What is the length of the radius of a circle with a center at the origin and a point on the circle at 8 + 15i?
Answer:
Hence, the length of the radius of a circle with center at origin is 17 units.
Step-by-step explanation:
" We know that radius of a circle is any line segment joining center to any point on the circle ".
We have to find the length of the radius of a circle with a center at the origin i.e. (0,0) and a point on the circle at 8 + 15i i.e. at (8,15).
( Since any complex number of the form z=x+iy has a point in the coordinate plane as: (x,y) ).
Hence , we have to find the distance between the point (0,0) and (8,15).
The distance between two points (a,b) and (c,d) is given by:
[tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]
Here (a,b)=(0,0) and (c,d)=(8,15)
Hence distance between (0,0) and (8,15) is:
[tex]\sqrt{(0-8)^2+(0-15)^2\\} \\=\sqrt{(8)^2+(15)^2\\} \\=\sqrt{64+225}\\ \\=\sqrt{289}\\ \\=17[/tex]
Hence, the length of the radius of a circle with center at origin is 17 units.
Answer: 17
Step-by-step explanation: the length of the radius of a circle with center at origin is 17 units.
A Broadway musical was attended by a total of 2,838 people, including men, women, and children. The number of women who attended the event was 5 more than 3 times the number of children, while the number of men was 3 less than 4 times the number of women. Write an equation to model this situation. Then, use the equation to find the number of men, women, and children who attended the musical.
Five hummingbirds drink 7.5 ounces of sugar water a day. How much sugar water is needed for 14 hummingbirds?
Which of the binomials below is a factor of this trinomial?
4x2 + 20x - 24
A. x + 4
B. x + 1
C. x - 1
D. x - 4
Answer: the correct option is (C) x - 1.
Step-by-step explanation: We are given to select the correct binomial that is a factor of the following trinomial :
[tex]T=4x^2+20x-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.
From (i), we have
[tex]T\\\\=4x^2+20x-24\\\\=4x^2+24x-4x-24\\\\=4x(x+6)-4(x+6)\\\\=(x+6)(4x-4)\\\\=4(x+6)(x-1).[/tex]
So, the factors of the given trinomial are 4, (x + 6) and (x - 1).
Since 4 and ( x + 6) are not in the options, so (x - 1), is the correct binomial.
Thus, (C) is the correct option.
Which of the following are linear factors of px=x^3-2x^2-5x+6
write 4(x+2) using the distributive property
A whale has a tracking device attached to it. The whale traveled 184 miles in 6 hours. About how fast did the whale swim per hour?
Final answer:
To find the whale's average speed per hour, divide the total distance of 184 miles by the time of 6 hours, resulting in an average speed of approximately 30.67 miles per hour.
Explanation:
The question asks for the speed of a whale per hour based on a certain distance traveled over a period of time. To calculate the speed of the whale, we can use the formula:
Speed = Distance ÷ Time
In this case, the whale traveled 184 miles in 6 hours. Using the formula, we divide 184 miles by 6 hours:
Speed = 184 miles ÷ 6 hours = 30.67 miles per hour
So, the whale swam at an average speed of about 30.67 miles per hour.
A chef uses 3 3/4 pounds of semolina flour and 1 5/8 pounds whole wheat flour for each batch of pasta she makes. One week she uses a total of 86 pounds of flour.
Write an equation to solve for b, the number of batches of pasta the chef makes during the week.
How many batches of pasta does she make? Show your work.
To find the number of batches of pasta, convert the amount of flour per batch to an improper fraction, create an equation based on the total flour used, and solve for the number of batches, which is 16.
To solve for b, the number of batches of pasta the chef makes during the week using a total of 86 pounds of flour:
First, convert the amounts of each flour from mixed numbers to improper fractions:
1 5/8 pounds = 13/8 pounds
Now add the two amounts together to get the total flour used per batch:
(15/4) + (13/8) = 30/8 + 13/8 = 43/8 pounds per batch
The equation to solve for b is:
(43/8) * b = 86
To find b:
b = 86 / (43/8)
Multiply both sides by the reciprocal of 43/8:
b = 86 * (8/43)
b = (86 * 8) / 43
Calculate the value of b:
b = 688 / 43
b = 16
Write the quadratic equation in factored form. Be sure to write the entire equation. x2 - 5x - 24 = 0
x² - 5x - 24 = 0
First, we have to solve the quadratic equation and find the two values of x that fit the equation.
[tex]x = \frac{5+- \sqrt{5^{2} + 4*1*24 } }{2*1} = \frac{5+- \sqrt{25 + 96} }{2} = \frac{5+- \sqrt{121} }{2} = \frac{5+-11}{2} [/tex]
There are two values of x that fit:
x₁ = (5+11)/2 = 16/2 = 8
x₂ = (5-11)/2 = -6/2 = -3
Now I can restate the original equation in terms of a product of factors, with this product being equal to zero:
(x - x₁) * (x - x₂) = 0
ANSWER (x-8) * (x+3) = 0
Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations:
x - 8 = 0 or x + 3 = 0
x = 8 or x = -3
We can check that these two values are the solution to the original quadratic equation.
x² - 5x - 24 = 0
First value
8² -5*8 -24 = 0
64 - 40 -24 = 0
0 = 0 ¡Checked!
Second value
(-3)² -5(-3) -24 = 0
9 + 15 -24 = 0
0 = 0 ¡Checked!
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
Answer:
(x+3)(x-8)=0
Step-by-step explanation:
Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert untis of measurement?
Which expression is equivalent to 10b - 25? 10(b - 15) 5(b - 5) 5(5b - 20) 5(2b - 5)
what number is equivalent to -55i to the second power
Which formula can be used to describe the sequence?
-3, 3/5, -3/25, 3/125, -3/625
A. f(x) = -3(1/5)^x-1
B. f(x) = -3(1/5)^x-1
C. f(x) = -1/5(3)^x-1
D. f(x) = -1/5(-3)^x-1
Answer:
Step-by-step explanation:
B
f(x) = -1/5(3)ˣ⁻¹ formula can be used to describe the sequence.
The given sequence is -3, 3/5, -3/25, 3/125, -3/625
We can observe that each term alternates between negative and positive.
Additionally, the denominator of each term is increasing by a power of 5, while the numerator alternates between -3 and 3.
The formula f(x) = -1/5(3)ˣ⁻¹, fits this pattern.
By plugging in the values of x = 1, 2, 3, 4, and so on, the formula generates the corresponding terms of the sequence:
f(1) = -1/5(3)¹⁻¹= -3/5
f(2) = -1/5(3)²⁻¹ = 3/25
f(3) = -1/5(3)³⁻¹ = -3/125
f(4) = -1/5(3)⁴⁻¹ = 3/625
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Which of the following can only be used after you prove triangles are congruent? Alternate Interior Angles Reflexive Substitution CPCTC
Final answer:
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and can only be used after proving triangles are congruent. It helps in confirming that corresponding parts of congruent triangles are congruent.
Explanation:
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It can only be used after you prove triangles are congruent. When two triangles are proven congruent, CPCTC allows you to show that corresponding parts like angles and sides are congruent as well.
what is the answer to m-1/6-4m+5/6
round 7.86 to the nearest tens
Shondra found large candles on sale at her favorite store. She has a large family and many friends, so she bought as many of the candles she could fit in her trunk to give as gifts. Her trunk is 2 feet deep, 4 feet wide, and 3 feet long. If each candle comes in a cube box with 1 foot edges, how many candles will fit in her trunk? A) 9 candles B) 10 candles C) 14 candles D) 24 candles
which of the following best describes this random sample
Suppose that the polynomial function A(x) = - 0.0082x2 + 0.06x approximates a person's blood-alcohol level x hours after drinking 5 ounces of 80-proof whiskey. What is the person's blood-alcohol level after 3 hours?
Consider the equation 5x-2y=3. If possible, find a second linear equation to create a system of equations that has: Exactly one solution Exactly two solutions No solutions Infinitely many solutions
Answer with explanation:
1.⇒ The given equation is
5x-2y=3
For one solution ,you should write linear equation in such a way
ax+by=c, such that
[tex]\frac{5}{a}\neq \frac{-2}{b}\neq \frac{3}{c}[/tex]
So, the linear equation will be
→3x+4y=8
You can write many more by yourself.
2.⇒Exactly two solutions
The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.
3.⇒No solutions
It means the two lines will never intersect.
For no solution ,you should write equation of line in such a way
ax+by=c, such that
[tex]\frac{5}{a}=\frac{-2}{b}\neq \frac{3}{c}[/tex]
So, the linear equation will be
→10x -4y=15
You can write many more by yourself.
4.⇒Infinitely many solutions
For Infinite number of solution ,you should write linear equation in such a way
ax+by=c, such that
[tex]\frac{5}{a}=\frac{-2}{b}=\frac{3}{c}[/tex]
→10x-4y=6
i need help on this one :)
"how few colors can be used so that each room is painted a color so in which no two adjacent rooms are the same color?"
We can see here that to guarantee that no two adjacent rooms are the same color, a minimum of four colors is generally needed.
To determine the minimum number of colors needed to paint each room in a way that no two adjacent rooms have the same color, we can use a coloring algorithm known as the "Four Color Theorem." According to this theorem, it is possible to color any map on a plane using at most four colors, ensuring that no two adjacent regions have the same color.
Applying this concept to the rooms, we can conclude that a minimum of four colors is needed to satisfy the given condition. By using these four colors, we can ensure that no two adjacent rooms share the same color.
which relation defined by mapping diagram is a function
which equation is the inverse of y=100-x2
Answer:
Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].
Step-by-step explanation:
Given : f(x) = y = 100 - x²
To find : Find inverse.
Solution : We have given that :
f(x) = y = 100 - x²
Step1) : Replace every x with a y and replace every y with an x .
x = 100 - y².
Step 2): Solve for y
On subtracting 100 from both sides
x - 100 = -y²
On multiplying both side by -1
100 -x = y²
Taking square root both sides and switching sides
y = ± [tex]\sqrt{100-x}[/tex].
Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Answer:
A on edge
Step-by-step explanation:
Keiko sold less than three fourths of his sister's sales
If the original 24 m edge length x of a cube decreases at the rate 5m/min, when x=3 at what rate does the cube's surface area change
The change in the cube's surface area is -180 m^2/min when the edge length is 3 m. This is found by differentiating the surface area with respect to time and substituting the given values.
Explanation:The subject of the question is related to rates of change in the context of the geometry of a cube. To address this problem, we use the formula for a cube's surface area, which is given by A = 6x^2, where x represents the length of an edge. If x changes with respect to time, we denote this change as dx/dt, which is given as -5m/min. You want to find how quickly the surface area, A, changes when x = 3.
First, let us differentiate the surface area A with respect to time t. By the chain rule of differentiation, dA/dt = dA/dx * dx/dt. Given A = 6x^2, dA/dx = 12x. substituting x=3 and dx/dt=-5, we find that dA/dt = 12*3*-5, which equals -180m^2/min.
Therefore, the change in the cube's surface area is -180 m^2/min when the edge length is 3 m.
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Which is a correct way of evaluating the expression 25x + 40x for x = 4?
Which binomial below is a factor of the polynomial 3a2+6a-2a-4?
Tom weighed 110 pounds at the beginning of the year. By June, he had gained 13 pounds, but in August he lost 5. How much did he weigh at the end of the year if he gained 4 more pounds during the month of November?
Tom weighed 122 pounds at the end of the year.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Tom weighed 110 pounds at the beginning of the year.
Pounds gained in June = 13
Pounds lost in August = 5
Pounds gained in November = 4
Now,
Total pounds at the end of the year.
= 110 + 13 - 5 + 4
= 110 + 17 - 5
= 110 + 12
= 122 pounds
Thus,
122 pounds at the end of the year.
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