Emily is training for a 10K race. On day one, she runs for 20 minutes. On day two, she runs for 30 minutes. On day three, she runs for 40 minutes. If this pattern continues, how many minutes will she run on day 8?
Answer:
90 minutes
Step-by-step explanation:
Given that On day one, she runs for 20 minutes. On day two, she runs for 30 minutes. On day three, she runs for 40 minutes, this pattern may be presented as an arithmetic sequence shown below
20, 30, 40 ...
For an arithmetic sequence whose first term is a, and a common difference d, the nth term of the sequence may be given as
Tn = a + (n - 1)d
Hence the first term is 20, the common difference d is 10
On the 8th day, the 8th term
T8 = 20 + (8 - 1) 10
= 20 + 70
= 90 minutes
Final answer:
Emily will run for 90 minutes on day 8, calculated by applying the formula for the n-th term of an arithmetic sequence with a first term of 20 minutes and a common difference of 10 minutes.
Explanation:
Emily is training for a 10K race with a pattern of increasing her running time by 10 minutes each day. On day one, she runs for 20 minutes, on day two for 30 minutes, and on day three for 40 minutes. To calculate how many minutes she will run on day 8, we can observe this as an arithmetic sequence where the common difference is 10 minutes.
Using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d, where:
a1 is the first termd is the common differencen is the term numberWe know that a1 is 20 minutes, d is 10 minutes, and n is 8 because we are looking for the time on day 8.
Therefore, a8 = 20 + (8-1)
10 = 20 + 70 = 90 minutes.
So, on day 8, Emily will run for 90 minutes.
simplify the expression 2(2+4v)
Step-by-step explanation:
2(2+4v)
multiply 2 with the number in bracket
4+8v=0
8v= -4
v=-4/8
v= -1/2
Step-by-step explanation:
2(2 + 4v)
4 + 8v
If you have to find the value of v
4 + 8v = 0
8v = - 4
V = - 4/8 = - 1/2
Can somebody help me find the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of the function f(x) = -2e^x + 4 ?
Answer:
Domain = R
Range = (-∞, 4)
Hor. asymp = y=4
Y intercept: f(0) = (0,2)
end behaviour:
x → -∞: f(x) → 4
x→ ∞: f(x) → -∞
Step-by-step explanation:
For the domain, it is R because e^x works for all values of x
For the range, y will never be above 4.
The hor. asymptote is found via [tex]\lim_{x \to -\infty} f(x)[/tex] there the e term will be zero, so what is left is y=4.
Y intercept, fill in f(0)
end behaviour: for small x, y goes to the asymptote, for large x, y goes to minus infinity.
Final answer:
Explained the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of f(x) = -2e^x + 4
Explanation:
Domain and Range:
Domain: All Real Numbers
Range: f(x) ≤ 4
Horizontal Asymptote:
Horizontal Asymptote: y = 4
Y-Intercept:
Y-Intercept: (0, 2)
End Behavior:
End Behavior: As x → ∞, f(x) → 4; As x → -∞, f(x) → -∞
You have $73.59 you ear additional money by mowing lawns when you purchase a new pair of shoes for $99.99 and have 23.51 left how much money do you ear mowing lawns
Answer:
50.00$
Step-by-step explanation:
99.99 minus 73.50
Gives you 27.50 so then you add up what you have left so that gives you 50.00$
A gym charges $30 per month plus $4 extra to swim in the pool for an hour. Because a member has just $50 to spend at the gym each month, the member can swim at most 5 hours. Find the inequality
Answer:
[tex]50\geq $30 + $4[/tex]
Step-by-step explanation:
Simplest Form...
Choose a fraction that is in the
simplest form. Make 15 new
equivalent fractions.
can someone help me please I don't know how to do that
Answer:
Pick any fraction that is already in its simplest form, for example:
[tex]\frac{1}{2}[/tex]
and do this;
[tex]\frac{1 \times x}{2 \times x}[/tex]
times the denominator and numerator with any number, but must be the same! and do it 15 times, like so;
[tex]\frac{1 \times 2}{ 2 \times 2} , \frac{1 \times 3}{2 \times 3}, \: \: continue...[/tex]
and u will get this:
[tex]\frac{1}{2} =\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}, \frac{6}{12}, \frac{7}{14}, \frac{8}{16}, \frac{9}{18}, \frac{10}{20}, \frac{11}{22}, \frac{13}{26}, \frac{14}{28}, \frac{15}{30}, \frac{16}{32}, \frac{17}{34}[/tex]
To create equivalent fractions, you choose a simple fraction like 1/2. You then multiply both the numerator and denominator of this fraction by the same number to get a new fraction. You can do this 15 times to get 15 different equivalent fractions.
Explanation:The subject is finding equivalent fractions. Let's start with a simple fraction like 1/2. Equivalent fractions are just multiples of this fraction. So, we multiply both the numerator (top number) and the denominator (bottom number) by the same number to get an equivalent fraction. Here are some examples:
1/2 x 2/2 = 2/4 1/2 x 3/3 = 3/6 1/2 x 4/4 = 4/8 And so on...
Following this method, you can create 15 different equivalent fractions for 1/2. Remember that the fractions should be in their simplest form, meaning that there's no number (except for 1) that could divide both the numerator and denominator evenly.
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8.98 to the nearest tenth
Answer:
9.0
Step-by-step explanation:
depends on the last digit of the number.If it's 5 or more it becomes 9.0.If it's less than 5, then it's 8.0.In this case it's greater so the answer is 9.0
Hope that was helpful.Thank you!!!
what is x + y = 12 if x = 2y
Answer:
x=8
y =4
Step-by-step explanation:
x + y = 12 if x = 2y
Replace x with 2y in the first equation
2y+y = 12
Combine like terms
3y =12
Divide by 3
3y/3 =12/3
y = 4
Now we can find x
x=2y
x=2(4)
x = 8
The number of calories in a muffin is directly proportional to the amount of sugar in the muffin. If a 200 calorie muffin has 500 grams of sugar. How many calories are in a muffin with 2,075 grams of sugar
Answer:
830 calories
Step-by-step explanation:
The number of calories in a muffin is directly proportional to the amount of sugar in the muffin.
Let the number of muffins be N and the amount of sugar in the muffin be A. This means that:
N α A
=> N = kA
where k = constant of proportionality
A 200 calorie muffin has 500 grams of sugar.
This implies that:
200 = k * 500
=> k = 200 / 500 = 2/5
The constant of proportionality is 2/5.
The number of calories in a muffin with 2075 grams of sugar is:
N = 2/5 * 2075
N = 830 calories
There are 830 calories.
Final answer:
A muffin with 2,075 grams of sugar contains 830 calories, calculated using a proportion based on a known ratio of calories to sugar grams.
Explanation:
The question asks: How many calories are in a muffin with 2,075 grams of sugar if we know a 200 calorie muffin has 500 grams of sugar? This is an example of a proportion problem.
First, let's establish the relationship between calories and grams of sugar. We know that 200 calories correspond to 500 grams of sugar. We can set this up as a ratio: 200 calories/500 grams = x calories/2,075 grams, where x is the number of calories in the muffin with 2,075 grams of sugar.
To find x, we cross-multiply and solve for x: (200 calories * 2,075 grams) / 500 grams = x calories
Thus, x = 830 calories.
Therefore, a muffin with 2,075 grams of sugar contains 830 calories.
Fiona is trying to prove that a pair of expressions are equivalent by using substitution. Which pair of expressions has the same value if she substitutes y = 3?
Answer:
the answer is A i finished that test now im on another test and timed sorry for no explanation
Step-by-step explanation:
A
Answer:
A
Step-by-step explanation:
A because I did all on the question and A was the one
#1 Find the area of the rhombus. Each indicated distance is half the length of its respective diagonal.
#2 Find the area of the rhombus.
Answer:
1 area = 864
2 area =384
Step-by-step explanation:
Answer:
1 area = 864
2 area =384
Step-by-step explanation:
Do you still have this worksheet I really need help
suppose you know the following facts about angle ABC and angle DEF
Answer:
i would say the third choice.
Step-by-step explanation:
both sides in question are all the hypotenuse(s) of the triangles , hence one gets the same way , i.e , the Pythogrean method
find the hypotenuse for the following
Answer:
6.403 units
or [tex]\sqrt{41}[/tex]
Step-by-step explanation:
We want the hypotenuse.
The hypotenuse is from the point (-3, -1) to point (2, 3)
D( (-3, -1), (2, 3)) = root ( (2 - (-3))^2 + (3 - -1)^2 ) =
D( (-3, -1), (2, 3)) = root ( 5^2 + 4^2) = root( 25 + 16)
D( (-3, -1), (2, 3)) = root ( 41)
D( (-3, -1), (2, 3)) = 6.403 units
Answer:
6.4 (rounded to nearest tenth)
Step-by-step explanation:
Distance from (-3,-1) to (2,-1) is 5 units
Distance from (2,-1) to (2,3) is 4 units
4^2+5^2=x^2 x=hypothenuse
16+25=x^2
41+x^2
(take square root of both sides)
x=6.4
Determine which graph represents a reflection across the x-axis of f(x) = 3(1.5)x.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and then decreases in quadrant 4. It crosses the y-axis at (0, negative 0.5).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and then decreases in quadrant 4. It crosses the y-axis at (0, negative 3) and goes through (2, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and then decreases in quadrant 4. It crosses the y-axis at (0, negative 3) and goes through (0.5, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and then increases in quadrant 1. It crosses the y-axis at (0, 3).
Answer:
its b
Step-by-step explanation:
i just did it
Answer:
graph B on edg
Step-by-step explanation:
The local skating rink pays Mary a fixed rate per pupil plus a base amount to work as a skating instructor. She earns $90 for
instructing 15 students on Monday afternoon. Last Friday, she earned $62 for working with 8 students. Lisa is also a skating
instructor. She receives half the base amount that Mary does, but she is paid twice as much per student. Who would eam
more money instructing a class of 20 students?
Lisa would earn $120 more than Mary.
Lisa would earn $65 more than Mary.
Mary would earn $15 more than Lisa.
Mary would earn $10 more than Lisa.
Mark this and return
Save and Exit
Next
Submit
Who earns
Answer:The expressions for the payment made to Mary are,
(Monday) 90 = 15m + b
(Tuesday) 62 = 8m + b
where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30.
The equation that represents Mary's earning is
y = 4x + 30
For 20 students,
y = 4(20) + 30 = 110
For Lisa's earnings,
y = 8x + 15
Substituting 20,
y =8(20) + 15 = 175
Thus, Lisa would earn more than Mary by $65.
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Step-by-step explanation:
Find the product using the number line. 3(-6) = A number line going from negative 7 to positive 3. An arrow goes from negative 6 to negative 4, from negative 4 to negative 2, and from negative 2 to 0. What error(s) are shown here? Check all that apply. The arrows should be a length of 2. The arrows should be a length of 6. The arrows should be pointing in the positive direction. The arrows should start at zero. The arrows should point in the negative direction.
Answer:
B - The arrows should be length of 6.
D - The arrows should start at zero.
E - The arrows should point in the negative direction
Step-by-step
since it is asking us to find the product you will have to start at negative 6 and then you are going to jump 3 spaces 3(-6)
Answer:
B - The arrows should be length of 6.
D - The arrows should start at zero.
E - The arrows should point in the negative direction
Step-by-step explanation:
Can someone please help me with this.
Answer: The answer it C. 135
Step-by-step explanation:
It is a supplementary angle so therefore it’s supposed to equal 180 degrees.
So, 180-45= 135
The graph of which function has an axis of symmetry at x = 3? Picture A, B, C, or D?
Answer:
The last graph f(x)=x^2-6x-1
Step-by-step explanation:
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
The graph shown in picture D with equation f(x) = x²-6x-1 , has axis of symmetry at x = 3.
4 graphs are given in order to identify which of them contains axis of symmetry at x = 3
The axis of symmetry is the center axis of the curves where the curve is equally divided.
For Picture A
The axis of symmetry is x = 1.5 so it is not the correct option.
For picture B
The axis of symmetry is x = 1.3 so it is not the correct option.
For picture C
The axis of symmetry is x = -3. So it is not correct option
For picture D
The axis of symmetry is x = 3. it is the correct option.
The graph shown in picture D with equation f(x) = x²-6x-1 , has axis of symmetry at x = 3.
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Ed lined up 10 guitar picks across his desk. Each pick weighs 12 mg wide. How many grams does his entire set of guitar picks weigh?
Answer:
120 milligrams because 12 mg *10 =120
Ed's entire set of guitar picks, with each pick weighing 12 mg and having 10 picks in total is 0.12 grams.
To calculate the total weight of the guitar picks in grams, we first need to know that there are 10 guitar picks and each pick weighs 12 mg.
Knowing that there are 1000 milligrams in a gram, we can convert the weight of one pick into grams:
Weight of one pick in grams = 12 mg / 1000 = 0.012 grams.
Next, we multiply this by the total number of picks to get the combined weight:
Total weight of 10 picks = 0.012 grams pick * 10 picks = 0.12 grams.
So, Ed's entire set of guitar picks weighs 0.12 grams.
Can anyone help with polynomials?
Yes. I can help. What do you need with help with concerning polynomials?
Ms. Davis schedules after-school group
activities for 18 girls and 24 boys. She wants
to make equal groups with the same number
of girls and the same number of boys in
each group. Ms. Davis says that the greatest
number of equal groups she can make is 3.
Answer:
Ms. Davis is wrong
Step-by-step explanation:
she can make equal groups of 6
A company that manufactures toy trains is making a new boxcar. To fit on the track, the smallest dimension of the toy boxcar must be 2 inches. What should be the length and height of the toy if the company wants the toy boxcar to be geometrically similar to an actual boxcar with the dimensions shown?
Answer:
Length = 12 inches, height = 3 inches
Step-by-step explanation:
First, you have to set up a proportion. 2/7, x/42.
Then, you cross multiply and get the setup of 84=7x
Finally, you divide 84 by 7 and get 12.
12 is the length, and there is no other answer that has 12 in the height. You could just do the same proportion to get 3, though.
Answer:
A: length = 12 inches, height = 3 inches.
Step-by-step explanation:
The company wants the boxcar to be geometrically similar to the original boxcar.
The first step to doing this is to create a ratio. They tell us the smallest dimension of the toy boxcar must be 2 inches.
The smallest dimension of the original boxcar is 7 feet. We can use these two numbers to create a ratio. A 7:2 ratio to be exact.
A 7:2 ratio can be represented as 7/2. 7/2 equals 3.5. All you have to do now is divide the dimensions in the original boxcar by
For example, the length of the original boxcar is 42 feet. If we put 42/3.5 into a calculator, you get 12 as your answer. The same thing is true for the height.
1.In the diagram of circle M shown, various points are located on the circle as shown. a) List three segments that are radii of this circle. b) List a segment that is a diameter of this circle. c) List a chord of this circle that is not a diameter.
Answer:
(a)|MA|, |MB| and |MC|
(b) |BD|
(c) |BC|
Step-by-step explanation:
An adapted diagram of this question is attached. You can vary the labelled letters as required.
Definition
A radius is a line drawn from the center of a circle to its circumference.A segment is a line that connects two points.A diameter is a chord which passes through the center of the circle.A chord is any line joining two points on the circles' circumference.By these definitions:
(a)Segments that are radii of this circle.
We have: |MA|, |MB| and |MC|
(b)Segment that is a diameter of this circle.
|BD|
(c)A chord of this circle that is not a diameter.
|BC|
Which description compares the domains of Function A and Function B correctly?
Function A: f(x)=−3x+2
Function B:
Half of a parabola graphed on a grid in Quadrant One with the x and y axis beginning at negative ten and increasing in increments of two until reaching ten. The parabola, labeled g of x, contains a filled in point at begin ordered pair zero comma zero end ordered pair, passes through begin ordered pair two comma two end ordered pair and begin ordered pair four comma eight end ordered pair, and as a smooth curve while extending to infinity.
The domain of both functions is the set of real numbers greater than or equal to 0.
The domain of both functions is the set of real numbers.
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than 0.
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than or equal to 0.
Answer:
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than or equal to 0.
The domain of a function is the set of its possible inputs. it means that the set of input values for which the function is defined.
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than or equal to zero.
Here, function A is given that, [tex]f(x)=-3x+2[/tex]
Since, above function can take any value as its input.
That is function is defined for every value of x.
Therefore, The domain of Function A is the set of real numbers.
Here, graph of function B is attached.
From graph of function B, it is observed that graph of function is right side of Y - axis and starting from x = 0. It means that function B can take any value greater than equal to zero.
Therefore, The domain of Function B is the set of real numbers greater than or equal to zero.
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if an inscribed angle has a measure of 100°, what is the measure of the intercepted arc?
Answer:
w
hi ut ir8fue j de bi 8d
Step-by-step explanation:
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How can you find the area of a two-dimensional composite figure, or the surface area of a three-dimensional composite figure?
Step-by-step explanation:
a. the area of a two-dimensional composite figure
In this situation, we need to draw any necessary segments to view the figure as basic shapes, then:
Step 1: add basic shape areas belonging to the composite shape Step 2: subtract basic shape areas NOT belonging to the composite shapeb. the surface area of a three-dimensional composite figure
As we know (3D) composite objects are made of two or more objects put together. To find the surface area of a 3D composite object, we need:
Step 1: find the outside surface area of each object Step 2: add the surface areas togetherHope it will find you well
Final answer:
To find the area of composite figures, break them down into simpler shapes and sum up their areas. For three-dimensional figures, find individual surface areas and add them up.
Explanation:
Area can be determined by counting the number of squares inside a shape on 1 cm x 1 cm graph paper. For composite figures, break them down into simpler shapes, find their individual areas using appropriate formulas, then add them up. For three-dimensional composite figures, calculate surface area by finding the sum of individual surface areas of each component shape.
What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction
Answer:
[tex]\dfrac{5}{y+5}[/tex]
Step-by-step explanation:
Here, we have to find the sum of 2 fractions:
1st fraction: [tex]\dfrac{3y}{y^{2}+7y+10}[/tex]
2nd fraction: [tex]\dfrac{2}{y+2}[/tex]
Considering the denominator of 1st fraction:
[tex]y^{2}+7y+10[/tex]
Using factorization method:
[tex]7y[/tex] can be written as [tex](2y + 5y)[/tex].
[tex]\Rightarrow y^{2}+2y+5y+10[/tex]
Taking 5 common from [tex]5y+10[/tex] and y common from [tex]y^{2}+2y[/tex]: [tex]\Rightarrow y(y+2)+5(y+2)[/tex]
Now taking [tex](y+2)[/tex] common:
[tex]\Rightarrow (y+5)(y+2)[/tex]
[tex]\dfrac{3y}{y^{2}+7y+10}[/tex] can be written as [tex]\dfrac{3y}{(y+5)(y+2)}[/tex]
Now, calculating the sum:
[tex]\dfrac{2y}{(y+5)(y+2)} + \dfrac{2}{y+2}[/tex]
Taking LCM and solving:
[tex]\Rightarrow \dfrac{3y+2(y+5)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5y+10}{(y+5)(y+2)}\\\Rightarrow \dfrac{5(y+2)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5}{(y+5)}[/tex]
Hence, answer is [tex]\dfrac{5}{y+5}[/tex].
Answer:
its c
Step-by-step explanation:
i have takin da test
What is 2+2? I cant figure it out I took 4 hours
Answer:
4
Step-by-step explanation:
Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base
Answer:
Slope of the base segment line is zero, hence base segment is horizontal
Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical
Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base
Step-by-step explanation:
Here we prove the required relation as follows;
Let the isosceles be ABC
The coordinates of the points are
C = (0, 0) (Vertex)
A = (-a, b)
C = (a, b)
P = (0, b) (Midpoint of base)
Therefore, the gradient or slope of the base AC is presented as follows;
[tex]Slope, m \, of \. base, \, AC= \frac{dy}{dx} = \frac{b - b}{a - (-a)} = \frac{0}{2\cdot a} = 0[/tex]
Hence, segment AC is vertical
[tex]Slope, m \, of \, segment \ CP \, joining \, vertex, \, to \, midpoint, P, on \,AC = \frac{0 - b}{0 - 0} = \frac{-b}{0} = Undifined.[/tex]
Hence, segment CP is vertical
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.
In an isosceles triangle with base BC, the segment from vertex A to the midpoint M of BC is vertical, whereas BC is horizontal. Since vertical and horizontal lines are perpendicular by definition, AM is perpendicular to BC.
Let's assign coordinates to the isosceles triangle ABC, where AB = AC and BC is the base. Assume the vertex A is at the origin (0, 0), the base endpoints B and C are at coordinates (-b, c) and (b, c) respectively.
First, find the midpoint M of BC. The coordinates of M will be the average of the x-coordinates and the y-coordinates of B and C. Thus, M = (0, c).Next, determine the slope of line AM (vertex to midpoint). Since A is at (0, 0) and M is at (0, c), the slope is:1.5d+3=-4.5 what does D equal
Answer:
d = − 5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
-1.5
Step-by-step explanation:
subtract 3 from both sides.
5d=-7.5
divide by 5
d=-1.5