Write an expression that shows how to use the halving and doubling strategy to find 28x50
Halving strategy means we divide by 2
Doubling strategy means we multiply by 2
We apply halving strategy for 28 and doubling strategy for 50
Half of 28 is 14
Double of 50 is 100
So 14 * 100 = 1400
Now we check with 28 * 50
28 x 50 = 1400
So required expression is
[tex]\frac{28}{2} * (50*2)[/tex]
write the number of laps completed per minute
laps per minute by:
- Mai- 12/3 = 4 laps
- Lena- 48/6= 8 laps
- Susan- 30/5= 6 laps
thus, the person who drove fastest was Lena, who drove 8 laps per minute.
Help ASAP!!!
First to answer with a correct answer gets brain...
Hey there!
First, let's multiply each side of the equation by 3 to get rid of the fraction [tex]\frac{2}{3}[/tex].
9 + 2x = [tex]\frac{6}{5}[/tex]
Next we can multiply each side of the equation by 5 to get rid of the fraction [tex]\frac{6}{5}[/tex].
45 + 10x = 6
There's your answer!
Hope this helps!
Help please 10 minutes
Slope Formula: (y² - y¹) / (x² - x¹)
1 + 7 = 8
-1-1 = -2
8/2 = 4
-2/2 = 1
4/1 = -4
Your answer is B.
Hope this Helps!!
The slope-intercept form:
[tex]y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (1, -7) and (-1, 1).
Substitute:
[tex]m=\dfrac{1-(-7)}{-1-1}=\dfrac{8}{2}=4[/tex]
Therefore we have
[tex]y=4x+b[/tex]
Substitute the coordinates of the first point to the equation of line:
[tex]-7=-4(1)+b[/tex]
Answer:
[tex]\dfrac{1+7}{-1-1}=-4;\ -7=-4(1)+b[/tex]
A horizontal plane passes through a cone that has a horizontal base.
Which figure or figures can be produced? Select all that apply.
If the horizontal plan passes through the cone that have horizontal base, the shaped form will be circular.
B AND C I THINK BUT IM NOT SURE
Which area is greatest?
a. b=4, h=3.5
b. b=0.8, h=20
c. b=6, h=2.25
d. b=10, h=1.4
the answer is b because to find the area of something you have to do Base(b) multiplied by the Height(h) and the area of B was 16
A: 14
B: 16
C: 13.5
D: 14
Answer Is Option(b.) :-To find the greatest area among the given rectangles, calculate the area of each rectangle by multiplying the base by height. The greatest area is of rectangle b.
Explanation:The subject matter of this question involves finding the area of rectangles. In mathematics, the area of a rectangle is calculated by multiplying its base (b) by its height (h), represented as A = b x h. In this question, you are given four different rectangles (a, b, c, and d) with varying base and height values. You need to calculate the area for each and determine which one is the greatest:
For rectangle a, the area is b x h = 4 x 3.5 = 14 For rectangle b, the area is b x h = 0.8 x 20 = 16 For rectangle c, the area is b x h = 6 x 2.25 = 13.5 For rectangle d, the area is b x h = 10 x 1.4 = 14
After calculations, you can see that rectangle b has the greatest area.
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Write a decimal that is 1 Tenth of 0.9.
0.09
-hope this helps
1. Suppose you invest $500 at 10% interest, compounded annually. After 5 years, how much money would you have in your account? Remember, the formula is A = P(1 + r)t.
2. If you invest $100 at 2% interest, compounded every 2 years, what would your balance be after 6 years?
4. Two friends are going on a road trip and are downloading podcasts to listen to on the drive. They choose two podcasts. They download A episodes of Podcast A, and B episodes of Podcast B. Each episode of Podcast A is x minutes long, and each episode of Podcast B is y minutes long. Tell what the following expressions represent in the situation.
a. Ax + By
b. A + B
Solution 1:
The compound interest formula to be used here is given by:
[tex]A=P(1+r)^{t}[/tex]
Now we are given:
P=$500
r=10% or 0.1
t=5 years
Plugging them in the formula ,
[tex]A=500(1+0.1)^{5}[/tex]
A=$802.255
Answer : After 5 years I will have $802.255 in my account.
Solution 2:
The formula for compound interest here is given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here interest is compounded after every two years, so n=2
r=2% or 0.02
t=6 years
P= $100
Plugging these into the formula:
[tex]A=100(1+\frac{0.02}{2})^{2*6}[/tex]
[tex]A=100(1+0.01)^{12}[/tex]
[tex]A=100(1.01)^{12}[/tex]
A=$112.683
Answer: The balance after 6 years would be $112.683.
Solution 4:
In this situation:
a. Ax+By
Ax represents duration of Podcast A episodes
By represents duration of Podcast B episodes
Ax+By represents total duration of Podcast A and Podcast B songs.
b. A+B
A+B represents total number of episodes of Podcast A and Podcast B.
Which graph represents the piece wise-defined function? y={−x+3 if x<12x−4 if x≥1
For the interval (-∞, 1), put x = 0.5, then y = - 0.5 + 3 = 2.5.
Therefore, (0.5, 2.5) is a point on y = -x + 3.
Put x = - 1, then y = -(-1) + 3 = 1 + 3 = 4.
Therefore, (-1, 4) is another point on y = -x + 3.
Joining (0.5, 2.5) and (-1, 4), we get the graph of the line y = -x + 3.
For the interval [1, ∞), put x = 1, then y = 2(1) - 4 = -2.
Therefore, (1, -2) is a point on y = 2x - 4.
Put x = 2, then y = 2(2) - 4 = 4 - 4 = 0.
Therefore, (2, 0) is another point on y = 2x - 4.
Joining (1, -2) and (2, 0), we get the graph of the line y = 2x - 4.
The graph of the piecewise-defined function is: [tex]function \(y = \begin{cases} 3 & \text{if } x < -2 \\ 0 & \text{if } x = 1 \\ -1 & \text{if } x > 1 \end{cases}\)[/tex]is attached accordingly.
What is a piecewise-defined function?A piecewise-defined function is a mathematical function that is defined by different rules or formulas over different intervals or regions of its domain.
The graph of the piecewise function is attached accordingly.
The graph of the piecewise function [tex]\(y\)[/tex] consists of two linear segments with a clear transition at [tex]\(x = 1\)[/tex]:
1. For [tex]\(x < 1\)[/tex], the equation [tex]\(y = -x + 3\)[/tex] defines a downward-sloping line that intersects the y-axis at [tex]\(y = 3\)[/tex].
2. For , the equation [tex]\(y = 2x - 4\)[/tex] defines an upward-sloping line that intersects the y-axis at [tex]\(y = -4\)[/tex].
These two segments meet at the point (1, -1), creating a kink in the graph. This piecewise function effectively combines two linear functions with different slopes, resulting in a non-continuous graph at [tex]\(x = 1\)[/tex].
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Victoria drove 211⁄2 miles in 2⁄3 of an hour. What was her speed? A.) 32 1/2 miles per hour B.) 32 1/3 miles per hour C.) 32 3/4 miles per hour D.) 32 1/4 miles per hour
change each to improper fractions
21 1/2 = (2*21 +1)/2 = 43/2
2/3 = 2/3
43/2 divided by 2/3
copy dot flip
43/2 * 3/2
129/4 = 32 1/4
Answer:
Speed of Victoria, [tex]v=32\dfrac{1}{4}\ miles/hour[/tex]
Step-by-step explanation:
It is given that,
Distance covered by Victoria, [tex]d=21\dfrac{1}{2}\ miles=\dfrac{43}{2}\ miles[/tex]
Time taken, [tex]t=\dfrac{2}{3}\ hour[/tex]
Speed (v) of Victoria is given by total distance divided by total time taken. It is given by :
[tex]v=\dfrac{d}{t}[/tex]
[tex]v=\dfrac{\dfrac{43}{2}\ miles}{\dfrac{2}{3}\ hour}[/tex]
[tex]v=\dfrac{129}{4}\ miles/hour[/tex]
or
[tex]v=32\dfrac{1}{4}\ miles/hour[/tex]
So, the speed of Victoria is [tex]32\dfrac{1}{4}\ miles/hour[/tex]. Hence, this is the required solution.
Least common factor of 17 and 6
That will be 1, since 17 can only be factored by itself and 1
Even though 6 can be factored by 3 and 2, the least common factor between 17 and 6 will be 1.
Hello there,
The correct answer is 2 the (LCM) or Least common factor of 17 and 6 is 2
If my answered helped you understand more greatly please mark me as brainliest thank you and have the best day ever!
Danny paid a total of $13.65 for two steaks that weighed 0.65 lb and 0.75 lb.
What was the average price per pound that Danny paid for the steaks?
To find the price per pound, simply add 0.65 + 0.75 then divide.
0.65 + 0.75 = 1.40 13.65 / 1.40 = 9.75
Danny paid $9.75 per pound!
Lets go through the steps
1) Add the weights together which gives us 1.4 lb
2) Divide the cost by the weight 13.65/1.4 = $9.75 lb
Which point satisfies both ƒ(x) = 2^x and g(x) = 3^x?
(0,1) I hope that helped
The only time that f(x) will equal g(x) occurs at x = 0.
What is the following sum? 5(3sq root x)+9(3sq root x)
[tex]Domain:\ x\geq0\\\\5\sqrt[3]{x}+9\sqrt[3]{x}=(5+9)\sqrt[3]{x}=14\sqrt[3]{x}[/tex]
The Sum of 3 and a number is 16
If "the sum of 3 and a number is 16" is given, we can rewrite it as an equation (note that "a number" refers to a variable, commonly x):
3 + x = 16
Now, simply use the Subtraction Property of Equality (subtract 3 from both sides):
3 + x - 3 = 16 - 3
x = 13
Therefore, the number, or x, is equal to 13.
Hope this short response helps! :)
What is the decimal equivalent of 9 and 11/27
The decimal equivalent of the mixed number, '9 and 11/27', is found by first converting the fraction into a decimal, followed by adding it to the whole number part. The answer is 9.4074.
Explanation:To find the decimal equivalent of a mixed number like 9 and 11/27, we first need to convert the fractional part into the decimal form. We do this by dividing the numerator (11) by the denominator (27).
The fraction 11/27, when written in decimal form, is approximately 0.4074
Then, the decimal equivalent of the mixed number '9 and 11/27' is found by adding this decimal (0.4074) to the whole number part (9). Hence, the answer is 9.4074.
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Simplify the expression. Write your answer as a power.
(23)^2⋅(23^)6
What is 0.8 divided by 0.6 and what would it be if I round it to the nearest hundred
Final answer:
0.8 divided by 0.6 is 1.33333... which, when rounded to the nearest hundredth, is 1.33. The rounding should be done to the nearest hundredth as 'rounding to the nearest hundred' typically does not apply to decimals.
Explanation:
To calculate 0.8 divided by 0.6, we simply perform the division:
0.8 ÷ 0.6 = 1.33333...
When we round this to the nearest hundredth, we look at the third decimal place. Since it's 3, we do not round up the second decimal place. Thus, 1.33333... rounded to the nearest hundredth is 1.33.
Rounding numbers and understanding division are fundamental skills in mathematics. They are essential for various applications, such as converting fractions to percentages or when dealing with metrics and customary units.
However, the question asked to round to the nearest hundred, which seems to be a typographical mistake, because we usually round numbers to the nearest hundredth or to the nearest hundred as a whole number, but not to the nearest hundred as a decimal. Assuming it's a typo and meant the hundredth, the result is 1.33. Otherwise, 1.33 rounded to the nearest hundred as a whole number is simply 100 (since this is the closest hundred to 1.33).
factorise 2p^2 - p - 10
(2p squared)
2p² - p - 10 = 0
2 = a
- 1 = b
- 10 = c
To factor, find two numbers that multiply to equal a·c and also that have a sum of b
2p² + 4p - 5p - 10 = 0
2p (p + 2) - 5 (p + 2) = 0
Answer: ( 2p - 5 ) ( p + 2 ) = 01. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. How many different combinations of players are possible?
2. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. If the selection is random, what is the probability of selecting a team of 5 girls and 5 boys? what is the decimal?
Answer: 1. 286 different combinations of players are possible.
2. The probability of selecting a team of 5 girls and 5 boys is [tex]\frac{63}{143}[/tex] and the decimal is 0.4405...
Step-by-step explanation:
1. Number of girls is 6 and number of boys is 7.
So, the total number of players = 6+7 = 13
A team of 10 players is to be selected from the class.
So, the total possible number of different combinations of players will be: [tex]^1^3C_{10} = \frac{13!}{10! (13-10)!}=\frac{13*12*11*10!}{10!*3!}= \frac{13*12*11}{6}=286[/tex]
2. Number of girls is 6 and number of boys is 7.
The possible number of teams by selecting 5 girls and 5 boys will be: [tex]^6C_{5}\times ^7C_{5} =6\times 21= 126[/tex]
and the number of total possible teams of 10 players [tex]= ^1^3C_{10} =286[/tex]
Thus, the probability of selecting a team of 5 girls and 5 boys [tex]=\frac{126}{286}= \frac{63}{143}[/tex] or [tex]0.4405...[/tex]
If f(x)= 6x+7, determine the value of f(m)
Write a slope intercept for a line passing through the point (4,-3) that is paralell to the line 4x+5y=7
First, we need to solve the equation 4x+5y=7 to make it slope intercept form and find the slope of the line, because parallel lines have the same slope.
4x+5y=7
Subtract 4x from both sides.
5y=-4x+7
Divide both sides by 5.
y=-4/5x+7/5
The slope of the line is -4/5x. Plug that in to the blank slope intercept form equation, y=mx+b, with m being the slope and b being the y-intercept.
y=-4/5x+b
Now, we need to solve for the y-intercept. We can do this by plugging in the given coordinates (4,-3) into the above equation for x and y respectively:
-3=-4/5(4)+b
-3=-16/5+b
Add -16/5 to both sides.
1/5=b
The y-intercept is 1/5, plug this into the equation:
[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]
Your equation is the above equation.
I hope this helps :)
Final answer:
To find the slope-intercept form of a line parallel to 4x + 5y = 7 and passing through (4, -3), first find the slope of the given line, then use the point-slope form with the given point to derive the final slope-intercept form, which is y = (-4/5)x + 1/5.
Explanation:
The student is asking for the slope-intercept equation of a line parallel to another line. Since parallel lines have the same slope, we first need to find the slope of the given line, 4x + 5y = 7. To do this, we solve for y to get it into the slope-intercept form, y = mx + b, where m is the slope.
To convert 4x + 5y = 7 into slope-intercept form, we subtract 4x from both sides to get 5y = -4x + 7, and then divide by 5, resulting in y = (-4/5)x + 7/5. The slope of this line is -4/5. Hence, our new line must have the same slope of -4/5 to be parallel.
We use the point-slope form of the equation, which is y - y1 = m(x - x1), to get the equation of the line passing through the point (4, -3). Plugging in the values, we have y - (-3) = (-4/5)(x - 4), which simplifies to y + 3 = (-4/5)x + 16/5. To get the slope-intercept form, we subtract 3 from each side and get y = (-4/5)x + 16/5 - 15/5, leading to y = (-4/5)x + 1/5.
Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers? It's participation so I just have to have an answer, it doesn't have to be right. Read comments for solution.
Let
n-------> the lesser even number
n+2----> the greater even number
we know that
[tex]3(n+2)=(n-10)[/tex]
Solve for n
[tex]3n+6=n-10[/tex]
Combine like terms
[tex]3n-n=-10-6[/tex]
[tex]2n=-16[/tex]
[tex]n=-8[/tex]
so
[tex]n=-8\\n+2=-8+2=-6[/tex]
therefore
the answer is
the lesser even number is [tex]-8[/tex]
the greater even number is [tex]-6[/tex]
what is the vertex of the quadratic function f(x)=1/2x^2+3x+3/2?
the vertex of the quadratic function
[tex]f(x)= \frac{1}{2}x^2+3x+\frac{3}{2}[/tex]
To find vertex we use formula x= -b/2a
from the given equation , a= 1/2 and b = 3
Now we plug in the values in the formula
[tex]x = \frac{-b}{2a}[/tex]
[tex]x= \frac{-3}{2\frac{1}{2}}=-3[/tex]
x coordinate of vertex is -3
Now plug in -3 for x in f(x)
[tex]f(-3)= \frac{1}{2}(-3)^2+3(-3)+\frac{3}{2}[/tex]
f(-3) = -3
the y coordinate of vertex is -3
So vertex is (-3,-3)
Answer:
(-3, -3)
Step-by-step explanation:
The standard form of a quadratic equation is [tex]y = ax^2+bx+c[/tex] where the coordinates of the highest point (x, y) indicate the vertex.
Here, [tex]a= \frac{1}{2} , b = 3[/tex] and [tex]c= \frac{3}{2}[/tex].
We know the formula to find the x coordinate = [tex]\frac{-b}{2a}[/tex]
[tex]x= \frac{-3}{2(\frac{1}{2}) }[/tex] = [tex]-3[/tex]
To find y, put this value of x in the function to get:
[tex]y = \frac{1}{2} x^2+3x+\frac{3}{2}[/tex]
[tex]y = \frac{1}{2} (-3)^2+3(-3)+\frac{3}{2}[/tex]
[tex]y = -3[/tex]
Therefore, the vertex (x, y) = (-3, -3)
A veterinarian treated 7 dogs, 13 cats, 4 horses, and 3 ferrets. What percentage of his patients were small animals?
As per your defention, horses are the only thing considered "not small". To find the percentage, you take the number of what you are trying to find the percentage of divided by the total number.
So, 7 dogs + 13 cats + 3 ferrets = 23 Small animals
7 dogs + 13 cats + 3 ferrets + 4 horses = 27 total animals.
So,
[tex]\frac{23}{27}*100[/tex]
The reason we multiply by 100 is because the division gives us a decimal, and a percentage is a part out of 100.
So by doing the calculation we get
85.18%
Mathematics defines a percentage as a number or ratio expressed as fraction of 100.
It is denoted using % sign.
General formula to calculate percentage is:
[tex]\rm Percentage=\dfrac{\rm Value}{\rm Total\: value} \times 100%.[/tex]
For the given question, percentage of small animals is [tex]\rm 85.19\%.[/tex]
Calculation of percentage of small animals:[tex]\begin{aligned} \rm Total\: animals &= 7 + 13 + 4 + 3\\&= 27 \end[/tex]
[tex]\begin{aligned} \rm Number\:of\:small\:animals &= 7 + 13 + 3\\&= 23\end[/tex]
Small animals includes all animals except horses.
Therefore, percentage of small animals will be:
[tex]\rm \begin{aligned}\rm Percentage &= \dfrac{\rm Small \:animals}{\rm Total\:animals} \times 100\\\\ &= \dfrac{23}{27} \times 100\\\\ &= 85.19\% \end{aligned}[/tex]
Percentage of patients to be small animals is [tex]\rm 85.19\%[/tex].
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Find the equation of the line that is parallel to y=-x+9 and contains the point (7,-13).
The equation of the line that is parallel to y = -x + 9 and passes through the point (7, -13) is y = -x - 6.
Now, we want to find the equation of a line that is parallel to this given line and passes through the point (7, -13). Since the new line is parallel, it will have the same slope of -1. Let's denote the equation of the new line as y = mx + b. We know the slope (m = -1), and we have a point (7, -13) that the line passes through. We can use this information to find the value of b.
To find b, we can plug in the coordinates of the point (7, -13) into the equation y = -x + b:
-13 = -1 * 7 + b
Now, solve for b:
b = -13 + 7
b = -6
Therefore, the value of b is -6.
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angle A and angle B are complementary angles. if the measure of angle B is 29 degrees, what is the measure of angle A?
The measure of angle A is 61 degrees.
Given that
Angle A and angle B are complementary angles.
If the measure of angle B is 29 degrees.
We have to determine
The measure of angle A?
According to the question
The measure of angle A is determined in the following steps given below.
When adding the two complementary angles the sum of the angle is equal to 90 degrees.
[tex]\rm \angle A + \angle B = 90[/tex]
The measure of angle B is 29 degrees.
Then,
The measure of angle A is,
[tex]\rm \angle A + \angle B = 90\\\\\rm \angle A + 29= 90\\\\\rm \angle A =90-29\\\\\rm \angle A =61[/tex]
Hence, the measure of angle A is 61 degrees.
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A mattress store charges 7% sales tax and a 50 delivery fee
We are given function f(a) = 1.07a for total amount including sales tax.
g(b) = b+50 total cost including delivery.
We need to write function g(f(a)).
g(f(a)) = g of f(a).
We need to substitute function f(a) in g(b) function for b.
g(f(a)) = g(1.07a) = 1.07a +50.
Therefore, g(f(a)) = 1.07a +50.We are given mattress price a = $1125.
In order to find the total cost including delivery charges, we need to plug a= 1125 in the above function 1.07a +50.
Plugging a= $1125, we get
g(1125) = 1.07a +50 = 1.07*1125 +50 = 1203.75 +50 = 1253.75.
Therefore, total cost including delivery charges is $1253.75.Answer:
g(f(a)) = 1.07a +50.
Total cost including delivery charges is $1253.75.
Please help me on this question!
Domain: {-10, -5, 0, 5}
Range: {-7, -4, -1, 2}
you just find the x and y values of the plotted points my friend!! make sure they're in order from least to greatest
ome friends are going on a coaster ride at an amusement park. They board their car on a platform that is 10 and one half feet above the ground. The car starts by going up 80 and one half feet. Then the car goes down 50 and one fourth feet and comes to a stop. What is the change in height from where the friends started on the platform to where they are when the car stops?
The change in height from the starting platform to the stopping point of the roller coaster is 40.75 feet above the ground.
To determine the change in height from where the friends started on the platform to where they stop, we need to calculate the total distance the car traveled vertically. The car first ascends 80 and one half feet and then descends 50 and one fourth feet. The starting platform is 10 and one half feet above the ground.
First, we add the height of the platform to the initial ascent:
10.5 feet (height of platform) + 80.5 feet (initial ascent) = 91 feetNext, we subtract the descent:
91 feet (total height after ascent) - 50.25 feet (descent) = 40.75 feetThe change in height is the final position above the ground minus the starting position, yielding a total change in height of 40.75 feet.
of the 125 guests invited to a wedding, 104 attended the wedding. what percent of the invited guests attended the wedding?
The answer is 83.2%, Hope this helps