Answer:
18 feet
Step-by-step explanation:
Given:
A cat is running away from a dog.
After 5 seconds it is 16 feet away from the dog
After 11 seconds it is 28 feet away from the dog.
Let x represent the time in seconds that have passed and y represent the
distance in feet, so there are two points are formed such as (5, 16) and (11,28).
We will find the distance between dog and cat. by using distance formula of the two points.
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Now we substitute the given value in above equation.
[tex]d=\sqrt{(11-5)^{2}+(28-11)^{2} }[/tex]
[tex]d=\sqrt{(6)^{2}+(17)^{2} }[/tex]
[tex]d=\sqrt{36+289}[/tex]
[tex]d=\sqrt{325}[/tex]
[tex]d=18.08\ feet[/tex]
18.08 ≅ 18
So [tex]d=18\ feet[/tex]
Therefore the distance between dog and cat is 18 feet.
To find the linear equation for the distance between the cat and the dog, we calculate the slope with the given points and use it with one of the points to establish the equation y = 2x + 6. A graph can be drawn with the points (5, 16) and (11, 28) to visualize the cat's path.
The linear equation describing the distance the cat is from the dog in relation to time can be determined using the two given points: (5, 16) and (11, 28), where 'x' is the time in seconds and 'y' is the distance in feet.
We first find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values we get:
m = (28 - 16) / (11 - 5) = 12 / 6 = 2
This means for each second that passes, the cat is 2 feet further away from the dog. Next, we use one of the points and the slope to write the equation in point-slope form. Using the point (5, 16) we have:
y - 16 = 2(x - 5)
Expanding and simplifying this equation gives us:
y = 2x + 6
This is the linear equation that describes the distance of the cat from the dog over time. To draw a graph, we plot the two points given and draw the line that passes through them, which will represent the cat's path. The slope of 2 indicates that for every 1 second, the distance increases by 2 feet.
A triangular banner has an area of 5ft squared. The height is 3 ft more than the base. Find the base and the
height.
Answer: base a=2ft
height hₐ=5ft
Step-by-step explanation:
use equation for area of triengle
A=a*hₐ/2
hₐ-height of tringle
a-base of triangle
hₐ=a+3
A=a(a+3)/2
2A=a²+3a
A=5ft
2*5=a²+3a
a²+3a-10=0
a=(-3±√9+40)/2
a=(-3±7)/2
a=-5ft
a=2 ft
hₐ=2+3=5ft
2 x 1296 +2 x 648 +2 x 648
Answer:
5184
Step-by-step explanation:
first of all we sove multiplication of terms then addition
2592+1296+1296
5184 ans
please answer this math question
Answer: 2/3
Step-by-step explanation:
7/9 - 2/8 =x 4/9
= 48/72
However, they are asking for the answer in SIMPLEST FORM.
48/72 in simplest form is 2/3.
The measure of the supplement of an angle is 12° less than twice the measure of the angle. What is the measurement, in degrees, of the angle and its supplement?
The measurement of the angle is ______ degrees.
The measurement of the supplement is ______ degrees.
Answer:
The measure of the angle is 64 degree.
The measure of the supplement is 116 degree.
Step-by-step explanation:
Let the measure of the angle be 'x'.
Given:
Supplement of the angle is 12 less than twice the measure of the angle.
Twice the angle means 2 times of the angle which is [tex]2x[/tex] and 12 less means 12 is subtracted from [tex]2x[/tex].
So, supplement of the angle = [tex]2x-12[/tex]
Now, by definition of supplementary angles, if two angles are supplement of one another, then their sum is 180 degrees.
Therefore, the sum of the given angles = 180°
⇒ [tex]x+2x-12=180[/tex]
⇒ [tex]3x-12=180[/tex]
⇒ [tex]3x=180+12[/tex]
⇒ [tex]3x=192[/tex]
⇒ [tex]x=\frac{192}{3}=64\°[/tex]
The measure of the supplement = [tex]2(64)-12=128-12=116[/tex]
The measure of the angle is 64 degree.
The measure of the supplement is 116 degree.
Does the data for Camille’s puppy show a function? Why or why not?
Answer: Yes, it does, because each input value has an unique output value.
Step-by-step explanation:
First, you need to know when a relation is considered a function.
By definition, a relation is a function if an only if each input value has one and only one output value.
It is important to remember that the input values are the values of "x" and the output values are the values of "y".
Then, in this case, you can observe in the graph attached ( which shows the data for Camille’s puppy), that each x-value (Weeks) has an unique y-value (Weight in pounds).
Therefore, based on this and keeping on mind the explained before, you can conclude that the data for Camille’s puppy shows a function.
Answer:
Yes it does
Step-by-step explanation:
Because it passes the vertical line test and it only touches 1 unit point in the line no need for big explanations you cant understand
3(9k - 4) - 4(5n - 3) simplify don’t get it
Answer:
27k-20n
Step-by-step explanation:
3(9k-4)-4(5n-3)
27k-12-20n+12
27k-20n-12+12
27k-20n
The science club is inflating a model of a hot air balloon. The graph below shows their progress. At what rate is the diameter increasing?
Answer:
12.5 centimeters per minute
Step-by-step explanation:
From the graph, the rate at which the diameter increasing would be inthe units of cm/min
The rate is basically the slope of the line. The slope (m) has formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
[tex](x_1,y_1)[/tex] is any point from the graph
and
[tex](x_2,y_2)[/tex] is another point from the graph
Let's take the origin (0,0) as the first point and (4,50) as the second point. Now lets calculate the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{50-0}{4-0}\\m=\frac{50}{4}\\m=12.5[/tex]
Thus, we can say:
The diameter of the hot air balloon is increasing at a rate of 12.5 centimeters per minute
20% of a number is 35 what is the number
Solve for x.
20% × x = 35
0.2x=35
x=175
answer: 175
Answer: 175
Step-by-step explanation: We can change this problem to mean the same thing but it will say 20% of what number is 35.
To answer the question 20% of what number is 35, we translate the question into an equation. First we have 20% which we need to write as a decimal and remember to write 20% as a decimal, we move the decimal point 2 places to the left and we get 0.20.
Next we have "of what number" that's times x, "is 35" = 35. Now we have the equation (.20)(x) = 35.
Not to solve for x, since x is being multiplied by .20, we need to divide by .20 on both sides of the equation. On the left side of the equation the .20's cancel and we have x. On the right side of the equation we have 35 divided by .20 which is 175.
This means that 20% of 175 is 35.
Choose as many answers as apply.
Questions you might ask a car dealer include:
Which options are factory installed and which are dealer installed?
Where did you buy that suit?
Is there a dealer advertising fee?
Are there charges for documents like taxes and tags?
Answer:
C,D,A
Step-by-step explanation:
Answer:
Was it factory or dealer-installed?
Are there charges for documents like taxes and tags?
Is there a dealer advertising fee?
Step-by-step explanation:
''Step two involves preparing a list of suitable questions for the dealers you wish to visit. For example, if you want rustproofing, was it factory-installed or dealer-installed? Are there charges for documents like taxes and tags? Is there a dealer advertising fee? These charges won't appear on a factory invoice, but you will pay for them.''
0.00035 + (4.2 x 10-5)
Step-by-step explanation:
Solve the bracket first. starting with multiplication and then subtraction
0.00035 + (4.2 x 10-5)
0.00035 + (42-5)
0.00035 + 37
0.01295
3. What is the solution to 3x2+3x+5=0? (7 point)
mm -
Cm 2COO
-3+1V17
3
31151
6
-1£i17
2
-3ti51
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x^2+3x+5 = 0[/tex]
We will use the quadratic formula for solving the given equation
The quadratic formula is:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}\ \ \ ,\ \ \ x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Here,
a = 3
b = 3
c = 5
[tex]x = \frac{-3+\sqrt{(3)^2-4(3)(5)}}{2(3)}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{(3)^2-4(3)(5)}}{2(3)}\\x = \frac{-3+\sqrt{9-60}}{6}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{9-60}}{6}\\x = \frac{-3+\sqrt{-51}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{-51}}{6}[/tex]
As we know
[tex]i = \sqrt{-1}[/tex]
So,
[tex]x=\frac{-3+\sqrt{51*-1}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{51*-1}}{6}\\x=\frac{-3+(\sqrt{51}*\sqrt{-1})}{6} \ \ \ , \ \ \ \ x = \frac{-3-(\sqrt{51}*\sqrt{-1})}{6}\\x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Hence,
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Keywords: Quadratic equation, quadratic formula
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I need help on this question someone plz help me
Answer:
The slopes of the lines are different.
Step-by-step explanation:
If you do convert the standard form equation to slope-intercept form, you get ...
y = -x +5
You see that the slope of this line is -1, whereas the slope of the other line is +1. Both lines have a y-intercept of 5. It is the slopes that are different.
_____
You can determine this to be the case without converting the form of the equation if you have some practice with the various forms of the equation of a line.
In standard form, if the variable signs are the same, the slope is negative. Of course, in slope-intercept form, the sign of the slope is the sign of the coefficient of x.
Write down the multiples of 9 between 25 and 50.
Answer:
27, 36, 45Step-by-step explanation:
9×3 = 27
9×4 = 36
9×5 = 45
HOPE IT HELPS
Answer : 9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,162,171,180,189,198,207,216,225,234,243,252,261,270,279,288,297,306,315,324,333,342,351,360,369,378,387,396,405,414,423,432,441
the population P of a bacteria culture is modeled by P=4300e^kt, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double?
Answer:
93 h
Step-by-step explanation:
P = 4300eᵏᵗ
1. Calculate the value of k
lnP = ln4300 + kt
ln5800 = ln4300 + k(40 h)
8.666 = 8.366 + 40k h
8.666 - 8.366 = 40k h
0.299 = 40 k h
k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹
2. Calculate the time for the population to double
2 × 4300 = 4300eᵏᵗ
2 = eᵏᵗ
ln2 = kt
t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h
It takes 93 h for the population to double.
The coffee shop is having a special where 2 pounds of coffee cost four dollars. Assume that the total cost in dollars y varies directly with the number of pounds of coffee x. This can be represented by y=2x. How much will 2.5 pounds of coffee cost
Answer:
Step-by-step explanation:
If 2 pounds costs $4, then 1 pound costs $2. That's why the equation is y = 2x and x is the number of pounds you buy. If you buy 2.5 pounds, then the cost is y = 2(2.5) so
y = $5
PLEASE HELP HURRY
If you solve an equation by graphing each side as a separate line, which of the following corresponds to the solution of the
equation?
a. there is only a solution if the lines are identical
c. the y-coordinate of the intersection point
b. both the x-coordinate and the y-coordinate of the
d. the x-coordinate of the intersection point
intersection point
Answer:
The x-coordinate gives the solution of the original equation.
Step-by-step explanation:
Let us assume that the original equation is 2x = x + 5 ........... (1) and the solution that this equation has will be x = 5.
But, if we solve the equation by graphing each side as a separate line i.e. y = 2x and y = x + 5, then solving those two equations we get the solution x = 5 and y = 10.
Therefore, the x-coordinate i.e. x = 5 gives the solution of the original equation (1). (Answer)
Answer:
D
Step-by-step explanation:
edge
what is 21.6 rounded to the nearest whole number
Answer:
22
Step-by-step explanation:
21.6 would round up because 6 is closer to 10 than it is 0
The number 21.6 rounded to the nearest whole number is 22.
What is Rounding Off?Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.
Rounding can be done for whole numbers as well as decimals.
Given a number 21.6.
We have to round the number.
Here the first digit after the decimal place is 6, which is greater than 5.
So we have to add 1 to the last digit in the whole part.
So 21.6 is rounded to 22 to the nearest whole number.
Hence the correct number is 22.
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Use the equation below to answer the question.
y = 3x + 6
Which equivalent equation is correctly matched with a key feature of the graph of the function it represents?
A
y = 3(x + 2) highlights that the y-intercept is at -2.
y = 3(x + 2) highlights that the y-intercept is at 2.
© y = 3(x + 2) highlights that the x-intercept is at -2.
y = 3(x + 2) highlights that the x-intercept is at 2.
Answer:
The equivalent equation is correctly matched with a key feature of the graph is
y = 3(x + 2) highlights that the x-intercept is at -2.
Step-by-step explanation:
Given:
[tex]y=3x+6[/tex]
Solution:
The Given Equation is in Slope - Point Form i.e
[tex]y=mx+c[/tex]
Where,
[tex]m=slope\\\\c=y-intercept[/tex]
On Comparing the given equation with above we get
[tex]slope=m=3\\\\y-intercept =6[/tex]
Now we Know that
Intercepts:
The line which intersect on x-axis and y-axis are called intercepts.
There are two intercepts:
y-intercept: The line which intersect at y-axis. So when the line intersect at y-axis X coordinate is zero.
x-intercept: The line which intersect at x-axis. So when the line intersect at x-axis Y coordinate is zero.
For x-intercept
Put y = 0 in
[tex]y=3(x+2)[/tex]
[tex]0=3x+6\\\\3x=-6\\\\\therefore x=\dfrac{-6}{3}=-2[/tex]
∴ x-intercept of
[tex]y=3x+6[/tex]
x-intercept = -2
The equivalent equation is correctly matched with a key feature of the graph is
y = 3(x + 2) highlights that the x-intercept is at -2.
Which number is a prime number?
Answer:
67
Step-by-step explanation:
9*7=63
13*5=65
23*3=69
Answer:
67
Step-by-step explanation:
Only number whose factors are 67 and 1
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On a coordinate grid, AB has an end point B at (24, 16). The midpoint of AB is P(4, -3). What is the y-coordinate of Point A?
The y-coordinate of point A is -22
Step-by-step explanation:
Given
B = (24,16)
P = (4,-3)
The formula for mid-point of AB will be given by:
[tex]P = (\frac{x_A+x_B}{2} , \frac{y_A+y_B}{2})[/tex]
As we already know the y-coordinate of midpoint
We can put the formula's y coordinate equal to the given value
[tex]\frac{y_A+y_B}{2} = -3\\\frac{y_A + 16}{2 } = -3\\y_A+16 = -3 * 2\\y_A +16 = -6\\y_A = -6-16\\y_A = -22[/tex]
Hence,
The y-coordinate of point A is -22
Keywords: Mid-point, coordinate geometry
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a dozen apples cost$4.92 for a dozen apples is a ratio of what per Apple
Final answer:
Each apple costs 41 cents when a dozen apples are bought for $4.92, determined by dividing the total cost by the number of apples.
Explanation:
The question asks to find the cost per apple when a dozen apples are purchased for $4.92. To find the cost per individual apple, you divide the total cost by the number of apples. There are 12 apples in a dozen, so:
$4.92 ÷ 12 apples = $0.41 per apple
So, each apple costs 41 cents. This exercise of finding the individual cost from a total is an example of a ratio used in basic arithmetic, often taught in middle school mathematics.
Leah has 280 toy cars she puts gift bags of toys together to sell at the flea market. She puts exactly 6 toys in each bag . She only sells full bags of toys. How many full bags of toys can she sell
Final answer:
Leah can make 46 full bags of toy cars to sell at the flea market when placing 6 toys in each bag out of her 280 toy cars, with 4 toys remaining unsold.
Explanation:
Leah has 280 toy cars and wants to sell them in gift bags, with 6 toys in each bag. To find out how many full bags she can sell, we need to divide the total number of toy cars by the number of toys per bag.
The calculation would be 280 ÷ 6 = 46 R4. This means Leah can make 46 full bags of toys and there will be 4 toys left over. Since she only sells full bags, the 4 extra toys will not be sold.
PLEASE HELP
Given: KLMN is a trapezoid, KL=MN, KM=15, m∠MKN=49° Find: The area of KLMN
Answer:
The area would be 111.41 unit² ( approx )
Step-by-step explanation:
Given,
KLMN is a trapezoid,
In which KL=MN, KM=15, m∠MKN=49°,
Suppose O and P are point in the segment LM, ( shown below )
Such that,
KN = OP,
In triangle MKO,
m∠KMO = 49° ( ∵ KM ║ LM, using alternative interior angle theorem ),
KM = 15 unit ( given )
[tex]\sin 49^{\circ} = \frac{KO}{KM}[/tex]
[tex]\implies KO = KM \sin 49^{\circ}=15 \sin 49^{\circ}[/tex]
i.e. height of the trapezoid KLMN is 15 sin 49°,
Again,
[tex]\cos 49^{\circ} = \frac{OM}{KM}[/tex]
[tex]\implies OM = KM \cos 49^{\circ}=15 \cos 49^{\circ}[/tex]
[tex]OP + PM = 15 \cos 49^{\circ}[/tex]
[tex]\implies KN + PM = 15 \cos 49^{\circ}----(1)[/tex]
Now, in right triangles KOL and NPM,
KL = MN,
OK = NP
By HL postulate of congruence,
Δ KOL ≅ Δ NPM
By CPCTC,
LO = PM,
⇒ LM = LO + OP + PM = PM + OP + PM = OP + 2PM = KN + 2PM-----(2),
Thus, the area of the trapezoid KLMN,
= 1/2 × height × sum of opposite parallel sides
[tex]=\frac{1}{2}\times KO\times (KN+LM)[/tex]
[tex]=\frac{1}{2}\times KO\times (KN+KN + 2PM)[/tex]
[tex]=\frac{1}{2}\times KO\times (2KN+2PM)[/tex]
[tex]=KO\times (KN+PM)[/tex]
[tex]=15 \sin 49^{\circ}\times 15 \cos 49^{\circ}[/tex]
[tex]=111.405157734[/tex]
[tex]\approx 111.41\text{ square unit }[/tex]
The area of a triangle can be found using the formula 1/2 x base x height. For a base of 166 mm and height of 930 mm, the area is 77.19 cm². However, for trapezoid KLMN, additional information is needed to calculate its area.
Explanation:To find the area of a trapezoid, especially when it has special properties like equal non-parallel sides (as trapezoid KLMN does with KL equal to MN), we often need to break it down into simpler shapes such as triangles and rectangles. However, with the information given, it's not straightforward to calculate the area of the trapezoid without additional height or angle information. The area of a triangle can be calculated using the formula ½ × base × height. For example, if you have a triangle with a base of 166 mm and height of 930.0 mm, the area is calculated as ½ × 166 mm × 930.0 mm which equals 77190 mm² or 77.19 cm² when converted to square centimeters, maintaining the proper number of significant figures.
1. 4/5 - (-3/10)=
2. 5.5 - 8.1=
3. -5 - 5/3=
4. -8 3/8 - 10 1/6=
5. -4.62 - 3.51=
Answer:
11/10
Step-by-step explanation:
4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10
9) Which one of the following expressions could be
used to find the average of the numbers x, y, and z?
Answer:
A) [tex]\frac{x+y+z}{3}[/tex]
Step-by-step explanation:
the formula for average is the sum of the digits, then divide that sum by the number of digits.
for example: let x = 1, let y = 2, let z = 3
so 1+2+3 is 6
then divided by the number of digits: 3
6/3=2
the average is 2
BRAINLIEST!!
A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find each probability.
selecting two blue chips without replacement
Answer:
[tex]\frac{1}{20}[/tex]
Step-by-step explanation:
First, we need to look at the # of chips. There are a total of 25, 6 of which are blue.
This means that the chance of getting the first blue chip would be [tex]\frac{6}{25}[/tex]
As there is no replacement, the total number of chips is 24 and there are only 5 blue left. This gives us the chance of [tex]\frac{5}{24}[/tex]
Now all we need to do is mulitply these two and then simplify
[tex]\frac{6}{25} *\frac{5}{24} =\frac{30}{600} =\frac{1}{20}[/tex]
Answer:
1/20
Step-by-step explanatio
pick without replacement must mean pick it two times without put back the first chip
6/25 x 5/24 = 1/20
Line segment AB with endpoints A(4, 16) and B(20,4) lies in the coordinate plane. The segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'. What will be the length of A'B'?
Answer:
The length of A'B' is 15 units
Step-by-step explanation:
As line segment AB has end points
A(4, 16)B(20, 4)The distance formula to calculate the distance between two points is given by:
[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]
[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]
[tex]d=\sqrt{16^2+(-12)^2}[/tex]
[tex]d=\sqrt{256+144}[/tex]
[tex]d=\sqrt{400}[/tex]
[tex]d=20[/tex]
[tex]d=20[/tex] is also the length of the line segment AB.
As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.
So,
The length of A'B' can be obtained by multiplying the length of AB by 3/4
Therefore,
The length of A'B' = 3/4 × 20 = 15
So, the length of A'B' is 15 units.
Keywords: dilation, distance formula, length, line segment
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Write the number 110 as a sum of hundred and tens
Answer:
100+10
Step-by-step explanation:
Which rule represents an inverse variation?
a. y= x^2
b. y= x/k
c. y= k ⋅ x
d. y ⋅x = k
Answer:
option C. and D.
Step-by-step explanation:
For two quantities with inverse variation, as one quantity increases, the other quantity decreases. For example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases.An inverse variation can be represented by the equation xy=k or y=kx .
does anyone know to do this
All the information is in the problem you just have to format it into an equation.
Point slope form: [tex]y_{2}-y_{2}=m(x_{2}-x_{1})[/tex] where "m" is the slope.
The equation would look like...
y+6=[tex]\frac{1}{5}[/tex](x+4)