Answer:
Step-by-step explanation:
The function f(x) = 4x/(x-16) has two vertical asymptotes at x = 16. This can be seen by taking the limit of the function as x approaches 16 from the left and right sides.
On the left side, as x approaches 16 from the left, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach -∞. This results in a limit of -∞, indicating a vertical asymptote at x = 16.
On the right side, as x approaches 16 from the right, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach +∞. This results in a limit of +∞, also indicating a vertical asymptote at x = 16.
The end behavior of the function is that as x approaches +∞, the function will approach +∞, and as x approaches -∞, the function will approach -∞.
Using f(x) = 2x-3 and g(x) = 5, find f(g(3)).
7
5
3
0
None of the choices are correct.
Answer: 7
Step-by-step explanation:
[tex]g(3)=5 \implies f(g(3))=f(5)=2(5)-3=7[/tex]
In the given figure, triangle QPS = triangle SRQ.Find each value.
(a) x (b)angle PQS (c)angle PSR
In the given figure, where triangle QPS = triangle SRQ, the value of
a. x = 47°
b. ∠PQS = 32°
c. ∠PSR = 74°
What is a triangle?A triangle is a 3-sided polygon that is occasionally (though not very frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which might be the same.
In a right triangle, the two sides opposite the right angle are referred to as the hypotenuse, and the other two sides are referred to as the legs. All triangles are bicentric and convex. The triangle's interior is that part of the plane it encloses; the exterior is the rest.
Given that ∆QPS ≈ ∆SRQ
a) ∠QPS = ∠QRS
106° = 2x + 12
106° - 12 = 2x
2x = 94°
x = 47°
b) ∠RSQ = ∠PQS
∠SQR + ∠SRQ + ∠RSQ = 180°
42° + 2(47°) + 12 + ∠RSQ = 180°
148 + ∠RSQ = 180°
∠RSQ = 180° - 148°
∠RSQ = 32°
∠PQS = 32°
c) ∠PSR = ∠PSQ + ∠RSQ
[ ∠PSQ = 42° = ∠SQR ; ∠RSQ = 32°]
∠PSR = 42° + 32°
∠PSR = 74°
Thus, In the given figure, where triangle QPS = triangle SRQ, the value of x = 47°, ∠PQS = 32°, ∠PSR = 74°.
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A school of salmon was swimming in the river 5 feet below the surface. To escape a hungry bear, they went down another 3 feet.
What is the position of the salmon now relative to the surface?
Using the addition operation, the position of the salmon currently relative to the surface is 8 feet below the surface.
What is the addition operation?The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.
The addition operation involves adding two or more addends to get a result known as the sum or total, using the equal symbol (=) and the addition operand (+).
The initial position of the school of salmon below the surface = 5 feet
The depth they went down further to escape the bear = 3 feet
The current position = 8 feet (5 + 3) below the surface.
Thus, based on the addition operation, the school of salmon can be located 8 feet below the surface as they attempted to escape the hungry bear.
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Assume that the number of liters of water remaining in the bathtub varies
quadratically with the number of minutes which have elapsed since you
pulled the plug. a. If the tub has 38.4, 21.6, and 9.6 liters remaining at 1, 2, and 3 minutes,
respectively, since you pulled the plug, find a function V(t) expressing the
volume of water t minutes after you pulled the plug.
b. How much water was in the tub when you pulled the plug?
c. When will the tub be empty?d. In the real world, the number of liters of water in the tub can never be
negative. What does the model predict is the least amount of water in the
tub? Is this number reasonable?e. Draw a graph of the function in the appropriate domain. Use a dotted curve
for any portion of the graph that is outside the reasonable domain.f. What is the reasonable domain and range for this model?g. Why is a quadratic function more reasonable for this problem than a linear
function would be?
The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.
What is parabola ?
A parabola is a symmetric, U-shaped geometric shape.
a)V(1) = 38.4 = a(1)^2 + b(1) + c
V(2) = 21.6 = a(2)^2 + b(2) + c
V(3) = 9.6 = a(3)^2 + b(3) + c
Solving the system of equations, we get ,
a = -2.4 , b = 11.2 , c = 46 , V(t) = -2.4t^2 + 11.2t + 46.
b)We can find the initial volume of water in the tub by plugging in t = 0 into the function V(t) = -2.4t^2 + 11.2t + 46. This gives us V(0) = 46 liters, so the tub had 46 liters of water when the plug was pulled.
c)t = (-11.2 +/- sqrt(11.2^2 - 4*(-2.4)46))/(2(-2.4))
t = (11.2 +/- sqrt(124.48 + 552.8))/-4.8
t = (11.2 +/- sqrt(677.28))/-4.8 = (11.2 +/- 26.16)/-4.8 = -14.96 or 2.16
d)V(4.6667) = -2.4*(4.6667)^2 + 11.2*(4.6667) + 46 = -2.4*21.778 + 46.4 + 46 = -52.6667. So the least amount of water the model predict is -52.6667 liters. This number is not reasonable as the volume of water can't be negative.
e) The graph of the function V(t) = -2.4t^2 + 11.2t + 46 is a parabola that opens downward and has its vertex at (4.6667, -52.6667). Any portion of the graph for t < 0 or t > 2.
The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.
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Which is closest to the volume of Mike's cup?
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3} \\\\\\ V=21\pi \implies {\Large \begin{array}{llll} V\approx 65.97 \end{array}} ~in^3 ~~ \approx 66~in^3[/tex]
Examine the composite figure formed by placing a triangular prism on top of a rectangular prism. All of the measurements have centimeters as their units.
The triangular base has height 12, base 14 & 2 other sides 13 & 15. The prism height is 20. The rectangular prism is 8 by 14 by 20. The prisms share a face that is 14 by 20.
© 2018 StrongMind
To find the surface area, Brad splits the figure into two pieces, the rectangular prism and the triangular prism.
He finds the total surface area of the rectangular prism by finding the area of each face to get 1,104 cm2.
He then finds the total surface area of the triangular prism by finding the area of each face to get 1,008 cm2.
Finally, he adds the surface areas together to get 2,112 cm2.
Is Brad's solution correct? Why or why not?
Answer:
Step-by-step explanation:
Brad's solution to find the surface area of the composite figure is not correct.
In his solution, Brad adds the surface areas of the triangular prism and the rectangular prism separately,
but it's not taking into account that the two prisms share a face that is 14 by 20.
When finding the surface area of a composite figure, it's important to take into account any shared faces.
Since the two prisms share a face that is 14 by 20, Brad should subtract this area from one of the prisms,
otherwise he will be counting it twice in the final result.
The correct method would be:
Rectangular prism: (2 * 8 * 14) + (2 * 14 * 20) + (2 * 8 * 20) = 1,104 cm^2
Triangular prism: (1/2 * 14 * 12) + (1/2 * 13 * 15) + (3 * 14 * 20) = 1,008 cm^2
Subtracting shared area: 1,104 cm^2 + 1,008 cm^2 - (14 * 20) = 2,096 cm^2.
So Brad's solution is incorrect, the correct surface area of the composite figure is 2,096 cm^2.
Answer:90x567
Step-by-step explanation:
Describe each correlation value.
A. r = 0.921
B. r=-0.873
C. r = -0.281
D. r = 0.303
[Select]
[Select]
[Select]
[Select]
>
>
The correlation coefficient having -negative value means inverse correlation and +positive value means direct relationship.
What Is the Correlation Coefficient?An analytical way to gauge how strongly two variables are linearly related is to use the correlation coefficient. Anywhere between -1 and 1 can be its value. A correlation coefficient of -1 indicates a perfect negative, inverse, or inverse-correlation, where values in one series increase as those in the other decline and vice versa. An exact positive correlation or direct relationship is indicated by a coefficient of 1, or 1. In the absence of a linear relationship, a correlation coefficient of 0 indicates.
When evaluating the level of association between two variables, factors, or data sets, scientists and financiers alike use correlation coefficients. Assuming, for instance, that there is a strong positive correlation between oil prices and forward returns on oil stocks given that high oil prices are advantageous for crude producers
Now,
For
A. r = 0.921 -Direct relationship.
B. r= -0.873 -Inverse relationship.
C. r = -0.281 -Inverse relationship.
D. r = 0.303 -Direct relationship.
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An Isoceles right triangle whose legs measure 6 is continously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a what?
Assuming an isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object, the three-dimensional object is a: D. cone with a diameter of 12.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees (90°).
Generally speaking, the resulting three-dimensional (3-D) geometric object that is formed when a right-angled triangle is continuously rotated about a leg would be a cone. Additionally, the radius of this cone would be equal to 6 because the base of the right-angled triangle is 6.
Therefore, the diameter of this cone can be calculated as follows;
Diameter of cone = 2 × radius of cone
Diameter of cone = 2 × 6
Diameter of cone = 12 units.
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Complete Question:
An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a
answer choices
cylinder with a diameter of 6
cylinder with a diameter of 12
cone with a diameter of 6
cone with a diameter of 12
Multiply. x^2-1/5xy * x^2y/1+x
The required expression is x(x - 1)/5 which is determined by multiplication.
The expression is given in the question, as follows:
(x² - 1)/5xy × x²y/(1 + x)
We have to determine the solution to the given expression by multiplication.
As per the given expression, we have
⇒ (x² - 1)/5xy × x²y/(1 + x)
Cancel out the equivalent terms in the above expression,
⇒ (x - 1)(x + 1)/5 × x/(1 + x)
Reduce the same in the above expression,
⇒ x(x - 1)/5
The required expression is x(x - 1)/5.
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Potatoes cost janice $1. 00 per pound, and she has $6. 00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1. 50, the second pound is worth $1. 14, the third pound is worth $1. 05, and all subsequent pounds are worth $0. 30 per pound.
Janice will spend $3.00 on 3 pounds of potatoes. If she only has $3.00, she will spend it all on potatoes and purchase 3 pounds of potatoes.
a) 3 pounds of potatoes
b) 3 pounds of potatoes
What is pounds?A pound is defined as 16 ounces, 7,000 grains (or 0.45359237 kg) of avoirdupois weight and 12 ounces, 5,760 grains (or 0.37324171216 kg) of troy and apothecaries' weight. The initials "lb" come from the Latin word "libra," which was the Roman equivalent of the modern "pound."
Janice can get potatoes once the price is set. As a result, she will buy those potatoes whose value is less than her willingness to pay. Her disposition to pay is what she feels the pound of potatoes is "worth". If the worth of the primary, second, and third pounds exceeds the price of the potato ($1.50, $1.14, $1.05 > $1.00), Janice will not purchase these because the worth is less than the price. (0.30 USD 1.00 USD).
Thus, Janice will spend $3.00 on 3 pounds of potatoes. If she only has $3.00, she will spend it all on potatoes and purchase 3 pounds of potatoes.
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the diameter of a wheel of a car is 50 cm. if the car travels at an average speed of 36 km per hour, what is the number of revolutions made by the wheel per minute? (use
The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.
Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute
1. Convert the speed from kilometers to meters per hour
36 km/hr = 36 x 1000 m/hr
2. Calculate the circumference of the wheel
Circumference of wheel = Diameter x π
Circumference of wheel = 50 cm x 3.14 = 157 cm
3. Calculate the number of revolutions per minute
Number of revolutions per minute = (Speed in m/hr) / (Circumference of wheel in cm)
Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute
The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.
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Find the gradient vector field ∇f of f and sketch it.
f(x, y) = 7 x2 + y2
∇f(x, y) =
The gradient vector field ∇f of f(x, y) = 7 x2 + y2 is ∇f(x, y) = <14x, 2y>.
The gradient vector field ∇f of a scalar function f(x, y) is given by the vector function
∇f(x, y) = <∂f/∂x, ∂f/∂y>.
In this case, the function f(x, y) = 7x^2 + y^2 and we can find the gradient vector field as follows:
∇f(x, y) = <∂f/∂x, ∂f/∂y> = <14x, 2y>
This vector field points in the direction of steepest ascent at each point in the xy-plane, and its magnitude at each point is equal to the rate of change of f in that direction.
To sketch the gradient vector field, we can plot the vector <14x, 2y> at various points in the xy-plane. The direction of the vector at each point will be the direction of steepest ascent of the function f, and the length of the vector will indicate the rate of change of f in that direction.
We can notice that for the function f(x,y) = 7x^2+y^2, the function is always increasing as we move along the direction of the vector <14x,2y> and the vectors are always pointing away from the origin, which means that the origin is a local minimum of the function.
It's important to note that this is a paraboloid. The direction of steepest ascent is the direction of the tangent of the paraboloid at any point, which is pointing upwards from the vertex of the paraboloid.
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In 1995 the Educational Testing Service (ETS) adjusted the scores of SAT
tests. Before ETS recentered the SAT Verbal test, the mean of all test scores was 450. Which statistic would not change if 50 points were added to each score?
The statistic that would not change if 50 points were added to each score in the SAT tests is the Standard Deviation.
What happens to the standard deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.
The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
Since they are used to determine standard deviation, sample size, mean, and data values all have an impact on standard deviation. By removing outliers, the sample size, mean, and standard deviation may all change.
Because 50 points was added to each score, they are still the same distance from each other which means the standard deviation will not change.
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An earthworm was in the soil 9 inches below the surface. To find moister soil, it moved down 7 inches.
What is the position of the earthworm now relative to the surface?
inches
Using the addition operation, the position of the earthworm relative to the surface is 16 inches below the surface.
What is the addition operation?One of the four basic mathematical operations, including subtraction, division, and multiplication, is the addition operation.
Using the addition operation involves adding two or more addends to determine the sum. It also involves using the addition operand (+) and the equal symbol (=).
The initial position of the earthworm below the surface = 9 inches
The depth it moved down to find moister soil = 7 inches
The current position = 16 inches (9 + 7) below the surface.
Thus, based on the addition operation, the earthworm is 16 inches below the surface in its endless search for moister soil.
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What transformation(s) have been applied to function f(x) to get g(x)? Check all that apply.translationreflectiondilationrotation
Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.
The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).
Whenever the function is "translated" it is moved in such a very way that it will not alter the shape or rotate in any way.The reflection is a modification of the function's graph all along the x or y-axis (or both).Dilation is defined as a stretch or shortening about in an axis caused by multiplying or subdivisions.Therefore, the answer is "translation , reflection , and dilation".
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Answer:
A) Translation
B) Reflection
C) Dilation
Step-by-step explanation:
Hi, I'm having a little bit of confusion answering this. What I did was:
Tan(20) = 9/x
9 x Tan(20) = x
But my answer was wrong, can someone tell me what I did wrong?
Thanks :)
Answer:
Step-by-step explanation:c
After its second bounce, a ball reached a height of 80 cm. The rebound factor for the ball was 0.7. From approximately what height, in cm, was the ball dropped?
A) 34
B) 49
C) 115
D) 163
Answer: The answer is C hope this helps :)
Step-by-step explanation:
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The height of a ball after its second bounce was 80 cm. The ball had a rebound factor of 0.7. Then the height of the ball from where it is dropped is given as,
0.7h = 80
h = 80 / 0.7
h = 14.3 cm
h ≈ 115 cm
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
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Point Q is the center of dilation. Line W Y is dilated to created line W prime Y prime. The length of Q W is 2 and the length of W W prime is 3.5. Line WY is dilated to create line W'Y' using point Q as the center of dilation. What is the scale factor
The scale factor of the given measurement is 1.75.
The scale factor of a dilation is determined by the ratio of the length of the image to the length of the preimage. In this case, line W'Y' is the image and line WY is the preimage. We know that the length of QW is 2 and the length of WW' is 3.5.
We can use these pieces of information to calculate the scale factor. The scale factor is the ratio of the length of the image to the length of the preimage, which means it is the ratio of 3.5/2 = 1.75.
Therefore the scale factor of the dilation is 1.75.
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four horizontal lines and four vertical lines are drawn in a plane. in how many ways can four lines be chosen such that a rectangular region is enclosed?
Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.
The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as
4C2 = 4!/ (2!×2!)
4C2 = 6
The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.
It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).
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In the figure, point $O$ is the center of the circle, the measure of angle $RTB$ is $28$ degrees, and the measure of angle $ROB$ is three times the measure of angle $SOT$. What is the measure of minor arc $RS$, in degrees
The measure of minor arc RS, in degrees, will be approximately 86.66
Call the intersection of BT and circle A.
And we have that angle measurement. RTB =(1/2) (a measure of minor arc RB - a measure of minor arc SA) (a measure of minor arc RB - the measure of minor arc SA)
But angle SOT equals the measure of angle SOA.
Moreover, because SOA is a central angle, its measure is the same as that of minor arc SA.
ROB has the same measure as minor arc RB since it is also a central angle.
The measure of minor arc SA= angle SOT= angle SOA=M
The measure of minor arc RB= angle ROB=4M
So we have this equation
28=(1/2)(4M-M)
56=3 M
[56/3]=M
So, minor arc S A=[tex](56 / 3)^{\circ}[/tex]
And minor arc RB =[tex]4(56/3)=(224/3)^{\circ}[/tex]
And minor arc RS =[180-(56/3)-(224/3)]=[tex](260/3)^{\circ} \approx 86.66^{\circ}[/tex]
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The complete question should be like this:
In the figure, point O is the centre of the circle, the measure of angle RTB is 28 degrees, and the measure of angle ROB is four times the measure of angle SOT. What is the measure of minor arc RS, in degrees?
The needed diagram is attached below:
Select 2 points in the solution of the inequality graphed below.
654-
21
3
x
k
a store manager wants to mix 20 lb of nuts worth $3 per pound with some nuts worth $10 per pound to make a mixture worth $5 per pound. how many pounds of $10 nuts must be used?
a telephone company charges $0.50 for the first 5 minutes of a call and $0.09 for each additional minute. which interval below represents how a person can talk for $3 (assume that a person cannot talk for a fraction of a minute)?
On solving the provided question, we can say that by equation 15+4 = total minutes, they can talk 19 minute
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x= total minutes -4 the 1st 4 minutes are included in the .30
total cost = .3 + .18 x
[tex]3 = .3 +.18 x\\2.7 = .18x\\2.7/.18 = x\\15 = x[/tex]
x = total minutes -4
15+4 = total minutes
they can talk 19 minute
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[(1/15−2/5)⋅(−3/4)³]÷(−9)
Answer:
[tex]-\frac{1}{64}[/tex]
Step-by-step explanation:
We have:
[tex][( \frac{1}{15} - \frac{2}{5}) * (-\frac{3}{4})^{3}] / (-9)[/tex]
Now, we will multiply the second fraction in the first parentheses by [tex]\frac{3}{3}[/tex] so we can subtract it from the [tex]\frac{1}{15}[/tex]. Then, we will multiply all of the [tex]\frac{3}{4}[/tex]'s. This gives us:
[tex][( \frac{1}{15} - \frac{2}{5} * \frac{3}{3} ) * (-\frac{3}{4} * -\frac{3}{4} * -\frac{3}{4})] / (-9)[/tex]
Which simplifies to:
[tex][( \frac{1}{15} - \frac{6}{15} ) * (-\frac{27}{64})] / (-9)[/tex]
Simplifying:
[tex][(-\frac{5}{15} ) * (-\frac{27}{64})] / (-9)[/tex]
Multiplying in our brackets gives us:
[tex]\frac{9}{64} / (-9)[/tex]
Now, using the rule of KCF (Keep, Change, Flip), we will keep our first fraction, change our division sign to a multiplication sign, and make the last number its reciprocal. This gives us:
[tex]\frac{9}{64} * -\frac{1}{9} = -\frac{1}{64}[/tex]
So, the equation simplified is [tex]-\frac{1}{64}[/tex].
Hope this helped!
A cell phone company charges 50$ for a phone plus 25$ per month. You get a gift card for 100$. When does the total spent on your phone service exceed the amount on you gift card?
A) Write an inequality to represent the money spent on a phone plan
B) when doe the total spent on your phone service exceed the amount of your gift card
Answer:
A) The money spent on a phone plan can be represented by the inequality:
50 + 25x > 100
B) The total spent on the phone service exceeds the amount of the gift card after the 2nd month.
Step-by-step explanation:
A. The inequality represents the total cost of the phone plan, where x represents the number of months for which the service is used.
The first part of the inequality, 50$, represents the initial cost of the phone.
The second part, 25x, represents the monthly cost of the service, 25$ per month.
So, the inequality represents the total cost of the phone plan as the sum of the initial cost of the phone and the monthly cost of the service for x number of months.
50 + 25x > 100
It states that the total cost (50 + 25x) of the phone plan is greater than 100$.
It's the total cost you have to pay for the phone and the service.
It's used to know when the total cost exceeds 100$, which is the gift card's value.
B. To find out when the total spent on the phone service exceeds the amount of the gift card, we can substitute in the inequality with the given values and solve for x.
50 + 25x > 100
x > (100-50)/25
x > 2
So, the total spent on the phone service exceeds the amount of the gift card after the 2nd month.
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a rectangular room is 2 times as long as it is wide, and its perimeter is 36 meters. find the dimension of the room
The dimension of the room is width = 6 meters and length = 12 meters.
What is rectangle ?
A rectangle is a four-sided polygon with opposite sides that are parallel and of equal length. It has four right angles. The two parallel sides are called the length and the width. The length is the longer of the two sides, while the width is the shorter of the two sides.
Let's assume the width of the rectangular room is "w" and the length of the rectangular room is "l"
We know that the perimeter of a rectangle is the sum of twice the length and twice the width: P = 2l + 2w
Given that the perimeter is 36 meters, we can substitute that into the equation ,
36 = 2l + 2w
We also know that the length is 2 times the width, so we can substitute that into the equation: I = 2w
Now we have two equations ,
36 = 2(2w) + 2w
36 = 6w
So the width of the room is 6 meters. To find the length, we can use the information that the length is 2 times the width ,
l = 2w = 2*6 = 12 meters
So the dimension of the room is width = 6 meters and length= 12 meters.
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Round off 987 416 to the nearest 5
round off 987 416 to the nearest 5 mean the 6 turns into 5 so the answer is 987 415.If the 6 was 2 the 2 will turn into 0 and if the 6 was 9 the 9 will turn into 10
Can anyone please help me?
Answer: C. 3
Step-by-step explanation:
Using the trapezoid midsegment theorem,
[tex]\frac{4x+8x+3}{2}=4x+7.5\\\\\frac{12x+3}{2}=4x+7.5\\\\12x+3=8x+15\\\\4x+3=15\\\\4x=12\\\\x=3[/tex]
Casey wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs %60 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
A line passes through the points (–1, –5) and (4, 5). the point (a, 1) is also on the line. a coordinate plane. what is the value of a? –2 –1 1 2
The value of a is 2
We can use the slope-intercept form of a line, y = MX + b, to find the equation of the line.
The slope (m) of the line can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So, m = (5 - (-5)) / (4 - (-1)) = 10/5 = 2
Now, we can use the point-slope form of a line, y-y1 = m(x-x1)
where (x1,y1) is any point on the line and m is the slope of the line.
In this case, we will use the point (x1, y1) = (–1, –5)
so, y-y1 = m(x-x1) = -5 - 2(-1-x) = -5-2+2x
Now we know that the point (a,1) is also on the line, we can substitute the value of x and y in the equation
so, 1 - (-5) = 2(a - (-1))
1 +5 = 2a+2
6 = 2a+2
4 = 2a
a = 2
Therefore, the value of a is 2.
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