An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.
We are given a rectangular prism.A rectangular prism is no different than a cuboid.Let the height of the rectangular prism be "h".The length of the rectangular prism is "h-3".The width of the rectangular prism is "h+5".The volume of the rectangular prism is the same as that of the cuboid.The volume of the rectangular prism is the product of its length, its width, and its height.The volume of the rectangular prism is (h - 3)*(h + 5)*h.An equation for the volume of the prism as a function of the height is :Volume = (h - 3)*(h + 5)*hVolume = (h² + 2h - 15)*hVolume = h³ + 2h² - 15hTo learn more about prism, visit :
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Someone please complete. will mark brainliest. 30 points given!!
The answer to all the subparts of the congruency of triangles is shown:
ΔABC and ΔPQR are congruent - SSS congruence.ΔGHJ and ΔUVW are congruent - SSS congruence.ΔGHJ and ΔPQR are not congruent.ΔPQR and ΔUVW are not congruent.What is the Congruence of a triangle?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.In ΔABC and ΔPQR
AB = PQAC = PRBC = QRThus from SSS congruence, we get ΔABC ≅ ΔPQR
In ΔGHJ and ΔUVW
GH = UVJH = WVJG = UWThus from SSS congruence, we get ΔGHJ ≅ ΔUVW
However, ΔGHJ and ΔPQR are not congruent because there are no two sides that are equal.
Also, ΔPQR and ΔUVW are not congruent because of the same reason mentioned above.
Therefore, the answer to all the subparts of the congruency of triangles is shown:
ΔABC and ΔPQR are congruent - SSS congruence.ΔGHJ and ΔUVW are congruent - SSS congruence.ΔGHJ and ΔPQR are not congruent.ΔPQR and ΔUVW are not congruent.Know more about the Congruence of a triangle here:
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Which recieves the more interest per annum:$150 invested at 4% or $180 invested at 3 1/2%? What is the annual difference
Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time. When the total principal amount and the rate of interest for a certain amount of time surpass the due date for payment, this is known as compound interest.
What do compound and simple interest mean?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued. S.I. = (P, T, and R) x 100 is the formula.For Example : $150 put up at 4%Total to Calculate Interest on - $150
Annual Interest Rate - 4%
Monthly interest - $0.50
Yearly interest - $6.00
Investing $180 at 3 1/2%Total to Calculate Interest on - $180
Annual Interest Rate - 3.5
Monthly interest - $0.53
Yearly interest - $6.30
Consider making a $100 (the principal) investment at a 5% yearly rate for a year. The computation for simple interest is as follows: $100 x.05 interest x 1 year = $5 in simple interest after a year.To learn more about Simple interest refer to:
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Paul receive about 13 advertisement via email each day. about how many advertisement emails will he receive in 30 days?
Answer:
390
Step-by-step explanation:
Paul receive about 13 advertisement via email each day. about how many advertisement emails will he receive in 30 days?
13 × 30 = 390
A study on students drinking habits wants to determine the true average number of alcoholic drinks all uf graduate students have in a one week period. We know from preliminary studies that the standard deviation is around 1. 8. How many students should be sampled to be within 0. 25 drink of population mean with 95% probability?.
The number of the students should be sampled to be within 0.25 alcoholic drinks of population mean with 95% probability is 62.
What is termed as the Margin of error?The margin of error measures the degree of uncertainty in the parameter estimates of parameter results.The reliability of a estimates decreases as the margin of sample error increases.α is the result of subtracting one from confidence interval as well as dividing by two.
α = (1 - 0.95) ÷ 2 = 0.25
Find z in the Z-table because z does have a p-value of 1 - α.
As a result, the p-value of z is (1 - 0.025) = 0.975.
Thus, z = 1.96
Now find M as;
M = z × (σ ÷ √n)
In which,
n is the sample size σ = population standard deviation.When M = 1,
The standard deviation, in accordance with the question, is approximately 1.
σ = 1
M = z × (σ ÷ √n)
0. 25 = 1.96 × (1 ÷ √n)
√n = 1.96 × (1 ÷ √n)
Squaring both sides,
(√n)² = ((1.96 × 1) ÷ 0.25)²
n = (7.84)²
n = 61.4656
n ≈ 62
Thus, the number of the students should be sampled to be within 0. 25 alcoholic drink of population mean with 95% probability is 62.
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The fox population in a certain region has a relative growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 20,200 foxes. a) Find an equation that models the population t years after 2000 (t = 0 for 2000). A = b) Use the equation from part (a) to estimate the fox population in the year 2009. Round to the nearest fox. foxes
Answer:
where is the question? plssss so im sorrry but where is the question i don't see a question?
Please help me because I got the answer wrong.
[tex]\cfrac{1}{3}x^2~~ = ~~\cfrac{4}{27}\implies \cfrac{x^2}{3}~~ = ~~\cfrac{4}{27}\implies x^2=\cfrac{(3)4}{27}\implies x^2=\cfrac{12}{27} \implies x=\pm\sqrt{\cfrac{12}{27}} \\\\\\ x=\pm\cfrac{\sqrt{12}}{\sqrt{27}} \implies x=\pm\cfrac{\sqrt{2^2\cdot 3}}{\sqrt{3^2\cdot 3}}\implies x=\pm\cfrac{2\sqrt{3}}{3\sqrt{3}}\implies x=\pm\cfrac{2}{3}[/tex]
Evaluate the numerical expression open parentheses 5 to the power of negative 4 close parentheses to the power of one half.
Answer:
1/25 or 0.04
Step-by-step explanation:
evaluated in fraction and decimal form i hope this helped :)
Comparing Attributes of 2-D Figure, (points, brainliest, stars)
The given figure is a Rhombus hence the last diagram is correct.
In planar Euclidean geometry, a rhombus—also known as a rhombi or rhombus—is a quadrilateral having four sides of equal length.
A quadrilateral with equally sized sides is referred to as a "equilateral quadrilateral." While the name "diamond" is usually used to refer to a rhombus with a 60° angle because it resembles the projection of an octahedral diamond from the playing card's diamond suitThe term "lozenge" is occasionally used to specifically refer to a rhombus with a 45° angle.Every single rhombus is a unique example of a parallelogram and a kite, and it is straightforward (does not self-intersect). A right-angled rhombus is a square.The given figure is a rhombus. All the sides are equal but the angles are not 90°. Hence its is not a square or a rectangle.
The correct diagram is attached below.
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you are traveling 150 miles to your cousins house. You travel at an average rate of 50 miles per hour. How long will it take to get to cousin house?
Answer
It will take 3 hours to get to your cousin's house.
Explanation
Firstky, note that Speed is given as
[tex]\text{Speed =}\frac{Dis\tan ce}{Time}[/tex]For this question, we are told that the distance to your cousin's house is 150 miles.
The speed is an average rate of 50 miles per hour.
We are then asked to calculate how long it will take to get to your cousin's house.
Speed = 50 miles/hour
Distance = 150 miles
Time = ?
[tex]\begin{gathered} \text{Speed = }\frac{Dis\tan ce}{Time} \\ 50=\frac{150}{Time} \\ \text{Cross multiply} \\ 50\times Time=150 \\ \text{Divide both sides by 50} \\ \frac{50\times Time}{50}=\frac{150}{50} \\ \text{Time = 3 hours} \end{gathered}[/tex]Hope this Helps!!!
you start at (1,7). you move left 1 unit and down 6 unit
The required point on the cartesian plane is (0,1).
What is a cartesian plane?Definition of a Cartesian Plane. The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line.
In a graph (1,7) lies in the first quadrant
And if we go 1 unit left then that means that we will be on the y axis
Then if we go down 6 units we will reach at point 1 unit away from the origin on the y axis . This particular point can be represented as (0,1).
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A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
(d) f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project
In the above question it is given that
A project is being created by a group of students by arranging layers.
The first layer is having 4 layers and as we move to the next layers, it is getting 2 times of the number of layers in the first layer.
i,.e f(1) = 4
Number of layers in the second layer = 8 layers
f(2) = 4.2 = 8
Now, we need to find the general arithmetic formula to determine the subsequent n number of layers in the project
As the subsequent layers are getting n times of the first layer, so we'll also find the similar arithmetic formula where addition to the first layer with n times of it is happening
So, after checking all the given options we find, (d) as the appropriate option
f(1) = 4
f(n) = 4 + d(n-1) , n>0
We'll find the number of layers in the 3 layers
Here, n = 3
Putting in the formula, we'll find.
f(3) = 4 + d(3-1)
f(3) = 4 + d(2)
where d(2) = 8 (given)
so, f(3) = 4 + 8 = 12
Hence, f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project
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if a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.
The diameter is decreasing at a rate of - 0.101 cm/min
Given that,
Surface area is decreasing at a rate of [tex]7cm^{2}[/tex]/min,
We know that,
Surface Area of a sphere:
S = 4 π r2
dS/dt = - 7cm2/min
our aim is to find rate of decrease of Diameter:
dD/dt =?
Substitute r in the equation with radius = 1/2*Diameter:
r = 1/2D
Take the derivative of the surface area function with respect to time:
d/dt [S = 4 π (1/2D)2]
d/dt [S = 4 π 1/4*D2]
d/dt [S = π *D2]
dS/dt = 2πD*dD/dt
Solve for dD/dt:
dD/dt = dS/dt / 2πD
Substitute, dS/dt = - 7cm2/min and D = 11 cm
dD/dt = dS/dt / 2πD
dD/dt = - 7cm2/min / 2π*11cm
dD/dt = - 7cm2/min / 22π cm
dD/dt = - 7cm / 22π min
dD/dt = - 0.101 cm/min
Therefore, the diameter is decreasing at a rate of - 0.101 cm/min
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0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm
if a snowball melts so that its surface area decreases at a rate of 7 cm2/min,
find the rate at which the diameter decreases when the diameter is 11 cm.
Surface area: S
radius: r
diameter: e
time: t
[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]
S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e
dS/dt = 7cm^2 / min
de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] / [2pi*11cm]
= 0.101331789 cm/min
Hence , 0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm
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a/6 -5=9 what’s the answer
Answer:
a = 84
Step-by-step explanation:
[tex]\frac{a}{6} - 5 = 9\\\frac{a}{6}} - \frac{5*6}{6} = \frac{9*6}{6}\\ a - 30 = 54\\ a = 54 + 30\\ a = 84[/tex]
which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?
The expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
We know that for any polynomial equation with roots:
[tex]a_{1}, a_{2}, a_{3} ,...[/tex]
with multiplicity:
[tex]m_{1}, m_{2}...[/tex]
the equation for the polynomial is given by:
[tex]f(x)=(x-a_{1}) ^{m_{1} }, (x-a_{2}) ^{m_{2} }...[/tex]
If the leading coefficient is negative we may take '-' sign in the starting of the expression.
Here we are given that, f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3
Hence, f(x) is given by:
= [tex]f(x)=(x-(-4)) ^{1 }, (x-2) ^{1}, (x-9) ^{1},(x-(-5)) ^{3}[/tex]
= [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
Hence, the expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
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Find the x- and y-intercepts of the graph of x+y=18. State each answer as an integer or an improper fraction in simplest form
The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.
What is the x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function. The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
For x intercept, y = 0
x + y = 18
x + 0 = 18
x = 18
Hence, the x-intercept is (18, 0)
For y intercept, x = 0
x + y = 18
0 + y = 18
y = 18
Hence, the y-intercept is (0, 18)
The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.
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The ratio of small dogs to large dogs at the dog show is 4:3. If there are 60 dogs in the
show, how many are large dogs?
Answer:
45 large dogs
Step-by-step explanation:
Step 1:
60 x 3 = 180
180 ÷ 4 = 45
I need help with this page for my math class
Answer:
(1) Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. Example, 1, 2, 3, 4,... are natural numbers.
Step-by-step explanation:
(2) Number Trick 1:
Let the single digit be: 1
Multiply by 2: 1 x 2 = 2
Add 8 to your answer: 2 + 8 = 10
Divide your answer by 2: 10 ÷ 2 = 5
Subtract original number: 5 - 1 = 4
(3) Final result is 4.
The trick will always work for all NATURAL NUMBERS.
PLS HELP
Lisa needs at least 870 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 200 gigabytes available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs. Lisa is going to use memory cards that each hold 256 gigabytes.
Let C represent the number of memory cards that Lisa buys.
Which inequality describes this scenario?
The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Given that lisa checks and finds that she has 200 gigabytes available on her phone. It is going to use memory cards that each hold 256 gigabytes.
Let consider that C represent the number of memory cards that Lisa buys.
Then the inequality ;
200 + 256C ≥ 870
Hence, The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.
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Which represents a total cost of 3 dance tickets at a price of c for each, less a one-time $2 discount?
A 2(c) - 3
B 3(2) - c
C 3(c - 2)
D 3(c) - 2
The correct answer is option D
3(c) - 2 represents the total cost of three dance tickets at a cost of c each, less a one-time $2 discount.
Explanation:A linear equation is one with a leading degree of one.A linear equation is an algebraic equation With only a constant and a first-order (linear) term of the formy = mx+b, where m is the slope and b is the y-intercept.
The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.Based on the question. We have the parameters listed below.
The total cost of three dance tickets is 3c (at c for each)
One-time offer = $2
Because discounts are always subtracted from the total cost,
the equation represents,
the total cost of three dance tickets at a cost of c each, less a one-time discount $2
= 3(c) - 2
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- student claims that there is no solution to the system of inequalities shown.
y≥x² + 3
y< x + 1
2
PART A (2 POINTS): Explain a method for proving that the student's claim is correct.
peaker notes
The system of inequalities has no solution because the lines do not meet at any point
How to prove the student's claim?The system of inequalities is given as
y ≥ x² + 3
y < x + 1
From the above system of inequalities, we can see that the function types are
Parabola: y ≥ x² + 3Linear: y < x + 1Next, we plot the graph of both inequalities in the system (see attachment for the graph)
From the graph, we can see that the lines and the curves of the functions do not intersect
This means that the system has no solution
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Complete all these questions and provide an explanation with complete sentences for full credit.
1) Which muraber is rational? Explain
+
√13
Root 13 is a non-recurring, infinite decimal. Since 13 is not a perfect square, its square root cannot be determined precisely. 13 cannot be expressed as a fraction, which is the definition of a rational number, because it cannot be expressed as a ratio of integers.
An illustration of a rational number?
If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Rational number examples include 1/3, 2/4, 1/5, 9/3, and so on.
Irrational number examples include: Any real number that cannot be expressed as a fraction is considered to be illogical.
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A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $80. A season ski pass costs $300. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive then the daily passes?
Answer: I think it's 9 days.
Step-by-step explanation:
For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the
height of his school building. He walks a distance of 10.25 meters from the building,
then places a mirror flat on the ground, marked with an X at the center. He then
walks 1.65 more meters past the mirror, so that when he turns around and looks
down at the mirror, he can see the top of the school clearly marked in the X. His
partner measures the distance from his eyes to the ground to be 1.55 meters. How tall
is the school? Round your answer to the nearest hundredth of a meter.
Answer:
x = 9.629 meters
Step-by-step explanation:
x / 10.25 = 1.55 / 1.65
x = 1.55 / 1.65 * 10.25
x = 9.629 meters
Drag graphs to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y=x.
Answer:
3rd Graph = 1st box
2nd Graph = 2nd Box
4th Graph = 3rd Box
Could someone please help? You do not have to draw a diagram.
The biggest area of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.
What is area of a quadrilateral?A quadrilateral made up of two triangles.Area of the quadrilateral = 2 * area of the traingleIf the diagonal and the length of the perpendiculars from the vertices are given, then the area of the quadrilateral is calculated as: Area of quadrilateral = (½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices.GIVEN:
The circumference of the circle is 20π units.The biggest area of a quadrilateral that can fit in a circle is of square.Deduce the radius of the circle.SOLVING:
2πR =20πr = 10 unitsArea of the quadrilateral is
100*2= 200 sq unitshence,The biggest area of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.
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What's the distance between -9 and 23
Answer:
32 units
Step-by-step explanation:
calculate the distance using the absolute value of the difference.
| - 9 - 23 | = | - 32 | = 32
or
| 23 - (- 9) | = | 23 + 9 | = | 32 | = 32
Determine the values of A, B, and C when y – 7=3(x−4) is written in standard form, Ax+By=C.
Answer:
Step-by-step explanation:
rearrange this equation y – 7=3(x−4) into this Ax+By = C
its pretty simple if you think about it :)
firstly, lets multiply the 3 with x - 4
y - 7 = 3x -12
we are going to bring the 3x to the right side to make the arrangement possible
-3x - y = -5 (minus twelve plus seven)
therefore, A is -3, B is -1 and C is -5
Which one of them is right?
Answer:
neither of them are right
The Earth is approximately 8.0 x 103 miles in diameter, from pole to pole.What number is the distance equivalent to? A- 800 thousand milesB- 80 thousand milesC- 8 thousand milesD- .8 thousand miles
Answer
Option C is correct.
8.0 × 10³ miles = 8 thousand miles.
Explanation
The number given in scientific notation is
8.0 × 10³ miles
= 8.0 × 1000 miles
= 8000 miles
= 8 thousand miles.
Hope this Helps!!!
11. (0, 2) and (4, -4)
12. (-2,-4) and (-3, -3)
Answer:
11. -3/2
12. -1
Step-by-step explanation:
To find slope, subtract the y's and put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction. Simplify if you can.
Subtract y's 2 - -4 is
2+4 which is 6, put that on top.
0 - 4 is -4 put it on the bottom.
Slope is 6/-4. Simplified, this is -3/2
The other question, same thing:
y-y over x-x
-4 - -3 / -2 - - 3
= -4+3 / -2 + 3
= -1 / 1
= -1