Answer:
Base = 8 feet
Step-by-step explanation:
[tex]area \: of \: \triangle = \frac{1}{2} \times base \times height \\ 16 = \frac{1}{2} \times base \times 4 \\ 16 = base \times 2 \\ base = \frac{16}{2} \\ base = 8 \: feet[/tex]
Identify the graph of 4y^(2)+12x^(2)=24 for T(-1,4) and write an equation of the translated or rotated graph in general form.
Answer:
b. ellipse; 3x^2 + y^2 + 6x - 8y + 13 = 0
Step-by-step explanation:
thats the answer on edg :)
The point T(-1,4) lies on the ellipse on the graph.
The equation of the ellipse in general form is:
(x/√2)² + (y/√6)² = 1
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The given equation, 4y² + 12x² = 24, can be simplified by dividing both sides by 24 to get:
y²/6 + x²/2 = 1
This is the equation of an ellipse centered at the origin, with a horizontal major axis of length 2√6 and a vertical minor axis of length 2√2.
To identify the graph of the ellipse passing through T(-1,4), we substitute x = -1 and y = 4 in the equation and simplify:
4(4)² + 12(-1)² = 24
64 - 12 = 52
Thus, point T(-1,4) lies on the ellipse.
To find the equation of the translated or rotated ellipse in general form, we can use standard transformations.
Let (h,k) be the center of the ellipse.
Then we have:
(x-h)²/a² + (y-k)²/b² = 1
where a and b are the lengths of the semi-major and semi-minor axes, respectively.
The center of the given ellipse is (0,0), so h = 0 and k = 0.
To determine the values of a and b, we note that a^(2) is the coefficient of x² in the equation, and b² is the coefficient of y².
Thus, we have:
a² = 2 and b² = 6
Taking square roots, we get:
a = √2 and b = √6
Therefore,
The equation of the ellipse in general form is:
(x/√2)² + (y/√6)² = 1
This is the equation of an ellipse with a horizontal major axis of length 2√2 and a vertical minor axis of length 2√6, centered at the origin and rotated counterclockwise by an angle of θ such that tan(2θ) = 4/3.
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Twenty disks with the given measurements are stacked on top of each other. Which expression does NOT give the volume of the cylinder that is formed? Plz help
The expression which is false in determining the volume of the cylinder is given by V₁ = π . 3 . 12²
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the volume of the 12 cylinders be V
Let the height of the cylinder be h = 1 cm
Let the radius of the cylinder be r = 3 cm
Now , Volume of Cylinder = πr²h
On simplifying , we get
Volume of the cylinder V = 12 x ( π x 3² x 1 )
Volume of the cylinder V = π x 3² x 12 cm³
Volume of the cylinder V = 108π cm³
So , the expression V₁ = π . 3 . 12² is false and cannot be used to determine the volume of the cylinder
Hence , the volume of cylinder is 108π cm³
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The complete question is attached below :
Twelve disks with the given measurements are stacked on top of each other. Which expression does NOT give the volume of the cylinder that is formed?
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The angles opposite the congruent sides of an isosceles triangle are congruent. Find the value of x in the triangle. Show all your work.
Answer:
x=40
Step-by-step explanation:
What the problem is telling you is that the unlabeled angle is the same as the 70 degree angle. Since all the angles of a triangle add up to 180 degrees. First take 70+70, which equals 140. Now take the 180-140=40 ,so 40 would be the missing angle.
Final answer:
In an isosceles triangle, the angles opposite the congruent sides are congruent. To find the value of x in the triangle, we can set up an equation using the fact that the sum of the angles in a triangle is always 180 degrees. Simplifying the equation, we can find a value for x.
Explanation:
In an isosceles triangle, the angles opposite the congruent sides are congruent. Let's assume that the value of the unknown angle is x.
Since the triangle is isosceles, the other two angles are congruent. Let's call them a and a.
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation: x + a + a = 180.
Simplifying the equation, we get: 2a + x = 180.
Since the other two angles are congruent, we can say that: 2a = 180 - x.
Dividing both sides of the equation by 2, we find: a = (180 - x)/2.
Therefore, the value of x in the triangle is (180 - a)/2.
Find the volume of the pyramid below.
Enter your answer as a number with no units.
14x − 5 − 8x = 1 A) 0 B) 1 C) 3 D) 5
Find the circumference of a model Ferris Wheel with a diameter of 10 inches. Use 3.14 for pi. Round to the nearest tenth.
Answer:31.42
Step-by-step explanation:First you need to find the radius of the circle,so you know the radius is half of the diameter,so you take the radius(2) and multiplys by the pi which is 3.14 the formula is r^ x π
Answer:
31.4 in^2
Explanation:
The Formula for finding circumference is π*d (d=Diameter) or in this case 3.14*d. all you have to do is plug in 10 into the formula and get 3.14*10= 31.4 in^2
Can someone help me with this problem?
Complete the table based on the given domain
Answer:
x = -6 ; y = 11
x = 3 ; y = 5
x = 15 ; y = -3
x = -12 ; y = 15
Step-by-step explanation:
y = -(⅔)x + 7
x = -6
y = -(⅔)(-6) + 7
y = 11
5 = -(⅔)x + 7
-2 = -(⅔)x
x = 3
y = -(⅔)(15) + 7
y = -3
15 = -(⅔)x + 7
8 = -(⅔)x
x = -12
3=x+3–5x
what’s the answer
Answer:
x =0
Step-by-step explanation:
3=x+3–5x
Combine like terms
3 = 3-4x
Subtract 3 from each side
3-3 = 3-3-4x
0 =-4x
Divide each side by -4
0/-4 = -4x/-4
0 =x
Answer:
x=0
Step-by-step explanation:
3=x+3-5x add like terms
3= -4x+3
3=-4x+3 subtract 3 from both sides
0=-4x divide on both sides -4/-4 and 0/-4
x would equal 0
this one example of a net of a cube. how many more possible nets could there be of a cube
Correct option is D) 10 .
Step-by-step explanation:
Net of a cube is : Basically , a cube consists of six square faces, twelve edges, and eight vertices. When the square faces of a cube are separated at the edges and laid out flat they make a two dimensional figure( 2D figure :- Comprises of x-axis & y-axis) called a net. There are eleven different nets for a cube.
Net -- a two-dimensional shape that can be folded into a three-dimensional figure is a net of that figure. Face -- a plane figure that serves as one side of a solid figure. Vertex -- the point at which two line segments, meet to form an angle. Edge -- the line segment where two faces of a solid figure meet.Since we have 11 nets of a cube ! According to question we have only one net given , that means there are 10 more net of a cub are left .Therefore , Correct option is D) 10 .
There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at
this store have increased at a rate of 3.75% per month. At this rate of growth, which function can
be used to determine the monthly cell phone sales x months after January?
f(x) = 417(1.375)*
f(x) = 417(3.75)
f(x) = 417(0.0375)*
Answer:
[tex]f(x)=417(1.0375)^{x}[/tex]
Step-by-step explanation:
This question is not complete; please find the question attached.
Sales of cell phones at the store is growing at the rate of 3.75% per month which reveals that the monthly sales of cell phone is growing exponentially.
Sales per month will be represented by the growth function,
[tex]f(x)=A(1+\frac{r}{100})^{x}[/tex]
Where f(x) = Monthly sales
A = Sales in the first month
r = rate of increase in the sales
x = Duration or time
Fro the given question,
A = 417, r = 3.75
So the function showing the monthly sales will be,
[tex]f(x)=417(1+\frac{3.75}{100})^{x}[/tex]
[tex]f(x)=417(1.0375)^{x}[/tex]
The sum of three consecutive even integers is 102. Find the largest of the three integers.
Answer to the question is..
32,34,36
largest is 36
What effect will introducing a constant have on an exponential function?
Answer:
exponential function is power
Step-by-step explanation:
because constantly have an exponential function
thanku
Introducing a constant to an exponential function will shift the graph of the function either vertically or horizontally, depending on how the constant is applied.
An exponential function typically has the form [tex]\( f(x) = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] is the initial value (the value of the function at [tex]\( x = 0 \))[/tex], and [tex]\( b \)[/tex] is the base of the exponential function (the rate at which the function grows or decays).
When a constant is introduced, there are two primary ways it can affect the function:
1. *Vertical Shift*: If the constant is added to or subtracted from the exponential function, it will result in a vertical shift of the graph. For example, if we have a function [tex]\( g(x) = a \cdot b^x + c \)[/tex], where [tex]\( c \)[/tex] is a constant, the graph of [tex]\( g(x) \)[/tex] will be the graph of [tex]\( f(x) = a \cdot b^x \)[/tex] shifted up by c units if [tex]\( c \)[/tex] is positive, or down by [tex]\( c \)[/tex] units if [tex]\( c \)[/tex] is negative.
2. *Horizontal Shift*: If the constant is introduced as an exponent, it will result in a horizontal shift of the graph. For example, if we have a function [tex]\( h(x) = a \cdot b^{(x - d)} \),[/tex] where [tex]\( d \)[/tex] is a constant, the graph of [tex]\( h(x) \)[/tex] will be the graph of [tex]\( f(x) = a \cdot b^x \)[/tex] shifted to the right by [tex]\( d \)[/tex] units if [tex]\( d \)[/tex] is positive, or to the left by [tex]\( d \)[/tex] units if [tex]\( d \)[/tex] is negative.
It's important to note that the type of shift (vertical or horizontal) depends on the location of the constant in the function. A constant added to or subtracted from the function's value will cause a vertical shift, while a constant added to or subtracted from the input variable [tex]\( x \)[/tex] (in the exponent) will cause a horizontal shift.
In summary, the introduction of a constant to an exponential function will not change the fundamental nature of the exponential growth or decay, but it will translate the graph of the function either up/down or left/right, depending on how the constant is incorporated into the function.
Lila is wallpapering one wall of her bedroom, as shown in the diagram. She will cover the whole wall
except for the doorway.
How many square feet of wallpaper does Lila need?
Answer:
126ft
Step-by-step explanation: 1. Find the area of the whole wall
2. Find the area of the door
3. Subtract the area of the wall from the door
Melissa picked 1 3/5 pounds of cherries. Rachel picked 2 1/3 times more cherries than Melissa. How many cherries did Rachel pick?
To find out how many cherries Rachel picked, the mixed numbers are converted to improper fractions, multiplied, and the result is converted back to a mixed number. Rachel picked 3 11/15 pounds of cherries.
Explanation:The question asks how many cherries Rachel picked, given that Melissa picked 1 3/5 pounds of cherries and Rachel picked 2 1/3 times more than Melissa. To find this out, we need to convert the mixed numbers into improper fractions, multiply and then convert back to a mixed number if necessary.
First, convert Melissa's cherries to an improper fraction: 1 3/5 = 8/5. Next, convert the number of times more Rachel picked: 2 1/3 times more = 7/3. Now, calculate Rachel's cherries: (8/5) * (7/3) = 56/15. Finally, convert 56/15 to a mixed number: 56/15 is 3 11/15. So, Rachel picked 3 11/15 pounds of cherries.
What is 2h+3 when h=6
Answer:
15
Step-by-step explanation:
After plugging in the 6, multiply 2 and 6 and then add 3. This equals 15.
Answer:
15
Step-by-step explanation:
2h+3 where h=6 (plug in 6 for h)
2(6)+3= (Multiply)
12+3= (Add)
15
The Franzes are purchasing a home for $195,000, and they are using a conventional loan. What is the best estimate for what their down
payment will be?
A. $5,850
B. $19,500
C. $39,000
D. $48,750
Answer:
c. 39,000
ppllaattoooo
The best estimate for what their down payment will be $5850
What is a conventional loan?A conventional loan is any mortgage loan that is not insured or guaranteed by the government.
Given that, The Franzes are purchasing a home for $195,000, and they are using a conventional loan.
We know, the minimum down payment required for a conventional mortgage is 3%
So, 3% of $195,000 = 195,000x3/100
= 5850
Hence, The best estimate for what their down payment will be $5850
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h(1)=−5
h(n)=h(n−1)+1.8
h(3)=
Answer:
-1.4
Step-by-step explanation:
h(2) = h(2-1) + 1.8
= h(1) + 1.8
= -5 + 1.8
= -3.2
h(3) = h(3-1) + 1.8
= h(2) + 1.8
= -3.2 + 1.8
= -1.4
As per the given expression h(n)=h(n−1)+1.8, then the value of h(3) is -1.4.
In this explanation, we will calculate the value of h(3) using the given recursive formula h(n) = h(n-1) + 1.8 with the initial condition h(1) = -5. We will follow the iterative approach to find the value of h(3) by step-by-step calculations.
We are given the recursive formula h(n) = h(n-1) + 1.8, where h(1) = -5. Let's find the value of h(3) using this formula.
Step 1: Calculate h(2)
To find h(2), we use the recursive formula:
h(2) = h(1) + 1.8
h(2) = -5 + 1.8
h(2) = -3.2
Step 2: Calculate h(3)
Now, to find h(3), we again use the recursive formula:
h(3) = h(2) + 1.8
h(3) = -3.2 + 1.8
h(3) = -1.4
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Using the discriminant, the following quadratic equation y=-3x^2+7x+6 has ___ solutions
A.2
B.1
C.0
Answer:
choice C. 0 no real solution
Step-by-step explanation:
y=-3x^2+7x+6
using the formula for discriminant
D = b^2 - 4ac
D = 7^2 - 4*3*6
D = 49 - 72 < 0
no real solutions
Twice a number is equal to negative four. Which equation could be used to find the number?
2 n = 4
2 n = -4
2 n - 4
2 n = -4 n
Answer:
2n=-4
Step-by-step explanation:
Let he number be n
N×2=-4
Further explanation
If we are to solve
Divide both sides by 2
n=-2
Answer:
2n=-4
Step-by-step explanation:
Make sure to give the other person brainliest!
Find the solution of 3.75x +15 = 63.75
Answer:
The answer is x = 13.
Step-by-step explanation:
first, move the constant to the right and change its sign, (+15)
3.75 x = 63.75 -15
next, subtract the numbers, (65.75 -15)
3.75x = 48.75
then, divide both sides of the equation by 3.75,
final answer, x = 13
Answer:
x = 13
Step-by-step explanation:
to solve this just simply collect the like terms and divide both sides by the coefficient of x
solution
3.75x +15 = 63.75
3.75x = 63.75 -15
3.75x = 48.75
divide both sides by the coefficient of x which is 3.75
3.75x/3.75 = 48.75/3.75
x = 13
a rectangular prism has a surface are of 3310 square inches. if the rectangular prism has a length of 15 inches and width of 32 inches.what is the height in inches
Answer:
25
step by step explanation:
Find the compound interest on $10,000 for 2 years at 6% pa
A college student ingests 300 mg of caffeine at 6:00 am. He metabolizes the caffeine at 18% per hour. About how much caffeine is still in his system by 9:00 am?
Answer:
the number of caffeine still in his system by 9:00 am is 192 mg.
Step-by-step explanation:
given information
the mass of initial caffein, m₁ = 300 mg
time, t = 9 - 6 = 2 hours
metabolised = 18%/hour = 0.18/h = 0.18 x 300 mg = 54 mg/h
the student metabolised the caffeine 54 mg/h. thus from 6 am to 9 am the caffeine metabolised is
metabolised in 2 hr = 2 x 54
= 108 mg
the remaining caffeine = initial caffeine - metabolised caffeine
= 300 - 108
= 192 mg
Answer:
The correct answer is 138 mg.
Step-by-step explanation:
To understand this problem we must first analyze it.
We know that the student's body metabolizes 18% of the caffeine ingested every hour.
Therefore we can solve that percentage to already have the number of metabolized caffeine per hour:
(300. 18): 100 =
5400: 100 = 54 mg
We now know that the student's body will metabolize 54 mg of caffeine per hour.
The question is much caffeine is still in his system by 9:00 am?
From 6:00 am to 9:00 am we have 3 hours of difference: 3 . 54 = 162
In three hours 162 mg of caffeine were already processed by his body, therefore, it still needs to be metabolized: 300 - 162 = 138 mg.
The graph of 2x + 3y = 8 is shown on the grid. Which ordered pair is in the solution set of 2x + 3y = 8?
es )
A)
(1,4)
(1,-4)
(4,1)
(1.4)
Answer:
None of these solutions
Step-by-step explanation:
Substitute the values for x and y into the equation and see if they work out:
2(1)+3(4)=8
14 is not equal to 8, so (1,4) is not a solution.
2(1)+3(-4)=8
-10 is not equal to 8, so (1, -4) is not a solution.
2(4)+3(1)=8
11 is not equal to 8, so (4,1) is not a solution.
You repeated the first option as the last one but with a period instead for some reason, perhaps a typo?
The parallelogram shown below has an area of 21 units.
Find the missing height.
Answer:
8
544+65+6+6+646546141
Answer:
Step-by-step explanation:
It it 7 becaues the base is 3 then 7 x 3 = 21
Combining Like Terms to Solve Equations
2x+3=23
Show how you got the answer
Answer:
X=10
Step-by-step explanation:
23-3=20
20÷2= 10
2(10)+3=23
at a math convention nora sold 13 rulers for $110.50 at the same price how much would 7 rulers cost?
Answer:
$59.50
Step-by-step explanation:
You need to find the price of 1 ruler.
[tex]\frac{110.50}{13}=$8.50[/tex]
Now you need to multiply the price of one, by 7 to find the answer.
[tex]8.5*7=59.5[/tex]
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Which statements are true about the triangle? Select all that apply.
Answer:
A, B, C, F
Step-by-step explanation:
A: Its is acute because it has 2 sides that are less than 90%
B: It is obtuse because there is 1 side that is over 90%
C: It has 2 equal sides.
F: 100% + 40% + 40% = 180%
which graph represent an odd function?
Answer:
The top one
Step-by-step explanation:
Hope it helps!
Answer:
option B
Step-by-step explanation:
Which expression is represented by the model?
Answer:
4x-3
Step-by-step explanation:
I have never worked with the program you are using, but if i were to assume,
there are four Xs (4x) and three minus signs, (-3)
so 4x-3 make the most sense to me.
i hope this helps!
:)
Answer:
4x-3
Step-by-step explanation:
Mr. Memio