The area of the prism is 12x² inches². Thus, the correct option is B.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
For a prism, the lateral sides of a prism are made up of rectangles which consist of the height and the length of the base. Therefore, a triangular prism has an equilateral base with a side length x inches. The height of the prism is four times as long as the side length. The lateral area will be,
Lateral Area = 3(x×4x) = 12x² inches²
Hence, the area of the prism is 12x² inches². Thus, the correct option is B.
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X =
(19) Find the values for X and Y, and then solve for the side lengths.
a group of 20 students in four adults are going on a field trip to the museum What is the ratio of students to adults complete the statement.
Answer:
5:1
Step-by-step explanation:
Originally the ratio is 20:4
but then it is simplified to 10:2
then 5:1
Can you help like fast
Answer:
(4, 3)
Step-by-step explanation:
How many full 4 2/3 in. Sheets can be cut from 22 1/6 in. Stick
Answer:
4
Step-by-step explanation:
Because i divided 4 2/3 by 22 1/6 = 4.75 and for full sheets it would be 4
Hope This Helped
Someone, please help! I really don't understand congruent triangles
Answer:
D. (CPCTC)
Step-by-step explanation:
Your proof that the triangles are congruent is complete at the 4th step. In Step 5, you are asked to draw a conclusion about corresponding angles in those congruent triangles.
__
what is congruence?Two geometric objects are congruent if they are identical in size and shape by any measure. If they are not labeled, you cannot tell them apart. Every measure of one is identical to the corresponding measure of the other. The location and orientation of congruent figures does not affect their congruence. You can move them, rotate them, flip them over, and they remain congruent.
This property, "corresponding parts of congruent triangles are congruent," is abbreviated "CPCTC." Once you have demonstrated objects are congruent, you can use this fact to relate measures of the objects that may not have been part of the demonstration.
proving congruencegeneral
We generally work with plane geometric figures that are polygons or have well-defined curved edges. Polygon figures are comprised of straight sides of fixed length. At each vertex, where sides meet, an angle is formed. Corresponding sides form corresponding angles.
The sides are generally named by the vertices at either end. The angles may be named by the vertex where it is located, or by the names of the sides that make it up.
In triangle ABC, for example, the vertices have labels A, B, and C. The sides are AB, AC, and BC. And the angles are A, B, and C, or BAC, ABC, ACB. (The vertex of the angle is the middle letter.)
To prove polygons are congruent, you must show corresponding angles are congruent, and corresponding sides are congruent. Generally, the number of sides will put constraints on the size of the angles. (A 6-sided polygon will have 6 angles that total 720°, for example.)
triangles
When the polygon is a triangle, the constraints on side lengths and angles generally mean there are shortcuts to proving congruence. The postulates that tell you what these are have been given mnemonic abbreviations. When we say, "angle" or "side" in this context, we are referring to congruent corresponding angles in the two triangles, or congruent corresponding sides.
AAS -- two consecutive angles and a side adjacent to one of them will prove congruenceASA -- two angles and the side between them will prove congruenceSAS -- two sides and the angle between them will prove congruenceSSS -- three sides will prove congruenceThese can also be applied to right triangles, where one angle is known to be 90°. In addition, there is a theorem that only applies to right triangles:
HL -- the hypotenuse and one leg will prove congruence. (Note that the hypotenuse is opposite the known 90° angle, so this is effectively an SSA congruence statement, only applicable to right triangles.)your proof
The triangles in your figure have a side marked with a single hash mark. This means those corresponding sides in the two triangles are congruent to each other.
There is an angle marked with two (2) arcs in each triangle. This marking means those corresponding angles are congruent. Likewise for the angles marked with three (3) arcs. You will notice the 3-arc angle, 2-arc angle, and 1-hash mark side are in the same order in the two triangles. This means the AAS congruence postulate applies, as is claimed on line 4 of your proof.
using congruenceAs you have seen, we only need to show some parts of a triangle are congruent in order to show all parts of the triangle are congruent. When we make a claim about corresponding parts that weren't an explicit part of the proof, we are essentially relying on the definition of congruent polygons. For triangles, that definition is summarized by the abbreviation CPCTC.
Line 5 of your 2-column proof is making a claim about corresponding angles of the triangle. That claim is supported by CPCTC.
_____
Additional comment
Choices A and C refer to congruence postulates, as discussed above. Those have no relation to the claim regarding angles ACB and XZY.
The "corresponding angles theorem" tells you corresponding angles are congruent where a transversal crosses parallel lines. It has no relation to the angles in this problem.
Dean started with 5 meters
of yarn. He used 300
millimeters of yarn each day
for 5 days. How many
meters of yarn does Dean
have left?
Answer:
3.5 meter is the answer.
Answer:
3.5 Meters
Step-by-step explanation:
5 Meters is equivalent to 5000 millimeters
1 day = 300mm
5 days = (300*5)
= 1500 mm
= 5000 mm - 1500 mm
Yarn left = 3500 mm
= 3.5 Meters
Graph the linear equation.
4x+6y=-12
Answer:
Step-by-step explanation:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
What is 2 raised to the power of 3?
Answer:
What is 2 raised to the power of 3?
2 x 2 x 2
= 8
Step-by-step explanation:
Hope this helps.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice. 120
Yam. 100
Beans. 140
Vegetable 140
Meat. 180
Sugar. 40
Palm oil. 60
Display using a pie chart
The pie chart below depicts a housewife's expenditures for a certain day.
What is a pie chart?A map wherein the round is split into segments, each one representing a percentage of the total.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice - 120
Yam - 100
Beans - 140
Vegetable - 140
Meat - 180
Sugar - 40
Palm oil - 60
The pie chart is given below.
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Dakota drained his 2,268 ft^3 pool to clean it. The pool is a rectangle with an area that can be expressed as 2x^4 + 10x^2 and a depth that can be expressed as x^2 if a gallon of water has a volume of 1/60 x^2 formulate a function which represents the gallons of water it takes to fill the pool.
The gallon of water required by Dakota to fill the pool will be given as:-
V(x) = 2x⁶ + 10x⁴.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
Given that:-
Dakota drained his 2,268 ft³ pool to clean it. The pool is a rectangle with an area that can be expressed as 2x⁴ + 10x² The depth that can be expressed as x² if a gallon of water has a volume of 1/60 x²The function which will represent the gallons of water will be:-
As it is given in the question the pool is of a rectangular shape so the volume of the pool will be calculated as:-
V = Area of the rectangular part x depth
V = ( 2x⁴ + 10x ²) ( x² )
V = 2x⁶ + 10x⁴.
Since the amount of the water will be equal to the volume of the pool so the function for the gallons will be given as;-
V (x) = 2x⁶ + 10x⁴.
Therefore gallon of water required by Dakota to fill the pool will be given as:-V(x) = 2x⁶ + 10x⁴.
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Which exponential model best represents the data?
Exponential model best represents the data is [tex]f(x)= 3(0.2)^{x}[/tex]
What is exponents?A symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.
The given table values satisfied the fourth function.
If we put one by one all the values of x given in a table we get the corresponding value of f(x).
like, if we put -2 we get f(x)= 75 closer to 71
Hence, Exponential model best represents the data is [tex]f(x)= 3(0.2)^{x}[/tex]
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Does anyone know how to do this I’m really confused
The size of the unknown angle "x"
Solution:The given polygon is a Pentagon so the sum of interior angle will be,
[tex]\large\boxed{Formula: ( n − 2 ) × 180}[/tex]
n means the number of sides
Let's substitute the values according to the formula.
[tex](5-2)×180[/tex]
[tex]=540°[/tex]
Now, we can find the sum of one interior angle.
[tex]\large\boxed{\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Let's substitute the values according to the formula.
[tex]x=\frac{540}{5}[/tex]
[tex]\large\boxed{x= 108°}[/tex]
Therefore, the size of the unknown angle "x" is 108°
rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Answer:
36 units²
Step-by-step explanation:
rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
we use the inverse formula
12 * 3 =
36 units²
-----------------------
check
36 : 12 = 3
the answer is good
An insulator is installing fiberglass insulation in exterior walls that total up to 1,623 square feet after windows and doors are deducted. Each roll can insulate 49 square feet. There are 28 rolls on hand. Will this amount be sufficient? If not, how many total rolls are needed? If necessary, round your answer up to the nearest whole number, since you cannot buy part of a roll of insulation.
Answer:
2
Step-by-step explanation:
How much will a sum of ¥4000 amount to in 1 1/2 yrs at 10% per annum compound interest,interest being paid half-yearly
Answer:
¥4630.50
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = 4000r = 10% = 0.1n = 2t = 1.5Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=4000\left(1+\dfrac{0.1}{2}\right)^{2 \times 1.5}[/tex]
[tex]\implies \sf A=4000\left(1.05\right)^{3}[/tex]
[tex]\implies \sf A=4630.50[/tex]
Answer:
¥4630.50
Step-by-step explanation:
Here,
P = ¥4000n = 1 1/2 = 3/2 yearsr = 10% per annumATQ, as well,the interest is payable in half-yearly.
We know that,
[By this formula,it could easily solved][tex] \boxed{\rm \: A = P \bigg(1+ \cfrac{ \cfrac{r}{2} }{100} \bigg) {}^{2n} }[/tex]
Substitute the values
[tex]A = 4000 \bigg(1 + \cfrac{5}{100} \bigg) {}^{2 \times \frac{3}{2} } [/tex]
Now solve.
[tex]A = 4000 * (21/20)^3[/tex]
[tex] \implies \: A = 4000 \times \cfrac{21}{20} \times \cfrac{21}{20} \times \cfrac{21}{20} = \cfrac{21 \times 21 \times 21}{2} [/tex]
[tex] \implies \: A = \: \yen \: 4630.50[/tex]
Hence,the sum of ¥ 4000 will be amounted to ¥4630.50 in 1 1/2 years.
[tex] \rule{225pt}{2pt}[/tex]
This question arises:Why we used that formula?
Reason:
The compound interest is calculated half-yearly, the formula changes a little.In this case for r we write r/2 and for n we write 2n because a rate of r% per annum is r/2% half-yearly and n years = 2n half year So this is the reason.
PLEASE HELP ITS DUE SOON IM SO CONFUSED! HELP NEEDED!!
Answer:
e
Step-by-step explanation:
According to Angle Sum Property :
∠A + ∠B + ∠C = 180°
============================================================
Given :
⇒ ∠A = 50°
⇒ ∠B = 32°
===========================================================
Solving :
⇒ 50° + 32° + ∠C = 180°
⇒ ∠C + 82° = 180°
⇒ ∠C = 98°
F(x)=x^2-3x-2 if shifted 4 units left. The relics it g(x). What is g(x)?
Saundra's credit has an APR of 18%, calculated on the previous monthly balance. Her credit card record for the last 7 months is hown in the table below. On what amount of money will Saundra be charged interest for month 8?
Answer:
I think the answer is $244.65 im not completely sure if this is the right answer so correct me if im wrong
PLEASE HELP ASAP WILL MARK BRAINLY
Mark the lines
tanD=BC/BDPut the values
tanD=√38/√53Done
Answer:
[tex]\sf \tan(D)=\dfrac{\sqrt{38}}{\sqrt{53}}[/tex]
Step-by-step explanation:
Tangent trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = DO = √38A = √53Substituting the given values into the formula:
[tex]\implies \sf \tan(D)=\dfrac{\sqrt{38}}{\sqrt{53}}[/tex]
Suponga que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. suponiendo que es lineal. Determine el precio cuando se requiere 50 unidades.
Considerando la ecuación lineal, cuando se requiere 50 unidades, el precio será $22.
Qué es la ecuación linealUna ecuación lineal o línea se puede expresar en la forma y = mx + b.
dónde
x e y son coordenadas de un punto.m es la pendiente.b es la ordenada al origen y representa la coordenada del punto donde la línea cruza el eje y.Conociendo dos puntos (x1, y1) y (x2, y2) de una recta, se puede calcular la pendiente m de dicha recta mediante la siguiente expresión:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Sustituyendo el valor de la pendiente m y el valor de uno de los puntos en la expresión de una ecuación lineal, y = mx + b, se obtiene el valor de la ordenada al origen b.
Precio de 50 unidades de un productoEn este caso, siendo la ecuación lineal Precio=m× cantidad + b, sabes que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. Esto es:
(x1, y1)= (60, 24)(x2, y2)= (40, 20)Entonces, la pendiente m es calculada mediante la siguiente expresión:
[tex]m=\frac{20-24}{40-60}[/tex]
Resolviendo:
m= 0.2
Entonces, considerando el valor de la pendiente m y el punto 1, el valor de la ordenada al origen b se calcula como:
24 = 0.2× 60 + b
24 = 12 + b
24 -12= b
12= b
Entonces. la relación entre la cantidad de unidades y precio es Precio=0.2×cantidad + 12
Entonces, cuando se requiere 50 unidades, el precio será calculado como:
Precio=0.2×50 + 12
Resolviendo:
Precio= 22
Finalmente, cuando se requiere 50 unidades, el precio será $22.
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Simplify surd need an answer asap please
Answer:
Step-by-step explanation:
Simplify Surd: Multiply the denominator and numerator with the conjugate of the denominator.Conjugate of denominator:[tex]\sf (\sqrt{x+1}) + (\sqrt{x-1})[/tex]
[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]
When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²
[tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]
This list shows the lengths in feet of the 25 longest bridges in the United States.
1010
1470
1600
2000
2800
1053
1495
1632
2150
3500
1200
1596
1750
2150
3800
1207
1600
1800
2300
4200
1380
1600
1850
2310
4260
Jamie made a frequency table of the bridge data.
U.S. Bridges
Length (ft)
Tally
Frequency
(first interval)
|||| ||
7
(last interval)
||
2
Based on the tallies and frequencies for the first and last intervals, how many intervals of what length did Jamie use?
a.
4 intervals of 1000 feet
c.
6 intervals of 500 feet
b.
5 intervals of 1000 feet
d.
7 intervals of 500 feet
Please select the best answer from the choices provided
A
B
C
D
The length of the intervals of the given frequency table is
500 ft.
The given list shows the lengths in feet of the 25 longest bridges in the United States.
we have to determine the median and mode of the bridge data.
The median is the middle number of the data set arranged in ascending order.
1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260.
The median is 1750.
Mode is the number that appears most often in the data set.
1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260
The mode is 1600.
Therefore the correct option is Median: 1750, Mode: 1600
So the length of the intervals of the given frequency table is
500 ft.
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A game decreased in price by 2/3. After the reduction it was priced at £13. What was the original price of the game?
Answer:
[tex]x = 39[/tex]
Step-by-step explanation:
Based on the given conditions, write: [tex]x=\frac{13}{1-\frac{2}{3}}[/tex]
Find common denominator and write numerators above common denominator: [tex]x=\frac{\frac{13}{3-2} }{3}[/tex]
Calculate the sum or difference: [tex]x=\frac{\frac{13}{1} }{3}[/tex]
Divide the fraction by multiplying its reciprocal: [tex]x=13*3[/tex]
Calculate the product or quotient: [tex]x=39[/tex]
Answer: [tex]x=39[/tex]
Answer:
£19.50
Step-by-step explanation:
let x be the original price , then
[tex]\frac{2}{3}[/tex] x = 13 ( multiply both sides by 3 to clear the fraction )
2x = 39 ( divide both sides by 2 )
x = 19.5
original price of game was £19.50
300 percent of m is 600. What is m?
Answer:
m=200
Step-by-step explanation:
percent means 100,so we duvude 300:by 100 then m=200
The function f(x) = x + 21 is one-to-one.
a. Find an equation for f1(x), the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¯¹ (f(x)) = x.
Answer:
a. D. f⁻¹(x) = x - 21, for all x
b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x
Step-by-step explanation:
See attached picture.
The required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:
x = y + 21
Now, let's solve for y:
y = x - 21
Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.
b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.
First, let's calculate f(f(x)):
f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42
Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.
Now, let's calculate f¯¹(f(x)):
f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x
Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.
Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Therefore, the required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
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what is the mean of 7,5,6,5,4,4,8,6,6,7,4,5,56,6
Answer:
5.6
Step-by-step explanation:
If you add all the numbers together then divide it by 15 you would get 5.6
a girl spent 1/6 of her pocket money on sweets and 2/5 on toys what fraction of her pocket money did she spend what fraction of her pocket money did she have remaning
Answer:
She spent 17/30 of her money and still has 13/30 of her money
Step-by-step explanation:
The first step to solve is to find a common denominator. The common denominator of this problem is 30. So 1/6 turns into 5/30, and 2/5 becomes 12/30. Then you add them together to get 17/30. If you subtract 17 from 30 you will get your answers.
Please show your work! I'll give you brainliest as well as a 5 star rating, thanks!
Answer:
281.3
Step-by-step explanation:
If the shapes are similar then the linear scale factor is :
15÷20 = 0.75
The area scale factor will be 0.75²
The area scale factor is 0.5625
500 × 0.5625 = Area of shaded rectangle
Area of shaded rectangle = 281.25
To the nearest tenth = 281.3
Hope you understood and brainliest please
Answer:
[tex]281.3 m^{2}[/tex]
Step-by-step explanation:
I've done this before I have the work attached below in a screenshot. Sorry that it's not much but I hope it helps!
Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!
Have a great day
:)
what is mean by migration
who will give me brainlest then I am follow you
Step-by-step explanation:
Movement from one place to another
ASAP!!!!
Lilly spent $2.20 at the candy store. Her friend spent three times as much. How much money did Lilly and her friend spend in all?
$8.80 because 2.20*3 is 6.60+2.20 is 8.80
Answer:
Step-by-step explanation:
Lilly= 2.20$ spent
Friend= 2.20$ x 3= 6.60$ spent
6.60$+2.20$=
8.80$ total spent together