6 inches more than 2 times the height, 54 square inches the base and height is
b=13.8 inches
h=3.9 inches
Let base and height be b and h respectively,
So ,
b=2h+6
Area = b*h= 54 square inches
So,
(2h+6)(h)=54
2h²+6h=54
h²+3h=27
h²+3h-27=0
h= [tex]\frac{-3 +\sqrt{3^{2}-4(-27)(1) } \\}{2}[/tex]
h=[tex]\frac{-3 +\sqrt{9+108} \\}{2}[/tex]
h=[tex]\frac{-3 +\sqrt{117} \\}{2}[/tex]
h=[tex]\frac{-3 +10.8\\}{2}[/tex]
h=3.9 inches
b=2h+6=13.8 inches
The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The quantity of unit squares necessary to completely cover a shape is its area. As a result, it is stated and measured in square units.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
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Meera works at the zoo's information desk. The total amount of time she spends giving directions is equal to 4 times the total amount of time she spends answering phone calls plus twice the amount of time she spends answering the phone and responding to emails. Which simplified expression represents the amount of time Meera spends giving directions?
A. 12a + r
B. 8s + r
C. 4a + 2 (a + r)
D. 6a + 2r
The simplified expression represents how much Meera spends giving directions is D. 6a + 2r.
What is a simplified expression?A simplified expression is a mathematical expression that has completed the mathematical operations of adding, subtracting, multiplying, and dividing with the known values.
Given a simplified expression, the work left would be to fill in the independent variables.
Data and Calculations:The total time spent answering phone calls = a
The total time spent responding to emails = r
The total time spent giving directions = 4a + 2(a + r) = 6a + 2r
Thus, we can conclude that Meera spends six times the amount she spends answering the phone and two times the time she spends responding to emails to give directions.
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How many sophomores do not do homework
Answer:
25%???
Step-by-step explanation:
A washer and a dryer cost $565 combined. The washer costs $85 less than the dryer. What is the cost of the dryer?
Data was collected on salaries of compliance specialists in corporate accounting firms. The salaries ranged from $58,000 to $238,000
If these values are grouped into six class intervals, indicate the class boundaries.
What class interval width was chosen?
What are the six class midpoints?
The class boundaries are:
1 58000 but less than 88,000
2 88,000 but less than 118,000
3 118,000 but less than 148,000
4 148,000 but less than 178,000
5 178,000 but less than 208,000
6 208,000 but less than 238,000
The class interval width for the distribution that we have here is given as $30000.
The six midpoints and the class boundaries are:
73000103,000133,000163000193000223000How to solve for the class boundary238,000 - 58,000= 180000
180000 / 6 = 30000
Class Boundaries1 58000 but less than 88,000
2 88,000 but less than 118,000
3 118,000 but less than 148,000
4 148,000 but less than 178,000
5 178,000 but less than 208,000
6 208,000 but less than 238,000
What is the class interval width?238,000 - 58,000= 180000
180000 / 6 = 30000
width = 30000
The six class midpoints58000 + 88000 / 2 = 7300088000 + 118000 / 2 = 103,000118000 + 148000 / 2 = 133,000148000 + 178000 / 2 = 163000178000 + 208000 / 2 = 193000208000 + 238000 / 2 = 223000Read more on class intervals here;
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FIND THE ERROR Grant read the following axioms for a video game he is playing.
. There are four keys hidden on each level.
Each level ends when the player collects the third key.
.
• The game has 10 levels.
.
From these axioms, Grant concluded:
• to complete the game, he will need to find 30 keys.
.
. there are 40 keys in the game.
• he can collect all 40 keys in the game.
Are Grant's conclusions correct? Explain your reasoning.
Step-by-step explanation:
hhiejrhrhrrhhrrhrjif
Idrissa collected pennies in a fundraiser. He measured the mass of all the pennies he collected to be 2,400 grams. Two pennies put together have a mass of 5 grams. How much money did Idrissa raise in this fundraiser?
Answer: Idrissa collected 240 pennies
Step-by-step explanation:
2400/5=480
The Chen family and the Aoki family each used their sprinklers last summer. The water output rate for the Chen family's sprinkler was 40L per hour. The water output rate for the Aoki family's sprinkler was 25L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 2000L. How long was each sprinkler used?
Answer:
Chen family used the sprinklers for 25 hours
Aoki family used the sprinklers for 40 hours
Step-by-step explanation:
Let C be the number of hours the Chen family used the sprinklers and let A be the number of hours the Aoki family used the sprinklers
Total hours used
=> C + A = 65 (1)
Total water usage for Chen family = 40C (40 L per hour x no. hour)
Total water usage for Aoki family = 25C (25 L per hour x no. hours)
Total used by both families = 2000 L
So
40C + 25A = 2000 (2)
Therefore we have two equations in 2 variables which can be solved simultaneously
Multiply (1) by 25:
==> 25C + 25A = 25 x 65
==> 25C + 25A = 1,625 (3)
Subtract (3) from (2) to eliminate the A term:
(2) - (3) ==>
40C + 25A - (25C + 25A ) = 2000 - 1625
40C + 25A - 25C - 25A = 375
40C - 25C = 375
15C = 375
C = 375/15
C = 25
So the Chen family used the sprinklers for 25 hours
Since C + A = 65
A = 65 - C
==> A = 65 - 25
A = 40
The Aoki family used the sprinklers for 40 hours
(ECSEPTEMBER 2019) QUESTION 8 8.1 8.2 Determine f'(x) from first principles if f(x) = 3 - 2x² Determine: 8.2.1 D₂[x(x-2)²] 8.2.2 dx MATHEMATICS PI if y = ax 2x √x +3
After differentiating the function f(x)=3 - 2 x ², we get the result as d y / d x = - 4 x
Differentiation is a process applied to a function which finds the function's rate of change compared to the rate of change of the independent variable.
We are given the function as:
f(x)=3 - 2 x ²
We need to find d y / d x
For this we need to differentiate the function with respect to x.
Differentiating the function with respect to x, we get that:
d y / d x = ( 0 ) - 2 ( 2 x ) ( 1 )
d y / d x = 0 - 4 x
d y / d x = - 4 x
Therefore, after differentiating the function f(x)=3 - 2 x ², we get the result as d y / d x = - 4 x
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I need help pls and thank u What is 5.3=z-2.7?
Answer: z=8
Step-by-step explanation:
5.3=z-2.7
5.3+2.7=z-2.7+2.7 ==> remove the 2.7 in 'z-2.7' to single out the variable z.
z=5.3+2.7
z=8
z = 8 ✅
Step-by-step explanation:Step 1:
Add 2.7 to both sides
5.3 = z - 2.7
5.3 + 2.7 = z - 2.7 + 2.7
⬆️ ⬆️
Step 2:
Simplify
5.3 + 2.7 = z - 2.7 + 2.7
( = 8 ) ⬇️ ( = 0 )
⬇️ ⬇️
8 = z
3. An arithmetic sequence a begins 11, 7,...
a. Write a recursive definition for this sequence using function notatio
b. Sketch a graph of the first 5 terms of a
We get the function notation as aₙ = 15 - 4 n for the arithmetic sequence beginning with 11, 7,...
We are given an arithmetic sequence:
11, 7, …
We get from the sequence that:
a = 11 ( initial term )
d = 7 - 11 = - 4 ( common difference )
Now the nth term will be given as:
aₙ = a + (n - 1) d
aₙ = 11 + (n - 1) ( - 4 )
aₙ = 11 - 4 n + 4
aₙ = 15 - 4 n
Third term = 7 - 4 = 3
Fourth term = 3 - 4 = - 1
Fifth term = - 1 - 4 = - 5
Therefore, we get the function notation as aₙ = 15 - 4 n for the arithmetic sequence beginning with 11, 7,...
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Tell whether the angles are complementary or supplementary. Then find the value of x.
Step-by-step explanation:
SUPPLEMENTARY because they are on a staright line and add up to 180°
[tex]76 + (2x + 4) = 180 \\ 2x + 76 + 4 = 180 \\ 2x = 180 - 76 - 4 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]
x=50°
Help me please !!!!
2. In the number 928,547,136, which digit is in the hundred thousands place?
Answer:
5.
Step-by-step explanation:
5 is in the hundred thousand place because starting from the right it goes ones, tens, hundreds, thousands, then thousands, and hundred thousand meaning 5 would be in that place.
Jesse has 414 inches of ribbon for making bows. She uses 3 inches of ribbon for each bow. How many bows can she make?
Write a division expression that can be used to answer this question.
Answer:
414/3
Step-by-step explanation:
If she has 414 inches of ribbon and uses 3 inches for each bow then that means that you would have to divide 414 by 3 in order to find the amount of bows that Jesse could make
what is the arctan (-1)?
B. [tex]-\frac{\pi }{4}[/tex]
Answer:
Option B. is correct.
Step-by-step explanation:
arctan(y) = tan - 1(y) = x+ kπ
for k = {...,-2,-1,0,1,2,...}
➫ e.g tan(45°) = 1
➫ and that would mean the arctangent of 1 is 45 degrees(We represent this in π/? form)
arctan(1) = tan-1(1) = 45° = -π/4
Hope this helps!
The function f is given below. Find f-¹(z) and evaluate f-¹(-6).
Answer:
find the formula of the inverse function of a given function. For example, find the inverse of f(x)=3x+2.
Step-by-step explanation:
Consider the two functions.
f(x) = 4 +6
g(x) = 4²-6
If g (x) = f(x) + k
what is the value of k?
Ebony earned scores of 70 , 72 , 89 , 92 , 89 and 80 on six math tests. Determine her score on the seventh test if her average for the seven tests was 80? Enter your answer as a whole number
Answer:
70
Step-by-step explanation:
2) At a bake sale there were 48 raisin cookies sold. If the ratio of raisin cookies sold to
oatmeal cookies sold was 8: 5, what is the combined amount of raisin and oatmeal cooki
sold?
Answer: The combined amount of raisin and oatmeal cookies sold=80. Step-by-step explanation: Let x be the combined amount of raisin and oatmeal cookies sold.
Step-by-step explanation: i really hope this helps but lmk if i am wrong have a good day/night (: <3
does the function f(x)=(0,68)^x represent exponential growth, decay ,or neither
The given function represents exponential decay.
In mathematics, exponential decay refers to the process of decreasing an amount at a constant percentage rate over time.If a quantity diminishes at a rate proportionate to its present value, it is susceptible to exponential decay.The given function is f(x) = (0.68)^xFor the numbers between 0 and 1, with an increase in the power of the number, the final value decreases.In the given function, 0.68 is greater than 0 but less than 1.As we increase the value of its power, i.e., "x", the value of the function decreases.A graph of the function has been attached below for better visualisation.To learn more about functions, visit :
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2^n * 3 * 5^m
Write 8A as a product of powers of its prime factors
8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex] is a product of powers of its prime factors of Polynomials.
What is Polynomials ?
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.Given - [tex]2^{n} * 3 * 5^{m}[/tex]
The numbers 2, 3 and 5 are already prime numbers.
Multiplying 8 on both sides
8 × A = [tex]2^{n} * 3 * 5^{m} * 8[/tex]
Expressing 8 as the product of prime numbers
8A = [tex]2^{n} * 3 * 5^{m} * 2 * 2 * 2[/tex]
8A = [tex]8A = 2^{n} * 3 * 5^{m} * 2^{3}[/tex] (When the base is same, the power is added)
Adding the power of base 2, we add n and 3
8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex]
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Find the area of a rectangle that has a length of (x + 5) and a width of (x-3)
Answer:
(x^2+2x-15) units
Step-by-step explanation:
Area=LW
=(x+5)(x-3)
=x^2-3x+5x-15
(x^2+2x-15) units
Armando’s home insurance has
a $2,500 deductible per incident. This means that he
pays $2,500 and the insurance company will pay all
costs beyond $2,500. If Armando files a claim for
$19,400.
a. how much will he pay?
b. how much will the insurance company pay?
Answer:
a. Armando pays 2500
b The insurance pays 16900
Step-by-step explanation:
Armando has to pay 2500 always and the insurance company will pay all thats left to pay is what i understand by the question and the total payment both have to do is 19400.
19400
2500 = 16900
Martín y Paulina realizan una inversión en acciones con la misma cantidad de dinero. Martín ganó
$ 8.000 y Paulina perdió $ 6.000; de tal manera que la cantidad que le quedó a Paulina es la tercera
parte de lo que le quedó a Martín.
Determine una expresión algebraica que represente la situación planteada.
i said right foot creep owww walking with that heat walk walking around stay low make sure that don't see
A
What is the missing table value?
A. 9.4
B. 9.84
C. 10.16
D. 11.2
Answer: the answer is C. 10.16
Step-by-step explanation: on the right each value is going up by 2.54 cm so for the forth row on the right you just need to multiply 2.54 x 4 which equals 10.16
hope this helps
Do the following sets of data represent a function? Justify your answer.
1. (1,4), (2, 4), (3, 5), (2, 2)
2. (10, 5), (12, 5), (7, 12), (12, 2)
3. (0, 0), (5, 4), (4, 5), (1, 0)
1. No, the set of data does not represent a function.
A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.
We are given with (1,4), (2, 4), (3, 5), (2, 2)
This is because every output of this data does not have unique input.
4 and 2 have the same input i.e. 2.
2. Yes, the set of the data represents a function.
We are given with (10, 5), (12, 5), (7, 12), (12, 2)
It is a function as every input has a single output.
So, (10, 12, 07) are the elements of the domain and (2, 5, 7, 12) is the range of the function.
3. Yes, it is a function as every input of this data represents the single and unique output.
We are given with (0, 0), (5, 4), (4, 5), (1, 0)
It has its unique elements and domain (0,1,4,5) and range is from (0, 1, 2, 3, 4, 5).
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You are building a model of a new roller coaster with a scale factor of 1/51. The model is 4ft yall. How tall is the actual roller coaster?
The actual roller coaster is 204 ft tall.
Given that, the length of the model roller coaster is 4 ft and the scale factor is 1/51.
What is a scale factor?The scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.
Let the length of the actual roller coaster be x.
We know that Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Now, 1/51 = 4 / x
⇒x=204 ft
Therefore, the actual roller coaster is 204 ft tall.
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1
A=h(B+b); A = 39, B = 8, b = 5
Solution,
Given,
A = 39
B = 8
b = 5
A = h(B+b)
Now,
A = h(B+b)
Putting the given values,
39 = h(8+5)
or, 39 = h×13
or, 39÷13 = h
or, 3 = h
or, h = 3
Therefore,the value of h is 3
Can anyone help me with this
Answer:
B. SAS
Step-by-step explanation:
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
HELLPPPP!!!!!! If the parent function f(x) = |x| is transformed to h(x) = |x| + 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
h(x) is a translation upwards of 2 units of f(x), and the new range of the function h(x) will be [2, ∞)
What transformation is applied to f(x)?
We know that f(x) is the parent absolute value function:
f(x) = |x|
It is transformed so we get:
h(x)= |x| + 2
Remember that a vertical translation of N units is written as:
h(x) = f(x) + N
if N > 0, the translation is upwards.if N < 0, the translation is downwards.Then h(x) is a translation upwards of 2 units of f(x), and the new range of the function h(x) will be [2, ∞)
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