Answer: sin(E) = 0.6
Step-by-step explanation:
10² = DF² + 8² ( Pythagoras theorem)
100 = DF² + 64
DF² = 36
DF = 6
sin(E) = opposite side/ Hypotenuse
= DF/EF
= 6/10 = 3/5 = 0.6
ZLE Add one set of parentheses to the expression 7x+3+8x+3x+8-9 so that it is equivalent to 2(9x + 10).
U EE ET² T₂
The expression should be added by 18 so the expression will be equivalent to the 2(9x+10).
Given that,
The expression is 7x+3+8x+3x+8-9.
We have to equivalent the given expression to the 2(9x+10).
Take the expression,
7x+3+8x+3x+8-9
Write in order the variable terms first and next constant.
7x+8x+3x+3+8-9
Now, Adding the variable terms
18x+3+8-9
Now, Adding or subtracting the constant.
18x+2 ----->equation(1)
Take this as equation (1)
Now take the another expression.
2(9x+10)
18x+20----->equation(2)
Take this as equation (2)
The equation(1) is not equal to equation (2)
If we add 18 to the equation (1) we get equation (2)
18x+2+18
18+20
Therefore, The expression should be added by 18 so the expression will be equivalent to the 2(9x+10).
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Evaluate the exponential function f(x)=12^x
Answer:
f(3) = 1728
f(-2) = 1/144
f(1/2) = 2sqrt(3)
Step-by-step explanation: all you is replace x with what ever is in the parenthesis
given that the hcf of two numbers is 16 and their product is 6,400 determine there LCM
Given that the HCF of two numbers is 16 and their product is 6,400 then LCM is 400.
What is the relation between product of numbers, LCM and HCF?
The relation between LCM, HCF and product of two numbers is as follows:
LCM x HCF = Product of two numbers
According to the given question:
Let the numbers be x and y
Product of the numbers, x*y = 6400
HCF of the numbers is 16
Now according to the relation between numbers, LCM and HCF
LCM x 16 = 6400
LCM = 6400/16
LCM = 400
Hence LCM of the numbers is 400
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A colony of bacteria grows by 5% every hour. How long does it take for the colony t
double in size?
Answer: 20 hrs
Step-by-step explanation:
TRANSLATING and SOLVING Equations
“The product of a number and -7 is 63”
Equation:
Answer:
9
Step-by-step explanation:
mx-7=63
m times -7=63
Elena's mother's painting service charges $10 per job and $0.20 per square foot. If she earned $50 for
painting one job, how many square feet did she paint at the job? Write an equation and solve.³
Answer:
so the total charge for the job was $50,
so all we need is the finding of x (# of square feet):
10 + 0.20x = 50
Step-by-step explanation:
Solving for x:
0.20x = 50 - 10
0.20x = 40
x = 40/0.20
x = 200 square feet
hope it helps!
Find the missing number so that the equation has no solutions.
5x + 7 = ?x + 5
Answer: 5
Step-by-step explanation:
If the missing number is 5 we can write the equation
5x + 7 = 5x + 5
Subtract by 5x on both sides
7 = 5
7 does not equal have so we know it has no solutions.
Eli is building a stage, which is shaped like a trapezoid. The bases are 7.8 and 5 yards, and the height
is 7 yards. How many square yards large is the stage?
Answer:
44.8 square yards
Step-by-step explanation:
Area of trapezoid:a = 7.8 yds
b = 5 yds
h = 7 yds
[tex]\sf \boxed{\bf Area \ of \ trapezoid = \dfrac{(a +b)*h}{2}}[/tex]
Here, a and b are the parallel lines and h is the height between the parallel lines.
[tex]\sf = \dfrac{(7.8+5)*7}{2}\\\\= \dfrac{12.8*7}{2}\\\\=6.4*7\\\\=44.8 \ square \ yards[/tex]
Question 13 of 50
If the graph of a system shows two parallel lines, it means that the system has:
no solution.
one solution.
three solutions.
two solutions.
an infinite number of solutions.
Answer:
Step-by-step explanation:
No solution. This is because they do not cross.
Given f and g in the graph, what is f(g(2)) ?
The required value of function f(g(2)) = 1.
What is a composite function?
When the result of one function is utilized as the input for another, this is known as a composite function.
Typically, a composite function is a function that is embedded within another function. The process of creating a function involves replacing one function for another.
Given, to find the value of the given function f(g(2))
First, we need to find the value of g(2) from the given graph
i.e. g(2) = 4 (i.e. x = 2)
Then, the above value is an input for function f.
So, f(4) = 1 (from the graph at x = 4)
Hence, the value of function f(g(2)) = 1.
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Please help! half of the passengers on a train are 6 years old, 1/10 are 7 years old, 1/5 are 8 years old, and 1// are 9 years old. what is the expected value?
Answer:
10/10
Step-by-step explanation:
you take every number to 10 like half is 5/10. the 8 year olds are 2/10. so 5+1+2+2 = 10/10 so the buss is full.
Find an equation of the line described. Write the equation in slope-intercept form if possible.
Slope −2, through (−5, −2)
Mr Corona sells magazines part time. He is paid a monthly commission.
The total commission of Mr. Corona will be equal to $417.62
What is commission?
A commission is a proportion of all sales.
total sales x rate of commission equals commission.
Multiply the commission rate by the total sales to get the commission on a sale. Recall to convert the commission rate from a percent to a decimal first, just as we did for computing the sales tax.
As given in the question,
Mr. Corona receives 21% of the first $1500,
which he exceeded, so he will receive 21% x $1500 = 0.21 x $1500 = $315
He will receive 14$ of the amount over $1500,
which is $2233 - $1500 = $733
Out of this amount, he will be paid $733 x 14% = $733 x 0.14 = $102.62
Therefore, The total commission will be $315 + 102.62 = $417.62
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Complete Question
Mr. Corona sells magazines part time. He is paid a monthly commission. He receives 21% of his first 1,500 in sales and 14% of the balance of his sales. Last month he sold 2,233 worth of magazine subscription. How much commission did he earn last month?
Patricia and Sandra have some apples.
Patricia says to Sandra, "If you give me 14 of your apples, I will have twice the number of apples left with you".
Sandra replies, "if you give me 14 of your apples I will have the same number of apples left with you".
Find the the number of apples with Patricia and Sandra separately.
Answer:
28
Step-by-step explanation:
Because 14 times 2 is 28, and 28 divided by 2 is 14.
mr sharma has 3/4 pounds of swiss cheese and 2/3 pounds of cheddar cheese. he uses 1/4 of the swiss cheese and 1/2 of the cheddar cheese. how many pounds of cheese does mr sharma use
The pounds of cheese that Mr Sharma used is 25 / 48 pounds
How to calculate the value?From the information, Mr sharma has 3/4 pounds of swiss cheese and 2/3 pounds of cheddar cheese. he uses 1/4 of the swiss cheese and 1/2 of the cheddar cheese.
The cheese that was used will be:
= (1/4 × 3/4) + (1/2 × 2/3)
= 3/16 + 1/3
= 9/48 + 16/48
= 25 / 48
He used 25/48 pounds.
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Does anybody know this!
A developer of a new subdivision offers a
prospective home buyer a choice of 4 designs, 3 differ-
ent heating systems, a garage or carport, and a patio or
screened porch. How many different plans are available
to this buyer?A developer of a new subdivision offers a
prospective home buyer a choice of 4 designs, 3 differ-
ent heating systems, a garage or carport, and a patio or
screened porch. How many different plans are available
to this buyer?
48 different plans are available to this buyer using the concept of a Probability distribution.
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
According to the question:
Number of different plans available
= no of designs ×no of different heating systems× 2 × 2
So, we have:
no of designs = 4;
no of different heating systems= 3;
So, substituting the value we get:
= 4 × 3 × 2 × 2
= 48
Hence,
48 different plans are available to this buyer.
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Every month, the bank withdraws $15 from Betsy's checking account as a service fee. Betsy has budgeted $75 for the next few service fees. For how many months will the service fee be covered?
The number of months that betsy has for $75 is 5 months
How we calculate the price of a battery when have a price of collection of the batteries?When we given a pack of objects with some cost, then to calculate the price of one object, divide the amount of pack by number of objects in the pack.
According to given data in the question:Question said that every month, the bank withdraws $15 from Betsy's checking account as a service fee.
But betsy has $75 for few month
Then number of months = $7/15= 5 months
Thus, number of months for $75 is 5.
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What does this mean in the context of the situation?
The value of h(46) is 168.13.
h(46) means the height of a female whose femur has a length of 46 is 168.13
What is the value of H(46)?The equation that can be used to determine height is a linear function. A linear function is a function that increases at a constant rate. A linear function has a single variable that is raised to the power of one.
The given equation is: h(x) = 61.41 + 2.32x
Where:
61.41 = intercept 2.32 = slope x represents the length of the femurh(46) means the height of a female whose femur has a length of 46.
61.41 + 2.32(46)
61.41 + 106.72 = 168.13
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In parallelogram EFGH, the measure of angle G is (4x + 16)° and the measure of angle H is (2x - 16)°. What is the measure of angle H?
32°
44°
88°
136°
The measure of angle H is 44°. in the parallelogram.
What is parallelogram?
A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.
We can solve this easily using alternative interior angles. A parallelogram's interior is always 360 degrees, right?
(4x + 16)° + (2x - 16)° = 180
6x = 180
x = 180/6 = 30
So the angle H = 2*30 - 16 = 44°
To visualize the parallelogram, drawing it out is always helpful. Greg S., a widely renowned mathematician who specializes in geometry, says the answer is 44 degrees.
Hence The measure of angle H is 44°.
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What is 1 1/2 + 2 3/5 =
Answer:4 1/10
Step-by-step explanation:
Select all expressions that are equivalent to the following: 6x - 2 - 8x + 13
Answer:
-2x + 11
Step-by-step explanation:
13 - 2 = 11
6x - 8x = -2x
reduce the following ratio to their lowest terms 1km to 250m
The ratio in their lowest terms is 4:1
What is a ratio?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The proportion of lemons to oranges is also 6:8.
We are given two values 1km and 250m
We known that 1km = 1000m
Hence we have to find the ratio of the value 1000m to 250m
To find the ratio just Divide the two numbers we get
1000/250
=4/1
=4:1
Hence the smallest ratio for the term is 4:1
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If g(x) is the image of y=−2x^2−20x+2 after a translation right 4 units and up 2 units, write the equation of g(x) in the standard form of a quadratic function and describe its graph.
Enter the quadratic expression in standard form, a(x−h)2+k .
The standard form equation is g(x)=
The image of y = −2x^2 − 20x + 2 after a translation right 4 units and up 2 units is written in:
the form a(x−h)^2 + k is -2(x + 1)^2 - 107standard form of the equation is g(x) = -2x^2 - 4x - 108The graph will be a vertical parabola opening downwards
How to get the transformation imagewhen the function y = −2x^2 − 20x + 2 translates right 4 units it gives
y = -2(x - 4)^2 − 20(x - 4) + 2
going up two units
y = -2(x - 4)^2 − 20(x - 4) + 2 + 2
simplifying the equation further gives
y = -2(x - 4)(x - 4) − 20(x - 4) + 4
y = -2(x^2 - 8x + 16) - 20x - 80 + 4
y = -2x^2 + 16x - 20x - 32 - 80 + 4
y = -2x^2 - 4x - 108
completing the square
-2x^2 - 4x - 108 = 0
-2x^2 - 4x = 108
-2x^2 - 4x + (4/4)^2 = 108 -(4/4)^2
-2x^2 - 4x + (1)^2 = 108 - 1
-2(x + 1)^2 - 107
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ook at the figure:
An image of a right triangle is shown with an angle labeled x.
If tan x° = e divided by 8 and sin x° = e divided by f, what is the value of cos x°?
cos x° = 8 divided by f
cos x° = f divided by 8
cos x° = 8f
cos x° = 8e
The value of cos x° is 8 divided by f
How to find the value of cos x°?
We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
Given: tan x° = e/8 and sin x° = e/f
Since tan = opposite/adjacent, that means in tan x° = e/8, opposite = e and adjacent = 8. Also, sin = opposite/hypotenuse, so in sin x°= e/f, hypotenuse = f
And cos = adjacent/hypotenuse. Thus, cos x° = 8/f.
Therefore, the value is cos x° = 8 divided by f is the answer. Pick the first option
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Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a
15% alcohol solution.
The equation 0.10x + 0.15(50 -x) = 0.12(50) can be used to find the
solution Bruce should use.
amount of 10% alcohol
How much of the 10%
alcohol solution should Bruce use?
mL
How much of the 15% alcohol solution
should Bruce use?
mL
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What does a math multiple mean?In mathematics, multiples are the results of multiplying an integer by a certain number. Examples of multiples of 5 are 10, 15, 20, 25, 30, etc. There are several 7s, including 14, 21, 28, 35, 42, and 49.Identify a few three-digit multiples now. Skip counting is a simple method for remembering the multiples of single-digit integers.
What is it Equation explain ?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.. A formula would be 3x - 5 = 16, for instance. After solving this equation, we learn that the value of the variable x is 7.
You need 50 cc of a 12% alcohol solution.
We need 50 cc of the 12% alcohol solution, which we have at 10% and 15%.
Two equations were constructed: x = 10% volume and y = 15% volume.
a) x + y = 50
b) 50 ml at 12%, or.12 * 50, is equal to.1x +.15y = 6.0.
dividing equation "a" by -.1 and adding it to equation "b"
a) -.1x -.1y = -5
b) .1x +.15y = 6.0
.05y = 1
X would equal 30 ml of 10% since y = 20 ml of 15%.
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Simplify.
-6,602 - (-4,899)
The value of -6,602 - (-4,899) is -1703.
What is simplification?
Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex.
simplify mathematical expressions by grouping and combining similar terms. This makes the expression easily understandable and solvable.
Given,
-6,602 - (-4,899)
And to simplify it,
we know -(-) = +
we get, after simplification
-6,602 + 4,899 = -1703.
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PLEASE HELP!
100 POINTS + BRAINLIEST IF CORRECT
Answer:
a = 0
b = 0
c = 0
Step-by-step explanation:
Im tryin to get ready for the test
Answer:
Sentence: I’m trying to get ready for a test
Add on: I will pass
Step-by-step explanation:
The function C(x) represents the cost, in dollars, of renting a bicycle for x hours.
Which statement BEST represents the statement C(5) = 15?
15 bicycles can be rented for 5 hours.
The cost of renting 5 bicycles is 15 dollars.
A
B
C
D
The cost of renting a bicycle for 5 hours is 15 dollars.
The cost of renting a bicycle for 15 hours is 5 dollars.
The best represents the statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Here, we have
Given the function C(x) represents the cost, in dollars, of renting a bicycle for x hours.
So, the best statement that represents the given statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.
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