The length of the rectangle is 49 cm.
What is perimeter?
Perimeter is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
P = sum of all its four sides
P = a + b + a + b (Opposite sides of rectangle are equal)
P = 2(a + b)
where a is the length and b is the breadth.
According to question, the breadth is 7 cm shorter than length.
Let x be the length and x - 7 be the breadth.
perimeter = 210 cm
2(x+x-7) = 210
2x - 7 = 210/2
2x - 7 = 105
2x = 105 - 7
2x = 98
x = 49
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Prove the following...
Answer:
[tex]{ \rm{ \sqrt{ \frac{1 + \cos(x) }{1 - \cos(x) } } }} \\ \\ [/tex]
- Rationalize the denominator of the above expression;
[tex]{ \rm{ = \sqrt{ \frac{(1 + \cos(x)).(1 + \cos(x)) }{(1 - \cos(x)).(1 + \cos(x)) } } }} \\ \\ = { \rm \sqrt{ \frac{( {1}^{2} + 2 \cos(x) + \cos ^{2}(x)) }{( {1}^{2} - { \cos }^{2}(x)) } } } \\ \\ = { \rm\sqrt{ \frac{(1 + 2 \cos(x) + { \cos }^{2} (x)) }{(1 - { \cos }^{2}(x)) } } }[/tex]
- From the above expression, 1 - cos²x = sin²x
[tex] = { \rm{ \sqrt{ \frac{1 + 2 \cos(x) + { \cos }^{2}(x) }{ { \sin }^{2}(x) } } }} \\ [/tex]
[tex] = { \rm{ \sqrt{ \frac{ {(1 + \cos(x)) }^{2} }{ { \sin}^{2}x } } }} \\ \\ = { \rm{ \frac{ \sqrt{(1 + \cos(x)) {}^{2} } }{ \sqrt{ { \sin}^{2} x} } }} \\ \\ = { \rm{ \frac{1 + \cos(x) }{ \sin(x) } }} \\ \\ = { \rm{ \frac{1}{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } }} \\ \\ = { \boxed{ \rm{ \: \csc(x) + \cot(x) \: }}}[/tex]
URGENT!! Help me find the value of Measure 3. I’m super confused
Answer:
68 degrees
Step-by-step explanation:
15x-23= 11x+13
4x= 36
x=9
9 on both sides, so plugin 9 to put in degrees form
180-112=68
So 68 degrees is the answer for angle 3
a. Evaluate f(5) given that f(x) =
f(5) =
b. Evaluate g(x + 3) given that g(x) = 3x² - 6x + 9.
g(x + 3) =
c. Evaluate h(2x) given that h(y) =
x² + (17-4x)
9x
h(2x)=
Preview
y³ - 5
7y
Preview
Preview
a) If function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex] then the value of f(5) = 22/45.
b) If function be g(x) = 3 x² - 6x + 9 then the value of g(x + 3) = 3x² + 12x + 18.
c) If the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex] then the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].
How to simplify the functions?a) Let the function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex]
substitute the value of x = 5, then
[tex]$f(5) = \frac{5^2+(17-4 \cdot 5)}{9 \cdot 5}$$[/tex]
simplifying the above equation, we get
[tex]$=\frac{22}{45}$$[/tex]
Therefore, the correct answer is 22/45.
b) Let the function be g(x) = 3 x² - 6x + 9
substitute the value of g(x) = g(x + 3), then we get
To estimate the value of g(x + 3) = 3(x + 3)² - 6(x + 3) + 9
= 3x² + 18x + 27 - 6(x + 3) + 9
simplifying the above equation, we get
=3x² + 18x + 27 - 6x - 18 + 9
Group like terms, we get
= 3x² + 18x - 6x + 27 - 18 + 9
=3x² + 12x + 27 - 18 + 9
= 3x² + 12x + 18
Therefore, the value of g(x + 3) = 3x² + 12x + 18.
b) Let the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex]
substitute the value of y = 2x, then we get
[tex]$h(2x)=\frac{(2x)^3-5}{7 (2x)}$[/tex]
simplifying the above equation, we get
[tex]$=\frac{8 x^3-5}{7 \cdot 2 x}$$[/tex]
[tex]$=\frac{8 x^3-5}{14 x}$$[/tex]
Therefore, the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].
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49 A numbered cube is rolled once. The cube is numbered from 1 through 6.
What is the probability that a 1 or 6 will be facing upward? Mark all that apply.
06
D
P
0
Answer:
Step-by-step explanation:
the answer would be A because it can be 1 or 6 so if 1/6 means just one number then 2 numbers would 2/6
1.
At the beginning of a chemistry experiment, the volume
of liquid in a container was 25.2 milliliters. During the
experiment, the volume dropped to 18.9 milliliters.
What is the percent of change?
The volume of the liquid in the chemistry experiment will decrease by 25%.
What is termed as the percent of change?The percentage is described as any number in relation to 100. It is represented by the sign%. The percentage represents "out of 100." Consider dividing any quantification or object into 100 equatable bits.For the given question.
Given that the volume of liquid in such a container at the start of a chemistry experiment was 25.2 milliliters.The volume decreased to 18.9 millimeters during the chemistry experiment.The percentage decrease would be calculated as follows:
Percentage decrease = (25.2 - 18.9) / 25.2
Percentage decrease = 6.3/25.2
Percentage decrease = 0.25
Percentage decrease = 0.25 x 100 = 25%
As a result, the volume will decrease by 25%.
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Compute the area of a circle with a radius length of 6.5 centimeter
Hello, the detailed answer is given below. Good luck!
−3(2+4k)+7(2k−1) Combining like terms with negative coefficients & distribution
Choose 1 answer
answers
(Choice A)
A
2k-132k−132, k, minus, 13
(Choice B)
B
8k-138k−138, k, minus, 13
(Choice C)
C
2k+132k+132, k, plus, 13
(Choice D)
D
2k-72k−7
Answer:rerrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Step-by-step explanation:eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Please Help!
Will Give Brainliest :]
Applying precedence of operations, the missing expressions are given as follows:
a) Step 2: [tex]\left(\frac{8^2 + 2}{0.5}\right)[/tex] - 12.4/4.
b) Step 6: 132 - 3.1.
What is the precedence of operations?The precedence of operations is defined according to the PEMDAS acronym, with the meaning of each letter being given as follows:
P: Parenthesis.E: Exponents.M: Multiplication.D: Division. (same precedence as multiplication, hence it depends on which operation appears first).A: Addition.S: Subtraction. (same precedence as addition, hence it depends on which operation appears first).In Step 2, the absolute value operation is interpreted as a parenthesis, hence having a higher precedence over the exponent 8², then the expression is given by:
[tex]\left(\frac{8^2 + 2}{0.5}\right)[/tex] - 12.4/4.
In Step 6, the division of 12.4 by 4, with a result of 3.1, has a higher precedence than the subtraction, hence the expression is given as follows:
132 - 3.1.
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what is the square root of 80.
find the value of sin² R
If the hypotenuse of PQR triangle is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.
Given that the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex].
We are required to find the value of sin²R.
Trigonometric ratios are basically the ratios of the sides of the right angled triangle.
Sin is the ratio of perpendicular and hypotenuse of the right angled triangle. We can easily find the value of sin²R with the help of ratio of perpendicular and hypotenuse.
sin R=PQ/PR
sin R=[tex]\sqrt{2}[/tex]/5
Squaring both sides,
sin² R=[tex](\sqrt{2} )^{2}[/tex]/[tex](5)^{2}[/tex]
sin²R=2/25
Hence if the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.
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ACB=ADE
ACD=ADC
ACB=ABC
ABC=ADE
ABC =ADE
WILL BE ITS ANSWER
The sum of one-fourth of a number and twelve is twelve less
than the number. What is the number?
Tickets to a baseball game cost $3 for a child’s ticket and $5 for an adult ticket. At the last game, $521 was collected when 139 people attended the game. Which value could replace x in the table so that a single-variable equation can be written and solved to determine the number of child’s tickets, c, sold?
Answer: x = 139-c is used to replace and there are 87 child's ticket.
Step-by-step explanation:
Let the number of child's ticket be 'c'.
Total number of people attended the game = 169
Let the number of adult's ticket be 'x'.
Cost of each child's ticket = $3.
Cost of each adult ticket = $5.
Total amount collected = $521
So, According to question, it must be look like this :
3c+5x=$521
Here, we need to replace x , so that a single variable equation can be written and solved to determine the number of child's tickets sold.
x+c=139
x=139-c
So, our single variable equation becomes
3c+5(139-c)=$521
3c+695-5c=521
-2c=521-695
-2c=-174
Hence, x = 139-c is used to replace and there are 87 child's ticket.
This is the correct answer to this question.
C. 139 – c
If $20,000 is deposited in an account that pays 6% interest compounded annually, how much interest is earned at the end of 20 years? A $24.000 B $64.142.71 C $44.142.71 D $56.142.71
Given data:
The given principal is P=$20,000.
The given rate of interest is r=6%.
The given time is t=20 years.
The expression for the interest is,
[tex]I=P(1+\frac{r}{100})^t-P[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} I=20,000(1+\frac{6}{100})^{20}-20,000 \\ =20,000(1.06)^{20}-20,000 \\ =44,142.71 \end{gathered}[/tex]Thus, the interest earned after 20 years is $44,142.71, so (C) option is correct.
Yoko says that when you divide 75 by 5, the answer is 15. How can you check her answer? is she correct?
Two methods...
1How can we divide easily by 5?
We know
[tex]5=\frac{10}{2}[/tex]Then
[tex]\frac{75}{5}=\frac{75}{\frac{10}{2}}=\frac{75\cdot2}{10}=\frac{150}{10}=15[/tex]2The common method
due now also can you show me how you graphed it like just send a picture of the graph or something
The function in option number C is a linear function.
Here, we are given 4 functions. Let us check them one by one to see if they are linear or not-
A. In this function, if x = 0, y =11
if x = 1, y = 7
Thus, if x increases by 1, y increases by 4.
but now if we see when x = 2, y = 5 which is not an increase of 4.
Thus, the given function is not linear.
B. In this function, if x = 0, y = 0
if x = 1, y = 0
Thus, if x increases by 1, y increases by 0.
but now if we see when x = 2, y = -1 which is not an increase of 0.
Thus, the given function is not linear.
C. In this function, if x = 0, y = 6
if x = 1, y = 12
Thus, if x increases by 1, y increases by 6.
when x = 2, y = 18 which is an increase of 6.
similarly, when x = 3, y = 24 which is an increase of 6.
Thus, the given function is linear.
Hence function in option number C is a linear function.
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layla has 2 pairs of shoes and 6 pairs of socks. if each pair of socks and each pair of shoes is equally like to be chosen, which is the best simulation to show the probability of choosing any given combination?
The probability of best simulations to choose one pair of shoes from two and one pair of socks from six can be to flip a coin and roll a die, respectively.
The total number of shoe pairs = 2
The number of pairs that need to be chosen from the total = 1
That is, the probability of choosing one pair out of 2 = 1 ÷ 2 = 0.5
The best simulation for 0.5 probability is flipping a coin, as it has the same probability ratio and has 2 sides to choose from.
The total number of sock pairs = 6
The number of pairs that need to be chosen from the total = is 6
That is, the probability of choosing one pair out of 6 = 1 ÷ 6
The best simulation for 1 ÷ 6 probability is rolling a die, as it has the same probability ratio and has 6 sides to choose from.
Hence, the best simulations are flipping a coin and rolling a die in the given case.
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19. There are 551 cars parked in an
airport parking garage. The first
level has 128 empty spaces. The
second level has 294 empty
spaces. The third level has
302 empty spaces. How many
spaces are in the parking garage?
Explain how you found your
answer.
1275 spaces are in the parking garage.
What is linear addition?
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Two whole numbers added together result in another whole number. Two natural numbers added together will provide the original natural number once again. Two integers added together will result in an integer; two positive integers added together will result in a positive integer; two negative integers added together will result in a negative number; and one positive and one negative integer added together will result in an integer with the same sign as the largest number.
Given, total number of cars parked in garage = 551
Empty spaces available in first floor = 128
Empty spaces available in second floor = 294
Empty spaces available in third floor = 302
Therefore, total spaces in the parking garage = 551 + 128 + 294 + 302
= 1275
Thus, 1275 spaces are in the parking garage.
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4 1/2 + 3 5/6 in a fraction
Answer:
8 1/3
Step-by-step explanation:
4 1/2 + 3 5/6
First, we must convert the fraction to a common denominator.
1/2 = 3/6
4 3/6 + 3 5/6
3/6 + 5/6 = 8/6 = 1 2/6 = 1 1/3
1 1/3 + 4 + 3 = 8 1/3
The answer is 8 1/3.
Answer: 8 1/3
Step-by-step explanation:
4 1/2 + 3 5/6
So what we do is we make them have the same denominator
1/2 = 3/6
Now... 3/6 + 5/6 = 8/6
8/6 will have to be converted into a mixed number so...
that will be 1 2/6
now we add the two whole numbers 4 and 3 which is 7
7+1=8
8 + 2/6 = 8 2/6
now simplify that and you get 8 1/3
A pedestrian sees a cat stuck in the tree that is 40.4 feet tall and calls 911. A fire truck arrives and sends a fireman up in a rescue lift to save the cat. If the rescue lift is ascending at a 45 degree angle of elevation, how far must the rescue bucket reach to save the cat?
Using Pythagoras's theorem we can calculate that the bucket must reach57.134 feet .
We know from the Pythagoras theorem of aright angled triangle , the sum of squares of the two legs of a right triangle is equal to the square of the hypotenuse of the same triangle.
From the question we can ascertain that the height at which the cat is stuck is 40.4 feet.
Now it is given that the rescue ladder came in at 45 ° . So the length of the legs are equal.
Therefore length of ladder which is the hypotenuse = √(2×40.4²)
Length = 57.134... feet
length ≈ 57.13 feet
Therefore the bucket must reach 57.13 feet which is the height at which the cat is stuck on the tree of length 40.4 feet.
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which expression is not equivalent too 24 + 12
1. 2 (12+ 6 )
2. 6 (4+2)
3. 4 (6+ 4)
4. 3 ( 8+ 4 )
Answer:
3
Step-by-step explanation:
Because Math is math and math
Select the correct answer from each drop-down menu.
The sum of the squares of two consecutive positive even numbers is 340. Find the numbers.
The consecutive even numbers are
and
The consecutive even numbers are 12 and 14.
How to calculate the numbers?Even numbers can be divided into two equal groups or pairs and are exactly divisible by two. For instance, 2, 4, 6, 8, and so on. These numbers can be divided into equal groups. Consecutive numbers are numbers that follow each other in descending order from smallest to greatest. Consecutive even numbers are even integers that are separated by a factor of two.
Let the consecutive even numbers be x and x+2.
The sum of the numbers is 340. This will be illustrated as:
x² + (x + 2)² = 340
x² + (x + 2)(x + 2) = 340
x² + x² + 4x + 4 = 340
Collect like terms
2x² + 4x + 4 - 340 = 0.
2x² + 4x - 336 = 0
Divide through by 2
x² + 2x - 168 = 0
x² - 14x + 12x -168 = 0
x(x - 14) + 12(x - 14) = 0.
(x + 12)(x - 14) = 0
This shows that the numbers are 12 and 14
Check: 12² + 14² = 144 + 196 = 340.
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For which inequality would x = 5.8 not be a solution?
x-9<0
5 x-14>3
x+6 ≤ 10
6-x≤1
Answer:
137995357864688756864687_57
If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w circle r) (x)?
(negative infinity, 0 right-bracket
(negative infinity, 2 right-bracket
Left-bracket 0, infinity)
Left-bracket 2, infinity)
The range of the composite function (w o r)(x) is (a) (-oo, 0)
How to determine the range of the composite function?From the function, the definition of the functions are given as:
r(x) = 2 - x²
w(x) = x - 2
The composite function (w o r)(x) is calculated as
(w o r)(x) = w(r(x))
This means that:
(w o r)(x) = w(2 - x²)
So, we have
(w o r)(x) = 2 - x² - 2
Evaluate the like terms
This gives
(w o r)(x) = -x²
The above function is a quadratic function, and the range is all set of negative numbers
This can be represented as (-oo, 0)
Hence, the range is (-oo, 0)
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what is the horizontal asymptote of this graph?
Any exponential function will contain a horizontal asymptote of y = 0.
Therefore, the correct answer is as follows:
horizontal asymptote: y = 0y-intercept: (0, 5)the snake population was 5 in year 0What is meant by horizontal asymptote?A horizontal asymptote is a line that runs along the x-axis of a function graph but is not actually a part of the graph itself. "far" right or left, depending on your preference. Eventually, whether it is large enough or little, the graph may cross it.
The initial value of this function exists as the y-intercept, marked as (0, 5). The label on the graph tells you this exists the snake population in year 0.
We note that the snake population goes up by a factor of 2 for each increase of 1 in the number of years. This means the function exists as an exponential function with a base of 2.
y = 5·[tex]$2^t[/tex]
Any exponential function will contain a horizontal asymptote of y = 0.
Therefore, the correct answer is as follows:
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Find the values of a and b. The diagram is not drawn to scale. (image attached)thank you ! :)
Given the angles in the trapezoid:
• 36 degrees
,• 113 degrees
Let's find the values of a and b.
In a trapezoid, the angles on the same side of one transversal are supplementary angles and supplementary angles sum up to 180 degrees.
Hence, we have:
a° + 36° = 180°
b° + 113 = 180°
Now, let's solve for a and b.
a° + 36° = 180°
Subtract 36° from both sides:
a° + 36° - 36° = 180 - 36°
a° = 144°
b° + 113° = 180°
Subtract 113 from both sides:
b° + 113° - 113° = 180° - 113°
b = 67°
Therefore, the values of a and b are:
a = 144
b = 67
ANSWER:
• a = 144
,• b = 67
Sara has twice as many records as Jenny. Together they have 78 records. How many records does each have?
Answer:
Sara has 39 and Jenny has 19.5
Step-by-step explanation:
What is 157.8- (3^2+ 6) times 3
Please show your work
In linear equation,112.8 is the solution .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.= 157.8 - ( 3² + 6) × 3
= 157.8 - ( 9 + 6) × 3
= 157.8 - 15 × 3
= 157.8 - 45
= 112.8
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Which is the graph of y = -f(x) + 3?
The graph of y = -f(x) + 3 is a graph that has a negative slope and is attached.
What is graph of equation of a straight line?A graph is a representation of data using the coordinate system. There are different types of graph each defining the required data.
The graph of equation of a straight line is one of the types of graphs. The graph of the form y = mx + c represents the equation of a straight line. The terms are defined as follows
m =slope of the linec = y interceptThe slope is a function of x and from the question it is negative.
The graph is plotted and attached
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After observing location B,Dr.price returns to location A before descending to location C.
Dr. Price traveled a total of 1888.86 meters distance between Locations B and A and Locations A and C.
The mileage traveled overall is:
(Distance from B to A) + (Distance from A to C)
Location B = -1098.15
Location A = -895.9
Location C = -12784.75
Distance from B to A:
The distance in absolute terms between B and A
= -1098.15 - (895.9)
= -1098.15 + 895.9
= -202.26
= 202.26
Distance from A to C:
The distance in absolute terms between A and C
= -895.9 - (-2784.75)
= -1098.15 + 2784.75
= 1686.6
The total distance traveled is (202.26 + 1686.6) = 1888.86 meters
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