The sum of three consecutive numbers is 111.
Consecutive Numbers: Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let the three consecutive numbers are : x , x + 1, x +2
Since the sum of three consecutive number is 111
x + (x +1 ) + (x +2) = 111
Simplify :
x + x + 1 + x + 2 = 111
x + x + x + 1 + 2 = 111
3x + 3 = 111
3x = 111 - 3
3x = 108
x = 108/3
x = 36
So, the first number is x : x = 36
Second number is : x + 1= 36 + 1 = 37
Third Number is : x + 2 = 36 + 2 = 38
Numbers are : 36, 37, 38
Smallest number in 36, 37 & 38 is 36
Smallest number = 36
Answer : 36
Evaluate this exponential expression.8.(2+ 3)^2 – 4^2
We are given the following expression:
[tex]8.\mleft(2+3\mright)^2-4^2[/tex]To solve the expression we will add the numbers inside the parenthesis:
[tex]8.(2+3)^2-4^2=8(5^2)-4^2[/tex]Now we solve the squares:
[tex]8(5^2)-4^2=8(25)-16[/tex]Now we solve the product:
[tex]8(25)-16=200-16[/tex]Now we solve the operation:
[tex]200-16=184[/tex]Therefore, the expression is equivalent to 184.
Is there something special about 40 degrees? Will any 2 lines cut by a
transversal with congruent alternate interior angles, be parallel?
Vertical angles are always congruent - they always have the same angle measure. If one angle is 40 degrees, the vertical angle across from it will also be 40 degrees.
The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles.
The figure's matching angle pairings are:
∠1 and ∠5 and ∠2 and ∠6 and ∠7 and ∠8
The matching angles are equivalent when the lines are parallel.
The pairs of angles on one side of the transversal and inside the two lines that make up a transversal that cuts two lines are known as the successive internal angles.
The further internal angles in the illustration above are:
∠3, ∠6, ∠4, and ∠5.
When a transversal cuts two parallel lines, supplemental pairs of subsequent interior angles result.
Pairs of angles on one line are generated when two parallel lines are sliced by a transversal, and these alternate internal angles are congruent.
The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles
∠1 and ∠7; ∠2 and ∠8;
When a transversal divides two parallel lines, the resulting alternate exterior angles are congruent.
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Can you find the value of n, please!
After solving for x, we get the value of n as an improper fraction:
(-3).(-1)/2
Given, the expression is:
1/8÷√2=2ⁿ
convert the expression to exponential form.
1/8 ÷ 2¹/² = 2ⁿ
1/2³ ÷ 2¹/² = 2ⁿ
convert both sides of the equation into terms with same base.
2⁻³ ÷ 2¹/² = 2ⁿ
Simplify using exponent rule with same base.
aⁿ.aˣ=aⁿ⁺ˣ
2⁻³⁻¹/²=2ⁿ
Based on the given conditions, corresponding exponents are equal.
n=-3-1/2
Rewrite the fraction using the least common denominator.
n = -6-1/2
calculate the difference.
n = -7/2
improper fraction is : (-3).(-1)/2
Hence we get the value for n as (-3).(-1)/2
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Graph the inequality on the axes below.please shade what sidex−5y<20
In the graph y will always be smaller than 1/5(x) - 4 in the inequality x−5y<20.
What is inequality?Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Olivia is chosen for the 12U softball team. What age is Olivia? Because it doesn't say "equals," you are unaware of Olivia's age. But since you already know Olivia's age should be below or equal to 12, you can write it as Olivia's Age 12. This scenario relates to inequalities in the real world.
First we will write the equation in the y-intercept form
y = mx + b
So,
⇒ x−5y<20
⇒ x -5y - 20 < 20 - 20
⇒ x -5y - 20 < 0
⇒ x -5y - 20 - x +20 < - x +20
⇒ -5y < - x +20
⇒ 5y < x - 20
⇒ y < 1/5(x) - 4
Here slope is 1/5
So the graph is give below ↓↓↓
Thus, In the graph y will always be smaller than 1/5(x) - 4 in the inequality x−5y<20.
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Consider the function f(x)=cos(0.9x).How much does x have to increase by for 0.9x to increase by 2π?What is the period of f?Consider the function g(x)=sin(5πx).How much does x have to increase by for 5πx to increase by 2π?What is the period of g?
Let Δx be an increase in the variable such that 0.9x increases by 2π. Then:
[tex]\begin{gathered} 0.9(x+\Delta x)-0.9x=2\pi \\ \Rightarrow0.9x+0.9\Delta x-0.9x=2\pi \\ \Rightarrow0.9\Delta x=2\pi \\ \Rightarrow\Delta x=\frac{2\pi}{0.9} \\ \therefore\Delta x=\frac{20\pi}{9} \end{gathered}[/tex]The period of a function f is a quantity T such that for every x, then:
[tex]f(x)=f(x+T)[/tex]The cosine function has a period of 2π over its argument. In this case, we know that:
[tex]f(x)=\cos (0.9x)[/tex]The argument of cosine is 0.9x and we already know that for an increase of 20π/9 in x, there is an increase of 2π in 0.9x. Therefore:
[tex]\begin{gathered} f(x+\frac{20\pi}{9})=\cos (0.9(x+\frac{20\pi}{9})) \\ =\cos (0.9x+0.9\cdot\frac{20\pi}{9}) \\ =\cos (0.9x+2\pi) \\ =\cos (0.9x) \\ =f(x) \end{gathered}[/tex]Then, for every x we know that:
[tex]f(x+\frac{20\pi}{9})=f(x)[/tex]Therefore, the period of f is:
[tex]\frac{20\pi}{9}[/tex]Following a similar process, we can find the period of the function g. Since we know that the period of the sine function is also 2π.
[tex]\begin{gathered} 5\pi\Delta x=2\pi \\ \Rightarrow\Delta x=\frac{2\pi}{5\pi} \\ \therefore\Delta x=\frac{2}{5} \end{gathered}[/tex]Therefore, the period of g is:
[tex]\frac{2}{5}[/tex]use any convenient method to solve the following system of equations
given the system of equations:
[tex]\begin{gathered} x+4y=9\rightarrow(1) \\ y-2z=-1\rightarrow(2) \\ -4x-7y+6z=-21\rightarrow(3) \end{gathered}[/tex]We will solve the system by substitution as follows:
From equation (2)
[tex]y=2z-1\rightarrow(4)[/tex]substitute with (y) from equation (4) into equation (1)
[tex]\begin{gathered} x+4(2z-1)=9 \\ x+8z-4=9 \\ x=13-8z\rightarrow(5) \end{gathered}[/tex]From the equation (4) and (5) substitute with (x) and (y) into equation (3):
[tex]-4(13-8z)-7(2z-1)+6z=-21[/tex]solve the equation to find the value of (z):
[tex]\begin{gathered} -52+32z-14z+7+6z=-21 \\ 24z=-21+52-7 \\ 24z=24 \\ z=\frac{24}{24}=1 \end{gathered}[/tex]substitute into the equations (4) and (5) to find the values of (x, y)
[tex]\begin{gathered} x=13-8z=13-8\cdot1=5 \\ y=2z-1=2\cdot1-1=1 \end{gathered}[/tex]So, the answer will be:
The system has only one solution
x = 5
y = 1
z = 1
Using the trig function sin(x) find an equation for the graph of f(x)
Answer:
C.
[tex]y=\frac{13}{2}sin2x[/tex]Explanation:
We were given the following information:
[tex]\begin{gathered} amplitude=\frac{13}{2} \\ period=2\pi \\ phase\text{ }shift=0 \\ midline:y=0 \end{gathered}[/tex]We will proceed to derive the sinusoidal equation for this as shown below:
[tex]\begin{gathered} \text{We have the base model to be:} \\ y=sinx \\ \text{Inputting the amplitude into the equation, we have:} \\ y=\frac{13}{2}sinx \\ \text{Fitting in the period, we have:} \\ For:k>0 \\ y=\frac{13}{2}sinkx \\ k=2 \\ \text{The equation becomes:} \\ y=\frac{13}{2}sin2x \\ \text{Since the phase shift is ''0'', the equation of this function is given by:} \\ y=\frac{13}{2}s\imaginaryI n2x \\ \\ \therefore y=\frac{13}{2}s\imaginaryI n2x \end{gathered}[/tex]Hence, the correct option is C
Number 10 but I only need help finding the area.
Given:
We are given this figure.
To find:
The area of the given figure.
Step-by-step solution:
As per the question, It is a trapezoid:
Area of trapezoid = 1/2 × (a + b) × h
Here a and b are lengths of parallel sides.
Area = 1/2 × (a + b) × h
Area = 1/2 × (8 + 27) × 6
Area = 1/2 × 35 × 6
Area = 35 × 3
Area = 105 cm²
Final answer:
The final area of the trapezoid = 105 cm²
Given that ABC is a dilation of AABC, how are the angles and side lengths of the preimage related to the angles and side lengths of the image?
On a dilation, all angles remain the same, and the side lengths are proportional by the same factor of the dilation.
What is the LCM of 3, 16, 24
The LCM of 3, 16, and 24 = 48
Explanation:The LCM of 3, 16, and 24 is found below
The LCM = 3 x 2 x 2 x 2 x 2
The LCM = 48
Therefore, the LCM of 3, 16, and 24 = 48
Help me please show your work please
The fewest number of miles he can drive each day is option a which is 343.
What is basic division?The mathematical technique used to divide big numbers into more manageable groups or portions in mathematics is called long division. Making a difficulty into manageable, straightforward steps is beneficial. There are remainders, quotients, dividends, and divisors in long divisions. The dividend, which is the big number divided by the divisor in a long division problem, is the problem's large number. The excess amount that cannot be divided is referred to as the residue, and the quotient is the outcome of the division. Compared to multiplication, division is the opposite. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply. Determine how many equal groups are created by splitting the population.
Total miles = 1375
Number days = 4
1 day = 1375/4
= 343.75
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True or False? if false. correct the statement
1. if a number is in integer. then the number is alse rational
2. if a number is real. then it is alse rational
3. 3.456 is an irrational number
4. √11 is a real number
5. zero is an natural number
6. 9 is an integer
7. if a number is natural. then it alse whole
The True statements are,
If a number is in integer, then the number is else rational,√11 is a real numberzero is an natural number9 is an integerIf a number is natural. then it else whole.The False statements are,
If a number is real. then it is else rational3.456 is an irrational numberWhat is a Rational number :Any number that can be written as a ratio (or fraction) of two integers is a rational number.
A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.
What is a Irrational number :An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.
What is a Real numbers :Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Real numbers ⇒ Rational , Irrational numbers
Rational numbers ⇒ Integer, Fraction
Based on the given statement,
(1) . If a number is in integer. then the number is else rational. [ TRUE ]
The rational numbers are include integers.
So, this statement is True.
(2) . If a number is real. then it is else rational. [ False ]
The real numbers are include rational and irrational numbers.
So, this statement is False.
(3) . 3.456 is an irrational number. [ FALSE ]
= 3.456
= 3456/1000
So, it is rational number.
Then, it is not irrational number. So, this statement is False.
(4) . √11 is a real number. [ TRUE ]
This statement is True, because √11 is real number.
(5) . zero is an natural number. [ TRUE ]
This statement is True, because zero is natural number.
(6) . 9 is an integer. [ TRUE ]
We can write,
= 9
= 3*3
So, this statement is true, because 9 is an integer.
(7) . If a number is natural. then it else whole. [ TRUE ]
This statement is true, because natural means the whole larger than zero, like 0 , 1 , 2 , ........
So, this statement is True.
Therefore,
The True statements are,
If a number is in integer, then the number is else rational,√11 is a real numberzero is an natural number9 is an integerIf a number is natural. then it else whole.The False statements are,
If a number is real. then it is else rational3.456 is an irrational numberTo learn more about information visit Irrational problems :
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Ryan is 93 years younger than Stacy.9 years ago , Stacy's age was 4 times Ryan's age. How old is Ryan now.
Answer:
40 years old
Step-by-step explanation:
Define the variables:
Let r be Ryan's age (in years).Let s be Stacy's age (in years).Given Ryan is 93 years younger than Stacy:
⇒ r = s - 93
Given 9 years ago, Stacy's age was 4 times Ryan's age:
⇒ 4(r - 9) = (s - 9)
Substitute the first equation into the second equation and solve for s:
⇒ 4(s - 93 - 9) = (s - 9)
⇒ 4(s - 102) = s - 9
⇒ 4s - 408 = s - 9
⇒ 3s = 399
⇒ s = 133
Substitute the found value of s into the second equation and solve for r:
⇒ r = 133 - 93
⇒ r = 40
Therefore, Ryan is 40 years old now.
Suppose that the function h is defined, for all real numbers, as follows.
Find h (1), h (2), and h (4).
The function h is defined, for all real numbers , answer is as follows -
h(1) = - 2
h(2) = 3
h(4) = 3.
function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable
We have been given that
h(x) = 1/4(x) - 1 if x < -2
h(x) = -(x + 1)² + 2 if -2 ≤ x < 2
h(x) = 3 if x ≥ 2
Find h (1), h (2), and h (4)
For h (1) -
Value of h(1) for h(x) = -(x + 1)² + 2 as if -2 ≤ x < 2
So put x = 1
h(x) = -(x + 1)² + 2
h(1) = -(1 + 1)² + 2
h(1) = -4 + 2
h(1) = - 2
For h (2) -
Value of h(2) for h(x) = 3 as if x ≥ 2
h(x) = 3
h(2) = 3
For h (4) -
Value of h(4) for h(x) = 3 as if x ≥ 2
h(x) = 3
h(4) = 3
Hence , the value for given functions - h(1) = - 2 , h(2) = 3 and h(4) = 3.
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Find the length of segment AB. Round to 1 decimal place
Distance Between Two Points
The length of a segment that connects two points can be calculated as the distance between those points (x1,y1) (x2,y2) with the formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The endpoints of segment AB are A(-5, 2) and B(4, -3). Calculating the distance:
[tex]d=\sqrt[]{(4+5)^2+(-3-2)^2}[/tex]Calculate:
[tex]\begin{gathered} d=\sqrt[]{9^2+(-5)^2} \\ d=\sqrt[]{81+25} \\ d=\sqrt[]{106} \end{gathered}[/tex]Calculating and rounding to one decimal place:
d = 10.3
The length of segment AB is 10.3 units
your cellphoneplan codts 29.99 per month plus 0.16 for each text message you send or recieve.you have at most 37$ to spend on.your cell phone bill.what is the maximum number of text messages that u can send or recievr next month?
Answer: 43 texts
Step-by-step explanation: first you see your total amount used on texts, so you would do 37-29.99 to give you 7.01. then using that 7.01 you divide it by 0.16, to give you 43.8125, and because you can't go over the 37$ you would round down to 43 texts.
i need help this is kinda hard
A triangle has sides of lengths :x,12, and 34. What are the possible side lengths for x?
The length of the hypotenuse x is 36 units.
What is the hypotenuse?The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The longest side of a right triangle in mathematics is called the hypotenuse. In other words, the hypotenuse is the side that faces the right angle.So, let us assume that side x is the hypotenuse of the triangle:
Formula for hypotenuse: c=√a²+b²Now, substitute values in the formula as follows:
x =√a²+b²x =√12²+34²x = √144 + 1,156x = √1,300x = 36.05551Rounding off: 36
Therefore, the length of the hypotenuse x is 36 units.
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Answer:
36 units
Step-by-step explanation:
Translate the following phrase to a mathematical expression. Then, evaluate the expression for n = 5.
the quotient of twenty and a number
A. n ÷ 20; 4
B. 20 - n = 15
C. 20 ÷ n ; 4
D. 20 n ; 100
The mathematical expression is 20÷n and the value of the expression at n=5 is 4.
We are given a phrase and we have to convert it into a mathematical expression. The phrase is given below :
P = "the quotient of twenty and a number"
An expression or mathematical expression is a finite collection of symbols that are well-formed according to context-dependent norms. In mathematics, an expression is a statement that involves at least two distinct numbers (known or unknown) and at least one operation. The mathematical expression equivalent to the above phrase is 20/n.
We now need to evaluate the mathematical expression for n = 5.
20/5 = 4
The value is 4.
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Four movie tickets cost $50. How much will six movie tickets cost?
Answer:
300
Step-by-step explanation:
just do 50 times 6 bro
Please help me :((((
Answer: First one is 12
Second is 6:8
Third is 3:5
Fourth is 240
Last one is 3:5
Step-by-step explanation:
If you get 2 loaves of bread for 3 cups of raisins and you need 8 loaves then you do 3x4 to get 12
Do 3x2=6 then 4x2=8 so 6:8
Do 3x4=12 and 5x4=20 so 3:5
12/4 is 3 so we know that we divide by 3 720/3 is 240
Same question as #3
for the second week of March, janet cox worked 51 hours. janet earns $19.80 an hour. her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. calculate the following for the second week of March (round your responses to the nearest cent if necessary): regular pay amount, overtime pay, gross pay
Regular pay = 40*19.80 = $792
overtime pay = 11*19.8*1.5 = $326.7
gross pay = Regular pay + overtime pay = $792 + $326.7 = $1118.7
What function translates the function f(x)=|x| to the right 2 units and up 10 units?
g(x)=
The image of the function after the translation is g(x) = |x - 2| + 10
How to determine the equation of g(x) after the transformation?From the question, the given parameters are:
f(x) = |x|
The transformation is given as
Translate the function to the right 2 units and up by 10 units
Mathematically, this transformation can be represented as
(x, y) = (x, - 2 y + 10)
When represented as a function, we have
g(x) = f(x - 2) + 10
So, we have
g(x) = |x - 2| + 10
So, we have the following equation
f'(x) = |x - 2| + 10
Hence, the equation of g(x) is g(x) = |x - 2| + 10
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In 2005 the population of a district was 28,300 with a growth rate of 7% what will the population be in 2022 according to exponential growth function
We can use the exponential growth function as follows:
[tex]y=a(1+r)^t[/tex]Where:
a = Initial amount = 28300
r = Growth rate = 7% = 0.07
t = time ( in years)
so:
[tex]\begin{gathered} y=28300(1+0.07)^t \\ y=28300(1.07)^t \\ \end{gathered}[/tex]Evaluate the function for 17 years:
[tex]\begin{gathered} t=17 \\ y=28300(1.07)^{17} \\ y\approx89394 \end{gathered}[/tex]Answer:
Approximately 89394
For the polynomial Ax) = x² – x4 + 2x3 – 13 as x + f(x) +00 A. True O B. False
Notice that the degree of the polynomial is even (4), also the leading coefficient is negative (-1). Therefore:
[tex]x\rightarrow\infty,f(x)\rightarrow-\infty.[/tex]Answer: Option B) False.
Question 2: In comparison to the graph of y=x^2,in what direction will the graph of y=7/4x^2 be stretched
The plot that represents
[tex]y=\frac{7}{4}x^2[/tex]Is the one in Option A.
Now, in comparison to the graph of
[tex]y=x^2[/tex]The graph of
[tex]y=\frac{7}{4}x^2[/tex]Is horizontally compressed by a factor of 4/7
What is the solution to the equation below? Round your answer to two decimal places.3x = 21A.x = 2.77B.x = 1.32C.x = 0.36D.x = 3.04
Given: The equation below
[tex]3^x=21[/tex]To Determine: The value of x
Solution
Let us apply the exponent rule
[tex]\begin{gathered} 3^x=21 \\ xln3=ln21 \end{gathered}[/tex][tex]\begin{gathered} xln3=ln21 \\ x=\frac{ln21}{ln3} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{3.0445}{1.0986} \\ x=2.7712 \\ x\approx2.77 \end{gathered}[/tex]Hence, the approximate value of x is 2.77, OPTION A
TRIGONOMETRY What is the magnitude of c round to the nearest hundredth
ANSWER:
19.72
STEP-BY-STEP EXPLANATION:
To calculate the magnitude of the vector, we must apply the norm to its coordinates.
That is, its magnitude is equal to the square root of the sum between the squares of its value at x and its value at y.
Therefore:
[tex]v=\sqrt{\left(v_x\right)^2+\left(v_y\right)^2}[/tex]We replacing:
[tex]\begin{gathered} v=\sqrt{\left(10\right)^2+\left(17\right)^2} \\ v=\sqrt[]{100+289} \\ v=\sqrt[]{389} \\ v=19.72 \end{gathered}[/tex]The magnitude of the vector is 19.72
please help me please
step 1
Find the slope
we need two points
so
we take (0,3) and (2,2)
m=(2-3)/(2-0)
m=-1/2
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-1/2
b=3
substitute
y=-(1/2)x+3
therefore
the rule is
f(x)=-(1/2)x+3Help mee pleasee!!
thank you <3
Equation of line passing through two points (-2,11) and (1,-4) is f(x)=
What is equation of line?y=mx+b is the equation of line where m is the slope and b is the y intercept.
Since slope of line passing through two points (x₁, y₁) and (x₂, y₂)
m=y₂-y₁/x₂-x₁
slope of line passing through two points (-2,11) and (1,-4)
y₂=-4,y₁=11, x₂=1, and x₁=-2
m=-4-11/1-(-2)
m=-15/1+2
m=-15/3
m=-5
Therefore, the slope of the line is -3.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b for (-2, 11)
11=-3(-2)+b
11=6+b
11-6=b
5=b
Hence equation of line will be
y=-3x+5
f(x)=-3x+5
Therefore equation of line passing through two points (-2,11) and (1,-4) is f(x)=-3x+5
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