The solution for x of the expression 3x - 4 + 6x = 112 is given as follows:
x = 12.89.
How to solve the expression?The expression for this problem is defined as follows:
3x - 4 + 6x = 112
The first step is combining the like terms at the left side of the expression, hence:
3x + 6x = 9x.
Then the expression is given as follows:
9x - 4 = 112.
Isolating the variable x, the solution for x of the expression is given as follows:
9x = 116
x = 116/9
x = 12.89.
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Need help pls
Tyyyyyyy
The area of the base of the pyramid is 35/4 m².
The volume of the pyramid is 14 m³.
How to find the area of the base of the pyramid?A pyramid is a three-dimensional geometric shape that has a base and triangular sides that meet at a common point, called the apex.
The formula for the area of the base of the pyramid is given as:
A = 1/2 bh
where b and h are the base and height of the triangle at the base of the pyramid.
Given b = 7/3 meters and h = 15/2 meters
A = 1/2 * 7/3 * 15/2
A = 35/4 m²
That is B = 35/4 m²
The formula for the volume of the pyramid is given as:
V = 1/3 Bh
where h is the height of the pyramid and h = 24/5 meters
V = 1/3* 35/4 * 24/5
V = 14 m³
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Desk was 794 mm what is width of her desk in cm
Answer:
79.4cm
Step-by-step explanation:
1cm = 10mm so 794mm / 10mm = 79.4cm
81 1/4 evaluated please help
Answer: 324/4
Step-by-step explanation:
I know i'm doing this totally wrong I don't know.
What is the area of triangle []
ABC
?
Triangle ABC. Angle A = 60 degrees. Angles B = 60 degrees. Angle D = 90 degrees. BC = 12.
Select the correct choice.
In a triangle ABC, angle B=90, angle C=60, angle A=30 and BC=12cm. The area of the triangle is 144 * (√3/2) sq cm
How did we get the value?In a right triangle with a 90 degree angle, the length of the side opposite the 90 degree angle is the height, and the length of the other two sides form the base. If angle C = 60 degrees, then angle A = 90 - 60 = 30 degrees.
If BC = 12 cm, then the height AC is equal to AB * sin(30) = 12 * (√3/2).
The area of the triangle is equal to (1/2) * base * height = (1/2) * 12 * (12 * (√3/2)) = (12 * 12 * (√3/2))/2 = 144 * (√3/2) sq cm
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The complete question goes thus:
In a triangle ABC, angle B=90, angle C=60, angle A=30 and BC=12cm. What is the area of the triangle?
The given graph represents the polynomial p(x). Find the number of zeros of the polynomial p(x).
The number of zeros of the polynomial p(x) is 3.
What does a polynomial mean?A polynomial is a mathematical expression that solely uses the addition, subtraction, and multiplication operations to combine variables (commonly called coefficients) and variables (often called x). The variables are raised to non-zero, and the coefficients can be any real value.
The number of x-intercepts, or the places where the graph crosses the x-axis, is equal to the number of polynomial roots, also known as zeros.
We can see from the above graph that the polynomial p(x) has three x-intercepts, which indicates that it has three roots or zeros. Consequently, the polynomial p(x) has three zeros.
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Complete question -
Line segment xy is dilated to create line segment x'y' using point t as the center of dilation. Point t is the center of dilation. Line segment x y is dilated to create shorter line segment x prime y prime. The length of t x prime is 6 and the length of t y prime is 9. The length of x x prime is 2. What is yt?.
Given that point T is the center of dilation, we know that the length of line segments TX' and TY' are proportional to the length of line segments TX and TY, respectively.
We can express this as:
TX' = k * TX
TY' = k * TY
where k is the scale factor.
We are given the lengths of TX' and TY':
TX' = 6
TY' = 9
So, we can solve for k:
9 / k = 6
k = 9 / 6 = 3 / 2
Now that we know the value of k, we can find TY:
TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9
Next, we are given the length of XX':
XX' = 2
And using the dilation formula, we can find XX:
XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)
Finally, we can find TX by using the Pythagorean theorem:
TX^2 = TY^2 + XX^2
TX^2 = 9^2 + (2 * (2 / 3))^2
TX^2 = 81 + (4 / 3)^2
TX^2 = 81 + 16 / 9
TX^2 = 81 + 16 / 9
TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97
So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.
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TX' = k * TX
TY' = k * TY
TX' = 6
TY' = 9
So, we can solve for k:
9 / k = 6
k = 9 / 6 = 3 / 2
Now that we know the value of k, we can find TY:
TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9
XX' = 2
XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)
TX^2 = TY^2 + XX^2
TX^2 = 9^2 + (2 * (2 / 3))^2
TX^2 = 81 + (4 / 3)^2
TX^2 = 81 + 16 / 9
TX^2 = 81 + 16 / 9
TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97
So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.
Calculate the length of the diagonal for the given rectangular prism. Round to the nearest tenth. Length= 10 Width= 4 Height= 10
Length of the diagonal of the rectangular prism is 14.69694. Here is the solution below
Given that the information:
Length of the rectangular prism - 10
Width of the rectangular prism - 4
Height of the rectangular prism - 10
Length of the diagonal of the rectangular prism -
Diagonal (d) = √l²+w²+h²= √10²+4²+10² = 14.69694
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid.
The correct answer of this question is 14.69
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greatest common factor 42,63
If you divide 63 by 3 you get 21.
If you divide 42 by 2 you get 21.
63 / 3 = 21
42 / 2 = 21
Therefore, the GCF(Greatest Common Factor)is 21.
Adding subtracting , multiplying and dividing fractions worksheets provide a wide variety of interactive exercises and problems based on this topic for students to efficiently grasp these foundational concepts. By practicing these basic arithmetic operations on fractions students can easily attain the core fundamentals required to solve advanced algebraic equations and functions. These worksheets also come with self-explanatory answer-keys for instant doubt clarification and self-learning.
Using basic arithmetic operations, the missing terms are a) 7/5 and b) 19/14.
There are four basic arithmetic operations which are addition, subtraction, multiplication, and division. These operations can be applied to whole numbers and fractions.
a) 14/16 x 8/7= y x 5/7
In order to solve for y, the numerator and denominator on LHS are simplified and multiplied:
14/16 x 8/7= 7/8 x 8/7 = (7 x 8)/(8 x 7)
As there are same numbers in both numerator and denominator, they are cancelled:
(7 x 8)/(8 x 7)=1
Hence,
1= y x 5/7
Multiply both side by 7/5
7/5 x 1= y x 5/7 x 7/5
y= 7/5
b) 1/2+ 4/7= y -2/7
In order to solve for y, add the fraction on LHS:
1/2+ 4/7= ((7 x 1)+(4 x 2))/((2 x 7)) = (7+8)/14=15/14
Hence,
15/14= y -2/7
Add 2/7 to both sides:
15/14+ 2/7= y -2/7 + 2/7
y = (15+4)/14=19/14
Note: The question is incomplete. The complete question probably is: Find the missing terms:
a) 14/16 x 8/7= y x 5/7
b) 1/2+ 4/7= y -2/7
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3. You have an inheritance of $100,000 from your grandparents, but you must invest the money in a
mutual fund until you are 21 years old, that will pay an annual interest rate of r% compounded
continuously. If you are 17 years old now, your balance, in dollars, can be defined as B = A(r).
Interpret the following statements related to your inheritance, use the appropriate units.
A. A(7) =13230
B. A'(7) =3307.50
On a principal of $100,000.00 with compound interest accrued at a rate of 7% per year compounded continuously over 4 years, the total sum is $132,312.98.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, You have an inheritance of $100,000 from your grandparents, you must invest the money in a mutual fund until you are 21 years old, which will pay an annual interest rate of r% compounded continuously.
From the general formula of compound interest:
A = Pe^rt,
where P is the principal balance,
r is the interest rate,
n is the number of times interest is compounded annually,
t is the number of years
In our case,
P = 100,000
t = 21 - 17 = 4
n = 12 for compounded continuously
thus,
A = 100,000(2.71828)^r4
For the value of r = 7
A = 100,000.00(2.71828)^(0.07)(4)
A = $132,312.98
Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $100,000.00 at a rate of 7% per year compounded continuously over 4 years is $132,312.98.
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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
Determine the equation of the line of fit.
y = 5x + 70
y = 5x + 80
y = 10x + 70
y = 10x + 80
Answer: y = 5x + 70
Step-by-step explanation:
if x has a geometric distribution what does (1-p)n-1 represent
The probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.
The formula (1-p)n-1 represents the probability of having n-1 failures (or successes, depending on which outcome the probability p is associated with) in a Geometric distribution. For example, if p=0.3, then the formula (1-p)n-1 would represent the probability of having two failures before the first success. This would be equal to (1-0.3)2-1, or 0.49. This means that there is a 49% chance of having two failures before the first success in this example. In general, this formula can be used to calculate the probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.
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Complete question:
What does (1-p)n-1 represent in a geometric distribution?
Compose a jingle citing a situation in real life where linear inequalities in two variables are presented
Jingle cites a situation in real life -Men make up about 95% of those detained by the police.
99 percent of bricklayers are men.
Men make up 99 percent of soldiers' fatalities.
When you want to know something, it is often apparent and overwhelming. But it's rarely brought up since "women" simply don't engage in those kinds of behaviors. Voluntarily.
Jordan Petersen uses these examples frequently to silence liberals who support equality of all kinds because they don't want to talk about how the equality they claim to want would actually be totalitarian and authoritarian.
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find f^1(x) and its domain
(image attached)
The solution is Option C.
The inverse of the function is f⁻¹ ( x ) = ( x + 5 )² and the domain is x ≥ 0
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is given as
f ( x ) = √x - 5 be equation (1)
On simplifying the equation , we get
y = √x - 5
To calculate the inverse of the function , solve for x , we get
Adding 5 on both sides of the equation , we get
√x = y + 5
Taking the square on both side of the equation , we get
x = ( y + 5 )²
Substitute the value of x = f⁻¹ ( x ) and y = x , we get
f⁻¹ ( x ) = ( x + 5 )²
And , the domain of the function is [ 0 , ∝ ]
Hence , the function is f⁻¹ ( x ) = ( x + 5 )²
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What is 1 + 1
A. 1
B. 2
C. 10,000,000
D. 5
Answer:
E. - 11
Step-by-step explanation:
This is by the simple quantum physics moving by the gravitational carbon dioxide in the air that causes the numbers to evolve into the number 11 while mixed together
find the orthogonal projection p of v = 10i 8j 3k on u = 2i 10j 3k
The projection of vector v on u is =[tex]\=109/\sqrt{113}(2i+10j+3k)[/tex]
Sometimes the inner product and the dot product are considered to be the same. The formal definitions of projection and rejection employ the inner product rather than the dot product whenever they don't coincide. The concepts of projecting a vector onto another and rejecting a vector from another can be applied to the concepts of projecting a vector onto a plane and rejecting a vector from a plane for a three-dimensional inner product space.
A vector's orthogonal projection on a plane is the vector's projection on that plane. A vector is rejected from a plane when it is projected in an orthogonal direction on a straight line. They're both vectors. The first is orthogonal to the plane, while the second is parallel.
we have v=10i+8j+3k and u=2i+10j+3k,
[tex]The\ projection\ v\ on\ w= ((v.u)/|u|)u\\\\the \proj=((20+80+9)/\sqrt{4+100+9})(2i+10j+3k)\\\\=109/\sqrt{113}(2i+10j+3k)[/tex]
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is a line segment or a ray or a line that intersects a given line segment at a 90o, and also it passes through the midpoint of the line segment.
A perpendicular bisector is a line that intersects a given line segment at a 90°.
A perpendicular bisector is a line segment, ray, or line that goes through the middle of a given line segment and crosses it at a 90° angle.
A line, ray, or line segment is a perpendicular bisector if it divides another line segment in half proportionately and makes a right angle (90o) with it at its halfway.
In other words, the perpendicular bisector serves as both a perpendicular line to the line segment and a bisector, cutting it in half.
The intersection of the perpendicular bisector with the line segment represents its midpoint.
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#3 1 Gender evious You randomly survey 40 students about whether they play an instrument. You find that 8 males play an instrument and 13 females do not play an instrument. A total of 17 students in the survey play an instrument. Make a two-way table that includes the marginal frequencies.
People who dislike cantaloupe are marginally more likely to be (0.455) likely to be.
How do you define marginal relative frequency?The joint relative frequencies in a row or column of a data table are added in this case.
Therefore, we will create a representation of the table using the findings from the survey of 200 randomly selected individuals as follows:
Watermelon The total is not a watermelon
Cantaloupes: 93, 16, and 109
Not a cantaloupe 66 25 91
Total 159 41 200
The marginal relative frequency for those who dislike cantaloupe is therefore 0.455.
The complete complete question is,
How common are those who dislike cantaloupe, on a relative basis? startfraction 91 over 200 endfraction startfraction 25 over 91 endfraction startfraction 66 over 200 endfraction startfraction 91 over 200 endfraction.
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Write the equation of the line in fully simplified slope-intercept form.
Answer
Y=-2x+1
-2 is the slope, and 1 is the y intercept
Can someone please help in number 12? Need to show work
Answer:
15 percent
Step-by-step explanation:
There are total 40 students in class because 6 plus 12 plus 14 plus 20 is 40. Fraction would be 6/40
PLEASE HELP! What is -1/5 x 10/11 ?!
Answer choices: (image)
Answer:
Step-by-step explanation:
-2/11
Answer:
-1/5 × 10/11 = -2/11
Step-by-step explanation:
If you multiply -1/5 by 10/11, it becomes the fraction -2/11 or 0.1818...
23.97xsquare root of 0.7124 divided by 3.877x52.18
The value of the expression 23.97 x √(0.7124) ÷ 3.877 x 52.18 is 0.1000069342.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
A phrase: 23.97xsquare root of 0.7124 divided by 3.877x52.18.
In numeric form,
23.97 x √(0.7124) ÷ 3.877 x 52.18.
= 0.1000069342.
Therefore, the value is 0.1000069342.
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Which of the following tables represents a linear relationship that is also proportional?
xy
00
42
84
xy
01
23
45
The table which represents a linear relationship that is also proportional is table 1.
Which tables represents a linear relationship that is also proportional?There is a linear relationship between y and x when the rate of change of y with respect to x will be equal.
Table 1:
xy
00
42
84
When x = 4
y = kx
2 = k×4
2 = 4k
k = 2/4
k = 0.5
y = kx
y = 0.5x
when x = 8
y = 0.5(8)
y = 4
Table 2:
xy
01
23
45
y = kx
when x = 2
3 = k × 2
3 = 2k
k = 3/2
k = 1.5
when x = 4
y = 1.5x
y = 1.5(4)
y = 6
Therefore, table 1 is proportional and represents a linear relationship with the equation y = 0.5x.
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Find the inverse of k(x)=x²-3. Define the restrictions to the domain.
Answer: The inverse of the function k(x)=x²-3 is k^(-1)(x)=±√(x+3). The domain restrictions for the inverse are x≥-3, since the square root is only defined for non-negative values.
The inverse of a function is the reflection of the original function over the line y=x. To find the inverse of k(x)=x²-3, we first swap the x and y variables: y=x²-3. Then, we solve for x: x=±√(y+3). This gives us the inverse function k^(-1)(x)=±√(x+3).
However, it is important to note that the square root function is only defined for non-negative values. Therefore, we must restrict the domain of the inverse function to x≥-3. This means that the inverse function can only be applied to input values that are greater than or equal to -3. For values less than -3, the inverse function is undefined.
Step-by-step explanation:
Answer:
Inverse function: [tex]\pm \sqrt{x + 3}[/tex]
Domain: [tex]x \ge -3[/tex]
Step-by-step explanation:
[tex]k(x) = x^2-3[/tex]
To find the inverse, set y = k(x)
==> y = x² - 3
Swap x and y
x = y² - 3
Add 3 to both sides
x + 3 = y²
y² = x + 3
[tex]y = \pm \sqrt{x + 3}[/tex]
or, in other words:
[tex]y = \sqrt{x +3} \:\;and\; y = -\sqrt{x + 3}[/tex] are the two solutions
Replace Swap x and y again to get the inverse as a function of x
[tex]k^{-1}(x) = \sqrt{x+3},\:-\sqrt{x+3}[/tex]
Since square roots of negative numbers are not defined, the term under the square root must be ≥ 0
x + 3 ≥ 0
==> x ≥ -3
There is no restriction on the upper bound it can go upto infinity
Domain of [tex]\sqrt{x + 3} : \:x\ge \:-3[/tex]
EASY POINTS, WILL MARK FIRST ANSWER BRAINLIEST
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $60, plus $28 per hour. What is the slope of this situation?
28
32
60
88
Answer:
28
Step-by-step explanation:
The slope of a line represents the rate of change between two variables. In the case of Superior Segway Tours, the cost of the tour is changing as the number of hours for the tour changes. The rate of change can be calculated by dividing the change in the dependent variable (cost) by the change in the independent variable (hours). In this case, the slope is $28 per hour. This means that for every hour that is added to the tour, the cost will increase by $28.
The slope of this situation can be represented as the change in cost (y-axis) per unit change in time (x-axis). The slope in this case would be $28 per hour.
Assume you have a balance of $1200 on a credit card with an APR of 18%. You start
making monthly payments of $300 but at the same time charge an additional $75 a
month. Assuming that interest for a given month is based on the balance for the previous
month, how long does it take you to pay off the credit card debt?
Assuming that interest for a given month is based on the balance for the previous month, it will take 6 months to pay off the credit card debt of $1,200 when making a net payment of $225.
How is the period determined?An online finance calculator can determine the period for a compound interest system.
The length of payment uses the beginning credit card balance of $1,200 and the net payment of $225 (since a monthly payment of $300 is made when an additional charge of $75 is withdrawn from the card).
I/Y (Interest per year) = 18%
PV (Present Value) = $1,200
PMT (Periodic Payment) = $-225 ($300 - $75)
FV (Future Value) = $0
Results:
Period (N #) = 5.6
Sum of all periodic payments = $-1,260.08
Total Interest = $60.08
Thus, within six months you can pay off the credit card debt.
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Can you please answer the question in the attachement!
Ty love
Answer:
I don't know. I hope this helps!
Step-by-step explanation:
Answer:
Tuna sandwich to likely
chicken sandwich to unlikely
Egg sandwich to impossible
Step-by-step explanation:
there is a lot more tuna than chicken sandwiches so it's likely
there is no egg sandwiches so it's impossible
Write as a power (-7) (-7) (-7)
Please explain with steps
Answer:
7^3
Step-by-step explanation:
since seven is being multiplied by itself 3 times, it is being cubed. So it needs to be raised to the third power.
hope this helps!!! :3
Answer: (-7)(-7)(-7) is equal to -7^3 (just imagine that the three is on the top right outer corner of the 7)
Step-by-step explanation:
A power is when you multiply a number by itself a certain number of times, in this case, we are multiplying the number 7 by itself 3 times. Every time it is multiplied by its self, the power of that number goes up (if you are using a power of one for any number, it will stay the same). Here is an example:
-7 to the first power is just -7.
-7 to the second power, or squared is just (-7)(-7) or (-7) x (-7).
-7 to the third power, or cubed, is just (-7)(-7)(-7) or (-7) x (-7) x (-7).
Hope this helps!!!
Given h(x) = -x + 1, solve for x when h(x) = 0.
Answer:
Step-by-step explanation:
2
BECUASE YEA
Answer:
Step-by-step explanation:
h(x) = -x + 1
h(x) = 0
0 = -x + 1
-1 = -x
x = 1
Make x the subject of the formula
√d= x -z^3
3a
After maxing x as a subject the solution becomes: x = z³ + √d 3a. This can be solved using the concept of solving equation.
What is an equation?Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
For instance, two equations with the identical variables, x and y, are x + y = 12 and 2x + 5y = 8. They are an equalization system.
Given that,
[tex]\sqrt{d} =\frac{ x - z^3}{3a}[/tex]
or, x - z³ = √d 3a
or, x = z³ + √d 3a
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