Answer:
Step-by-step explanation:
The area of a trapezoid is A=(a+b/2)*h
So if you plug in what you know
3/4x-1/4 = (a+b/2)h
You would need the height but if you do have the height you can plug that in then just add a and b together as one variable so you can make a pair that equals that.
I need to solve for each part the part above the red line and the part under the red line please help QUICK
So upper most rectangle area is given as,
[tex]\begin{gathered} \text{A}_1=\text{ length}\times breadth\text{ } \\ \text{A}_1=\text{ 8}\times2 \\ \text{A}_1=16\text{ sq.ft.} \\ A_2=\text{ (8-3)}\times6 \\ \text{A}_2=5\times6 \\ \text{A}_2=30\text{ sq.ft.} \end{gathered}[/tex]Makhail currently has a balance of $5,400 in his bank account. this is 60% of the balance he had when he opened the account. How much money will be in his account when the balance is down to 35% of the balance he had when he opened the account?
Mikhail will have $2940 in his bank account when he has 35% balance left.
The difference between the amount of debit entries and the total of credit entries made into an account during a specific financial period is referred to as the "balance" in bookkeeping.
When total debits spent exceed total credits, the account displays a debit balance. When total credits surpass total debits, the account balance is displayed as a credit. If the debit and credit totals are equal, the balances are regarded as being eliminated. The term "balance" in an accounting period should represent the net worth of assets and liabilities so that the accounting equation's concept of equilibrium may be better understood.Let Mikhail has $x in his account.
Now 60% of x = 5400
or, 0.6x = 5040
or, x = $8400
When he has 35% he will have = 35% of 8400 = $2940
Hence he will have $2940 in his account.
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Two sides of a ∆ have lengths 28cm and 82 cm. The measure of the third side is a whole number of centimeters. • What is the longest the third side can be? • What is the shortest the third side can be?
You need to remember the Triangl inequality Theorem. This states that
Let be "a", "b" and "c" the sides of a triangle. According to the Theorem mentioned above:
[tex]\begin{gathered} a+b>c \\ b+c>a \\ a+c>b \end{gathered}[/tex]In this case, knowing two sides of the triangle, you can set up that:
[tex]\begin{gathered} a=28\operatorname{cm} \\ b=82\operatorname{cm} \end{gathered}[/tex]Let be "c" the third side of this triangle. You know that:
[tex]\begin{gathered} 28\operatorname{cm}+82\operatorname{cm}>c \\ 110\operatorname{cm}>c \end{gathered}[/tex]Therefore, as you can notice, the third side can be less than 110 centimeters.
Based on the explained before, you can conclude that the third side can be:
[tex]\begin{gathered} c<110\operatorname{cm} \\ \end{gathered}[/tex]And it can be:
[tex]\begin{gathered} c>82\operatorname{cm}-28\operatorname{cm} \\ c>54\operatorname{cm} \end{gathered}[/tex]The answers are:
- The longest the third side can be is:
[tex]109\operatorname{cm}[/tex]- The shortest the third side can be is:
[tex]55\operatorname{cm}[/tex]help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
i need help i also put a screenshot
Answer:
6.2
Step-by-step explanation:
every minute 6.2 gallons fill into the pool.
2a² + b²-8a²
+ x²y - 3x + 9xy²
Answer:
mi madre va a entender eso
The value of the 3 in 395,047 is
£10 times greater than the value of the
3 in which of these numbers
386592
283429
136258
123694
The value of the 3 in 395,047 is 10 times greater than the
value of the 3 in 136,258.
What is the place value of a number?
In mathematics, place value refers to a digit's location within a number. A number has a slot for each digit. The placement of each digit will be enlarged when we represent the number in general form. These positions begin at the unit place, often known as the individual's position. Units, tens, hundreds, thousands, ten thousand, one hundred thousand, and so on are the place values of a number's digits from right to left.
Given, the number in consideration is 395,047.
The place value of 3 in the given number is hundred thousands.
A value 10 times smaller than this given number must have three in the ten thousands place.
Out of 386592, 283429, 136258, 123694; only 136258 has three in ten thousands place.
Therefore, the value of the 3 in 395,047 is 10 times greater than the
value of the 3 in 136,258.
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pls help me ty i feel this should be easy
The value of x and y if [tex]T_{(-2,7)}(x,y)=(3,-1)[/tex] are 5 and - 8 respectively.
When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.
We have,
[tex]T_{(-2,7)}(x,y)[/tex] = ( 3, - 1 )
The translation of T( - 2, 7 ) acts in the way as:
[tex]T_{(-2,7)}(x,y)[/tex] = ( x - 2, y + 7 )
Now, it is given that:
[tex]T_{(-2,7)}(x,y)[/tex] = ( x - 2, y + 7 ) = ( 3, - 1 )
Comparing the points,
We have,
x - 2 = 3
Adding 2 on each side of the equation,
x - 2 + 2 = 3 + 2
x = 5
And;
y + 7 = - 1
Subtracting 7 from each side of the equation,
y + 7 - 7 = - 1 - 7
y = - 8
Hence, the value of x and y are 5 and - 8 respectively.
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The laminated block consists of a layer of wood between two layers of plastic. If each plastic layer is one-third as thick as the wooden layer, and the thickness of each layer is an integer, what is one possible height of a stack of such blocks? A. 18 B. 33 C. 42 D. 45
The possible height of a stack of such laminated blocks is 45
How to determine the possible height of the laminated blockinformation given in the question
each plastic layer is one-third as thick as the wooden layer
the thickness of each layer is an integer
The laminated block has three layers
2 plastic layers and one wooden layer
let the thickness of the plastic layer be x
such that the thickness of the wooden layer = 3x
the total thickness
= x + x + 3x
= 5x
for x to be an integer it is a multiple of 5. the only multiple of five in the options is D hence the answer
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This is a math problem that involves finding the height of a stack of laminated blocks. Let’s try to solve it together.
First, we need to find the thickness of each layer in a single block. Let x be the thickness of the wooden layer in centimeters. Then, each plastic layer is one-third as thick as the wooden layer, so it has a thickness of 3x centimeters. The total thickness of one block is the sum of the thicknesses of all three layers, which is x+3x+3x=35x centimeters.
Next, we need to find the number of blocks in a stack. Since the thickness of each layer is an integer, we can assume that the thickness of one block is also an integer. Therefore, we can divide the height of the stack by the thickness of one block to get the number of blocks. Let h be the height of the stack in centimeters, and n be the number of blocks. Then, we have n=35xh=5x3h.
Finally, we need to check which of the given options for h satisfies the condition that n is also an integer. We can do this by plugging in each value of h and simplifying the fraction 5x3h. If the fraction has no remainder, then n is an integer.
Option A: h=18. Then, 5x3h=5x3(18)=5x54. This fraction has a remainder of 4 when divided by 5, so n is not an integer.
Option B: h=33. Then, 5x3h=5x3(33)=5x99. This fraction has a remainder of 4 when divided by 5, so n is not an integer.
Option C: h=42. Then, 5x3h=5x3(42)=5x126. This fraction has no remainder when divided by 5, so n is an integer. For example, if x = 3, then n = 5(3)126=15126=8.4.
Option D: h=45. Then, 5x3h=5x3(45)=5x135. This fraction has no remainder when divided by 5, so n is an integer. For example, if x = 6, then n = 5(6)135=30135=4.5.
Therefore, one possible height of a stack of such blocks is 42 centimeters or 45 centimeters. Option C and option D are both correct answers.
Determine which expression is equivalent to the expression 3 over 4 times g minus 6 minus 7 over 8 times g minus the expression one over 2 times g plus 13.
The expression that is equal to the given expression is [tex]-\frac{5g+100}{8}[/tex]
A mathematical expression that uses integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).
However, transcendental numbers like such and e are not algebraic because they are not created by employing integer constants and algebraic processes.Although an unlimited number of mathematical functions are required to define e, the creation of is typically stated as a geometric equation.the given expression is:
[tex]\frac{3}{4} g -6-\frac{7}{8} g-\frac{1}{2} (g+13)[/tex]
Simplifying the expression we get
[tex]\frac{6g-48-7g-4g-52}{8} \\\\=-\frac{5g+100}{8}[/tex]
Therefore on simplification using the general operations of fractions and integers we get that the expression is equivalent to [tex]-\frac{5g+100}{8}[/tex] .
The properties of fractions and expressions are used in this simplification.
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Solve the quadratic equations in questions 1 – 5 by factoring.Need my answers checked1. x2 – 49 = 02. 3x3 – 12x = 03. 12x2 + 14x + 12 = 184. –x3 + 22x2 – 121x = 05. x2 – 4x = 51.x^2-49=0x^2-7^2=0(x-7)(x+7)=0Solution x=7, x=-7 2.3x^3-12x=03x(x^2-4)=03x(x^2-2^2)=03x(x-2)(x+2)=0 3.12x^2+14x+12=1812x^2+14+12-18=012x^2+14x-6=02(6x^2+7x-3)=02(6x^2-2x+9x-3)=02(2x(3x-1)+3(3x-1)=02(2x+3)(3x-1)=0Solution X=-3/2, X=1/3 4.-x^3+22x^2-121x=0-x(x^2-22x+121)=0-x(x-11)^2=0-x(x-11)(x+11)=0Solutions x=11,x=-11 5.x^2-4x=5x^2-4x-5=0x^2+z-5x-5=0(x^2+x)-(5x+5)=0x(x+1)-5(x+1)=0(x-5)(x+1)=0Solutions x=5,x=-1
Given:
The quadratic equation is:
[tex]\begin{gathered} (1)x^2-49=0 \\ \\ (2)3x^3-12x=0 \\ \\ (3)12x^2+14x+12=18 \\ \\ (4)-x^3+22x^2-121x=0 \\ \\ (5)x^2-4x=5 \\ \end{gathered}[/tex]Find-:
Solve the quadratic equation is:
Explanation-:
The factoring of the equation is:
(1)
[tex]\begin{gathered} x^2-49=0 \\ \\ (x+7)(x-7)=0 \\ \\ x+7=0\text{ and }x-7=0 \\ \\ x=-7\text{ and }x=7 \end{gathered}[/tex](2)
The equation is:
[tex]\begin{gathered} 3x^3-12x=0 \\ \\ 3x(x^2-4)=0 \\ \\ 3x=0\text{ and }x^2-4=0 \\ \\ x=0\text{ and }(x+2)(x-2)=0 \\ \\ x=-2\text{ and }x=2\text{ and }x=0 \end{gathered}[/tex](3)
The equation is:
[tex]\begin{gathered} 12x^2+14x+12=18 \\ \\ 12x^2+14x+12-18=0 \\ \\ 12x^2+14x-6=0 \\ \\ 6x^2+7x-3=0 \\ \\ 6x^2+9x-2x-3=0 \\ \\ 3x(2x+3)-1(2x+3)=0 \\ \\ (2x+3)(3x-1)=0 \end{gathered}[/tex]So the value of "x" is:
[tex]\begin{gathered} 2x+3=0\text{ and }3x-1=0 \\ \\ x=-\frac{3}{2}\text{ and }x=\frac{1}{3} \end{gathered}[/tex](4)
[tex]\begin{gathered} -x^3+22x^2-121x=0 \\ \\ x(-x^2+22x-121)=0 \\ \\ x=0\text{ and }-x^2+22x-121=0 \\ \\ -x^2+22x-121=0 \\ \\ -x^2+11x+11x-121=0 \\ \\ -x(x-11)+11(x-11)=0 \\ \\ (x-11)(-x+11)=0 \\ \\ x=11\text{ and }x=11 \end{gathered}[/tex]So, the value of "x" is:
[tex]x=0\text{ and }x=11[/tex](5)
[tex]\begin{gathered} x^2-4x=5 \\ \\ x^2-4x-5=0 \\ \\ x^2-5x+x-5=0 \\ \\ x(x-5)+1(x-5)=0 \\ \\ (x-5)(x+1)=0 \\ \\ x=5\text{ and }x=-1 \end{gathered}[/tex]The value of x is:
[tex]x=5\text{ and }x=-1[/tex]Graph the equation and state its domain and range. Use interval notation.x^2 + y^2 = 4
We know the the equation has the form of a circle, and that the center is in the coordinate (0,0) because c and w are not been modificated.
we also know that the radius of the circol will be:
[tex]r=\sqrt[]{4}=2[/tex]no with this information we can grph the equation:
Now in the graph we can see that x can just take values between (-2, 2) and y can take values of (-2, 2) so:
Domain: [-2, 2]
Range: [-2,2]
What are the coordinates for point A?A.(0, 1)B.(4, 5)C.(-4, 5)D.(5, -4)
To find the coordinates (x, y) of a point on a plane, we have to draw a line parallel to the y-axis and look at the value on the x-axis, this is the x-coordinate. In this case, the x-coordinate is -4.
Similarly, to find the y-coordinate, we have to draw a line parallel to the x-axis and look at the value on the y-axis. In this case, the y-coordinate is 5.
Therefore, the coordinates for point A are (-4, 5)
Answer: a
Step-by-step explanation:
Remember, the equation to be solved is5x + 8 = 43. When the first step of subtractingeight is completed, what is the new equation thatresults?
Explanation
We are given the equation
[tex]5x+8=43[/tex]We are also asked to find the next step to be followed when the first step of subtracting eight is completed
To do so, the steps will be
Step 1: Subtract 8 from both sides
[tex]\begin{gathered} 5x+8-8=43-8 \\ 5x=35 \end{gathered}[/tex]The new equation will be
[tex]5x=35[/tex]Step 2: Divide both sides by the coefficient of x (5)
We will divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{35}{5} \\ \\ x=7 \end{gathered}[/tex]Thus, the answer is 7.
A principal of $500 is deposited in an account that pays 7% annual interest compounded yearly. Find thebalance after 10 years. Y=C(1+r)^t ( the t is floating btw)
We can find the balance after t years in the account by means of the following formula:
[tex]Y=C(1+r)^t[/tex]Where C is the initial amount deposited in the account
r is the interest rate as a decimal number
t is the year
In this case, C equals $500, r is 0.07 (7%) and t equals 10.
Replacing these values into the above formula, we get:
[tex]Y=500(1+0.07)^{10}=983.6[/tex]Then the total amount of money in the account after 10 years equals $983.6
In ADEF, the measure of ZF=90°, FE = 84, ED = 85, and DF = 13. What ratiorepresents the sine of ZE?
ANSWER:
[tex]\frac{13}{85}[/tex]STEP-BY-STEP EXPLANATION:
The first thing is to draw the triangle DEF
The sine of an angle is given as follows:
[tex]\begin{gathered} \sin \theta=\frac{\text{ opposite}}{\text{ hypotenuse}} \\ \text{ForDwayne stated that the slope of the line perpendicular to y = -2x is 2. Describe Dwayne's error.
The product of slople of two lines wchich are perpendicular to each other is negetive one.
The given expression of the line is,
[tex]y=-2x[/tex]The general expression for a stright line with slope 'm' is,
[tex]y=mx+c[/tex]Here, 'm' is the slope and 'c' is a constant.
Conparing the given equation of line with the general expression of a stright line,
[tex]m=-2[/tex]Thus, the slope of the given line is -2.
Let the slope of the perpendicular line to the given line be 'k'. Since the product of slope of perpendicular line is -1.
[tex]\begin{gathered} m\times k=-1 \\ k=\frac{-1}{k} \end{gathered}[/tex]Substitute value of m=-2 in the above expression.
[tex]\begin{gathered} k=\frac{-1}{-2} \\ k=\frac{1}{2} \end{gathered}[/tex]Thus, the slope of the perpendicular line is -1/2, and thus Dyne's statement is wrong.
The slope of the perpendicular line is -1/2, and the Dyne's statement is wrong.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The given expression of the line; y = -2x
The general expression for a straight line with slope 'm' is;
y = mx + c
where 'm' is the slope and 'c' is a constant.
Therefore, the slope of the given line is; -2.
Assume the slope of the perpendicular line to the given line be 'k'. Since the product of slope of perpendicular line is -1.
m x k = -1
m = -1/k
Substitute value of m=-2 in the given expression.
k = 1/2
Hence, the slope of the perpendicular line is -1/2, and the Dyne's statement is wrong.
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Help mee pleasee!!
thank you <3
C(x) = 75 +0.25x is the function.
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given Data
A $75 setup fee for formatting and editing is included in the price of creating a newsletter and $0.25 for each copy that is printed.
If there are x copies, then
Function:
C(x) = $75 +0.25x
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the angle of elevation for the first Hill of a roller coaster is 55°. If the length of the track from the beginning to the highest point is 98 ft what is the approximate height of the roller coaster when it reached the top of the first Hill? options, 80 ft, 98 ft, 56 ft, 43 ft
Using trigonometric property in the figure,
[tex]\sin \theta=\frac{opposite\text{ side}}{hypotenuse}[/tex][tex]\begin{gathered} \sin \text{ }55^{\circ}=\frac{h}{98\text{ }} \\ h=98\times\sin 55^{\circ} \\ \cong80\text{ ft} \end{gathered}[/tex]Here, h is the height of the hill.
Therefore, the approximate height of the of the roller coaster when it reached the top of the first Hill is 80 ft.
Option A is the answer.
Solve for x.4(x-5)-5-6x+5-4x
Given:
[tex]4\left(x-5\right)-5-6x+5-4x[/tex]To find:
Solve for x
Explanation:
Using the distribution property,
[tex]4\left(x-5\right)-5-6x+5-4x=4x-20-5-6x+5-4x[/tex]Adding or subtracting the like terms with respect to the sign, we get
[tex]-6x-20[/tex]Final answer:
The simplest form is,
[tex]-6x-20[/tex]Angles A and B are complementary. If the measure of ∠A is 20°, what is the measure of ∠B?
Answer
Option A is correct.
Angle B = 70°
Explanation
Complementary angles sum up to give 90°
If A and B are complementary angles, then,
A + B = 90°
20° + B = 90°
B = 90° - 20°
B = 70°
Hope this Helps!!!
QuestionThe graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.Three normal distribution curves.A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is evenly spread out, curve Upper B is tall and the least spread out, and curve Upper C is short and more evenly spread out from the center.Select the correct answer below:ABC
Curve B normal distribution has the smallest standard deviation.
What is Normal Distribution?The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation
Given,
Three normal distribution curves.
A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C.
Curve Upper A is evenly spread out,
curve Upper B is tall and the least spread out,
and curve Upper C is short and more evenly spread out from the center.
We need to find which curve shows low standard deviation.
Among the three curves, curve B has less width. Hence standard deviation will be small for curve B.
Hence curve B normal distribution has the smallest standard deviation.
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Around answer to 1 decimal place.
Answer:
x ≈ 5.5 cm
Step-by-step explanation:
using the sine ratio in the right triangle
sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{9.1}[/tex] ( multiply both sides by 9.1 )
9.1 × sin37° = x , then
x ≈ 5.5 cm ( to 1 dec. place )
The population (in millions) of a certain country can be approximated by the function: P(x)=50*1.02^x where x is the number of years after 2000. Which of the following calculations will tell in what year the population can be expected to reach 100 million? a. ln(2/1.02)+2000 b. ln(2)/ln(1.02)+2000 c. ln(2/1.02) d. ln(2)/ln(1.02)
The calculation that tells us the year the population can be expected to reach 100 million is log 2/log 1.02 + 2000.
i.e
x = log 2/log 1.02 + 2000
Option B is the correct answer.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
P(x) = 50 x [tex]1.02^x[/tex]
P(x) = Number of population in millions after x years
For 100 million populations we have,
100 = 50 x [tex]1.02^x[/tex]
Divide both sides by 50.
100/50 = [tex]1.02^x[/tex]
2 = [tex]1.02^x[/tex]
Putting log on both sides.
log 2 = x log 1.02
x = log 2 / log 1.02
Since x is the number of years after 2000 we have,
x = log 2/log 1.02 + 2000
Thus,
The calculation that tells us the year the population can be expected to reach 100 million is log 2/log 1.02 + 2000.
i.e
x = log 2/log 1.02 + 2000
Option B is the correct answer.
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Please help ASAP questions and answer selection in screenshot
The domain of the function consists of all real numbers greater than 0.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Next, we would determine the function which models the amount of gas as follows:
Function, f(x) = rate × x
Function, f(x) = 2.25 × x
Function, f(x) = 2.25x
Based on the function above, we can reasonably and logically deduce that the amount of gas cannot be negative. Therefore, the domain of this function is given by:
Domain = [0, ∞]
In conclusion, the domain is equal to all real numbers that are greater than zero (0).
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35 + 3x -11 =23 round the solution to two decimal places
You have the following equation:
35 + 3x - 11 = 23
In order to solve the previous equation for x, proceed as follow:
35 + 3x - 11 = 23 order terms left side
35 - 11 + 3x = 23 simplify like terms 35 and -11
24 + 3x = 23 subtract 24 both sides
3x = 23 - 24
3x = -1 divide by 3 both sides
x = -1/3
x ≈ -0.33
Hence, the solution for x is approximately -0.33
Find 2 positive numbers whose difference is 7 and whose is 294
Lets name the two numbers x and y, so:
[tex]x-7=y[/tex]And
[tex]x\cdot y=294[/tex]Using the first in the second we have:
[tex]x(x-7)=294[/tex][tex]x^2+7x=294[/tex][tex]x^2+7x-294=0[/tex]Using the quadratic formula we get two values 14 and -21, the only one that satisfies both conditions is 14.
So the numbers are 14 and 21.
[tex]21-14=7[/tex][tex]21\cdot14=294[/tex]Factor the polynomial if possible. If the expression cannot be factored enter
x^2 -19x + 88
Replace -19x by -8x -11x
x^2 -8x - 11x + 88
Common factor of both pairs:
x (x-8) - 11(x-8)
Write in factor form
(x-11) (x-8)
Slove equation with variables on both sides4 - m = -1 + 4m
Which sum or difference is modeled by the algebra tiles?
The most appropriate choice of Quadratic equation will be given by
Second option is correct
What is quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A two degree equation is known as quadratic equation.
Here,
In the upper row, there are one tile of [tex]-x^2[/tex], two tiles of [tex]-x[/tex] and four tiles of 1
Required equation = [tex]-x^2[/tex][tex]-2x[/tex] + 4
In the lower row, there are one tile of [tex]-x^2[/tex], two tiles of [tex]-x[/tex] and 1 tiles of -1
Required equation = [tex]-x^2[/tex][tex]-2x[/tex] -1
( [tex]-x^2[/tex][tex]-2x[/tex] + 4) + ( [tex]-x^2[/tex][tex]-2x[/tex] -1) = [tex]-2x^2 -4x + 3[/tex]
Second option is correct
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