Answer:
128
Step-by-step explanation:
solve for inside parentheses:
-22x21÷4-12
do multiplication and division:
-115.5-12
subtract:
-127.5
Hope this helps
the sum of the digits in a three digit mumber is 9. the tens digit is half the sum of the other two amd the hundreds digit is half the unit digit. fond the number.
The number is 234.
Step-by-step explanation:
Let the 3 digits be H , T and U so the number is HTU.
H + T + U = 9
T = 0.5H + 0.5U
U = 2H
So from the last 2 equations
T = 0.5H + 0.5(2H)
T = 0.5H + H
T = 1.5H
So substituting for T and H is the first equation:
H + 1.5H + 2H = 9
4.5H = 9
H = 2.
So T = 1.5*H = 1.5 *2 = 3.
Sandra recorded the distances that 6 beetles crawled in 10 seconds down a 36 inch track. The fractions represent the distances that Sandra recorded. 7 2 1 11 5 17 18' 3' 9' 36' 18 3 36. Which list shows distances Sandra recorded in order from least to greatest?
Distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.
Given that, the fractions represent the distances that Sandra recorded is 7/18, 2/3, 1/9, 11/36, 5/18, 17/36.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Here, distance is 10/36
So, the equivalent fractions for the given fractions are
7/18 = 14/36
2/3 = 24/36
1/9 = 4/36
11/36
5/18 = 10/36
17/36
So, least to greatest is
4/36 < 10/36 < 11/36 < 14/36 < 17/36 < 24/36
1/9 < 5/18 <11/36 <7/18 <17/36 <2/3
Therefore, distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.
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How can I work out the size of angle y?
Answer:
180 degrees converted is 3.14159 i think
Step-by-step explanation:
Answer:
< y = 17 degrees.
Step-by-step explanation:
x + y = 180 - 112 = 68 (as there are 180 degrees in a triangle)
Also, x = 3y, so substituting for x in the first equation:
3y + y = 68
4y = 68
y = 17.
So,
x = 3*17 = 51,
A tent pole that is 9 feet tall is secured to the ground with a piece of rope that is 15 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
The number of feet from the tent pole to the rope along the ground will be 12 Feet.
Let:
PR be the tent pole 9 Feet tallPQ be the piece of rope 15 Feet longRq be the distance between the tent pole and the rope along the groundRQ = x
According to Pythagoras Theorem:
[tex]Hypotenuse^{2} = Perpendicular^{2} + Base^{2} \\PQ^{2} = PR^{2} + RQ^{2} \\15^{2} = 9^{2} + x^{2} \\225 = 81 + x^{2} \\x^{2} = 225 - 81\\x^{2} = 144\\x = 12[/tex]
Therefore, the number of feet from the tent pole to the rope along the ground will be 12 Feet.
Pythagoras Theorem is widely used to establish the relation between the three sides of a right-angled triangle. The applications of Phythagoras Theorem are the angle of depression, angle of elevation, etc. Even the Eiffel tower is one of its applications.
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the cost of a computer repair is worked out using the formula C = 35 + 15h.
C represents the cost in dollars.
H is the time taken in hours.
use the formula to find the cost of repair that takes 3 hours.
Answer: C = 35 + 15 x 3 = 80
Step-by-step explanation:
15h = 15 x (h) = 15 x 3 = 45 + 35 = $80
C = (15 x 3) + 35 = 80
PLS HELP WITH 15. (GIVING EXTRA POINTS)
Answer:
[tex]4^{6}[/tex] or 4096
Step-by-step explanation:
When the bases are the same, you add the exponents.
Answer:
Step-by-step explanation:
[tex]\boxed{\bf\\a^n*a^m=a^{n+m}}[/tex]
[tex]\displaystyle(4)^2\cdot(4)^4\cdot(4)^0=(4)^{2+4+0}=4^6=4096[/tex]
Please help me with this
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP
3. Arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p²
The required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.
Given that,
To arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p².
The algebraic expression consists of constant and variable. eg x, y, z, etc.
Here,
(a)
= 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
= 7x⁵ - 7x⁴ - 4x⁴+ 2x³ + 11x³– x
= 7x⁵ + 13³ - 11x⁴ - x,
(b)
= -2p - 3p² + 1 - 5p + 8p²
= 1 -2p - 5p -3p² + 8p²
= 1 - 5p + 8p²
Thus, the required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.
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The required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵ – x and - 7p + 5p²+ 1.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.
The polynomials are given in the question :
2x³ - 7x⁴ + 7x⁵, and 11x³ - 4x⁴ – x
-2p - 3p² and,1 - 5p + 8p²
According to the question,
⇒ 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
Rearrange the terms and apply the arithmetic operation,
⇒ 2x³ + 11x³- 7x⁴- 4x⁴ + 7x⁵ – x
⇒ 13x³- 11x⁴+ 7x⁵ – x
⇒ -2p - 3p² + 1 - 5p + 8p²
Rearrange the terms and apply the arithmetic operation,
⇒ -2p - 5p - 3p² + 8p²+ 1
⇒ - 7p + 5p²+ 1
Thus, the required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵ – x and - 7p + 5p²+ 1.
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Describe how to transform the graph of f(x)=x^2 into the graph of g(x)=4(3x-1)^2+5.
Please help me with this question! Thank You
The transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
The given functions are f(x) = x² and g(x)= 4(3x-1)²+5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The transformation is
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 0.333 Units
Vertical Shift: Up 5 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
Therefore, the transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
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write the linear equation in slope-intercept form passing through the point with the given slope. 1. (0,3):slope = -2 2. (-5,-3); slope = -3/5 3. (-8,6); slope 1/4 write the linear equation in slope-intercept form that passes through the given points. 4.
The equation of each line in slope-intercept form are:
1. y = -2x + 3
2. y = -3/5x - 6
3. y = 1/4x + 8
How to Write the Equation of a Line in Slope-intercept Form?If we are given a point (a, b) and the slope of a line (m), we can write the linear equation in slope-intercept form by first plugging in the given values into y - b = m(x - a), then rewrite it in the slope-intercept form as y = mx + b.
1. Slope (m) = -2
Point (a, b) = (0, 3)
Plug in the values into y - b = m(x - a):
y - 3 = -2(x - 0)
y - 3 = -2x + 0
y = -2x + 0 + 3
y = -2x + 3 [slope-intercept form]
2. Slope (m) = -3/5
Point (a, b) = (-5, -3)
Plug in the values into y - b = m(x - a):
y - (-3) = -3/5(x - (-5))
y + 3 = -3/5x - 3
y + 3 - 3 = -3/5x - 3 - 3
y = -3/5x - 6 [slope-intercept form]
3. Slope (m) = 1/4
Point (a, b) = (-8, 6)
Plug in the values into y - b = m(x - a):
y - 6 = 1/4(x - (-8))
y - 6 = 1/4(x + 8)
y - 6 = 1/4x + 2
y - 6 + 6 = 1/4x + 2 + 6
y = 1/4x + 8 [slope-intercept form]
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what is the probability that when a coin is flipped six times in a row, it lands heads up every time? (enter the value of probability in decimals. round the answer to three decimal places.)
The probability that the coin lands heads up six times in a row is 0.016
Probability is the term used in mathematics to understand how likely an event is to happen or can also be described as how likely it is that a proposition is true.
It can be determined by dividing the favorable outcomes or events by the total number of outcomes.
As the coin has two sides, the probability that when the coin lands, it lands heads up is determined as follows;
Probability = 1 / 2
Now the probability that the coin lands heads up six times in a row can be calculated as follows;
Probability = (1^6) / (2^6)
Probability = 1 / 64
Probability = 0.015625
Rounding it to three decimal places as follows;
Probability = 0.015625 = 0.016
Therefore, the probability that the coin lands heads up six times in a row is calculated to be 0.016
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please explain how you got it
Answer:
30y^5 x^8
Step-by-step explanation:
3x^8 * 5y^4 * 2y
Add 4 and 1 and you'll get 5 so it'll be:
3x^8 * 5y^5 * 2
Which it'll look like
15x^8 y^5 *2=
30x^8 y^5
a bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after that which statement is true
The equation for the cost when the bowling alley charges $14 for the first game $10 for the second game is 24 + 5x.
What is a equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
In this case, the bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after.
Let the number of games be illustrated as x.
Therefore, the equation will be:
14 + 10 + (5 × x)
= 24 + 5x
This illustrates the cost.
An overview was given as the information given is incomplete.
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A rectangular gardan is surrounded by a walk of uniform width. The area of the garden is 200 square yards. If the dimensions of the garden plus the walkway are 18 yards by 26 yards, find the dimensions of the garden.
***NOTE*** This is a Quadratic Word Problem, so please use the Quadratic Method when solving and show all steps!!
Answer: [tex]6\sqrt{6}+4 \times 6\sqrt{6}-4[/tex] yards
Step-by-step explanation:
Let the length of the walkway be x yards. Then,
[tex](18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=\frac{22 \pm \sqrt{22^2 -4(77)}}{2}\\\\=11 \pm 3\sqrt{6}[/tex]
However, [tex]x=11+3\sqrt{6} > 18[/tex], which is illogical, so we take [tex]x=11-3\sqrt{6}[/tex].
So,
[tex]18-2x=18-2(11-3\sqrt{6})=6\sqrt{6}-4\\\\26-2x=26-2(11-3\sqrt{6})=4+6\sqrt{6}[/tex]
Drag each label to the correct location on the table. Match each equation with its number of unique solutions. y = -52 – 41 +7 y = –202 + 91 - 11 y = 3.12 – 61 + 3 Two Real Solutions One Real Solution One Complex Solution Two Complex Solutions Reset Next reserved
When b²−4ac=0 there is one real root.
When b²−4ac>0 there are two real roots.
When b²−4ac<0 no real roots or two complex roots
First equation
-x²-4x+7
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-4\mright)^2-4\mleft(-1\mright)\cdot\: 7 \\ 16+28=44 \end{gathered}[/tex]b²−4ac>0, then equation -x²-4x+7 has two real roots.
Second equation
-2x²+9x-11
[tex]\begin{gathered} b^{2}-4ac \\ 9^2-4\mleft(-2\mright)\mleft(-11\mright) \\ 81-88=-7 \end{gathered}[/tex]b²−4ac<0, then equation -2x²+9x-11 has two complex roots.
[tex]x1=\frac{9}{4}-i\frac{\sqrt{7}}{4},\: x2=\frac{9}{4}+i\frac{\sqrt{7}}{4}[/tex]Third equation
3x²-6x+3
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-6\mright)^2-4\cdot\: \: 3\cdot\: \: 3 \\ 36-36=0 \end{gathered}[/tex]b²−4ac=0, then equation 3x²-6x+3 has one root.
The instructions on a jar of instant coffee say to add 5 cups of water to every 4 tablespoons of coffee granules. How many cups of water are needed for 10 tablespoons of coffee granules?
Answer:
12.5 cups
Step-by-step explanation:
10/4 = 2.5
2.5 × 5 = 12.5
12.5 cups
at a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate (in ft/min) is the height of the pile changing when the pile is 22 feet high? (hint: the formula for the volume of a cone is v
When the pile is 22 feet high, the height of the pile changes to 20/1089π.
Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?
The volume of cone is V = 1/3 * pi * r ^ 2 * h
d=3h
2r = 3h
r = (3h)/2
V = 1/3 * pi * r ^ 2 * h
= 1/3 * pi * ((3h)/2) ^ 2 * h
= 1/3 * pi((9 * H ^ 2 )/4) * h
= (9pi)/12 * h ^ 3
Differentiate w.r.to t
(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)
(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)
(dV)/(dt)=20, h=22 feet
20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)
(dh)/(dt) = 80/ (9pi * (22^ 2))
h^ t = 20/ 1089 *pi ft / min
Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π
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GEOMETRY
Circle the one contradictory piece of information in each of the following sets of information
Answer:
Step-by-step explanation:
Item 1
<RSL is not ≅ < XYM
Item 2
< LST and < QRX are not supplementary (they are congruent)
Item 3
m < LST = 120 - there is no evidence for this.
Item 4
< JRS = <LST
so, If < LST = 120, then this can't be 195
Kadeem and Quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles and hour. Quinn drives at a constant of 75 miles an hour. Who takes longer to drive 25 miles? How much longer?
Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.
Who takes longer to drive 25 miles?
Remember the relation:
Speed*time = distance.
Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.
Here we know that:
Kadeem drives at a constant speed of 50mi/h
Quinn drives at a constant speed of 75 mi/h.
Replacing that in the equation:
Kadeem's case:
(50 mi/h)*t = 25mi
t = (25 mi)/(50 mi/h) = 0.5 hours.
Quinn's case:
t = (25mi)/(75 mi/h) = 0.33 hours.
So Kadeem takes longer.
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Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work. PLSSSSSSS HELPPPP SHOW UR WORK TO ON HOW YOU FIGURED IT OUT THE EQUATION FOR IT USE SLOPE TOO ILL INCLUDE AN IMAGE TOO
The trend line is linear and the trend line has an equation of y = 500/9x + 100
The type of the trendFrom the graph, we can see that:
The points appear to be on a straight line and it increases along the x-axis
This means that the points can appear on an approximate straight line
So, we can conclude that the trend is a linear trend
The equation of the lineOn the line, we have the following points
(x, y) = (0, 100) and (9, 600)
We start by calculating the slope of the points using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (600 - 100)/(9 - 0)
Evaluate
Slope = 500/9
The equation is then calculated as
y = Slope(x - x₁) + y₁
Where
(x₁, y₁) = (0, 100) and Slope = 500/9
So, we have
y = 500/9 * (x - 0) + 100
Evaluate
y = 500/9x + 100
Hence, the equation is y = 500/9x + 100
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How do the laws of exponents apply to algebraic expressions
The laws of exponents are useful to solve algebraic expression as shown below.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
The laws of exponents (sometimes referred to as the rules of exponents) allow us to simplify expressions by using our understanding of what an exponent implies.
The goal is to write algebraic expressions as simply as you can in both situations.
Recall that an exponent indicates the number of times to multiply a number, variable, or expression by itself.
[tex]x^4=x \cdot x\cdot x\cdot x[/tex]
and, [tex](x+5)^3=(x+5)(x+5)(x+5)[/tex]
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n your initial post, answer the following questions: identify the many variables that a hospital needs to consider in layout design? what are the advantages of the circular pod design over the traditional linear hallway layout at arnold palmer? what suggestions about wheeled coach layout would you make to bob collins?
The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.
What is the layout of a hospital?Layout design generally seeks to arrange organizational units inside a building so that the space is used to its fullest potential and total distances are kept to a minimum.
The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. It must be able to endure the pressure and environmental conditions that they might encounter.
A facility's layout and design are crucial to a company's overall operations because they may both suit the needs of employees and maximize the efficiency of the production process. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.
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Rectangles DEFG with vertices D(1,0) E(7,2) F(8, -1) and G (2, -3)
A. Translations along the the rule (x, y) —> (x -8 y -3)
Part A
[tex]D(1,0) \longrightarrow D'(1-8, 0-3)=D'(-7, -3)\\\\E(7,2) \longrightarrow E'(7-8, 2-3)=E'(-1, -1)\\\\F(8,-1) \longrightarrow F'(8-8, -1-3)=F'(0, -4)\\\\G(2,-3) \longrightarrow G'(2-8, -3-3)=G'(-6, -6)[/tex]
Part B
Reflecting over the x axis means [tex](x, y) \longrightarrow (x, -y)[/tex].
[tex]D'(-7, -3) \longrightarrow D''(-7, 3)\\\\E'(-1, -1) \longrightarrow E''(-1, 1)\\\\F'(0, -4) \longrightarrow F''(0, 4)\\\\G'(-6, -6) \longrightarrow G''(-6, 6)[/tex]
Decide whether each statement is sometimes true, always true, or never true. If the statement is sometimes true give one example of when it is true and an example of when it is not. See Instructions."The linear regression line passes through the average of the x-values and the average of the y-values."Your answer:See Instructions. "A positive correlation coefficient means that the points in the scatterplot are very close together."Your answer:See Instructions."A correlation coefficient close to 1 means that a linear model is most appropriate for the data."Your answer:
In general, the linear regression formula is shown below
[tex]undefined[/tex]If a rectangular solid has a volume of 32 and then each dimension is doubled, what happens to the volume? A. The volume is multiplied by 3.B. The volume is multiplied by 8.C. The volume is multiplied by 6.D. The volume is doubled.
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height
V1=LWH= 32
[tex]\begin{gathered} V2=2L\cdot2W.2H \\ V2=8(\text{LWH)} \end{gathered}[/tex]Ex
2*4*4=32
Let's multiply all dimension by 2
4 * 8 * 8 =256
Answer:B. The volume is multiplied by 8.
The sum of 4 consecutive integers is 170. What is the largest number in the group?
The largest number when the sum of 4 consecutive integers is 170 will be 44.
According to the question,
We have the following information:
Sum of four consecutive integers = 170
Now, let's take the first integer to be x.
So, the next 3 integers will be (x+1), (x+2) and (x+3) respectively.
Now, the largest number will be (x+3).
Adding 4 consecutive integers:
x+ (x+1) + (x+2) + (x+3) = 170
4x+6 = 170
4x = 170-6 (Moving 6 from the left hand side to the right hand will result in the change of the sign from plus to minus.)
4x = 164
x = 164/4
x = 41
So, the next three consecutive integers will be 42, 43 and 44.
Hence, the largest of the four consecutive integers is 44.
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Please Help Please ASAP
What values of x and y make △QRS≅△FDE?
help me out *warning* its hard jk
Answer:
0.321 repeating 1
Step-by-step explanation: