In order to represent three consecutive odd numbers, we can use the expressions "x", "x+2" and "x+4".
If we add the square of each number, the result is 83, so we can write the following inequality:
[tex]\begin{gathered} x^2+(x+2)^2+(x+4)^2=83\\ \\ x^2+x^2+4x+4+x^2+8x+16=83\\ \\ 3x^2+12x+20=83\\ \\ 3x^2+12-63=0\\ \\ x^2+4x-21=0 \end{gathered}[/tex]Let's solve this quadratic equation using the quadratic formula, with a = 1, b = 4 and c = -21:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4a}c}{2a}\\ \\ x=\frac{-4\pm\sqrt{16+84}}{2}\\ \\ x=\frac{-4\pm10}{2}\\ \\ x_1=\frac{-4+10}{2}=\frac{6}{2}=3\\ \\ x_2=\frac{-4-10}{2}=\frac{-14}{2}=-7 \end{gathered}[/tex]If we assume the numbers are positive, the numbers are 3, 5 and 7.
(The other result, with negative numbers, would be -7, -5 and -3).
A recipe requires 2 and 1 third cups of flower the chef needs to increase the recipe bya factor of 4 how many cups of flower does the chef need
The number of cups needed by the chef is 9 1/3 cups.
How to calculate the fraction?A fraction simply means a part of a whole number.
In this case, the recipe requires 2 and 1 third cups of flower the chef needs to increase the recipe by a factor of 4.
The cups needed will be:
= 2 1/3 × 4
= 7/3 × 4
= 28/3
= 9 1/3 cups.
This illustrates the concept of fractions.
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Find the product and write your answer in proper scientific notation (4.5 x 10³)/(3 x 10⁶)
Answer:
[tex]1.5\times10^{-3}[/tex]Explanation:
Given the rational expression
[tex]\frac{4.5\times10^3}{3\times10^6}[/tex]We can rewrite the fraction as:
[tex]=\frac{4.5}{3}\times\frac{10^3}{10^6}[/tex]We then simplify and apply the division law of indices to obtain:
[tex]\begin{gathered} =1.5\times10^{3-6} \\ =1.5\times10^{-3} \end{gathered}[/tex]Note: When you have the same base of an exponent and the terms are being divided, we simply subtract the power of the numerator from that of the denominator.
Find the area and perimeter of a rhombus with a diagonals 15 in and 20 in
Given data:
The diagonals of rhombus d1 = 15 in and d2 = 20 in
The area of the rhombus,
[tex]\begin{gathered} A=\frac{1}{2}\times d1\times d2 \\ A=\frac{1}{2}\times15\times20 \\ A=150\text{ inches sq.} \end{gathered}[/tex]Now, to find the perimeter of rhombus we first find the side of rhombus.
The diagonal of the rhombus is considered as diameter, so the radius will be
d1 = r1 = 7.5
d2 = r2 = 10
So, by using the pythagorean theorem we find the side of the rhombus
[tex]\begin{gathered} h^2=(7.5)^2+(10)^2 \\ h^2=56.25+100 \\ h^2=156.25 \\ h=12.5 \end{gathered}[/tex]The perimeter of the rhombus is,
[tex]\begin{gathered} P=4\times side \\ P=4\times12.5 \\ P=50\text{ inches} \end{gathered}[/tex]Thus, the area is 150 in. sq. and perimeter is 50 in.
Are the triangles congruent using AAS?
True
False
Answer: True
Step-by-step explanation:
If you look both triangles have the same angles, so that means that they are congruent.
Ganymede is one of Jupiter’s moons. It takes Ganymede 7 days, 3 hours, and 15 minutes to make one rotation around Jupiter. How many hours does it take Ganymede to complete a full rotation? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
The number of hours it will take Ganymede to complete a full rotation is; 171.25 hours.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The first step must be to convert days to hours. A day is equivalent to the 24 hours.
1 day = 24 hours
24 x 7 = 168 hours
The second step must be to convert minutes to hours,
60 minutes = 1 hour
15 / 60 = 0.25 hours
Now, add up all the converted hours together;
Total hours = 168 hours + 3 hours + 0.25 hours
Total hours = 171.25 hours
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Timothy Tools is a company that produces hand-crafted hammers and wrenches. The following equations can be used to determine how many hammers the company can produce each day if x people are making hammers
The domain of the function of the equation cannot include zero because h(0) is not real.
A scale used to weigh objects is analogous to an equation. When the two pans are filled to the same level with anything, the scale will balance and the weights will be considered to be equal (such as grain).
To keep the balance in check, whenever any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. In general, if the same operation is carried out on both sides of an equation, the equation remains in balance.Equations that involve one or more functions and their derivatives are known as differential equations. By locating a derivative-free formulation for the function, they can be resolved.The equation is given as [tex]h(x) = \sqrt{2x^2+5x+3}[/tex]
The equation at x=0 given
h(0) = √(0+0-3)
or, h(0) = √(-3) which is an imaginary number
Therefore for the equation the value of x at 0 is undefined.
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A car rental company offers two plans for renting a car.
Plan A: 35 dollars per day and 10 cents per mile
Plan B: 55 dollars per day with free unlimited mileage
How many miles would you need to drive in one day for plan B to save you money?
Answer:
Less than 200 miles, A is cheaper
At 200 miles, they are the same
Over 200 miles, B is less expensive
Step-by-step explanation:
A packing carton has a square bottom 18 inches by 18 inches. If the capacity of the carton is 3cubic feet, how deep is the carton?
The packing carton has a square bottom with measures 18in x 18in and has a volume of V=3ft³
The volume of cubic prims can be calculated by multiplying its width by its length and height:
So the formula to calculate the volume is
[tex]V=w\cdot l\cdot h[/tex]If we know the width, length, and volume we can determine the height. First, write the formula for h, that is, divide the volume by the width and height:
[tex]h=\frac{V}{wl}[/tex]The units of the width and length are in inches and the volume is in cubic feet, to determine the height of the box, all units must be the same. To make the calculations easier I will pass the units from inches to feet.
The unit rate between inches and feet is the following:
[tex]1^{\doubleprime}=\frac{1}{12}ft[/tex]To express 18 inches in feet you have to multiply them by 1/12
[tex]18\cdot\frac{1}{12}=1.5[/tex]This means that the width and length of the box measure 1.5ft
Now we can determine the height of the box as follows:
w=l=1.5ft
V=3ft³
[tex]\begin{gathered} h=\frac{V}{wl} \\ h=\frac{3}{1.5\cdot1.5} \\ h=\frac{4}{3}ft \end{gathered}[/tex]The height of the box is 3/4ft, if you multiply it by 12 you can express the measure in inches:
[tex]\frac{3}{4}\cdot12=9[/tex]The box has a deph of 9 inches.
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
In triangle JKL, tan(b°) = 3/4 and sin(b°) = 3/5 If triangle JKL is dilated by a scale factor of 3, what is cos(bº)?
ANSWER
cos(bº) = 4/5
EXPLANATION
When a triangle is dilated, the resulting triangle is similar to the original triangle. Therefore, the interior angles of the dilated triangle are congruent to the interior angles of the original triangle. This means that cos(bº) is the same for both triangles.
Using the relationship between these three trigonometric ratios:
[tex]\tan (bº)=\frac{\sin (bº)}{\cos (bº)}[/tex]We can find the cosine:
[tex]\cos (bº)=\frac{\sin (bº)}{\tan (bº)}[/tex][tex]\cos (bº)=\frac{\frac{3}{5}}{\frac{3}{4}}=\frac{3}{5}\colon\frac{3}{4}=\frac{3}{5}\times\frac{4}{3}=\frac{4}{5}[/tex]Please explain this to me
If a perpendicular b and b parallel to c, then the value of x = 8
Here b and c are parallel lines
The parallel lines are two lines in the same plane that are at equal distance from each other and that do not intersect at any point
Then a is perpendicular to b
The perpendicular lines are the line that forms the angle of 90 degrees for both angles
Therefore the given angles are 90 degrees
9x+18 = 90
9x = 90-18
9x = 72
x = 72/9
x = 8
Hence, If a perpendicular b and b parallel to c, then the value of x = 8
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100 POINTS ANSWER CORRECTLY PLS
Answer:
1.) y = -3/4x +2
2.) y = x - 4
3.) y = 2/3x - 4
4.) y = -1/2x + 5
5.) y = 8/3x +5
Step-by-step explanation:
1.)
Parallel means that the slopes will be the same.
So, m = -3/4
To find the equation, we must first use point-slope form.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
y-(-1) = -3/4(x-4)
Now we clean this up and solve for y to get the answer in slope intercept form.
y+1= -3/4x + 3 => y = -3/4x +2
2.)
Perpendicular means that the slope is the negative reciprocal of the slope of the first line.
So, m = 1 as the negative reciprocal of -1 is +1.
Once again, we use point-slope form and the clean it up and solve for y to get the answer in slope-intercept form.
y - (-3) = 1(x-1) => y + 3 = x-1 => y = x - 4
3.)
Similar to the previous one, but with slope m = 2/3 (negative reciprocal)
y - (-4) = 2/3 (x - 0) => y + 4 = 2/3x => y = 2/3x - 4
4.)
Similar to the previous one, but with slope m = -1/2 (negative reciprocal)
y - 4 = -1/2(x-2) => y - 4 = -1/2x +1 => y = -1/2x + 5
5.)
Similar to the previous one, but with slope m = 8/3 (negative reciprocal)
y - (-3) = 8/3(x - (-3)) => y + 3 = 8/3x +8 => y = 8/3x +5
?? i am not good at this please help me thanks
Answer:
If I am not mistake I am pretty sure its graph B.
Step-by-step explanation:
Four points W, X, Y, Z are chosen at random on the circumference of a circle. What is the probability that WX > YZ?
The probability to choose WX > YZ is 1/2.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Four points W, X, Y, Z are chosen at random on the circumference of a circle.
Now,
By the four points W, X, Y, Z we make two line WX and YZ.
So, There are two relation between the line WX and YZ.
Thus, The probability to choose WX > YZ is;
Probability = Possible event / Total possibility
= 1/2
Therefore, The probability to choose WX > YZ is 1/2.
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What does n mean?????
a. Data values are 13.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5
b. ∑x = 91
c. n = 6
What is mean and data values?Adding all numbers in the data and then dividing by the number of values is called mean. Median is defined as the middle value when a data set is in such a way that it goes from least to the greatest value. Whereas the number that occurs most often in a data set is mode. Sample size is represented by "n". Whereas, symbol Σ denotes the summation.
For the given mean,
The data values are 3.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5
Summation, ∑x = 3.4+ 16.3+ 14.2 + 15.4 + 14.2 +17.5
= 91
n is the number of data that is 6.
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Sorry if it's blurry but could you help me with this please :)
We have the following:
We can see in the figure that it up by two units and shift 5 units to the right.
Therefore, que the answer is thr first option
What is the value of the function at x=−3? Responses y = 3 y, = 3 y = 0 y, = 0 y = 4 y, = 4 y=−3
The function has a value of y = 4 when x =-3
How to determine the value of the function?The graph that completes the question is added as an attachment
From the graph, we can see that:
The graph of the function is a linear function
This is so because the function is a straight line
Note that:
Linear equations are equations that have constant average rates of change.
On the straight line, we can see that
The value of the function when x = -3 is 4
This means that
y = 4
Hence, the value of the function at x = -3 is y = 4
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Help please. Catching up on missed work from being out due to medical issues. Thank you in advance!
Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.
Therefore, we can set the following equation:
[tex]\begin{gathered} B+I=3, \\ 220B+32I=110\cdot3. \end{gathered}[/tex]Subtracting B from the first equation we get:
[tex]\begin{gathered} B+I-B=3-B, \\ I=3-B\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]220B+32(3-B)=330.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 220B+96-32B=330, \\ 188B+96=330. \end{gathered}[/tex]Subtracting 96 to the above equation we get:
[tex]\begin{gathered} 188B+96-96=330-96, \\ 188B=234. \end{gathered}[/tex]Dividing the above equation by 188 we get:
[tex]\begin{gathered} \frac{188B}{188}=\frac{234}{188}, \\ B\approx1.24. \end{gathered}[/tex]Substituting B=1.24 at I=3-B we get:
[tex]I=3-1.24=1.76.[/tex]Answer:
[tex]\begin{gathered} 1.26\text{ cups of boiling water.} \\ 1.74\text{ cups of ice.} \end{gathered}[/tex]9.2 x 108 is how many times the value of 2.3 x 10²?
A. 4 x 104
B. 4 x 106
C. 6.9 x 104
D. 6.9 x 106
Answer:
B. [tex]4*10^6[/tex]
Step-by-step explanation:
All you have to do is divide the first value by the second value to find the ratio between the two numbers.
The equation would look like this:
[tex]\frac{9.2*10^8}{2.3*10^2}[/tex] or [tex]\frac{920000000}{230}[/tex]
Solving this gives you [tex]4 * 10^6[/tex], or 4000000.
You can also figure this out without a calculator. Simply subtract the smaller power from the larger power to get your exponent.
Since this problem has [tex]10^8[/tex] and [tex]10^2[/tex], subtract 2 from 8 to get 6. This will be the exponent in your answer, ruling out answers A and C.
Then, just estimate 9.2/2.3. You can do 9/2 to get 4.5, which is closer to 4. Therefore, D is ruled out, so the answer must be B.
Hope this helps :)
Mark made the following shape using two rectangles and one triangle. What is the area of the figure he made?
Answer:
44 square centimetres.
Explanation:
The shape consists of two rectangles and one triangle with the following dimensions:
• A rectangle (Rectangle 1) with dimensions of 4cm by 2cm.
,• A rectangle (Rectangle 2) with dimensions 6cm by 4cm.
,• A triangle with base 6cm and height of 4cm.
Thus, the area of the figure made will be:
[tex]\begin{gathered} \text{Area of figure=Area of rectangle 1+Area of rectangle }2+\text{Area of }\triangle \\ =(4\times2)+(6\times4)+(\frac{1}{2}\times6\times4) \\ =8+24+12 \\ =44\operatorname{cm}^2 \end{gathered}[/tex]The area of the figure is 44 square centimetres.
A. F(x) = -x^7+4x^3-2x^2B. F(x)= x^9+12x^8+x^7C. F(x) =x^8+4x^4+20x^2D. F(x) = -x^6+x^3-x^2
answer:
A. F(x) = -x^7+4x^3-2x^2
Lin is paid $90 for 5 hours of work. She used the following table tocalculate how much she would be paid at this rate for 8 hours of work.1. What is the meaning of the 18that appears in the table?IAmount earned($)Time worked(hours)9052. Explain how Lin used this table tosolve the problem3. At this rate, how much would Linbe paid for 3 hours of work? For21 hours of work?1811448
From the table :
Lin worked for 5 hours and earned 90$
LIn worked for 1 hour and earned 18$
Lin worked for 8 hour
so the earning is
[tex]8\times18=144[/tex]Lin worked for 8 hours so the earning is 144$
If lin works for 3 hours then the earning is
So the answer for 3 hours is 54$.
[tex]3\times18=54\text{ dollar}[/tex]If lin works for 21 hours then the earning is
[tex]21\times18=378\text{ dollar}[/tex]so the answer for 21 hours is 378$.
There area 17,60 gaffs in a mile . What is the number of yards in a mile rounded to the nearest hundred? 1- How many places are in this number?2- What are the places? 3- What place are you rounding to?4- What digit is in that place?5- What place is to the right of the place you are rounding to?6- What digit is in that place?Is this digit 5 or greater?7- What is the rule for digits 5 or greater? 8- Will you need to change the hundreds digit? If so, to what? 9- Which places will you change to 0s?10- What is the number of yards in a mile rounded to the nearest hundred?
itWe were given the following:
[tex]1760yard=1mi[/tex]1.
There are 4 places in this number
2.
1 thousand + 7 hundred + 6 tens + 0 units
3.
We are rounding to the hundreds place
4.
Seven (7)
5.
To the right, we have the ''tens''
6.
Six(6). Yes, the digit is 5 or greater
7.
Digits that are 5 or greater than are approximated to the next digit
8.
Yes. From 7 to 8
9.
The tens place will be changed to 0
10.
The number of yards in a mile rounded to the nearest hundred is:
[tex]\begin{gathered} 1,760yards=1mi \\ 1,760\approx1800 \\ =1,800yards(to\text{ the nearest hundred)} \end{gathered}[/tex]What is the measure of angle 1 in the picture below?2135°O 90 degreesO 225 degreesO 45 degreesO 135 degrees
1 and 135 are corresponding angles.
Corresponding angles on parallel lines are equal
m<1= 135 degrees
Jordan is constructing a aregular hexagon inscribed in a circle. He labels the points on the circle as shown
Given,
The diagram of the circle with the vertex of the hexgon.
Required
The measure of arc VX, angle ZXV.
As known that,
The measure of the circle is 360 degree.
The measure of arc VX is,
[tex]Arc\text{ VX = 60 degree.}[/tex]The measure of angle ZXV is,
[tex]\angle ZXV=60^{\circ}[/tex]The measure of arc WZ is 180 degree.
Answer:
VX=120
ZXV=60
WZ
Step-by-step explanation: YOUR WELCOME PUTAS
7/9 ÷ 3/9 = ????????
7/9 ÷ 3/9 =
= (7•9)/( 3•9)
= 63/27 = 7/3
Answer is 7/3
Which graph best represents the solution set for all possible combinations of x, the number of hours she worked at her 1st job, and y, the number of hours she worked at her second job, in one week?
The equation must be x + y < 48
Graph
Evaluate.
1045+(834−612)
Enter your answer as a mixed number in simplest form by filling in the boxes.
The value of the expression given as 1045 + (834 − 612) is 1267
How to evaluate the expression?The expression is given as
1045+(834−612)
Evaluate the brackets in the above expression
So, we have the following equation
1045 + (834 − 612) = 1045 + 222
Evaluate the sum in the above expression
So, we have the following equation
1045 + (834 − 612) = 1267
The above equation/expression cannot be solved further
So, we make our conclusion
Hence, the solution to the expression is 1045 + (834 − 612) = 1267
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Find the turning point of y=h(x) if h(x)=f(-x)f(x)=x^2-4x+12
Given:
[tex]y=h(x)\text{ where }h(x)=f(-x)\text{ and }f(x)=x^2-4x+12.[/tex]Required:
We need to find the turning point of y=h(x).
Explanation:
Replace x =-x in the function f(x) to find h(x).
[tex]f(-x)=(-x)^2-4(-x)+12.[/tex][tex]f(-x)=x^2+4x+12.[/tex]Replace f(-x)=y in the equation.
[tex]y=x^2+4x+12.[/tex][tex]y=x^2+2\times2x+4+8.[/tex][tex]y=x^2+2\times2x+2^2+8.[/tex][tex]Use\text{ }(a^2+2ab+b^2)=(a+b)^2.[/tex][tex]y=(x+2)^2+8.[/tex]Which is of the form
[tex]y=a(x-h)^2+k.[/tex]where a=1, h=-2, and k=8.
The point (h,k)=(-2,8) is the turning point.
Final answer:
The turning point of y=h(x) is (-2,8).
Find the particular antiderivative F(x) of f(x) = 18x - 13 that satisfies F(1) = 11.
To get the antiderivative of the function, we will integrate F(x), as follows:
[tex]\begin{gathered} \int (18x-13)dx=\int 18xdx-\int 13dx \\ =\frac{1}{2}(18x^2)-13x+C \\ =9x^2-13x+C \end{gathered}[/tex]Now, to get the particular antiderivative, we evaluate the antiderivative for x = 1, and it must be equal to 11. This can be shown as:
[tex]\begin{gathered} 9(1)^2-13(1)+C=11 \\ 9-13+C=11 \\ C=11+13-9 \\ C=24-9 \\ C=15 \end{gathered}[/tex]Hence, the particular antiderivative is
[tex]F(x)=9x^2-13x+15[/tex]