Solve the inequality -30 10-40x and write the solution using:
Inequality Notation:
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Answer:
Step-by-step explanation:
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PLEASE HELP!!
Ninas math class is 6 and 4/5 meters long and 1 and 3/8 meters wide. What is the area of the classroom?
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Answer: 374/40 or 9.35 or 9 and 7/20
Step-by-step explanation: see photo for explanation
I I need help solving problem number 8 please :)
Answers
Answer:
(8, -1)
Explanation:
Given the below system of equations;
[tex]\begin{gathered} y^2+x^2=65\ldots\ldots\ldots\text{.Equation 1} \\ y+x=7\ldots\ldots\ldots\ldots\text{.Equation 2} \end{gathered}[/tex]Let's go ahead and test each of the given solutions and see which of them is the correct one;
For (8, -1), we have x = 8 and y = -1;
Substituting the above values in Equation 1, we have;
[tex]\begin{gathered} (-1)^2+(8)^2=65 \\ 1+64=65 \\ 65=65 \end{gathered}[/tex]Substituting the values into Equation 2;
[tex]\begin{gathered} (-1)+8=7 \\ -1+8=7 \\ 7=7 \end{gathered}[/tex]We can see that (8, -1) is a solution to the given system of equations
8.
What is the measure of angle x in the figure?
40°
A 69°
B 71°
C 109°
D 111°
Answers
Answer:
C 109
Step-by-step explanation:
First add all the known angles inside the triangle first to get 109°
Then since all angles in a triangle add to 180°
you take away 109 from 180 so
180-109 which equals 71
Then since all angles on a straight line add up to 180°
you take 71 from 180 so
180-71 = 109
so x = 109°
Find a polynomial f (x) of degree 3 that has the following zeros.6 (multiplicity 2), -7Leave your answer in factored form.
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If a polynomial has a zero of "a" with multilicity b, the factor would be:
[tex](x-a)^b[/tex]So, accordingly the factors would be:
[tex]\begin{gathered} (x-6)^2 \\ (x-(-7))^1 \end{gathered}[/tex]They are
[tex]\begin{gathered} (x-6)^2 \\ (x+7) \end{gathered}[/tex]We can write out the polynomial, f(x), as:
[tex]f(x)=(x-6)^2(x+7)[/tex]Please help me and tell me the process I have a test in an hour.Value of x.
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Vertical angles are congruent.
From the figure, angle 3 and angle (7x + 3) are vertical angles, therefore angle 3 is (7x + 3)
Angle 1 and 127 degrees are supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle1+127=180 \\ \angle1=180-127 \\ \angle1=53 \end{gathered}[/tex]Angle 2 and 133 degrees are also supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle2+133=180 \\ \angle2=180-133 \\ \angle2=47 \end{gathered}[/tex]Now we have angles 1, 2 and 3 which are angles in a triangle, and the sum of interior angles in a triangle is 180 degrees.
[tex]\begin{gathered} \angle1+\angle2+\angle3=180 \\ 53+47+(7x+3)=180 \\ \text{Solve for x :} \\ 100+7x+3=180 \\ 7x+103=180 \\ 7x=180-103 \\ 7x=77 \\ x=\frac{77}{7} \\ x=11 \end{gathered}[/tex]ANSWER :
x = 11
It's a gross thought, but the number (N) of bacteria in refrigerated food is given by latex- 1≤T≤20 where T is the temperature of the food in degrees Celsius. When you take the food out of the refrigerator, the temperature of the food is given by T(t)=3t+2, 0≤t≤6 where t is the time in hours. Find the composition N(T(t)) and interpret what it means in this context.
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Given that the concentration of bacteria in the refrigerated food is
[tex]10T^2-20T-6----\mleft\lbrace1\mright\rbrace[/tex]and the temperature of the food is given by
[tex]T(t)=3t+2-----\mleft\lbrace2\mright\rbrace[/tex]Therefore, N(T(t) is given by
[tex]N\mleft(T(t)\mright)=10(3t+2)^2-20(3t+2)^{}-6[/tex]Then,
[tex]\begin{gathered} N(T(t))=10(3t+2)^2-20(3t+2)^{}-6 \\ =10(9t^2+6t+6t+4)-60t-40-6 \\ =10(9t^2+12t+4)-60t-46 \\ =90t^2+120t+40-60t-46 \\ =90t^2+60t-6 \end{gathered}[/tex]Answer: The composition is
[tex]N(T(t))=90t^2+60t-6[/tex]It can be interpreted as the concentration of bacteria in the food when outside of the refrigerator with time.
Hello, I need some assistance with this homework question please for precalculusHW Q1
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To transform a function about the y axis
f(x) becomes f(-x)
y = sqrt( x) +2
To transform replace x with -x
y = sqrt(-x) +2
The 2 is a vertical translation up 2
Determine the probability of flipping a heads, rolling a number less than 5 on a number cube and picking a heart from a standard deck of cards.
1/12
16/60 or 4/15
13/156
112
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The probability of flipping a heads is 1/2, probability of rolling a number less than 5 is 2/3, and probability of picking a heart from a standard deck of cards is 1/4.
What is probability?
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is always a number b/w 0 and 1, with 0 approximately says impossibility and 1 says surity.
We can find probability using the formula:
P = required out comes/ total outcomes
In first case the required out come is only one which is heads and total outcomes include both heads and tails,
Therefore, required outcome = 1
total outcome = 2
Probability = 1/2
In second case the required out come are number less than five which are 1, 2, 3, 4 and a number cube have numbers till 6.
Therefore, required outcome = 4
total outcome = 6
Probability = 4/6 = 2/3
In third case the required out come hearts card and there are 13 hearts card in a card deck and total outcomes include all types of cards which are 52,
Therefore, required outcome = 13
total outcome = 52
Probability = 13/52 = 1/4
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Write an equation of the line with the given slope and y-intercept.
Slope
1
6
, y−intercept (0, −2)
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The equation of line is [tex]6y=6x$-$12[/tex].
The given slope is [tex]\frac{1}{6}[/tex].
The [tex]y $-$[/tex]intercept is [tex](0, $-$2)[/tex].
We have to write the equation of line using the given slope and [tex]y $-$[/tex]intercept.
The equation of line with the slope m and [tex]y $-$[/tex]intercept of [tex](0,a)[/tex] is [tex]y=mx+a[/tex].
From the question,
The value of [tex]m=\frac{1}{6}[/tex]
The value of [tex]a= $-$2[/tex]
Now putting the value of [tex]m[/tex] and [tex]a[/tex] in the equation of line.
[tex]y=\frac{1}{6}x+( $-$2)\\y=\frac{1}{6}x$-$2[/tex]
Multiply by [tex]6[/tex] on both side
[tex]y\times6=6\times(\frac{1}{6}x$-$2)\\6y=6\times\frac{1}{6}x$-$6\times2\\6y=6x$-$12[/tex]
The equation of line is [tex]6y=6x$-$12[/tex].
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What is period of the function, give the exact value
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Solution
Step 1:
Find the midline
[tex]\begin{gathered} Midline\text{ = }\frac{maximum\text{ + minimum}}{2} \\ Maximum\text{ = 11.4} \\ minimum\text{ = -5.5} \\ midline\text{ = }\frac{11.4\text{ + \lparen-5.5\rparen}}{2} \\ midline\text{ = }\frac{5.9}{2} \\ midline\text{ = 2.95} \end{gathered}[/tex]Step 2:
Find the amplitude
[tex]\begin{gathered} Amplitude\text{ = }\frac{maximum\text{ - minimum}}{2} \\ Amplitude\text{ = }\frac{11.4\text{ - \lparen-5.5\rparen}}{2} \\ Amplitude\text{ = 8.45} \end{gathered}[/tex]Step 3:
Period:
To find the period, use the values of x.
[tex]\begin{gathered} Period\text{ = 2\lparen11.4 + 5.5\rparen} \\ Period\text{ = 2 }\times\text{ 16.9} \\ period\text{ = 33.8} \end{gathered}[/tex]Final answer
Period = 33.8
Jalisa needs to purchase a cover for her oval-shaped pool. The pool's length and width measurements, as marked by dotted lines, are 30 feet and 13 feet.If Jalisa wants the pool cover to extend one foot from the pool's edge, as shown in the drawing, what will be the area of therectangular pool cover?A. 390 square feetOB. 434 square feetOC 480 square feetD. 86 square feet
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She wants to cover the pool with a rectangular pool cover that extends one foot from the pool edges in every direction.
The length of the pool is 30ft and the width is 13ft, if the pool cover must extend 1ft over the pool's edge, then you have to add 2ft to the length and 2ft to the width, as shown below:
So, the length of the pool cover will be equal to the length of the pool plus two feet:
[tex]length=30ft+2ft=32ft[/tex]And the width of the pool cover will be equal to the width of the pool plus two feet:
[tex]width=13ft+2ft=15ft[/tex]Once you determined the width and length of the rectangular pool cover, you can calculate its area:
[tex]\begin{gathered} A=wl \\ A=15*32 \\ A=480ft^2 \end{gathered}[/tex]The area of the rectangular pool cover is 480 square feet (option C)
Find the next two numbers in the pattern -243, 81, -27, 9
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Find the next two numbers in the pattern -243, 81, -27, 9
Notice that all the values in the series are value of 3 raise to the power of a number.
-243 =
Dunoga cycled 15.26 kilometres and then ran 740 metres. What was the total distance he covered in kilometres?
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Answer:16 Kilometers
Step-by-step explanation:15.26km+.74km
Dunoga covered a distance of 16 km in total.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given that, Dunoga cycled 15.26 kilometers and then ran 740 meters. We need to find the distance he covered in kilometers,
To find the total distance, we will add the distance he covered by cycle and by running,
But the units of both the distances are not same and to add we need to convert the units,
Since, the answer required in kilometers, so we will convert meter into kilometers,
1 km = 1000 m
Therefore,
740 m = 740 / 1000 = 0.74 km
Therefore, the distance he covered in kilometers = 0.74+15.26
= 16 km
Hence, Dunoga covered a distance of 16 km in total.
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which of the following liner equations passes through points (-1,5) and (1,5)?
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Hence, the correct option is Option D. None of the choices are correct.
can u help me w this i got it incorrect and can’t figure out why
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1) We can see here a case in which there are two secant lines coming from a single point over that circle.
2) So, we can write out the following relation
[tex]\begin{gathered} PA\cdot PB=PC\cdot PD \\ 4(4+x)=5(5+7) \\ 16+4x=25+35 \\ 16+4x=60 \\ 16-16+4x=60-16 \\ 4x=44 \\ \frac{4x}{4}=\frac{44}{4} \\ x=11 \end{gathered}[/tex]Jane needs $20 to buy her radio.She has saved $15.What precent of the cost of the radio has she saved?
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Let's begin by listing out the information given to us:
Cost of Radio (c) = $20
Jane's saving (s) = $15
% of radio cost saved = (Jane's saving / Cost of Radio) * 100%
[tex]\begin{gathered} x=\frac{s}{c}\cdot100 \\ x=\frac{15}{20}\cdot100=75 \\ x=75 \end{gathered}[/tex]Jane has saved 75% of the radio cost
Write an equation that represents a reflection in the y-axis of the graph of g(x)=|x|.
h(x)= ?
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the reflection of the function g(x)=|x| in the y-axis will be h(x) = |x|
What is reflection in coordinate geometry ?
this represents the flip or mirror image of transformation about the given axis.
For every point in the plane (x, y), a 90° rotation can be described by the transformation P(x, y) → P'(-y, x). We can achieve this same transformation by performing two reflections.
Here, the given function is :
g(x)=|x|
Now, the reflection in the y-axis will be same that is :
h(x)= g(x)
h(x) = |x|
Therefore, the reflection of the function g(x)=|x| in the y-axis will be h(x) = |x|
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What number is 3/4 of 17
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3/4 of 17 is equal to the product of 3/4 times 17, that is,
[tex]\frac{3}{4}\times17=\frac{3\times17}{4}[/tex]which gives
[tex]\frac{3\times17}{4}=\frac{51}{4}[/tex]in decimal form, the answer is 12.75.
Write the slope-intercept form of the equation of the line with the given characteristics. Perpendicular to y = -5x + 2 and passing through (3,-1).
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The slope intercept form of a line can be expressed as,
[tex]y=mx+c[/tex]Here, m is the slope of the line and c is the y intercept.
Comparing the above equation with the given equation of a line y=-5x+2, we get
m=-5.
The slope of a line perpendicular to line with slope m is -1/m.
Hence, the slope of line perpendicular to y=-5x+2 is,
[tex]m_1=\frac{-1}{m}=\frac{-1}{-5}=\frac{1}{5}[/tex]The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).
The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,
[tex]\begin{gathered} y-y_1=m_1(x-x_1) \\ y-(-1)=\frac{1}{5}(x-3) \\ y+1=\frac{1}{5}x-\frac{3}{5} \\ y=\frac{1}{5}x-\frac{3}{5}-1 \\ y=\frac{1}{5}x-\frac{3-5}{5} \\ y=\frac{1}{5}x-\frac{8}{5} \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,
[tex]y=\frac{1}{5}x-\frac{8}{5}[/tex]A middle schooler is H inches tall at the beginning of the school year is the height of the middle school at the end of the year can be represented by the expression H + 0.02h, which statement is true?
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Answer:
A
Step-by-step explanation:
h + 0.02h = (1+0.02)h = 1.02h
1.02h * 100% = 102%
102 - 100 = 2%
Hello. I think I have this one correct but I'm not 100% sure. Would you mind helping me work this through?
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1) To better set the measurements in that picture, we need to consider that parallel line segments in this picture have the same measurements.
2) Based on that, we can look at that picture this way:
And set the following equation, given that Perimeter is the sum of all lengths of a polygon:
[tex]\begin{gathered} P=2+2+1+2+3+3+1+1+1+1+4+3 \\ P=24\:cm \end{gathered}[/tex]In a survey, 300 adults and children were asked whether they preferredhamburgers or pizza. The survey data are shown in the relative frequencytable.
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Answer:
Step-by-step explanation:
From the data in the table given
frequency of people who like pizza 0·36 +0·29=0·65
percentage of people who like pizza
0.65 × 100
=65%
For the equation y = -2x + 1 A) complete the Table: X l Y -4 04B) Use the appropriate tool to graph the given equation
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ANSWER:
a)
b)
EXPLANATION:
Given:
[tex]y=-2x+1[/tex]a) When x = -4, let's go ahead and solve for y;
[tex]\begin{gathered} y=-2(-4)+1 \\ y=8+1 \\ y=9 \end{gathered}[/tex]When x = 0, let's go ahead and solve for y;
[tex]\begin{gathered} y=-2(0)+1 \\ y=0+1 \\ y=1 \end{gathered}[/tex]When x = 4, let's go ahead and solve for y;
[tex]\begin{gathered} y=-2(4)+1 \\ y=-8+1 \\ y=-7 \end{gathered}[/tex]b) Using the above values, we can go ahead and the equation as seen below;
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.f(x)=sqrt(x)+2g(x)=x^2+7f(g(x))= ?g(f(x))= ?
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Answer:
[tex]\begin{gathered} \begin{equation*} f(g(x))=\sqrt{x^2+7}+2 \end{equation*} \\ \begin{equation*} g(f(x))=x+4\sqrt{x}+11 \end{equation*} \end{gathered}[/tex]Explanation:
Given the functions f(x) and g(x) below:
[tex]\begin{gathered} f(x)=\sqrt{x}+2 \\ g\mleft(x\mright)=x^2+7 \end{gathered}[/tex]Part A
We want to find the simplified form of f(g(x)).
[tex]f(x)=\sqrt{x}+2[/tex]Replace x with g(x):
[tex]f(g(x))=\sqrt{g(x)}+2[/tex]Finally, enter the expression for g(x) and simplify if possible:
[tex]\implies f\mleft(g\mleft(x\mright)\mright)=\sqrt{x^2+7}+2[/tex]Part B
We want to find the simplified form of g(f(x)). To do this, begin with g(x):
[tex]g\mleft(x\mright)=x^2+7[/tex]Replace x with f(x):
[tex]g(f(x))=[f(x)]^2+7[/tex]Finally, enter the expression for f(x) and simplify if possible:
[tex]\begin{gathered} g\mleft(f\mleft(x\mright)\mright)=(\sqrt{x}+2)^2+7 \\ =(\sqrt{x}+2)(\sqrt{x}+2)+7 \\ =x+2\sqrt{x}+2\sqrt{x}+4+7 \\ \implies g(f(x))=x+4\sqrt{x}+11 \end{gathered}[/tex]Therefore:
[tex]\begin{equation*} g(f(x))=x+4\sqrt{x}+11 \end{equation*}[/tex]It takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 10 inches wide, and 14 inchestall. How long will it take the same hose to fill an aquarium measuring 23 inches by 25 inches by 26inches?minutesEnter an integer or decimal number [more..]Round your answer to the nearest minuteSubmit
Answers
Answer:
[tex]40\text{ minutes}[/tex]Explanation:
Firstly, we have to calculate the rate at which the hose works
We can get that by dividing the volume of the first aquarium by the time taken to fill it
The volume of the first aquarium can be calculated using the formula:
[tex]V\text{ = L}\times B\times H[/tex]Where:
L is the length of the aquarium
B is its width
H is its height
The volume of the first aquarium is thus:
[tex]V\text{ = 8}\times10\times14\text{ = 1120 in}^3[/tex]We have the filling rate as:
[tex]\frac{1120}{3}\text{ in}^3\text{ per minute}[/tex]Now, let us get the volume of the second aquarium
We use the same formula as the first
We have the volume as:
[tex]23\times25\times26\text{ = 14,950 in}^3[/tex]Now, to get the time taken, we divide the volume of the second aquarium by the rate of the first
Mathematically, we have that as:
[tex]14950\text{ }\times\frac{3}{1120}\text{ = 40 minutes approximately}[/tex]What is the current population of elk at the park?
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Given the following function:
[tex]\text{ f\lparen x\rparen= 1200\lparen0.8\rparen}^{\text{x}}[/tex]1200 represents the initial/current population of elk in the national park.
Therefore, the answer is CHOICE A.
how to find the width to a pyramid with the volume height and length
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The volume of a pyramid is given by the formula
[tex]V_{\text{pyramid}}=\frac{1}{3}\times base\text{ area}\times height[/tex]Write out the given dimensions
[tex]\begin{gathered} \text{Volume}=80\operatorname{cm}^3 \\ \text{Height}=10\operatorname{cm} \\ \text{length}=6\operatorname{cm} \\ \text{width}=\text{unknown} \end{gathered}[/tex]Since the base of the pyramid is a rectangle, the base area is
[tex]A_{\text{rectangle}}=\text{width }\times length[/tex]Substituting the given dimensions to get the value of the width\
[tex]\begin{gathered} V_{\text{pyramid}}=\frac{1}{3}\times width\times length\times height \\ 80=\frac{1}{3}\times width\times6\operatorname{cm}\times10\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} 80\operatorname{cm}=20\times width \\ \text{width}=\frac{80}{20} \\ \text{width}=4\operatorname{cm} \end{gathered}[/tex]Hence, the width of the pyramid is 4cm
omg i lost my tutor in the middle of math i need another one btw in fith grade not in middle school yet
Answers
by definition the division of fractions can be found by
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{b\cdot c}{a\cdot d}[/tex]According to this
[tex]\frac{\frac{6}{10}}{\frac{1}{5}}=\frac{6\cdot5}{10\cdot1}=\frac{30}{10}=3[/tex]Hello Professor i was confused in this question, will appreciate if u could help me with it!
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The hypotenuse is 20 V 3
Explanation:Given that longer leg = 30
Hypotenuse is given as:
[tex]\begin{gathered} 2\times\frac{30}{\sqrt[]{3}} \\ \\ =\frac{60}{3}\sqrt[]{3} \\ \\ =20\sqrt[]{3} \end{gathered}[/tex]Jan draws a card from the set below, replaces it and then draws another card. Which of the following tree diagrams correctly shows the sample space?
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Given the word problem, we can deduce the following information:
1. Jan draws a card from the set below, replaces it and then draws another card.
Based on the given information, there is a replacement happening. It means that Jan put a card back in the set before selecting another card. So the tree diagram that shows all the possible outcomes is Diagram A.
Therefore, the answer is A.
