It is known that in the I and III quadrants, the signs of the x- and y- are the same.
Jackie claims that the points with the same x - and y - coordinates must lie in the I or III quadrant.
His claim is true.
The points with the same x - and y - coordinates are of the form (a,a) or (-a,-a). If the point is of the form (a,a), it lies in the quadrant I
If the point is of the form (-a,-a), it lies in quadrant III.
I need help with this problem
we know that
In this problem the answer is true
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
If F is similar a G and G is similar a H , then F is similar a H
answer is true
Problem N 2
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem we have that
triangle CAS is similar to triangle TEC
that means
and
CA/TE=AS/EC=CS/TC
so
Its not always trueSelect all the correct answers.
Which statements are true about the graph of function f?
f(x) = log x
Step-by-step explanation:
Simplify [tex]5 \sqrt{11} - 12 \sqrt{11} - 2 \sqrt{11} [/tex] a) [tex] - 33 \sqrt{9} [/tex]b)[tex] - 11 \sqrt{9} [/tex]c)[tex] - 9 \sqrt{11} [/tex]d) [tex] - 9 \sqrt{33} [/tex]
In the given equation, the radical term is same in each term(radical is the being the square root of 11)
5sqrt(11)-12sqrt(11)-2sqrt(11)
Take the sqrt(11) common
sqrt(11){5-12-2}
sqrt(11){5-14}
sqrt(11){-9}
{-9}sqrt(11)
The correct answer is (c). -9Sqrt(11)
The number of bacteria in a culture is given by the function n(t)=985e^.2twhere t is measured in hours.(a) What is the relative rate of growth of this bacterium population?(b) What is the initial population of the culture (at t=0)(c) How many bacteria will the culture contain at time t=5
Answer:
(a) The relative rate of growth is 0.2
(b) The initial population is 985
(c) The amount of bacteria at time t = 5 is 2677.5
Explanation:
An exponential equation to model exponential growth is:
[tex]G(t)=Ie^{rt}[/tex]Where:
• I is the initial population
,• r is the rate of relative growth
,• t is the time
We have in this problem:
[tex]n(t)=985e^{0.2t}[/tex]Then:
(a) The relative rate is 0.2
(b) The initial population is 985
(c) To find the population at t = 5, we evaluate the equation:
[tex]n(5)=985e^{0.2\cdot5}=985e^1=985e\approx2677.5[/tex]
Which is the value of x in the triangle?1245°2O 12V2O6V3O 62O 43
C) 6√2
1) Examining this triangle, we can conclude this is a right triangle and state that we can find the missing side (the adjacent leg) to angle 45º using the following trigonometric ratio Cosine:
[tex]\cos (45)=\frac{adjacent\text{ leg}}{hypotenuse}[/tex]2) So we can plug into that the given values for those legs:
[tex]\begin{gathered} \cos \text{ (45)=}\frac{x}{12} \\ \frac{\sqrt[]{2}}{2}=\frac{x}{12} \\ \\ 2x=12\sqrt[]{2} \\ \frac{2x}{12}=\frac{12\sqrt[]{2}}{12} \\ \frac{x}{6}=\sqrt[]{2}\text{ x 6} \\ x=6\sqrt[]{2} \end{gathered}[/tex]Note that we cross multiplied those ratios, and divided them by 12. Finally, to get rid of the fraction x/6 we multiplied that by 6 on both sides.
3) Hence, the answer is 6√2
Find the value of that makes m n.
43
m
n
150°
(3x - 15)°
since m and n are || lines :
150°+(3x-15)°=180°(Co-interior angles are supplementary)
[tex]150 + 3x - 15 = 180 \\ 3x + 150 - 15 = 180 \\ 3x + 135 = 180 \\ 3x = 180 - 135 \\ 3x = 45 \\ \frac{3x}{3} = \frac{45}{3} \\ x = 15[/tex]
x=15°
HOPE THIS HELPS
Answer:
x = 15
Step-by-step explanation:
If m and were parallel then
3x - 15 and 150 would be same- side interior angles and sum to 180° , so
3x - 15 + 150 = 180
3x + 135 = 180 ( subtract 135 from both sides )
3x = 45 ( divide both sides by 3 )
x = 15
then for m and m to be parallel , x = 15
using question 1, what is the answer to question 9?
The daily cases parabola peaks at T:
[tex]T=\frac{1}{r}\ln \frac{N_{\infty}-N_0}{N_0}[/tex]r in the first page is:
[tex]r=\frac{\ln 2}{3}[/tex]Given data:
[tex]\begin{gathered} N_{\infty}=3.3M \\ N_0=10 \end{gathered}[/tex]Calculate T with the given data.
[tex]\begin{gathered} T=\frac{1}{\frac{\ln2}{3}}\ln \frac{3.3M-10}{10} \\ \\ T=\frac{3}{\ln2}\ln \frac{3299990}{10} \\ \\ T=\frac{3}{\ln2}\ln 329999 \\ \\ T\approx55 \end{gathered}[/tex]Then, the daily cases peak is at T=55 (approximately)
if f(x)=3x+2, find f(2)
f(x)=3x+2
To fin f(2) replace x by 2 and solve:
f(2) = 3(2)+2 = 6 +2 = 8
Select the correct answer.Rectangle is dilated by a scale factor of 3 with the origin as the center of dilation, resulting in the image . If the slope of is , what is the slope of ?
Hello there. To solve this question, we'll have to remember some properties about finding slopes of lines and dilations.
Given that the rectangle KLMN is dilated by a scale factor of 3 with the origin being the center of the dilation, resulting in the image K'L'M'N', we need to find the slope of K'L' knowing the slope of KL is -3.
We start by drawing the situation:
Just as an example. The rectangle many not pass through the same points, but the center is at the origin, which means it intersects the x and y axis at symmetric points.
Now, remember a dilation is a transformation that stretches every side at once, or in other words, re-scales the entire figure by a factor.
Since this factor is 3, we would have something like the following:
Find the range of allowable values based on the given information. Round to the nearest tenth 49; can vary by 8.1%
49 rounded to the closest tenth; possible 8.1% variation. The range of allowable values to the nearest tenth is 4.
Given that,
We have to find using the information provided, determine the permissible value range. 49 rounded to the closest tenth; possible 8.1% variation.
The range in statistics refers to the distribution of your data between the lowest and greatest value in the distribution.
Measurements of variability provide you with descriptive statistics for summarizing your data set in addition to measures of central tendency.
By deducting the lowest value from the greatest value, the range is computed. A short range indicates low variability in a distribution, whereas a big range denotes significant variability.
We now,
49×8.1%=3.969
The nearest tenth is 4.
Therefore, the range of allowable values to the nearest tenth is 4.
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A bird spots a worm on the ground. The bird is 36 feet above the ground and with a horizontal distance of 45 feet to the worm. What is the angle of the bird's view on the worm? Round your answer to the nearest hundredth.
Let's take a look at the situation:
We know, because of the Pythagorean theorem, that:
[tex]\begin{gathered} d^2=45^2+36^2\rightarrow d=\sqrt[]{45^2+36^2} \\ \rightarrow d=57.63 \end{gathered}[/tex]Thereby, using the law of sines:
[tex]\begin{gathered} \frac{d}{\sin90}=\frac{45}{\sin a} \\ \rightarrow d\sin a=45\sin 90\rightarrow\sin a=\frac{45}{d} \\ \rightarrow a=\arcsin (\frac{45}{57.63}) \\ \rightarrow a=51.34 \end{gathered}[/tex]The angle of the bird's view on the worm is 51.34°
what is the measure of the third angle in right triangle if one angle measures 28 degrees?
In a right triangle, two of the sides meet at 90 degrees
This means that one of its angles is 90 degrees
we have also been told that another angle is 28 degrees
To get the third angle:
The Sum of angles in a triangle is 180 degrees
let the unknown side be represented by y
y + 28 + 90 = 180
y + 118 = 180
y = 180 - 118
y = 62
The third side is 62 degrees
Rocco’s family is planning a reunion. Family members traveling from out of town have two options for airfare and hotels. As shown in the table, the cost of airfare for Option 2 is 0.75 times the cost of airfare for Option 1. For the same total cost, 12 family members can attend the reunion if they choose Option 2. Only 10 family members can attend if they choose Option 1. What is the cost of airfare for Option 1?
Option 1's airfare will set you back $2600.
The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired. See.
We have been given that
For option 1
Airfare = $x
Hotel = $600
For option 2
Airfare = $0.75x
Hotel = $800
Only 10 family members can attend if they choose Option 1.
10x + $600 .........eq 1.
12 family members can attend the reunion if they choose Option 2.
12(0.75)x + $800
9x + $800 ........eq 2.
By using Eq (1) and Eq (2)
10x + $600 = 9x + $800
10x - 9x = $800 - $600
x = $200
Put the value of x in the eq (1)
Then we get 10x + $600
= 10 x 200 + $600
= 2000 + $600
= $2600
Hence , the cost of airfare for Option 1 is $2600.
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Can anyone help me with #18?
Answer:
SubtractSquareSum(add)DivideSquare RootRoundStep-by-step explanation:
The standard deviation of a data set is computed using the formula:
[tex]\sigma = \sqrt{\dfrac{\sum_{i=1}^{n}(x_i - \mu)^{2}}{n}}[/tex]
where [tex]\sigma[/tex] is the standard deviation, [tex]x_i[/tex] are the individual data values, [tex]\mu[/tex] is the mean and [tex]n[/tex] is the number of observations
So we first subtract the mean from each data value
then we square the result
then we sum(add) up all these values
then divide by n
and finally find the square root
The round operation will occur after all the above calculations
Convert 81.3 to a fraction in simplest form
Answer:
813/10
Step-by-step explanation:
convert 81.3 to fraction by shifting the point once then making it over 10 cuz you shifted your point once;then break down to the simplest form
Find the area of the following regular polygons. Round all answers to nearest 10th
Step 1
Draw the regular polygon to find out how many triangles are in it.
We can, therefore, conclude the regular polygon has 5 triangles in it
Step 2
Find the area of 1 triangle
[tex]\begin{gathered} \text{The angle at the center = 360}^o \\ \text{But since they are 5 triangles, each will have an angle of }\frac{360}{5}=72^o \end{gathered}[/tex]Since the two sides of each triangle are radius, then they share the same angle. Hence,
[tex]\begin{gathered} \text{The angle at the base of each triangle is given by} \\ 180=72+x+x \\ 180-72=2x \\ \frac{2x}{2}=\frac{108}{2} \\ x=54^o \end{gathered}[/tex]We can then find the k and y thus
[tex]\begin{gathered} \sin 54=\frac{k}{6} \\ k=\text{ 6sin54} \\ k=\text{ 4.854101966 units} \\ \cos 54=\frac{y}{6} \\ y=6\cos 54 \\ y=3.526711514\text{ units} \\ 2y=7.053423028 \end{gathered}[/tex]The area of one of the triangles is
[tex]\begin{gathered} A=\frac{1}{2}\times base(2y)\times height(k) \\ A=\frac{1}{2}\times7.053423028\times\text{4.854101966} \\ A=17.11901729\text{ units} \end{gathered}[/tex]The area of the 5 triangles will be
[tex]17.11901729\text{ }\times5=85.59508647unit^2[/tex]Hence the area of a regular polygon to the nearest tenth is given as;
[tex]85.6units^2[/tex]A starship is orbiting Milgram, a large moon of the planet Bourbakon. The ship's sensor arraydetects that the temperature on the surface of the moon is -3.8 °F. What is this temperature indegrees Celsius (°C)?Use the given formulas as necessary, and round your answer to the nearest tenth of a degree.
Concept use formula for converting degree Fahrenheit to degree celsius
[tex]\begin{gathered} ^oC\text{ = }\frac{5}{9}^{}(^oF\text{ }-\text{ 32 )} \\ ^oC\text{ = }\frac{5}{9}\text{ ( -3.8 - 32 )} \\ ^oC\text{ = 0.5555556 }\times\text{ (- 35.8 )} \\ ^oC\text{ = -19.888} \\ ^oC\text{ = -19.9} \end{gathered}[/tex]Final answer = - 19.9
The sum of 5 and a number, where n represents the unknown number
Answer:
5+n
Step-by-step explanation:
question didnt specify what was needed so this was the equation
Kathy and Mark Smith believe investing in retirement is critical. Kathy begin investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than mark who begin saving when he was 25 if there total retirement savings equals 1,450,000 how much are Kathy’s and Mark’s investments worth
Kathy’s retirement savings is $11,60,000
Mark’s retirement savings is $2,90,000
Total retirement savings amount is $1,450,000
Kathy’s investment is 4 times more than Mark
Calculation of future value at the end of 6 years:
Particulars Values
Total retirement savings $1450000
Mark investment (times) 1
Number of times kathy's investment is more B3x4 = 4
Total B34 = B3+B4 = 5
Kathy's retirement savings (B2*B4)/B5 = $11,60,000
Mark's retirement savings B7/B4 = $2,90,000
What is investment ?Investing is holding assets with the goal of achieving value over a period of time. Investing requires the sacrifice of some current asset, such as time, money, or effort. The purpose of financial investments is to obtain income from the invested property. Investments typically fall into three main categories: stocks, bonds, and cash. Each group has many different rankings. Here are six types of investments you can consider for long-term growth, and what you should know about each
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A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 10 cm. (Note: Enter a positive value).
The volume of the snowball is decreasing at the rate of 502.56cm/min when the radius is 10 cm.
The volume of a sphere is given by the following equation:[tex]\frac{4\pi r^{3} }{3} ^{}[/tex]
We have to do the implicit differentiation of V in function of t. The are only two variables(V and r). So
[tex]\frac{dv}{dt} = \frac{4\pi }{3} 3r^{2} \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt} = 4\pi r^{2} \frac{dr}{dt}[/tex]
We have to find[tex]\frac{dv}{dt} when[/tex] [tex]\frac{dr}{dt} = - 0.4[/tex] r = 10
[tex]\frac{dv}{dt} = 4\pi (10)^{2} \times -0.4[/tex]
[tex]\frac{dv}{dt} = -502cm/m[/tex]
The negative means that the volume is decreasing.
So the answer is 502.56 cm/min.
What is volume?Volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, cuboid, cone, cylinder or sphere.
Different shapes have different volume. In 3D geometry, we studied various three-dimensionally defined shapes and solids such as cubes, cubes, cylinders, cones, etc. For each of these shapes, we learn to find volume.
The volume of a solid substance is measured in cubic units. For example, if the dimensions are given in meters, the volume is in cubic meters. It is a standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimetre, cubic meter, cubic meter, etc.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line shown in simplest form is 3.
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
The equation of a line in slope intercept form is:
y = mx + b
Where m is the slope and b is the y intercept
The slope of a line is the ratio of rise to run. It is given by:
Slope = rise / run
For the line, using the point (0, -5) and (3, 4), the slope is:
Slope = rise / run
Substituting:
Slope = [4 - (-5)] / (3 - 0) = 9/3 = 3
Slope = 3
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Find the measure of angles 1-7 that lines m and n are parallel and t is transversalm<1 =
First, from the diagram and the fact that lines m and n are parallel we get that:
1)
[tex]39^{\circ}+\measuredangle1=180^{\circ}.[/tex]Therefore:
[tex]\measuredangle1=180^{\circ}-39^{\circ}=141^{\circ}.[/tex]2) Angles 1 and 3 are opposed by the vertex, and the same occurs for angles 5 and 7, 4 and 6, and the angle of measure 39 degrees and 2, therefore:
[tex]\begin{gathered} \measuredangle1=\measuredangle3\text{ }\Rightarrow\measuredangle3=141^{\circ}, \\ \measuredangle2=39^{\circ}, \\ \measuredangle5=\measuredangle7, \\ \measuredangle4=\measuredangle6. \end{gathered}[/tex]3) Angles 3 and 5 are alternate interior angles, and the same occurs for angles 2 and 4, therefore:
[tex]\begin{gathered} \measuredangle5=\measuredangle3=141^{\circ}, \\ \measuredangle4=\measuredangle2=39^{\circ}. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} \measuredangle1=141^{\circ}, \\ \measuredangle2=39^{\circ}, \\ \measuredangle3=141^{\circ}, \\ \measuredangle4=39^{\circ}, \\ \measuredangle5=141^{\circ}, \\ \measuredangle6=39^{\circ}, \\ \measuredangle7=141^{\circ}. \end{gathered}[/tex]Ms. Frank made some costumes. The table shows the fabric she used. Color of Fabric Blue Gold Red Amount of Fabric (in yards) LOLO 3 4. moo Part A Did she use more blue fabric or red fabric? Use a number line and words to prove your answer.
Hence, she used more blue fabric
B)
[tex]\text{Amount of Gold fabric = }\frac{3}{4}=\frac{3\times2}{4\times2}=\frac{6}{8}[/tex]Therefore,
[tex]\text{Amount of Gold fabric = }\frac{6}{8}>\frac{3}{8}=Amount\text{ of Red fabric}[/tex]That is
[tex]\text{Amount of Gold fabric > Amount of Red fabric}[/tex]C)
Hence,
the equivalent fractions are:
[tex]\begin{gathered} \frac{1}{4}=\frac{2}{8} \\ \frac{2}{4}=\frac{4}{8} \\ \frac{3}{4}=\frac{6}{8} \\ \end{gathered}[/tex]InstructionsChoose the best answer. If necessary, use the paper you were given.QuestionHow many cubical blocks, each with edges of length 2 centimeters, are needed to fill a rectangular box thathas inside dimensions 10 centimeters by 12 centimeters by 16 centimeters?O 240480O 960O 1.920
Since the dimensions of the rectangular box are 10 cm, 12 cm, 16, cm
Since the length of the cubical block is 2 cm
Then we need to see how many lengths of the cube can be put on each dimension of the rectangular box
[tex]\begin{gathered} L\rightarrow\frac{10}{2}=5 \\ W\rightarrow\frac{12}{2}=6 \\ H\rightarrow\frac{16}{2}=8 \end{gathered}[/tex]Then we can feet 5 cubs on the length and 6 cubes on the width and 8 cubes on the height
The total number of cubes will be the product of them
[tex]\begin{gathered} N=5\times6\times8 \\ N=240 \end{gathered}[/tex]We can fit 240 cubical blocks in the rectangular box
The answer is A
Find a polynomial function that has zeros of -3 and +6
Answer
P(x) = x² - 3x - 18
Explanation
We are asked to find the polynomial function which has zeros -3 and +6.
x = -3 and x = 6
(x + 3) (x - 6) = 0
x (x - 6) + 3 (x - 6) = 0
x² - 6x + 3x - 18 = 0
x² - 3x - 18 = 0
Hope this Helps!!!
the equation of line v is y= 9/2x + 5. line w is perpendicular to v. What is the slope of line w? Simplify your answer
Answer:
-9/2x
Step-by-step explanation:
if its perpendicular to it then you just add a negative sign
The black line is the graph of y= x. Which of theseequations could represent the blue line?yty = 0.001xy = 2xy = -xy = 1/2x
lets discard the other options:
- for y=2x: the slope of this line is greater than the slope of the black line, so it would be more steep, but the blue line is not, so this is not the answer.
-for y=-x: by seeing the picture we see that the slope of the blue line has the same sign of the black one, so it discard this option.
Solve the equation. 5x – 2 (2x + 6) = 15
ANSWER:
The value of x is 27
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]5x-2\cdot(2x+6)=15[/tex]solving for x:
[tex]\begin{gathered} 5x-4x-12=15 \\ x=15+12 \\ x=27 \end{gathered}[/tex]Find (f • g) (0) when f(x) = 4x + 7 and g(x) = 1/x.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Given\text{ that:} \\ (f\text{ o g \rparen \lparen x \rparen = f\lparen g\lparen x\rparen\rparen} \\ But\text{ g\lparen x\rparen = }\frac{1}{x} \\ Then,\text{ we have that:} \\ f(\frac{1}{x}) \\ But\text{ f\lparen x\rparen = 4 x + 7} \\ Then\text{ f\lparen}\frac{1}{x})\text{ = 4\lparen}\frac{1}{x})\text{ + 7}_ \\ This\text{ means that: } \end{gathered}[/tex][tex]\begin{gathered} (f\text{ o g\rparen \lparen x\rparen = f\lparen g\lparen x\rparen \rparen = f\lparen}\frac{1}{x})\text{ =4\lparen}\frac{1}{x}\text{ \rparen + 7} \\ Then,\text{ we have that:} \\ (f\text{ o g \rparen \lparen 0 \rparen = 4 \lparen}\frac{1}{0})\text{ + 7 = undefined \lparen OPTION A \rparen} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]undefined\text{ \lparen OPTION A \rparen}[/tex]At a store, a hat has a regular price of x dollars. During a sale, the price of the hat is discounted by 20%.
The final discounted price of the hat can be calculated by subtracting the discount from the regular price, like this:
discounted price = regular price - discount
By calling x to the regular price, we can rewrite the equation to get:
discounted price = x - discount
The discount, is calculated by multiplying the regular price by the discount percentage, in this case, a 20% (0.2) discount is applied, then we can rewrite the above equation to get:
discount price = x - 0.2x
Then, option D x - 0.2x describes the discount price
