The following is true about similar triangles DOT and ANG. DO AN OT NG DT AG 3 3 1 Which could be the length of DT and AG?
Answers
Answer:
DT=6 and AG=2
C
Explanation:
Given that the Triangle DOT and ANG are similar.
The ratio of their corresponding sides will be equal;
[tex]\frac{DO}{AN}=\frac{OT}{NG}=\frac{DT}{AG}=\frac{3}{1}[/tex]So, according to the given ratio, the ratio of the corresponding sides of triangle DOT to ANG is equal to 3/1.
From the given options, the correct option is the one whose ratio is equal to 3/1;
[tex]\frac{DT}{AG}=\frac{3}{1}[/tex][tex]\begin{gathered} A\text{.} \\ \frac{9}{6}\ne\frac{3}{1} \end{gathered}[/tex][tex]\begin{gathered} B\text{.} \\ \frac{6}{4}\ne\frac{3}{1} \end{gathered}[/tex][tex]\begin{gathered} C\text{.} \\ \frac{6}{2}=\frac{3}{1} \end{gathered}[/tex][tex]\begin{gathered} D\text{.} \\ \frac{9}{4}\ne\frac{3}{1} \end{gathered}[/tex]Therefore, the only option whose ratio of side DT to AG is equal to 3/1 is C;
DT=6 and AG=2
Related Questions
which expression went to be easier to simplify if you used a communicative property to change the order of the numbers?
Answers
The communicative property is :
[tex]a+b=b+a[/tex]So, we will check the options to show which expression will be easier if we used communicative property
A.
[tex]\frac{1}{7}+(-1)+\frac{2}{7}=\frac{1}{7}+\frac{2}{7}+(-1)=\frac{3}{7}-1=-\frac{4}{7}[/tex]As we can see at option A it is easy to add the fractions first then subtract 1
The other options can be done without making communicative property
So, the answer is option A
find the slope that passes throught the pair of points (4,4),(8,-2)
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The slope between two points is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then:
[tex]\begin{gathered} m=\frac{-2-4}{8-4} \\ =-\frac{6}{6} \\ =-1 \end{gathered}[/tex]Therefore, the slope between the points is -1.
A parallelogram is……..a rectangle AlwaysSometimesNever
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We have the following kind of parallelograms:
And in the case where A and B are equal, we have a parallelogram that is a rectangle. But for any other combination of A and B, it will not be a rectangle.
From the solution developed above, we are able to conclude that the solution for the present question is:
A parallelogram is SOMETIMES a rectangle
The gravitational attraction betweentwo bodies varies inversely as thesquare of the distance between them.If the force of attraction is 64 poundswhen the distance between the bodiesis 9 feet, what is the distance betweenthem when the force is 36 pounds?
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The force for the case 1 is 64 pounds and the distance is 9 feet, it is:
[tex]\begin{gathered} \frac{k}{9^2}=64 \\ k=5184 \end{gathered}[/tex]Now, if the force is 36 pounds, let solve for the distance:
[tex]\begin{gathered} \frac{k}{r^2}=36 \\ \frac{5184}{r^2}=36 \\ r^2=144 \\ r=12 \end{gathered}[/tex]Hence the answer is 12 feet.
Solve for n and p by using substation 6n +2p =-3 and 4n + 2p= -1
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Let's subtract the equations. To do this let's multiply by (-) the second equation and sum:
[tex]\begin{gathered} +6n+2p=-3 \\ -4n-2p=+1 \\ -------- \\ +2n+0p=-2 \end{gathered}[/tex]Now simplify
[tex]\begin{gathered} 2n=-2 \\ n=\frac{-2}{2} \\ n=-1 \end{gathered}[/tex]Now replacing the n value in the first equation
[tex]\begin{gathered} 6(1)+2p=-3 \\ 6+2p=-3 \end{gathered}[/tex]Solving for p
[tex]\begin{gathered} 2p=-3-6 \\ p=-\frac{9}{2} \end{gathered}[/tex]Answer: n=-1 and p=-9/2
Factor out the GCF from the polynomial. 32xy – 18x?
Answers
To factorize 32xy - 18x :
The GCF is 2x
The answer is 2x( 16y - 9)
find the indicated sum for each geometric series.Pleaseee someone help I need this before 10 pm. I tried to do it but I keep failing.
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We will have that it is solved as follows:
[tex]\sum ^9_{k=1}256(\frac{1}{2})^{k-1}=256+128+64+32+16+8+4+2+1=511[/tex]***
To solve we replace the values in the formula given:
[tex]S_n=a_1(\frac{1-r^n}{1-r})[/tex]Now, we have to determine the ratio, which is 1/2, and since we want to know the value at n = 9 and the fist value of the series (a1) is 256, we replace it as well:
[tex]S_9=256(\frac{1-(\frac{1}{2})^9}{1-\frac{1}{2}})\Rightarrow S_n=511[/tex]PLS ANSWER IF YOU ACTUALLY KNOW THE ANSWER its a select all that apply
Answers
-The weight of an object cannot be represented by a negative number since it represents the mass of an object and by definition, mass cannot be negative.
-The ocean depth is measured with respect to the sea level. The sea level is considered the point of elevation/depth zero. Any distance below sea level (depth) can be expressed as a negative number, so the ocean depth of 100feet can be expressed as an "elevation of -100ft", the negative number indicates that the measure is below sea level.
-Temperatures can be expressed as negative numbers if they are below 0ºC (cold temperatures)
-The elevation above sea level indicates that it is above 0ft, by definition any number greater than zero is positive so an elevation of 30ft cannot be expressed as a negative number.
-A debt of $60
If you make a balance of debts and earnings, a balance of $0 indicates that there are no debts and there are no earnings.
A balance above $0, indicates that there are earnings, for example, +$60 would represent that you earned sixty dollars.
A balance below $0, indicates that there is a debt, so a balance of "-$60" would indicate that you owe sixty dollars.
-Angles can be expressed as positive or negative values depending on their direction with respect to a point. If the angle rotates in a counter-clockwise direction, it can be expressed as a positive value, for example, 90º
If the angle rotates in a clockwise direction can be expressed as a negative angle, for example, -90º
The situations that can be expressed by a negative number are the ocean depth, the temperature, the debt and the angles
find at least 2 fraction combimations that are equivalent to 2/3
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To find 2 fractions that are equivalent to 2/3, you only need to multiply both the numerator and the denominator by the same numbers.
This way:
[tex]\frac{2}{3}\cdot\frac{4}{4}=\frac{8}{12}[/tex][tex]\frac{2}{3}\cdot\frac{7}{7}=\frac{14}{21}[/tex]In this case, we used 4 and 7 but you can use any number you want.
Answer: 8/12 and 14/21 are 2 fractions combinations that are equivalent to 2/3.
Name the 2 segments that are congruent if it is given [line segment] BD bisects [line segment] YZ at T
Answers
Since BD bisects YZ at T
That means BD intersect YZ at its mid-point, so
T is the mid-point of YZ
Since T is the mid-point of YZ, then
YT = TZ
The congurent segments are YT and TZ
complete the table so that there is a proportional relationship between the number of apples and the weight what is the constant of proportionality write an equation for this situation
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We have to complete the table so that there is a proportional relationship between the number of apples and the weight.
The only complete row we have is 5 apples has a weight of 0.6 kg. So the constant of proportionality is:
[tex]\begin{gathered} \text{We call k the constant of proportionality:} \\ k=\frac{0.6}{5}=0.12\frac{\operatorname{kg}}{apple} \end{gathered}[/tex]Now, we can write the equation for the relationship:
[tex]\begin{gathered} x=\text{number of apples} \\ y=\text{weight in kilograms } \\ y=k\cdot x \\ \text{Note that k is the constant of proportionality} \end{gathered}[/tex]Now, we can complete the table:
[tex]\begin{gathered} \text{For x=}2\text{ apples:} \\ y=0.12\cdot2=0.24\operatorname{kg} \\ \text{For y=}1.44\operatorname{kg}\colon \\ 1.44=0.12\cdot x\Rightarrow x=\frac{1.44}{0.12}=12\text{ apples} \\ For\text{ x=1 apple:} \\ y=0.12\cdot1=0.12\operatorname{kg} \end{gathered}[/tex]The area of the rectangular floor inTamara's room is 95 5/6 square feet. Thewidth of the room is 8 1/3 feet.estimate the length of tamara’s room
Answers
Solution:
Given that;
The area of the rectangular floor in Tamara's room is 95 5/6 square feet, i.e.
[tex]\begin{gathered} A=95\frac{5}{6}\text{ square feet} \\ A=\frac{575}{6}\text{ square feet} \end{gathered}[/tex]The width of the room is 8 1/3 feet, i.e.
[tex]\begin{gathered} w=8\frac{1}{3}\text{ feet} \\ w=\frac{25}{3}\text{ feet} \end{gathered}[/tex]To find the length, l, of the rectangular floor in Tamara's room, we will apply the formula to find the area, A, of a rectangle below,
[tex]\begin{gathered} A=lw \\ Where \\ l\text{ is the length} \\ w\text{ is the width} \end{gathered}[/tex]Substitute the values of the area and width into the formula above, to find the length as shown below
[tex]\begin{gathered} A=lw \\ \frac{575}{6}=l\times\frac{25}{3} \\ \frac{575}{6}=\frac{25l}{3} \\ Crssomultiply \\ 6\times25l=575\times3 \\ l=\frac{575\times3}{6\times25} \\ l=\frac{23}{2}\text{ feet} \\ l=11\frac{1}{2}\text{ feet} \end{gathered}[/tex]Hence, the length of tamara’s room is 11 1/2 feet
How to put -3•2a+5(-7b)+(12•c•4) in standard form
Answers
The standard form of a linear equation is given by:
[tex]Ax+By+Cz=D[/tex]so:
[tex]-3\cdot2a+5(-7b)+(12\cdot c\cdot4)=-6a-35b+48c[/tex]You have 2.5 pounds of egg whites. You need 36 Oz to make one serving of Consomme. How many servings can you make?
Answers
ANSWER
1 serving
EXPLANATION
You have 2.5 pounds of egg whites and you need 36 Oz to make one serving of Consomme.
To find the number of servings that can be made, you need to divide the total weight of egg whites by the weight needed to make one serving.
But before doing that, you need to convert one of the weights so that they have the same unit. Let us convert pounds(lbs) to ounces(Oz).
We have that:
1 pound = 16 ounces
=> 2.5 pounds = 2.5 * 16
2.5 pounds = 40 ounces
Now, divide:
[tex]\frac{40}{36}=1.11\text{ }[/tex]As we can see, 40 ounces can only make 1 serving of Consomme.
You take a picture of a painting at an art gallery. The painting is above eye level, and you frame the painting so the top and bottom match with the top and bottom of your view ſindur. Your camera's auto-focus feature focuses at the height of the angle bisector shown in the diagram. How far from the bottom of the painting is the focus? 92 in. 52 in. Camera's line of focus 68 in.
Answers
Let us first find the complete angle that the camera is making
Recall from the trigonometric ratios
[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]From the figure, we see that the opposite is 52 in and adjacent is 68 in
[tex]\begin{gathered} \tan \theta=\frac{52}{68} \\ \theta=\tan ^{-1}(\frac{52}{68}) \\ \theta=37.405\degree \end{gathered}[/tex]Since the camera's line of focus is the angle bisector then
[tex]\theta=\frac{37.405\degree}{2}=18.7\degree[/tex]So, again using the trigonometric ratio, we can find x
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan (18.7)=\frac{x}{68} \\ x=\tan (18.7)\cdot68 \\ x=0.338\cdot68 \\ x=23.017\: in \end{gathered}[/tex]Therefore, the value of x is 23.017 inches.
The custom-made Purple and Gold Omega Air Force Ones (a type of shoe), were onsale for 35% OFF the original price. The discounted price was $84.99, what was theoriginal price of the shoe? (3 pts)
Answers
ANSWER
$130.75
EXPLANATION
Let x be the original price of the shoe. The discounted price, y, is the original price minus the 35% of the original price,
[tex]y=x-\mleft(x\cdot\frac{35}{100}\mright)[/tex]To simplify for x, divide 35 by 100,
[tex]y=x-x\cdot0.35[/tex]And factor out x,
[tex]y=x(1-0.35)=x\cdot0.65[/tex]We know that the discounted price was $84.99,
[tex]84.99=0.65x[/tex]To find the original price, divide both sides by 0.65,
[tex]x=\frac{84.99}{0.65}\approx130.75[/tex]Hence, the original price of the shoe was $130.75.
which of the relationships below represents a function with a greater slope than function y= -1/4 + 2?
Answers
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For table A we have:
[tex]m=\frac{13-(-3)}{4-0}=\frac{13+3}{4}=\frac{16}{4}=4[/tex]This is greater than -1/4, therefore the answer is A.
The results for all 10 grocery surveys were actually generated using a mathematical simulation, found on the Simulation tab of the spreadsheet. To use it, enter a population mean and population standard deviation in the two yellow cells at the top of worksheet and follow the instructions. Every time a new set of data is generated, the data changes, providing a new sample. You can copy this data and paste it into the histogram tool to analyze it. (You don't have to do that in this activity, but it's there for you to experiment with, if you like.) Any given set of sample data generated in this way would not typically have the same mean, distribution, and standard deviation as the population values, but the simulated sample data would be consistent with a randomly selected sample from such a population. Note that the simulated population mean is 1.73, and the simulated standard deviation is 0.657. Imagine that this random sample survey was simulated an infinite number of times. In that case, the population mean (1) of all the samples would be $1.73. All the sample means would be normally distributed, according to the central limit theorem. Question 1 If the standard deviation of the population is $0.657 (as it is in the simulation), what is the standard error of the mean? Round up your answer to the nearest tenth of a cent.
Answers
The standard error of the mean is given by:
[tex]\frac{\sigma}{\sqrt[]{n}}[/tex]where sigma is the standard deviation and n is the sample size. In this case the sample size is 10 and the standard deviation is 0.657, then the standard error is:
[tex]\frac{0.657}{\sqrt[]{10}}=0.208[/tex]Therefore the standard error is $0.208.
Answer:$0.093
Step-by-step explanation:
The coordinates of the point Q are (-10, – 7) and the coordinates of point Rare(2, – 7). What is the distance, in units, between the point Q and point R?
Answers
The distance between two points (a,b) and (c,d) is given by the formula,
[tex]d=\sqrt[]{(c-a)^2+(d-b)^2}[/tex]Here a = -10, b=-7, c=2, d = -7
Hence, the distance is given by
[tex]\begin{gathered} d=\sqrt[]{(2+10)^2+(-7+7)^2} \\ =\sqrt[]{12^2} \\ =12 \end{gathered}[/tex]Hence the distance is 12.
What is the y coordinate of the ordered pair that identifies the location of Phoenix
Answers
Given data:
The given cartesian plane.
The coordinate of Phoenix is(-8, -8).
Thus, the y-coordinate of Phoenix is -8.
a lap around the track is 1/4 of a mile Cal ran six laps in 5 minutes and 30 seconds what was his average speed in miles per minute
Answers
Given:
Time= 5 minute 30 second
=5.5 minute
Distance= 6 laps
then:
[tex]\begin{gathered} 1\text{ lap=}\frac{1}{4}mile \\ 6\text{ laps=}\frac{6}{4}miles \end{gathered}[/tex]so speed in miles per minute is:
[tex]\text{speed}=\frac{dis\tan ce\text{ }}{time}[/tex]then speed of cal is:
[tex]\begin{gathered} \text{speed}=\frac{\frac{6}{4}}{5.5} \\ =\frac{6}{22} \\ =0.2727 \end{gathered}[/tex]The speed of cal is 0.2727 miles per minute
The domain of the given function in interval notation is ____f(x) = 5x - 9 —————- 5x + 2
Answers
Answer:
[tex](-\infty,-\frac{2}{5})\cup(-\frac{2}{5},\infty)[/tex]Explanation:
Given the function:
[tex]f(x)=\frac{5x-9}{5x+2}[/tex]We are required to find the domain of the given function.
The domain of a rational function are the set of values of x for which the denominator is not equal to 0.
To find the domain of f(x), set the denominator equal to 0 to find the excluded values.
[tex]\begin{gathered} 5x+2=0 \\ 5x=-2 \\ x=-\frac{2}{5} \end{gathered}[/tex]The excluded value in the domain of f(x) is -2/5.
Therefore, the domain of f(x) in interval notation is:
[tex](-\infty,-\frac{2}{5})\cup(-\frac{2}{5},\infty)[/tex]Find the indicated complement . A certain group of women has a 0.28% rate of redgreen color blindnessIf a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Answers
Answer:
99.72%
Explanation:
• Given:, The rate of red/green color blindness = 0.28%
,• To find:, The probability that a randomly selected woman does not have red/green color blindness.
To find the required probability, recall that the sum of the probability of an event and its complement is always 1. That is:
[tex]\begin{gathered} P(A)+P(A^c)=1 \\ \implies P(A^c)=1-P(A) \end{gathered}[/tex]Let A be the event that an individual has red/green color blindness.
[tex]P(A)=0.28\%[/tex]Therefore, the probability that a randomly selected woman does not have red/green color blindness will be:
[tex]P(A^c)=(100-0.28)\%=99.72\%[/tex]The required probability is 99.72%.
O is the center of the regular nonagon below. Find its perimeter. Round to the nearest tenth if necessary.
Answers
Solution:
The circumradius of the polygon is given below as
[tex]R=17[/tex]Concept:
The perimeter of the nonagon will be calculated using the formula below
[tex]\begin{gathered} P=9\times s \\ \text{Where,} \\ s=\text{length of the side} \end{gathered}[/tex]The Length of a side can be calculated using the formula below
[tex]\begin{gathered} s=R\times2\sin (\frac{180}{n}) \\ \text{where,} \\ n=9 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} s=R\times2\sin (\frac{180}{n}) \\ s=17\times2\sin (\frac{180}{9}) \\ s=34\sin 20 \\ \end{gathered}[/tex]Hence,
Substitute the value of s=34sin20 to get the perimeter in the formula below
[tex]\begin{gathered} P=9\times s \\ P=9\times34\sin 20 \\ P=104.658 \\ P\approx\text{nearest tenth} \\ P=104.7 \end{gathered}[/tex]Hence,
The final answer is P =104.7 units
Write the compound statement "If the food is not good, I won't eat too much" in symbols. Then, construct a truth table for the symbolic statement.r = "The food is good"p = "I eat too much"
Answers
We see that the prase is compounded by the negation of r and q (~r and ~q), and with the following structure:
If the food is not good, I won't eat too much
If ~r then ~p
Represented symbolically as:
~r -> ~p
We can build the truth table:
r p ~r ~p ~r->~p
T T F F T
T F F T T
F T T F F
F F T T T
This, recalling that in the conditional (->), the statement is false only when the first part is true and the second false.
Then, the correct answer is option A.
The current (I) in a wire varies directly as the voltage (v) and inversely as the resistance (r). If the current is 27.5 amps when the voltage is 110 volts and the resistance is 4 ohms, find the current when thevoltage is 180 volts and the resistance is 12 ohms. (Round your answer to two decimal places.)
Answers
From the information provided in the question, we have that the current (I) varies directly as the voltage (v). This is written mathematically to be:
[tex]I\propto v[/tex]It is also given that the current varies inversely as the resistance (r). This is written mathematically as:
[tex]I\propto\frac{1}{r}[/tex]Combining both relationships, we have that:
[tex]I\propto\frac{v}{r}[/tex]Applying a constant so that we can have an equation relating all 3 parameters, we have:
[tex]I=\frac{kv}{r}[/tex]If the current is 27.5 amps when the voltage is 110 volts and the resistance is 4 ohms, we have that:
[tex]\begin{gathered} I=27.5 \\ v=110 \\ r=4 \end{gathered}[/tex]Substituting these values into the equation to get the value of the constant, we have:
[tex]\begin{gathered} 27.5=\frac{k\times110}{4} \\ k=\frac{27.5\times4}{110} \\ k=1 \end{gathered}[/tex]Therefore, the equation becomes:
[tex]I=\frac{v}{r}[/tex]When the voltage is 180 volts and the resistance is 12 ohms, we can get the current by making the following substitution into the equation above and solving as follows:
[tex]\begin{gathered} v=180 \\ r=12 \\ \therefore \\ I=\frac{180}{12} \\ I=15 \end{gathered}[/tex]The current is 15.00 amps.
Y=10+5x What is the slope? What is the y intercept?
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1) Considering the function y=10+5x, the slope i.e. the measure of how steep the line can be is the coefficient of x, in this case, m= 5
2) The Y-intercept. i.e. the linear coefficient "b" of the y=mx+b form. In this case, it's number 10. So b=10 the point where the line intercepts the y-axis
What is the area of a circle with a radius of 10.2 feet?
Answers
Area of a circle = π * r^2 = π*(10.2)^2 = 326.85 ft^2
simplify the expression using exponent laws. Use the least number of bases possible and only positive exponents.(4/5)^-6
Answers
What is the Greatest Common Factor (GCF) of the numbers 24 and 40?
Answers
Solution
For this case we can do the following:
24= 8*3= 2*4*3 = 2*2*2*3
40= 20*2 = 2*10*2= 2*2*2*5
And from the descomposition above we can see that the GCF is :
2*2*2
Since represent the common numbers in both descompositions then the answer is:
GCF= 8