What additional piece of information is needed to show that ABC ≅ XYZ by AAS?
There are two triangles, triangle ABC and triangle XYZ. Side BC is congruent to side YZ and angle ABC is congruent to angle XYZ.
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There are several congruence criteria between triangles. The case of your figure, the congruence must be given by the equality of the sides BC and ZY.
If we have an equal side on both sides, we need 2 angles at the end of that segment to be equal to each other. Your exercise shows that angle B and angle Y are equal.
So for them to be congruent, the angle C and the Z need to be equal.
Then the answer would be the letter C.
The first thing we have to do is identify all the angles, as shown in the figure. Triangles also show lines in yellow (single and double) in both triangles and this notation means that those sides are the same length. In other words, both triangles are isoceles.
What information can we get:
- By opposite vertices we know that R1 = R2=R
- The angles of the isosceles triangles are equal at their ends, that is: P=Q and S=R2=R
We also know that the internal sum of the angles of the triangles gives 180º. This gives us 2 more equations
[tex]\begin{gathered} S+R+44º=180º \\ Q+R+P=180º \end{gathered}[/tex]We replace the equalities taken from the isosceles triangles
[tex]\begin{gathered} S+S+44º=180º \\ 2S=180º-44º \\ S=\frac{136º}{2} \\ S=68º=R \\ P+S+P=180º \\ 2P+68º=180º \\ P=\frac{112º}{2} \\ P=56º=Q \end{gathered}[/tex]
Related Questions
PLEASE HELP ME IM SO DESPERATE
Answers
Two linear functions with point (1,4) are given by:
y = 2x + 2.y = -2x + 6.The graph with these two functions is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).A line with slope of 2 is given by:
y = 2x + b.
Supposing that it goes through point (1,4), when x = 1, y = 4, hence we can find the intercept as follows:
4 = 2 + b
b = 2.
Hence the first equation is:
y = 2x + 2.
A line with slope of -2 is given by:
y = -2x + b.
Then the intercept is found as follows, supposing that it also goes through the point (1,4):
4 = -2 + b
b = 6.
Then the equation is:
y = -2x + 6.
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I need help solving number 4 I have a test tomorrow and this is a review
Answers
We will have the following:
Right away we can see that if we are to plug in x = 35 in one of the expressions, the only one that would give as solution y = 1 is the solution; thus, the solution is the function:
[tex]y=\frac{1}{35}x[/tex]Jevonte is saving money. Jevonte started with $21 and added $17.50 every week. Find the rate of change.
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The rate of change is $17.5 per week.
A rate in mathematics is the comparison of two related values expressed in different units.
The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable). When viewed broadly, a rate (or ratio) can be conceived of as an output-input ratio or a benefit-cost ratio. For instance, in the transportation industry, miles per hour is the output (or benefit) in terms of miles of travel that one receives from travelling for one hour (a cost in time) (at this velocity).Jevonte adds $17.50 every week. so the rate of change in his account each week is 17.5 dollars.
Therefore the rate of change is 17.5 dollars per week.
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Colby put $100 in a savings account. The graph below shows how the amount in the
account would increase over the next ten years. y=mx
a) Write the equation of the line.
b) What does the y-intercept represent?
c) Interpret the slope.
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Find the slope of the line that goes through the given points.
(-8, 7), (-8, 6)
Group of answer choices
16
0
- (16/13)
Answers
Answer:
0 or undefined
Step-by-step explanation:
Hey! Let's help you with your question here!
So, you're trying to find the slope of a line that goes through two given points. To recall, we're trying to find m from the slope-intercept form ([tex]y=mx+b[/tex]). Now we have two points, so is it possible to find the slope given that? Yes! It is! And that is using the slope between two points! Here's how it works:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
This is the formula! Essentially, we'll be able to figure out the slope based on two points in just plugging in the x and y coordinates into the formula. So it becomes:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{6-7}{-8-(-8)}[/tex]
[tex]m=\frac{-1}{0}[/tex]
Now, a problem arises here. While the numerator does give us a value of -1, the denominator ends up being a value of 0. We cannot divide anything by 0 because there's nothing to divide -1 into. In this case, the slope of this line would be classified as undefined. However, in the case of your answer choices, if we were to plot the points on the graph, you'll notice that it's a vertical straight line. So the slope would technically 0.
solve for the variable X: X+7=-4 someone pls help what even is this
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The equation to solve is:
[tex]X+7=-4[/tex]We need to solve for the variable X, which means to take X to one side and numbers to another.
In solving equations, remember this golden rule.
Side Change = Sign Change
Now, looking at the equation, we can keep X on the left hand side and take "+7" to the right hand side. So we are changing sides of "+7" so taking it to the right hand side, it becomes "-7", so:
[tex]\begin{gathered} X+7=-4 \\ X=-4-7 \end{gathered}[/tex]We know
-4 -7 = -11
Thus,
[tex]\begin{gathered} X=-4-7 \\ X=-11 \end{gathered}[/tex]The variable X is -11
A) What do you know for sure about a number with the following clues:
part of the expanded form includes 3 × 105
the expanded form includes only three powers of 10
the expanded form includes 103
B) When a number is given to you in expanded form using powers of 10, what do you know about the number?
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Answer:
hi iiiiiii8888888888iiiiii55
I am trying to do 0.03 squared but my calculator is giving me the answer 9E-4 what does this mean
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Answer:
[tex]0.03^2=0.0009\text{ or 9}\times10^{-4}[/tex]Step-by-step explanation:
The E on the calculator means ''times ten to the power of''
Therefore, 0.03 square would be 9 times ten to the power of -4. That means:
[tex]0.03^2=0.0009\text{ or 9}\times10^{-4}[/tex]What’s the range of grades on the fifth exam that results in earning a B is _. If the highest grade is 100 then _ .
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Let x be the grade of the last exam, then the average is:
[tex]\frac{71+76+88+92+x}{5}=\frac{x+327}{5}[/tex]now, to get a B we need this to be greater or equal than 80 and less than 90, that is:
[tex]80\leq\frac{x+327}{5}<90[/tex]Solving for x we have:
[tex]\begin{gathered} 80\leq\frac{x+327}{5}<90 \\ 5\cdot80\leq x+327<5\cdot90 \\ 400\leq x+327<450 \\ 400-327\leq x<450-327 \\ 73\leq x<123 \end{gathered}[/tex]Therefore the range of grades on the fifth exam that results in earnings a B is
[tex]73\leq x<123[/tex]If the highest grade is 100, then
[tex]73\leq x\leq100[/tex]Answer:
73-100
Step-by-step explanation:
Steve has a pretty lenient grading system! (Usually 85-93 is a B.)
He needs at LEAST an 80 , so the average of his five scores must meet this
(71+76+88+92+x) / 5 = 80
solve for x = 73
If he scores less than a 90 average , he will still get a B
(71+ 76 + 88+92 +x) / 5 < 90 shows x < 123 ( which he cannot score)
so the range of scores on fifth test to get a final grade B is 73 - 100 .
Find the distance between the two points shown below. Round your answer to 2 decimal places.
A- (-4,-3)
B- (0,0)
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The distance between the two points A- (-4,-3) and as B- (0,0) shown in the question is 5 units.
What is Distance ?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
The distance formula in coordinate geometry is used to calculate the distance between two given points. The distance formula to calculate the distance between two points (x1,y1) ( x1 , y1 ) , and (x2,y2) ( x2 , y2 ) is given as, D=√(x2−x1)²+(y2−y1)².
We have given the coordinates which is A- (-4,-3) and B- (0,0).
Now, we will determine the distance between these points,
Distance (d) = √(x2−x1)² + (y2−y1)²
(x1, y1) = Coordinates of the first point
(x2, y2) = Coordinates of the second point
Distance = √{0-(-4)}² + {0-(-3)}²
= √16 + 9 = √25
= 5
Hence the distance between the points AB is 5 units.
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2x + 8 = 6 need help
Answers
The given expression is
[tex]2x+8=6[/tex]First, we subtract 8 from each side
[tex]\begin{gathered} 2x+8-8=6-8 \\ 2x=-2 \end{gathered}[/tex]Then, we divide the equation by 2.
[tex]\begin{gathered} \frac{2x}{2}=-\frac{2}{2} \\ x=-1 \end{gathered}[/tex]Hence, the solution is x = -1.Answer:
x=-1
Step-by-step explanation:
2x+8=6
-8. -8
2x=-2
/2. /2
X=-1
You spend 25$ on supplies to make cookies abd plan to sell them for 0.75$ each ehat numbers of cookies can you sell in order to make profit
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34 cookies must be sold to make a profit .
Profit is defined as the difference between an economic entity's revenue from its products and the financial costs of its inputs.
It is the total of all revenues less all outlays, which includes both outlays that are explicit and those that are not. Because it only refers to costs that are expressly listed on a company's financial accounts, it differs from accounting profit. Accounting profit is determined by deducting all explicit expenditures from the company's total revenue. An economist considers both apparent and implicit economic costs while analyzing a firm. Therefore, economic profit is lower than accounting profit. Economic theory states that a business can only be profitable if its whole revenue is greater than its opportunity cost.let the number of cookies to be sold is x.
Cost of x cookies = 0.75x
Now we know that 0.75x > 25 since the sell price is more than the cost price profit is made.
Now solving the inequality:
0.75x > 25
or, x > 33.33
Therefore the number of cookies needed to be sold is 34 .
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There are two bags containing only purple and white marbles.Bag A has 6 purple marbles and 4 white marbles.Bag B has 8 purple marbles and 8 white marbles.A marble is randomly chosen from each bag.List these events from least likely to most likely.Event 1: choosing a red marble from Bag A.Event 2: choosing a purple marble from Bag A.Event 3: choosing a white marble from Bag B.Event 4: choosing a purple or white marble from Bag B.Least likelyMost likelyEvent (1)EventEvent |Event
Answers
Given:
There are two bags containing only purple and white marbles.
Bag A has 6 purple marbles and 4 white marbles.
so, the probability of choosing purple = 0.6
and the probability of choosing white = 0.4
And Bag B has 8 purple marbles and 8 white marbles.
So, the probability of choosing purple = 0.5
And the probability of choosing white = 0.5
Now, we will find the probability of the following events:
Event 1: choosing a red marble from Bag A.
There are no red colors in the bags
So, the probability will be = 0
Event 2: choosing a purple marble from Bag A.
the probability of choosing purple = 0.6
Event 3: choosing a white marble from Bag B.
the probability of choosing white = 0.5
Event 4: Choose a purple or white marble from Bag B.
So, all the marbles are purple or white
so, the probability = 1
So, the events from least likely to most likely will be as follows:
Event 1
Event 3
Event 2
Event 4
2) During the month of January, the depth, d, of snow in inches at the base of one ski resortcould be approximated by d = -2t + 69, where t is the number of days since December31st. Graph the equation and use the graph to estimate the depth of snow on January 24th.
Answers
To find the depth of snow on january we need to calculate the number of days since december 31st, which will be equal to 24, this value will be used on t. We have:
[tex]d=-2\cdot24+69=-48+69=21[/tex]To graph the line we need another point. We can use december 31st as our second point, since t is the number of days since december 31st than for this t will be equal to 0.
[tex]d=-2\cdot0+69=69[/tex]Now we can graph the equation.
A single, six sided die is rolled. Find the probability of rolling an odd number or a number less than 4
Answers
SOLUTION
The odd numbers in a six sided die are 1, 3 and 5. That is 3 numbers
The numbers less than four are 1, 2 and 3. That is 3 numbers
The probability of rolling an odd number becomes
[tex]\begin{gathered} Pr(odd)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Probability of rolling a number less than 4 becomes
[tex]\begin{gathered} Pr(less\text{ than 4\rparen = }\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Now looking at the odd numbers and the numbers less 4, we have
1, 3, 5 and 1, 2, 3. So between these numbers are 1 and 3. which is 2. Probability of this is
[tex]\begin{gathered} =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]Hence the probability of rolling an odd number or a number less than 4 becomes
[tex]\begin{gathered} \frac{1}{2}+\frac{1}{2}-\frac{1}{3} \\ \frac{3+3-2}{6} \\ =\frac{4}{6} \\ =\frac{2}{3} \end{gathered}[/tex]Hence the answer is 2/3
write an equation of the line in slope intercept form given the following information: slope: 3, through (2, 5)
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we already have the slope so in this case we can use the equation of the slope and replace its values, ane coordinate (2,5) and replace x=0 so:
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ 3=\frac{y-5}{0-2} \end{gathered}[/tex]and we solve for y so:
[tex]\begin{gathered} -2\cdot3=y-5 \\ -6+5=y \\ -1=y \end{gathered}[/tex]So the equation is:
[tex]y=3x-1[/tex]which graph shows the line that has x-intercept -2 and y-intercept 4
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You have to determine which graph shows a line with x-intercept -2 and y-intercept 4
The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is zero. So the x-intercept must have coordinates (-2,0)
The y-intercept is the point where the line crosses the y-axis, at this point the x-coordinate is zero. So the y-intercept of the line we have to identify has coordinates (0,4)
You have to determine the x and y-intercepts of each line graphed and compared with the given coordinates.
Assuming each dot corresponds to one unit:
Graph A
The line crosses the x-axis at point (2,0) and the y-axis at point (0,-4)
→ The x-intercept and y-intercept of this line do not correspond to the line we are looking for.
Graph B
The line crosses the x-axis at point (2,0) and the y-axis at point (0,4)
→ The x-intercept and y-intercept of this line do not correspond to the line we are looking for.
Graph C
The line crosses the x-axis at point (-2,0) and the y-axis at point (0,-4)
→ The x-intercept and y-intercept of this line do not correspond to the line we are looking for.
Graph D
The line crosses the x-axis at point (-2,0) and the y-axis at point (0,4)
→ The x-intercept and y-intercept of this line correspond to the line we are looking for.
So the line that has x-intercept -2 and y-intercept 4 is the one in graph D
Find the measure of an angle in a regular polygon with 28 sides.
Answers
The internal angle of a regular polygon with n sides is found as follows:
[tex]\frac{(n-2)\cdot180}{n}[/tex]Replacing with n = 28:
[tex]\frac{(28-2)\cdot180}{28}=167[/tex]167 degrees
A store buys 15 sweaters for $165 and sells them for $405. If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, write a proportional equation for p in terms of s that matches the context.
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A proportional equation for p in terms of s that matches the context is p = 16s.
How to write a proportional equation?Mathematically, a proportional equation can be represented by the following equation:
y = kx
For this exercise, we would have:
Let the total profit be represented by p.Let the number of sweaters be represented by s.Next, we would determine the cost price and sales price per sweater as follows:
Cost price = $165/15
Cost price = $11.
Sales price = $405/15
Sales price = $27
Therefore, an equation for the total profit is given by:
Total profit, p = Cost price - Sales price
Total profit, p = 27s - 11s
Total profit, p = 16s
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A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $69. A season ski pass costs $300. The skier would have to rent skis with either pass for $20 per day. How many
days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
The skier would have to go skiing days.
(Type a whole number.)
Answers
Answer:
3
Step-by-step explanation:
69+20= 89
89 X 3= 267
17. The table shows the record high and
record low temperatures for certain U.S.
states. Which state in the list had the
greatest variation in temperature? the
least?
Utah, nevada
State
Alaska
Idaho
Nevada
Utah
Record High
Temperature (°F)
100
118
125
117
Record Low
Temperature (
-80
-60
-50
-69
Answers
The highest variation in the temperature if found for Utah.
What is defined as the temperature variation?Temperature is the degree to which an object is hot or cold.In weather forecasting, daily temperature variation refers to the difference between a high and a low air temperature on the same day.There are many factors that contribute to temperature variations in the atmosphere. Temperature fluctuations are caused by four natural factors: latitude, altitude, location from the sea, as well as ocean currents.For the given question;
The maximum and minimum temperatures of the U.S states are given;
The variation in temperature is found by;
Temperature variation = Maximum temperature - Minimum temperature
Alaska = 100 - (-80) = 180
Idaho = 118 - (- 60) = 160
Nevada = 125 - (-50) = 175
Utah = 117 - (-69) = 186
Thus, the highest variation in the temperature if found for Utah.
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How many different ways can a senior project manager and an associate project manager and a technician be selected for an analytics project if there are eleven data scientists available?
Answers
The number of different ways that a senior project manager and an associate project manager and a technician can be selected for an analytics project if there are eleven data scientists available is; 990 ways
How to carry out Permutations?
When we pick a particular set of objects in order, it means that we are constructing a permutation. The number of permutations that can be constructed in this way is defined as the product of the number of ways that each object in the given set can be selected.
The formula for permutation is;
P(n,r) = n!/(n-r)!
Thus, different ways can a senior project manager and an associate project manager and a technician be selected for an analytics project if there are eleven data scientists available is;
P(11, 3) = 11!/(11 - 3)!
= 990 ways
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Write the quadratic function in standard form. f(x) = −2x2 − 8x f(x) = Give the vertex. (x, y) = Find the intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =
Answers
Answer:
[tex]f\mleft(x\mright)=-2\left(x+2\right)+8[/tex][tex]\begin{gathered} x-\text{ intercept: \lparen-4,0\rparen \lparen0,0\rparen} \\ y-intercept:\text{ \lparen0,0\rparen} \\ \text{ Vertex: \lparen-2,8\rparen} \end{gathered}[/tex]Step-by-step explanation:
The quadratic function in standard form is represented as:
[tex]ax^2+bx+c=0[/tex]Therefore, for the given function:
If the vertex is (-2,8) the equation would be represented as;
[tex]\begin{gathered} f(x)=a(x+2)^2+8 \\ \text{ Use one of the given points on the graph:} \\ x-\text{ intercept: \lparen-4,0\rparen \lparen0,0\rparen} \\ y-intercept:\text{ \lparen0,0\rparen} \end{gathered}[/tex][tex]\begin{gathered} 0=a(-4+2)^2+8 \\ 0=4a+8 \\ 4a=-8 \\ a=-\frac{8}{4}=-2 \end{gathered}[/tex]Hence, the function of the quadratic in standard form is represented as:
[tex]f\mleft(x\mright)=-2\left(x+2\right)+8[/tex]Please help me with this
Answers
The two triangles are congruent and it is by the HL rule because the triangles have the same hypotenuse and leg. Therefore, the correct option is HL.
What are congruent triangles?When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
In simpler terms, when two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
There are techniques used to ascertain if triangles are congruent.
For example SSS, SAS, ASA, AAS, and HL
where
S = sideA = anglesHL is only applicable to right triangles.
where
Hypotenuse sideLeg of the right triangleTherefore, the triangles are congruent by HL because it has the same length of the hypotenuse and the same length for one of the other two legs.
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how do you solve for x in the following problem... 23 + 6x = 29
Answers
The expression we have to solve for x is:
[tex]23+6x=29[/tex]In any given equation, to solve for a variables we need to leave that variable alone in one side of the equation.
In this case we need to get rid of the 23 that is besides the 6x on the left side.
For that:
Step 1. Substract 23 from both sides of the equation:
[tex]23-23+6x=29-23[/tex]23-23 in the left side cancel each other. And we are left with:
[tex]6x=29-23[/tex]since 29-23 is equal to 6:
[tex]6x=6[/tex]Step 2. Divide both sides of the equation by 6:
[tex]\frac{6x}{6}=\frac{6}{6}[/tex]and since 6/6=1 we are left with the following result:
[tex]\begin{gathered} x=\frac{6}{6} \\ \\ x=1 \end{gathered}[/tex]Answer: x = 1
The Brady family received 31 pieces of mail on January 28. The mail consisted of bills,letters, and magazines. How many bills did they receive if they received three more letters than ads, the same number of bills as ads, and five more magazines than letters.
Answers
The Solution.
Let the number of ads be = x
Number of Letters = x+3
Number of bills = x
Number of magazines = x+3+5 = x+8
Given that the total number of mail is 31, we have
[tex]x+x+3+x+x+8=31[/tex]Collecting the like terms, we get
[tex]\begin{gathered} x+x+x+x+11=31 \\ 4x=31-11 \\ 4x=20 \\ \text{Dividing both sides by 4, we get} \\ x=\frac{20}{4}=5 \end{gathered}[/tex]So, the number of bills they received is 5.
Hence, the correct answer is 5 bills.
What number is the opposite of 2.6?A. -2.6B. 6.2C. 26D. -6.2
Answers
Explanation
The opposite of a number is a number that is the same distance from 0 as another number,but in the opposite direction
they have the same value, but in opposite directions,hence the opposite of a positive number is its negative value.
then
[tex]\begin{gathered} 2.6 \\ 2.6\text{ is a positive number, so} \\ \text{its opposite is} \\ A)-2.6 \end{gathered}[/tex]so, the answer is
[tex]A)-2.6[/tex]I hope this helsp you
Solve for t in the formula above to obtain a formula expressing tas a function of V.V= 14.5 – 1.3t t=
Answers
Given the equation:
[tex]V=14.5-1.3t[/tex]We want to make t the subject of formula;
firstly, let us subtract 14.5 from both sides.
[tex]\begin{gathered} V=14.5-1.3t \\ V-14.5=14.5-14.5-1.3t \\ V-14.5=-1.3t \\ -1.3t=V-14.5 \end{gathered}[/tex]Then let's divide both sides by -1.3;
[tex]\begin{gathered} \frac{-1.3t}{-1.3}=\frac{V-14.5}{-1.3} \\ t=\frac{-V+14.5}{1.3} \end{gathered}[/tex]Expres
The length of the banner is 3 times its width. The area of the whole banner is 75 square feet. What is the banner’s width and length in feet?
Answers
times this number 5x3 15 then this 3x70 you get this 210 add them up 225feet
2. Which expression is equivalent to 15,314? A 806 x 19-13,314 B 807x19= 15,333 C 808 x 18 =147544 D 809 181450
Answers
ANSWER
[tex]B)4\frac{1}{8}\text{ cups}[/tex]EXPLANATION
We have that two ingredients are mixed to make a sauce.
The sauce contains 1/2 cup of chopped onions and 3 5/8 cups of crushed tomatoes.
To find the total number of cups of ingredients the sauce contains, we have to add the two fractions of ingredients.
That is:
[tex]\begin{gathered} \frac{1}{2}+3\frac{5}{8} \\ =3+\frac{1}{2}+\frac{5}{8} \\ =3+\frac{9}{8}=3+1\frac{1}{8} \\ =4\frac{1}{8}\text{ cups} \end{gathered}[/tex]The answer is option B.
