Geometry Question: If the median to a side is a triangle is also an altitude to that side, then the triangle is isosceles. (#8 in picture)
Answers
8.
A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. So:
[tex]\begin{gathered} AM\cong MB \\ MC\cong CM_{\text{ }}Reflexive_{\text{ }}property \\ m\angle AMC\cong m\angle BMC_{\text{ }}Perpendicular_{\text{ }}bisector \end{gathered}[/tex]Therefore:
[tex]\Delta AMC\cong\Delta BMC_{\text{ }}SAS_{\text{ }}Theorem[/tex][tex]m\angle CAM\cong\angle CBM_{\text{ }}CPCTC[/tex]We can conclude that:
[tex]\Delta ABC[/tex]Is an isosceles triangle
Related Questions
use the product, quotient, and power rules of logarithms to rewrite the equation as a single logarithm.
Answers
We are given the following expression:
[tex]\log a-3\log b+4\log c[/tex]we are asked to simplify this expression. To do that we will first use the following property:
[tex]a\log b=\log ^{}b^a[/tex]we will apply this to the second and third terms, like this:
[tex]\log a-\log b^3+\log c^4[/tex]Now we will use the following property:
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]we will use this property for the first and second terms:
[tex]\log (\frac{a}{b^3})+\log c^4[/tex]Now we will use the following property:
[tex]\log a+\log b=\log ab[/tex]We will use the property in the last two terms, like this:
[tex]\log (\frac{ac^4}{b^3})[/tex]And thus, we have simplified the logarithmic expression into one single logarithm
An irregular figure is shown on the coordinate plane below. Part A: Find the area of the irregular figure above. Answer:__________________________ square units
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In the present question, we will calculate the area of each of the three regular figures that are parts of the irregular figure. They are:
A: a rectangle 4x3
B: a rectangle 9x3
C: a rectangle 3x5
The area of each rectangle is just the multiplication of the two sides, and the area of the irregular figure is the sum of them. From this, we calculate:
[tex]\begin{gathered} A_A=4\times3=12\text{ square units} \\ A_B=9\times3=27\text{ square units} \\ A_C=3\times5=15\text{ square units} \\ \\ A_{\text{Total}}=A_A+A_B+A_C \\ A_{\text{Total}}=12+27+15=54\text{ square units} \end{gathered}[/tex]From the solution presented above, we are able to conclude that the area of the irregular figure is 54 square units.Clarissa and Koko solve 3x + 5 = 2x + 4 by graphing the related function. Is either of them correct? Explain your reasoning.
Answers
Answer:
clarissa
Step-by-step explanation:
What is the common difference for the arithmetic sequence?
3.2, 5, 6.8, 8.6, 10.4
help me please!
Answers
Answer:
the difference is 1.8
Step-by-step explanation:
5-3.2=1.8
6.8-5=1.8
8.6-6.8=1.8
ect
16 oz harbor peanut butter for 2.49 or a 64 oz jar of peanut butter for 6.99 round everything up to the nearest cent or hundreth. yes mam
Answers
We have to find the "better buy" between two options:
1) 16 oz jar for $2.49
2) 64 oz jar for $6.99
We can compare this two options with the unit price of each one. The unit price will be expressed in "$ per oz" or "$/oz". The option with the smaller unit price is the "better buy".
We can calculate the unit price as teh quotient between the price and the weight of each option.
Unit price for Option 1:
[tex]u_1=\frac{2.49\text{ \$}}{16\text{ oz}}\approx0.16\frac{\$}{oz}_{}[/tex]Unit price for Option 2:
[tex]u_2=\frac{6.99\text{ \$}}{64\text{ oz}}\approx0.11\frac{\$}{oz}[/tex]As the Option 2 (64 oz jar) has a smaller unit price, the better buy is the 64 oz jar for $6.99.
Answer: the better buy is the 64 oz jar for $6.99.
I need help please with [tex]6409 \div 61[/tex]. I know the answer is 105.06the problem is it has to be written as a a whole number with a fraction. we put 105 and 3/50 but its saying it's wrong.
Answers
Given the expression
[tex]\frac{6409}{61}[/tex]Next is to know how many 61 can go in 6409. Using the calculator, you can see that it is 105 with a remainder of 4
We will then have to express the fraction in the form:
[tex]Q\text{ +}\frac{R}{D}[/tex]Q is the quotient = 105
R is the remainder = 4
D is the divisor = 61
Substituting these values into the expression we will have:
[tex]\begin{gathered} \frac{6409}{61}=105+\frac{4}{61} \\ \frac{6409}{61}=105\frac{4}{61} \end{gathered}[/tex]Hence the solution written as a whole number and fraction is 105 4/61
The table shows the rational approximation of several irrational numbers.
Which is the approximate value of √3?
Answers
The approximate value of √3 is 1.732 which is an irrational number.
Given that,
We have to find the value of root3.
√3 is an irrational number.
Real numbers that cannot be represented as a ratio are referred to as irrational numbers. Or to put it another way, irrational numbers are actual numbers that defy logic.
Irrational numbers are real numbers that cannot be represented by a straightforward fraction. These can't be stated as ratios, like p/q, where p and q are both integers, q≠0. In terms of statistics, it defies reason.
The approximate value of √3 is 1.732.
Therefore, The approximate value of √3 is 1.732 which is an irrational number.
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Rides, r Cost, c5 $25.506Use the table shown to answer problems10-11.10. A state fair charges $8 for generaladmission and $3.50 for each ride. Usethe pattern in the table to find the cost of7 rides and 10 rides. Then write anequation for the pattern.11. Find the cost c for 18 rides.$29.0078$36.0010C= 8 + 3.50rUse the operation symbols in the math palette as needed. Type an equation. Use integers or decimals for anynumbers in the equation.)11. Find the cost c for 18 rides.
Answers
We want to know the cost for 7 rides and for 10 rides. We see that for each ride the price increases by $3.50. And thus the price for 7 rides will be:
[tex]29.00+3.50=32.50[/tex]And the price for 10 rides will be:
[tex]36.00+3.50+3.50=39.50+3.50=43.00[/tex]Now, for finding the equation we use that the state fair charges $8 for a general admission, and $3.50 for each ride. This can be written as:
[tex]y=8+3.50x[/tex]where x represents the number of rides.
For example, if we want to know the cost for 18 rides, we replace the value of x by 18, and we get:
[tex]\begin{gathered} y=8+3.50(18) \\ =8+63 \\ =71 \end{gathered}[/tex]Then, the cost for 18 rides is $71.
A bag contains 15 cards numbered 1 through 15. A card is randomly chosen from the bag. What is the probability that the card has an odd number on it? Write your answer as a fraction in simplest form.
Answers
There are 15 cards numbers are from 1 to 15.
From the numbers 1 to 15:
• 8 numbers, are ,odd
,• 7 numbers, are ,even,
The probability is the possibility of an event occuring.
Probability of event to happen P(A) = Number of favourable outcomes/Total Number of outcomes
Thus, the probability of an odd card is:
total number of odd cards/total number of cards
= 8/15
the Correct Answer is:
[tex]\frac{8}{15}[/tex]Estimate the sum or difference, by rounding each number to its largest place (front-end rounding)–36.673+39.999
Answers
Answer:
0
Explanation:
Given the difference:
[tex]-36.673+39.999[/tex]In front-end rounding, we consider the number with the largest place value.
In -36.673, the number with the largest place value is 3.
The digit after 3 us 6, so we round up as follows:
[tex]-36.673\approx-40[/tex]Likewise, In 39.999, the number with the largest place value is 3.
The digit after 3 us 9, so we round up as follows:
[tex]39.999\approx40[/tex]Therefore:
[tex]-36.673+39.999\approx-40+40=0[/tex]The diffrence is 0 using front-end rounding.
Yvette maps out several locations in her town, with distances and angles between them. Two triangles are formed within the map.
To conclude that these triangles are congruent by SAS Congruence Postulate, what must the distance between the school and the park be
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To be both triangles to be congruent the distance between the school and the park be 1.1 miles.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
As per the given two triangles,
The side 2.7 miles is the common side.
The angle is 52 degrees in both triangles same.
To be congruent any one side must be the same by the SAS rule.
Thus, the school-to-park corresponding side is school-to-store.
school to park = 1.1 miles
Hence "To be both triangles to be congruent the distance between the school and the park be 1.1 miles".
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Xavier Knox's annual salary is $61,100. He is paid semimonthly. His personal exemptions total $4,000. How
much does his employer deduct from each of Knox's paychecks for state income tax of 3.5 percent?
a. $166.54
c.
b. $83.27
$83.13
d. $166.26
Answers
The amount that Xavier Knox's employer deducts from his paychecks for state income tax is b. $83.27
How to find the state income tax?First find his taxable income:
= Annual salary - Personal exemptions
= 61, 100 - 4, 000
= $57, 100
The state income tax per year is:
= 57, 100 x 3.5% state income tax rate
= $1, 998.50
The semimonthly state income tax deducted is:
= 1, 998.50 / (12 months x twice a month)
= $83.27
In conclusion, on a semimonthly basis, $83.27 is deducted for state income tax.
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The radius of the front wheel of Terry's bike is 61cm.
Terry goes for a cycle and travels 60.32km.
How many full revolutions did Terry's front wheel complete?
Answers
In linear equation, 157 did Terry's front wheel complete.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Terry goes for a cycle and travels 60.32km.
so, 60.32 * 1000 ÷ ( 2 * 3.14 * 61 )
= 60320 ÷ 2 * 3.14 * 61
= 60320 ÷ 6.28 * 61
= 60320 ÷ 383.08
= 6032000/ 38308
= 1508000/9577
= 157
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Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
Answers
SOLUTION
The coordinate of the vector P and Q are
[tex]\begin{gathered} P(-13,\text{ 11)} \\ \text{And } \\ Q(-18,2) \end{gathered}[/tex]To find the vector PQ. we have
[tex]\begin{gathered} t=\bar{PQ} \\ PQ\text{ is having the coordinate } \\ PQ=(-18-(-13),2-11)=(-5,-9) \end{gathered}[/tex]To find the vector, we use
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \text{Where } \\ x=-5,y=-9 \\ r=\sqrt[]{(-5)^2+(-9)^2}=\sqrt[]{25+81}=\sqrt[]{106}=10.296 \end{gathered}[/tex]Then we obtain the angle using
[tex]\begin{gathered} \text{tan}\theta=(\frac{y}{x})_{} \\ \text{Substituting the value of x and y, we have } \\ \tan \theta=(\frac{9}{5})=\tan \theta=(1.8) \end{gathered}[/tex]Hence
[tex]\begin{gathered} \tan \theta=1.8 \\ \theta=\tan ^{-1}(1.8) \\ \theta=60.945 \end{gathered}[/tex]Hence
The vector in trigonometry form will be
[tex]\begin{gathered} t=r(i\cos \theta+j\sin \theta) \\ \text{Then} \\ t=10.296\cos 60.945i+10.296\sin 60.945j \end{gathered}[/tex]Therefore
t= 10.296 cos 60.945 i + 10.296 sin 60.945j
Answer: Option C(third option ).
Lines AB, CD, and LK intersect as shown in the figure below. AB I CDKA
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The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent.
Given that:
[tex]\begin{gathered} m\angle\text{LRB}=86\degree,\text{ its alternate exterior angle is }m\angle\text{CSK} \\ \\ \text{Therefore,} \\ m\angle\text{CSK}=m\angle\text{LRB} \\ m\angle\text{CSK}=86\degree\text{ (final answer)} \end{gathered}[/tex]95% of ____ is 427.5
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Answer: Hi! The answer is 406,125.
Step-by-step explanation: You can either go by 1%, meaning you divide 427,5 by 100 and then do x95, which gives you 95%, or you can do 427,5x0,95. Either way you get 406,125!
Answer:
406.125
Step-by-step explanation:
I don’t under stand help
Answers
E is the same shape and around the same size as A. A tales up a total of around 6 squares as well as E. E would be a rotation of 90°
please help me dhdjjdjejejejdjejejejejejkenensndd
Answers
Answer: area=8cm
Step-by-step explanation:
Answer:
a) Area of shape = 8 square cm.
Step-by-step explanation:
Area of composite shape:
Area of shape = area of rectangle + 2* area of triangle
Rectangle:l = 3 cm ; w = 2 cm
[tex]\sf \boxed{\text{Area of rectangle = l *w}}[/tex]
= 3 * 2
= 6 cm²
Triangle:
b = 2 cm
h = 1 cm
[tex]\sf \boxed{\text{Area of triangle=$\dfrac{1}{2}*b*h$}}[/tex]
[tex]\sf = \dfrac{1}{2}*2*1\\\\\\ = 1 \ cm^2[/tex]
Area of two triangles = 2 *1
= 2 cm²
Area of shape = 6 + 2
= 8 cm²
b) Area of rectangle ABCD = 4 * 2
= 8 cm²
what is the 1/3 of 24
Answers
ANSWER:
8
STEP-BY-STEP EXPLANATION:
They ask us for 1/3 of 24, what we must do multiply both values, just like that
[tex]\frac{1}{3}\cdot24=8[/tex]Which means that 1/3 of 24 is 8
Nell participated in a 3-day charity walk. Sheraised $0.50 for each 1/3 of mile that she walked. Thefirst day, Nell walked 12 miles. The second day, shewalked 8 miles. The third day, she walked 16 miles.How much money did Nell raise?
Answers
the Numbers of days = 3
The second statement(She raised $0.50 for each 1/3 of mile that she walked) means
1/3 miles = $0.50
For first day walk we have:
1/3 miles = $0.50
12 miles = 12 x 0.50 x 3 = $18
For Second day walk we have:
1/3 miles = $0.50
8miles = 8 x 0.50 x 3 = $12
For Third day walk we have:
1/3 miles = $0.50
16miles = 16 x 0.50 x 3 = $24
The amount she raised for the three days becomes
$18 + $12 + $24
=$54
Three functions are shown.
Linear
Quadratic
Exponential
Which of the following statements is true?
Answers
The correct statement C. Exponential growth will always exceed linear growth.
What is termed as the Exponential growth?Exponential growth is a data pattern that exhibit good increases over time, resulting in the curve of such an exponential function.Whereas exponential growth is frequently used in corporate finance, the actuality is frequently more complex. In the case of a savings account, the implementation of exponential growth did work well because the rate of interest is assured and does not change over time. This isn't the case with the majority of investments.For the given question;
In the end, a "exponential growth function" would always outperform a "linear growth function" because "x-values" tend to increase in continuation, and as such the change rate affiliated with the "exponential function" as well increases in continuation, whereas the "linear function's" change rate is considered constant.
Thus, Exponential growth will always exceed linear growth.
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The complete question is-
Three functions are shown.
A. Linear growth will always exceed exponential growth.
B. Quadratic growth will always exceed exponential growth.
C. Exponential growth will always exceed linear growth.
I don't understand this
Answers
Answer:
∠F = 29
Step-by-step explanation:
There is a property of angle of triangles.
Exterior angle = Sum of opposite interior angles
58 = x + x
58 = 2x
2x = 58
x = 58/2
x = 29
∠F = x = 29
Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
x 25 35 45 55
y 85 77 69 61
The equation that represents this relationship is y =
Answers
The equation of the linear relationship in slope-intercept form is y = (-4/5)x + 105.
Given:
x 25 35 45 55
y 85 77 69 61
slope between (25,85) and (35,77) is m = 77-85/35-25
= -8/10
m= -4/5
y=mx+c passes though (25,85)
85 = -4/5*25 + c
85 = -4*5+c
85 + 20 = c
c = 105.
y = mx + c
y = (-4/5)x + 105
Therefore the equation of the linear relationship in slope-intercept form is y = (-4/5)x + 105.
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Zeke wants to build a fence around his backyard with the 200 feet (ft) of fencing he bought at Lowe's. Zeke wants to use all of the fencing he bought. he also wants the length of the fencing to be 10 times the width. the equation A=200w-10w^2 can be used to find the area of the garden, where w is the width of the garden, in ft
Answers
Considering the vertex of the quadratic equation, the width that will maximize the area of the garden, and the maximum area, are as follows:
Width: 10 ft.Maximum area: 1000 ft².What is the vertex of a quadratic equation?A quadratic equation is defined as follows:
y = ax² + bx + c.
The vertex can be either a maximum point or a minimum point, depending on the coefficient a, as follows:
Maximum: a < 0.Minimum: a > 0.The coordinates of the vertex are given as follows:
x = -b/2a.y = -(b² - 4ac)/4a.For this problem, the equation is:
A(w) = -10w² + 200w.
Hence the coefficients are:
a = -10, b = 200, c = 0.
The width that will maximize the area is:
w = -200/(2(-10)) = 200/20 = 10 ft.
The maximum area is of:
A = -(200)²/(4(-10)) = 1000 ft².
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the width that will maximize the area of the garden, and the maximum area.
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There are f flavors of ice cream at the shop. Dominic has sampled 7 of them. Choose the expression that shows the number of flavors Dominic has not sampled.
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In linear equation, Jen planned to spent 3.75 hours paddleboarding.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Dominic has sampled = 7
flavors of ice cream at shop = f
the expression that shows the number of flavors Dominic has not sampled
= 7 * f = 7f
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there are 55 stickers in each box how many stickers are in 7 boxes
Answers
explanation: 7x55=385
what is the value of the expression y - x?
Answers
Answer:
[tex]y-x=-10[/tex]
Step-by-step explanation:
In any trapezoid, the sum of all angles is 360°. Additionally, the sum of both angles on the same side of the trapezoid is 180°. Therefore, we know that:
[tex](7x+40)+(68-6y)=180[/tex]
[tex](17y+73)+(121-4x)=180[/tex]
To solve for [tex]x[/tex] and [tex]y[/tex], we must set up a system of equations and solve by substitution, elimination, or graphing.
To start, simplify the first formula, then isolate the [tex]x[/tex] variable:
[tex](7x+40)+(68-6y)=180[/tex]
[tex]7x-6y+68+40=180[/tex]
[tex]7x-6y+108=180[/tex]
[tex]7x-6y=72[/tex]
[tex]7x=72+6y[/tex]
[tex]x=\frac{72+6y}{7}=\frac{72}{7}+\frac{6}{7}y[/tex]
Next, simplify the second formula, then substitute the value above for [tex]x[/tex]:
[tex](17y+73)+(121-4x)=180[/tex]
[tex]-4x+17y+121+73=180[/tex]
[tex]-4x+17y+194=180[/tex]
[tex]-4(\frac{72}{7}+\frac{6}{7}y)+17y+194=180[/tex] (substituted for [tex]x[/tex] here)
[tex]-\frac{288}{7}-\frac{24}{7}y+17y+194=180[/tex]
[tex]-\frac{288}{7}-\frac{24}{7}y+\frac{119}{7}y+\frac{1358}{7}=\frac{1260}{7}[/tex]
[tex]-288-24y+119y+1358=1260[/tex]
[tex]95y+1070=1260[/tex]
[tex]95y=190[/tex]
[tex]y=2[/tex]
Finally, substitute 2 for [tex]y[/tex] in the first formula as simplified:
[tex]7x=72+6y[/tex]
[tex]7x=72+6(2)[/tex]
[tex]7x=72+12[/tex]
[tex]7x=84[/tex]
[tex]x=12[/tex]
Therefore:
[tex]x=12[/tex] and [tex]y=2[/tex]
And the expression [tex]y-x[/tex] equals:
[tex]y-x=2-12=-10[/tex]
2. The following data set is given:5041414546364436513736494345454136Construct a dot plot:
Answers
As given by the question
There are given that the numbers;
[tex]50,\text{ 41, 41, 45, 46, 36, 44, 36, 51, 37, 36, 49, 43, 45, 45, 41, 36.}[/tex]Now,
First make a table of numbers and their frequency.
So,
[tex]\begin{gathered} \text{Number}\rightarrow\text{frequency} \\ \text{ }36\rightarrow4 \\ \text{ 37}\rightarrow1 \\ \text{ }44\rightarrow1 \\ \text{ 45}\rightarrow3 \\ \text{ 46}\rightarrow1 \\ \text{ 49}\rightarrow1 \\ \text{ 50}\rightarrow1 \\ \text{ 51}\rightarrow1 \\ \text{ 41}\rightarrow3 \\ \text{ 43}\rightarrow1 \end{gathered}[/tex]Now,
From the dot plot of the given numbers and their frequency.
So,
The dot plot of the given number is shown below:
Find the distance between the points J(-8, 0) and K(1, 4).
Answers
The distance between two points of coordinates (x₁, y₁ ) and (x₂, y₂) is calculated using the formula:
[tex]undefined[/tex]three times the measure of an angle is equal to twice the measure of the angle's supplement. what is the measure of the angle
Answers
Answer:
The angle has measure 72°.
Step-by-step explanation:
Definition:
Two angles are supplementary angles if the sum of their measures equals 180°.
Let x and y be the supplementary angles.
According to the definition above, then,
x + y = 180
We can the above equation for y:
x + y = 180
y = 180 - x
The two angles have measures:
x
180 - x
Now we look carefully at this statement:
"three times the measure of an angle is equal to twice the measure of the angle's supplement"
We translate the above statement into an equation, using x for one angle, and 180 - x for the supplement.
3x = 2(180 - x)
Solve the equation for x.
Distribute 2 on the right side.
3x = 360 - 2x
Add 2x to both sides.
5x = 360
Divide both sides by 5.
x = 360/5
x = 72
The angle has measure 72°.