Prove that the altitude to the base of an isosceles triangle is also the median to the base in complete sentences:
Explanation:
The altitude to the base of an isosceles triangle meets the base at right angles, dividing the triangle into two right triangles. The hypotenuse of each of these triangles is one of the congruent sides of the isosceles triangle, so the hypotenuses are congruent. The altitude is congruent to itself, so comprises congruent legs of the right triangles.
The right triangles are congruent to each other by the HL congruence theorem. The remaining side of each of the right triangles is part of the base of the original isosceles triangle. Those sides are congruent by CPCTC, so the altitude meets the base at its midpoint. Hence the altitude to the base is a median of the isosceles triangle.
__
Here's the same argument with vertices defined.
Define isosceles triangle ABC such that AB≅AC. Define altitude AD⊥BC. Then ΔADB and ΔADC are right triangles with AB≅AC and AD≅AD. Then ΔADB≅ΔADC by the HL theorem, and DB≅DC by CPCTC. Hence D is the midpoint of BC, and AD is a median.
Greg purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Greg paid.
Answer:
c = 4n
Step-by-step explanation:
The total cost (c) is going to be of the 4 notebooks together
We don't know how many notebooks Greg got, so it's represented by n.
It doesn't matter how many notebooks Greg purchased, because each of them were $4.
So to represent the total cost of the notebooks, you would write c = 4n
Question:
n-sided regular polygons are arranged side-by-side to form a ring of a p-sided regular polygon.
(a) Express p in terms of n.
(b) Hence explain if a 12-sided polygon can be formed by arranging a number of regular polygons in a ring.
Please help! Answers with explanations will be marked brainliest!
Answer: Well if you were going to think of a circle you can divide it into 4 equal sizes in one of the is equal to two pentagons and a half. If you add all is equal to a loop full of pentagons [which makes 10 pentagons]. Because the ring is made out of regular pentagons, we can work out that each of the interior angles of each pentagon is 108* degrees. By extending the lines that two pentagons share, assuming they will all meet in the middle, it will create a triangle. As we know each angle of a [regular] pentagon is 108* degrees, we know the two base angles of the triangle would equal to 72** which leaves the top angle to be 36 degrees. As [the sum of] angles at a point is 360 degrees, and 36 is divisible by 360, it will make a complete ring. Also, as 360 ÷ 36 = 10, we know that the ring will be made out of 10 pentagons. as formula to calculate the the size of a interior angle of a polygon is (n×180−360)÷n (for n being the number of sides that the polygon has). because the triangle is made by extending the lines, and angles on a line is 180 degrees, 180−108 (an interior angle of a pentagon) =72.
PLS HELP ASAP! Which of the following sets shows all the numbers from the set {0, 0.5, 1, 2.5, 3} that make the inequality 2a + 3 ≥ 8 true?
{2.5, 3}
{1, 2.5, 3}
{0, 0.5, 1}
{0.5, 1}
Answer:
first one, [2.5, 3]
Step-by-step explanation:
2a + 3 [tex]\geq[/tex] 8
2a [tex]\geq[/tex] 8 - 3
a [tex]\geq[/tex] 5/2
a [tex]\geq[/tex] 2.5
if we put a =2 .5 in the equation
2a +3 [tex]\geq[/tex] 8
2(2.5) + 3 [tex]\geq[/tex] 8
5+3 [tex]\geq[/tex] 8
8 [tex]\geq[/tex] 8
which is true.
if we put a = 3 in the equation
2a + 3 [tex]\geq[/tex] 8
2(3) +3 [tex]\geq[/tex] 8
6+3 [tex]\geq[/tex] 8
9 [tex]\geq[/tex] 8
which is also true.
What is the opposite of -3?
-3
- 1/3
3
1/3
Answer: 3
Step-by-step explanation: I think
(01.01 LC)What should be added to 3 to make the sum 0?
−3
−2
0
3
Answer:
-3
Step-by-step explanation:
math
Answer:
-3
Step-by-step explanation:
Adding -3 to 3 makes the sum equal to 0:
3 + (-3) = 3 - 3 = 0
Find an equation of the line: through the point (2,-4) with a y-intercept oof -2
Answer quick please !!!!!
Answer:
y = -x-2
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = mx-2
Using the point (2, -4)
-4= m(2) -2
Add 2 to each side
-4+2 = 2m-2+2
-2 =2m
Divide by 2
-2/2 = 2m/2
-1 =m
y = -1x -2
y = -x-2
Answer:
y=-x-2
Step-by-step explanation:
Since we know two points on the graph (2,-4) and (0,-2) we can find the slope because slope= change in y over change in x. By doing so, we can see that the slope is -1. We know that y=mx+b and m is slope and b is y-intercept so we have all the variables needed. y=-1x-2 or y=-x-2.
I NEED HELP PLEASEEEE
Answer:
D
Step-by-step explanation:
a,b,c are the same thing just in different forms so d is the right one.
also a is suppose to be a/1 i think for question d
Stacey earns money by walking dogs she walks the same route seven days a week each week she walks a total of 56 miles what is her walking rate in miles per day
Answer:
8
Step-by-step explanation:
56/7 = 8
Andrea uses 3.12 cups of flour in a recipe that makes 8 key lime cupcakes. Corey uses 2.52 cups of flour in a recipe that makes 7 key lime cupcakes. How much more flower per cupcake is needed for Corey’s recipe?
I will give Brian list plz help
Answer:
The Answer is 0.03
Step-by-step explanation:
Andrea = 3.12/8 flower per cupcake
3.12/ 8 = .39
Corey = 2.25/ 7 flower per cupcake
2.25/ 7 = .36
So Corey's recipe needs
( 0.39 - 0.36) = 0.03 flower per cupcake
Simplify the following expression: 7a + 5b - 3a + 4b
Circle only ONE
A. 4a + 9b
B. 10a + 9b
C. 4a - b
D. 10a - b
Answer:
A
Step-by-step explanation:
7a+5b-3a+4b
first rearrange
7a-3a+5b+4b
4a+9b
please help me answer for this quickly
Choose the correct equation. Then solve the equation.
A sales representative earns weekly base salary of $250 and a commission of 8% on her weekly sales. (A commission is money earned that equals a percent of the sales.) At the end of one week, she earned $410. How much did she sell that week? Let s represent the total sales.
A. 250 + 0.08s = 410
B. 250 + 410 = 0.08s
Question 1
Click the refresh button until you get a right triangle with A as the right angle. Fill in the fraction forms of sin B, cos B, tan B and then the
associated measure of B using sin^-1, cos^-1, and tan^-1, rounded to three decimal places each. Then fill in the fraction forms of sin C, cos C, tan C, and the associated measure of C using sin^-1, cos^-1, and tan ^-1 rounded to three decimal places.
x=width of pool
2x=length of pool
the dimensions of the rectangle forming the walkway and the pool are x+4 and 2x+4
the area of this rectangle minus the area of the pool is 196 square feet
(2x+4)(x+4)-(x)(2x)=196
2x^2+4x+8x+16-2x^2=196
combine similar terms
12x+16=196
12x=196-16
12x=180
x=180/12
x=15 feet is the width of the pool
check: 34*19-30*15=196
646-450=196
196=196
Answer:
Step-by-step explanation:
Figure A is a scale image of Figure B.
whas the value of x?
The expression (F - 32) • 5/9 can be used to convert a temperature from Fahrenheit to Celsius.
1. Find the temperature in Celsius if it is 50°F.
2. Find the temperature in Celsius if it is -10°F.
Answer:
1.) 10
2.) 14
Step-by-step explanation:
Hey can someone help with this problem!?
Answer:
5 spaces
2×(-5)=-10
Answer=10
Step-by-step explanation:
Answer:3
Step-by-step explanation:
looks like 3
questions
solve for k.
4m+5k=3t
solve for b.
a/7 + b/3 = x/21
Please help me! I will give brainly
Question 1
An ear of corn has about $16$ rows of kernels. Each row has about $50$ kernels of corn.
a. About 0.2 of the kernels are white and the rest are yellow. How many kernels are yellow?
____ kernels
Question 2
b. Each ear of corn has about $0.25$ pound of corn kernels. How many pounds of kernels are in a dozen ears of corn?
_____pounds
Answer:
a. 640 kernels
b. 3 pounds
Step-by-step explanation:
a:
Total kernels = 16 * 50 = 800
White kernels = 800 * 0.2 = 160
Yellow kernels = 800 * 0.8 = 640
b:
1 ear weight = 0.25 pounds
12 ears weight = 12 * 0.25 = 3 pounds
a. The number of kernels which are yellow is 640.
b. The amount of kernels will be 3 pounds.
An expression is a combination of symbols, variables, numbers, and operators that represents a value or a computation. It can consist of constants, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more.
Expressions can be simple or complex, involving multiple terms and operations. They are commonly used in mathematics, computer programming, and symbolic logic to represent calculations, equations, and relationships between quantities.
a:
Total kernels = 16 x 50 = 800
White kernels = 800 x 0.2 = 160
Yellow kernels = 800 x 0.8 = 640
b:
1 ear weight = 0.25 pounds
12 ears weight = 12 x 0.25 = 3 pounds
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Question 4
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>
B0/1 pt 53
Write a polynomial in standard form that has the following characteristics.
leading coefficient: -1/3
zeros: 0,9, -21, -3
Answer:
-(x^5)/3+2x^4+(23/3)x^3+8x^2+36x
Step-by-step explanation:
The polynomial is - 1/3(x-9)(x)(x-2i)(x+2i)(x+3)=-(x^5)/3+2x^4+(23/3)x^3+8x^2+36x
I’ll mark brainliest
Which problem solving strategy would be best to solve this problem? Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn? A. write an equation B. make a table, chart or list C. compute or simplify D. guess, check and revise
Answer:
a...............
Step-by-step explanation:
125.00 ÷ 2
what is the gradient?
Answer:
[tex]{ \tt{gradient = \frac{ - 3 - 1}{0 - ( - 1)} }} \\ = \frac{ - 4}{1} \\ = - 4[/tex]
Answer:
The gradient (slope) is -4.
Step-by-step explanation:
Note that two points on the graph through which the blue line passes exactly are (-2, 5) and (0, -3). As we move from the first point to the second, x increases by 2 (the 'run') and y (the 'rise') decreases by 8. Thus, the gradient, or slope, of this line is m = rise/run = -8/2, or m = -4.
Quadrilateral
A
R
M
Y
ARMYA, R, M, Y is rotated
9
0
∘
90
∘
90, degrees about the origin.
Answer:
See explanation
Step-by-step explanation:
From the question, we understand that the quadrilateral is rotated by 90 degrees about the origin.
The question is incomplete; so, I will give a general explanation.
The rule for 90 degrees rotation about the origin is:
[tex](x,y) \to (-y,x)[/tex]
For instance:
A point (4,6) will become (-6,4) after rotation.
MacKenzie surveys 80 of her classmates and finds that 65% of them like sports. She also finds that 75% of her 64 relatives like sports. How many more of her classmates like sports as compared to her relatives? Pls help
Answer:
65%×80=52
(80-52=28) no of classmates who liked sports
75%×64=48
(64-48=16) no of relatives who liked sports
no of classmates who liked sports - no of relatives who liked sports
= 28-16 = 12
Hence, 12 more of her classmates like sports as compared to her relatives
There are total 4 more of her classmates like sports as compared to her relatives.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the information given in the question,
Total number of students surveyed = 80
Percentage of students who like sports = 75%
So,
(80 × 65)/100
= 5200/100 = 52
Total number of Relatives = 64
Percentage of relatives who like sports = 75%
So,
(64 × 75)/100
= 4800/100 = 48
Then, the number more of her classmates like sports compared to relatives will be:
52 - 48
= 4
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What is 1/2[4x + 6(2 + 2x)]
Answer:
8x+6
Step-by-step explanation:
1/2[4x + 6(2 + 2x)]
Work inside out
Distribute inside
1/2[4x + 12 + 12x)]
Combine like terms
1/2[16x +12]
Distribute
8x+6
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{\dfrac{1}{2}[4x+6(2+2x)] }[/tex] [tex]\sf{\dfrac{1}{2}[4x+12+12x] }[/tex] [tex]\sf{\dfrac{1}{2}[16x+12] }[/tex] [tex]\sf{\dfrac{1}{2}[2(8x+6)] }[/tex] [tex]\sf{\dfrac{1}{\cancel{2}}×\cancel{2}(8x+6) }[/tex] [tex]\sf{ 8x+6 }[/tex][tex]\sf{ }[/tex]
Express the extended fraction at the right as a simple fraction in lowest terms.
Answer: 5/2
Yes it has to be 5/2
Answer:
5/2
Step-by-step explanation:
HELP QUICK.
The problem solving plan identifies the letter W as "What do you need to do to solve the problem?" Which of the following answer choices are included in the problem solving plan for the letter W? A. Solve the problem and change your strategy if necessary. B. Did you check the answer and did you answer the question asked. C. Read the problem carefully, find the question, understand the problem and find out what you know. D. Organize the problem and find the question.
Answer:
c
Step-by-step explanation:
Olivia pays $189 for a painting, including tax.
If the actual price is $179.50, what is the sales tax rate?
The sales tax rate = 5.29%
What is the formula for tax rate?"Tax rate = (Tax amount / Price before tax) × 100% "
What is the formula for tax amount?"Tax amount = Final price - Price before tax"
For given question,
Olivia pays $189 for a painting, including tax.
⇒ Final price = $189
The actual price of the painting is $179.50
⇒ Price before tax = $179.50
Using the formula of tax amount,
⇒ Tax amount = Final price - Price before tax
⇒ Tax amount = 189 - 179.50
⇒ Tax amount = 9.5
Now we find the sales tax rate.
Using the formula of tax rate,
⇒ Tax rate = (Tax amount ÷ Price before tax) × 100%
⇒ Tax rate = [tex]\frac{9.5}{179.50} \times 100~\%[/tex]
⇒ Tax rate = 5.29%
Therefore, the sales tax rate = 5.29%
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Can Some1 Tell Me the answer?
Answer: D
Step-by-step explanation:
Answer: D(2.8a-12a-3.6
hope that helped <3
Please answer this question will give brainiest please answer
Answer:2 and 3
Step-by-step explanation:
