Answer:
Question 16 = 22
Question 17 = 20 cm²
Step-by-step explanation:
Concepts:
Area of Square = s²
s = sideArea of Triangle = bh/2
b = baseh = heightDiagonals of the square are congruent and bisect each other, which forms a right angle with 90°
Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Question # 16
Step One: Find the total area of two squares
Large square: 5 × 5 = 25
Small square: 2 × 2 = 4
25 + 4 = 29
Step Two: Find the area of the blank triangle
b = 5 + 2 = 7
h = 2
A = bh / 2
A = (7) (2) / 2
A = 14 / 2
A = 7
Step Three: Subtract the area of the blank triangle from the total area
Total area = 29
Area of Square = 7
29 - 7 = 22
-----------------------------------------------------------
Question # 17
Step One: Find the length of PT
Given:
PR = 4 cmRT = 6 cmPT = PR + RT [Segment addition postulate]
PT = (4) + (6)
PT = 10 cm
Step Two: Find the length of S to PT perpendicularly
According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal
Length of Diagonal = 4 cm
4 ÷ 2 = 2 cm
Step Three: Find the area of ΔPST
b = PT = 10 cm
h = S to PT = 2 cm
A = bh / 2
A = (10)(2) / 2
A = 20 / 2
A = 10 cm²
Step Four: Find the length of Q to PT perpendicularly
Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.
Length of Diagonal = 4 cm
4 ÷ 2 = 2 cm
Step Five: Find the area of ΔPQT
b = PT = 10 cm
h = Q to PT = 2 cm
A = bh / 2
A = (10)(2) / 2
A = 20 / 2
A = 10 cm²
Step Six: Combine area of two triangles to find the total area
Area of ΔPST = 10 cm²
Area of ΔPQT = 10 cm²
10 + 10 = 20 cm²
Hope this helps!! :)
Please let me know if you have any questions
Use a double-angle or half-angle identity to find the exact value of each expression
If 180° < θ < 270°, then 90° < θ/2 < 135°, which places θ/2 in the second quadrant so that sin(θ/2) > 0 and cos(θ/2) < 0.
Recall that
cos²(θ/2) = (1 + cos(θ))/2
==> cos(θ/2) = -√[(1 + (-15/17))/2] = -1/√17
and
sin²(θ/2) = (1 - cos(θ))/2
==> sin(θ/2) = +√[(1 - (-15/17))/2] = 4/√17
Then
tan(θ/2) = sin(θ/2) / cos(θ/2)
… = (4/√17) / (-1/√17)
… = -4
what is the reason for statement 8
a. third angle theorem
b. triangle proportionality theorem
c. congruent complements theorem
Can anyone help me please
Answer:
1
Step-by-step explanation:
Basically you just need to find the square root of all of them
36=6 -1=1 9=3 . -1=1
6-1-3-1=1
Caroline,Colin & Sarah share some money in the ratio 5:9:6.
In total, Caroline and Sarah receive £44. How much does Colin get?
Answer:
Caroline gets 4*5 = 20 pounds
Colin gets 9 * 4 = 36 pounds
Sarah gets 6*4 = 24 pounds.
Step-by-step explanation:
The ratios are 5x + 9x + 6x
5x + 6x = 11x
Caroline and Sarah get a total of 44 pounds. They don't get 44 pounds each.
11x = 44 Divide by 11
x = 44/11
x = 4
Colin gets 9x
x = 4
9*4 = 36
Colin gets 35 pounds.
Caroline gets 4*5 = 20 pounds
Colin gets 9 * 4 = 36 pounds
Sarah gets 6*4 = 24 pounds.
Caroline and Sarah get 20 + 24 = 44
Can someone help me please ?
Answer:
I would say D is your answer
Step-by-step explanation:
Answer:
the fourth one
use mathaway its like my best friend for math!!!
Step-by-step explanation:
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (20, -6)
B. (-1, 0)
C. (-1, -6)
D. (20, 0)
Answer:
(-1,-6)
Step-by-step explanation:
(13 + x)/2 = 6
13+x= 12
x = -1
~~~~~~~~~~~~~~~
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
The coordinates of the other endpoint will be (-1,-6). The correct option is C.
What is the midpoint of the line?Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that the midpoint of a segment is (6,−4) and one endpoint is (13,−2).
The x- coordinate will be calculated as:-
(13 + x)/2 = 6
13+x= 12
x = -1
The y-coordinate will be calculated as:-
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
Therefore, the coordinates of the other endpoint will be (-1,-6). The correct option is C.
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Construct 5 equivalent equations for the equation - 3 + 2x = -4.
Answer:C
Step-by-step explanation:
Help!!
I think I got these wrong, so please help!! Thank you!
Answer:
(x+3)(x+4)(x-4)
x+2 and x-3 are not factors but x-4 is
Step-by-step explanation:
let's factor it :)
x^3 + 3x^2 - 16x -48
first we will factor this:
x^3 + 3x^2
x^2(x + 3)
then factor the second part :
- 16x - 48
-16(x + 3)
so now,
x^2(x + 3) - 16(x + 3)
factor out x+3
(x+3)(x^2 - 16)
factor x^2 - 16
(x+3)(x+4)(x-4)
1 pump can fill a pool in 8 hours the other pump can fill the pool in 10 hours if both of the pumps were turned on at the same time to fill the pool how long will it take
Answer:
4 4/9 hoursStep-by-step explanation:
In one hour pump1 can fill 1/8 of the tank and pump2 can fill 1/10 of the tank.
Two pumps can fill:
1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the tank in one hourTime required to fill the tank:
1/(9/40) = 40/9 = 4 4/9 hoursHELP ITS DUE IN THE MORNING AND ITS 3:57
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
Tiana uses the equation c = 21h to figure out the total amount, c, she should
charge a customer for babysitting for h hours.
a. What is the constant of proportionality? What does it mean?
b. Tiana charges $94.50 for a job. How long did she babysit for?
Show your work.
Answer:
a. The constant of proportionality is, 21
b. Tiana charges $94.50 for a job, so, c=94.50
from the given equation,
c = 21h
or, 94.50 = 21h
or, h = 94.50/21
or, h = 4.5
She babysit for 4.5 hours.
Answered by GAUTHMATH
c = 21h
94.50 = 21h
h = 94.50 ÷ 21
h = 4.5hours.
Therefore, Tiana spent 4½ hours babysitting.
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help pls with explanation!!!
Answer:
18c - 30d + 36
Step-by-step explanation:
To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.
6(3c - 5d + 6)
(6 · 3c) + (6 · -5d) + (6 · 6)
18c + -30d + 36
As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.
Guys Help me
Does (4, 7) make the equation y = 2x + 7 true?
Answer:
false
Step-by-step explanation:
x=4andy=7
2×4+7 isnot equal to 7
Answer:
Tue equation is
y=2x+7
So, the answer is
(2,7)
And (4,7) is wrong
Which segment is the hypotenuse?
Answer:
SU
Step-by-step explanation:
The hypotenuse is opposite the right angle
The hypotenuse is US or SU
We have to pick,
The segment which is hypotenuse,
Hypotenuse will be the opposite segment of the right angle.
Now it will be,
→ SU (or) US
Hence, SU is the hypotenuse.
Express 0.00506 in standard form
Answer:
[tex]5.06 x 10^{-3}[/tex]
Step-by-step explanation:
Move decimal 3 place to right.
Because the decimal was moved to right, the exponent is negative.
PLEASE PLEASE PLEASE HELP. I WILL BE SO SO SO HAPPY!! WILL GOVE BRANLIEST! AND FOREVER BE SO HAPPY! POINTS!
Answer:
a
Step-by-step explanation:
follows geometric sequence. starting value is 1/3 and is multiplied by 1/3 every time
Help what is x
When x^5 is 225
Answer:
Solution given:
x^5=225
we have
x=[tex] \sqrt[5]{225} [/tex]
x=2.9541
Hello!
[tex] \bf {x}^{5} = 225[/tex]
Extract the radical on both sides of the equation.[tex] \bf x = \sqrt[5]{225} [/tex]
[tex] \bf x ≈2.95418[/tex]
Answer: x ≈ 2,95418
Good luck! :)
can someone please help me with this?!?!!
Answer:
I can't help but I hope you succeed
2. What are the last 2 digits of 1 + 2 + 3 + + 2005 2006
Let S be the sum. So you have
S = 1 + 2 + 3 + … + 2004 + 2005 + 2006
as well as
S = 2006 + 2005 + 2004 + … + 3 + 2 + 1
Then
2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)
2S = 2007 + 2007 + … + 2007 + 2007
2S = 2006 × 2007
S = (2006 × 2007)/2
S = 2,013,021
which makes the last two digits 21.
Estimate the product of 32 and 19 ?
Answer:
608
Step-by-step explanation:
32 x 19
= 32 x ( 10 + 9 )
= 320 + 288
= 608
The equation of line a is y=-x+ 3. If line b runs perpendicular to line a and
passes through (2, 6), what would be the equation of line b?
Answer:
y = 4x -2
Step-by-step explanation:
y = 4x + b
6 = 4(2) + b
6 = 8 + b
-2 = b
Graph: f(x) = 3/2 (2)x
Step 1: Calculate the initial value of the function.
f(0)=
Answer:
Step 1: 1.5
Step 2: Plot the points (0, 1.5)
Step 3: 3, then 0.75
Step 4: Plot the points (1, 3) and (-1, 0.75)
Step 5: y=0
Step-by-step explanation:
Ur welcome and have a nice day :>
The initial value of the function f(x) = 3/2 (2)^x is 3/2
How to calculate the initial value of the function?The function expression is given s:
f(x) = 3/2 (2)^x
Substitute 0 for x
f(0) = 3/2 (2)^0
Evaluate the exponent
f(0) = 3/2 * 1
Evaluate the product
f(0) = 3/2
Hence, the initial value of the function is 3/2
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Anyone knows the answer?
Answer:
D) (2,-1)
Step-by-step explanation:
These are two concentric circles of radius 3 and 4 at the origin. That means that any point within the inner is also within the outer. So focusing on the inner, the points plugged into its equation must be less than or equal to the radius squared or 9. That is only valid with point D.
Instructions: Find the measure of the indicated angle to the nearest degree.
Step-by-step explanation:
I don't have a calculator with me right now but I can give you the equation to work out your answer.
cos-1(35/38)
There should be a function of "cos-1" on you're calculator, not just "cos"
hope it helps :)
How many gallons equal 26 liters
Answer:
6.8 gallions i believe. im not quite sure
A triangle and a parallelogram have the same base and the same area.
If the sides of the triangle are 26 cm, 28 cm and 30 cm and the
parallelogram stands on the base 28 cm. Find the height of the
parallelogram.
Answer:
12 centimeters
Step-by-step explanation:
The side lengths of the triangle are: 26, 28, and 30 centimeters
a = 26 cm, b = 28 cm, c = 30 cm
To find the area, we first must find the semi-perimeter with the following equation:
s = (a+b+c)/2
= (28+26+30)/2
= 42 centimeters
Now, to find the area, we can use Heron's formula:
A = [tex]\sqrt{s (s-a)(s-b)(s-c)}[/tex]
[tex]\sqrt{42(42-28)(42-26)(42-30)[/tex]
[tex]\sqrt{42(14)(16)(12)}[/tex]
[tex]\sqrt{112896}[/tex]
336 squared centimeters
Since the area of the parallelogram is equal to the area of our triangle:
Area of Parallelogram = Area of Triangle
base ⋅ height = 336 squared centimeters
28 ⋅ height = 336 squared centimeters
height = 336/28
height = 12 centimeters
If m ≠ 1 and mn - 3 = 3 - n , then what is the value of n?
A) 6/ m+1
B) 6/ m-1
C) 6/ m+n
D) 6/ m-n
[tex]n = \frac{6}{m + 1} [/tex]
Hope it helps you...
The value of n is n= 6/( m+1).
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
Given:
mn - 3 = 3 - n
mn + n = 6
n(m+ 1) =6
n= 6/( m+1)
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Solve the following quadratic function
by utilizing the square root method.
y = 100 – x2
Answer:
x = ± 10
Step-by-step explanation:
To solve the equation let y = 0 , that is
0 = 100 - x²( add x² to both sides )
x² = 100 (I take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
Then solution is x = - 10, x = 10
Answer:
10
Step-by-step explanation:
the guy on top put -10 he's right but it's just 10
HELPPPP MEEEEE OUTTTTT PLEASEEEE ASAPPPP!!!!
Answer:
sin X =35/37
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin X = opp side / hypotenuse
sin X =35/37
Please help out with this question..
Answer:
Step-by-step explanation:
C = 16 * 3 = 48