Answer:
10 cm
Step-by-step explanation:
The diagonal d divides the rectangle into 2 right triangles with legs 8 and 6 and hypotenuse d
Using Pythagoras' identity in one of the right triangles, then
d² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )
d = [tex]\sqrt{100}[/tex] = 10 cm
Answer:
[tex]\huge\boxed{c = 10\ cm}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of diagonal, a and b are the length of the rest 2 sides
=> [tex]c^2 = 8^2+6^2[/tex]
=> [tex]c^2 = 64 + 26[/tex]
=> [tex]c^2 = 100[/tex]
Taking sqrt on both sides
=> c = 10 cm
C is between B and D. BC=4x + 10 and CD=25. Find BD.
A: BD=105
B: BD=45
C: BD=17.5
D:BD=80
Answer:
A: =105
Step-by-step explanation:
Prove that “The sum of the angles in a triangle is 180“.
Answer
See below :)
Step-by-step explanation:
Experimental Verification
Step 1 : Three triangles with different shapes and sizes are drawn. Suppose the name of each triangle is ABC.
( Draw the triangles in such a way that you can each angle by using a protractor )
( See attached picture )
Step 2 : Measure each angle of these three triangles with the help of protractor and fill up the following table.
_________________________________
Figure < A < B < C < A + <B + <C Result
-------------------------------------------------------------
( i ) 180°
--------------------------------------------------------------
( ii ) 180°
-------------------------------------------------------------
(iii) 180°
________________________________
Conclusion : The sum of the angles of any triangle is equal to 180°
Theoretical proof
( See attached picture )
Given : <ABC , <BCA and <BAC are the angles of ∆ABC.
To prove : <ABC + <BCA + <BAC = 180°
Construction : Through the vertex A , a straight line XY parallel to BC is drawn.
Proof :
_________________________________
Statements Reasons
------------------------------------------------------------
1. < XAB = <ABC 1. XY // BC and alternate
angles
------------------------------------------------------------
2. <YAC = <BCA 2. XY//BC and alternate
angles
------------------------------------------------------------
3. <XAB + <BAC + 3. whole part axiom
<YAC = <XAY
----------------------------------------------------------
4. <XAB + <BAC + 4. < XAY is a straight angle.
<YAC = 180°
-------------------------------------------------------------
5. <ABC + <BAC + 5. from statements ( 1 ),
<BCA = 180° ( 2 ) and (4)
_______________________________
Proved
Hope I helped!
Best regards!!
please help me on this
Answer: (1,-1/2)
Step-by-step explanation:
Point C on the coordinate plane has the coordinates (4,-2) after a dilation with a scale factor of 1/4 we will have to multiply the coordinates each by 1/4 to find the new coordinates.
So x = 4 * 1/4 = 1 Now the new x coordinate is 1
-2 * 1/4 = -2/4 = -1/2 Now the new coordinate for y is also -1/2
So we will now have the coordinates (1,-1/2)
One card is to be drawn from a deck of 52 cards.The deck includes four types of cards.Red heart, red stars , black triangles , black circles .Each type has 13 cards numbered 1-13.What is the probability of drawing a red one a, black three , or a six of hearts.Give your answer in the simplify form .
Answer:
1/26 ; 1/26 ; 1/52
Step-by-step explanation:
Given the following :
A deck of 52 cards contains :
Red hearts, Red stars, black triangles, black circles
Each type of card is numbered from 1 - 13
Therefore,
Number of each type of card = 13, all numbered distinctly with digits between 1 - 13
Probability = (number of required outcomes / total number of possible outcomes)
If one card is drawn from the deck:
Probability of picking a red one :
This is either a red heart numbered 1 or a red red star numbered 1,
Therefore, Required outcomes = 2
Total possible outcomes = 52
P(a red one) = 2 / 52 = 1/26
B) A black three
This is either a black triangle numbered 1 or a black heart numbered 1,
Therefore, Required outcome = 2
Total possible outcomes = 52
P(a black three) = 2 / 52 = 1/26
C.) A six of hearts :
A hearts numbered six = 1
Therefore, Required outcome = 1
Total possible outcomes = 52
P(a black three) = 1 / 52 = 1/52
select all the equations where b=11 solution
Answer:
b + 18 = 7
77 = 7b
9 = b - 2
Joel took out a car loan for 12000 he paid 4800 in interest at a rate of 8% per year how many year will it take him to pay off the loan.
Answer:
5 years
Step-by-step explanation:
Simple interest on a loan of P for t years at rate r per year is ...
I = Prt
4800 = 12,000(0.08)(t)
4800/960 = t = 5
It will take Joel 5 years to pay off the loan.
Help ASAP!! I’m confused on only this question!
Answer:
Second choice
Step-by-step explanation:
f(x) = (1/4)(x + 4)^2 - 9
f(x) = (1/4)(x^2 + 8x + 16) - 9
f(x) = (1/4)x^2 + 2x + 4 - 9
f(x) = (1/4)x^2 + 2x - 5
(1/4)x^2 + 2x - 5 =
= (1/2 x + 5)(1/2 x - 1)
Answer: Second choice
Loryn,brian,and edna are donating book to the library.loryn donated 7 more books than brian.enda donated twice as many books as loryn. Together they donated a total of 53 books how many books did loryn donate
Answer:15
Step-by-step explanation: We know L+B+E=53 books
Loryn=L
Enda=2L
Brian=L-7
L+2L+L-7=53
Then solve for L
Leaving you with L=15
Check
15+2(15)+(15-7)
15+30+8=53
3х +3y-2х-у
I’m trying to combine like terms plz help
Answer:
1X+2Y
Step-by-step explanation:
3x - 2x = 1x
3y - 1y = 2Y
Answer:
3x+2y
Step-by-step explanation:
Let's simplify step-by-step.
3x+3y−y
=3x+3y+(−y)
Combine Like Terms:
=3x+3y+(−y)
=(3x)+(3y+(−y))
=3x+2y
Answer:
=3x+2y
HOPE THIS HELPS!!!!!! :)
<333333
r - 7 = 1
can someone help me with this
Answer:
[tex]r=8[/tex]
Step-by-step explanation:
[tex]r-7=1[/tex] add seven to both sides
[tex]r=1+7\\r=8[/tex]
Hope this helps
Answer:
The correct answer to this problem is r = 8.
Step-by-step explanation:
To solve this problem, we have to remember that our goal is to get the variable (in this case, r) by itself on one side of the equation. To do this, we have to get rid of the -7 on the left side of the equation. Therefore, our first step is to add 7 to both sides of the equation. This gives us:
r - 7 = 1
r - 7 + 7 = 1 + 7
r = 8
Thus, your answer is r = 8.
Hope this helps!
Noah has one dollar composed of dimes and nickles. He has twice as many 1 point
dimes as nickels, How many nickles does he have? *
Your answer
no❤️ ,,,,,,,,,,,,,,,,,,,
8 dimes 4 nickels
ur crazy bb why’d you even ask this question
Someone please help me!!!!
Answer:
Below.
Step-by-step explanation:
Left side = 2 cos^2 ( π/4 - A/2) - 1
= 2 ( cos π/4 cos A/2 + sin π/4 sin A/2)^2 - 1
Now sin π/4 and cos π/4 = 1 /√2 so:
= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1
= 2 * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1
But cos^2 a/2 + sin^2 A/2 = 1 so we have:
2 * 1/2( 1 + 2sin A/2 cos A/2) - 1
= 1 + 2 sin A/2 cos A/2 - 1
= 2 sin A/2 cos A/2
Using the identity 2 sin A cos A = sin 2A
2 sin A/2 cos A/2 = sin A = right side.
So left side = right side and the identity is proved.
Answer: see proof below
Step-by-step explanation:
Use the Double Angle Identity: cos 2A = 2cos²A - 1
Use the Difference Identity: cos (A - B) = cosA · cosB + sinA · sinB
Use the Unit Circle to evaluate: cos (π/2) = 0 & sin (π/2) = 1
Proof LHS → RHS
[tex]\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A[/tex]
LHS = RHS: sin A = sin A [tex]\checkmark[/tex]
If line a has a greater slope than line b, is line a steeper than line b? Explain, giving examples to support your answer. ( PLEASE HELP)
Answer:
No a greater slope is not always steeper
Step-by-step explanation:
If line A has a slope of 10 and line B has a slope of 6. The slope of line A will definetely be steeper than line B. In a negative slope, if line A's slope is -20 and line b's slope is 5 the line A will be steeper even though it is actually less than 5.
A certain number is increased by 30 and the result is divided by two. The number obtained is three times the original number. Find the number.
Plss show working
Answer:
x = 6, PLEASE MARK AS BRAINLIEST
Step-by-step explanation:
Let this number be x:
1) Increase x by 30 = x + 30
2) Divide the result by 2 = [tex]\frac{x+30}{2}[/tex]
3) The number obtained is 3 times the original number =
[tex]\frac{x + 30}{2} = 3x[/tex]
[tex]{x + 30} = 6x[/tex]
[tex]30 = 5x[/tex]
[tex]x = \frac{30}{5}[/tex]
[tex]x = 6[/tex]
Find the Slope of the line on the graph. write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
3
Step-by-step explanation:
Please explain how you get the answer.
Convert decimals to fractions
10) 0.34
11) 0.252525....
12) 5.7777....
Answer:
0.34 ends in the hundredths place. so the fraction will be over one hundred
34/100 -- simplify this by dividing each side by 2: 17/50
0.252525... is a repeating decimal
set up an equation so the numbers to the right of the decimal place are the same
100x = 25.2525...
x = 0.2525...
subtract
99x = 25
divide
x = 25/99
5.7777... is also a repeating decimal
set up an equation so the numbers to the right of the decimal place are the same
10x = 57.777...
x = 5.777...
subtract
9x = 52
x = 52/9
Which operation involving complex numbers requires the use of a conjugate to be carried out?
Answer:
Step-by-step explanation:
Rationalization.
2 + i
For example: " rationalize the denominator of --------- "
-3 + i
Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°.
Answer:
La altura del globo con respecto al suelo es 449,6 metros.
Step-by-step explanation:
La afirmación está incompleta. El enunciado completo es: "Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?
El diagrama geométrico de la situación se encuentra descrita en el archivo adjunto. La altura aproximada del globo puede obtenerse con ayuda de las funciones trigonométricas, en este caso, se recomienda utilizar la función tangente de los ángulos de depresión:
Ciudad A
[tex]\tan 27^{\circ} = \frac{h}{1500\,m-x}[/tex]
[tex]0,510 = \frac{h}{1500\,m-x}[/tex]
Ciudad B
[tex]\tan 36^{\circ} = \frac{h}{x}[/tex]
[tex]0,727 = \frac{h}{x}[/tex]
Donde [tex]h[/tex] y [tex]x[/tex] son la altura con respecto al suelo y la distancia horizontal con respecto a la ciudad A.
A continuación, se elimina la altura de ambas ecuaciones por igualación y se determina la distancia horizontal del globo con respecto a la ciudad A:
[tex]0,727\cdot x = 0,510\cdot (1500\,m-x)[/tex]
[tex]1,237\cdot x = 765\,m[/tex]
[tex]x = 618,432\,m[/tex]
Finalmente, la altura del globo con respecto al suelo es:
[tex]h = 0,727\cdot x[/tex]
[tex]h = 0,727\cdot (618,432\,m)[/tex]
[tex]h = 449,600\,m[/tex]
La altura del globo con respecto al suelo es 449,6 metros.
Is 2/3+4/5 a rational number
Answer:
Yes
Step-by-step explanation:
What is the inverse of the function g(x)=-2(x-4)? g^-1(x)=___
Step-by-step explanation:
g(x) = y = 8 - 2x
(A) First transform the function in terms of x :
x = y - 8 / 2
(B) Replace x with y :
[tex] {g}^{ - 1} (x) = y = \frac{x}{2} - 4[/tex]
alex is traveling by train to a vacation spot that is 810 miles away. The train is traveling at 90 miles per hour, and it has already covered 180 miles. In exactly how many hours will alex reach his destination from his current position
Answer:
7 hours
Step-by-step explanation:
810 - 180 = 630
630/ 90 = 7
Answer:
x = 7 h
Explanation:
First, we write the data of the problem.
Alex travels 810 miles away
Train - 90 miles / h
Alex covers 180 miles.
How many hours does Alex walk in the distance?
1. Calculate the distance Alex still has to travel.
810 miles - 180 miles = 630 miles
2. We take into account the speed of the train to calculate how many hours Alex will cover the remaining distance.
90 miles .... 1 h
630 miles .... x h
x = 630 milesx1h / 90 miles
x = 7 h
-6 times (-6) times (-6)
Answer:
-216
Step-by-step explanation:
-6 x -6 =36
36 x -6 = -216
Answer:
-216
Step-by-step explanation:
The midpoint of JK is M(8,9). One endpoint is J(10, 10). Find the coordinates of the other
endpoint K.
Write the coordinates as decimals or integers.
K= (1,7)
Answer:
[tex]K(6,8)[/tex]
Step-by-step explanation:
Given
Midpoint, M = (8,9)
J = (10,10)
Required
Find K
The midpoint of segments is calculated using;
[tex]M(x,y) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
Where [tex]x = 8[/tex] and [tex]y = 9[/tex]
Take J as J(x1,y1);
So:
[tex]x_1 = 10[/tex] [tex]y_1 = 10[/tex]
Substitute values for x and y in the given formula
[tex](8,9) = (\frac{10 + x_2}{2}, \frac{10 + y_2}{2})[/tex]
Solving for x2, we have
[tex]8 = \frac{10 + x_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 8 = \frac{10 + x_2}{2} * 2[/tex]
[tex]2 * 8 = 10 + x_2[/tex]
[tex]16 = 10 + x_2[/tex]
Make x2 the subject of formula
[tex]x_2 = 16 - 10[/tex]
[tex]x_2 = 6[/tex]
Solving for y2
[tex]9 = \frac{10 + y_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 9 = \frac{10 + y_2}{2} * 2[/tex]
[tex]2 * 9 = 10 + y_2[/tex]
[tex]18 = 10 + y_2[/tex]
Make y2 the subject of formula
[tex]y_2 = 18 - 10[/tex]
[tex]y_2 = 8[/tex]
So,
[tex](x_2,y_2) = (6,8)[/tex]
So, the coordinates of K is
[tex]K(6,8)[/tex]
3x-2y=6 and 5x-5y=5 Solve each system of equations
Answer:
x=4 and y=3
Step-by-step explanation:
what is the midpoint of 2-3i and -4+6i
O2+31
-4-6i
0 -1+1.51
2-31
explain how a rational number and an irrational number and different
Answer:
Rational numbers: fractions with an integer numerator and a nonzero integer denominator.
Irrational numbers: numbers that are not rational such as π, root 3, and any non repeating, non ending decimal.
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:
The SQ Root of 493
Step-by-step explanation:
Becaues this triangle is a right triangle, we can find the missing side usiing the pythagorean theorum.
The pythagorean theorun states A^2 + B^2 = C^2, so 18^2 + 13^2= 439
Then all you have to do is find the sq root of 439, but this question askes you not to.
Hope this helps :)
find the value of
[tex]3 log_{2}4[/tex]
Answer:
6
Step-by-step explanation:
log ₐ (aˣ) = x
3 log ₂ (4)
3 log ₂ (2²)
3 * 2
6
what does (x + 3)(x - 5)=
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2 1/2. What is the value of x? PLEASE ANSWER ASAP!!
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Figure B = 2½ the size of figure A
One side of figure B is given as 5, therefore, 5 = 2½ of x in figure A.
Thus, [tex] 5 = 2\frac{1}{2}*x [/tex]
Solve for x
[tex] 5 = \frac{5}{2}*x [/tex]
[tex] 5*2 = \frac{5x}{2}*2 [/tex]
[tex] 10 = 5x [/tex]
[tex] \frac{10}{5} = \frac{5x}{5} [/tex]
[tex] 2 = x [/tex]
[tex] x = 2 [/tex]