Answer:
The answer is below
Step-by-step explanation:
a) T=2.25h+1.75d
To rewrite the equation to find d, we have to make d the subject of the formula.
T=2.25h+1.75d
Subtract 2.25h from both sides:
T - 2.25h = 2.25h + 1.75d - 2.25h
1.75d = T - 2.25h
Divide both sides by 1.75
1.75d/1.75 = (T - 2.25h) / 1.75
d = (T - 2.25h) / 1.75
b) Additive property and law of division
c) The money spent (T) = $18.25 and the number of hot dogs (h) = 5. To get the number of drinks, substitute the value of h and T in the equation d = (T - 2.25h) / 1.75. Hence:
d = (T - 2.25h) / 1.75
d = (18.25 - 2.25(5)) / 1.75
d = (18.25 - 11.25) / 1.75 = 7 / 1.75
d = 4
The number of drinks that can be bought is 4
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]
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)=
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]
What is (0,6) after a reflection over the y-axis?
Answer:
Still (0,6)
Step-by-step explanation:
The point is actually on the y-axis. It can't change in a y-axis reflection, only in an x-axis reflection.
2
A circle has the equation x^2+ y^2 + 6x - 8y + 21 = 0.
a) Find the coordinates of the centre and the radius of the circle.
The point P lies on the circle.
b) Find the greatest distance of P from the origin.
Answer:
a) (-3, 4) and radius = 2.
b) 7 cms.
Step-by-step explanation:
x^2+ y^2 + 6x - 8y + 21 = 0
x^2 + 6x + y^2 - 8y = -21
Completing the square on the x and y terms:
(x + 3)^2 - 9 + (y - 4)^2 - 16 = -21
(x + 3)^2 + (y - 4)^2 = -21 + 9 + 16 = 4
a) So the center is (-3, 4) and the radius = sqrt4 = 2.
Ill come back to you later with the second part.
(b) For the point P to be a maximum distance from the origin the line must pass through the center of the circle:
Distance of the center from origin:
= √(-3 - 0)^2 + (4 -0)^2)
= 5.
So the dsitance of P from the origin is 5 + radius
= 7 cm.
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!
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.
Joshua is preheating his oven before using it to bake. The initial temperature of the
oven is 75º and the temperature will increase at a rate of 25° per minute after being
turned on. What is the temperature of the oven 7 minutes after being turned on?
What is the temperature of the oven t minutes after being turned on?
Temp after 7 minutes:
Temp after t minutes:
Answer:
1) [tex]\huge\boxed{ 250\°}[/tex]
2) [tex]\huge\boxed{75\° + 25\°t }[/tex]
Step-by-step explanation:
Initial Temperature = 75°
Per minute Increase = 25°
After 7 minutes:
=> 75 + 25 ( 7 )
=> 75 + 175
=> 250°
After t minutes:
=> 75 + 25 (t)
=> 75° + 25°t
Answer:
[tex]\Large \boxed{\mathrm{a) \ 250\° \ \ \ b) \ 75\° +25\°t}}[/tex]
Step-by-step explanation:
Before baking, Joshua preheats the oven at an initial temperature of 75°. The temperature increases at a rate of 25° per minute.
Temperatute after 7 minutes,
[tex]75 \° + 25 \°(7)=75\° +175 \° =250 \°[/tex]
Tempertaure after t minutes,
[tex]75 \° +25 \° t[/tex]
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]
Hi there, can anyone help me with this question?
A bag contains 1p, 2p and 5p coins. 2/5 of the bag are 2p coins. There are twice as many 1p coins than 5p coins in the bag. There are 630 coins in total. Work out the number of 5p coins in the bag.
i know im dumb srry but help plz....
If two angles are complementary, then the
sum of their measures is 90 degrees.
We can find the m<B by taking 90 minus the measure of <A.
So here, we have 90 - 15 which is 75.
So m<A is 75 degrees.
Is (0,3), (0,7), (4,0) a function
Answer:
no because it has 2 of the same x-intercepts.
Step-by-step explanation:
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:
Fully simplify.
-11xy2(13x2y3)
Answer:
-11xy\26x\2y\6
Step-by-step explanation:
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.
what is the midpoint of 2-3i and -4+6i
O2+31
-4-6i
0 -1+1.51
2-31
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
Naya sells half the paintings in her collection and gives one-third of her paintings to friends, while she keeps the remaining paintings for herself. What fraction of her original collections does she keep?
Answer:
[tex]R = \frac{1}{6}[/tex]
Step-by-step explanation:
Given that she sold half the paintings and gives out one-third
Required
Determine the fraction left with her
The relationship between the paintings is as follows;
Sold Paintings + Giveaway Paintings + Remaining Paintings = 1
From the question;
Sold Paintings = 1/2
Giveaway = 1/3
Represent Remaining Paintings with R
Substitute these values in the above formula
[tex]\frac{1}{3} + \frac{1}{2} + R = 1[/tex]
Take LCM
[tex]\frac{2+3}{6} + R = 1[/tex]
[tex]\frac{5}{6} + R = 1[/tex]
Make R the subject of formula
[tex]R = 1 - \frac{5}{6}[/tex]
Take LCM
[tex]R = \frac{6-5}{6}[/tex]
[tex]R = \frac{1}{6}[/tex]
Hence, the fraction of the paintings left with her is [tex]\frac{1}{6}[/tex]
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
-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:
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
select all the equations where b=11 solution
Answer:
b + 18 = 7
77 = 7b
9 = b - 2
4 + 6x + 5 = 7x Could someone help me? Thanks :) And could you also show how u did it
Answer:
x=9
Step-by-step explanation:
combine like terms
[tex]4+6x+5=7x[/tex]
4+5=9
9+6x=7x
to get 6x with 7x subtract 6x from both sides as its positive
6x-6x=0
7x-6x=x
9=x
x=9
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]
Is 2/3+4/5 a rational number
Answer:
Yes
Step-by-step explanation:
1. There are 10 students in the class and 40 eggs. If
the eggs are divided equally among the students how
many does each student get?
Answer:
4 eggs
Step-by-step explanation:
40 divided by 10 = 4
Answer:
4
Step-by-step explanation:
40/10=4
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!!
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
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.