[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \sin(40 - x) = \cos(3x) [/tex]
[tex]\qquad \sf \dashrightarrow \: \cos\{90 - (40 - x ) \} = \cos(3x) [/tex]
[tex]\qquad \sf \dashrightarrow \:90 - (40 - x) = 3x[/tex]
[tex]\qquad \sf \dashrightarrow \:90 - 40 + x = 3x[/tex]
[tex]\qquad \sf \dashrightarrow \:3x - x = 50[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 50[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 25 \degree[/tex]
3. Use the GCF and the Distributive Property to factor, 60a + 45.
a. 3(20a +15)
b. 5(12a +9)
с. 20(За + 2)
d. 15(4a + 3)
Answer:
D. 15(4a + 3)
Step-by-step explanation:
15 is the least possible factorisation for both sides, therefore D is the most efficient on of all of them
Using the GCF and Distributive property, the expression can be factorized as, d. 15 (4a + 3).
What is GCF?GCF is the abbreviated form for Greatest Common Factor.
As the name suggests, GCF of two or more numbers or expressions is the greatest of all the common factors of them.
The given expression is 60a + 45.
Distributive property for 3 numbers, a, b and c states that,
a (b + c) = ab + ac
There are two terms here 60a and 45.
We can find the GCF using Prime factorization.
60 = 2 × 30
= 2 × 2 × 15
= 2 × 2 × 3 × 5
45 = 3 × 15
= 3 × 3 × 5
Common factors are 3 and 5.
GCF = 3 × 5 = 15
60a + 45 = (15 × 4a) + (15 × 3)
= 15 (4a + 3) [Using the distributive property]
Hence the factorized form is 15 (4a + 3)
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Solve the system of inequalities and indicate all the integers which are in the solution set: The answer isn't an inequality like -5
Answer:
{- 4, - 3, -2, -1, 0, 1, 2, 3}Step-by-step explanation:
Solve each inequality in the system:
3 - 2a < 13 ⇒ 2a > 3 - 13 ⇒ 2a > - 10 ⇒ a > - 55a < 17 ⇒ a < 17/5 ⇒ a < 3.4The solution is:
- 5 < a < 3.4The integer solution set is:
{- 4, - 3, -2, -1, 0, 1, 2, 3}[tex]\\ \rm\rightarrowtail 3-2a<13[/tex]
[tex]\\ \rm\rightarrowtail -2a<10[/tex]
[tex]\\ \rm\rightarrowtail -a<5[/tex]
[tex]\\ \rm\rightarrowtail a>-5[/tex]
And
[tex]\\ \rm\rightarrowtail 5a<17[/tex]
[tex]\\ \rm\rightarrowtail a<17/5[/tex]
[tex]\\ \rm\rightarrowtail a<3\dfrac{2}{5}[/tex]
So
solution set
[tex]\\ \rm\rightarrowtail a\in\left(-5,3\dfrac{2}{5}\right)[/tex]
So
a={-4,-3,-2,-1,0,1,2,3}What is the area of this rectangle?
Answer:
39
Step-by-step explanation:
You find the area by multiplying the length times the height which is what I did 13 x 3 = 39
Which of the states in the table below has the least area?
State Population in 2020 Population Density (people/mi?) Indiana 6,785,528 186.32 Mississippi 2,961,279 61.14 Iowa 3,190,369 56.69 Arizona 7,151,502 62.74
Indiana
Mississippi
Iowa
Arizona
According to the information in the table, it can be inferred that the state with the least area is Mississippi, with an area of 61.14 square miles.
How to read the table?The table shows the population density of some states in which the number of people and the area of that state are mentioned.
Based on this information, it can be inferred that the state with the fewest number of miles is the one with the smallest area. So Mississippi is the one with the least area.
On the other hand, the one with the largest area would be Indiana which is 186.32 square miles in area.
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Which expression is equivalent to 2x- 3(y- 2x
Answer:
The answer is 8x-3y hope this helps!
Find the measure of the three missing angles in the rhombus below.
Answer:
Angles x and y measure 115°. Angle Z measures 65°.
Step-by-step explanation:
Since a rhombus is a parallelogram, opposite angles are congruent, and consecutive angles are supplementary.
The measure of the angles x, y, and z will be 115°, 115°, and 65°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The adjecent angle of the rhombus is supplementary. Then the value of 'x' is given as,
65° + ∠x = 180°
∠x = 180° - 65°
∠x = 115°
The opposite angle of the rhombus is congruent to each other.
∠y = ∠x
∠y = 115°
∠z = 65°
The measure of the angles x, y, and z will be 115°, 115°, and 65°, respectively.
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Which sentence is correct?A.B.C.D.
Answer: B is correct
Step-by-step explanation:
if you do 2 ÷ 5 you get 0.4. But that isn't an option. So, the only other possibility would be -2 ÷ 5 which gives us -0.4, and that makes sense.
I'm not the greatest at explaining this one but hopefully, this helps!
Help with this question here please
Answer:
that is 4.6 m that the answer
Problem 2
Write each expression as a multiple of a power of 10.
Expression
As a Multiple of a Power of 10
42300
2000
9200000
Four thousand
80 million
32 billion
Whoever does this quicker gets Brainly and stuff
Answer:
4.23 x 10 to the 4, 2 x 10 to the 3, 9.2 x 10 to the 6, 4 x 10 to the 3, 8 x 10 to the 7, and 3.2 x 10 to the 10.
Step-by-step explanation:
I will explain in the comments to this response
The Scientific notation of the number 42300 is 4.23×10⁴.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Here, 42300 in Scientific notation as 4.23×10⁴.
2000 in Scientific notation as 2×10³.
9200000 in Scientific notation as 9.2×10⁶.
42300 in Scientific notation as 4.23×10⁴.
4000 in Scientific notation as 4×10³.
80 million=80000000 in Scientific notation as 8×10⁷.
32 billion=32,000,000,000 in Scientific notation as 3.2×10¹⁰.
Therefore, the Scientific notation of the number 42300 is 4.23×10⁴.
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What are the volume and the surface area of this storage chest?
Answer:
Surface Area: [tex]18ft^3[/tex]
Volume: [tex]44ft^2[/tex]
Step-by-step explanation:
Volume Formula --> base * height
[tex](4.5 * 2) * 2 = 9*2=18ft^3[/tex]
Surface Area Formula --> 2(width*length + height*length + height*width)
[tex]2((2*4.5) + (2*4.5)+(2*2)) = 2(9+9+4) = 2(22) = 44ft^2[/tex]
Answer:
Volume = 18 ft³
Surface area = 44 ft²
Step-by-step explanation:
Volume
Volume of a cuboid = base length × base width × height
Given:
base length = 4.5 ftbase width = 2 ftheight = 2 ftSubstitute given values into formula:
⇒ Volume = 4.5 × 2 × 2 = 18 ft³
Surface Area
Surface area = 2(base width × height) + 2(base length × height) + 2(base length × base width)
=2(2 × 2) + 2(4.5 × 2) + 2(4.5 × 2)
= 8 + 18 + 18
= 44 ft²
Find the coordinates of A.
Answer:
(-4, 1)
Step-by-step explanation:
Coordinates on the plane are written (x, y), meaning you write where the point is located on the x-axis (across) and then you write where the point is located on the y-axis (up and down).
You can see that A's location on the x-axis is -4, so now we have (-4, y). We can also see that A's location on the y-axis is 1, so we have (-4, 1) as our coordinates of A.
I hope this helps! Have a lovely day!! :)
According to the Current Population Report of the United States census, 32. 3% of males aged 25 or older have earned a bachelor's degree or higher. Suppose that Nancy works for the city of Peoria, AZ. City officials have asked her to estimate the proportion of males aged 25 or older in Peoria who have earned a bachelor's degree or higher. They have requested that her estimate have confidence level of 95% and a margin of error of 2%, or 0. 2. Determine the sample size n needed for the 95% confidence interval to be no more than 0. 2.
Answer:
i did this on study island
Step-by-step explanation:
What are the measures of the interior angles of the triangle?
m∠1 =
°
m∠2 =
°
m∠3 =
°
Answer:
Step-by-step explanation:
a and b are parallel lines. So, alternate interior angles are congruent.
∠2 = 64.8°
∠3 = 30.5°
Sum of all angles of triangle = 180
∠1 + ∠2 + ∠3 = 180
∠1 + 64.8 + 30.5 = 180
∠1 + 95.3 = 180
∠1 = 180 - 95.3
∠1 = 84.7°
A cone-shaped container has a height of 240 in. and a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week.
How many weeks will it take for all of the chemical to evaporate?
Use 3.14 to approximate pi.
Enter your answer in the box.
____ weeks
Solve the following system by graphing. 5x+2y=10 4x−y=−18
Answer:
x = -2, y = 10
Step-by-step explanation:
in the figure triangle XYZ is similar to triangle XTU if XT measures 12cm what is the length of TY
Answer:
20
Step-by-step explanation:
It is stated that the triangles in the figure are similar:
We can use the side lengths' proportions to find the length of TY
UT/ZY = XT/TY
(9.6)/16 = 12/TY cross multiply expressions:
192 = (9.6)TY divide both sides by 9.6
20 = TY
-3 x 7 -:- 5 x 1/7
please show the steps :)
is the sign that you mean ÷ ?
if so:
-3×7÷5×1/7
= -21÷5×1/7
=-21/5 × 1/7
= (-21×1) / (5×7)
= -21/35
=-3/5
=-0.6
To which family does the function y = (x 2) superscript one-half baseline 3 belong? quadratic square root exponential reciprocal
The function y = √(x + 2) + 3 is a quadratic function. Then the correct optin is A.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The equation is given below.
[tex]y = (x+2)^{1/2} + 3[/tex]
The equation can be written as
[tex]y - 3= (x+2)^{1/2}[/tex]
Square on both sides, we have
[tex]\begin{aligned} (y - 3)^2 &= [(x+2)^{1/2}]^2 \\\\x + 2 &= y^2 + 9 -6y \\\\x &= y^2 -6y +7 \end{aligned}[/tex]
The equation is a quadratic equation.
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Answer:
A) Quadratic
Explanation:
Hope you have a great day!
Show all steps when completing the square to solve 2x^{2} - 4x - 5 = 25.
Answer:
x = 5,-3
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Answer:
See attachments
Step-by-step explanation:
Hope this helps! (I hope you can open them)
Cody and Darry each improved their yards by planting day lilies and shrubs. They bought their supplies from the same store. Cody spent $84 on 2 day lilies and 6 shrubs. Darry spent $120 on 6 day lilies and 6 shrubs. What is the cost of one day lily and the cost of one shrub?
One lily is $9
One shrub is $11
Step-by-step explanation:
Let the lillies be x
Let the shrub be y
2x + 6y= 84.........i
6x + 6y = 120..........ii
Lets make x the subject formula in eq(I)
2x= 84- 6y
x = 42 - 3y........iii
Put the value of x into eq (ii)
6(42-3y) + 6y = 120
252 - 18y + 6y= 120
252 - 12y= 120
12y= 252-120
12y= 132
Y= 11
Put the value of Y into eq (I)
2x + 6(11)= 84
2x + 66= 84
2x= 18
X= 9
Therefore,the cost of one day lily is $9 and the cost of one shrub is $11.
Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A?
Enter your answer in the box. C is labeled 74
Answer:
Step-by-step explanation:
An angle measures 62 degrees less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
40 and 67
Step-by-step explanation:
What is the equation of a hyperbola with a = 8 and c = 20? Assume that the transverse axis is horizontal.
Answer:
[tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]
Step-by-step explanation:
The equation of hyperbola is given by:
[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} }[/tex]
Where [tex]c^{2} =a^{2} +b^{2}[/tex]
∵ [tex]a=8,c=20[/tex]
∴ [tex]b^{2} =c^{2} -a^{2}[/tex]
⇒ [tex]b= \sqrt{20^{2} -8^{2} } =4\sqrt{21}[/tex]
Now, [tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]
⇒ [tex]\frac{x^{2} }{8^{2} } -\frac{y^{2} }{y(4\sqrt{21} )^{2} } =1[/tex]
⇒ [tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]
Hence, equation is [tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]
Hope this helps,
ROR
Jules draws the incenter of ABC. Which term describes the three segments Jules draws inside the triangle?
a.medians
b.angel bisector
c.altitudes
d.perpendicular bisectors
Answer:
b) angle bisector of angle ABC
How do we do this? The sub gave us the wrong work and isn’t explaining it! Help please!!!
Answer:
1) 18b - 3c - 10
2) [tex]1\frac{3}{4}[/tex]g + 7
3) 0.3y
4) -4n - 5
Step-by-step explanation:
1) 16b + 5c - 10 - 8c + 2b
like terms: 16b + 2b = 18b
like terms: 5c - 8c = -3c
like terms: -10
simplified: 18b - 3c - 10
____________
2) 1/2g + 2g - 3/4 g + 7
like terms: 1/2g + 2g - 3/4g
2 1/2 - 3/4
improper fraction > 5/2 > same denom > 10/4
10/4 - 3/4 = 7/4 > mixed number> 1 3/4g
like terms: +7
simplified: 1 3/4g + 7
____________
3) -0.9y + 4.4y - 3.2y
like terms: -0.9y + 4.4y - 3.2y
simplified: 0.3y
____________
4) 4 - 8n + 7n - 3n - 9
like terms: -8n + 7n - 3n = -4n
like terms: 4 - 9 = -5
simplified: -4n - 5
____________
The table shows the atomic radii of four elements.
Element Atomic Radii (m)
Potassium 2.2 × 10-7
Argon 7.1 × 10-8
Boron 8.5 × 10-8
Silver 1.6 × 10-7
Which list shows the atomic radii of the elements ordered from greatest to least?
[tex]\sf Potassium \ : \ 2.2 * 10^{-7}[/tex]
[tex]\sf Argon \ : \ 7.1 * 10^{-8}[/tex]
[tex]\sf Boron \ : \ 8.5 * 10^{-8}[/tex]
[tex]\sf Silver \ : \ 1.6 * 10^{-7}[/tex]
greatest to least :
Potassium < Silver < Boron < ArgonThe order is
Potassium>Silver>Boron>ArgonShortcut trick :-
The nature of atomic radii in. periodic table
Decrease in a period from left to right.Increase in a group from up to downwrite an inequality that means 2 times a number (d) plus 3 is less than or equal to 9.
Answer: 2d+3<=9
Step-by-step explanation:2 times a number is 2d plus 3 is +3 less than or equal to is <=
. It took Erin the same time to drive 21 miles as it took Brent to drive 15 miles. Erin's speed was 10 mph
faster than Brent's speed. How fast did Erin drive?
The speed at which Erin drove from the given parameters was calculated as; 35 mph
How to work with speed rates?
Let Erin's speed rate be X. Now, since it took erin 21 miles, then;
Erin's time = 21/X
Now, erin's speed was 10 mph faster than Brent's speed. Thus;
Brent's speed = (X - 10) mph
Thus, Brents time = 15/(x - 10)
Now, since they took the same time, then we know that;
21/x = 15/(x - 10)
15x = 21x - 210
6x = 210
x = 210/6
x = 35
Thus, Erins speed = 35 mph
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Find the surface area of this figure.
Answer: 297 in.^2
Step-by-step explanation:
Area of a triangle: b*h/2 ---> (9*12)/2=544 triangles--->4*54(area of triangle)= 216Area of square: b*h ----> 9*9 = 81Add area of all four triangles plus are of square-----> 216+81 = 297 in.^2
A boat is traveling at 28 knots in a direction of 36 degrees. It encounters wind moving at 10 knots in a direction of 22 degrees. What is the true velocity and direction of the boat? round to the nearest whole #
a) 38knots;58 degrees
b) 32knots;30 degrees
c) 1,427knots;58 degrees
d) 38knots;32 degrees
The magnitude of the total velocity of the boat is 38 knots, and the direction is 32°, so the correct option is d.
How to get the velocity of the boat?
First, we need to write need to find the component of the two given velocities.
For the boat, the magnitude is 28 knots and the angle is 36°, then the components are:
x-component = (28 knots)*cos(36°) = 22.65 knotsy-component = (28 knots)*sin(36°) = 16.46 knotsFor the wind, the components are:
x-component = (10 knots)*cos(22°) = 9.27 knotsy-component = (10 knots)*sin(22°) = 3.75 knotsAdding these, the total components of the boat's velocity are:
x-comp = 22.65 knots+ 9.27 knots = 31.92 knotsy-comp = 16.46 knots + 3.75 knots = 20.21 knotsThen the magnitude of the velocity is:
|V| = √( (31.92 knots)^2 + (20.21 knots)^2) =37.78 knots
That can be rounded to 38 knots
To get the angle, we take the arctangent of the quotient between the y-component and the x-component:
a = Atan(20.21 knots/31.92 knots) = 32.34°
Then the correct option is d) 38 knots and 32°
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Answer:
It is 38 knots; 32 degrees
Step-by-step explanation:
The answer below is right
I took the test
