Step-by-step explanation:
15a)
[tex]x^2+4x=21[/tex] Subtract both sides by 21
[tex]x^2+4x-21 =0[/tex]
15b)
7 and -3 multiply to -21 and add to 4
The factors are (x+7)(x-3)
15c)
x+7 =0
x=-7
x-3=0
x=3
A kite is staked to the ground and blowing in the wind. It currently has a string let out to a length of 45 meters. It has an altitude of 38 feet. To the nearest tenth of a degree, find the angle of elevation. ______°
Answer:
40.2
Step-by-step explanation:
To better analyze this problem, we can first draw a picture. Looking at the one attached, we can see that the stake is represented by the point in the bottom right of the screen, and the kite is 45 meters away from it, representing the 45. Then, the height is 38, and this is directly above the 45 meters away from the stake.
This forms a right triangle, and we can use sohcahtoa to help use. As we don't have the hypotenuse, we can use tan. Tan(θ) = opposite/adjacent, or 38/45. Thus, arctan(38/45) = θ, and plugging that into a calculator, we get 40.2 as our answer
Convert 150 base 10 to a binary
number.
Answer:
10010110
Step-by-step explanation:
A binary number is basically a number in base 2. So, each place represents a power of two. The ones place represents 1 or 2^0, the tens represents 2 or 2^1, the hundreds represents 4 or 2^2 and so on. To find the highest place needed to make in the number in binary, we find the greatest power of two that is below 150. In this case, it is 128. We can start by writing 128 in binary:
10000000
Now, we subtract 128 from 150 and find the largest power of two that is smaller than the difference. The largest power of 2 smaller than 22 is 16, so we put a one in the place for 2^4:
10010000
We can subtract 16 from 22 to get what is leftover to continue the process. We get 6, and the largest power of 2 smaller is 4. We can place a one in the hundreds place to represent it:
10010100
What is left is 6-4 or 2, which is just 2^1, so we can place it in the tens place:
10010110
Let $z$ and $w$ be complex numbers satisfying $|z| = 5, |w| = 2,$ and $z\overline{w} = 6+8i.$ Then enter in the numbers \[|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \]below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark. Don't even know where to start.
I got 49 for the first one, 100 for the second one, 9 for the 3rd one, and 6.25 for the 4th one. But it was wrong, so I don't know how to do this question.
Answer:
1st entry: 41
3rd entry: 17
Step-by-step explanation:
The 1st and 3rd entry are incorrect.
We will use the following for the 1st and 3rd:
[tex]|z+w|=|z|^2+|w|^2+2R(z\overline{w})[/tex]
[tex]|z-w|=|z|^2+|w|^2-2R(z\overline{w})[/tex]
where [tex]R(z\overline{w})[/tex] means 'real part of [tex]z\overline{w}[/tex]'.
Let's do part 1 now)
25+4+2(6)
29+12
41
Let's do part 3 now)
25+4-2(6)
29-12
17
the pythagorean theorem equation
Answer:
(Altitude)^2+(Base)^2=(Hypotenuse)^2
Select the correct answer. Which statement describes ? A. It is an irrational number. B. It is a rational number that has a repeating decimal expansion. C. It is a rational number that has a terminating decimal expansion. D. It is not a rational number because it is negative.
Answer:
the answer is c okay g;)
Step-by-step explanation:
hope this helps
in a class of 37 students,the number of students who like martial art only is double than the number of students who like athletics only .if students like both 4 like none of the games . find how many students like
Answer:
number of students who like Athletics only = x = 10 students
number of students who like marshal arts only = 2x = 20 students
Step-by-step explanation:
In a class of 37 students, the number of students who like marshal arts only is
double than the number of students who like athletics only. If 3 students like both
and 4 like none of the games, find out how many students like:
i. Marshal arts
ii. Athletics
Total students in the class = 37
number of students who like Athletics only = x
number of students who like marshal arts only = 2x
Number of students who like both = 3
Number of students who like none = 4
Total = athletics + marshal art + both + none
37 = x + 2x + 3 + 4
37 = 3x + 7
37 - 7 = 3x
30 = 3x
x = 30/3
x = 10
number of students who like Athletics only = x = 10 students
number of students who like marshal arts only = 2x
= 2(10)
= 20 students
The profit for a car company can be represented by the function P=−0.5 x² +4 x+ 12,
where P is the profit in hundred thousands of dollars and x represents the number of cars sold in thousands. What is the maximum profit the company can make?
Answer:
3x+12
Step-by-step explanation:
-0.5x*2+4x+12
Multiply 0.5x*2=x
= -x+4x+12
Add similar elements -x+4x+12
= 3x+12
Write the slope-intercept form of the linear equation that has a slope of 3
and a y-intercept of -1.
Answer:
y = 3x - 1
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
if a number is divided by three and then two is added,the answer is twenty-nine.what is the number
Answer:
81
Step-by-step explanation:
the answer is 81, just out this in the solution
Answer:
81
Step-by-step explanation:
29-2=27
27*3=81
if we divide 81 by 3 we get 27 and 27 plus 2 is 29 so it is 81
Will give branliest
Find l.
l= [?] in
I need the answers and it's due today, please help
Answer:
1. 3
2. 1
3. 2
4. 4
5. 5
Step-by-step explanation:
Use the figure below, If m
Answer:
m anglw ABD answers is 50 degree
Write an equation for the line that passes through E(4, -3) and is parallel to the line
0 = 5x - 7y - 27 Write the equation in general form.
Answer:
y= 5x/7 -27/7
if they are parallel there gradient is the same
m1=m2
y-y1=m(x-x1)
plug in the gradient and points E
y-(-3)=5/7( x-4)
y= 5/7(x) -20/7 +3
final answer
y= 5/7(x) +1/7
m∠RST =______because they are __________ (Fill in the blanks)
Answer:
∠RST = ∠SRU because they are alternate angles.
Step-by-step explanation:
Hope it helps .
Solve for b in the literal equation y = 12x + 12b.
b=
Answer:
[tex]b = \frac{y-12x}{12}[/tex]
Step-by-step explanation:
subtract 12x from both sides, then divide by twelve.
Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line
Answer: A. perpendicular
Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.
what is the value of J
Answer:
Step-by-step explanation:
Since all 3 of these angle come off a straight line, they all add up to equal 180. Thus,
2j + 32 + 6j - 2 + 30 = 180 and
8j + 60 = 180 and
8j = 120 so
j = 15
Suppose the hypotenuse of a right triangle is 13 cm and one of the legs is 10 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg.
Answer:
3
Step-by-step explanation:
Pythagorean rule
[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]
opp=13-10
opp=3
If a triangle has one interior angle measuring 102°, what is a possible pair of measurements for the other two
interior angles
it edmentum guided notes so it has to be a writing answer
Answer:
a2+a3=78
a2 and a3 must both be positive numbers that add up to 78
so a2 = a3 = 39
a1=102, a2=39, a3=39
Step-by-step explanation:
a1=102
a1+ a2 + a3=180 (all interrior angles of a triangle add up to 180)
a2+a3=78
a2 and a3 must both be positive numbers that add up to 78
The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 12. The part of the overlapping side that extends above the smaller triangle is labeled 3. The leg of the smaller triangle that is a ray of the straight angle is labeled 3 x plus 1. The leg of the larger angle that is a ray of the straight angle is labeled 4 x.
Answer:
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x=
The value of x is 7 units.
What is Similarity of Triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given :
AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and
∠DEB ≅ ∠ACB
Now, AB = AD + BD
= 8 + 6 = 14 units
Now, In ΔABC and ΔDBE,
∠DBE = ∠ABC ( Each of 90° )
∠DEB = ∠ACB ( given )
So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE
Now, proportion of the corresponding sides will be equal.
AD/ DB= BC/ BE
14/8 = 3x/ 2x-2
4x= 28
x= 7
Hence, the value of x is 7 units.
Learn more about similarity of Triangle here:
https://brainly.com/question/11923416
#SPJ6
give me one secondddd..
Answer:
mark me as a brainleast
Step-by-step explanation:
iam not undeerstand on your qiestion write it beautiful words
Help please I’ll give you the brainliest I really got to get this done
Answer:
56
Step-by-step explanation:
What is the area of this figure? Round to the tenth if necessary.
Answer:
b) 850.1 centimeters.Step-by-step explanation:
To find the area of this figure, we must first find the areas of the shapes that compose this figure.
This figure is made up of a rectangle and a semicircle.
Remember: To find the area of a semicircle, multiply the radius by itself twice, then multiply the product pi, lastly divide the product by 2.
[tex]a=\pi r^2/2[/tex]
3.14 will be used for pi!
To find the area of a rectangle, multiply the length by the width. The product is the area of the rectangle.
[tex]a=lw[/tex]
Now, let's solve.
The diameter of the semicircle is 32 centimeters.
To find the radius of a semicircle, divide the diameter by 2.
[tex]32/2=16[/tex]
The radius of the semicircle is 16 centimeters.
Now that we have the radius, we can find the area of the semicircle.
[tex]\pi 16^2/2=401.92[/tex]
The area of the semicircle is 401.92 centimeters.
Furthermore, we find the area of the rectangle.
[tex]14*32=448.[/tex]
The area of the circle is 448 centimeters.
Next, we add the areas of both shapes to find the area of this figure.
[tex]401.92+448[/tex]
[tex]=849.92[/tex]
The final step is to round 849.92 to the nearest tenth.
Even though 849.92 to rounded to the nearest tenth is 849.9, there is no answer choice for this. The closest one to this answer is choice 'b.'
I, therefore, believe the area of this figure is 850.1 centimeters.
I will give brainliest if you add details:
A recent study asked the same 15 students their favorite subject at three different times: in elementary school, in middle school, and when getting ready to graduate from high school.
What percentage of students said that Math was their favorite subject in elementary school?
What is the percent of change for History being the favorite subject between elementary school and graduating from high school?
Answer:
53 1/3% for the first answer, and 33 1/3% increase for the second answer
Step-by-step explanation:
Ok, lets start up witht eh first question.
We need to find the percentage of studens that find math the be their favorite subject in elementary school.
We know that there are 15 kids in total.
We specificly see that 8 of those kids like math the most.
To find percentage, divide 8 by 15.
Using a calculator you should find 53 1/3% of the students found math to be their favorite subject.
Next we need to find the percentag eof change that history is over elementary school to high school.
This might sound confusing, but this is basically just a change of 3 students to 4 students.
To find percentage, just divide 3 by 4:
This gets you 33 1/3%
Hope this helps!
Sarah accepted a new job at a company with a contract guaranteeing annual raises. Sarah's salary after working for nn years can be determined using the equation S=90000+3500n.S=90000+3500n. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
Slope = 3500
Sarah's salary will increase by 3500 per year
Step-by-step explanation:
Given that Sarah's salary after working n years is given as :
S=90000+3500n
The equation given is similar to a linear equation :
y = bx + c ;
Where, b = slope of the linear equation
Therefore, relating the equation to that of a linear model ; the slope, b is equivalent to 3500 in Sarah's salary equation.
Slope is simply described as the rate of change, the change in y per unit change in x ;
Therefore, this means Sarah's salary will increase by 3500 per year
plzz helpppp.........
Answer:
B) Unequal
Step-by-step explanation:
yun po yung sagot
p follow po at pa rate at heart
Can someone please help me with this. ANYONE!
Answer:
Step-by-step explanation:
1 OF 3OR5
Determinar el valor de las siguientes progresiones:
1)4, 12, 36, 108,…
2)4, 20, 100, 500,…
3)5, 10, 20, 40,…
Answer:
Step-by-step explanation:
1) . .324, 972, 2916
2) ...2500, 12500, 62500
3). . 80, 160, 320
An article bought for $125 was sold %175. The percentage profit
Answer:
40% profit
Step-by-step explanation:
There is a profit of $50.
If you were to find the percentage, you would divide 50 by 125. This would give you 0.4
Kate is 1 year and six months younger than her sister. If her sister is 14 years and 2 months old, how old is Kate?
Answer:
Kate is 13years and 4 months old,I suggest.
