Answer:
[tex]x=-7,-3[/tex]
Step-by-step explanation:
Completing the square means you are changing the polynomial so that it is a perfect square trinomial. Since the middle term is 10, we need the last term to be 25 since 5+5=10, thus, 5*5=25:
[tex]x^2+10x+21=0\\x^2+10x+21+4=0+4\\x^2+10x+25=4\\(x+5)^2=4\\x+5=\pm2\\x=-7,-3[/tex]
As you can see, because we change [tex]x^2+10x+21[/tex] to [tex]x^2+10x+25[/tex] by adding 4 to both sides, we were able to reduce it to [tex](x+5)^2[/tex], a perfect square, and solve the rest of the problem.
Please help me with these, first to answer receives 5 stars if correct and probably BRAINLIEST! The following are daily high temperatures (℉) in Auckland, New Zealand:
75 67 83 90 79 74 70 71 72 78 76 67 66 80 77 77 84 74
1. Using the data above, make a stem-and-leaf plot. (4 points)
2. Using the data above, make a box-and-whisker plot. If the set has outliers, use an * to show
them.
Answer:
6 6, 7, 7
7 0, 1, 2, 4, 4, 5, 6, 7, 7, 8
8 0, 3
9 0
Step-by-step explanation:
If you don't know how to make a stem and leaf plots this how. First you will draw a T-chart then you put the first integer or 10th place number on the left and the ones place number on the right.
Please help me solve this problem
Answer:
$46,800,000
Step-by-step explanation:
1. Find the total number of shares that Live Fund has. They have 24% of the total shares, which is 78,000. To find their portion of the shares, multiply the total amount by the percent they own; 78,000 * .24. This gives us 18720 shares.
2. Since they are selling half of their shares, divide their total number of shares by 2. This gives us 9360.
3. Each share is worth $5000, so multiply 9360 by 5000. This gives us a final answer of $46,800,000.
Alternatively, we could have just found half of the percent of shares that they own in step 1, so what 12% of 78,000 is instead, and multiplied by 5000.
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)
Considering the definition of axis of symmetry and vertex of a quadratic function, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).
Quadratic function
The general form of a quadratic function is f(x = ax²+ bx+ c, whose graph is a parabola.
Axis of symmetry and vertex of a quadratic function
Quadratic functions have a maximum (if a<0) or a minimum (if a>0). This point is the vertex of the parabola.
That is, the vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is in the plane of symmetry of the parabola; anything that happens to the left of this point will be an exact reflection of what happens to the right.
In other words, the vertex divides the graph into two halves that are mirror images of each other, so that the axis of symmetry always passes through the vertex.
Vertex of f(x) = −x² − 10x + 16
In this case, you know that the axis of symmetry for the function is x = −5.
So the vertex on the x-axis has a value of -5. To calculate the value of the vertex on the y-axis, you must substitute the value of the vertex on the x-axis in the function:
f(-5) = −(-5)² − 10×(-5) + 16
Solving:
f(-5)= 41
In summary, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).
Learn more about the vertex of a quadratic function:
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Answer:
a
Step-by-step explanation:
a
On the southeast corner of Millennium Park, there is a garden walk. It is marked off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row along which flowers will be planted.
If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and explain your reasoning. (2 points)
Answer:
150 feet
Step-by-step explanation:
a²+b²=c²
90²+120²=c²
8100+14400=22500
√22500 = 150
c = 150 feet
Arnold is about to go on a 500-mile car trip. His mechanic recommends that he buy
a special highway engine oil that will save him 50 cents in gas for every 25 miles of the
trip. This new oil, however, will cost $20. Is it worthwhile for Arnold to buy the oil if he
has a coupon for $4 dollars off the price?
500 miles/ 25 = 20 x 0.50 = $10
He will save a total of $10
20-4 = $16
it will cost him $16 for the oil which is more than what he saves in gas so buying the oil is not worth it.
consecutive integers differ by, such as 15 and
Answer:
integers are not fractions so there you go
A=bh (b=8, h=5) what does A equal to evaluate this problem using the equation below
Answer:
40
Step-by-step explanation:
What is the radius of the circle?
Answer:
13cm
Step-by-step explanation:
In this case you have to use the Pythagorean theorem.
cy = 24/2
cy=12 cm ( a perpendicular drawn to a chord from the center bisects the chord..
ac=5 cm (given)
now,
ay^2= 25cm + 144 cm
ay^2 = 169 cm
√169 = 13 cm
Answer:
13 cm
Step-by-step explanation:
Since AC is perpendicular to XY , and XA and AY are both radii of the same circle, you can say that AC is a perpendicular bisector.
From there, we can say that XC is 1/2 of 24 cm, or 12 cm.
We can then form triangle ACX use the Pythagorean theorem to find the length of AX.
The square root of 12^2 + 5^2 is 13.
Therefore, the radius of the circle is 13 cm
The hypotenuse of a right triangle measures 7 cm and one of its legs measures 2 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth
[tex]\begin{equation}\text { Question: If } \ln (x+y)=4 \times y \text {. Find } \frac{d^{2} y}{d x^{2}} \text { at } x=0 \text {. }\end{equation}[/tex]
I think you meant to say
[tex]\ln(x+y) = 4xy[/tex]
and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.
Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives
[tex]\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}[/tex]
Note that when x = 0 and y = 1, we have dy/dx = 3.
Differentiate both sides again with respect to x :
[tex]\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}[/tex]
No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get
[tex]\dfrac{d^2y}{dx^2} \bigg|_{x=0} = \boxed{40}[/tex]
A scale drawing of an American flag is 6 inches tall. The actual flag is 3 feet tall. What is the scale of the drawing?
A boy bought 1,567kg of frozen chicken,657g of vegetables and 95g of corn oil from a shopping mall. What is the total weight of the items she bought in kilograms
Answer:
1567.752
Step-by-step explanation:
1000g = 1 kg. Before you can add them together, you have to multiply the vegetables and corn oil by 0.001 so that they are now in the unit of Kilograms. Then just add all of them together
Answer:
1567.752
Step-by-step explanation:
Find teh value of teh coefficient a in the equation ax +2y =8 if a solution to the equation is the pair x=2 and y= 1
Answer:
a(2)+2(1)=8
2a+2=8
2a=8-2
2a=6
a=3
Mrs Silverstein has 14 boys and Il girls in her
class. She must select two students at random to
serve as the class presidents What is the
probability that she will choose a boy followed by a
giri?
Answer:
Step-by-step explanation:
Here, I will instead go through the process for finding the probability of choosing two girls. Then once you understand how it was done, hopefully you will be able to answer the actual question for yourself.
Finding the probability of choosing two girls. Let's make it simpler by starting with the probability of choosing the first girl only.Probability of choosing the first girl. (Note: the letter chosen to represent the event is not important. Pick something that makes sense to you and be consistent)
P(G1) = # of girls / # of total outcomesSo the number of girls we know to be 11. What is the number of total outcomes? Well a boy or a girl can be chosen, and there are 14 boys and 11 girls, for a total of 25 students.
P(G1) = 11/ 25Let's find the probability of choosing the second girl from here.
P(G2) = # of girls / # of total outcomesHowever, this time things have changed. We've already chosen one girl, so the number of girls remaining to choose from is reduced 11 to 10. And the total number of students to choose from is reduced from 25 to 24.
P(G2) = 10 / 24Now we have the probability of choosing the first girl and the probability of choosing the second girl. From here, we just need to combine them to find the probability of both things happening together. To calculate the probability of two different events occurring, you multiply the two probabilities together.
Probability of choosing two girls. Let's use T for Two girls.
P(T) = P(G1) × P(G2) = (11 /25) × (10/24)
From here you can use a calculator to find the answer. This answer can either be written as a fraction, a decimal, or a percentage.
= 0.19 = 19 / 100 = 19%
If IN = 2x + 10 and AT = 26, find x. Group of answer choices 10 8 12 6
Answer:
your answer is B. 8
Step-by-step explanation:
Substitute x for 8.
2(8)+10
16+10=26
What is the normal approximation for pi?
Answer:
Most people use 3 or 3.14
Help picture below problem 18
Answer:
X⁶
Step-by-step explanation:
x⁹/x³
= x⁹-³
= x⁶ is the answer
Answer:
E. [tex]x^{6}[/tex]
Step-by-step explanation:
To divide two fractions we subtract the power of second expression from the first one:
[tex]x^{(9-3)} = x^{6}[/tex]
help me please :( I need this rlly badly no cap
Answer:
given below
Step-by-step explanation:
1 a. Sample space : 2 green, 1 red, 10 blue
b. Sample space : top surface, bottom surface, curved surface ( side)
c. shooting a free throw in a basketball game ( sorry I dont know this one )
solve it in form of cos and sin pls
[tex]\text{L.H.S}\\\\=\dfrac{\cot A}{1- \tan A} + \dfrac{\tan A}{1- \cot A}\\\\\\=\dfrac{\tfrac{\cos A}{\sin A}}{1- \tfrac{\sin A}{\cos A}} + \dfrac{\tfrac{\sin A}{\cos A}}{1-\tfrac{\cos A}{\sin A}}\\\\\\=\dfrac{\tfrac{\cos A}{\sin A}}{\tfrac{\cos A- \sin A}{\cos A}} + \dfrac{\tfrac{\sin A}{\cos A}}{\tfrac{\sin A - \cos A}{\sin A}}\\\\\\=\dfrac{\cos^2 A}{\sin A(\cos A-\sin A)} + \dfrac{\sin^2 A}{\cos A(\sin A - \cos A)}\\\\\\[/tex]
[tex]=\dfrac{\cos^2 A}{\sin A(\cos A-\sin A)} - \dfrac{\sin^2 A}{\cos A(\cos A - \cos A)}\\\\\\=\dfrac 1{\cos A - \sin A} \left( \dfrac{\cos^2 A}{\sin A} - \dfrac{\sin^2 A}{\cos A}\right)\\\\\\=\dfrac 1{\cos A - \sin A} \left(\dfrac{\cos^3 A - \sin^3 A}{\sin A \cos A} \right)\\\\\\=\dfrac 1{\cos A - \sin A} \left[\dfrac{(\cos A - \sin A)(\cos^2 A + \sin^2 A + \sin A \cos A)}{\sin A \cos A} \right]\\\\\\=\dfrac{\cos^2 A + \sin^2 A+\sin A \cos A}{\sin A \cos A}\\\\\\[/tex]
[tex]=\dfrac{\cos^2 A}{\sin A \cos A}+\dfrac{\sin^2 A}{\sin A \cos A}+\dfrac{\sin A \cos A}{\sin A \cos A}\\\\\\=\dfrac{\cos A}{\sin A} + \dfrac{\sin A}{\cos A} + 1\\\\\\=\cot A + \tan A + 1\\\\\\=1 + \tan A + \cot A\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
2x +5 > -1 on the number line
Answer:
Below
Step-by-step explanation:
2x + 5 > -1
Treat the equality sign (ex. < >) as the costumary equal sign (=).
2x + 5 + (-5) > -1 + (-5) ---- -5 will cancel out the 5 on the left
2x/2 > -6/2 ------ divide by 2 to single out the x
x > -3
Remember to draw an open dot. Draw an arrow from -3 to the extreme right.
Someone please help me with this
Answer:
A
Step-by-step explanation:
writting only because answer need 20 words
i need help please
Answer:
The answer is 35 degrees
Step-by-step explanation:
Subtract 105 degrees and 40 degrees from 180 degrees
So just 180 - 105 - 40 =35
Answer:
35 degrees
Step-by-step explanation:
Find the area and perimeter of the figure below.
Answer:
x to the 3rd power
Step-by-step explanation:
x+x to the 2nd power = x to the 3rd power
Step-by-step explanation:
The area is the sum of three figures
A = 1*1 + 1*x + x²
= x² + x + 1
The perimeter is the sum of border segments
P = x*4 + 1*4
= 4x + 4
convert 30 g 519 mg to g
Answer:
30.519 g
Step-by-step explanation:
The relation
1 g = 1000 mgSolving
30 g 519 mg30 g + 519 mg30 g + (519/1000) g30 g + 0.519 g30.519 gWork out the value of 5^8 x 5^-2/5^4
Answer:
This is how i arrived at an answer 25
step by step
short answer please
Two forces of 560 N and 222 N act at a point. The resultant force is 634 N. Find the angle between the forces.
The angle between the two forces of 560 N and 222 N is 80.96°
What is the resultant of two vectors?The resultant of two vectors P and Q refer to the magnitudes of the vectors and it can be expressed by the formula [tex]\mathbf{R = \sqrt{P^2 +Q^2 +2PQ cos \theta }}[/tex]
Now, using the above equation, we can easily determine the angle between the forces of the two vectors as follows:
[tex]\mathbf{634 = \sqrt{560^2 +222^2 + 2(560 \times 222) \ Cos \theta }}[/tex]
[tex]\mathbf{401956 =313600 +49284 + 248640 \ Cos \theta }}[/tex]
[tex]\mathbf{401956 -313600 -49284 = 248640 \ Cos \theta }}[/tex]
[tex]\mathbf{39072= 248640 \ Cos \theta }}[/tex]
[tex]\mathbf{ Cos \theta = \dfrac{39072}{248640}}}[/tex]
[tex]\mathbf{Cos \theta =0.1571}[/tex]
[tex]\mathbf{ \theta =80.96^0}[/tex]
Therefore, we can conclude that the angle between the forces is 80.96°
Learn more about the resultant of two vectors here:
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You invest $5000, add 50 each month, at 7.9% for 11 years.
Answer:
???
Step-by-step explanation:
i need help please !!
Answer:
D. d-0.29
Step-by-step explanation:
29÷(0.29)=100
29÷0.29=100
They both equal 100 meaning that D is the answer.
Triangle ABC is situated inside of a green square. The perimeter of the square is 33.6 feet. What is the area of triangle ABC?
Step-by-step explanation:
solution for the triangle ABC
