Answer:
[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
Step-by-step explanation:
An equation in the vertex form is written as
[tex]y = a (x-h) + k[/tex]
Where the point (h, k) is the vertex of the equation.
For an equation in the form [tex]ax ^ 2 + bx + c[/tex] the x coordinate of the vertex is defined as
[tex]x = -\frac{b}{2a}[/tex]
In this case we have the equation [tex]y = 9x^2 + 9x - 1[/tex].
Where
[tex]a = 9\\\\b = 9\\\\c = -1[/tex]
Then the x coordinate of the vertex is:
[tex]x = -\frac{9}{2(9)}\\\\x = -\frac{9}{18}\\\\x = -\frac{1}{2}[/tex]
The y coordinate of the vertex is replacing the value of [tex]x = -\frac{1}{2}[/tex] in the function
[tex]y = 9 (-0.5) ^ 2 + 9 (-0.5) -1\\\\y = -\frac{13}{4}[/tex]
Then the vertex is:
[tex](-\frac{1}{2}, -\frac{13}{4})[/tex]
Therefore The encuacion excrita in the form of vertice is:
[tex]y = a(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
To find the coefficient a we substitute a point that belongs to the function [tex]y = 9x^2 + 9x - 1[/tex]
The point (0, -1) belongs to the function. Thus.
[tex]-1 = a(0 + \frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
[tex]-1 = a(\frac{1}{4}) -\frac{13}{4}\\\\a = \frac{-1 +\frac{13}{4}}{\frac{1}{4}}\\\\a = 9[/tex]
Then the written function in the form of vertice is
[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
Answer:
The vertex form of a parabolic function has the general formula:
f(x) = a(x-h)^2 + k where (h,k) represent the vertex of the parabola.
Therefore, to write the given equation in vertex form, we will need to transform it to the above formula as follows:
y = 9x^2 + 9x - 1
y = 9(x^2 + x) - 1
y = 9(x^2 + x + 1/4 - 1/4)-1
y = 9((x+1/2)^2 - 1/4)-1
y = 9(x + 1/2)^2 - 9/4 - 1
y = 9(x + 1/2)^2 - 13/4 ..............> The equation in vertex form
Step-by-step explanation:
Hope this helps!!! Have a great day!!! : )
What is the simplified form of this expression?
Answer:
[tex]\large\boxed{7c^2d-7c+4d-10}[/tex]
Step-by-step explanation:
[tex]5c^2d-4c+3d-3+2c^2d-3c+d-7\qquad\text{combine like terms}\\\\=(5c^2d+2c^2d)+(-4c-3c)+(3d+d)+(-3-7)\\\\=7c^2d-7c+4d-10[/tex]
what are the minimum, first quartile, 20 70 13 15 23 17 40 51
Answer:
Minimum 13
First quartile 16
Step-by-step explanation:
Rewrite the sample 20 70 13 15 23 17 40 51 in ascending order:
13 15 17 20 23 40 51 70
The minimum is 13.
The median is the middle number
13 15 17 20 23 40 51 70
The middle number between 20 and 23 is
[tex]\dfrac{20+23}{2}=21.5[/tex]
Consider first half of the sample
13 15 17 20
The first quartile is the middle number of this part. The middle number of
13 15 17 20
is
[tex]\dfrac{15+17}{2}=16[/tex]
Find the radius of the circle whose equation is x^2 + y^2 = 4.
Answer:
Radius of the given circle is r = 2.
Step-by-step explanation:
Given equation of the circle is [tex]x^2 + y^2 = 4[/tex].
Now we need to find the radius of the given circle [tex]x^2 + y^2 = 4[/tex].
To find that let's compare with the formula of the circle with is [tex]x^2 + y^2 = r^2[/tex], where r is the radius.
We get [tex]r^2 = 4[/tex]
take square root of both sides.
[tex]r=2[/tex]
Hence radius of the given circle is r = 2.
ANSWER
The radius is 2
EXPLANATION
The given equation of the circle is
[tex] {x}^{2} + {y}^{2} = 4[/tex]
.This is the same as
[tex]{x}^{2} + {y}^{2} = {2}^{2} [/tex]
We campare to the equation of the circle with center at the origin.
[tex]{x}^{2} + {y}^{2} = {r}^{2} [/tex]
We have
[tex]r = 2[/tex]
.Hence the radius of the circle is 2
Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 4.
Answer:
First Iterate: 11-2i
Second Iterate: 25-6i
Third Iterate: 53-14i
Step-by-step explanation:
Given:
f(z)=2z+(3-2i)
And
z_0=4
For the first iterate we have to put the value of z0 into the function in place of z.
First Iterate:
z_1=f(z_0 )=2z_0+(3-2i)
=2(4)+(3-2i)
=8+3-2i
=11-2i
Second Iterate:
For the second iterate we have to put the value of z1 into the function in place of z.
z_2=f(z_1 )=2z_1+(3-2i)
=2(11-2i)+(3-2i)
=22-4i+3-2i
=25-6i
Third Iterate:
For the third iterate we have to put the value of z2 into the function in place of z.
z_3=f(z_2 )=2z_2+(3-2i)
=2(25-6i)+(3-2i)
=50-12i+3-2i
=53-14i
Answer:d
Step-by-step explanation:
Cuz
Assume that two chords in a given circle are congruent. Which of the following must also be true?
Answer:
If the two chords are congruent, then they must be equidistant from the centre of the circle.
Ans: D
The diagram attached below shows that if two congruent chords are in a given circle, a statement that will be true is:
the two congruent chords must be equidistant from the center of the circle.Facts about congruent chords in a given circle:
The diagram attached below shows two chords that have the same length in the given circle O.The diagram shows that distance from the midpoint of one chord to the center of the circle, O, is the same as the distance from the middle of the other chord to center, O.The diagram attached below therefore shows that if two congruent chords are in a given circle, a statement that will be true is:
the two congruent chords must be equidistant from the center of the circle.Learn more here:
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K= 2/3 is a solution to the inequality 18k + 4 >18 true or false
Answer:
The answer will be: false.
18k = 12
12 + 4 = 16
16 > 18
So the equation is false.
Hope this helps! :D
Step-by-step explanation:
complementary or supplement and also solve for X.
Answer:
see explanation
Step-by-step explanation:
The 2 indicated angles form a straight angle and are supplementary.
4x + 5 + 41 = 180
4x + 46 = 180 ( subtract 46 from both sides )
4x = 134 ( divide both sides by 4 )
x = 33.5
a restaurant owner has a large trash container in the shape of a rectangular prism with a height of 4 ft and a base that is 4 ft wide by 6 feet long. during a one month period the container needed to be empty 4 times. how many cubic feet of trash were taken away during the month?
96 ft^3
192 ft^3
288 ft^3
384 ft^3
Answer:384ft^3
Step-by-step explanation:
4x4=16x6=96x4=384^3
Answer:
D) 384
Step-by-step explanation:
i just took the test
The distance between the points (5, -2) and (-7, 3) is
For this case we have that the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the points:
[tex](x_ {1}, y_ {1}) = (5, -2)\\(x_ {2}, y_ {2}) = (- 7,3)[/tex]
Substituting:
[tex]d = \sqrt {(- 7-5) ^ 2 + (3 - (- 2)) ^ 2}\\d = \sqrt {(- 7-5) ^ 2 + (3 + 2) ^ 2}\\d = \sqrt {(- 12) ^ 2 + (5) ^ 2}\\d = \sqrt {144 + 25}\\d = \sqrt {169}\\d = 13[/tex]
Thus, the distance between the points is 13
Answer:
[tex]d = 13[/tex]
Select the expression that is equivalent to (x-3)^2
The answer is C. X^2-6x+9
Answer:
C. [tex]x^2-6x+9[/tex]
Step-by-step explanation:
We have the expression [tex](x-3)^2[/tex] we can rewrite it as:
[tex](x-3)^2=(x-3)(x-3)[/tex] and solve it with distributive property or we can use the formula to multiply a binomial by itself. The formula is:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
or
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Then:
[tex](x-3)^2=x^2-2.x.3+3^2\\(x-3)^2=x^2-6x+9[/tex]
The correct option is C. [tex]x^2-6x+9[/tex]
Which fraction is equivalent to 0.75?
Answer:75/100
or 3/4
Step-by-step explanation:
Answer:
3/4ths
Step-by-step explanation:
100 divided by 4 is 25. 25 times 3 is 75.
What is the answer to number 4.
Answer: 2x-7, 2+4.
Explanation: An expression is a mathematical phrase that has a + or - but no equal sign.
1.
Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: The two lines are not perpendicular.
Conclusion: Two lines intersect at right angles.
Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.
Hypothesis: The two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are perpendicular.
it is the second one
Answer: Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.
Step-by-step explanation:
A conditional statement is written as "if p then q" , where symbol 'p' represents the hypothesis and symbol 'q' represents the conclusion.
For example : If a coin has two heads , then the coin is biased.
here , Hypothesis : a coin has two heads
Conclusion : coin is biased
Given conditional statement : If two lines intersect at right angles, then the two lines are perpendicular.
Here, Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.
For the right triangle shown, what is the tangent of angle A?
A) 2/3
B) 3/2
C) 3/4
D) 4/3
Answer:
The correct answer is option C 3/4
Step-by-step explanation:
It is given a right angled triangle ABC
To find the value of x
Hypotenuse² = Base² + height²
(x + 2)² = x² + (x + 1)²
x² + 4x + 4 = x² + x² + 2x + 1
x² -2x -3 = 0
We get x = 3 and x = -1
We take positive value x = 3
To find Tan A
Tan A = Opposite side/Adjacent side
= BC/AB = x/(x + 1) = 3/4
Therefore the correct answer is option C. 3/4
i am a number. my number squared is equal to 1/16. hat number am i
Answer: 1/4
Step-by-step explanation: 1/4 x 1/4= 1/16
Write the equation that is the translation of y=|x| right 7 units and down 9 units.
Answer:
[tex]y=|x-7|-9[/tex].
Step-by-step explanation:
The given function is [tex]y=|x|[/tex].
When this function is translated to the right 7 units and down 9 units, then the equation becomes
[tex]y=|x-7|-9[/tex].
Always remember that; [tex]y=|x-c|-k[/tex] is a transformation that translates the graph of [tex]y=|x|[/tex] c units to the right and k units down.
The correct choice is the first option.
Yuma is solving the inequality 3x−23≥−5.
To solve the inequality, he begins by solving the equation as shown.
Which number line represents the solution to the inequality?
Urgent answer plz. Thank u.
[tex]3x \geqslant 23 - 5 \\ 3x \geqslant 18 \\ x \geqslant 6 \\[/tex]
Answer: x≥ 6
Step-by-step explanation:
To solve this inequality
3x - 23 ≥ -5
First, what you need to do is to add 23 to both-side of the inequality, Hence;
3x -23 + 23 ≥ -5 + 23
(-23 + 23 = 0, also -5 + 23 = 18)
3x ≥ 18
To get the value of x, we need to divide both-side of the inequality by 3
3x / 3 ≥ 18/3
(On the left hand side of the equation, the three at the numerator will cancel out that of the denominator, then on the right hand side of the equation, 3 will divide 18 which will give 6)
x ≥ 6
In an experiment, Seth was given a substance known as ammonium carbonate, (NH4)2CO3. Seth connected a bunsen burner to the gas valve using a gas hose. He turned on the gas valve and lit the bunsen burner. Using a test tube, Seth heated a piece of ammonium carbonate. Seth noticed the following:
- Condensation appeared on the sides at the top of the test tube.
- An ammonia smell was coming from the test tube.
Seth continued to light a wooden splint and stick it down the test tube and it immediately was extinguished.
Throughout this experiment, how many signs of chemical changes were observed and actual chemical changes took place?
A) 4
B) 5
C) 6
D) 7
Answer: B
Step-by-step explanation: do you still need help with this let me know :P
Answer:
B. 5
Step-by-step explanation:
In an experiment, Seth was given a substance known as ammonium carbonate, (NH4)2CO3. Seth connected a Bunsen burner to the gas valve using a gas hose. He turned on the gas valve and lit the Bunsen burner. Using a test tube, Seth heated a piece of ammonium carbonate. Seth noticed the following: - Condensation appeared on the sides at the top of the test tube. (Condensation is not a chemical change, but it was a sign of a chemical change.) - An ammonia smell was coming from the test tube. Seth continued to light a wooden splint and stick it down the test tube and it immediately was extinguished.
The area of the base of a rectangular prism is 36 cm2. The height of the prism is 3
5
6
cm. What is the volume of the prism?
Answer:
Height 356: 12816 cm3
Height 6: 216 cm3
Height 5: 180 cm3
Height 3: 108 cm3
Step-by-step explanation:
base * height = volume
hello please help asap ( 15 points)
First 816
second 143
Third 4207.5
A set of stairs is being built as shown. The length of each stair is 11 inches. What is the rise, r, for each stair? Round to the nearest inch.
2 inches
7 inches
17 inches
24 inches
Answer:
7 inches just took test
Step-by-step explanation:
The rise, r, for each stair is 7 inches.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
From the given figure the length of each stair is 11 inches.
We have to find the rise of each stair.
From the pythagoras theorem we find the value of r.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
11²+r²=13²
121+r²=169
r²=169-121
r²=48
Take square root on both sides
r=6.9
r= 7 inches.
Hence, the rise, r, for each stair is 7 inches.
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For questions 1-2 identify the zeros of the function
Answer:
Step-by-step explanation:
The zeros of a function are where it crosses the x axis, so just find the coordinates for the x intercepts.
1.
[tex](2,0)[/tex] and [tex](-1,0)[/tex]
2.
[tex](3,0)[/tex] and [tex](-3,0)[/tex]
Slove -4(x+1)-3=(x-4)
Answer:
[tex]x=-\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]-4(x+1)-3=(x-4) \\ \\ -4x-4-3=x-4 \\ \\ -4x-7=x-4 \\ \\ -7=5x-4 \\ \\ 5x=-3 \\ \\ x=-\frac{3}{5}[/tex]
- 4 ( x + 1) - 3 = ( x - 4)
Distribute- 4x - 4 - 3 = (x - 4)2. Take away the parenthesis at the end
- 4x - 4 - 3 = x - 43. Combine like terms
- 4x - 7 = x - 44. Add 4x to each side
-7 = -3x - 45. Add 4 to each side
-3 = -3x6. Divide
-3 / -3 = -3x / -3x = 1 what is the question mark represent
15/100=375/?
hey so here ya go, ? = 2500 :)
Answer:
56.25
Step-by-step explanation:
A simple way to answer questions like these is to
Step 1: Multiply 15 and 375. This equals = 5625
Step 2: divide 100 and 5625. This equals = 56.25
Number 14 please! An Astronaut standing on the moon would weigh about 16% of her weight on earth. If an astronaut Weighs 150 pounds on earth, about how much would she weigh on the moon?
Answer: 24 pounds
weight on moon=(.16)(weight on earth)
weight on moon= (.16)(150)=24
Ky wants to buy three shirts, which were originally priced 49.96 each. The store will discount the price of the third shirt by 50% and then apply a 7.1% tax to the total cost of all three shirts. Including the tax, what will be the mean cost of each shirt?
49.96 + 49.96 + (49.96x.5)
99.92+24.94=124.86 divide 7.1 and 124.86 which gives you 17.58591549295775 but I’m guessing u round so 17.59 and add that to 124.86which equals 142.45. The total cost is 142.45. But each shirt is 49.96 and the third is 24.94. Don’t forget the dollar sign and have a good day! :)
Answer:
it's 44.59
Step-by-step explanation:
HELPPPPPPPPPP Add & subtract matrices .....
PLZ GIVE THE ANSWER .. THANKSSSSS .
Answer:
[tex]\left[\begin{array}{cc}0&-1\\-1&0\\-1&-1\end{array}\right][/tex]
Step-by-step explanation:
In this question we have to subtract the corresponding entries of column of matrix 1 and the matrix 2 corresponding entries
[tex]=\left[\begin{array}{cc}-1&0\\1&-2\\1&3\end{array}\right]-\left[\begin{array}{cc}-1&1\\2&-2\\2&4\end{array}\right] \\=\left[\begin{array}{cc}-1-(-1)&0-1\\1-2&-2-(-2)\\1-2&3-4\end{array}\right]\\=\left[\begin{array}{cc}-1+1&-1\\-1&-2+2\\-1&-1\end{array}\right]\\=\left[\begin{array}{cc}0&-1\\-1&0\\-1&-1\end{array}\right][/tex]
simplify by rationalizing the denominator: 4 over the square root of 10 minus square room of 6
Answer:
[tex]\large\boxed{\dfrac{4}{\sqrt{10}-\sqrt6}=\sqrt{10}+\sqrt6}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{\sqrt{10}-\sqrt6}\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\ \text{and}\ (\sqrt{a})^2=a\\\\=\dfrac{4}{\sqrt{10}-\sqrt6}\cdot\dfrac{\sqrt{10}+\sqrt6}{\sqrt{10}+\sqrt6}=\dfrac{4(\sqrt{10}+\sqrt6)}{(\sqrt{10})^2-(\sqrt6)^2}=\dfrac{4(\sqrt{10}+\sqrt6)}{10-6}\\\\=\dfrac{4(\sqrt{10}+\sqrt6)}{4}=\sqrt{10}+\sqrt6[/tex]
The rationalization of the given expression will be equal to
[tex]\dfrac{4}{\sqrt{10}-\sqrt{6}}=\sqrt{10}+\sqrt{6}[/tex]
What is rationalization?Rationalization is a procedure used in elementary mathematics to remove the irrational number from the denominator.
The rationalization of the given fraction will be :-
[tex]=\dfrac{4}{\sqrt{10}-\sqrt{6}}\times \dfrac{\sqrt{10}+\sqrt{6}}{\sqrt{10}+\sqrt{6}}[/tex]
[tex]\dfrac{4\sqrt{10}+\sqrt{6}}{\sqrt{10}^2-\sqrt{6}^2}=\dfrac{4\sqrt{10}+\sqrt{6}}{10-6}[/tex]
[tex]\dfrac{4\sqrt{10}+\sqrt{6}}{\sqrt{10}^2-\sqrt{6}^2} =\dfrac{4\sqrt{10}+\sqrt{6}}{4}=\sqrt{10}+\sqrt{6}[/tex]
Hence rationalization of the given expression will be equal to
[tex]\dfrac{4}{\sqrt{10}-\sqrt{6}}=\sqrt{10}+\sqrt{6}[/tex]
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does anyone know any of these bc my brother needs help and i don’t know!?!?!?
Answer:
the third one all the way to the right
Step-by-step explanation:
the other two have two or more congruent sides and that one doesnt and also the one that doesn'r belong has a right angle and the others dont
Which of the following integers represents the opposite of the opposite of 4?
4
-4
1/4
-1/4
Answer:
[tex]4[/tex]
Step-by-step explanation:
To find the opposite of the opposite, multiply the given number by -1 twice, or just 1 since [tex]-1*-1=1[/tex].
[tex]4*-1*-1=4[/tex] or [tex]4*1=4[/tex]
The opposite of a number is its additive inverse. Therefore, the opposite of the opposite of a given number will always be the original number itself. In this instance, the opposite of the opposite of 4 is 4.
Explanation:The question asks for the opposite of the opposite of a given number. In mathematics, the 'opposite' of a number is its additive inverse. If the original number is positive, its opposite is the same number as a negative. Vice versa, if the original number is negative, its opposite would be positive. For example, the opposite of 4 is -4 and the opposite of -4 is 4.
So let's apply this concept to the given number, which is 4. The opposite of 4 is -4. Now, the opposite of -4 is 4. Hence, the opposite of the opposite of 4 is 4.
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