Answer:
[tex]y=-6(x-1)^{2}-7[/tex]
Step-by-step explanation:
we have
[tex]6x^{2} -12x+y+13=0[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+13=-6x^{2} +12x[/tex]
Factor the leading coefficient
[tex]y+13=-6(x^{2} -2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+13-6=-6(x^{2} -2x+1)[/tex]
[tex]y+7=-6(x^{2} -2x+1)[/tex]
Rewrite as perfect squares
[tex]y+7=-6(x-1)^{2}[/tex]
[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form
The vertex is (1,-7) is a maximum, the parabola open downward
To convert 6x^2 - 12x + y + 13 = 0 to vertex form, follow the steps to complete the square and rewrite the equation as (x - 1)^2 = -y/6 - 7/6.
Explanation:The equation 6x^2-12x+y+13=0 is in the general form of a quadratic equation. To convert it into the vertex form, we need to complete the square.
First, let's group the x terms together: 6x^2 - 12x = -(y + 13).
Next, let's complete the square: 6(x^2 - 2x) = -(y + 13).
Now, we can add (2/2)^2 = 1 to both sides to complete the square: 6(x^2 - 2x + 1) = -(y + 13) + 6.
Simplifying further, we get 6(x - 1)^2 = -y - 7.
Finally, we can write the equation in vertex form by dividing both sides by 6: (x - 1)^2 = -y/6 - 7/6.
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22.....................
Answer:
a=11,b=7
Step-by-step explanation:
To get to the result we firs multiply the figures on the left hand side.
multiplication of each term with its similar term is shown:
5×-4=-20
x⁷ₓx⁴=x¹¹. Here we add the powers because we are multiplying indices to the same base.
y²ₓ y⁵= y⁷
Thus the correct answer is a=11 and b=7
Answer:
[tex]a=11,b=7[/tex]
Step-by-step explanation:
The given equation is
[tex](5x^7y^2)(-4x^4y^5)=-20x^ay^b[/tex]
Recall that [tex]a^m\times a^n =a^{m+n}[/tex]
We simplify the left hand side to obtain;
[tex]-20x^{7+4}y^{2+5}=-20x^ay^b[/tex]
This implies that;
[tex]-20x^{11}y^{7}=-20x^ay^b[/tex]
Comparing exponents, we have
a=11,b=7
The first choice is correct.
Is the point (5,-1) a solution of y=2x-11
if the given point satisfies this equation then it would be its solution
(-1)=2(5)-11
-1=10-1
-1=-1
lHS=RHS
Hence (/,-1) is the solution of y=2x-11
Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2? (–2, 0) and (0, 1) (0, –2) and (1, 0) (–2, 0) and (1, 0) (0, –2) and (0, 1) Mark this and return
ANSWER
[tex](0,-2), (1,0)[/tex]
EXPLANATION
The first equation is
[tex]y = {x}^{2} + x - 2[/tex]
The second equation is
[tex]y = 2x - 2[/tex]
We equate both equations to get,
[tex] {x}^{2} + x - 2 = 2x - 2[/tex]
[tex] {x}^{2} + x - 2x - 2 + 2 = 0[/tex]
Simplify
[tex] {x}^{2} - x = 0[/tex]
Factor
[tex]x(x - 1) = 0[/tex]
Either
[tex]x = 0[/tex]
Or
[tex]x - 1 = 0[/tex]
[tex]x = 1[/tex]
Put x=0 or x=1 into the second equation to get,
[tex]y = 2(0) - 2 = - 2[/tex]
Or
[tex]y = 2(1) - 2 = 0[/tex]
Therefore the solutions are;
[tex](0,-2), (1,0)[/tex]
Answer:
(0, -2) (1, 0)Step-by-step explanation:
I got it right on the test... Have a great day :)
Pls pls help with number 4 I really need help with this
Answer:
your answer is 8 cups. to find the answer first make the fraction in to a improper fraction. that will give you 8/3 cups. then multiply by 3. that will give you 24/3. then simplify it. you will get 8
Step-by-step explanation:
Acute △ABC with angles α, β, and γ is inscribed in a circle. Tangents to the circle at points A, B, and C intersect in points M, N, and P. Find measures of angles of the △MNP.
In an acute triangle ABC Inscribed angles in a circle with another triangle MNP formed by the intersections of tangents to the circle at points A, B, and C, the angles of triangle MNP are the sum of the opposite angles of triangle ABC. Therefore, ∠M = α + γ, ∠N = β + α, and ∠P = γ + β.
The question is about an acute triangle ABC inscribed in a circle and another triangle MNP formed by the intersections of tangents to the circle at points A, B, and C.
From the properties of circle and geometry, in such a scenario, the angles of triangle MNP correspond to sum of the opposite angles of triangle ABC.
The measures of angles in △MNP are as follows:
∠M = α + γ
∠N = β + α
∠P = γ + β
This relation comes from the fact that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
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An umbrella is in the shape of a regular octagon as shown. The umbrella is separated into sections, as shown by the dashed lines that intersect in the center of the octogon. What is the value of x?
A: 22.5 degrees
B: 37.5 degrees
C: 45 degrees
D: 50 degrees
Answer:
C. 45 degrees.
Step-by-step explanation:
The degree of the entire circle is 360 degrees, and the circle is divided into 8 equal sections, therefore x = 360/8 = 45 degrees.
The central angle of a regular octagon is computed by dividing the total degrees in the circle (360 degrees) by the number of sides in the octagon (8). Hence, the value of 'x' is 45 degrees.
Explanation:The question is asking for the measure of 'x', which represents the angle in the center of the octagonal umbrella. To solve this, we need to remember that the total degrees in a circle (or in this case, an octagon) is 360 degrees. As a regular octagon consists of 8 equal angles, we simply divide 360 by 8 to find the measure of each angle. Therefore, 'x' equals to 45 degrees. This corresponds to option C.
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What is 4 + 4?
Right answer gets brainiest!
(Free points because I hit 111 questions answered, I'll maybe do one when I get 123 questions answered!)
Answer:
8
Step-by-step explanation:
The answer is 8 but maybe it is 21
Which algebraic expression is a polynomial?
Answer: The answer is B.
Step-by-step explanation: "Poly" means "many", and "nomial", in this case, meaning "term".
B is the only one with 3 or more different terms.
(negative number, whole number, two unknowns, and a square root)
The expression which is a polynomial is:
[tex]-6x^3+x^2-\sqrt{5}[/tex]
Step-by-step explanation:A polynomial expression is a expression of the form:
[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+........+a_1x+a_0[/tex]
where n belong to non-negative integers and [tex]a_i's[/tex] are real numbers.
1)
[tex]4x^2-3x+\dfrac{2}{x}[/tex]
This is not a polynomial because the third term:
[tex]\dfrac{2}{x}=2x^{-1}[/tex] has a negative poswer of x which violates the definition of polynomial.
2)
[tex]-6x^3+x^2-\sqrt{5}[/tex]
In this each of the term satisfy the definition of polynomial and hence the expression is a polynomial expression.
3)
[tex]8x^2+\sqrt{x}[/tex]
Here the second term is not a integer power and hence violate the definition of polynomial.
4)
[tex]-2x^4+\dfrac{3}{2x}[/tex]
which could also be written as:
[tex]-2x^4+\dfrac{3}{2}x^{-1}[/tex]
Here the second term contain a negative power of x and hence is not a polynomial.
√x+3=5
[tex] \sqrt{x} + 3 = 5[/tex]
Answer:
Let's solve your equation step-by-step.
√x+3=5
Step 1: Add -3 to both sides.
√x+3+−3=5+−3
√x=2
Step 2: Solve Square Root.
√x=2
x=22(Square both sides)
x=4
Check answers. (Plug them in to make sure they work.)
x=4(Works in original equation)
Answer:
x=4
In a spelling bee, the winner and three other competitors each spelled 18 words correctly. About how many total words did these students spell correctly?
Answer:72.
Step-by-step explanation:
There are three competitrs, one winner, four people in all. multiply four by 18,and you have seventy two
Answer:
72
Step-by-step explanation:
In Brooke’s class of 25 students, 15 students report that math is their favorite class and 40% of the students report that science is their favorite class. Do students prefer math or science
Answer:
The students prefer Math 60%, to Science 40%
Step-by-step explanation:
15/25= 3/5= 5 is then divided into 3 to get the per cent= 60%
how many faces does a pyramid with a square base have?
A. 7
B. 5
C. 6
D. 8
Answer:
B. 5
Step-by-step explanation:
Each edge of the base has one triangular face attached to it (which then come together). Since it is a square base, this gives you 4 faces, and the base itself makes 5 faces.
Explain why a commercial that says "80% of dentists use this toothpaste" might be misleading?
Answer:
This may be misleading because it leaves room for doubt.
Step-by-step explanation:
If they're only saying that 80% use the toothpaste, that is saying that there is 20% who don't like it.
Final answer:
A commercial claiming "80% of dentists use this toothpaste" may be misleading due to lack of context, potential selection bias, and vagueness surrounding the term 'use.' Historical instances, like deceptive advertising by Colgate-Palmolive in the 1950s, alert consumers to be cautious of such claims.
Explanation:
A commercial claiming that "80% of dentists use this toothpaste" might be misleading because it does not provide a full context. Without additional information, such a statement can create false impressions. For instance, the sample size could be too small or not representative of the general population of dentists. The selection criteria for the dentists might be biased towards those who prefer the product or are somehow affiliated with the toothpaste's manufacturer. Furthermore, the term "use" is vague and could simply mean the dentists have tried the product rather than regularly using it. It is also important to question whether dentists recommend the toothpaste to their patients or if their usage is based on personal preference only.
As history has shown with the deceptive advertising practices of the 1950s, like those of Colgate-Palmolive with their Rapid Shave product, companies have sometimes engaged in advertising that misrepresented the effectiveness of their products. Therefore, it's essential for consumers to be wary of such claims and seek more information before making a purchase decision based on such endorsements.
Plz help me i need it
Answer: [tex]\bold{b)\quad y=\dfrac{log_4-9}{2}}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
[tex]y=4^{2x+9}\\\\\text{Swap the x's and y's:}\\x=4^{2y+9}\\\\\text{Apply }log_4\text{ to both sides:}\\log_4x=log_44^{2y+9}\\\\log_44\text{ cancels out:}\\log_4x=2y+9\\\\\text{Subtract 9 from both sides:}\\log_4x-9=2y\\\\\text{Divide both sides by 2:}\\\dfrac{log_4x-9}{2}=y[/tex]
What is the median of the following distribution? 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48, 55, 56
Step-by-step explanation:
To find the median of a distribution, we first need to arrange the data in ascending order. Then, if the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.
Given the distribution: 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48
Arranging the data in ascending order: 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48
There are 15 data points, which is an odd number. The middle value is the 8th value, which is 35.
Therefore, the median of the given distribution is:
OE. 35
For the next one, also put the answers because they will not always give you the correct answer since they do not know what it will be :/
The median of the given distribution is the ninth number in the ordered set, which is 37.
Explanation:To find the median of the given distribution, you will first need to order the data from smallest to largest, which has been done. The data set consists of 17 values, so the median will be the value in the middle position, which is the 9th value when the data is ordered. Since the data set is already in ascending order, you count nine values from the start, and the 9th value is the median.
The sequence of numbers is: 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48, 55, 56.
The median of the distribution is 37, which is the value in the middle of the ordered set.
A graduated cylinder that is 24cm tall can hold 1L of water. What is the radius of the cylinder? What is the height of the 500 ml mark? The 250 ml mark? Recall that 1 liter is equal to 1000 millimeters
Answer:
Part A) The radius of the cylinder is [tex]r=\sqrt{\frac{125}{3\pi}}\ cm[/tex]
Part B) The height of the 500 ml mark is [tex]12\ cm[/tex]
Part C) The height of the 250 ml mark is [tex]6\ cm[/tex]
Step-by-step explanation:
Part A) What is the radius of the cylinder?
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1\ l=1,000\ ml=1,000\ cm^{3}[/tex]
[tex]h=24\ cm[/tex]
substitute and solve for r
[tex]1,000=\pi r^{2} (24)[/tex]
[tex]r^{2}=\frac{1,000}{24\pi}[/tex]
[tex]r=\sqrt{\frac{1,000}{24\pi}}\ cm[/tex]
simplify
[tex]r=\sqrt{\frac{125}{3\pi}}\ cm[/tex]
Part B) What is the height of the 500 ml mark?
using proportion
[tex]\frac{24}{1,000}\frac{cm}{ml}=\frac{x}{500}\frac{cm}{ml}\\ \\x=500*24/1,000\\\\x=12\ cm[/tex]
Part C) What is the height of the 250 ml mark?
using proportion
[tex]\frac{24}{1,000}\frac{cm}{ml}=\frac{x}{250}\frac{cm}{ml}\\ \\x=250*24/1,000\\\\x=6\ cm[/tex]
Final answer:
Explanation of finding cylinder radius, heights at 500ml and 250ml marks in a graduated cylinder.
Explanation:
A liter is equal to 1000 milliliters (mL) or cubic centimeters (cm³).
To find the radius of the cylinder:
Use the formula for the volume of a cylinder: V = πr²h
Substitute the known volume (1000 mL or cm³) and height (24 cm) to find the radius.
Height at the 500ml mark: Half the height of the cylinder, so 12 cm. Height at the 250ml mark: One-fourth the height of the cylinder, so 6 cm.
the pair of variables x=5, y=7 is the solution to the equation ax–2y=1. Find the coefficient a.
Answer:
a=3
Step-by-step explanation:
This should be very simple, just substitute xy and y for 5 and 7 respectively, so 5a-2*7=1, or 5a-14=1, or 5a=15, if we divide both sides by 5, we get a=3
Answer:
A=3 5a-14=1
Step-by-step explanation:
Add 14 to both sides then divide 5 and 15 to get 3
Change .45 to a fraction in lowest terms.
Answer:
9/20
Step-by-step explanation:
.45 = 45/100
Divide the top and bottom by 5
45/5 = 9
100/5 = 20
The fraction becomes 9/20
Answer: 9/20
Step-by-step explanation: .45 equals the fraction 45/100.
To reduce the fraction divide the top and bottom by 5:
45/100 = 9/20, which is in the lowest terms.
Dana colored 1/6 of her picture,and Brendan colored 1/4 of his picture.Who Coloed more?
Answer:
Brenden colored more.
Explanation:
1
6
,
1
4
=
4
1
24
6
,
6
1
24
4
∴
1
4
>
1
6
Wouldn’t it be 1/25 because you just multiply
Halp plz first to get right gets brainlyist (don't mind my spelling)
When you multiply a number by 10,100,1,000 and so forth do you move the decimal point to the left or to the right as many places as there are zero in the multiplier
Answer:
right
Step-by-step explanation:
You would move it towards the right because that adds a place value while moving it to the left takes away a place value.
When you multiply a number by powers of 10, the decimal point moves to the right as many places as there are zeros in the multiplier. For example, multiplying 1.2 by 10 gives 12, because the decimal point moves one place to the right.
Explanation:In mathematics, when you multiply a number by 10, 100, 1,000, and so forth (powers of 10), you move the decimal point to the right as many places as there are zeros in the multiplier. This is because you are increasing the value of the number by a factor of 10 for each move to the right.
For instance, if you multiply 1.2 by 10, the result is 12. The decimal point has moved one place to the right because there is one zero in 10. If you multiply 1.2 by 1,000, the result is 1,200. The decimal point has moved three places to the right because there are three zeros in 1,000.
This understanding makes it easier to handle multiplication of numbers by powers of 10. But remember, this only applies when multiplying. When dividing, the decimal point moves to the left.
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College Algebra hw. Need help, don’t understand it, can someone explain this to me step-by-step?
55, 57, and 58 ONLY
Answer:
1, 9 and 12
Step-by-step explanation:
55
(f ○ g )(2) = f(g(2) ← from table g(2) = 3, thus
f(g(2)) = f(3) = 1 ← from table f(3) = 1
57
(g ○ f )(3) = g(f(3)) = g(1) = 9
58
(g ○ f )(6) = g(f(6)) = g(9) = 12
59
(f ○ f)(4) = f(f(4)) = f(3) = 1
EASY! WILL MARK BRAINEST! Find the slope of the line in the image below!
Answer: The slope is 1
Step-by-step explanation: Rise(how many time u go up) -over- Run (how many times u go over)
Answer:
The slope is -1.16 with 6 repeating If rounded to nearest whole number Will simply be -1
Step-by-step explanation:
m = Y2-Y1/X2-X1 is what you use to find the slope
1) Identify the points
(-4,4) and (2,-3) are the points
2) plug it into the formula for slope
-3 - 4 = -7 for the Y value
2 - (-4) = 6 For the X value 2 Multiplying 2 negative sign give you a positive.
3) Divide
-7/6 = -1.16 with 6 repeating Rounded to the nearest whole number is -1
Hopes this help!
which of the following does not show a line of reflection for A and A'
Answer:
last one maybe
Step-by-step explanation:
A and A' does not mirror the image with reference to the given Line.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given Two cartesian planes and we need to calculate if Points A and A' are mirror images with respect to the given reference line,
For graph 1,
Since the Given line is horizontal the normal distance between Point A and point A' is observable,
In our case,
Distance from point A to the line = Distance from A' to the line = 1 unit.
For graph 2,
Since the Given line is horizontal the normal distance between Point A and point A' is observable,
In our case,
Distance from point A to the line = 6 units
Distance from A' to the line = 3 units
Thus, A and A' does not mirror the image with reference to the given Line.
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Find the volume of the figure: a cone with a square pyramid of the same height cut out. The pyramid has height l, and its square base has area l2.
Answer:
The volume of the figure is [tex]\frac{l^{3}}{3}[\frac{1}{2}\pi-1]\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the figure is equal to the volume of the cone minus the volume of the square pyramid
step 1
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=l\frac{\sqrt{2}}{2}\ units[/tex]
[tex]h=l\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (l\frac{\sqrt{2}}{2})^{2}l[/tex]
[tex]V=\frac{1}{3}\pi (\frac{l^{3}}{2} )[/tex]
[tex]V=\frac{1}{6}\pi (l^{3})\ units^{3}[/tex]
step 2
Find the volume of the square pyramid
[tex]V=\frac{1}{3}Bh[/tex]
we have
[tex]B=l^{2}\ units^{2}[/tex]
[tex]h=l\ units[/tex]
substitute
[tex]V=\frac{1}{3}(l^{2})l[/tex]
[tex]V=\frac{1}{3}(l^{3})\ units^{3}[/tex]
step 3
Find the difference
[tex]\frac{1}{6}\pi (l^{3})-\frac{1}{3}(l^{3})=\frac{l^{3}}{3}[\frac{1}{2}\pi-1]\ units^{3}[/tex]
Kate is 10 years older than her Brother. In three years time, she will be twice as old as her Brother. Find their present age.
Can anyone help me with this question , I’m really weak in Age question.
Step-by-step explanation:
Let kate age be x
and Her brother age be x - 10
according to equation
x + 3 = 2(x-10+3)
x + 3 = 2x - 14
2x - x = 14 + 3
x = 17
Therefore ;
Kate's present age = 17
Her brother's present age = 17-10 = 7
what is the answerrrrrrr
Answer:
the answer is 118
Step-by-step explanation:
since one pound is equal to 16 ounces you just convert
Answer: D =118 ounces
Step-by-step explanation:There is 6 pounds plus the the other pound then your left with 22-16=6 7 pounds times 16 112+6=118
PLEASE HELP I NEED THE ANSWER BY TODAY! thanks :)
Answer:
[tex]\large\boxed{C.\ \dfrac{7}{2}}[/tex]
[tex]\large\boxed{B.\ \$3,600}[/tex]
Step-by-step explanation:
[tex]orange\ area-35\%\\\\light\ blue\ area-10\%\\\\the\ ratio:\ \dfrac{35}{10}=\dfrac{35:5}{10:5}=\dfrac{7}{2}[/tex]
[tex]Food-18\%\ of\ \$20,000.\\\\p\%=\dfrac{p}{100}\to18\%=\dfrac{18}{100}=0.18\\\\18\%\ of\ \$20,000\to0.18\cdot\$20,000=\$3,600[/tex]
aproxímate the value of square root of 5 to the nearest hundredth
Answer:
2.24
Step-by-step explanation:
5 is not a perfect square and therefore its square root is not an integer.
it is a decimal which can partly be presented as 2.236068. the digits after the decimal point occupy the following decimal spaces
2-tenths
3-hundredths
6-thousandths.
If the digit in the thousandths position is 5 or greater then we add one to the digit in the hundredths position to get the nearest hundredth while if it is less than 5 we truncate at the hundredth position and retain the digit at this position as the nearest hundredth.
in this question, the digit in the thousandth position is 6 thus we add 1 to the digit in the hundredth position that is,3 to get 4
therefore the square root of 5 to the nearest hundredth is 2.24
The equation, a + (b + 7) = (b + 7) + a, is an example of which property?
A. distributive property
B. associative property of addition
C. commutative property of addition
D. associative property of multiplication
Answer:
B. Commutative Property
Step-by-step explanation:
A. Distributive property :
for example we take 256 × 1008
256 × 1008
256 ×(1000 +8)
(256 × 1000) + (256 × 8)
256000 + 2064
Answer : 258064
Distributive is distributing a number that contains 0's to make it easier for one self
B. Associative Property of Addition :
for example (230 + 125) + (390 + 460)
if we change it like this or in any order than particularly changes the grouping
(230 + 460) + (390 + 125)
D. Associative Property of Multiplication
(230 × 125) × (390 × 460)
it's the same as the previous example just in Multiplication
The equation demonstrates the commutative property of addition, which states that the order of addition does not affect the sum. Hence option C is the answer.
The equation a + (b + 7) = (b + 7) + a is an example of the commutative property of addition. This property states that the order in which two numbers are added does not change the sum.
In other words, for any numbers a and b, the equation A+B = B+A holds true. This principle applies to ordinary numbers; for example, adding 2 + 3 will give the same result as adding 3 + 2.