Answer:
f(x) = (x + 3)² - 14
Step-by-step explanation:
f(x) = x² + 6x - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
f(x) = x² + 2(3)x + 9 - 9 - 5
= (x + 3)² - 14 ← in vertex form
The function in vertex form is f : x → (x + 3)² - 14.
To convert the equation.
f : x → x² + 6x - 5 into the vertex form, you will need to complete the square.
First, you will need to add and subtract the square of half of the coefficient of the x term, which is (6/2)² = 9.
This will give you the equation.
f : x → x² + 6x - 5 + 9- 9
Next, you will need to factor the left side of the equation,
f : x → (x² + 6x + 9) - 5 - 9
Now, you can see that the left side of the equation is the square of
(x + 3)² so you can rewrite it as:
f : x → -(x + 3 )² - 5 - 9
Finally, you can simplify the right side of the equation to get:
f : x → (x + 3)² - (5 + 9)
f : x → (x + 3)² - 14.
Therefore, the vertex form is f : x → (x + 3)² - 14.
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The statistical technique used to make predictions of future outcomes based on present data is ______ Group of answer choices correlational analysis repeated measures linear regression analysis of variance
The type of statistical technique that is employed in future predictions of outcomes based on presented data is: C. linear regression.
What is a Linear Regression?Linear regression can be described as a statistical technique that is used to make future predictions using the regression equation of a line of best fit that models the relationship between variables Y and X.
Through the regression equation, outcomes of the future can be predicted. This statistical technique is known as: C. linear regression
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by factoring, identify the zeros of the quadratic function f (x) = x²-9x-22
Answer:
x= -2, x= +11
Step-by-step explanation:
I hope this is right!
To factorise, we need two numbers that add to make -9 and multiply together to make -22.
2 - 11 works, so we put it in the brackets in this order.
(x + 2) (x - 11)
so x + 2 = 0 and x - 11 =0
but we could also simplify this to say that x could be either -2 or + 11.
I hope this helps.
Have a lovely day.
Solve for y 4/7t+2:7=6
Answer:
1/7
Step-by-step explanation:
QUICKLY!!
Which of the following formulas is used to calculate the probability of mutually exclusive events
Answer:
P(AUB)=P(A)+P(B)
Step-by-step explanation:
I found it somewhereI don't know?Trust me:)
Need help don't understand
Answer:
she should get ready by 11:10
Step-by-step explanation:
Add All the time up 75(1 hour 15min=60+75)+40+25+30=170minutes
170minutes/60= 2 hour 50minutes
subtract 2 hour 50minutes from 2:00
= 11:10
Se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.
Se sabe que el volumen de A es el doble del de B, que las tres medidas llenan el
depósito y que las dos primeras lo llenan hasta la mitad. ¿Qué capacidad tiene cada
medida?
(Necesito saber el sistema de ecuaciones)
Teniendo en cuenta la definición de sistema de ecuaciones lineales, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.
Qué es un sistema de ecuacionesUn sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.
Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.
Capacidad de cada medidaEn este caso, se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.
Se sabe que el volumen de A es el doble del de B → A=2B
Las tres medidas llenan el depósito → A+ B +C= 24 L
Las dos primeras medidas llenan hasta la mitad del recipiente → A +B= 24 L÷2 → A +B= 12 L
Entonces, el sistema de ecuaciones a resolver es el formado por las tres ecuaciones anteriormente mencionadas.
Existiendo diversos métodos para resolver un sistema de ecuaciones, se decide resolver mediante el método de sustitución, que consiste en despejar una de las dos variables en una de las ecuaciones del sistema y sustituir su valor en la otra ecuación.
En este caso, reemplazando la primer ecuación en la tercera ecuación se obtiene:
2B +B= 12 L
3B= 12 L
B= 12 L÷3
B= 4 L
Reemplazando este valor en la primer ecuación se obtiene:
A=2B
A=2×4 L
A= 8 L
Finalmente, para obtener el valor de C se reemplaza el valor de A y B en la segunda ecuación:
A + B + C= 24 L
8 L + 4 L + C= 24 L
12 L + C= 24 L
C= 24 L - 12 L
C= 12 L
Finalmente, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.
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If = 152°, what is m∠ABC? 152° 38° 76° 104°
The value of ABC when AC is given as 152 will be 76°.
How to calculate the angle?It should be noted that the angles that are opposite to equal sides are equal and that the angle sum property of triangle is 180°.
In this case, (2 × ABC) = 152°
2ABC = 152°
ABC = 152°/2
ABC = 76°
In conclusion, the correct option is C.
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14. The two-way table shows whether the 576
students at Jim's school rode the bus or in a car to
school. Of the 6th graders, find the relative frequency
of those who rode in a car to the nearest percent.
Using it's concept, it is found that the relative frequency of 6th graders who rode a car is given by:
D. 55%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The number of 6th graders is given by:
N6 = 576 - (219 + 189) = 168.
The number of 6th graders who rode a car is:
N6C = 168 - 75 = 93
Hence the relative frequency is given by:
r = 93/168 = 55%.
Hence option D is correct.
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Which point is graphed at (2, 1)?
Point B
Point C
Point A
Point
Answer:
Point A
Step-by-step explanation:
Please Mark me as brainliest
Answer: point A
Step-by-step explanation:
You move two to the right and up one because the two is the x-coordinate so on the x-axis you start from (0,0) and move to the right since it’s positive. If it was negative it would be to the left. Same as when dealing with y. The y coordinate is one so you move up on the y-axis(always start from the origin which is (0,0)). If it was negative you move down. Rise/run in this case 1/2.
Identify the expressions for which limits exist.
Answer:
Step-by-step explanation:
Limits exist for:
[tex]\lim_{x \to4 \4} \frac{x^2 -x-12}{4-x}[/tex] = [tex]\frac{(x-4)(x+3)}{4-x}[/tex] = ( - 1 )( x + 3 ) = - 7
[tex]\lim_{x \to \ 2} \frac{x^2 +2x-8}{2-x}[/tex] = [tex]\frac{(x+4)(x-2)}{2-x}[/tex] = ( - 1 )( x + 4 ) = - 6
[tex]\lim_{x \to2 } \frac{x^2 +3x - 10}{x^2 -4}[/tex] = [tex]\frac{(x+5)(x-2)}{(x+2)(x-2)}[/tex] = [tex]\frac{x+5}{x+2}[/tex] = [tex]\frac{7}{4}[/tex]
For what power of q is its value 1?
Answer:
0, for q ≠ 0 and q ≠ 1
Step-by-step explanation:
Assuming q ≠ 0, you want to find the value of x such that ...
q^x = 1
This is solved using logarithms.
__
x·log(q) = log(1) = 0
The zero product rule tells us this will have two solutions:
x = 0
log(q) = 0 ⇒ q = 1
If q is not 0 or 1, then its value is 1 when raised to the 0 power. If q is 1, then its value will be 1 when raised to any power.
_____
Additional comment
The applicable rule of logarithms is ...
log(a^b) = b·log(a)
Twice the price of a book is $12 less than the price of 4 books. find the price of three books.
Answer:
$18
Step-by-step explanation:
One book=$6
Two books=$12
6(price of one book)x4(four books)=24
So then it says find it for three books
So then you do $6x3 books which is $18 :)
Area of a rectangular playground in residential society is 2 2/5 km square and one of its sides is 1 2/5 km/ find the length of the other side
Step-by-step explanation:
area of a rectangle is
length × width
so, in our case
2 2/5 km² = 1 2/5 × width (or length, it does not matter)
12/5 km² = 7/5 × width
width = 12/5 / 7/5 = 12×5 / 7×5 = 12/7 = 1 5/7 km
Can someone help me with this problem?
The length of the rope Kurt started with is 13 1/3 inches
Calculating lengthsFrom the question, we are to determine the total length of the rope
From the given information,
The first piece was 4 4/5 inches long
and
The second piece was 8 1/2 inches long
Then,
The length of the rope Kurt started with will be
4 4/5 + 8 1/2
[tex]4\frac{4}{5} + 8\frac{1}{2}[/tex]
First, convert the fractions into improper fractions
[tex]\frac{24}{5} + \frac{17}{2}[/tex]
The Lowest common multiple (LCM) of the denominators is 10.
Then, we get
[tex]\frac{(2\times 24) + (5 \times 17)}{10}[/tex]
= [tex]\frac{48 + 85}{10}[/tex]
= [tex]\frac{133}{10}[/tex]
= [tex]13 \frac{1}{3}[/tex]
Hence, the length of the rope Kurt started with is 13 1/3 inches.
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Which graph represents a linear function?
Can give brainliest!!
HELP ASAP!!
What is the midpoint of the line segment graphed below?
choice (A) is correct
hope it helps
Which is the area between the x-axis and y=x^2 from x=2 to x=6
For this problem, we need to use our integral knowledge to set up the problem:
The bounds will be from 2 to 6, cutting tiny horizontal bars into the graph, to approximate the area
Now for the function inside the integral:
⇒ it is the top function minus the bottom function
top function: y= x²bottom function: x-axis ⇒ y =0⇒ function within integral = x² - 0
Let's put it all together and solve:
[tex]Area=\int\limits^6_2 {x^2-0} \, dx =\int\limits^6_2 {x^2} \, dx=\frac{6^3}{3} -\frac{2^3}{3} \\Area=\frac{6^3-2^3}{3} =\frac{216-8}{3} =\frac{208}{3}[/tex]
Answer: 208/3 ≈ 69.333
Hope that helps!
four subtracted from twice a number is two. what is the number
Answer: 3
Step-by-step explanation:
First, we will write a mathematical equation for the phrase given.
-> Let n be "a number"
four subtracted from twice a number is two
four subtracted from twice a number = 2
(twice a number) - 4 = 2
2n - 4 = 2
Now, we will solve this equation by isolating the variable.
2n - 4 = 2
2n = 6
n = 3
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How does the diagram show that the slope between any
two points on a line is the same?
OA)
It does not show this because the triangles are not
the same size.
OB)
The triangles have the same vertical heights and
horizontal lengths.
OC)
The distance between A and B is the same as the
distance between B and C.
OD)
The triangles are similar so the ratios of their vertical
heights to their horizontal lengths are equivalent.
The diagram shows that the triangles on the graph had similar ratios, as such their vertical heights to their horizontal are equivalent.
Option D is correct.
What is the slope of a graph?The slope of a graph determines the steepness of the graph and it is the difference between two points on the y-coordinate(rise) and the difference between two points on the x-coordinate(run).
[tex]\mathbf{slope = \dfrac{rise}{run}}[/tex]
[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]
[tex]\mathbf{slope = \dfrac{ y_2-y_1}{x_2-x_1}}[/tex]
From the diagram attached, we can see that the triangles on the graph had similar ratios, as such their vertical heights(y-coordinates) to their horizontal (x-coordinates) are equivalent.
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how many whole numbers are less than n?
The whooping crane is Canada’s tallest bird. When the angle of elevation of the sun
decreases from 30° to 25°, the length of a whooping crane’s shadow increases by 62 cm.
How tall is the whooping crane?
The crane is 139.8cm tall.
what is angle of elevation?The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Using Trigonometry
tan 30 = h/y
1/√3 = h/y
y= h√3
and, tan 25= h/y+62
0.96= h/(h√3 +62)
h= 0..96 (h√3 +62)
h= 0.96*h*1.732+0.96*62
h=0.796h +28.52
0.2404h= 28.52
h= 139.8 cm
Hence, whooping crane is 139.8 cm.
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Please I need help I'm in grade 5 and I don't understand this so make me understand in a easy way.
9. If A = x - y + z, B = 2x - 3y +4z and C = 4x - 5y - 6z, find
(I) A + B + C
(II) A - B + C
(III) A + B - C
Answers:
A+B+C = 7x - 9y - zA-B+C = 3x - 3y - 9zA+B-C = -x + y + 11z======================================================
Explanation:
Skip to the "Work Shown" section below to see the steps for each part.
Each variable is a place holder for some unknown number. We can think of it like a box that holds a number. Luckily the letter x is found in the word "box" to help cement this line of thinking.
1x = 1 box
2x = 2 boxes
3x = 3 boxes
and so on
This shorthand notation allows us to quickly add boxes
2 boxes + 3 boxes = 5 boxes
So 2x+3x = 5x
And we can subtract boxes as well
7 boxes - 3 boxes = 7x - 3x = 4x = 4 boxes
The same number must go in box x for this to work out.
When it comes to dealing with negative numbers, it might help to use a vertical number line. I like to think of it like going up and down an elevator on a skyscraper. Negative integers represent basement levels.
It's possible to have boxes within boxes. The box A has the three boxes x-y+z inside it. So wherever we see an "A", replace it with x-y+z. Unfortunately we don't know what numbers go in the boxes for x, -y and z. Use the same type of thinking for B and C.
Don't forget to use the distributive property to distribute the negative through to each term.
Example: (x+y)-(w+z) = x+y-w-z
Many students make the mistake in saying that (x+y)-(w+z) = x+y-w+z which is not true. The +z should be -z at the very end.
Let me know if you have any other questions.
The next section below shows the steps needed to get the three answers.
----------------
Work Shown:
Part (I)
A+B+C = (x-y+z)+(2x-3y+4z)+(4x-5y-6z)
A+B+C = (x+2x+4x)+(-y-3y-5y)+(z+4z-6z)
A+B+C = 7x - 9y - z
Part (II)
A-B+C = (x-y+z)-(2x-3y+4z)+(4x-5y-6z)
A-B+C = x-y+z-2x+3y-4z+4x-5y-6z
A-B+C = (x-2x+4x)+(-y+3y-5y)+(z-4z-6z)
A-B+C = 3x - 3y - 9z
Part (III)
A+B-C = (x-y+z)+(2x-3y+4z)-(4x-5y-6z)
A+B-C = x-y+z+2x-3y+4z-4x+5y+6z
A+B-C = (x+2x-4x)+(-y-3y+5y)+(z+4z+6z)
A+B-C = -x + y + 11z
75 points! pls help me! find the lateral area, total surface area, and volume?
Answer:
8
Step-by-step explanation:
8 is the answers I think
Answer:
To find the lateral area, total surface area, and volume of a geometric shape, I need to know the specific shape you are referring to. Could you please provide more details about the shape you are interested in? For example, is it a cube, cylinder, sphere, or some other shape? Once I have this information, I can provide you with the calculations for the lateral area, total surface area, and volume of that particular shape.can you help me please
there you go hope it helps :)
Mr. Hussein is wrapping present. She has 2 yards of ribbon to use for 4 presents. How many yards or ribbon can she use for each present? Show with numbers, words, and a picture or diagram CAN SOMEONE HELP ME
Answer: you can use .5 yards of ribbon
Step-by-step explanation: this equals 18inches or 1.5 feet hope this helps
Danielle Cecil's driver-rating factor is 1.60 and her car is in age group D and insurance-rating group is 12.
She wants 100/300 bodily injury and $50,000 property damage coverage.
102377
The value of the annual premium will be $1134.40
How to calculate the premium?From the information given, the annual base premium will be:
= Liability premium + Collision premium + Comprehensive premium
= $383 + $240 + $86
= $709
The annual premium will be:
= Annual base premium × Driver eating factors
= $709 × 1.60
= $1134.40
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What is the volume of a rectangular prism that has a length of 18 inches, a width of 1 foot, and a height of 14 inches?
252 in. 3
568 in. 3
1,272 in. 3
3,024 in. 3
Answer:
252 in^3
Step-by-step explanation:
give brainliest, please!
hope this helps :)
to figure out the volume we have to multiply the base, and height together.
the base is 18 and the height is 14.
18 times 14 = 252
252 in^3
Answer:
3,024 in. 3
Step-by-step explanation:
1 foot = 12 inches
18x12x14= 3024
I just did this assignment
Which of the following best describes the slope of the line below?
Answer:
Zero
Step-by-step explanation:
the line is not going up or down therefore there is no slope
help me with my math please
(2 -1/2 * 7 1/3)^6
Answer:
21 316/729
Key rules to solve:
[tex]\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex][tex]\frac{1}{\frac{b}{c}}=\frac{c}{b}[/tex]Convert mixed numbers to improper fractionsStep-by-step explanation:
[tex]\left(\frac{2-1}{2\cdot \:7\frac{1}{3}}\right)^6[/tex]
[tex]=\left(\frac{2-1}{2\cdot \frac{22}{3}}\right)^6[/tex]
[tex]=\frac{\left(2-1\right)^6}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]
[tex]=\frac{1}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]
[tex]=\frac{1}{\frac{7256313856}{729}}[/tex]
[tex]\rightarrow 21 \frac{316}{729}[/tex]
A bottle contains 20 blue bags and 15 red bags. If two bags are picked at random one after the other with replacement, what is the probability that the first bag is blue and then red?
Answer:
12÷49Step-by-step explanation:
The total number of bags in the bottle = 20 + 15 = 35
Then
the probability that the first bag is blue = 20/35
If we replace the first bag :
the probability that the second (picked) bag is blue = 15/35
Conclusion:
If two bags are picked at random one after the other with replacement
Then
the probability that the first bag is blue and then red is :
(20÷35)×(15÷35)
= (4÷7)×(3÷7)
= 12÷49
= 0.244897959184