Answers
Answer:
Substitute the given value into the function and evaluate.
2 x 3 + 7 x 2 − 4 x − 15
Step-by-Step Process
Related Questions
Hi . Please I need help with these questions :
See image for question.
Answer no 5 and 6.
Answers
Answer:
(i) √23
(ii) 196√23
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define
Standard Form: x² - 10x + 2 = 0
Step 2: Define variables
a = 1
b = -10
c = 2
Step 3: Find roots
Substitute: [tex]x=\frac{10\pm\sqrt{(-10)^2-4(1)(2)} }{2(1)}[/tex]Exponents: [tex]x=\frac{10\pm\sqrt{100-4(1)(2)} }{2(1)}[/tex]Multiply: [tex]x=\frac{10\pm\sqrt{100-8} }{2}[/tex]Subtract: [tex]x=\frac{10\pm\sqrt{92} }{2}[/tex]Simplify: [tex]x=\frac{10\pm 2\sqrt{23} }{2}[/tex]Factor: [tex]x=\frac{2(5\pm \sqrt{23}) }{2}[/tex]Divide: [tex]x=5\pm \sqrt{23}[/tex]Step 4: Define roots
α > β
α = 5 + √23
β = 5 - √23
Step 5: Evaluate
i
Substitute: [tex]\frac{1}{5-\sqrt{23} } -\frac{1}{5+\sqrt{23} }[/tex]Subtract: [tex]\sqrt{23}[/tex]ii
Substitute: [tex](5+\sqrt{23})^3-(5-\sqrt{23})^3[/tex]Evaluate: [tex](98\sqrt{23} +470)-(470 - 98\sqrt{23} )[/tex]Subtract: [tex]196\sqrt{23}[/tex]Answer:
(i) √23(i) 196√23Step-by-step explanation:
Given equation:
x² - 10x + 2 = 0Roots are:
α and βSum of the roots:
α + β = -b/a ⇒ α + β = -(-10)/1 ⇒ α + β = 10Product of the roots:
αβ = c/a ⇒ αβ = 2/1 ⇒ αβ = 2Finding the following:
(i)
1/β - 1/α =(α - β)/αβ =√(α - β)² / αβ =√((α + β)² - 4αβ) / αβ = √(10² - 4*2) / 2 =√92 / 2 =2√23 / 2 =√23(ii)
α³ - β³ =(α - β)(α² + αβ + β²) =√(α - β)²× ((α + β)² - αβ)√((α + β)² - 4αβ) × ((α + β)² - αβ) =√(10² - 4*2) × (10² -2) =√92 × 98 =2√23 × 98 =196√23It takes 111 pounds of seed to completely plant a 12-acre field.
How many acres can be planted per pound of seed?
Answers
Answer:
0.108 Acres
Step-by-step explanation:
We find the rate by dividing the amount of acres to the pounds
12/111
= 0.108
0.108 acres of land can be planted per pound of seed
The sum of three numbers is 24. Twice the middle number is 2 more than the largest number, and the largest number is equal to the sum of the other two.
Answers
Answer:
x = 5, y = 7, z = 12Step-by-step explanation:
Let the numbers be x, y and z
x + y + z = 242y = z + 2z = x + ySolving by substitution:
x + y + z = z + z = 242z = 24z = 122y = z + 22y = 12 + 22y = 14y = 7z = x + yx = z - y x = 12 - 7 = 5The answer:
x = 5, y = 7, z = 12A shape is shown on the centimetre grid below.
Work out the area of the shape after it has been enlarged by scale factor 2.
State the units of your answer.
Answers
Answer:
The area of the shape after it has been enlarged by
scale factor 2 will be: 10 cm²
Step-by-step explanation:
The Area is basically a measure of how much space in square units there is inside an object.
As the shape is shown on the centimeter grid.
The shape clearly occupies the space of 5-centimeter squares.We also know that If the scale factor > 1, the image is enlarged.
As we know to determine the area of the shape after it has been enlarged by scale factor 2, all we need to do is to multiply the area of the original shape by 2.
The area of original shape = 5 cm²
The area of the shape after the dilation by a scale factor 2 = 5 × 2 = 10 cm²
Thus, the area of the shape after it has been enlarged by
scale factor 2 will be: 10 cm²
the answer is wrong, can anyone tell me what the answer is
Step-by-step explanation:
PLEASE HELP ME ASAP PIC ATTACHED
8.
ABC is an isosceles triangle.
• AB = AC = 11 cm
E
. E and F are the midpoints of AB
and AC respectively,
• EF is parallel to BC.
55
B
Find the area of the trapezium BEFC.
Answers
Answer: 90,75. cos 55°. sin55° ≈ 42,64
through E, draw EK perpendicular to BC (F ∈ BC)
because E is the midpoint of AB => BE = 11/2 = 5.5
ΔBEF is a right triangle at K
=> sin 55° = EK/BE
=> EK = 5,5.sin 55°
ΔABC has E and F is the midpoints of AB and AC
=> EF is the median line of the triangle
=> EF = 1/2.BC
through A, draw AD perpendicular to BC
=> ΔABD is a right triangle at D
=> BC = 11.cos 55°.2 = 22.cos 55°
=> EF = 11.cos 55°
=>the area of the trapezium BEFC is:
[tex]\frac{5,5.sin55(11.cos55+22.cos55)}{2}=90,75.cos55.sin55[/tex]
Step-by-step explanation:
What is 1/2 + 1/4 =?????
Answers
Answer: 0.75
Step-by-step explanation:
Your Turn (Activity 1): Find the LCM of 6 and 9 using the multiples of each:
Answers
Answer:
LCM of 6 and 9: 18
I give Brainliest. Can somebody help me with this pls??
Answers
Answer:
Ok so we see that at the end there is a +2 so the first thing we want to do is start our first point at (0,2). After that we can see that our slope is -1/2, since slope equals x/y we know that it is asking us to go 1 to the right, however since it is negative we will be going 2 down. the Y intercept is the point where the line intercepts the Y-axis which is (0,2)
Step-by-step explanation:
Answer:
slope= -1/2
y-intercept = (0,2)
Step-by-step explanation:
The y-intercept is what y equals when x equals zero. On the graph, it is where the graph crosses through the y axis.
To find the y-intercept, plug in 0 for x, so x = 0
y = -1/2 (0) + 2
y=2
and we know x =0
So the point is (0,2)
Need help on this question! :)
Answers
Answer:
i think it's 42
Step-by-step explanation:
42 tiles
1 figure = +4 tiles
7 figures x 4 tiles = 28 tiles
28 + 14 = 42
3x2 A match like terms
Answers
Answer:
A common technique for simplifying algebraic expressions. When combining like terms, such as 2x and 3x, we add their coefficients. For example, 2x + 3x = (2+3)x = 5x.
Step-by-step explanation:
Find x.
9x – 15=7x-1
Answers
Answer:
x=7
Step-by-step explanation:
First, add 15 to both sides (whatever you do to one side, do it to the other), this will help cancel out the -15 on the right side of the equation,
so 9x-15+15=7x-1+15, the 15 cancels out and we get 9x=7x+14
Now we want to simplify this further, lets subtract 7x from both sides,
9x-7x=7x-7x+14, 2x=14
Let's divide both sides by 2 because the 2 and x are held together by "multiplication" so we will break that bond with division and that will leave us with x.
2x/2=14/2
x=7
Our goal is to have a variable on one side and a number on the other, so that is why we are doing this. Also, notice that to solve this equation we were doing the reverse operation. For example, when we added 15 to both sides, we were performing the opposite of subtraction because we had a -15. Remember that variables are connected to numbers through multiplication, so 9x would be the same thing as 9*x
if you need a further explanation, feel free to ask in the comments!
x=7
Please help, I've been stuck on this one for a while...
Simplify: 4 3/2
Answers
Answer:
4 3/2 is simplified into 5 1/2
Step-by-step explanation:
There are three halves in the improper fraction 3/2. Two of those halves make another whole number, and you are left with one half and 1. 4 + 1 1/2 is equal to 5 1/2.
3. Orenda has a total of 41 loonies ($1 coin) and toonies ($2 coin) in her piggy bank. Their total value is $59.
a. Write one equation for the total number of coins and a second equation for the total value.
b. Graph both lines and determine the coordinates of the point of intersection of the lines.
Answers
Answer:
20 toonies and 1 loonie
how to solve V = 1/3 Ah for h
Answers
Answer:
(3V)/A = h
Step-by-step explanation:
V = 1/3 Ah
Solve the literal equation using inverse operations;
V = 1/3 Ah
*3 *3
3V = Ah
/A /A
(3V)/A = h
Is the statement true? Explain.
Answers
Answer:
The statement is true.
Step-by-step explanation:
We know that line IJ=JK and that line IH=HK. We also know that the two triangles share a side meaning that every side of each triangle is equivalent to each other making them congruent by the Side Side Side postulate.
Nathan and Tyler are making snowballs in preparation for a big snowball fight. It takes Nathan 4 minutes to make 7 snowballs.
This equation describes the number of snowballs, y, Tyler can make in x minutes:
y=1.5x
Who makes snowballs at a faster rate?
How much faster does he make snowballs?
Write your answer as a whole number or a decimal rounded to the nearest hundredth.
________ snowballs per minute faster
Answers
50 POINTS!! Picture attached
Answers
Answer: SLAPS and TAPS GAPs And djfjkfkfc.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Question 2: Here are some transformation rules. For each rule, describe whether the
transformation is a rigid transformation (rotation, reflection or translation), a non-rigid
transformation (dilation), or neither.
1. (20, y) + (1 - 2,5 - 3)
2. (x, y) (2x, 39)
3. (x,y) → (38,3y)
4. (2,y) → (2 – 3,4)
Answer:
1.
2.
3.
4.
Answers
9514 1404 393
Answer:
rigidnon-rigidnon-rigidrigidStep-by-step explanation:
The transformations of 1 and 4 are translations (1 and 4) and reflection (4), so are rigid transformations.
The transformation of 3 is a dilation by a factor of 3, so is non-rigid.
The transformation of 2 is a horizontal stretch by a factor of 2 and a vertical stretch by a factor of 3. It, too, is a non-rigid transformation, but is not strictly dilation.
I have a problem, it says, identify the set of numbers that best describes each situation. The situation is, the amount of money in a bank account. we are working with, real, rational, irrational, integers, and whole numbers. Is it irrational or rational?
Answers
Answer:
Rational
Step-by-step explanation:
We first have to define what these numbers mean:
Real numbers are all the numbers on the number line, they are not imaginary numbers that cannot be quantified on the number line.
Rational numbers are numbers that have either terminating decimals or recurring decimal, for example 5.3 (terminating decimal) or 1.333...(recurring decimal). I did not use the traditional definition of "a/b where a and b are integers and b ≠ 0" because it poses some problems. For instance 22/7 fulfills this condition but it is not a rational number! So it is best defined the way I just defined it.
An irrational number is a number that does not have terminating and recurring decimal, like 3.565215805.....
Integers are real numbers that are whole numbers.
Looking at the situation, which is the money in a bank account. The value will be a number that is rational because it is always an exact amount and this implies that it will always be a terminating decimal. Note that 45.00 is also a terminating decimal.
multiply (x+1)^2
a. x^2+1
b. x^2+2x+2
c. x^2+x+1
d. x^2+2x+1
PLEASE HELP
Answers
Answer:
D
Step-by-step explanation:
We have:
[tex](x+1)^2[/tex]
Expand:
[tex]=(x+1)(x+1)[/tex]
Distribute Property:
[tex]=(x+1)x+(x+1)(1)[/tex]
Distribute:
[tex]=x^2+x+x+1[/tex]
Add:
[tex]=x^2+2x+1[/tex]
Hence, our answer is D.
Answer:
d. x^2 + 2x + 1
Step-by-step explanation:
(x+1)(x+1)
use the FOIL method:
x^2 +1x +1x +2
combine like terms 1x and 1x
x^2 +2x +1
what is the equation a line passes through the points p(2,4) q(-1,3) A y=3x+10 B y=x+10 C -x-10 D y=3x-8
Answers
Answer:
D
Step-by-step explanation:
Niah has 34 gems and gives 8 to her sister how much does Niah have now?
Answers
Answer:
answer is 26 gems
Step-by-step explanation:
you subtract 8 from 34 and you get 26 as your answer
The equation of the line with slope -3 that goes through the point (-9,-7) can be written in the form y=mx+b
where m is:
and where b is:
Answers
Answer:y= -9x-25
Step-by-step explanation: Write the slope-intercept form of an equation of the line with slope -9 and passes through the point (-2, -7).
--------
Form:: y = mx + b
Solve for "b"::
-7 = -9*-2 + b
-7 = 18 + b
b = -25
-----
Equation:
y = -9x - 25
---------------
Cheers,
Stan H.
-----------
point slope formula
y-y1=m(x-x1)
y+7= -9(x+2). Notice that we are subtracting a negative, so we have to add.
y+7=-9x-18
y= -9x-25
A fruit basket contains 4 plums, 6 oranges, and 5 apples. There are also bananas in the fruit basket. If there are a total of 18 pieces of fruit in the basket, what is the ratio of bananas to oranges?
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Xvnkdvndfjv!dbff!u43&&7)'34&97-€&)+_€'")+€":)€_8
Answers
Answer:
Mental Hospital is on the way!
Answer:
Dont know
Step-by-step explanation:
Thinks for free pints
given the function f(x) = 8x2 -14x - 10, find f(-2)
Answers
Answer:
-32 I think (plz dont be mad at me if this is wrong)
Step-by-step explanation:
Answer:
f(-2) = 50
Step-by-step explanation:
f(x) = 8x^2 - 14x - 10, find f(-2)
Just like how -2 replaced x in f(x), you will replace x with -2 in the equation
f(-2) = 8(-2)^2 - 14(-2) - 10
f(-2) = 8(4) + 28 - 10
f(-2) = 32 + 18
f(-2) = 50
9.
A triangle has sides with lengths of 9 m, 12 m and 15 m.
Answers
Answer:
perimeter = 36m
Step-by-step explanation:
Its perimeter is 9 + 12 + 15 = 36m
Translate the sentence into an equation.
Seven times the sum of a number and 9 is 2.
Answers
Answer:
7(x+9)=2
Step-by-step explanation:
i think that’s right sorry if not
Ayudaaaa porfavorrr se los suplico me
Answers
Consider the conditional statement of N is the midpoint of CD then CD =2CN what is the hypothesis
Answers
Answer:
Step-by-step explanation:
If N is the midpoint of CD, it means that N bisects the line CD. Hence;
CN + ND = CD .... 1 and;
CN = ND .... 2
Substitute equation 2 into 1;
CN + CN = CD
2CN = CD
Rearrange;
CD = 2CN (proved)
The hypothesis is the midpoint hypothesis and the hypothesis is TRUE