Answer:
(x-9) (x-5)
x = 9 x = 5
Step-by-step explanation:
find out which 2 numbers when multiplied give 45 and
when added give -14
they are -9 and -5
(x-9) (x-5)
x = 9 x = 5
Answer:
[tex]x_{1}=9, x_2=5[/tex]
Step-by-step explanation:
Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Notice the constant in the given equation [tex]x^2-14x+45[/tex]:
[tex]a=1, b=-14, c=45[/tex]
Substitute the values into the formula:
[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]
Calculate the values:
[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]
It follows that there are two solutions:
[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex] and [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].
Sound waves can be ranked by their intensity, I, given in this formula, where r is the distance from the source of a sound with a power output of P=4 πIr^2 Which equation correctly rewrites the formula to solve for I?
Answer:
See below
Step-by-step explanation:
P = 4pir^2 l divide both sides by 4 pi r^2
l = P /(4pir^2)
The slope indicates how fast y increases or decreases as x increases.
O True
O False
The answer is : True
Trust me char HAHA
BÁKLA KA POR TODEYS BEDYO.
a square pyramid has side length 9 in. and volume = 270 in^3. find the height.
If the square pyramid has side length 9 inches and volume of 270 inches cube then by putting the values within the formula of volume height are going to be 10 inches.
Given Length and volume of a square pyramid are 9 inches and 270 inches cube. Square pyramid is the pyramid having square base. It is a right square pyramid.
We know that the amount of square pyramid is 1/3 *[tex]l^{2} *h[/tex]
Put the values in formula to induce the values oh h.
Volume=1/3*[tex]9^{2}*h[/tex]
270=1/3* 81*h
h=(270*3)/81
h=810/81
h=10
Hence the peak of the square pyramid having length 9 inches and volume of 270 inches cube is 10 inches.
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Function g can be thought of as a translated (shifted) version of f(x)=x^2
Answer:
g(x)=x^2 -6x +5
Step-by-step explanation:
Answer:
g(x) = (x - 3)² - 4
Step-by-step explanation:
When values are directly added to the "x" variable (usually inside of parentheses), the function shifts to the left that many units.
When values are directly subtracted from the "x" variable, the function shifts to the right that many units.
When values are added to an overall function, the function shifts upwards that many units.
When a value is subtracted from an overall function, the function shifts downwards that many units.
We can determine how the function has been translated by looking at the changed position of the vertex (the lowest point of the line).
As you can see, the new vertex now lies on x = 3 rather than x = 0.This means that there should be a -3 directly next to the "x" variable in the new function.
The new vertex also now lies on y = -4 rather than y = 0. Therefore, there should be a -4 added to the overall equation.
These changes make the new function:
g(x) = (x - 3)² - 4
The diagonal of a rhombus is 24m and 10m. Find the perimeter.
Answer:
52m
Step-by-step explanation:
rhombus
its like a slanted square
all its 4 sides are equal like a square
both pairs of opposite sides are parallel
when the diagonals criss cross they make 4 triangles inside
the sides of the rhombus become the hypotenuse of a triangles inside
if the diagonal is 24 and 10 then
its radius is 12 and 5
the sides of the rhombus become the hypotenuse of a triangle that have the sides 12 and 5
hypotenuse of a triangle that has the sides 12 and 5 is
13
(its a special triangle: its a 5, 12, 13 right triangle)
13 times 4 is 52
A fish tank has a length of 12 cm a width of 15 cm and a depth of 25 cm find the volume of the fish tank
Answer:
The formula of volume of cube is l*b*h
45*25*10=11250 cubic cm
Step-by-step explanation:
volume =length×width ×height
given:
length:45 cm
width:25 cm
height(depth):10 cm
according to the question
45 cm×25cm ×10cm
11250 cubic cm
In △ABC, we are told that c=11, ∡C=75∘, and ∡B=29∘. Solve for a and b.
The value of a and b are 5.5 and 11.0.
How to find side of a triangle?
The sides a and b of the triangle can be found as follows:
∠B = 29°
c = 11
∠C = 75°
∠A = 180 - 75 - 29 = 76°
Using sine ratio,
b / sin 29° = 11 / sin 75
b sin 75 = 11 sin 29
b = 11 sin 29 / sin 75
b = 5.33290582271 / 0.96592582628
b = 5.51816958277
b = 5.5
Let's find a,
a / sin 76 = 11 / sin 75
a sin 75 = 11 sin 76
a = 11 sin 76 / sin 75
a = 10.673252989 / 0.96592582628
a = 11.0466922042
a = 11.0
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If f(x) = 3x + 2, what is f(5)?
Answer:
If a numbed substitutes x in f (x), you must substitute that number in the function for x.
Step-by-step explanation:
f(5) = 3(5) + 2
f(5 )= 17
PLEASE HELP NOW
help
Your image attached has not sufficient criteria for Brainly users to answer. We will assume for now that you are asking what the line is equal to. This question will be deleted eventually due to Brainly ToS most likely
We note that this line is not linear, or squared. This means it might be cubical.
If it is cubical the line must be a variant of
f(x)=[tex]x^{3}[/tex].
However f(x)=[tex]x^{3}[/tex] points the opposite direction so we must make it negative.
We also noticed we had to stretch it, so we had to add a fraction.
Your answer is f(x)=[tex]-\frac{1}{8} x^{3}[/tex]
Select the correct answer.
A triangular tabletop has the given dimensions. Vinyl is placed around the outer edges of the tabletop.
3 ft
45°
45°
What is the approximate length of vinyl needed for the outer edges of the tabletop?
OA.
OB.
OC.
O D.
10.2 ft
14.2 ft
9 ft
11.2 ft
The length of the vinyl must be 10.2ft
How to get the length of the vinyl?We know that two of the angles of the triangle measure 45°, then we have a right triangle of 45°, 45°, 90°.
We know that the catheti measure 3 ft, using the pithagorean theorem, we know that the length of the hypotenuse is given by:
[tex]H^2 = (3ft)^2 + (3ft)^2[/tex]
[tex]H = \sqrt{2*(3ft)^2} = 4.2ft[/tex]
Then the perimeter of the triangle is:
P = 3ft + 3ft + 4.2ft = 10.2ft
The length of the vinyl must be 10.2ft
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Show that the 4 points form a square. A. DA = AB = BC =CD = √32 DB = AC =8 B. DA = AB = BC = CD = √32 C. DB = AC =8 D. DA = AB = BC = CD = √7 DB = AC = 8
Finding the distances between the 4 consecutive points, using the formula, all will be equal, hence the points will form a square.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, four consecutive points will be given in the cartesian plan, and their distances should be calculated. If they are equal, these points will form a square.
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Decide if the function is an exponential function. If it is, state the initial value and the base. (5 points) y = - 6.1 ⋅ 3x
The function is an exponential function; the initial value is -6.1 and the base is 3
How to determine the function type?The equation of the function is given as:
y = -6.1 *(3^x)
An exponential function is represented as:
y = ab^x
Where:
Initial value = a
base = b
By comparison, we have
a = -6.1 and b = 3
Hence, the function is an exponential function; the initial value is -6.1 and the base is 3
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Graph the following features:
Slope = -7/5
Y-intercept = 1
Answer:
Step-by-step explanation:
1) in order to graph the required direct line it needed two points:
2) one of these two points is Y-intercept. According to the condition it is (0;1);
3) in order to find the second point, it is enough to apply the given slope: to start in point (0;1), then to move to the left direction (-5 units, move no. 1), then to move up (+7 units, move no. 2);
4) to graph the line between two points (red line); y= -7/5x +1.
All the details are in the attachment.
What type of system of linear equations is this?
y = -5x-4
y=1/2x+3
A. consistent and independent
B. consistent and dependent
C. inconsistent
D. independent and inconsistent
Answer:
B
Step-by-step explanation:
consistent and dependent
An international anime fan club surveyed 200 of its members regarding their viewing
habits over the long weekend: 120 watched Psycho-Pass, 90 watched Demon Slayer, 70 watched
My Hero Academia, 40 watched Psycho-Pass and Demon Slayer, 50 watched Psycho-Pass and
My Hero Academia, and 20 watched something else entirely.
a.
How many of the club members watched exactly one show?
b. What percentage of members watched all three anime?
The triangles below are similar. Find x.
Answer: 105
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{x}{14}=\frac{97.5}{13}\\\\=\frac{x}{14}=7.5\\\\x=\boxed{105}[/tex]
You have been saving $25 a week to make the trip; you now have $200. This money will be budgeted to include gas, food, and entertainment. Write an equation to model your savings plan and then graph it. What would be the domain and range in this situation?
Match the multiplication problem on the left with the simplified polynomial on the right.
4x(4x²-x+3)
16x²
(8x + 1)(2x - 3)
4x² (4x)
(2x + 3) (8x² - 4x + 3)
►
16x²-22x-3
16x³
16x³4x² + 12x
16x³4x² + 4x - 12
16x³ + 16x² - 6x +9
The match of the multiplication problem with the simplified expressions is as follows:
4x(4x²-x+3) ⇒ 16x³ - 4x² + 12x(8x + 1)(2x -3) ⇒ 16x² - 22x - 3 4x² (4x) ⇒ 16x³(2x + 3) (8x² - 4x + 3) ⇒ 16x³ + 16x² - 6x + 9Multiplication of polynomial expressions.The process involved in multiplying polynomial expression requires using all the parameters in parentheses to multiply each other.
From the given information:
[tex]\mathbf{4x(4x^2-x+3)}[/tex]
By using distributive law m(a+b+c) = ma + mb + mc
[tex]\mathbf{=4x(4x^2)+4x(-x)+4x(3))}[/tex]
= 16x³ - 4x² + 12x
(8x + 1)(2x -3)
By applying FOIL method: (a+b)(c+d) = ac + ad + bc + bd
= (8x (2x)) + (8x(-3)) + (1 × 2x) + (1 × (-3))
= 16x² - 22x - 3
4x² (4x)
Applying exponent rule; [tex]\mathbf{a^b*a^c = a^{b+c}}[/tex]
[tex]\mathbf{= 4x^2 (4x)= x^2*4^{1+1}x}[/tex]
[tex]\mathbf{= x^2*4^{2}x}[/tex]
[tex]\mathbf{= 4^{2}x^{2+1}}[/tex]
[tex]\mathbf{= 4^{2}x^{3}}[/tex]
[tex]\mathbf{= 16x^{3}}[/tex]
(2x + 3) (8x² - 4x + 3)
Using distributive parentheses:
= 2x(8x² - 4x + 3) + 3(8x² - 4x + 3)
= 16x³ + 16x² - 6x + 9
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Soil sells for 8 1/4 cents per pound. How much would you save if you bought a 100- pound sack for $7.45?
Answer:
$0.80
Step-by-step explanation:
If the 100 pounds was bought separately (of course in real life you will probably not)
= 100 pounds x $0.0825/pound
= $8.25
As you can see it will cost more than if you buy a 100 pound sack.
Cost Difference = $8.25 - $7.45 = $0.80
That means you will save $0.80 from it.
There will be a profit of $0.8 if the soil is bought for $7.45 for 100- pound sack and sold for 8 1/4 cents per pound.
What is Multiplication?Multiplication in mathematics is the process of adding a number repeatedly up to the times of another number. If two numbers, namely a and b are multiplied, this is denoted by a × b. This means that 'a' is added repeatedly to itself up to b times or b is added repeatedly up to 'a' times.
Amount got for 1 pound soil after selling = 8 [tex]\frac{1}{4}[/tex] cents
= 33/4 cents
= 8.25 cents
= 8.25 / 100 dollars
= 0.0825 dollars
For 100 - pound sack, amount got after selling = 0.0825 × 100
= 8.25 dollars
Cost for 100 - pound sack = $7.45
Profit = $8.25 - $7.45
= $0.8
$0.8 will be saved if you bought a 100- pound sack for $7.45.
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Given that a bag of skittles has 15 blue candies, 16 orange candies, 12 yellow, 14 red, and 5 green candies, find the following probabilities.
Step-by-step explanation:
If you are asking about the probability of Getting Blue, Orange, Yellow, Red and Green
P=N(E)/N(S)
Probability of Blue=15/62
probability of Orange= 16/62
probability of yellow=12/62
probability of Red=14/62
probability of Green=5/62
Which of the following results in the difference of two squares?
The difference of two squares expression is (c) (5x + 3y)(5x - 3y)
How to determine the difference of two squares?The difference of two squares expression is represented as:
a^2 - b^2 = (a + b)(a - b)
Using the above as a guide, we have the following expression in option (c)
(5x + 3y)(5x - 3y)
Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)
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emilio bought 5.65 of green grapes and 3.07 pounds of red grapes
The weight of each bag is 0.545 lb .
What is weight ?Weight in maths is the value of the mass of an object on a measuring scale , It is measured in pound , ounce , kilogram etc.
It is given that
Total weight of green grapes = 5.65 lb
Total weight of red grapes = 3.07lb
Total weight = 5.65 +3.07 = 8.72 lb
Total number of bags = 16
the weight of each bag
= 8.72 / 16
= 0.545 lb
Therefore the weight of each bag is 0.545 lb .
The complete question is
Emilio bought 5.65lb of green grapes and 3.07lb of red grapes. He divided the grapes equally into 16 bags. If each bag of grapes has the same weight, how much does each bag weigh?
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Which of the following is equal to
(x²y³)*
(x°y³z)°
✓
1
48 36
(x²y³)
(x°y³z)°
x-12-18
?
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!THE ANSWER IS THE SECOND ONE.
A B D
I did it and this was the correct answers
S and Tare mutually
exclusive events. Find P(sort)
P(S) = 12% P(T) =27%
The value of the probability P(S or T) is 39%
How to determine the probability?The probability values are given as:
P(S) = 12% P(T) =27%
For mutually exclusive events,
P(S or T) = P(S) + P(T)
This gives
P(S or T) = 12% + 27%
Evaluate the sum
P(S or T) = 39%
Hence, the value of the probability P(S or T) is 39%
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which equation would match the table the most?? pls help ☠️☠️
Solve the quadratic equation by completing the square.
x^2+2x-2=0
The solution to the quadratic equation by completing the square is x = -1 + √3, x = -1 - √3
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
x² + 2x - 2 = 0
x² + 2x + 1 - 1 - 2 = 0
(x + 1)² - 3 = 0
(x + 1)² = 3
x + 1 = ± √3
x = -1 ± √3
Thus, the solution to the quadratic equation by completing the square is x = -1 + √3, x = -1 - √3
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QUESTION IS DOWN BELOW 15 POINTS EACH
Answer:
See below
Step-by-step explanation:
density = mass/volume
re-arrange to density * volume = mass
20 * 64 = 1280 gm
Density = mass/volume
re-arrange to volume = mass / density
560 / 14 = 40 cm^3
Find the equations for a helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane).
By the equations according to the cylindrical system of coordinates, the equation for a helix are x = 8 · cos (2π · t /T), y = 8 · sin (2π · t /T) and z = 6 · (t/T).
How to derive the equations of a helix in cylindrical form
According to the cylindrical system of coordinates, helix can be described by the following equations:
Radius
x = r · cos (2π · t /T) (1)
y = r · sin (2π · t /T) (2)
Height
z = H · (t/T) (3)
Where T is the period of one complete revolution.
If we know that r = 8 and H = 6, then the equations for the helix is:
x = 8 · cos (2π · t /T)
y = 8 · sin (2π · t /T)
z = 6 · (t/T)
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Note: When solving for k, round to four decimal places.
A country's population in 1994 was 107 million. In 1997 it was 112 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.
Answer: 132 million
Exponential growth formula: [tex]P=A e^{rt}[/tex]
[P is final amount, A is initial amount, r is growth rate, x is time intervals]
To find growth rate:
[tex]112 = 107 e^{r(3)}[/tex]
[tex]3r= ln(112/107)[/tex]
[tex]r= ln(112/107)/3 = 0.01522334561[/tex]
Population in 2008:
[tex]P_{2008}=107 e^{(0.01522334561(14))}[/tex]
[tex]P_{2008}=132.4169522[/tex]
[tex]P_{2008}=132\:million \quad (rounded \:to\:nearest\:million)[/tex]
how to estimate 11578995 to the nearest lakh
Answer:
1,16,00,000
Step-by-step explanation:
To round to the nearest lakh, identify the digit that is to the right of the number place representing 1 lakh. If it is 5 or greater, round up.
Round to nearest lakhThe value 1,15,78,995 is 115.78995 lakh. The digit to the right of the decimal point in this number is 7, which is greater than 4. Hence the nearest lakh is 116 lakh, or ...
1,16,00,000