This solution is arrived at using the principles of Quadratic Functions and Inequalities. It is to be noted that the function increases at (-8, 4).
What are Quadratic Functions?A quadratic function can be defined as that is written in the following way: f(x) = ax2 + bx + c: Where a, b, and c are numbers not equal to zero.
How do we solve the problem above?To solve the problem f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4), we:
A) 4x - 3 ≥ 2 - x²
Rewrite as: x² + 4x - 2 - 3 ≥ 0
B) Collect the like terms
x² + 4x - 5 ≥ 0
C) Expand to have x² + 5x - x - 5 ≥ 0
D) Factorizing the expression we have
x(x + 5) - 1(x + 5) ≥ 0, from this we Factor away x + 5
(x - 1)(x + 5) ≥ 0
E) Solving for x we obtain: x ≥ 1 or x ≥ -5
This can also be rewritten to read:
-5 ≤ x ≤ 1
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How many protons, neutrons, and electrons are found in a neutral atom of carbon-13?
Since both are neutral, we know that each has 6 electrons as well. The sum of protons plus neutrons equals the mass number 12 in 12-C, so carbon-12 has 12 – 6 protons = 6 neutrons. The sum of protons plus neutrons equals the mass number 13 in 13-C, so carbon-13 has 13 - 6 protons = 7 neutrons.
Tritium is a radioactive isotope of hydrogen that decays by about 5% per year. A large bottle of water that contained 450,000 tritium atoms remained undisturbed for 11 years. How much tritium does the bottle contain now?
If necessary, round your answer to the nearest whole number
Using an exponential function, it is found that the bottle contains 255,960 atoms of tritium after 11 years.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
The bottle initially contained 450,000 tritium atoms, hence A(0) = 450000.The amount decays by about 5% per year, hence r = 0.05.Thus, the equation is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 450000(1 - 0.05)^t[/tex]
[tex]A(t) = 450000(0.95)^t[/tex]
After 11 years, the amount is given by:
[tex]A(11) = 450000(0.95)^{11} = 255960[/tex]
The bottle contains 255,960 atoms of tritium after 11 years.
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Expand the brackets
a. 3(p-q-r)
b. -11(8a-2b)
c. 2(y-1)
Answer:
a. 3p-3q-3r
b. -88a+22b
c. 2y-2
Answer: Here are your answers...
a.) 3p - 3q - 3r
b.) -88a + 22b
c.) 2y - 2
Step-by-step explanations:
For A: 3 × p - 3 × q - 3 × r
For B: -11 × 8a -11 × -2b
For C: 2 × y - 2 × 1
I hope this helped you!
For the table, enter an equation that expresses y in terms of x.
x 12 11 10
y 9 8 7
Answer: y= X-3
Step-by-step explanation:
I plugged it into the calculator. You can also use the formula y2-y1 all over x2-x1. Then use the formula y-y1=m(x-x1).
5. Gina performed an experiment by rolling small steel balls of different masses down a
ramp and recording the distance that each ball rolled.
Gina wants to draw a line of best fit to represent the data. Through which two points
should she draw the line?
Answer:
the answer is h and L
Step-by-step explanation:
A rectangular carpet is 2 times as long as it is wide. Its width is 5
yards. What is the perimeter of the carpet?
Answer:
30 units
Step-by-step explanation:
If the w=5 and we know that the length is 2(5)=10
For perimeter, there are two sides.
2(10)+2(5)=30 units
In rectangle ABCD, find x and y.
What is the rate of change of the function y = − 1/4 x + 1
Answer:
-1/4
Step-by-step explanation:
Hello!
The rate of change is also known as the slope.
Standard equation of a line: y = mx + b
y: outputm: slopex: inputb: y-interceptSo, if we match the standard form to the given function:
y = mx + by = -1/4x + 1-1/4 is m, or the rate of change.
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Determine whether a triangle with the given side lengths is a right triangle.
Answer:
1st one is not a right triangle.
2nd one is not a right triangle.
3rd one is not a right triangle.
4th one is a right triangle.
Step-by-step explanation:
1, 2, and 3 could also be "not enough information".
I will mark brainiest
Answer:
C
Step-by-step explanation:
Got it right on edge 2022
Answer:
B is the correct answer because this is stem and leaf
Step-by-step explanation:
the range of it ranges from 61, 92 because it starts at 61 and ends at 92.
309,303,297,... Find the 31st term.
Answer:
129
Step-by-step explanation:
The easiest thing to do would be an equation.
Since the value is decreasing by 6 each time you have -6x
-6x+?=?
Next thing you do, to get the y-intercept, would be to add 6 to the 309, which is the first term in order to get the zeroth term. This would make 315 the y-intercept
-6x+315=?
To solve for the 31st term, plug in 31 for x to get 129
♡ You got this! Have a great day! ♡In the diagram below, lines X and Y are parallel and cut by a transversal. The measure of ∠1 is 65°.
Which argument explains why the measure of ∠3 is also 65°?
SBC is an isosceles triangle with main vertex S.
→ Let D be the symmetric of B with respect to C and A the symmetric of C with respect to B.
1) Compare AB and CD
2) Compare the angles SBA et SCD.
3) Deduce that the triangles SBA and SCD are congruent.
4) What is the nature of the SAD triangle?
Help me if u help me u get points I’m poor help me I don’t have much time :(
Answer + Step-by-step explanation:
1) D be the symmetric of B with respect to C then CD = BC
A the symmetric of C with respect to B then AB = BC
We obtain :
CD = BC
AB = BC
Then AB = CD
2) m∠SBA = 180 - SBC = 180 - SCB = m∠SCD
3) we have :
BA = CD
BS = CS
m∠SBA = m∠SCD
Then
the triangles SBA and SCD are congruent
4)
the triangles SBA and SCD are congruent Then SA = SD
Therefore SAD is an isosceles triangle.
Answer:
its SAD
Step-by-step explanation:
I did the test
I need help please......
Answer:
Sorry the picture isn't clear, click it again
Find the value of x. Segments that appear to be tangent are tangent. Round your answer to the nearest tenth. Do not include "x=" in your answer.
The square of the hypotenuse is equal to the sum of the square of other two sides. The value of x from the given diagram to the nearest tenth is 11.2
Pythaogram theoremAccording to the theorem, the square of the hypotenuse is equal to the sum of the square of other two sides.
From the diagram
hypotenuse = 5.6 + 8.4 = 14
Other sides are x and 8.4
According to the theorem:
14^2 = x^2 + 8.4^2
x^2 = 14^2 - 8.4^2
Simplify
x^2 = 196 - 70.56
x^2 = 125.44
x = 11.2
Hence the value of x from the given diagram to the nearest tenth is 11.2
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Answer:
11.2
Step-by-step explanation:
just did it
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Answer:
56 degrees
Step-by-step explanation:
The total amount of degrees in a triangle is 180: all three angles add up to 180. We can set up an equation to solve this.
40 + 2x + 3x = 180
Let's add like terms:
40 + 5x = 180
Subtract 40 on both sides:
5x = 140
Divide by 5 on both sides to solve for x:
x = 28
Angle A is equal to 2x. Plug in 28 for x. 2*28 = 56. Therefore, Angle A is 56 degrees.
Answer:
∠ A = 56°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2x + 3x + 40 = 180
5x + 40 = 180 ( subtract 40 from both sides )
5x = 140 ( divide both sides by 5 )
x = 28
then
∠ A = 2x = 2(28) = 56°
20) Angel asked some of her friends to write down the types and number of pets they own. The bar graph shown here displays the information she received.
Angel predicts that the next friend she asks will not own a rabbit.
Which statement justifies Angel's prediction?
A) None of Angel's friends owns a rabbit.
B) There are more rabbits owned than birds.
C) There are fewer rabbits owned than any pet.
D) There are just as many birds owned as rabbits.
Answer: c
Step-by-step explanation: Its most likely rabbit was very few compared to other pet on the graph
Need help ASAP !!!!!!!!!!
Answer:
y =1/2x + 2
Step-by-step explanation:
Rise/run and then the y intercept
Manny drew a scale diagram of his classroom. His real classroom is 20 feet wide. Manny's drawing is 4 centimeters (cm) wide. What is the scale factor of the drawing?
Answer:
1 cm : 5 feet
Step-by-step explanation:
4 cm : 20 feet
1 cm : 5 feet
20 has been divided by 4.
Please help will give 5 stars on your answers.
Answer:
it's the third one
Step-by-step explanation:
( ) means multiple
$80 x 12months plus the original 375
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. Connor sells pretzels for
$1.50 each. The pretzels cost $0.45 each to
make. How much profit will Connor make
if he sells 40 pretzels?
0.2
Answer:
$42.00 . . .
Step-by-step explanation:
Answer: Connor will only make 42 dollars.
Step-by-step explanation: multiply the 40 by 1.50. After you do that u then multiply 40 by 0.45. Then when you have your two answers subtract then there.
How many framed prints did mr. carandang sell? 329 475 517 1,034
Using the table that describes the amounts, it is found that Mr. Carandang sold 517 framed prints.
What does the table state?
Researching the problem on the internet, it is found that:
Hence:
1790 - 1273 = 517, hence Mr. Carandang sold 517 framed prints.
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Answer:
C. 517
Step-by-step explanation:
I just took the test
what is 90 by 25% decreased
Answer:
- 22.5
Step-by-step explanation:
Answer:
90 decreased by 25% = 67.5
Absolute change (actual difference):
67.5 - 90 = - 22.5
Answer: 67.5
Step-by-step explanation:
What’s the standard form of a circle?
Answer: (x−h)2+(y−k)2=r2. The center is (h,k) and the radius measures r units.
Step-by-step explanation:..hope this helps uwu have a great day xlXCherryColaXlx..(pls mark me brainliest)
Help I will give brainlist
Answer:
D
Step-by-step explanation:
21+16=37, so 37 gallons.
1+2=3, so 3 quarts.
In triangle ABC, m∠A=23° and m∠B=33°. What is m∠C?
The measure of angle C is 122 degrees.
We have given that,
In triangle ABC, m∠A=23° and m∠B=33°
We have to determine the remaining angle of the triangle.
What is the sum of the angle of the triangle?
The sum of the angles in a triangle is 180 degrees.
Therefore we get
angle A+ angle B+ angle C= 180 degrees
23+33+angle C=180
angle C=180-56
angle C=122
Therefore the measure of angle C is 122 degrees.
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AB is tangent to circle O find the length of radius r to the nearest tenth please answer ASAP will mark as brainlist
Answer:
7.62
Step-by-step explanation:
Using Phythagoras' theorem...
Hyp^2 = a^2 + b^2
that is:
8^2 = 11^2 + r^2
64 = 121 + r^2
64-121 = r^2
58 = r^2
therefore r = sqrt of 58
NB: Not sure but there you go.
Answer:
r ≈ 3.6
Step-by-step explanation:
∠ OAB is right ( angle between tangent and radius at point of contact )
then Δ OAB is a right triangleΔ
using Pythagoras' identity in the right triangle
with hypotenuse OB = r + 8 , then
OB² = OA² + AB² , that is
(r + 8)² = r² + 11²
r² + 16r + 64 = r² + 121 ( subtract r² from both sides )
16r + 64 = 121 ( subtract 64 from both sides )
16r = 57 ( divide both sides by 16 )
r = [tex]\frac{57}{16}[/tex] ≈ 3.6 ( to the nearest tenth )
50 POINTS PLS ANSWER QUICK!!
Which of the following equations is not a linear equation?
(LOOK AT PHOTO!!!)
Answer:
I think that B is not a linear equation.
Step-by-step explanation:
Linear eqautions can not contain exponents in them. B has x to the power of 3 and y to the power of 2, ruling it out to be a linear equation.
I hope this helps! :)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Linear equation has a degree of 1, that means the maximum power of a variable in a linear equation/expression should be 1. if an equation doesn't satisfy this condition then it's not a linear equation.
So, by Observing the choices, we get to the conclusion that the one which isn't a linear equation is B
[tex]\qquad \sf \dashrightarrow \: {x}^{3} - 5 {y}^{2} = 4[/tex]
Here, the variables have greater powers tham one, and degree is 3. so it's the required Answer ~
The volume of this cube is 125 cm³. What is the length of each side?
Answer: 5
Step-by-step explanation: A cube has all lengths equal.
Volume is 125 find the cube root