Answer:
a - 8
Step-by-step explanation:
1/2 a - 4
if we scale both numbers by the same factor, we will be creating an equivalent expression.
So, let's say we multiply the equation by 2.
1/2 a (2) = 1 a = a
-4 (2) = -8
One equivalent expression would be
a - 8
[If you want to test this out, try plugging in any number for a. For example, if you plug in 10...
1/2 of 10 = 5, 5 - 4 = 1
1 times 10 = 10, 10 - 8 = 2
These answers are the same scaled as the original equation, the answer for the first expression is multiplied by 2 to get the second expression]
Find all real $x$ that satisfy $$(2^x - 4)^3 (4^x - 2)^3 = (4^x 2^x - 6)^3. $$
The polynomial-like expression is satisfied by the real value x = 1.
How to determine the real solution of a polynomial-like expression
In this question we must apply the concepts of logarithms and algebra properties to solve the entire expression. Initially, we expand the right part of the expression:
[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (4^{x}+2^{x}-6)^{3}[/tex]
[tex](2^{x}-4)^{3} + (4^{x}-2)^{3} = [(2^{x}-4)+(4^{x}-2)]^{3}[/tex]
[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (2^{x}-4)^{3}+3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2}+(4^{x}-2)^{3}[/tex]
[tex]3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2} = 0[/tex]
[tex]2^{x}-4 + 4^{x}-2 = 0[/tex]
[tex]2^{x}\cdot 2^{x} + 2^{x}-6 = 0[/tex]
[tex]u^{2}+u - 6 = 0[/tex]
[tex](u+3)\cdot (u-2) = 0[/tex]
Hence, the roots of the pseudopolynomial are [tex]u_{1} = -3[/tex] and [tex]u_{2} = 2[/tex]. Only the second one have a real value of x. Hence, we have the following solution:
[tex]2^{x} = 2[/tex]
[tex]x\cdot \log 2 = \log 2[/tex]
[tex]x = 1[/tex]
The polynomial-like expression is satisfied by the real value x = 1. [tex]\blacksquare[/tex]
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1.) 7x+8=29
2.) 6x+6=36
3.) 7+6x=19
how do you solve these problems?
Answer:
1.) x= 3
2.) x=5
3.) x=2
Step-by-step explanation:
1) 7x+8=29
( -8). 7x=21. (-8)
(÷7). x=3. (÷7)
2). 6x+6=36
6x=30. subtract 6
x=5. divide by 6
3). 7+6x=19
6x+7=19. rearrange it
6x=12. subtract 7
x=2. divide by 6
[tex] \huge\mathbb\red{ANSWER} [/tex]
[tex] \mathsf \purple{7x + 8 = 29}[/tex]
[tex] \mathsf \pink{7x + 8 - 8 = 29 - 8}[/tex]
[tex] \mathsf \purple{7x = 21}[/tex]
[tex] \mathsf \pink{ \frac{7x}{7} = \frac{21}{7} }[/tex]
[tex] \mathsf \purple{x = 3}[/tex]
[tex] \mathsf \red{6x + 6 = 36}[/tex]
[tex] \mathsf \green{6x + 6 - 6 = 36 - 6}[/tex]
[tex] \mathsf \red{6x = 30}[/tex]
[tex] \mathsf \green{ \frac{6x}{6} = \frac{30}{6} }[/tex]
[tex] \mathsf \red{x = 5}[/tex]
[tex] \mathsf \blue{7 + 6x = 19}[/tex]
[tex] \mathsf \orange{ - 7 + 7 + 6x = 19 - 7}[/tex]
[tex] \mathsf \blue{6x = 12}[/tex]
[tex] \mathsf \orange{ \frac{6x}{6} = \frac{12}{6} }[/tex]
[tex] \mathsf \blue{x = 2}[/tex]
Which expression is the factorization of x2 10x 21?
The factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.
It is given that the expression [tex]\rm x^2+10x+21[/tex]
It is required to find which expression is the factorization of the given expression, the options are:
a) (x + 3)(x + 7)
b) (x + 4)(x + 6)
c) (x + 6)(x + 15)
d) (x + 7)(x + 14)
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an expression:
[tex]\rm x^2+10x+21[/tex]
[tex]\rm x^2+7x+3x+21[/tex]
Breaking 10x into 7x and 3x because the multiplication of 7x and 3x is [tex]\rm 21x^2[/tex] and the addition is 10x.
[tex]\rm x^2+7x+3x+21\\\\\rm x(x+7)+3(x+7)\\\\\rm (x+7)(x+3)[/tex]or
[tex]\rm (x+3)(x+7)[/tex]
Thus, the factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.
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What is the equation of a line that is perpendicular to y = x + 4 and passes through (–2,8)?
Answer:
y= -x+6
Step-by-step explanation:
G1xG2= -1
G2= -1
-1 = (y-8)
-------
(x+2)
-1 (x+2)=y-8
-x-2=y-8
-y=x+2-8
y= -x+6
Can someone do this for me
Answer:
A - 10 feet
D - 5 seconds
Step-by-step explanation:
Insert 12 for r the radius and 1500 for V the volume.
12 = [tex]\sqrt{}\frac{3(1500)}{\pi h}[/tex]
Square both sides
144 = [tex]\frac{4500}{\pi h}[/tex]
Solve 144 = [tex]\frac{4500}{\pi h}[/tex]: h = [tex]\frac{125}{4\pi }[/tex]
h = [tex]\frac{125}{4\pi }[/tex] or 9.9 rounded to the nearest foot,
h = 10
t = [tex]\sqrt\frac{2(200)}{16}[/tex]
t = [tex]\sqrt\frac{400}{16} = 25[/tex]
t = [tex]\sqrt{5^{2} }[/tex]
t = 5
Walmart has jeans on sale for $42.89 the regular price is $59.99 what’s the savings before tax
59.99 - 59.99 x saving rate = 42.89
with saving rate = r%
59.99 - 59.99 x r% = 42.89
so 59,99 ( 1 - r%) = 42.89
1 - r% = 42.89 : 59.99
1 - r% = 0,7150
r% = 1 - 0,7150
r = 28,5%
PLEASE HELP 100 POINTS!!!
Identify the vertex of the function graphed below. A. (1,1) B. (2,2) C. (3,1) D. (0,-2)
Answer:
See below.
Step-by-step explanation:
The vertex is the point where it stops the arch. In this case, the answer would be (2,2).
-hope it helps
Answer:
B: (2, 2)
Step-by-step explanation:
it's the point where the parabola changes directions
if brainly doesn't let me put this question..
Answer:
8-4+9+3+6-6=36 this is my answer
PLEASE HURRY
Solve the inequality and express your answer in interval notation.
x2 + 8x-7<0
The path from the whales to the sharks is parallel to the path from the penguins to the stingrays. What is the distance between the penguins and the stingrays? StartFraction 81 Over 7 EndFraction feet 28 feet 45 feet 63 feet.
The distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.
What is proportional segment between parallel lines?In two triangle in which the one side of the first triangle is parallel to the one side of the other triangle, two similar triangle formed.
Due to this similar triangle the segment formed by the parallel line are proportional segment.
The path from the whales to the sharks is parallel to the path from the penguins to the stingrays.
The map of the zoo is attached below.
The distance from whale to shark is 18 ft, and this side is parallel to the path from the penguins to the stingrays. Suppose the distance between the penguins and the stingrays is x meters.
Thus, in the given triangle, the ratio of these two sides will be equal to the ratio of their corresponding sides. Hence,
[tex]\dfrac{x}{18}=\dfrac{42}{27}\\x=\dfrac{42}{27}\times18\\x=28\rm\; ft[/tex]
Thus, the distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.
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Answer:
28
Step-by-step explanation:
Did on edge 2022
Help me with this question on congruent triangles? 20 points
Answer:
a) 5.7 cm
b) 3.05 cm
Step-by-step explanation:
a)
Since BE is parallel to CD,
Then AB/AC = BE/CD
So Length of CD = 12.3/8.2 x 3.8 = 5.7 cm
b)
AB/AC = AE/AD
So length of AE = 8.2/12/3 x 9.15 = 6.1 cm
ED = AD - AE = 9.15 - 6.1 = 3.05 cm
hello, anyhelp? if anybody likes they can answer, show work
when filing taxes what do you need to know
Answer:
You must know all forms of additional payment and expenses, like medical bills and community expenses that can happen at any given time.
~Hope it helps~
~Be great~
6. On Marika's 8th birthday, in 2004, her father said, "My age is now four times your age."
In what year will Marika's father be able to say, "My age is now three times your age," on
Marika's birthday?
Answer:
2008
Step-by-step explanation:
when she is 12 (4 years after 2004) her dad will be 36, which is 3 x 12, therefore, in 2008 he will be able to say this.
Answer:
2008
Step-by-step explanation:
The difference in their ages is ...
4m -m = 3m = 3(8) = 24 . . . years (Marika was 8 in 2004)
__
Marika's age when the father was 3 times her age was ...
3m -m = 2m = 24 . . . years
m = 12 . . . . . Marika was 12 when her father was 3 times her age
That is 12 -8 = 4 years from 2004, so it will be true in 2008.
i need help with this
Answer:
Answer: (b) 5.
Step-by-step explanation:
Simple and best practice solution for (c-5)d=2 equation. ... If it's not what You are looking for type in the equation solver your own equation and let us solve it. ... 2 + 5d cd = 2 + 5d Divide each side by 'd'. c = 2d-1 + 5 Simplifying c = 2d-1 + 5 Reorder ... 11/4-t8 | | (3x^2+5x+2)+(4x^2+3x+2)= | | 4Y+7-Y=4+2Y-8 | | 10x+190=360 ...
For example, let's say with have the equation x+5 ... If we evaluate the same expression when x=10, we get 3(10)+7=30+7=37. Here's a variable expression with two variables: 3x−2y ... How do you express the phrase "a number z divided by 19" as an algebraic expression? ... How do you simplify 11c+5d−9c−9d?Let the number of cows be x and their legs be 4x. ... or, x = 7 [dividing by 2 on both sides]. ... The roots of the equation ax2 + bx + c = 0 will be reciprocal if: ... A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC ... (a) 15, (b) 30, (c) 60, (d) 90, (e) 120. Circle Problem Answers. Answer: (b) 5.
Can someone work this one out with me please
Answer:
46°
Step-by-step explanation:
Since the side mn is tangent, the angle in M is a right angle. The sum of internal angles needs to add to 180°, so subtacting you're left with 46°
Hi there!
Since MN is tangent to Circle K, we know that MK and MN are PERPENDICULAR.
Therefore, m∠M = 90°.
Since we now know two angles in the right triangle, we can solve for m∠K knowing that angles in a triangle sum up to 180°.
180° = ∠M + ∠N + ∠K
180° = 90° + 44° + ∠K
Combine like terms:
180° = 134° + ∠K
Subtract:
180° - 134° = ∠K
∠K = 46°
The value of a vase n years after it was
made is given by this formula:
value in pounds (£) = 500 x 1.28"
=
a) What was the original value of the
vase?
b) By what percentage does the value of
the vase increase each year?
The answers are
a)640-500
b) + 28%
The amount of money you have after investing $400 for 8 years and $600 for 6 years at the same interest rate is represented by 400x^6 + 600x^6. where x is the growth factor. classify the polynomial by the number of terms. what is the degree?
The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.
What is a polynomial?Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.
Polynomials are classified based on degree as linear, cubic, quadratic, etc.
A polynomial with two terms is known as a binomial. Hence:
The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.
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Help I’ll give brainlessly find tqs
Your answer for TQS is 43.
89 - 46 = 43
Maya bought 20 ounces of nuts at the store. How much is this in pounds? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
1.25 pounds
Step-by-step explanation:
20 divided by 16 because 16 ounces are in a pound
QUESTION 1 1.1 Consider the quadratic sequence : 8; 18; 30; 44 ... 1.1.1 Write down the next two terms of the sequence. 1.1.2 Calculate the nih term of the sequence. 1.1.3 Which term of the sequence is equal to 330?
Answer:
Below in bold.
Step-by-step explanation:
8 18 30 44
the differences are 10 12 14 .etc
1.1.1 Next 2 terms are 44+ 16 = 60 and 60+ 18= 78.
1.1.2 8 = 1^2 + 7
18 = 2^2 + 14
30 = 3^2 + 21
44 = 4^2 + 38
So the nth term = n^2 + 7n.
1.1.3 n^2 + 7n = 330
n^2 + 7n - 330 = 0
(n + 22)(n - 15) = 0
n = -22, 15
As the term sequence must be positive the answer is 15.
what is the area of the triangle in square yards 10 3/4 yards and 7 yards
can somone help? ill give brainlist
Answer:
13.99+.75+.75=15.49
Part A ) 15.49
Part B) Anna is correct because her pizza only cost 15.49 and if you subtract 15.49 from 20 it is 14.51
Step-by-step explanation:
Help if you understand thanks
Step-by-step explanation:
Table A represents an arithmetic sequence with a common difference d=+7.5
so for x=4, it's y³+7.5=25+7.5=32.5
for x=5, it's y⁴+7.5=32.5+7.5=40
Table B represents a geometric sequence with a common ratio r=4, so you're essentially multiplying by 4.
for x=4, y⁴=y³×4=160×4=640
for x=5, y⁵=y⁴×4=640×4=2560
The perimeter of the shape below is 24. One side is 5 in. What is the missing side?
Answer:
14
Step-by-step explanation:
5+5=10 and 7+7=14 and 14+10=24
Simplify:
Q1) 4k – 8p + 4k - 5p
Answer:
- 13p + 8k
Step-by-step explanation:
[tex]4k-8p+4k-5p[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=-8p-5p+4k+4k[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:-8p-5p=-13p[/tex]
[tex]=-13p+4k+4k[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:4k+4k=8k[/tex]
[tex]=-13p+8k[/tex]
[RevyBreeze]
Is my answer correct?
Answer:
No, x = 3 inStep-by-step explanation:
The area of the rhombus is half the product of its diagonals
A = 1/2(2x*16) = 4816x = 48x = 48/16x = 3[tex]area \: of \: rectangle \\= 4 \times area \: of \:identical \: triangle[/tex]
Explanation :-[tex]area \: of \: rectangle =\\ 4 \times area \: of \:identical \: triangle[/tex]
[tex]48 {in}^{2} = 4 \times \frac{1}{2} \times base \times height \\ 48 {in}^{2} = 2 \times base \times height \\ \frac{48}{2} = 8 \times height \\ \frac{ \cancel{48} {}^{ \: \: 24} }{ \cancel{2}} = 8 \times height \\ \frac{24}{8} = height \\ \frac{ \cancel{24} {}^{ \: \: 3} }{ \cancel{8}} = height \: \\ height = x = 3in \: [/tex]
Let x be a random variable with uniform distribution on (100,200). Find the probability that x assumes a value
The probability that x assumes a value less than three standard deviations from the mean is 1.
What is uniform distribution?The continuous uniform distribution, sometimes known as the rectangle distribution, is a family of symmetric probability distributions in probability theory and statistics.
We have:
x be a random variable with uniform distribution on (100,200).
It is required to find the probability that x assumes a value less than three standard deviations from the mean.
From the empirical rule, the data falls within three standard deviations of the mean in 99.7% of cases.
99.7% data from the (100, 200) is up to 199.7
Total number of favourable outcomes = 99.7
The probability that x assumes a value less than three standard deviations from the mean:
= 99.7/(200-100)
= 0.997 ≈ 1
Thus, the probability that x assumes a value less than three standard deviations from the mean is 1.
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Two of which shape can make a circle
Answer:
2 semi circles put together
Step-by-step explanation:
just cut the circle in half
Margaret is building storage boxes. each box will have a length of 8 feet, a width of 512 feet, and a height of 412 feet. a pint of paint covers 50 square feet. how many pints of paint does margaret need to buy in order to paint 3 boxes? 7 pints 10 pints 12 pints 13 pints
The surface area of a cuboid is the area of all the six faces of a cuboid. The Paint that is required to paint 3 boxes is 13 pints.
What is the surface area of a cuboid?The surface area of a cuboid is the area of all the six faces of a cuboid. It is given by the formula,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
As it is given the dimensions of the storage box are a length of 8 feet, a width of 5 1/2 feet(5.5 feet), and a height of 4 1/2 feet(4.5 feet). Therefore, the surface area of the box can be written as,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
[tex]\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2[/tex]
As it is given that the surface area that can be covered with a pint of paint is 50 square feet, therefore, the paint that will be required to paint 209 square feet is,
[tex]\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}[/tex]
[tex]\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints[/tex]
Now, we know that the surface area of the box is 209 square feet, while the paint required to paint a complete box is 4.19, therefore, the paint that will be required to paint 3 boxes will be,
[tex]\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13[/tex]
Hence, the Paint that is required to paint 3 boxes is 13 pints.
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