The correct order to solve the equation is given below .
In the question ,
it is given that ,
the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 ,
Step(1) , adding 4 to each side of the equation ,
3*([tex]2^{2 t - 5}[/tex]) = 14
Step(2) , dividing both sides of the equation by 3 ,
we get , ([tex]2^{2 t - 5}[/tex]) = 14/3 .
Step(3) , taking log on each side ,
log([tex]2^{2 t - 5}[/tex]) = log(14/3)
Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,
we get ,
(2t - 5)*log(2) = log(4.67)
Step(5) , Dividing each side by log(2) ,
we get , 2t-5 = log(4.67)/log(2) .
Step(6) , Add 5 to each side of equation
we get , 2t = 2.23 + 5 ;
Step(7) , Simplifying we get ,
we get , t = 3.625 .
Therefore , the the solution of the given equation is t = 3.625 .
The given question is incomplete , the complete question is
Arrange the steps in the correct order to solve the equation,
3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 .
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Find a point-slope form for the line with slope 5 and passing through the point (- 8, -4)
Answer:
y + 4 = 5(x + 8)
Step-by-step explanation:
Slope: 5 => m = 5
Point: (-8, -4) => x = -8 and y = -4
y - y1 = m(x - x1)
y - (-4) = 5(x - (-8))
y + 4 = 5(x +8)
A while ago, Kinsley bought shares of stock in a high-tech firm. At that time, the selling price was $18 per share. According to today's newspaper, a share is currently worth 50% more. What is the current value of one share?
Answer:
$27
Step-by-step explanation:
We find 50% of $18 and add it to $18.
50% of $18 = 5/100 × $18 = 0.5 × $18 = $9
Today, it is worth $9 more.
$18 + $9 = $27
The function f(x) = e2x+1 when graphed could be described as:
a decreasing exponential graph.
an increasing exponential graph. an increasing linear graph.
None of these choices are correct.
The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
How to Interpret Exponential Graphs?The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.
Now, we are given the exponential function as; ƒ(x) = e^(2x + 1)
Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.
Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
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FORMATIVE AND SUMMAT assessment unit 4 Draw the figure's reflection in the y-axis.
The reflection of the quadrilateral across the y-axis is shown in the graph below.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
The reflection does not change the shape and size of the geometry. But flipped the image.
The quadrilateral has four sides and four angles. And the sum of the internal angles of the quadrilateral is 360 degrees.
The quadrilateral is given in the figure.
The reflection of the quadrilateral across the y-axis is shown in the graph below.
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15 PTS I NEED HELP IMMEDIATLEY!! A textbook store sold a combined total of 447 biology and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of biology textbooks sold. How many textbooks of each type were sold?
Answer:
biology = 255 ; sociology = 192
Step-by-step explanation:
b + s = 447
s = b - 63
b + b - 63 = 447
2b = 447 + 63
2b = 510
2/2 b = 510/2
b = 255
s = 255 - 63
s = 192
Answer: 192 sociology textbooks, 255 biology textbooks
Step-by-step explanation:
Let the number of biology be x, and the number of sociology be x
The number of the sociology textbook is x+63
So the equation is
x + x + 63 = 447
2x = 384
x= 192 sociology textbooks
To find the number of biology textbooks, just take 447- 192 = 255 biology textbooks
Select all of the following that represent direct variation.
1. y = 5x
2. y = 2x + 1
3. 3 = xy
4. b = 1/2a
5. y= 2/x
6. m = 5n
The equations, y=5x, b = 1/2 a, m=5n are direct variations.
What is direct variation?A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.
We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.
y = 5x is in the form of y = kx, where k =5, hence this is a direct variation
y = 2x + 1 is not in the form of y = kx, hence this is not a direct variation
xy = 3 is not in the form of y = kx, hence this is not a direct variation
b = 1/2 a is in the form of y = kx, where k =1/2, hence this is a direct variation
y = 2/x is not in the form of y = kx, hence this is not a direct variation
m = 5n is in the form of y = kx, where k =5, hence this is a direct variation
Thus, y=5x, b = 1/2 a, m=5n are direct variation
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NO LINKS! PLEASE HELP ME!
Answer:
[tex]\dfrac{17}{8}[/tex]
Step-by-step explanation:
Given statement:
The quotient of (8/5 divided by 8/10) is added to the product of (8/14 × 7/12 × 3/8):[tex]\implies \dfrac{\frac{8}{5}}{\frac{8}{10}}+\left(\dfrac{8}{14} \times \dfrac{7}{12} \times \dfrac{3}{8}\right)[/tex]
To divide two fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:
[tex]\implies \left(\dfrac{8}{5} \times \dfrac{10}{8}\right)+\left(\dfrac{8}{14} \times \dfrac{7}{12} \times \dfrac{3}{8}\right)[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]
[tex]\implies \left(\dfrac{8 \times 10}{5\times 8}\right)+\left(\dfrac{8 \times 7 \times 3}{14 \times 12 \times 8}\right)[/tex]
Carry out the multiplications:
[tex]\implies \dfrac{80}{40}+\dfrac{168}{1344}[/tex]
Simplify the fractions by dividing the numerator and denominator by the GCF:
[tex]\implies \dfrac{80 \div 40}{40\div 40}+\dfrac{168 \div 168}{1344 \div 168}[/tex]
[tex]\implies \dfrac{2}{1}+\dfrac{1}{8}[/tex]
Make the denominators of both fractions the same:
[tex]\implies \dfrac{2 \times 8}{1\times 8}+\dfrac{1}{8}[/tex]
[tex]\implies \dfrac{16}{8}+\dfrac{1}{8}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{16+1}{8}[/tex]
[tex]\implies \dfrac{17}{8}[/tex]
Rectangular pyramid B is the image of rectangular pyramid A after
dilation by a scale factor of 3. If the surface area of rectangular
pyramid A is 87 cm², find the surface area of rectangular pyramid B,
the image.
Answer: 261 cm²
Step-by-step explanation: 87 x 3 = 261
Answer:
783 cm²------------------------------
The area is the function of two dimensions.
The scale factor is 3. It means each dimension is 3 times greater.
Therefore the surface area is 3*3 = 9 times greater:
S(B) = 9*S(A) = 9*87 = 783 cm²Can you explain step by step how "a cube has a side length of 10 cm. The cube is dilated by a scale factor of 5. How does the volume of the new cube compare to the volume of the original cube?" The answer is the volume is 125 times the volume of the original cube but how is this the answer.
After the dilation, the new volume of the cube is 125 times the original volume of the cube.
How does the new volume compare to the original volume?Remember that for a cube of sidelength S, the volume is written as:
V = S^3
If we apply a dilation of scale factor 5 to the cube, then the new sidelength of the cube is 5*S
Replacing that in the volume formula we will get the volume of the dilated cube, it is:
V' = (5*S)^3
V' = 5^3*S^3
V' = 125*S^3
Where S^3 is the original volume, so we can write:
V' = 125*V
So the new volume is 125 times the original volume.
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Last year, students planted 8 tomato plants and 16
garden. This year, the students planted
pepper plants in a school
15 tomato plants. They want to have the
same ratio of tomato plants to pepper plants as last year. Pepper plants cost
$4.33 each. What is the cost, in dollars, of the pepper plants for this year's garden?
Answer:
Step-by-step explanation:
From the ratio gotten, the total cost of the pepper will be $129.90.
How to solve a ratio
Since the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:
= 8/16 = 1:2
This year, the students planted 15 tomato plants, the number of pepper will be:
= 15 × 2 = 30
Since pepper plants cost $4.33 each, the total cost will be:
= 30 × $4.33
= $129.90
which graph represents the solution to the system of equations? y=1/2x+1 y=-2x+8
Answer:
The answer is Bottom Left
the set of integers that satisfy (x-2)(2x+1)=2x^2-3x-2
Please help guys please
Answer: 3
Step-by-step explanation: (x-2)(2x+1)=2x^2-3x-2 = 3
please put brainiest, please.
Sqrt (cos (x)) * cos (300x) + sqrt (abs (x)) - 0. 7) * (4- x * x) ^ 0. 01, sqrt (6-x ^ 2), -sqrt (6-x ^ 2) from -4. 5 to 4. 5
The graph of your equation: [See in attachment]
What is graph?
A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
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A. 3(2x-3)-5(2+x) B. -2(2x+3)(x+2)-(x+2) C. 3(2-x)+3(2-x) 2. Solve and check each of the following equation. i.3x+5=29 ii. x-1=14 3. Solve each of the following questions. i. 2(x+2)-3(2-x)=2(x-3) ii. -3(2-2x)-(x+2)=2x+3 iii. 2/3(x+2)=7/8(2-x) iv. 4/3(2-x)=3/5(x+3) v. 5[x-(4x-5)]-2=2-7x iii. x=21 4. Locate each of the following on the coordinate plane bra
Answer:
[tex] {x + 2x}^{2} [/tex]
HELP ASAP ITS URGENT!!!!!!!
ILL GIVE 50 POINTS
Answer: It's in the picture
Step-by-step explanation:
Watch help video
23.4 is what percent of 288? Round to the nearest tenth.
23.4 is 8.125 percentage of 288.
What are percentages?Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.
Calculation:1. Since 288 is the output value of the task, we assume that it is 100%.
2. We make the assumption that the value we are looking for is x.
3. If 100% = 288 then we can express that as 100% = 288.
4. Since we already know that the output result of x% equals 23.4, we can write it down as x%=23.4.
5. We now have two straightforward equations:
1) 100%=288
2) x%=23.4 where both of their right sides and left sides have the same units, allowing us to write something like this: 100%/x%=288/23.4
6. All that is left for us to do is solve the straightforward equation, and we will have our answer.
7. Calculate 23.4 as a percentage of 288.
100%/x%=288/23.4
We multiply both sides of the equation by x 100=12.307692307692 to get *x=(288/23.4)*x.
*x - we get x 100/12.307692307692=x 8.125=x by dividing both sides of the equation by (12.307692307692) to get x=8.125.
23.4 is 8.125 percentage of 288.
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Please Help Me with this Problem if you can
Thank you
Answer:
C
Step-by-step explanation:
-2x + 10 Means that the line crosses the y axis at 10. The slope is -2 that means that as the y changes by -2, the x changes by 1.
The second equations means that we have a horizontal line with no slope that goes through -28 1/2
A solid metal cuboid has length 9 cm, width 6 cm and height 4 cm
The cuboid is melted down and all metal is used to make a solid cube.
calculate the length of one side of the cube.
The cube has a side that is 6 cm long.
Volume of cuboid:-
Height × width × depth
⇒9 cm × 6 cm × 4 cm
⇒ 216 cm³
when the cuboid is melted and a cube is made using just metal.
So, the cube's volume is 216 cm³.
side³ = volume of cube
⇒ Side³ = 216
⇒ Side = ∛216
⇒ Side = ∛6×6×6
⇒Side = 6 cm
As a result, the cube's side measures 6 cm.
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Answer and show work
Using Pythagoras theorem the hypothenuse of the figure is 32.5 feet
What are Pythagoras's TheoremPythagoras theorem is defined as “In a right-angled triangle, the square of the hypotenuse must be equal to the sum of squares of the other two sides". The sides of this triangle are legs and hypotenuse. The hypotenuse is the longest side, as it is opposite to the angle 90°.
The formula of Pythagoras theorem is given as
c² = a² + b²
Taking the two sides given, we can find the hypothenuse of the right angle triangle figure
c² = 26² + 19.5²
c² = 676 + 380.25
c = √1056.25
c = 32.5
The distance from the top of the pole to the stake is 32.5 feet
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Find x, y and z for the diagram below.
X =
y =
Z=
88
2x+18
y+10
3x-7
I need help on this please:
show that the two quadrilaterals are congruent
The volume of a cylinder is given by the formula V = ²h,
where r is the radius and h is the height of the cylinder.
Determine the volume of a soup can with a 3-inch radius and
a 5.5-inch height.
Use 3.14 for T.
a 145.51 in ³
b 245.51 in ³
c 103.62 in ³
d 155.43 in ³
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Go to Settin
(LOTS OF POINTS) The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $175.50 for each ton of sugar. The second company charges $4995 to rent trucks plus an additional fee of $200.75 for each ton of sugar.
a) For what amount of sugar do the two companies charge the same?
b) What is the cost when the two companies charge the same?
The amount of sugar that both companies would charge the same is 20 tons.
The cost when the two companies would charge the same is $9010.
What is the amount of sugar that both companies would charge the same?The linear equation that represents the total charge of the companies : cost to rent truck + (ton of sugar x cost per ton)
The linear equation that represents the total charge of the first company : $5500 + ($175 x s)
$5500 + $175s
The linear equation that represents the total charge of the second company : $4995 + ($200.75 x s)
$4995 + $200.75s
When the two companies charge the same, the two linear functions above would be equal.
$4995 + $200.75s = $5500 + $175s
In order to determine the value of s, take the following steps:
200.75s - 175.50s = $5500 - $4995
25.25s = 505
s = 505 / 27.25
s = 20
In order to determine when the cost of the two companies would be the same, substitute for s in either of the above linear functions.
$5500 + $175.50(20)
$5,500 + 3510 = $9010
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In the function g(x)=9-5x what is the value of g(3)
Answer:
g(3) = - 6
Step-by-step explanation:
g(3) = 9 - 5(3)
g(3) = 9 - 15
g(3) = - 6
Determine which set of side measurements could be used to form a right triangle.
A. 3, 11, 20
B. 5, 9, 17
C. 6, 7, 8
D. 6, 8, 10
Answer:
D. 6, 8, 10
Step-by-step explanation:
Apply the Pythagorean theorem equation to all set of number, and see which one works.
A.
3² + 11² ≠ 20²
9 + 121 ≠ 400
131 ≠ 400
B.
5² + 9² ≠ 17²
25 + 81 ≠ 289
106 ≠ 289
C.
6² + 7² ≠ 8²
36 + 49 ≠ 64
85 ≠ 64
D.
6² + 8² = 10²
36 + 64 = 100
100 = 100
.... ineed help past due
Answer:
a worker can plant 2/5 acres in 7/8 days
or a worker can plant 2/5 acres in 7/8 hrs=21hrs
in one hrs he can plant 2/5×21 acres
in 24 hrs he can plant 2/105 ×24 acres
Therefore in one day he can plant 16/35 Acres
{0.2x+0.6y=3.6 0.4x-0.9y=-1.2} what is the answer
Answer:
68266==874624./4
Step-by-step explanation:
77353877473=287365-2874662kkh=2875
The function is defined by the following rule.
Complete the function table.
The complete table of function is,
x h(x)
-4 -11
0 -3
2 1
4 5
5 7
What is function?
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.
Let, the function h is defined by the rule,
h(x) = 2x - 3
We have to complete the function table.
x = -4 ⇒ h(-4) = 2(-4) - 3 = -8 - 3 = -11
x = 0 ⇒ h(0) = 2(0) - 3 = -3
x = 2 ⇒ h(2) = 2(2) - 3 = 4 - 3 = 1
x = 4 ⇒ h(4) = 2(4) - 3 = 8 - 3 = 5
x = 5 ⇒ h(5) = 2(5) - 3 = 10 - 3 = 7
Hence, the table becomes,
x h(x)
-4 -11
0 -3
2 1
4 5
5 7
This is the complete table of function.
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Question 10 of 25
The polynomial (x-2) is a factor of the polynomial 5x² - 6x +4.
O A. True
OB. False
Answer:
B. False
Step-by-step explanation:
5x² - 6x + 4 | 5 × 4 = 20
Can't factor it normally
√b² - 4ac
-b ± ---------------
2a
√(-6)² - 4(5)(4)
-(-6) ± ---------------
2(5)
√36 - 80
6 ± ---------------
10
6 ± √-44
---------------
10
6 ± √-4 × 11
---------------
10
6 ± 2i√11
---------------
10
The answer is actually
3 ± i√11
---------------
5
I hope this helps!
Answer:
B. False
Step-by-step explanation:
You want to know if (x -2) is a factor of 5x² -6x +4.
RemainderThere are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:
5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12
The value is not 0, so (x -2) is not a factor.
Other factorAnother way to tell is to determine what the other factor would be.
The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...
(5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial
The polynomial 5x² -6x +4 does not have a factor (x -2).
GraphThe graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.
HELP MEE 45 POINTS!!!
Solve. What is r in the inequality? 6 (r– 10) + 8r ≤ 7
Answer in image
Step-by-step explanation:
Simplify both sides of the inequality.
Add 60 to both sides.
Divide both sides by 14.
r = 67/14 or 4.78571...