Answers
Related Questions
The product of a quarter of 3 more than a number a and two times a number b as an algebraic expression?
Answers
Algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex]
What is an algebraic expression?" An algebraic expression is defined as the expression which is represents using variables, number and mathematical operation."
According to the question,
'a' represents a number
'b' represents another number
Algebraic expression as per the given condition we get,
The product of
Quarter of 3 more than a number a = [tex]\frac{3}{4} +a[/tex]
Two times a number b = 2b
Algebraic expression = [tex](\frac{3}{4} +a)[/tex]× [tex](2b)[/tex]
Hence, algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex].
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Which expression is the simplest form of 4(3x + y) + 2(x - 5y) + x²?
A. x² +14x-9y
B. x² +14x-6y
C. x² + 13x-9y
D. x² + 14x-y
Answers
Answer: [tex]x^{2}+14x-6y[/tex]
Step-by-step explanation:
[tex]4(3x+y)+2(x-5y)+x^{2} \\ \\ 12x+4y+2x-10y+x^{2} \\ \\ \boxed{x^{2}+14x-6y}[/tex]
Carol buys a house for £234 900
She pays a 10% deposit.
Work out the amount of deposit paid by Carol.
Answers
Answer:
£23490
Step-by-step explanation:
10/100×£234900=23490
What is the missing coefficient of the x-term of the product (-x-5)² after it has been simplified?
O-25
O-10
O10
25
Answers
The missing coefficient of the x-term after finding the product of (-x - 5)², is: C. 10.
What is the Coefficient of a Variable?The coefficient of a variable is the numerical value that comes before the variable and multiplies it.
Find the product of (-x - 5)²:
(-x - 5)(-x - 5)
-x(-x - 5) -5(-x - 5)
x² + 5x + 5x + 25
x² + 10x + 25
The x-term is "10x". The coefficient is: 10.
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Find the area of the triangle with the given vertices.
(2, 4), (-1,0), (5,9)
Answers
Answer: 1.5
Step-by-step explanation:
If we translate the triangle right one unit, we get it has vertices (3,4), (0[tex]\frac{1}{2}|(9)(3)-(4)(6)|=\boxed{1.5}[/tex],0), and (6,9).
So, the area is
Find the derivative of [tex]tan^{-1} x[/tex] by 1st principle of derivative.
Answers
Answer:
[tex]\dfrac{\text{d}}{\text{d}x} \tan^{-1}x=\dfrac{1}{1+x^2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Identity}\\\\$\tan^{-1}(A)-\tan^{-1}(B) \equiv \tan^{-1}\left(\dfrac{A-B}{1+AB}\right)$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{3 cm}$\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}[/tex]
Given function:
[tex]\text{f}(x)=\tan^{-1}x[/tex]
[tex]\implies \text{f}(x+h)=\tan^{-1}(x+h)[/tex]
Differentiating from first principles:
[tex]\begin{aligned}\text{f}\:'(x) & =\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}(x+h)-\tan^{-1}x}{(x+h)-x}\right]\end{aligned}[/tex]
Using the trigonometric identity to rewrite the numerator:
[tex]\begin{aligned}& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{x+h-x}{1+x(x+h)}\right)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{h}\right]\end{aligned}[/tex]
[tex]\textsf{Multiply the denominator by }\dfrac{1+x^2+xh}{1+x^2+xh}:[/tex]
[tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h(1+x^2+xh)}{(1+x^2+xh)}}\right][/tex]
Separate:
[tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h}{(1+x^2+xh)}} \right] \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]
[tex]\textsf{Use }\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1:[/tex]
[tex]= 1 \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]
As h gets close to zero:
[tex]= 1 \cdot \left[\dfrac{1}{1+x^2}\right][/tex]
Simplify:
[tex]=\dfrac{1}{1+x^2}[/tex]
Answer:
To find the derivative of [tex]\tan^{-1} x[/tex] using the first principle of derivative, we need to use the definition of the derivative:
f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]
where f(x) = [tex]\tan^{-1} x[/tex].
Substituting f(x) into the definition of the derivative, we get:
f'(x) = lim(h->0) [([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) / h]
To simplify this expression, we can use the formula for the inverse tangent of a sum:
[tex]\tan^{-1}[/tex](a + b) = [tex]\tan^{-1}[/tex]a + [tex]\tan^{-1}[/tex]b - [tex]\pi[/tex]/2
Using this formula, we can rewrite the numerator of the expression above as:
([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) = [tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))
Now, substituting this expression back into the definition of the derivative, we get:
f'(x) = lim(h->0) [[tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))] / h
We can simplify this expression using algebra and trigonometry, and we get:
f'(x) = lim(h->0) [h / (1 + x^2 + hx + h^2 + x^2h + xh^2)] / h
f'(x) = lim(h->0) 1 / (1 + x^2 + hx + h^2 + x^2h + xh^2)
Now we can simplify this expression by dropping the terms that contain h^2 or higher powers of h, since they will approach zero faster than h as h approaches zero. We also drop the term containing x^2h, since it is a second-order term and will also approach zero faster than h. This leaves us with:
f'(x) = lim(h->0) 1 / (1 + x^2 + hx)
Now we can evaluate the limit as h approaches zero:
f'(x) = 1 / (1 + x^2)
Therefore, the derivative of [tex]\tan^{-1} x[/tex] by first principle of derivative is:
[tex]\frac{d}{dx}[/tex][tex]\tan^{-1} x[/tex] = 1 / (1 + x^2)
In a certain Algebra 2 class of 28 students, 14 of them play basketball and 19 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answers
Answer:
23/28 (82.1%)
Step-by-step explanation:
See attached Venn Diagram
23 out of 28 play basketball or baseball
Which two angles below are
complementary?
Select one:
O 20° and 160°
O 45° and 145°
O 1° and 89°
O 30° and 130°
Answers
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The correct option is C.
What are Complementary Angle?When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
The two angles which are complementary angles are 1° and 89° because their sum is 90°.
Hence, the correct option is C.
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Select three deductions someone would see on their paystubs.
Marital Status Tax
Excise Tax
Medicare Tax
Federal Income Tax
Social Security Tax
Answers
The three deductions someone would see on their paystubs are:
A. Social Security Tax
C. Federal Income Tax
D. Medicare Tax
What is paystubs?Paystubs is a paycheck and can be defined as a check that an employer issued out to the employee for the service the employee rendered to the employer.
The three deductions someone would see on their paystubs are:
Social Security Tax
Federal Income Tax
Medicare Tax
Therefore the correct options are A, C, D.
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Homework Due Tomorrow please help me it would be great
Answers
Answer:
c
Step-by-step explanation:
work out the average for the data below
Identify the remainder when -2x2 + 15x is divided by x - 7.
Answers
Answer:
The remainder is 9
Step-by-step explanation:
x-7=0
x=7
Plug x=7 into the given fxn
-2(7)²+15(7)
-2(49)+105
-96+105
9
Many animals have skeletons that provide support so that they can remain upright. In contrast, plants cells depend on a cellular structure for support. What structure provides support for a plant cell? A. nucleus B. cell wall C. chloroplast D. cell membrane
Answers
Answer:
B. Cell Wall
unlike animal cells, plant cells have walls instead of just membranes
Answer:
b cell wall
Step-by-step explanation:
How many times does 17 go into 553?
Answers
Emanuel used the calculations below to find the product of the given fractions.
(Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)
Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction
Step 2 StartFraction negative 12 over negative 90 EndFraction
Step 3 StartFraction 12 over 90 EndFraction
Step 4 StartFraction 2 over 15 EndFraction
In which step did his first error occur?
step 1
step 2
step 3
step 4
Answers
Answer:
step 1
Step-by-step explanation:
The product of fractions is the quotient of the product of the numerators and the product of the denominators. When negative fractions are involved, the sign of the result will be negative if the number of minus signs among the factors is odd.
__
setupThe product Emanuel wanted to compute was ...
[tex]\dfrac{3}{5}\cdot\dfrac{4}{9}\cdot\left(-\dfrac{1}{2}\right)[/tex]
step 1The first calculation step used was ...
[tex]=\dfrac{3\cdot4\cdot(-1)}{5\cdot9\cdot(-2)}\qquad\textbf{Error}\text{ -- a minus sign added}[/tex]
The error was in the first step where a minus sign was added. This brings the total to an even number of minus signs, changing the sign of the result.
__
A more appropriate first step might have been ...
[tex]=-\dfrac{3\cdot4\cdot1}{5\cdot9\cdot2}\qquad\text{correct first step}[/tex]
Which equation has the same solution as x^2+8x+15 = -4x
2
+8x+15=−4?
Answers
The equation that has the same solution as x² + 8x + 15 = -4x is x = -6± √21.
Step 1 - Move terms to the left
x² + 8x + 15 = -4x
x² + 8x + 15-(-4x) = 0
Step 2 - Combine the terms
x² + 8x + 15 + 4x = 0
x² + 12x + 15 = 0
Step 3 - Apply the quadratic formula
x = (-b ± √(b² - 4ac) )/ 2a
Recall that form our equation:
a = 1
b = 12
c = 15
Thus, x = (-12 √(12² - 4 * 1 *15) )/2 *1
⇒x = -6 ± √21
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Students in MA238 spend on average 3.75 hours a week studying (with a population standard deviation σ = 5.17). (i) Given this fact, describe the sampling distribution of the mean if all possible random samples of size 50 were chosen. (ii) What can you say about the mean of all the possible sample means? (iii) If 250 such samples were chosen at random and for each you calculated a 95% C.I for the mean, how many such intervals would you expect to contain the true mean? (iv) If instead you calculated a 99% C.I. for the mean, how many intervals would you now expect to capture the true mean.
Answers
The sampling distribution of the mean if all possible random samples of size 50 were chosen will be 0.731.
How to depict the sample?From the information given, the mean of all the possible sample means will be:
= 5.17/✓50
= 5.17/7.071
= 0.731
It should be noted that the sample means will have the same mean as the population.
The intervals that you would expect to contain the true mean will be:
= 0.95 × 250
= 237.5 intervals
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A 2100-square-foot home is for sale. The finished basement has an area of 455 square feet. The basement accounts for what percent of the total square footage?
Answers
Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.
What is Percentage?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given that;
Area of the house = 2100ft²Area of the basement = 455ft²Percentage of area occupied by the basement = ?Percentage = ( Part / Whole ) × 100%
Percentage = ( 455ft² / 2100ft² ) × 100%
Percentage = 0.21666 × 100%
Percentage = 21.67%
Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.
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if a pen and a pencil cost 1.10$ but the pen cost is 1$ more than pencil
Answers
Answer:
The pencil cost $0.05 and the pen cost $1.05.
Step-by-step explanation:
Let, the price of the pencil is $ .
Given that the pen costs a dollar more than the pencil,
So, the price of the pen=$+1.
Therefore, ++1=1.10
, 2+1=1.10
, 2=1.10–1
, 2=0.10
, =0.10/2
, =0.05
The pencil cost $0.05 and the pen cost $1.05.
The graph of a linear function is shown.
Which word describes the slope of the line?
• positive
• negative
• zero
• undefined
Answers
Answer:
Slope is positive
Answer:
• positive
Step-by-step explanation:
Here is what you need to know:
slope up to the right: positive slope
slope down to the right: negative slope
horizontal line: zero slope
vertical line: undefined slope
Look at the graph. the line slopes up to the right, so it is a positive slope.
Select whether the pair of lines is parallel, perpendicular, or neither.
y=2x+4, y=2x−10
Answers
Answer:
parallel
Step-by-step explanation:
the equations of the the 2 lines have the same gradient 2x . this makes them parallel.
When a retired police officer passes away, he leaves $45,000 to be divided among his three children and three grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
Answers
The answer that I got is 7 500
select all of the statements that are true for the given parabola?check all that apply(everything in picture)
Answers
The x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
Here the graph or equation is not given:
So we are assuming the equation for the parabola is:
y = x²—4
If we plot the graph of the parabola, we can say:
The x-intercepts are (-2, 0) and (2, 0) The minimum is at (0, -3)The line of symmetry is x = 0Thus, the x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4
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the distance on a ruler between 8cm and 26cm =
Answers
Answer:
18 cm
Step-by-step explanation:
To find the distance, take the larger number and subtract the smaller number
26 cm - 8 cm
18 cm
an isosceles triangle has two 5.5 cm sides and two 32.4 angles. find the area and primeter of this triangle.
Answers
The area and perimeter 10.7625 sq. cm and 11.5536 cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
let us construct perpendicular bisector.
Using trigonometry
cos [tex]\theta[/tex]= B/H
cos 32.4 = x / 5.5
5.5 cos 32.4 =x
We will consider the third side 2x.
So, 2( 5.5 cos 32.4) is the third side
P = 5.5 + 5.5 + 2( 5.5 cos 32.4)
= 11 + 0.5536
= 11.5536 cm
Area= 1/2* 5*5* sin 115.2
= 12.5 * 0.861
= 10.7625 sq. cm
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Need help ASAP
A gives the area of the rectangle. Find the
11.
12.
A-35 m²
5 m
b
6 ft
Answers
Answer:
Area of a rectangle = l × b
11. 35 = 5 × b
b = 35/5
b = 7 m
12. 48 = 6 × h
h = 48/6
h = 8 ft
13. 24 = b × 3
b = 24/3
b = 8 in
Hope it helps!
Given: ABC is a right triangle with right angle C. AB = 18 centimeters and mZA = 22°.
What is BC?
Enter your answer, rounded to the nearest tenth, in the box.
cm
Answers
How much of an 80% orange juice drink must be mixed with 12 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice
Answers
Answer:
12 gallons
Step-by-step explanation:
The amount of juice in the mix is the sum of the amounts of juice contributed by each of the constituents of the mix. Those amounts will be the product of the quantity of constituent and the fraction that is juice.
__
setupLet x represent the amount of 80% juice drink that must be added to the mix. The total amount of orange juice in the mix is ...
20% × 12 gallons + 80% × x gallons = 50% × (12 +x) gallons
__
solutionDividing by gallons, eliminating parentheses, and using decimals for percentages, we have ...
2.4 +0.80x = 6.0 +0.50x
0.30x = 3.6 . . . . . . . . subtract 0.50x+2.4
x = 12 . . . . . . . . . . . divide by 0.30
12 gallons of 80% juice drink must be added to obtain the desired mix.
_____
Additional comment
We notice that 50% is the average of 20% and 80%, so each must be half of the mix. If there are 12 gallons of 20%, then there must be 12 gallons of 80%.
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hosting a dinner party for 38 people, you plan to serve peach pie for dessert. Each pie has 8 slices. how many pies must your buy to ensure each guest gets 1 slice
Answers
Answer:
4.75 or round up to 5.
Step-by-step explanation:
if each pie has 8 slices, then you must do 8+8+8... and so on until u reach 38. However you wont get exactly 38 because 8 doesn't add up evenly into 38. You can find the exact number by divding the amount of people, 38, by the number of slices per pie, 8. The answer will be 4.75 but you can not buy a fraction of a pie so you must round up to 5 whole pies. There will be extra left over in the end, but you cant round down because 4 pies would not be enough, so you must buy 5.
Write the equation of the graph of y = cos(x) was shifted downwards by 3 units, shrink horizontally by a fourth of a unit, inverted horizontally and shifted 60° to the left. if it has an amplitude of 5 units.
Answers
The equation of the transformed function is y = 5cos(x/4 + 60) - 3
How to determine the equation?The equation of the graph is given as:
y = cos(x)
The rule of downward shift is:
(x, y) ⇒ (x, y - h)
So, the function when shifted downwards by 3 units is
y = cos(x) - 3
The rule of horizontal shrink is:
(x, y) ⇒ (x/k, y)
So, the function when shrink horizontally by a fourth unit is:
y = cos(x/4) - 3
The rule of left shift is:
(x, y) ⇒ (x +h, y)
So, the function when shifted left by 60 units is
y = cos(x/4 + 60) - 3
The amplitude is given as:
A= 5
So, we have:
y = 5cos(x/4 + 60) - 3
Hence, the equation of the transformed function is y = 5cos(x/4 + 60) - 3
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6. Resuelve las ecuaciones. Anota la solución y tu procedimiento.
a) 2x - 6=4
Procedimiento:
Solución: x =
b) 3x-3 = 3
Procedimiento:
Solución: x =
Procedimiento:
Solución: x =
c) x + 3 = 4
Answers
Answer:
Step-by-step explanation:
a)
Planteamiento:
2x - 6 = 4
Procedimiento:
2x - 6 + 6 = 4 + 6
2x + 0 = 10
2x = 10
2x/2 = 10/2
1x = 5
x = 5
Comprobación:
2*5 - 6 = 4
10 - 6 = 4
Solución:
x = 5
b)
Planteamiento:
3x - 3 = 3
Procedimiento:
3x - 3 + 3 = 3 + 3
3x - 0 = 6
3x = 6
3x/3 = 6/3
1x = 2
x = 2
Comprobación:
3*2 - 3 = 3
6 -3 = 3
Solución:
x = 2
c
Planteamiento:
x + 3 = 4
x + 3 - 3 = 4 -3
x + 0 = 1
x = 1
Comprobación:
1 + 3 = 4
Solución:
x = 1