Answer:
[tex]\large \boxed{87.5 \, \%}[/tex]
Step-by-step explanation:
Let x = the original number of books
Then 0.375x = the total number of biographies
and 0.20 x = the original number of biographies
[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]
Find the perimeter of a square with a diagonal of 15√2.
Answer:
15
Step-by-step explanation:
Answer:
21.213
Step-by-step explanation:
pls answer asap i need this answer quick plus the full explanation #7
Two boxes have the same volume. One box has a base that is 5cm by 5cm. The other box has a base that is 10cm by 10 cm. How many times as tall is the box with the smaller base?
Answer:
x=4
Step-by-step explanation:
5^2X=10^2X
25X=10X
2X=100/25
The Box with a smaller base has a height that is 4 times taller than the Box having a larger base.
What is the volume of a cuboid?We know the volume of a cuboid is the product of its length, breadth, and height or v = l×b×h.
Given, we have two boxes let us denote them by B₁ and B₂ and their respective heights are h₁ and h₂.
To obtain how many times one box is relative to the other we have to equate their respective volumes.
Given, one box has a base that is 10cm by 10 cm and another box has a base that is 5cm by 5cm.
∴ 5×5×h₁ = 10×10×h₂.
25h₁ = 100h₂.
h₁ = 4h₂.
So, h₁ is 4 times taller than h₂.
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Simplify each expression.
1) 3(8Z² - 52 - 7)
2) 8d(2d-4)
6) 6(5x - 4)
7) 6q- 4
Answer:
1) 24Z^2 - 177.
2) 16d^2 - 32d.
6) 30x - 24.
7) 6q - 4.
Step-by-step explanation:
1) 3(8Z^2 - 52 - 7)
= 3(8Z^2 - 59)
= 24Z^2 - 177
2) 8d(2d - 4)
= (8d * 2d) - (8d * 4)
= 16d^2 - 32d
6) 6(5x - 4)
= (6 * 5x) - (6 * 4)
= 30x - 24
7) Already simplified. 6q - 4.
Hope this helps!
Explain please --
Find the measure of angle A to the nearest degree.
a. 26
b. 27
c. 63
Explanation:
We'll use the tangent ratio to connect the opposite and adjacent sides with the reference angle
tan(angle) = opposite/adjacent
tan(A) = 14/7
Then use the arctangent function (aka inverse tangent) to fully isolate A
A = arctan(14/7)
A = 63.4349 degrees approximately; make sure your calculator is in degree mode
Round this to the nearest whole number to get 63.
find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.
Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
anyone plss heeelp me...i only need answer 6c..
Answer:
6c1; [tex]Area = 81.12m^2[/tex]
6cii: See Explanation
Step-by-step explanation:
Given
[tex]A = 3p^2[/tex]
[tex]0 \leq p \leq 6[/tex]
Where A represents Area and P represents Width
Required
Solve 6c
Please note that because you only need 6c, I'll solve using calculations;
Solving 6ci:
Area of the cage, when width is 5.2m
Substitute 5.2m for p in[tex]A = 3p^2[/tex]
[tex]A = 3 * 5.2m^2[/tex]
[tex]A = 3 * 27.04m^2[/tex]
[tex]A = 81.12m^2[/tex]
Hence, the area of the cage is 81.12m²
Solving 6cii:
Area of the cage, when width is 40m
From the range of value of p: [tex]0 \leq p \leq 6[/tex], 40m is out of range of the values of p
However, if the range is extended; the value of Area is as follows;
Substitute 40m for p
[tex]A = 3 * 40m^2[/tex]
[tex]A = 3 * 1600m^2[/tex]
[tex]A = 4,800m^2[/tex]
The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$[tex]The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$[/tex]
Using the factor theorem, we have
[tex]7x^2+x-5=7(x-a)(x-b)[/tex]
and expanding gives us
[tex]7x^2+x-5=7(x^2-(a+b)x+ab)\implies\begin{cases}ab=-5\\a+b=-1\end{cases}[/tex]
So we have
[tex](a-4)(b-4)=ab-4(a+b)+16=-5-4(-1)+16=\boxed{15}[/tex]
What is the result of adding these two equations?
62 + 2y = -2
3x - 2y = -5
Answer:
x = -7/9; y = 4/3.
Step-by-step explanation:
I will assume that the top equation is 6x + 2y = -2, and the bottom one is 3x - 2y = -5.
If you add the two...
(6x + 3x) + (2y + (-2y)) = (-2 + (-5))
9x + 0 = -7
9x = -7
x = -7/9
6(-7/9) + 2y = -2
-42/9 + 2y = -18/9
2y = 24/9
y = 24/18
y = 12/9
y = 4/3
Hope this helps!
The path followed by a roller coaster as it climbs up and descends down from a peak can be modeled by a quadratic function, where h(x) is the height, in feet, and x is the horizontal distance, also in feet. The path begins and ends at the same height, covers a total horizontal distance of 100 feet, and reaches a maximum height of 250 feet. Which of the functions could be used to model this situation? A. h(x)=-0.1x^2-50x+250 B. h(x)=-0.1(x-50)^2+250 C. h(x)=-0.1(x-100)^2+250 D. h(x)=-0.1x^2+100x+250
Answer:
C
Step-by-step explanation:
0.1(x - 100)² + 250
0.1[(x - 100)(x - 100)] + 250
0.1(x² -200x + 10000) + 250
0.1x² - 20x + 1000 + 250
0.1x² - 20x + 1250
0.1x² - 25x + 5x + 1250
0.1x(x - 250) + 5(x + 250)
∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)
The cosine function reaches a value of 0 when x is equal to
Answer:
Step-by-step explanation:
The values of the cosine function are represented by the axis OX of the goniometric circumference (circumference centered at the origin and of radius 1). Therefore the cosine is zero for the 90º and 270º angles.
Which best describes the relationship between the lines with equations 5x +y = 4 and 20.0 + 4y = 16?
Answer:
There is no relationship, except they do intersect at the point (1, -1). Hope this helps :)
Brainliest?
Both given lines are going to intersect at ( 1,-1 ) that's it.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that
Line 1 ; 5x +y = 4
Line 2 ; 20 + 4y = 16 ⇒ y = -1
At y = -1 the first line is
5x - 1 = 4 ⇒ x = 1
So,
It is clear that line 1 has a point ( 1 .-1 ) and line 2 also passes
through it hence there will an intersection.
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Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere?
Answer:
Volume of the sphere is 66.67r/h
Step-by-step explanation:
Hello,
Volume of a sphere = ⁴/₃πr³
Volume of a cylinder = πr²h
The volume of the cylinder = 50ft³
But the cylinder and sphere both have the same radius and height
Volume of a cylinder = πr²h
50 = πr²h
Make r² the subject of formula
r² = 50/πh
Volume of a sphere = ⁴/₃πr³
Put r² into the volume of a sphere
Volume of a sphere = ⁴/₃π(50/πh)r
Volume of a sphere = ⁴/₃ × 50r/h
Volume of a sphere = ²⁰⁰/₃ r/h
Volume of a sphere = 66.67r/h
The volume of the sphere is 66.67r/h
Eiko is wearing a magic ring that increases the power of her healing spell by 30\%30%30, percent. Without the ring, her healing spell restores HHH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
Answer:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
which geometric solid is formed by rotating the rectangle about line m?
Answer:
rectangular prism
Step-by-step explanation:
check by rotating the shape in images
F(x) = 3x+2 what is f(5)
Answer:
f(5) = 17Step-by-step explanation:
f(x) = 3x + 2
To find f(5) substitute 5 into f(x)
That's
f(5) = 3(5) + 2
= 15 + 2
= 17
Hope this helps you
Answer:
17
Step-by-step explanation:
You just plug 5 into the equation
f(5)= 3(5)+2
=15+2
=17
Hope this helped! :)
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
Find the vertex of the graph
Answer:
(-3, -11)
i needed to put more characters so here
Solve sin 20 = COS CE-30)
Answer:
CE = 100°
Step-by-step explanation:
Using the cofunction identity
sin x = cos(90 - x)
Given x = 20°, then 90° - 20° = 70° thus
CE - 30 = 70° ( add 30 to both sides )
CE = 100°
Thus
sin20° = cos(100 - 30)° = cos70°
Answer:
CE = 100
have a nice day!
Step-by-step explanation:
Heyy umm I need help
Answers
B, D and E are proportional
A, C, and F are not proportional
y = 3+x .... not proportional
y = 1.6x .... proportional
y = 3/(4x) .... not proportional
y = x .... proportional
y = 12x .... proportional
y = 2x+1 ... not proportional
=================================================
Explanations:
Anything in the form y = k*x is a direct proportional equation. As x goes up, so does y. The same happens if x decreases, and we'll have y also decrease. They go up together or down together. This is where the "direct" comes from. Specifically they change the same amount each time (hence the term "proportional").
For something like y = 1.6x, we have k = 1.6
In the equation y = x, we have y = 1x in reality so k = 1 here.
Lastly, y = 12x has k = 12.
----------------------
The other equations are not in the form y = kx. Whenever we have y = mx+b, with b nonzero, then y = mx+b is not proportional. The value of b must be 0 for it to fit y = kx form. This rules out y = 2x+1 and y = 3+x or y = x+3.
The equation y = 3/(4x) is an inversely proportional equation in the form y = k/x. It cannot be written as y = kx. Note how x is in the denominator for y = 3/(4x) while the same can't be said for y = kx. Inversely proportional equations have x increase and y decrease, or vice versa. They go in opposite directions.
plzzzz answer right away will mark BRAINLIST AND FIVE STARS PLUS The table below shows the possible outcomes of rolling a six-sided number cube and flipping a coin. A 7-column table with 2 rows. Column 1 has entries H, T. Column 2 is labeled 1 with entries H 1, T 1. Column 3 is labeled 2 with entries H 2, T 2. Column 4 is labeled 3 with entries H 3, T 3. Column 5 is labeled 4 with entries H 4, T 4. Column 6 is labeled 5 with entries H 5, T 5. Column 7 is labeled 6 with entries H 6, T 6. What is the probability of getting a number less than 3 and a tails? StartFraction 1 over 12 EndFraction StartFraction 1 over 6 EndFraction One-fourth One-third
Answer:
P((1 or 2) and Tail) = 1/6 = StartFraction 1 over 6
Step-by-step explanation:
A six-sided die and a coin.
Probability of getting <3 and tail.
P((1 or 2) and Tail)
= 2/6 * 1/2
= 1/6
Answer:
1/6
Step-by-step explanation:
In a different plan for area codes the first digit could be any number from 3 through 6 the second digit was either 5,6,7 or 8 and the third digit could be any number except 5. With this plan how many different area codes are possible?
Answer:
144 codes are possible
Step-by-step explanation:
Okay for the first digit, we shall be selecting one out of 3,4,5,6.
Meaning we are selecting one out of four choices
The number of ways this can be done is 4C1 ways = 4 ways
For the second digit, we have 5,6,7 or 8, we are still selecting 1 out of 4 selections and the number of ways we can do this is also 4 ways
And lastly , we can choose any digit for the last number expect 5 , so from 0 to 9, we are removing 1 which means we are left with 9 choices
So the number of different area codes possible are ; 9 * 4 * 4 = 144 codes
find three examples of corporate logos. do they incorporate symmetry? if so, and what kind? your response should be 3-5 sentences long
Answer:
Symmetry is the property of an object to retain its shape even if it is turned or turned.
The three corporate logos are McDonald, Shell, Snapcaht
McDonald company logo is symmetrical and it is a reflective symmetry.
Shell logo is symmetrical and it is also reflective symmetry.
Snaphcat logo is symmetrical and it is also reflective symmetry.
My age if I am half as old as two more than twice Mack's age if Mack is m years old.
Answer:
You are m + 1 years old.
Step-by-step explanation:
Let's say that you are x years old, and Mack is m years old.
x = 1/2( two plus twice m)
x = 1/2(2 + 2m)
x = 1 + m
x = m + 1
Hope this helps!
Prove that. 1-sin2A=2sin^2(45-A)
Answer:
Proved
Step-by-step explanation:
2 sin square( 45°-A)
(therefore;
by trigonometry ratios
sin45°=1)
=2sin2(1-A)
=2sin(1-A)
=1+sin2A
hence proved
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Tysm
Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and the other is quadratic–without graphing the system of equations.
Answer:
To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic
1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation
We simplify and check the number of real roots with the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] for quadratic equations the form 0 = a·x² - b·x + c
Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.
Step-by-step explanation:
Answer:
Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.
Step-by-step explanation:
I just took the test on Edge 2020
A restaurant catered a party for 40 people. A child’s dinner (c) cost $11 and an adult’s dinner (a) cost $20. The total cost of the dinner was $728. How many children and adults were at the party? Use the table to guess and check. 8 children and 32 adults 9 children and 31 adults 10 children and 30 adults 12 children and 28 adults
Answer:
x=8 number of children
y=32 number of adults
Step-by-step explanation:
x be children and y for adults
x+y=40 ⇒ y=40-x
11x+20y=728 solve by substitution of y=40-x
11x+20(40-x)=728
11x+800-20x=728
-9x=728-800
x=72/9 ⇒ x=8 number of children
y=40-x
y=40-8⇒ y=32 number of adults
Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.f(x)=7cos^2x
Answer:
Step-by-step explanation:
Using the double angle formulas,
cos(2x) = cos^2(x) - sin^2(x) ............(1)
1 = cos^2(x) + sin^2(x)............(2)
add (1) and (2)
1 + cos(2x) = 2 cos^2(x)
=> cos^2(x) = (1/2) (1+cos(2x)) ..............(3)
f(x) = 7 cos^2 (x)
substituting (3)
f(x) = (7/2) (1+cos(2x))