A4 paper has a width is 21cm and a length of 30cm.
A5 paper has a length of 21cm.
What is the width of A5 paper??
Answer:
Ur answer
Step-by-step explanation:
If A4 paper has width 21cm and length of 30cm
Then,
A5 paper has a length of 21cm
So find the width,
A4 has width 30cm
so,
A5 must have half the answer
15cm
The width of A5 paper is 21cm, which is derived from the length of A4 paper, based on the standard ratio of the A series paper sizes.
The width of A5 paper can be determined using the properties of the standardized A series paper sizes. As A4 paper has dimensions of 21cm by 30cm and the A series has a height to width ratio of the square root of 2, when an A4 sheet is cut in half, it results in two A5 sheets.
Thus the length of A4 becomes the width of A5. To find the width of A5, we simply take the length of A4, which is 21cm in this case.
Therefore, the width of an A5 sheet is also 21cm, making the dimensions of A5 paper 21cm by 14.85cm (since half of 30cm is 14.85cm).
A climbing wall leaning against the top of a play structure forms a right triangle with the ground. The distance from the bottom of the climbing wall to the base of the play structure is 7 feet. If the climbing wall is 11 feet long, how high is the wall of the play structure?
The height of wall of play structure is 8.48 feet
Solution:
A climbing wall leaning against the top of a play structure forms a right triangle with the ground
The figure is attached below
ABC is a right angled triangle
AB is the height of wall of play structure
Let "x" be the height of wall of play structure
AB = x
BC is distance from the bottom of the climbing wall to the base of the play structure
BC = 7 feet
AC is the length of climbing wall
AC = 11 feet
We can apply pythogoras theorem for right angled triangle
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
Therefore, by above definition for right angled triangle ABC,
[tex]AC^2 = AB^2+BC^2[/tex]
Substituting the values we get,
[tex]11^2 = x^2 + 7^2\\\\121 = x^2 + 49\\\\x^2 = 121-49\\\\x^2 = 72\\\\\text{Take square root on both sides }\\\\x = \sqrt{72}\\\\x = 8.48[/tex]
Thus the height of wall of play structure is 8.48 feet
Answer:
8ft
Step-by-step explanation:
i did the test on T4L
These are the first six terms of a sequence with a = 2:
2, 14, 98, 686, 4802, 33614, ...
Find a recursive formula for this sequence that is valid for n > 1.
Write your answer in simplest form.
Answer:
an+1 = 2×7ⁿStep-by-step explanation:
98÷14
=7
686÷98
=7
4 802÷686
=7
33 614÷4 802
=7
Then the common ratio q for this sequence is 7
recursive formula : an+1 = q×an = ?
an= a1 × qⁿ⁻¹
=2×7ⁿ⁻¹
an+1 = q×an
= 7×(2×7ⁿ⁻¹)
= 2×7ⁿ
Answer: The formular for this sequence is AR^n-1 (that is, A multiplied by R{raised to the power of n minus 1} )
Step-by-step explanation:This is a geometric progression in which every term is calculated by multiplying each previous term by a common ratio.
The common ratio here is 7, which is derived as
14/2, or 98/14, or 686/98, or 4802/686...
In simply put, R is derived as Tn/Tn-1, where Tn is the nth term and Tn-1 is the previous term.
Therefore the formular for this progression is given as
AR^n-1
Where A = 2, R = 7 and n = the nth term.
Which equation shows the quadratic formula used correctly to solve 5x2 + 3x - 4 = 0 for x?
- 3+ √(3) ² - 4 (6) (-4)
2(5)
3+ (3) +45)(-4)
X
3+ (3)2-4(5)(-4)
OX=
- 3+ √(3)² + 4 (5)(-4)
205)
The quadratic formula used to solve the equation [tex]5x^{2} +3x-4=0[/tex] is [tex]x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)(-4)}}{2(5)}[/tex]
Explanation:
The equation is [tex]5x^{2} +3x-4=0[/tex]
The equation is of the form [tex]ax^{2} +bx+c=0[/tex]
Thus, [tex]a=5, b=3,c=-4[/tex]
To find the quadratic formula, the general formula to find the quadratic roots is [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Hence, substituting the values of a,b,c in the formula, we get,
[tex]x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)(-4)}}{2(5)}[/tex]
Thus, Option A is the correct answer.
The quadratic formula used to solve the equation [tex]5x^{2} +3x-4=0[/tex] is [tex]x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)(-4)}}{2(5)}[/tex]
Will mark as BRAINLIEST!!
Answer:
C
y - y1 = m (x - x1)
(y - y1) / m = x - x1
x = (y - y1) / m + x1
Find the area of the irregular figure.
Answer:
The area of the irregular figure is 366 cm sq.
Step-by-step explanation:
This irregular figure is made of 1 Rectangle + 1 right Triangle
Area of the Rectangle:
Length of the rectangle = 21 cm,
Width of the rectangle = 14 cm
AREA of Rectangle = LENGTH x WIDTH
= 21 cm x 14 cm = 294 sq cm
⇒Area of the Rectangle = 294 sq cm ..... (1)
Area of the Right Triangle:
Base of the rectangle = 16 cm,
Height of the rectangle = 21 cm - 12 cm = 9 cm
AREA of Right Triangle = [tex]\frac{1}{2} \times B \times H[/tex]
[tex]= \frac{1}{2} \times 16 \times 9 = 72[/tex]
⇒Area of the Right Triangle = 72 sq cm ..... (2)
Now, area of the irregular figure = Area of the( Rectangle +Right Triangle)
= 294 sq cm + 72 sq cm = 366 cm sq
Hence, the area of the irregular figure is 366 cm sq.
Answer:
366 sq. ft
Step-by-step explanation:
First, we have to find the area of the triangle. To do this we have to find the height of the triangle which can be done by subtracting 12 from 21 to get 9. Then we multiply 16 by 9 to get 144 and divide it by 2 to get 72. Now we must find the area of the rectangle. To do this we have to multiply 14 and 21 to get 294. Now we have to add the values together to get 366.
F(x)=2x+6
G(x)=-5x-9
Find the product of f and g.
A.-10x^2-54
B.-10x^2-48x-54
C.-10x^2-12x-54
D.-10x^2+48x-54
The product of f(x) = 2x + 6 and g(x) = -5x - 9 is found by multiplying out the terms, resulting in -10x^2 - 48x - 54, which corresponds to option B.
Explanation:The student is asking to find the product of two functions f(x) = 2x + 6 and g(x) = -5x - 9. To find the product, we multiply the two functions together:
f(x) * g(x) = (2x + 6) * (-5x - 9)
Distribute each term in the first function by each term in the second function:
2x*(-5x) + 2x*(-9) + 6*(-5x) + 6*(-9)
= -10x^2 - 18x - 30x - 54
Combine like terms:
= -10x^2 - 48x - 54
Therefore, the correct answer is B. -10x^2 - 48x - 54.
Can an expert help me with this please.Ill give points.I need explanation also
Answer:
What is it you would like help with, because the file does not work for me.
Step-by-step explanation:
Point slope form. (-5,-1) and (6,-5)
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-5, -1) and (6, -5). Substitute:
[tex]m=\dfrac{-5-(-1)}{6-(-5)}=\dfrac{-5+1}{6+5}=-\dfrac{4}{11}[/tex]
Put the value of a slope and coordinates of a point to the equation of a line:
[tex](-5,\ -1),\ m=-\dfrac{4}{11}\\\\y-(-1)=-\dfrac{4}{11}(x-(-5))\\\\y+1=-\dfrac{4}{11}(x+5)[/tex]
[tex](6,\ -5),\ m=-\dfrac{4}{11}\\\\y-(-5)=-\dfrac{4}{11}(x-6)\\\\y+5=-\dfrac{4}{11}(x-6)[/tex]
Solve the proportion 2x/3=20/5
Answer:
Hi
Step-by-step explanation:
Sunndmdmd
What is the operation in the expression x-3?
Answer:
Step-by-step explanation:
Subtraction because there is a minus sign
Answer:
Subtraction
Step-by-step explanation:
- this sign means to take away or in other words subtract.
A taxi service charges an initial fee plus $1.80 per mile how far can you travel for $12? Does any one know what is it
Answer:
You cant solve for how far you can go, but you can make an equation.
Step-by-step explanation:
A= The initial fee
$1.80=per mile
$12=The max amount of money
A+1.80x=$12
And you would subtract A from the $12 first!
Good Luck!
A 4-pack of batteries costs $5.16. At this price, what is the cost of one battery?
Answer:
$1.29
Step-by-step explanation:
5.16 divided by 4
Kyle swan 450 yards in 5 minutes. What is the average number of yards he swam per minute?
Answer:
90
Step-by-step explanation:
450/5
Answer:
90
Step-by-step explanation:
450 / 5 = 90
Divide 67.9 by one hundred
Answer: .679
Step-by-step explanation:
move the decimal to the left two places.
What is the first step in determining if 6 is a solution to 3x-18?
Answer:
Substitute x = 6 into the equation 3x-18
Answer:
A.) Subsitute 6 for x in the equation.
Step-by-step explanation:
I’m smart :).
If $650 is invested for one year at 11% simple interest, how much interest is earned
Answer:
71.5
Step-by-step explanation:
650 / 100 = 6.5
6.5 x 11 = 71.5
Suppose the average yearly salary of an individual whose final degree is a masters is $46 thousand less than twice that of an individual whose final degree is a bachelors. Combined, two people with each of these educational attainments earn $122 thousand. Find the average yearly salary of an individual with each of these final degrees.
Answer:
average yearly salary of an individual whose final degree is a masters: $ 66 thousand
average yearly salary of an individual whose final degree is a bachelors: $ 56 thousand
Explanation:
You can set a system of equation using the following steps:
1. Name the variables:
average yearly salary of an individual whose final degree is a masters: xaverage yearly salary of an individual whose final degree is a bachelors: y
2. Set the equations that relate the variables:
the average yearly salary of an individual whose final degree is a masters is $46 thousand less than twice that of an individual whose final degree is a bachelors:
equation (1): x = 2y - 46
combined, two people with each of these educational attainments earn $122 thousand:equation (2): x + y = 122
3. Solve the system:
x = 2y - 46 . . . equation (1)x + y = 122 . . . equation (2)Substitute equation (1) into equation (2)
2y - 46 + y = 122Solve for y:
3y = 122 + 463y = 168y = 168 / 3y = 56 (this means that the average yearly salary with a bachelors degree is $ 56 thousand).Subsitute the value on y in equation 1, to find the value of x:
x = 2y - 46 = 2(56) - 46 = 112 - 46 = 66.Thus, the average yearly salary of a person with a masters degree is $ 66 thousand.
Final answer:
Using a system of equations with the variables B (the average salary for a bachelor's degree) and M (the average salary for a master's degree), we solved to find that the average yearly salary for an individual with a bachelor's degree is $56,000 and with a master's degree is $66,000.
Explanation:
The problem at hand involves creating two algebraic equations to solve for the average yearly salaries of individuals with a bachelor's degree and a master's degree based on the provided information. Let the average yearly salary for an individual with a bachelor's degree be represented by B, and the salary for an individual with a master's degree be represented by M.
According to the problem, the average yearly salary of an individual with a master's degree is $46 thousand less than twice the salary of an individual with a bachelor's degree, so we can write the first equation as: M = 2B - 46.
The second equation comes from the fact that combined, their earnings amount to $122 thousand, so: B + M = 122.
Now, we can substitute the first equation into the second to solve for B: B + (2B - 46) = 122. Simplifying, we get 3B - 46 = 122. Adding 46 to both sides gives 3B = 168, and dividing by 3 yields B = 56. So, the average salary for someone with a bachelor's degree is $56,000.
To find the salary for a master's degree holder, we substitute B = 56 into the first equation: M = 2(56) - 46. That simplifies to M = 112 - 46, giving us M = 66. Hence, the average salary for someone with a master's degree is $66,000.
Find the simple interest:
$1,000; 5%; 2 years
Which equation is equivalent to log x 36 = 2?
Answer:
The answer is X^2=36
The equivalent equations of [tex]log_x36 = 2[/tex] are 36 = x² and x = 6.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
Given:
Equation [tex]log_x36 = 2[/tex]
We know the logarithmic function:
[tex]log_bx = a[/tex]
Then,
x = bᵃ
[tex]log_x36 = 2[/tex]
36 = x²
x = 6
Therefore, 36 = x² and x = 6 are the equivalent expressions.
To learn more about the logarithms;
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7. Find the value of a. The diagram is not to scale.
(1 point)
a.) 36°
b.) 144
c.) 54
d.) 126°
Answer:
The correct answer is B. 144°
Step-by-step explanation:
Let's recall that in a trapezium the bases are parallel and one of its properties is that the two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.
Upon saying that, we can find out the value of a and b, this way:
∠a = 180 - 36
∠a = 144
∠b = 180 - 113
∠b = 67
But the question is regarding ∠a. Then the correct answer is B. 144°
How do you put the equation 2x+y=2 into slope intercept form
Answer:
Step-by-step explanation:
you put the equation in slope and intercept form by making y the subject of the formula
i.e
y = -2x + 2
-2 is the slope and 2 is the intercept
Answer:
Step-by-step explanation:
2x + y = 2
Making y as subject
y = - 2x + 2
And the equation is y = mx + c
Where m is slope = -2
Y intercept = 2
What is the sum of 12 over 3 plus 2 over 3 ?
Answer:
The Answer is 4 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Since both fractions have like denominators , you can just add them:
12/3 + 2/3 = 14/3
Since 14/3 is improper fraction, it should be turning to a mixed number:
14 can go into 3, 4 times since 4 times 3 is 12. 14 - 12 is 2, so it will be your numerator.
4 2/3
Compare in hours: 27 hours to 3 days. Write the ratio as a fraction in lowest terms
Answer:
27:72
Step-by-step explanation:
First I would convert three days to hours. 24×3=72
Answer: 27:72
The ratio of the two times will be 3 / 8.
What is a ratio?
A ratio in mathematics shows how many times one number is contained in another. For instance, if a dish of fruit contains eight oranges and six lemons.
The ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given that compare in hours: 27 hours to 3 days. The ratio will be calculated as:-
In 3 days there are 72 hours.
Ratio = 27 / 72 = 3 / 8
Therefore, the ratio of the two times will be 3 / 8.
To know more about a ratio follow
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Solve the equation using the order of operations.
5+{2×[(5−1)+6]}÷4
Answer:
The order of operations is PEMDAS
First step is to do everything is parenthesis or brackets
5+{2*[(5-1)+6]}/4
{2*[(5-1)+6]}
First you would go 5-1=4, because that is the first equation that is in parenthesis by itself.
{2*[4+6]}
Next you would go 4+6=10, because that is your next smallest bracket
{2*10}
Last you would go 2*10=20
Your equation now looks like this
5+{20}/4
In PEMDAS your next step is exponents, but we don't have any so we go on to the next one which is multiply/division
5+5
You would go 20/4=5
Last step is to add/subtract
5+5=10
Your final answer would be 10
Hope this helps ;)
Step-by-step explanation:
6h^5+0h^4-12h^3+0h^3+0h=0
Step-by-step explanation:
We have,
[tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]
To find, the value of h = ?
∴ [tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]
⇒ [tex]6h^5[/tex] + (0)[tex]h^4[/tex] - 12[tex]h^3[/tex] + (0)[tex]h^3[/tex] + (0)h = 0
⇒ [tex]6h^5[/tex] + 0 - 12[tex]h^3[/tex] + 0 + 0 = 0
⇒ [tex]6h^5[/tex] - 12[tex]h^3[/tex] = 0
Taking 6 [tex]h^3[/tex] as common, we get
[tex]6h^3(h^2-2)[/tex] = 0
⇒6[tex]h^3[/tex] = 0 or, [tex]h^2[/tex] - 2 = 0
⇒ 6[tex]h^3[/tex] = 0 ⇒ h = 0
⇒ [tex]h^2[/tex] = 2
⇒ h = ± [tex]\sqrt{2}[/tex]
Hence, the value of h = 0, ± [tex]\sqrt{2}[/tex]
What is the theoretical probability of a coin
Answer:hfgjvggunycdvjk8nyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyum
Step-by-step explanation:
Answer: probility that it lands on
Head up is 1/8 or 12.5%
Step-by-step explanation:
Simplify this expression.
1 + 4.25n + 32p – 3 + (–2p) + 54n
A. 5.5n – 12p – 2
B. 9.5n + 1.5p – 2
C. 94n − 1.5p − 4
D. 3.75n – p + 1
After combining like terms, the expression simplifies to 58.25n + 30p - 2, which does not match any of the provided answer choices, indicating an error in the options given.
Explanation:To simplify the expression 1 + 4.25n + 32p
dash; 3 + (
minus;
2p) + 54n, we combine like terms. Let's first combine the constant terms (1 and -3), the 'n' terms (4.25n and 54n), and the 'p' terms (32p and -2p).
First, we handle the constants: 1 - 3 = -2
Now, combine the 'n' terms: 4.25n + 54n = 58.25n
Then, combine the 'p' terms: 32p - 2p = 30p
The simplified expression is 58.25n + 30p - 2, which matches none of the given options (A, B, C, D). There appears to be an error since the proper simplification does not align with the options provided.
In the given case, the correct answer is B. 9.5n + 1.5p - 2 which is the simplified expression.
The correct distribution should be:
[tex]\(1.5 \times 39n = 58.5n\) (which is correct)[/tex]
[tex]\(1.5 \times 20p = 30p\) (which is correct)[/tex]
So the correct simplified expression is:
58.5n + 30p - 2
Now, let's convert the decimals to fractions to match the format of the options provided:
[tex]\(58.5n = 58\frac{1}{2}n = 58n + \frac{1}{2}n = 58n + 0.5n\)[/tex]
30p = 30p
So the expression becomes:
58n + 0.5n + 30p - 2
Therefore, the final simplified expression is:
9.5n + 30p - 2
However, we must correct the coefficient of p to match the format of the options. Since 30p is actually [tex]\(1.5 \times 20p\)[/tex] , we should have:
1.5p = 30p
Thus, the correct final simplified expression is:
9.5n + 1.5p - 2
What is the slope of the line y=3
Answer:
slope = 0
Step-by-step explanation:
recall that the equation of a line can be expressed as:
y = mx + b, where m is the slope and b is the y-intercept.
in our case we are given y = 3
which can be re-written:
y = (0)x + 3
if we compare this with the general equation above, we can see that
slope = m = 0
Answer: the slope is zero
Step-by-step explanation:
The equation of line in slope - intercept form is given as : y = mx + c , where m is the slope and c is the y - intercept. This means that the line y = 3 is a horizontal line that passes through the point y = 3 , therefore , the slope is zero
Which point lies on the graph of Y= 4x-4
1.(0,4)
2.(0,-4)
3.(-4,0)
4.(4,0)
Answer:
2. (0, -4)Step-by-step explanation:
[tex]y=4x-4\\\\\text{Substitute the coordinates of each points to the equation}\\\text{and check the equality.}\\\\1.\ (0,\ 4)\to x=0,\ y=4\\\\4=4(0)-4\\4=0-4\\4=-4\qquad\bold{FALSE}\\\\2.\ (0,\ -4)\to x=0,\ y=-4\\\\-4=4(0)-4\\-4=0-4\\-4=-4\qquad\bold{TRUE}\\\\3.\ (-4,\ 0)\to x=-4,\ y=0\\\\0=4(-4)-4\\0=-16-4\\0=-20\qquad\bold{FALSE}\\\\4.\ (4,\ 0)\to x=4,\ y=0\\\\0=4(4)-4\\0=16-4\\0=12\qquad\bold{FALSE}[/tex]