a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?
The ladder would reach a distance of 6 feet up the wall.
The Pythagorean theorem.This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:
/hyp/^2 = /opp/^2 + /adj/^2
In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.
So that, let the height of the ladder on the wall be represented by t. Then;
10^2 = t^2 + 8^2
100 = t^2 + 64
t^2 = 100 -64
= 36
t = (36)^1/2
t = 6 feet
Thus the ladder is placed 6 feet up the vertical wall.
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1.) What is the length of x?
2.) What is the area of the right triangle inside of the parallelogram?
Answer:
The area of x is 4
The area of the right triangle is 6
Step-by-step explanation:
The Pythagorean Theorem can be used when dealing with right triangles. So, if we use the equation a^2 + b^2 = c^2, we can find that 3^2 + x^2 = 5^2 or 9 + x^2 = 25. If we calculate, we can find that x is equal to 4. Now if we multiply by 3 and divide by 2, we can get the answer of 6 as the area of the right triangle.
pls help with question image is linked
The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg
How to determine the amount sold each dayFrom the question, we have the following parameters that can be used in our computation:
Day 2 = Day 1 - 25
Day 3 = 2/7 * (Day 1 + Day 2)
Total weights = 315
Next, we use the following representations
x = Day 1, y = Day 2 and z = Day 3
So, we have the following equations
y = x - 25
z = 2/7(x + y)
x + y + z = 315
Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315
z = 2/7(x + x - 25) = 2/7(2x - 25)
x + y + z = 315 ⇒ x + x - 25 + z = 315
So, we have
z = 2/7(2x - 25)
2x + z = 340
Substitute z = 2/7(2x - 25) in 2x + z = 340
2x + 2/7(2x - 25) = 340
So, we have
7x + 2x - 25 = 1190
Evaluate the like terms
9x = 1215
Divide by 9
x = 135
So, we have
y = x - 25 = 135 - 25 = 110
z = 2/7(x + y) = 2/7 *(135 + 110) = 70
Hence, the amounts are 135 kg, 110 kg and 70 kg
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If you could buy 500 individual nerd candies for $5 or 186 g of individual nerd candies for $5, which would be the better deal
The better deal would be 500 individual nerds candy for $5.
One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. The equal partition of bigger groupings into smaller parts is referred to as division.
The order of work assigned to and completed by the team of employees in order to optimize efficiency is known as the division of labor.
The splitting down of a job into multiple separate parts that make up the total is referred to as the division of labor. 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.
Thus, The better deal would be 500 individual nerds' candy for $5 since you will have more candy and it will last longer.
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LCM of 2, 6 and 11 must show work
The Least Common Multiple (LCM) of 2, 6, and 11 is 66.
What is the LCM of 6 and 11?We shall divide the numbers (6, 11) by their prime factors in order to determine the LCM of 6 and 11 using the division method (preferably common). The LCM of 6 and 11 is determined by the product of these divisors.
Step 1:Find the smallest prime number that at least one of the numbers, 6, or 11, can be factored into. As indicated by the ladder arrangement, place this prime number (2) to the left of the supplied numbers (6 and 11).
Step 2: Divide any of the supplied integers (6, 11) by 2 and write the quotient below it if it is a multiple of 2. Any number that is not divisible by the prime number should be brought down.
Step 3: Continue the procedure until there are only 1s left in the
The LCM of 6 and 11 is the product of all prime numbers on the left, i.e. LCM(6, 11) by division method = 2 × 3 × 11 = 66
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Is 9x² 24x 16 a perfect square trinomial?
9x² + 24x + 16, which is the full quadratic trinomial expressed as (3x +4)².
What is a trinomial expression?A trinomial expression is an algebraic expression containing three distinct terms, hence the name "trinomial expression". An algebraic expression called a trinomial expression contains three nonzero terms. A trinomial expression is formed when three monomials are added or subtracted from each other. A quadratic trinomial has the form: ax² + bx + c, where a, b, and c are nonzero real values.
Given that
9x² + 24x + 16
= (3x)² + 2(12x) + 16
= (3x)² + 2(3x)(4) + 4²
This is similar to a² + 2ab + b² = (a + b)².
So you can write:
= (3x + 4)²
= (3x +4) (3x + 4)
So this is a complete quadratic trinomial.
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The ratio of the measures of three sides of a triangle is 1/4:1/3:1/6. its perimeter is 31.5 inches
Answer:
10.5 inches, 14 inches, 7 inches
Step-by-step explanation:
Let's say x is the multiplier of the ratio value and the actual length of the sides:
1/4 * x = side 1
1/3 * x = side 2
1/6 * x = side 3
Since the perimeter is the sum of all sides, the perimeter is equal to:
31.5 = 1/4 * x + 1/3 * x + 1/6 * x ==> 31.5 inches is the perimeter
(31.5 = x/4 + x/3 + x/6)*12 ==> multiply the equation by 12 since 12 is the
LCM (Least Common Multiple) of 4, 3, and 6
12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6 ==> multiply each term by 12
378 = 12x/4 + 12x/3 + 12x/6 ==> simplify
378 = 3x + 4x + 2x
378 = 9x
x = 378/9 ==> divide both sides by 9
x = 42
Now find each side length [Refer to the first three equations] :
Side length 1: 1/4 * 42 = 42/4 = 10.5 inches
Side length 2: 1/3 * 42 = 42/3 = 14 inches
Side length 3: 1/6 * 42 = 42/6 = 7 inches
Answer: 10.5 inches, 14 inches, 7 inches
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Write an expression to represent the area of the shaded region in simplest from
We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!
We can come up with two expressions:
Shaded Area:
[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]
Blank area:
[tex](x)(x+7)\\x^2+7x[/tex]
Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.
[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]
Therefore, your final answer should be:
14x^2 - 6x - 2
Julia take a bead from the bag at random
c) how that the probability that thi bead i purple
The probability that the bead taken from the bag is purple or red is total is 0.75 or 3/4.
The total number of beads in the bag is 12.
Out of these, 3 are purple and the rest are red (12-2-1-3 = 6). So, the probability of drawing a purple bead is 3/12 and the probability of drawing a red bead is 6/12.
To find the probability of drawing either a purple or red bead, we add the individual probabilities together: (3/12) + (6/12) = 0.25 + 0.5 = 0.75. This means that there is a 75% chance that the bead taken from the bag will be purple or red.
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The complete question is -
Write down the letter of the event that is likely. bag contains 12 beads_ 2 of the beads are blue: of the beads are green: 3 of the beads are purple: The rest of the beads are red: Julia takes a bead from the bag at random c) Show the probability that this bead is purple Or red is Totulmen.
when processing an invoice what account is credited
a. accounts receivable
b. cash
c. accounts payable
d. the answer depends on the transaction
Answer:
accounts payable
Step-by-step explanation:
Because amount of money you owe
The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.512.512, point, 5 years; the standard deviation is 2.42.42, point, 4 years.
Use the empirical rule (68 - 95 - 99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a lion living longer than 10.110.110, point, 1 years.
The probability of a lion living longer than 10.1 will be 0.1585.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years.
The lifespan of a lion in a particular zoo is normally distributed with average lion lives:
Mean u = 12.5 years
Standard deviation s = 2.4 years
We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.
The empirical rule ( 68-95-99.7% ) states:
P ( u - s < X < u + s ) = 68%
P ( u - 2s < X < u + 2s ) = 95%
P ( u - 3s < X < u + 3s ) = 99.7%
The test has the following number of standard deviations (s):
u - s < X < u + s = 12.5 - 2.4 < X < 12.5 + 2.4 = 10.1 < X < 14.9
u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8 = 7.7 < X < 17.3
u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2 = 5.3 < X < 19.7
Then the probability is calculated as,
P ( 10.1 < X < 14.9 ) = 0.68
P ( 7.7 < X < 17.3 ) = 0.95
P ( 5.3 < X < 19.7 ) = 0.997
We need P ( X < 10.1 ) and P ( X < 5.3 ):
P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2
P ( X < 10.1 ) = [ 1 - 0.68 ] / 2
P ( X < 10.1 ) = 0.16
P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2
P ( X < 5.3 ) = [ 1 - 0.997 ] / 2
P ( X < 5.3 ) = 0.0015
P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )
P ( 5.3 < X < 10.1 ) = 0.16 - 0.0015
P ( 5.3 < X < 10.1 ) = 0.1585
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What type of triangle do the points 3 2 (- 2 3 and 2/3 form a right triangle B equilateral triangle C isosceles triangle d none of these?
Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).
Let the given points be,
A = (3, 2), B = (-2, -3) and C = (2, 3)
The formula for the distance between two points:
The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].
Therefore,
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)
[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex] units
B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex] units
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex] units
By using the Pythagorean theorem:
According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Now, we can see that,
[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]
[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]
Therefore, the given triangle is a right angled triangle.
Therefore, option(A) s correct.
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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.
A. right triangle
B. equilateral triangle
C. isosceles triangle
D. none of these
How do you graph exponential functions and logarithms?
Graphing exponential functions and logarithms involves understanding the key characteristics of these functions and how they are represented on a graph.
Asymptotes: The graph of an exponential function does not have any asymptotes.
Domain and range: The domain and range of an exponential function are all real numbers.
Increasing or decreasing: An exponential function is always increasing.
Shape: The graph of an exponential function is concave up.
y-intercept: The y-intercept is (0,1)
x-intercept: The x-intercept does not exist.
To graph an exponential function, you can start by plotting the y-intercept (0,1) on the graph. Then, you can use the information about the shape of the graph (concave up) and the increasing nature of the function to determine the general shape of the graph.
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5^3 x 7^5+9^8+0+0+0+0+0+0+(9^7x5^6)
Answer:
74,779,038,221
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]
We can eliminate all the zeroes.
[tex]5^3*7^5+9^8+9^7*5^6[/tex]
Evaluate each term.
Raise 5 to the power of 3.
[tex]125*7^5+9^8+9^7*5^6[/tex]
Raise 7 to the power of 5.
[tex]125*16807+9^8+9^7*5^6[/tex]
Raise 9 to the power of 8.
[tex]125*16807+43046721+9^7*5^6[/tex]
Raise 9 to the power of 7.
[tex]125*16807+43046721+4782969*5^6[/tex]
Raise 5 to the power of 6.
[tex]125*16807+43046721+4782969*15625[/tex]
Multiply 125 by 16807.
[tex]2100875+43046721+4782969*15625[/tex]
Multiply 4782969 by 15625.
[tex]2100875+43046721+74733890625[/tex]
Add 2100875 and 43046721.
[tex]45147596+74733890625[/tex]
Add 45147596 and 74733890625.
[tex]74779038221[/tex]
A calculator would help but here you go.
A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
PLEASE HELP
The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.
How to illustrate the percentage?From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.
Let the length be Illustrated as 10cm.
Width = 10% × 10cm
= 1cm
New Length = 10cm + (10% × 10cm)
= 11cm
The old perimeter will be:
= 2(1 + 10)
= 22cm
New perimeter will be:
= 2(1 + 11)
= 24cm
The percentage increase will be:
= (24 - 22) / 22 × 100
= 2/22 × 100
= 9.1%
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Find the measure of angle A.
110°
O 80°
O 105°
O 30°
O100°
14 + 6x
A
3x-3
Answer:
[tex]80^{\circ}[/tex]
Step-by-step explanation:
The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].
Angles in a triangle add to [tex]180^{\circ}[/tex].
[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]
So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].
Please I need the 3 of them
The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:
Case 1
Horizontal translation, vertical translation. Horizontal stretch.
Case 2
Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.
Case 3
Horizontal translation, vertical translation. Horizontal stretch.
How to determine the magnitude of horizontal and vertical translations for quadratic equations
In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:
y - k = a · (x - h)²
Where:
a - Vertex constant(h, k) - Coordinates of the vertex.This parabola is translated both horizontally and vertically by using the following definitions:
Horizontal translation
x → x - a, where a > 0 for rightward translation.
Vertical translation
y → y - b, where b > 0 for upward translation.
Horizontal dilation
f(x) → f(k · x), where k is a non-negative real number.
Vertical dilation
f(x) → k · f(x), where k is a non-negative real number.
Reflection in the x-axis
f(x) → - f(x)
The procedure is summarize below:
Write the original function, that is, the equation of the parabola with vertex at origin.Apply dilation, translation and reflection definitions.Finally, we summarize the procedure for each case:
Case 1
g(x) = x²
g(x) = [(1 / 2) · x²]
g(x) + 4 = [(1 / 2) · (x - 2)]²
Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.
Case 2
f(x) = x²
f(x) = - (1 / 2) · x²
f(x) - 2 = - (1 / 2) · (x - 4)²
Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.
Case 3
h(x) = x²
h(x) = 2 · x²
h(x) - 5 = [2 · (x + 2)]²
Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.
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Which expression represents the length of the hypotenuse C of the triangle below
Answer:
[tex] \sqrt{a {}^{2} + b {}^{2} }[/tex]
2789\36 help me psss i have to take this test lie be so fl i like right nowww pls haelp me
Answer:
77.472222 etc
Step-by-step explanation:
What is the value of S unit?
Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
Given information:
From the given figure, the following information can be extracted:
Triangle ABD is a right-angled triangle.
Base AB is 8 units, Height BD is 15 units.
s is the hypotenuse of the triangle ABD.
Use the Pythagoras theorem to solve for the value of s or AD,
AD²=AB²+BD²
s²=8²+15²
s²=289
s=17 units
Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.
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how many times bigger is b than c
Can you help me with this
Answer: (-4, -6)(9, 2):
y=8/13x - 46/13 (Point slope form: y + 6 = 8/13 *(x+4)
latifa writes down a number. she says
if i find a cube root of that number and then quadruple the answer, i get 16
what number did latifa write down?
Answer:
8
Step-by-step explanation:
the cubed root of 8 equals 2
if you quadruple 2 (multiply it by 4), you will get 8
I need help with these questions can someone help please
Answer:you just have to find the slope
Step-by-step explanation:
so all you have to do is start by doing y=Mx+b. You start by placing down you b point on the y axis and then Do your Mx it should look something like this
16 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold?
How many quarts of soil are used to fill 3 flower pots?
9.6 quarts
First, find the unit rate, which is that when you divide 16 and 5 and you will get 3.2, then you multiply it with 3 for the 3 flower pots, and that's how you end up with the answer
Find the flux of F across S,
F. N dS
where N is the upward unit normal vector to S.
F(x, y, z) = xi + yj + zk
S: z = 1 − x^2 − y^2, z ≥ 0
The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]
A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.
A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.
[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]
[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]
[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]
=1+x^2+y^2
[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]
[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]
[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]
[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]
[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]
[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]
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y = -5x + 50 and y= 5x + 10
( Pls find the x for the frist question) And the Y for the secound equation
Pls Answer for 100 brainlist
The values of x and y in the Simultaneous equation are 4 and 30 respectively
What are Simultaneous equations?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.
y = -5x + 50 equation 1
y = 5x+ 10 equation 2
subtract equation 1 from 2
5x-(-5x) +10-50 = 0
10x -40 = 0
10x = 40
x = 40/10
x = 4
substitute 4 for x in equation 2
y = 5(4)+10
y = 20+10
y = 30
Therefore the value of x and y are 4 and 30 respectively
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Your colleague’s computer stops working, and no one from the IT department is available to fix it. You have basic knowledge of computer hardware. Which action should you take as an ethical employee?
A.
Initiate help by offering to check the computer.
B.
Start a conversation with your colleague and provide a distraction.
C.
Take a quick break and offer your computer for a short time.
D.
Ignore it because it is beyond your designated scope of work.
Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.
What is a computer hardware?A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.
In Computer technology, there are various examples of a computer hardware and these include the following:
Power supply unit (PSU).Hard-disk driveKeyboardMonitor (screen)MouseMotherboardCentral processing unit (CPU).Network interface card (NIC).Memory moduleBased on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.
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Which polynomial is prime?
O x3 + 3x2 - 2x - 6
O x° - 2x- + 3x - 6
O 4x4 + 4x3 - 2x - 2
O 2x + x3-x+2
Dylan invested some money in his bank.
He agreed a simple interest rate of 3% per annum fo a period of 2 years.
At the end of the 2-year period the value of his investment increased by £72
Work out the value of Dylan's initial investment
The amount invested by Dylan will be £1200.
What is simple interest?Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate.
Given that Dylan invested some money in his bank. He agreed on a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period, the value of his investment increased by £72.
The amount of money invested will be calculated as,
SI = ( P x R x T ) / 100
72 = ( P x 3 x 2 ) / 100
7200 = 6P
P = 7200 / 6
P = £1200
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