Answers
1) Given the altitude BD, let's find its measure using some trigonometric relations on the Right Triangle:
1.2) Pythagorean Theorem to find the other leg
b²=a²+c² The hypotenuse, in this case, is labeled as "b"
32²=16²+a²
1024=256+a²
1024-256=a²
768=a²
√768=√c²
a=16√3
2) Now, let's use one trigonometric relation on the Right Triangle, based on the similarity of the triangles:
ah=bc Adjusting it:
bh=ac
32h=16√3*16
32h=256√3
h=256√3/32
h=8√3 ≈ 13.85 ≈13.9
3) So the altitude BC of that triangle is approximately 13.9
Related Questions
don’t need an explanation just the answer. Community takes too long lol
Answers
SOLUTION
Step 1: Find the area of the wall.
[tex]\begin{gathered} A=l\times b \\ A=42\times25.5 \\ A=1071ft^2 \end{gathered}[/tex]Step 2: Find the cost of wallpaper per square foot
[tex]=\frac{total\text{ cost of wallpaper}}{Area\text{ of the wall}}[/tex][tex]\begin{gathered} =\frac{771.12}{1071} \\ =0.72\text{ dollars} \end{gathered}[/tex]The correct answer is B: $0.72
If f(x) = |x – 1] + 2 is changed to g(x) = -2f(x) + 8, how is the graph of the function transformed?
Answers
we have
f(x) = |x – 1] + 2
g(x) = -2f(x) + 8
substitute the value of f(x) in g(x)
so
g(x)=2(|x – 1] + 2) +8
g(x)=2|x – 1] + 4 +8
g(x)=2|x – 1] + 12
Using a graphing tool
see the attached image
find thevsurface area of a square pyramid wuth side length 3 km and slant height 5 km
Answers
The Total Surface Area = 4 triangles + 1 square
The TSA of the Pyramid = 4(1/2 bh) + LxL
[tex]\begin{gathered} d^2=3^2+3^2 \\ d^2=9+9 \\ d=\sqrt[]{18}\text{ =}\sqrt[]{9\times2}=\sqrt[]{9}\text{ }\times\sqrt[]{2}\text{ =3 }\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} 5^2=h^2+(\frac{3}{2})^2 \\ 25-\frac{9}{4}=h^2 \\ 25-2.25=h^2 \\ h=\sqrt[]{22.5}\text{ =1.5km} \end{gathered}[/tex]TSA of the pyramid =
[tex]4(\frac{1}{2}\times5\times3)+(3^2)=(2\times15)+9=30+9=39km^2[/tex]If Z has a standard normal probability distribution, find P(Z > −0.75).
Answers
Given that Z has a standard normal probability distribution, you need to find the following Probability:
[tex]P(Z>-0.75)[/tex]Therefore, you can find it using the Standard Normal Distribution Table.
By symmetry, you can determine that:
[tex]P(Z>-0.75)=1-P(Z<-0.75)[/tex]Using the Standard Normal Distribution Table (Left Tail), you get that:
[tex]P(Z<-0.75)\approx0.2266[/tex]Therefore:
[tex]P(Z>-0.75)=1-0.2266\approx0.7734[/tex]Hence, the answer is:
[tex]P(Z>-0.75)\approx0.7734[/tex]From the diagram below, if AC is a tangent line, and if PD = 8 and DC = 9, find the length of BC.
Answers
Given,
PD = 8 and DC = 9
Required
The length of line BC.
Here, PB and PD are the ardius of the circle. By the definition of circle, the measure of all radius is equal.
So, PB = PD = 8.
The tangent is always perpendicular to the radius at the point of tanjency.
By the pythagoras theorem,
[tex]\begin{gathered} PB^2+BC^2=PC^2 \\ 8^2+BC^2=(17)^2 \\ BC^2=289-64 \\ BC^2=225 \\ BC=15 \end{gathered}[/tex]Hence, the measure of BC is 15 units.
A teacher buys packs of notebooks to give to their students. The tape diagram represents the ratio of brown notebooks to red notebooks. Brown notebooks Red notebooks Based on the ratio, if there are 24 red notebooks, what is the number of brown notebooks?
Answers
The number of brown notebooks is 40.
What is the ratio?
A ratio displays the multiplicity of two numbers. For example, if there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-fruit ratio is 8:14.
We have,
24 red notebooks,
∴ 5/3 = x/24.
Cross-multiply, and we now have
120 = 3x.
Divide both sides by 3,
x = 120/3
x = 40
x = 40 brown notebooks.
Hence, the number of brown notebooks is 40.
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what is the answer to 24+12x=-12
Answers
X=-3
You just subtract 24 from both sides then divide by 12
Solve p3 = −343.
p = ±18
p = −18
p = ±7
p = −7
Answers
Answer:
p = -7
Step-by-step explanation:
[tex] {p}^{3} = - 343[/tex]
[tex]p = \sqrt[3]{ - 343} = - 7[/tex]
Which exponential function matches the values in the table below?3521612967776y=21631y = 6xy=6(67y=(6
Answers
Verify each equation
option A
For x=3 ------> y=216(3^3)=
(6×10 to the ninth power)divided by (2.4×10 to the third power)
Answers
Answer:
2.5×10 to the sixth power
Step-by-step explanation:
6÷2.4=2.5
10^9÷10^3=6
Priya practiced the violin for 152% as much time as Han practiced the piano hiw long did she practiced, if Han practiced for 74 minutes
Answers
To find the time that Priya spent practicing violin, calculate what is 152% of 74 minutes by multiplying 74 times 152/100:
[tex]\frac{152}{100}\times74=112.48[/tex]Therefore, Priya practiced for 112.48 minutes.
Find the slope of the line that passes through (2, 7) and (-4, 19).
m =
Answers
The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.
According to the question,
We have the following information:
A line is passing through two points (2,7) and (-4,19).
We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:
m = (y2-y1)/(x2-x1)
(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)
In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.
m = (19-7)/(-4-2)
m = 12/(-6)
m = -2
Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.
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what is the value of f(-9) to the nearst hundredth
Answers
For this problem, we are given the expression for a function, f(x), and we need to determine the value of f(-9) to the nearest hundredth.
The expression is:
[tex]f(x)=2^{8+x}+7[/tex]We need to replace "x" with the value "-9", and simplify the expression.
[tex]\begin{gathered} f(-9)=2^{8-9}+7 \\ f\mleft(-9\mright)=2^{-1}+7 \\ f\mleft(-9\mright)=\frac{1}{2}+7 \\ f\mleft(-9\mright)=0.5+7=7.5 \end{gathered}[/tex]The value of f(-9) is 7.5
A number time 5 less that number has a product of -4. What are the two numbers?
Answers
Let the first number be x.
The second number is 5 times less than x => x - 5
Therefore, we can write the statement as
[tex]\begin{gathered} x\times(x-5)=-4 \\ x^2-5x=-4 \\ \therefore \\ x^2-5x+4=0 \end{gathered}[/tex]Solving the quadratic equation:
Let us replace -5x in the equation with -4x and -x to be able to factorize.
Hence,
[tex]\begin{gathered} x^2-4x-x+4=0 \\ x(x-4)-1(x-4)=0 \\ (x-4)(x-1)=0 \\ \text{Therefore} \\ x-4=0\text{ } \\ or \\ x-1=0 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x=1 \\ or \\ x=4 \end{gathered}[/tex]Therefore, the number can be 1 or 4.
The second number can be
[tex]\begin{gathered} 1-5=-4 \\ or \\ 4-5=-1 \end{gathered}[/tex]Therefore, the pair of numbers can be
[tex](1,-4)\text{ or (4, -1)}[/tex]i need help with the question where I wrote +1 and +2. to find the slope do I just do 2/1
Answers
To find out the slope we need two points
from the table
we take
(0,1) and (1,3)
so
m=(3-1)/(1-0)
m=2/1
m=2write parallel and perpendicular equation thru (-3,5) y=2/3x + 1
Answers
Answer:
Step-by-step explanation:
1 Simplify (-3,5)y(−3,5)y to -3,5y−3,5y.
-3,5y=\frac{2}{3}x+1
−3,5y=
3
2
x+1
2 Simplify \frac{2}{3}x
3
2
x to \frac{2x}{3}
3
2x
.
-3,5y=\frac{2x}{3}+1
−3,5y=
3
2x
+1
3 Switch sides.
\frac{2x}{3}+1=-3,5y
3
2x
+1=−3,5y
4 Break down the problem into these 2 equations.
\frac{2x}{3}+1=-3
3
2x
+1=−3
\frac{2x}{3}+1=5y
3
2x
+1=5y
5 Solve the 1st equation: \frac{2x}{3}+1=-3
3
2x
+1=−3.
x=-6
x=−6
6 Solve the 2nd equation: \frac{2x}{3}+1=5y
3
2x
+1=5y.
x=\frac{3(5y-1)}{2}
x=
2
3(5y−1)
7 Collect all solutions.
x=-6,\frac{3(5y-1)}{2}
x=−6,
2
3(5y−1)
combine like terms algebra
Solve the equation 20 + 0.44x + 4 = 19 + 1.69x.
A. x = 4
B. x = 2.14
C. x = 5
D. x = 34.4
Answers
Answer: A
Step-by-step explanation: The starting equation is 24 + 0.44x = 19 + 1.69x,
First, combine the x's on the RHS, and the integers on the LHS.
1.69x - 0.44x = 1.25x
24 - 19 = 5
So the equation will be 1.25x = 5
Divide both sides by 1.25 to isolate the x.
x = 4
A carpenter is using a lathe to shaper the final leg of a handcrafted table. In order for the leg to fit, it needs to be 150 mm wide allowing for a margin of error of 2.5mm. Find the range of widths for the table leg can be.
Answers
(-5p+8)(-3p-5) pls help me solve this asappp
Answers
Step-by-step explanation:
(-5p + 8)(-3p - 5)
[tex]15p^2 +25p - 24p -40[/tex]
[tex]15p^2 +p -40[/tex]
A building security code has 2 numeric digits, 0 through 9, followed by 2 letters. What is the probability that the first digit is nine and the last letter is a?.
Answers
The probability of the event that the first digit is nine and the last letter is a is 1/260.
The building security code has 2 numeric digits in between 0-9 and 2 letters.
The choices for letters is 26 each and the choices for digits is 10 each.
So, the total possible security code can be,
Total security codes possible = 10 × 10 × 26 × 26
Total security codes possible = 67600
Now, the number of codes that starts with 9 and end with a are,
= 1 × 10 × 26 × 1
= 260
The probability that the first digit is nine and the last letter is a is,
P(E) = 260/67600
P(E) = 1/260
So, the probability that the first digit is nine and the last letter is a is 1/260.
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need help with error analysis assingment, im in high school and ive always struggled with math alot pls help
Answers
Given
A) The angles A and B are supplementary.
If,
[tex]\begin{gathered} \angle A=x+6 \\ \angle B=7x+30 \end{gathered}[/tex]B) The figure,
To find
A) The value of x.
B) The value of x.
Explanation:
A) It is given that,
Angle A and angle B are supplementary.
Then,
[tex]\angle A+\angle B=180\degree[/tex]Hence, the error is in the statement,
Since the angles are supplementary, when added together they equal 90.
As, the correct answer is when added together they equal 180.
That implies,
[tex]\begin{gathered} x+6+7x+30=180 \\ 8x+36=180 \\ 8x=180-36 \\ 8x=144 \\ x=\frac{144}{8} \\ x=18\degree \end{gathered}[/tex]Hence, the value of x is 18 degrees.
B) It is given that,
From, the figure the given angles are interior angles.
Also, the interior angles on the same side of the transversal is supplementary.
Which means when you add them they equal 180.
Hence, the error is in the statement,
Since the angles are adjacent, they are complementary angles.
Which means when you add them they equal 180.
As, the angles are interior angles on the same side of the transversal.
Also,
[tex]\begin{gathered} 64+x=180 \\ x=180-64 \\ x=116\degree \end{gathered}[/tex]Hence, the value of x is 116 degrees.
Find the volume and surface area of the hexagonal pyramid.
Answers
Solution
A hexagonal pyramid is a three-dimensional object with a hexagon-shaped (6 sides) base and six triangular faces originating from each side to a common vertex.
The distance between the center of the hexagonal base and the common vertex is the altitude or height (h) of the pyramid.
The length of the base's side is the base edge or base length (a) of the pyramid.
what is the gcf for 18x^3 y^2, 9xyz
Answers
Given,
[tex]18x^3y^2,9xyz[/tex]To find GCF we will factor constant and variable terms individually,
First factorize 18:
[tex]18=1,2,3,6,9,18[/tex]Factors of 9:
[tex]9=1\times3\times9[/tex]Now,
[tex]\begin{gathered} 18=1,2,3,6,9,18 \\ 9=1,3,9 \end{gathered}[/tex]Now GCF of 18,9 is 9.
GCF of
[tex]x^3=x,x,x[/tex]GCF of
The difference of the digits of a 2-digit number is 3. If the digits are interchanged and the new number is added
to the original number, the result is 77. Find the original number.
Answers
Answer:
Original number = 10x + y = 52
Step-by-step explanation:
(2x+1)(x-2)(x+3)
please help
Answers
Answer: 2x^3 + 3x^2 - 11x - 6
Step-by-step explanation: simplified
if i have 12 cupcakes and i have to take away 80% how many cupcakes do you have
Answers
You have remains 2.4 cupcakes when taking away 80% of the cupcakes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that
The total number of cupcakes was 12
Then take away 80% of cupcakes
The number of cupcakes you have = 12 - (80% of 12)
The number of cupcakes you have = 12 - (80/100) × 12
The number of cupcakes you have = 12 - 0.80 × 12
The number of cupcakes you have = 12 - 9.6
Apply the subtraction operation,
The number of cupcakes you have = 2.4
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Write the fraction 27/72 in simplest form
Answers
Therefore, 27/72 simplified to lowest terms is 3/8.
Please answer this question!
Answers
Answer: 1/4
Step-by-step explanation: 1/2 turned into decimal form is 0.5 but halved equals 0.25 which in fraction form is 1/4
3024 divided by 42 with remainder
Answers
Answer:
72 Remainder: 0
Step-by-step explanation:
3024 / 42 = 72
Remainder of 0!
Answer:
Step-by-step explanation:
72 Remainder 0
a. Complete the area model and the
equation.
23 x 62 =
Answers
Answer:
Step-by-step explanation: