Answers
[tex] \frac{CD}{BD} = \frac{BD}{AD} [/tex]
Notice that we know for our problem that [tex]BD=h[/tex]. Also, we can find the length of AD by subtracting CD from AC:
[tex]AD=AC-CD[/tex]
[tex]AD=25-16[/tex]
[tex]AD=9[/tex]
Now we can replace the values in our proportion:
[tex] \frac{CD}{BD} = \frac{BD}{AD} [/tex]
[tex] \frac{16}{h} = \frac{h}{9} [/tex]
Solving for [tex]h[/tex]:
[tex]h^2=(16)(9)[/tex]
[tex]h^2=144[/tex]
[tex]h= \sqrt{144} [/tex]
[tex]h=12[/tex]
We can conclude that the correct answer is: B. 12
Triangle BCD:
BD=h
CD=16
Triangle ABD:
BD=h
AD=AC-CD=25-16→AD=9
Suppose <CBD is x and the <ABD is y
x+y=90°
The <BCD must be equal to y; and the <BAD must be equal to x, then the triangles ABD and BCD are similars, because they have two congruent angles (x and y), so theirs sides must be proportionals:
Opposite to angle x / opposite to angle y
Triangle ABD Triangle BCD
BD / AD = CD / BD
Replacing values:
h/9=16/h
Solving for h. Cross multiplication:
(h)(h)=(9)(16)
h^(1+1)=144
h^2=144
sqrt(h^2)=sqrt(144)
h=12
Answer: The value of h in the figure is 12
Related Questions
In an isosceles trapezoid the length of a diagonal is 25 cm and the length of an altitude is 15 cm. Find the area of the trapezoid.
Answers
area=median*height=20cm*15cm
=300cm^2
Answer:
300
Step-by-step explanation:
GETS BRAINLIEST AND 11 PTS
Hazel covered a box with felt. The dimensions of the box are shown in the figure below: A rectangular prism is shown. The length of the rectangular prism is labeled as 11 inches, the height is labeled as 6 inches, and the width is labeled as 8 inches. The felt costs 9¢ per square inch. She will only pay for the felt used to cover the box, even if there is waste or extra. How much money did Hazel spend on the felt? $18.18 $27.72 $36.36 $45.54
Answers
The surface area of a rectangular prism is:
A=2(xy+xz+yz), where x,y, and z are the dimenisions
We are told that she will spend .09 per in^2, x=11, y=6, and z=8 so we can say cost is:
C=2(9/100)(11*6+11*8+6*8)
C=(18/100)(66+88+48)
C=$36.36
NEED HELP ASAP ON GEOMETRY!! ONLY 3 QUESTIONS ATTACHED WITH PHOTOS. THANK YOU
Answers
Use Pythagorean theorem:
[tex]x^2=3.6^2+5.5^2\\\\x^2=12.96+30.25\\\\x^2=43.21\to x=\sqrt{43.21}\\\\\boxed{x\approx6.6}[/tex]
4.
Use Pythagorean theorem:
[tex]3^2+\left(\dfrac{x}{2}\right)^2=6.5^2\\\\9+\dfrac{x^2}{4}=42.25\ \ \ |-9\\\\\dfrac{x^2}{4}=33.25\ \ \ \ |\cdot4\\\\x^2=133\to x=\sqrt{133}\\\\\boxed{x\approx11.5}[/tex]
5.
[tex]\widehat{AB}\ \cong\ \widehat{DE}[/tex]
A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist wants to make 684 milliliters of the drug, how many milliliters of compound A are needed?
Answers
So the ration between compound A and B will be:
A:B = 5:7
Total amount of drug = 684
Therefore, the amount of drug A needed will be:
[tex] \frac{5}{5+7}*684 \\ \\ = \frac{5}{12}*684 \\ \\ =285[/tex]
Therefore, out of 684 milliliters 285 would be the compound A and the rest would be compound B
Where 5 mm of A per 7mm of B. That should be the equation.
Given that the total mm is 684
A + B = 684
A = 5/7 * B
5/7 B + B = 684
B=400
A = 5/7 * 400 = 285mm
A = 285mm
Below is the table of values of a function. Write the output when the input is
n
input 1 4 9 n
output 5 8 13 ?
What is the last output ?
Answers
Input: 1 4 9 9 + 7
Output: 1+4 4+4 9+4 9+7+4
Output: 5 8 13 20
Last output is 20
Answer:
n + 4
Or 20
Step-by-step explanation:
Depends on how you see it the answer could be n´+4 since that´s how the function is working, and almost all of the time the independent clauses are actually independent and do not follow any progression.
But if there is a progression in the input, we can see that they are adding up uneven numbers to the input, so first we added 3, then we added 5, and last we should add 7: so the input would be 7+9= 16, the input in the forth spot should be 17, and the output should be 20.
a strip of wood 78 inches long is to be cut into pieces of 3 and 3/4 inches long how many pieces can be cut
Answers
let's firstly convert the mixed fraction to "improper", and then divide,
[tex]\bf \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{15}{4}}\\\\ -------------------------------\\\\ \cfrac{\quad 78 \quad }{\frac{15}{4}}\implies \cfrac{\quad \frac{78}{1} \quad }{\frac{15}{4}}\implies \cfrac{78}{1}\cdot \cfrac{4}{15}\implies \cfrac{26}{1}\cdot \cfrac{4}{5}\implies \cfrac{104}{5}\implies 20\frac{4}{5}[/tex]
so, if we nevermind the 4/5 part, only 20 whole of those then.
Triangle ABC has angles measuring 137°, 15°, and 28°. Classify the triangle by its angle measures.
Answers
Find a function that models the population after t years
Answers
[tex]f(0) = 270000\\
f(1) = 1.04f(0), \\
f(2) = 1.04f(1) = 1.04(1.04f(0)), \\
f(t) = 1.04f(t-1) = 1.04(1.04f(t-2)) ... = 1.04^{t}f(0) = 1.04^{t}*270000 [/tex]
b) [tex]f(2004-1998) = 1.04^{2004-1998} * 270000 = 341636[/tex]
c)
[tex]1.04^{x-1998} * 270000 \geq 534094 \\ x - 1998 \geq {ln( \frac{534094}{270000} )}/{ln(1.04)} x \geq 2015.4 x = 2016[/tex]
The month of the year is December. What is the type of data is December?
discrete data
categorical data
continuous data
Answers
Data that is collected can be either categorical or numerical data.Categorical variables represent types of data which may be divided into groups.
December is the twelfth and last month of the year .The word December is a categorical discrete data which is also known as qualitative, because it is a name instead of a number.Among the options given December is a month of a year.
The month of the year is December is a categorical data .
What is the similarity ratio of the smaller to the larger similar cones? Enter your answer as a:b
Answers
To find similarity ratio a:b
We take the sides and make a proportion
[tex]\frac{height \ of \ smaller \ cone}{height \ of \ larger \ cone} = \frac{radius \ of \ smaller \ cone}{radius \ of \ larger \ cone}[/tex]
[tex]\frac{9}{15} = \frac{6}{10}[/tex]
[tex]\frac{3}{5} = \frac{3}{5}[/tex]
So the ratio a:b is 3:5
Explain what is a Fungi?
Answers
the equation d=1/2n (n-3) gives the number of diagonals D for polygon with n sides. use this equation to find the number of sides n for a polygon that has 65 diagonals
Answers
1. You have that:
- The equation d=1/2(n(n-3)) gives the number of diagonals for the polygon.
- The polygon that has 65 diagonals..
2. When you clear n, you obtain:
d=n(n-3)/2
d=(n^2-3n)/2
2x65=n^2-3n
n^2-3n-130=0
3. When you solve the quadratic equation, you obtain:
n=13
Therefore, the answer is: 13 sides.
Answer: 13
Step-by-step explanation:
Given : The equation [tex]d=\dfrac{1}{2}n(n-3)[/tex] gives the number of diagonals d for polygon with n sides.
To find the number of sides n for a polygon that has 65 diagonals, we substitute the value of d= 65 in the given equation, we get
[tex]65=\dfrac{1}{2}n(n-3)[/tex]
Multiply 2 on both sides , we get
[tex]n(n-3)=130\\\\\Rightarrow\ n^2-3n-130=0\\\\\Rightarrow\ n^2-13n+10n-130=0\\\\\Rightarrow\ n(n-13)+10(n-13)=0\\\\\Rightarrow\ (n-13)(n+10)=0\\\\\Rightarrow\ n= -10\ or\ n= 13[/tex]
But number of sides cannot be negative, so the number of sides n for a polygon that has 65 diagonals = 13
A person who needs a car for a few weeks while visiting family out of state would most likely choose which of the following?
Answers
A person needing a car for a few weeks while visiting family out of state would most likely choose A. Car rental for its short-term flexibility and convenience.
Car rental is the ideal choice for short-term car needs while visiting family out of state.
It offers flexibility in terms of duration, allowing individuals to rent vehicles for specific periods, such as a few weeks, without the commitment of ownership or long-term contracts.
With a wide range of vehicle options and rental locations available, car rental services provide convenience and accessibility.
Additionally, rental agreements typically include insurance coverage and roadside assistance, offering peace of mind to travelers during their stay.
Overall, car rental meets the temporary transportation needs of visitors efficiently and effectively.
Complete Question:
A person needing a car for a few weeks while visiting family out of state would most likely choose which of the following?
A. Car rental
B. Car share
C. Carpool
D. Car lease
Justin collected data from his classmates on the type of condiment they prefer on their sandwich. Based on the data collected, if one hundred boys and one hundred girls are given a sandwich of their choice which statement is true?
9)
Boy Girl
Mayonnaise 12 14
Mustard 18 13
Plain 5 15
Answers
Answer:
The answer is C
Step-by-step explanation:
Boy likes mayonnaise:
12
(12 + 18 + 5)
=
12 /35
= 0.3429 ≈ 34%
Girl likes mayonnaise:
14
(14 + 13 + 15)
=
14 /42
= 0.3333 ≈ 33%
thus,
boys (34 of 100) > girls (33 of 100)
what is the poorest country in the world
Answers
Its economic basically is dependent on diamonds export, the most of the diamonds is soled on the 'black' market, which allow to pass the taxes of government...
The poorest countries in the world are primarily in Africa and Asia, according to the World Bank's 2020 report. These countries struggle with governance issues, economic struggles, conflict, and other socio-economic problems, inhibiting their growth. The Democratic Republic of Congo, despite its wealth in resources, significantly exemplifies this due to political instability.
Explanation:According to the World Bank rankings, many of the poorest countries globally share common traits such as governance failures, economic struggles, and conflicts. These factors, among others, inhibit economic growth and improvement across sectors such as healthcare, education, and infrastructure.
As detailed in the World Bank's 2020 report, the ten lowest income countries include nations primarily located in Africa and Asia. Due to various socioeconomic issues, these countries have low gross national income (GNI) per capita, with notable examples including Afghanistan, Ethiopia, and Zimbabwe.
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Find the probability of each outcome if you randomly choose a letter in the worrd probability
Answers
p = 1/11
r = 1/11
o = 1/11
b=2/11
a = 1/11
i = 2/11
l = 1/11
t = 1/11
y = 1/11
Which of the following is equal to the rational expression when x ≠ 5 or -1?
[tex] \frac{(x-7)(x+1)}{(x+1)(x-5)} [/tex]
a. [tex] \frac{x+1}{x-7} [/tex]
b. [tex] \frac{x+1}{x-5} [/tex]
c. [tex] \frac{x-7}{x+1} [/tex]
d. [tex] \frac{x-7}{x-5} [/tex]
Answers
Answer:
[tex]\frac{(x-7)}{(x-5)}[/tex]
option D is correct
Step-by-step explanation:
[tex]\frac{(x-7)(x+1)}{(x+1)(x-5)}[/tex]
In an rational expression , if we have same factors at the top and bottom then we cancel it out
In our given rational expression we have x+1 at the top and bottom
so we cancel out x+1
After cancelling out x+1, we are left with
[tex]\frac{(x-7)}{(x-5)}[/tex]
option D is correct
Which of the following is equivalent to -6
A) 9-(-17)
B) 3*(-2)*(-1)
C) -2(4-1)
D) 4-16/-2
Answers
-2(4-1)
Distributing: (-8 +2) = -6
-2(4-1) put in a calculator that’s your answer
hey can you please help me posted picture of question
Answers
From the given options, only the pair given in option B result in the composition equal to x.
[tex]F(x)= \frac{12}{x}-18 \\ \\ G(x)= \frac{12}{x+18} \\ \\ F(G(x))= \frac{12}{ \frac{12}{x+18} }-18 \\ \\ F(G(x))= \frac{12(x+18)}{12}-18 \\ \\ F(G(x))=x+18-18=x [/tex]
This proves, F(x) and G(x) are inverse of each other.
So the answer to this question is Option B
You planted 488 acres of corn last season. you sold all your corn: 8,120 bushels in August and 64,100 bushels in September. what is your yield pet acre, rounded to the nearest bushel per acre
Answers
[total amount of bushels sold]/[area of the field]
Total amount sold=64100+8120=72220
area=488 acres
thus
72220/488
=147.992~148 bushels per acre
Answer:
There will be approx 148 bushels in per acre.
Step-by-step explanation:
You planted 488 acres of corn last season.
you sold all your corn: 8,120 bushels in August and 64,100 bushels in September.
Total bushels = [tex]8120+64100=72220[/tex]
Now, this amount of bushels were in 488 acres of land.
So, per acre will contain = [tex]72220/488=147.99[/tex]≈ 148 bushels
Hence, there will be approx 148 bushels in per acre.
Simplify the given polynomial expressions, and determine the degree and number of terms in each expression.
Answers
[tex]6 { x}^{3} - 10 {x}^{2} + 4x[/tex]
Degree: 3
Terms:3
2)
[tex] - {x}^{5} - 3 {x}^{4} + 12 {x}^{3} - 6[/tex]
degree:5
terms:4
3) 9x^4-9
degree:4
terms:2
Degree and number of terms in each polynomial expression are as follow,
[tex]6x^{3} -10x^{2} +4x[/tex] degree : [tex]3[/tex] and Number of terms : [tex]3[/tex][tex]-x^{5} -3x^{4} +12x^{3} -6[/tex] degree : [tex]5[/tex] and Number of terms : [tex]4[/tex][tex]9x^{4} -9[/tex] degree : [tex]4[/tex] and Number of terms : [tex]2[/tex]What is expression?" Expression is defined as the relation between two or more variables or numbers are represented using mathematical operation."
According to the question,
Given polynomial expression,
[tex]4x + 2x^{2} ( 3x-5)[/tex]Simplify the given expression we get,
[tex]4x + 6x^{3} -10x^{2}\\\\= 6x^{3} -10x^{2} +4x[/tex]
Degree of the polynomial expression : [tex]3[/tex]
Number of terms : [tex]3[/tex]
2. [tex](-3x^{4} +5x^{3} -12) + (7x^{3} -x^{5} +6)[/tex]
Simplify the given expression we get,
[tex]-3x^{4} +12x^{3} -6 -x^{5} \\\\= -x^{5} -3x^{4} +12x^{3} -6[/tex]
Degree of the polynomial expression : [tex]5[/tex]
Number of terms : [tex]4[/tex]
3. [tex](3x^{2} -3)(3x^{2} +3)[/tex]
Simplify the given expression we get,
[tex]9x^{4} -9[/tex]
Degree of the polynomial expression : [tex]4[/tex]
Number of terms : [tex]2[/tex]
Hence, degree and number of terms in each polynomial expression are as follow,
[tex]6x^{3} -10x^{2} +4x[/tex] degree : [tex]3[/tex] and Number of terms : [tex]3[/tex][tex]-x^{5} -3x^{4} +12x^{3} -6[/tex] degree : [tex]5[/tex] and Number of terms : [tex]4[/tex][tex]9x^{4} -9[/tex] degree : [tex]4[/tex] and Number of terms : [tex]2[/tex]Learn more about expression here
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look across each row and down each column what pattern do you see
Answers
Let P(2, 3) be a point on a figure. The figure is dilated by a scale factor of 4.
What are the coordinates of P′?
Write the ordered pair.
Answers
If (2,3) is a point and 4 is the scale factor, we need to multiply both x and y by 4 to dilate the figure. Doing this gives us (8,12).
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
If g(x)= 2x^4+3x^3-x^2, find g(-1)
Answers
Answer: x=0
Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth. 5x2 + 16x – 84 = 0
Answers
x + 6 = 0 or 5x - 14 = 0
x = -6 or 5x - 14 = 0
x = -6 or 5x = 14
Therefore, x = -6 or x = 14/5 (Two solutions found)
Good luck :)
in the linear equation, y = 7x - 15, the y- intercept of the line is
Answers
kevin had 13 coins in his pocket. all of his coins are either dimes or quarters. when he emptied his pocket, kevin found that he had 2.05. how many dimes and quarters does he have?
Answers
10x8=80
25x5=125
125+80=205
The blades on a wind turbine trace a circular path with radius 100 feet. Suppose the turbine spins at 20 revolutions per minute. What is the linear velocity, in miles per hour (1 mile equals 5,280 feet), of a point on the tip of a blade? Round the answer to the nearest tenth.
Answers
Angular velocity = w= 20 revolutions per minute = 20 x 2π radians per minute
Angular velocity = w = 40π radians per minute
Linear velocity = v = r w
So,
Linear velocity = v = 100 x 40π = 4000π feet per minute
v = 4000π x 60/5280 miles per hour
v = 142.8 miles per hour
Thus the Linear Velocity of the turbine will be 142.8 miles per hour
The linear velocity of a point on the tip of a blade on a wind turbine is approximately 0.05 miles per hour.
Explanation:To find the linear velocity of a point on the tip of a blade on a wind turbine, we need to convert the rotational speed to linear speed. The formula to do this is linear speed = radius × angular speed. In this case, the radius is 100 feet and the turbine spins at 20 revolutions per minute. First, we convert the revolutions per minute to radians per second by multiplying by 2π/60. Then, we multiply the angular speed by the radius to find the linear speed.
Angular speed = 20 revolutions per minute × 2π/60 = 20π/60 = π/3 radians per second
Linear velocity = 100 feet × π/3 = 100π/3 feet per second
Finally, to convert the linear velocity to miles per hour, we divide by 5280 (since 1 mile equals 5280 feet).
Linear velocity = (100π/3) / 5280 ≈ 0.05 miles per hour
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Suppose that an open box is to be made from a square sheet of cardboard by cutting out squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 576 cubic inches, find the original dimensions of the sheet of cardboard.
Answers
A shop sells 200 chocolate vanilla and strawberry ice creams 45% of the ice cream sold are vanilla and 30% are strawberry how many chocolate ice creams are sold
Answers
(1) Chocolate
(2) Vanilla
(3) Strawberry
There are three types of flavors.
45% of the ice creams are vanilla
30% of the ice creams are strawberry
x percent of the ice creams are chocolate
The total amount of ice creams is 200 that corresponds to 100%. Therefore:
45% + 30% + x = 100%
Solving for x:
x = 25%
Then the number of chocolate ice creams are:
[tex]25\%(200) = 50 [/tex]
Finally:
50 chocolate ice creams are sold
Final answer:
The answer explains how to calculate the number of chocolate ice creams sold in a situation where vanilla and strawberry ice creams are already accounted for.
Explanation:
The total number of ice creams sold is 200.
45% are vanilla ice creams. 45% of 200 is 90.
30% are strawberry ice creams. 30% of 200 is 60.
To find the number of chocolate ice creams sold:
Chocolate ice creams = Total ice creams - (Vanilla ice creams + Strawberry ice creams)
Chocolate ice creams = 200 - (90 + 60)
Chocolate ice creams = 200 - 150 = 50
Therefore, 50 chocolate ice creams are sold.