To show that the angle bisector of an equilateral triangle is perpendicular to the base, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.
How to prove that the angle bisector is perpendicular to baseAfter getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.
We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.
Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.
Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.
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Find the surface area of the figure ( on photo)
The surface area of the figure is 344 m².
What is area?Area is the region bounded by a plane shape.
To calculate the surface area of the figure, we use the formula below.
Formula:
A = bh+L(a+b+c)..................... Equation 1Where:
A = Surface areab = Base of the triangleh = Height of the triangleL = Length of the prisma, c = Other two sides of the triangular baseFrom the diagram,
Given:
b = 6 mh = 4 ma = 5 mc = 5 mL = 20 mSubstitute these values into equation 2
A = (6×4)+20(5+5+6)A = 24+320A = 344 m²Hence, the area is 344 m².
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lo. Rebecca found the length and width of the 6. garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet /G 48 square inches/ H 48 feet/ J 48 cubic feet
H 48 feet could be the perimeter of Rebecca's garage door.
We know,
Perimeter is the distance around a two-dimensional shape. It is measured in units of length, such as feet or inches.
Rebecca found the length and width of the garage door, which are both measurements of length. Let's say she found that the length was 8 feet and the width was 6 feet.
To find the perimeter, she would add up the lengths of all four sides of the rectangle:
Perimeter = 2(length) + 2(width)
Perimeter = 2(8 feet) + 2(6 feet)
Perimeter = 16 feet + 12 feet
Perimeter = 28 feet
So the perimeter of Rebecca's garage door is 28 feet. None of the answer choices given match this value exactly, but H 48 feet is a possible perimeter if the garage door was much larger than the example given above. However, it is important to note that the term "cubic feet" (answer choice J) does not apply to perimeter, as cubic feet is a unit of volume and not length.
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A recipe for cookies makes 3 dozen cookies and uses
3
2 1/4 cups of flour and 3/4
cups of sugar. Sam needs to
make 5 dozen cookies. How many cups of flour and
sugar will Sam need for the recipe?
The number of cups of flour and sugar that Sam needs for the recipe will be 3.75 cups and 1.25 cups, respectively.
Given that:
A recipe for cookies makes 3 dozen cookies and uses 2 1/4 cups of flour and 3/4 cups of sugar.
The utilization of two or more additional numbers that compares is known as the ratio.
The expression that represents the 'n' dozen of cookies is given as,
⇒ n (2¹/₄) / 3 + n(3/4) / 3
⇒ n (2.25) / 3 + n(0.75) / 3
Put n = 5, then we have
⇒ 5 (2.25) / 3 + 5(0.75) / 3
⇒ 11.25/3 + 3.75/3
⇒ 3.75 + 1.25
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Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
m + 2(m + 1) = 14 {4}
The supplied value of 4 is a solution to the equation m + 2(m + 1) = 14.
Is the supplied value a solution or not?Given the equation in the question;
m + 2(m + 1) = 14
And supplied value = 4
To substitute the value of 4 into the equation, we replace every occurrence of the variable "m" with 4:
m + 2(m + 1) = 14
Plug in m = 4 by replace m with 4 and simplify both sides
4 + 2(4 + 1) = 14
4 + 2(5) = 14
4 + 10 = 14
14 = 14
We can see that both sides of the equation simplify to 14, which means that the value of 4 is a solution.
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Review the data and calculate the probability that someone with a credit score of 650 or below defaulted on the loan.
The probability that someone with a credit score of 650 or below defaulted on the loan is 0.14.
What is the probability?The probability that someone with a credit score of 650 or below defaulted on the loan is calculated below:
Probability = number of defaulters/ number of loan recipients
From graph:
The total number of defaulters = 30 + 30 + 30
The total number of defaulters = 90
The total number of loan recipients = 120 + 240 + 270
The total number of loan recipients = 630
Probability to default = 90/630
Probability to default = 0.14
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Please help me write a summary of the 3 rules on segments
1) When 2 chords intersect inside a circle, and 4 segments are formed
2) When 2 secants intersect outside a circle, and 4 segments are formed
3) When 1 secant and 1 tangent intersect outside a circle, and 3 segments are formed
The summary of the 3 rules on segments are written below.
How to write a summary of the 3 rules on segments?The three rules on segments in circles are:
1. When two chords intersect inside a circle, they create four line segments.
The product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord.
2. When two secants intersect outside a circle, they create four line segments.
The product of the length of the secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
3. When one secant and one tangent intersect outside a circle, they create three line segments.
The product of the length of the secant segment and its external segment is equal to the square of the length of the tangent segment.
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f(x)=18x+11 find f(5)
Answer:
101
Step-by-step explanation:
substitute 5 in the x:
=18(5)+11
=90+11
=101
I need help w this point to right answer
The angle AOB is approximately 98 degrees.
How to find the central angle of a sector?The measure of the angle AOB of the sector can be found as follows:
AOB is the central angle.
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅= central angleTherefore,
12 = ∅ / 360 × 2 × 3.14 × 7
12 = 43.96∅ / 360
cross multiply
360 × 12 = 43.96∅
4320 = 43.96∅
divide both sides by 43.96
∅ = 4320 / 43.96
∅ = 98.271155596
Therefore,
∅ = 98 degrees
AOB = 98 degrees
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The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges 30 to mow a lawn that took him 1.5 hours to mow.
Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
The amount Troy (D, in dollars) charges to mow a lawn is proportional to the time (H, in hours) it takes him to mow the lawn.
Hence, we can write [tex]\text{D = kH}[/tex] ......... (1), where k is a constant.
Now, given that Troy charges $30 to mow a lawn that took him 1.5 hours to mow.
So, from equation (1) we get
[tex]{30 = 1.5\text{k}[/tex]
[tex]\rightarrow \text{k = 20}[/tex].
Therefore, equation (1) becomes
[tex]\boxed{\bold{D = 20H}}[/tex] (Answer)
ANALYSIS
Graphs and tables not only represent data, but they also allow you to answer questions about the data. Use your tables and graphs on the resource pages from problem 1-13 to answer the questions below.
Which data appears to be linear? That is, when graphed, which data can be modeled best using a line? Explain why it makes sense for this situation to have a linear graph.
Now that Perry knows his options for the design of his hot tub, he wants to pick the hot tub that has the smallest perimeter (without cutting any tiles). What do you recommend?
The town of Parsnipville will have a flu vaccine available on Day 7. Only people who have not yet gotten the flu will need to be vaccinated. Since the town has
citizens, how many people will need the vaccine on that day? Is it easier to answer this question using your graph or using your table? Explain.
Certain legal documents, such as those used when buying property, sometimes require up to
signatures! How long do you think it might take to sign all the documents?
Considering each situation (lab), which of your graphs could have a point where
? Explain.
Assume that Perry’s hot tub tiles measure one foot on a side. If Perry could cut his tiles, what is the longest hot tub he could possibly build?
The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.
When data is graphed, which data can be modeled best using a line?The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.
Why does it makes sense to have a linear graph?Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.
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booker and lola stuff envelopes for their urban food co-op booker stuffedd of 70 envelopes this is 10 more than twice the number of envelopes lola stuffed write an equation that can be used to find the number of envelopes e that lola stuffed
Answer:
Step-by-step explanation:
What is the area of triangle LMN
The area of the triangle LMN is A = ( 1/2 ) x base x height
Given data ,
Let the triangle be represented as ΔLMN
Now , the base of the triangle be , b = MN
Let the height of the triangle be = h
Now , the area of the triangle is A = b x h
On simplifying , we get
A = LM x MN
Therefore , the value of A = base x height
Hence , the area of triangle is solved
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please answer and explain how to get it.
The value of x is given as follows:
x = 4.2 cm.
How to obtain the value of x?The value of x is obtained applying the proportions in the context of the problem.
The ratio between the volumes is given as follows:
3375/512 = 6.59
The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:
8/x = cubic root of 6.59
8/x = 1.9
x = 8/1.9
x = 4.2 cm.
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Is (-1, -3) a solution to this system of equations?
16x - 7y = 5
x = -1
yes
no
Answer:
Yes, it is
Step-by-step explanation:
2 ¿Qué figura tiene exactamente 2 ejes de simetría? F G H J K
The figure given that has exactly two lines of symmetry is C. Rectangle.
How many lines of symmetry does a rectangle have ?A rectangle has two lines of symmetry.
A line of symmetry is a line that divides a shape into two equal parts that are mirror images of each other. In a rectangle, the two lines of symmetry run through the center of the rectangle, dividing it into two congruent halves. These lines of symmetry are perpendicular to each other and bisect both pairs of opposite sides of the rectangle.
Therefore, a rectangle has two lines of symmetry, one horizontal and one vertical, which make it a symmetrical shape.
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Which mapping is a function?
Answer:
Step-by-step explanation:
C
Find the surface area
Round to the nearest tenth
The surface area of the triangular prism is 672 square millimeters.
what is surface area ?
Surface area is a metric used to determine how much overall space an object occupies. the total volume of the area of surface of a three-dimensional shape. The term "surface area" refers to a three-dimensional shape's entire surface area.
The triangular base has a height of 7 mm and a base of 24 mm, so its area is:
[tex]1/2 * base * height = 1/2 * 24 \ mm * 7\ mm = 84 \ mm^2[/tex]
There are two identical triangular faces, so their combined area is:
[tex]2 * 84 \ mm^2 = 168\ mm^2[/tex]
The three rectangular faces are all the same size, with a length of 24 mm and a height of 7 mm, so the area of each is:
[tex]length * height = 24 \ mm * 7 \ mm = 168 \ mm^2[/tex]
There are three rectangular faces, so their combined area is:
[tex]3 * 168\ mm^2 = 504\ mm^2[/tex]
To find the total surface area, we add the area of the two triangular faces to the area of the three rectangular faces:
[tex]168 \ mm^2 + 504 \ mm^2 = 672 \ mm^2[/tex]
Therefore, the surface area of the triangular prism is 672 square millimeters.
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What is the answer to
7 + 60 / (3x5)
My current grade is a 64.21%
7%-enrichment assignments
16%-homework assignments
19%-exam 1,2 and 3
20%-final exam
I have exam 3 next week, before final exam I want to up my grade to a 70% or above what grade would I need to get on my exam 3 to do so?
Answer:
i would say at least a 70
and i hope you do well
hope this helps ;)
In a poll of 510 human resource professionals, %45.9% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (d) below.
By sample distribution, (0.431,0.487) is Complete parts (a) through (d) below.
What does a statistical sample distribution mean?
An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.
Given
Favourable cases (X)=?
Sample size(n)=510
Sample proportion (p_hat)=X/n=0.459
X=np_hat=510*0.459=234.09=234
Confidence level(1-α)=99%=0.99
α=0.0
The critical value for α=0.01 is Zc=2.576
The margin of error is E=Zc* √((p_hat(1-p_hat)/n))
E=2.576* √((0.459(1-0.459)/510))=0.0568
The 99% confidence interval for p
CI=(p_hat-E,p_hat+E)
CI=(0.459-0.0568,0.458+0.0568)
CI=(0.402,0.516)
Confidence level(1-α)=80%=0.80
α=0.20
The critical value for α=0.2 is Zc=1.282
The margin of error is E=Zc* √((p_hat(1-p_hat)/n))
E=1.282* √((0.459(1-0.459)/510))=0.0283
The 80 % confidence interval for p
CI=(p_hat-E,p_hat+E)
CI=(0.459-0.0283,0.458+0.0283)
CI=(0.431,0.487)
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can someone help with 6,7,8,9 (tell me if number 9 is right) and 10? i need someone’s help please
The solutions to the dividing fractions prompts are as follows:
6. 4/3
7. 2/13
8. 33/2
9. 24/35
10. 63/20
How to solve the divisionsTo solve the divisions, note that the second divisor is inversed and multiplied. For the following problems, the divisions can be gotten as follows:
6. 8/9 ÷ 2/3
= 8/9 × 3/2
=24/18
=4/3
7. 12/13 ÷ 6
= 12/13 × 1/6
= 12/78
=6/39
= 2/13
8. 11/5 ÷ 2/15
= 11/5 × 15/2
165/10
= 33/2
9. 6/7 ÷ 5/4
6/7 × 4/5
= 24/35
10. 7/2 ÷ 10/9
7/2 × 9/10
63/20
So, the above are ways to determine the step-by-step answers.
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A parallelogram has one angle that measures 12°. What are the measures of the other three angles in the parallelogram?
Answer:
I think like 60∘, 60∘, 60 ∘ , 60 ∘ , and 120∘?
A theater is hosting a film festival for Hispanic Heritage Month. The Moore family buys
5 tickets and spends $28.75 at the concession stand. Each ticket costs the same amount.
They spend a total of $76.75. Which equation shows the cost of each ticket, t?
Answer:t = 9.6.
Step-by-step explanation:
Find the volume of the solid.
Answer:
64cm³
Step-by-step explanation:
( 4 x 4 x 4) cm x cm x cm
Question # 6 Multiple Choice Which of the following minerals is made of more than one element? Responses copper silver gold hornblende
Out of the following minerals hornblende is made up of more than one element. Therefore, option D is the correct answer.
What are minerals?Solid, naturally occurring materials known as minerals have a particular chemical makeup and crystal structure. They can be discovered in rocks, soil, and water and are primarily created by geological processes. Minerals are crucial for our bodies' nutritional needs as well as for the construction of structures and the manufacture of electronics, among other facets of our daily life.
Hornblende is a mineral made up of multiple elements, including calcium, magnesium, iron, aluminum, silicon, and sometimes sodium and potassium. The other minerals listed, copper, silver, and gold, are each made up of a single element.
Therefore, the correct option is d. Hornblende
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Q1 Logarithmic Functions
An initial amount of $1200 is invested into an account earning 4.25% interest compounded annually.
Q1.1 Part a)
Write the equation for the amount of money in the account after t years. Hint: "compounded annually" means that the money will be compounded one time per year.
Q1.2 Part b)
How long will it be until the amount of money in the account reaches $3000 (use a logarithm to find the exact amount of time, and then round your answer to 2 decimal places)?
Q2 Logarithmic Functions
According to the CDC, the relationship between the median weight of a female child and the age of a female child (from 0 to 36 months) can be modeled approximately by W=7.5+5.9ln(M+1), where
M is the age in months and W is the median weight in pounds.
Q2.1
Graph this function in an appropriate window. Make sure to label axes, scale, and all important features of the graph.
Q2.2
Determine W ^−1(28). What does this mean in the given context?
This means that the median weight of a female child at 31.48 months is 28 pounds (approximately) base on logarithmic function.
Logarithmic function calculation.
Q1.1: The equation for the amount of money in the account after t years, compounded annually, can be given by:
A = P(1 + r/100)^t
where A is the amount of money in the account after t years, P is the principal amount invested, r is the annual interest rate, and t is the number of years.
Plugging in the values given in the problem, we get:
A = 1200(1 + 4.25/100)^t
Q1.2: We need to solve for t in the equation:
3000 = 1200(1 + 4.25/100)^t
Dividing both sides by 1200, we get:
2.5 = (1 + 4.25/100)^t
Taking the natural logarithm of both sides, we get:
ln 2.5 = t ln (1 + 4.25/100)
Solving for t, we get:
t = ln 2.5 / ln (1 + 4.25/100) ≈ 15.91 years
So, it will take approximately 15.91 years for the amount of money in the account to reach $3000.
Q2.1: To graph the function W = 7.5 + 5.9 ln(M + 1), we can use a graphing calculator or software. Here is a possible graph:
Graph of W = 7.5 + 5.9 ln(M + 1)
Q2.2: To find W ^−1(28), we need to solve the equation:
28 = 7.5 + 5.9 ln(M + 1)
Subtracting 7.5 from both sides, we get:
20.5 = 5.9 ln(M + 1)
Dividing both sides by 5.9, we get:
ln(M + 1) ≈ 3.474576
Taking the inverse logarithm of both sides, we get:
M + 1 ≈ e^3.474576
M ≈ e^3.474576 - 1 ≈ 31.48 months
So, W ^−1(28) ≈ 31.48 months. This means that the median weight of a female child at 31.48 months is 28 pounds (approximately).
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Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = x2 − 4x + 1 and y = −x2 + 4x − 5 for x in [0, 3]
The areas of the region between the curves is -40/3square units.
We must first graph the curves in order to identify which one is on top in order to calculate the area of the region bounded by the curves for x in [0, 3]. y = x²− 4x + 1 and y = −x²+ 4x − 5
The vertex of the graph of y = x²− 4x + 1is at (2, -3), and it opens upward. The vertex of the graph of y =−x²+ 4x − 5 is at (2, -1), and it opens downward.
Thus, the curve y = x²− 4x + 1 is on top for x in [0, 1], and the curve y = −x²+ 4x − 5 is on top for x in [1, 3].
To determine which curve is on top, we can set them equal to each other and solve for x:
x²− 4x + 1 = −x²+ 4x − 5
2x² - 8x + 6 = 0
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0
x = 1 or x = 3
Thus, the curves cross at x = 1 and x = 3. To find which curve is on top between these two points, we can test a point in between, such as x = 2:
y = x²− 4x + 1 = 1
y = −x²+ 4x − 5 = -1
Using integration, we can find the area of the region:
∫[0,1] (x²− 4x + 1) dx + ∫[1,3] (−x²+ 4x − 5) dx
= [(1/3)x³ - 2x² + x] from 0 to 1 + [(-1/3)x³ + 2x² - 5x] from 1 to 3
=[1/3-2+1]+[{-9+8-15}-{-1/3+2-5}]
=-2/3+-38/3
=-40/3 square units.
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worth 30 points!!!!
pls screenshot and answerrr
Firefighters have a 52-foot extension ladder. In order to reach 48 feet up a building, how far away from the building should the foot of
the ladder be placed?
OA. 36 feet
OB. 20 feet
OC.28 feet
OD.32 feet
if h(x)=x+2/x-2, then dy/dx=? A. x-2 B. -5/2 C. 1/(x-2)². D. none
1/(x-2)². The correct option is C
What is quotient rule ?The quotient rule is a formula used in calculus to find the derivative of a function that is the quotient of two other functions. Specifically, it gives the formula for finding the derivative of a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are both functions of x.
We can use the quotient rule to find the derivative of h(x):
h(x) = (x+2)/(x-2)
h'(x) = [ (x-2)(1) - (x+2)(1) ] / (x-2)^2 (apply quotient rule)
Simplifying the numerator, we get:
h'(x) = [ x-2 - x-2 ] / (x-2)^2
h'(x) = -4 / (x-2)^2
Therefore, the answer is (C) 1/(x-2)².
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