The sum of any two sides of a triangle must be greater than the other thus 32 feet,21 feet, and 12 feet will be the correct so options (A),(B), and (D) are correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
As per the given,
To be a triangle of three side polygon the sum of any two sides must be greater than the third side.
If we take 32 feet,21 feet, and 8 feet.
21 + 8 = 29 < 32 so it will not form any triangle.
Thus, 8 cannot be taken. now let's take 32,21 and 12 here 21 + 12 = 33 > 32 so it will form a triangle this will be used for the project.
Hence "The right answer will be 32 feet, 21 feet, and 12 feet because the sum of any two sides of a triangle must be bigger than the other".
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Konrad buys a skateboard that costs c dollars. After 7.5% sales tax is added, the total cost can be expressed by the expression c+0.075c . What is this expression written in simplest form?
When the skateboard's price, c, and the 7.5% sales tax are included, the simplified expression for the provided expression, c+0.075c, becomes 1.075c.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Here,
Given expression,
=c+0.075c
total cost=1.075c
The simplified expression for the given expression c+0.075c will be 1.075c when the skateboard cost c and the sales tax of 7.5% is added.
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(1 point) a true-false test contains 7 questions. in how many different ways can the 7-question test be answered? (give an exact answer.) your answer is :
The possible number of ways the 7-question test can be answered: 128
In this question, we have been given a true-false test contains 7 questions.
We need to find the possible number of combinations (ways) the 7-question test can be answered.
As, it is a true-false test, there are 2 choices per problem.
The number of problems = 7
so, the possible number of ways the 7-question test can be answered: 2*2*2*2*2*2*2
= 2^7
= 128
Therefore, in 128 different ways the 7-question test can be answered.
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How much compound interest will $50,000 have earned in 10 years at
6.4% annual interest compounded quarterly?
Answer:
Step-by-step explanation:
To find the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:
compound interest = principal * (1 + rate/n)^(n*t) - principal
where "principal" is the initial amount of money, "rate" is the annual interest rate, "n" is the number of times the interest is compounded per year, and "t" is the number of years.
Plugging in the given values, we get:
compound interest = $50,000 * (1 + 0.064/4)^(4*10) - $50,000
= $50,000 * (1.016)^40 - $50,000
= $50,000 * 2.6335 - $50,000
= $78,167.50 - $50,000
= $28,167.50
Therefore, the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly is $28,167.50.
Square ABCD has an area of 64 units^2
2
. It is rotated 270^{\circ}
∘
clockwise around vertex C resulting in square A'B'C'D'.
What is the side length of C'D'?
On solving the provided question, we got to know that side length of the square is 8 units.
What is a square?Four sides that are equally spaced apart make up a square. Around us, a lot of things are rectangular. Equal sides and a 90° interior angle serve as a visual cue to identify a square. A closed square has four sides and exists in two dimensions (2D). A square has an equal number and parallel alignment of its four sides.
What to identify a square?A four-sided shape known as a square has sides that are all the same length and angles that are all right angles with a 90 degree angle.
Here,
Area of square = [tex](side)^2[/tex]
64 = [tex](side)^2[/tex]
[tex]Side = \sqrt{64}[/tex]
Side = 8 units
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question is in the image, i need the method answer for part b.
the question says: "the diagram shows the position of two ships, A and B, and the coastguard station, C."
Step-by-step explanation:
it seems like you understood the law of cosine (extended Pythagoras for non-right-angled triangles) and applied it mostly correctly for a).
but you made a little typo : suddenly, in the second half of the formula you changed the side length BC from 83.1 to 81.3. but it is 83.1.
so, the correct calculation is
a² = 83.1² + 95.5² - 2×95.5×83.1×cos(101) =
= 16,025.86 - 15,872.1×cos(101) =
= 16,025.86 - -3,028.539456... =
= 19,054.39946...
a = sqrt(19,054.39946) = 138.037674...
the rounded result is the same (138 km), but just for your information, and also, I want to use the correct numbers for b)
for b) we need to know :
bearings are angles, measured clockwise from north (north would be 0°).
when ship A looks to station C, the bearing is 146°.
when ship A looks to ship B, the corresponding bearing is 146 - the triangle angle at A (because that is how far we have to turn from looking at C to looking at B).
so, now, we need to apply the law of cosine again. this time to get angle A, as we have now side a.
c² = a² + b² - 2ab×cos(C)
and we want to get C, means now (since you called the baseline "a" in the first part)
83.1² = 95.5² + a² - 2×a×95.5×cos(angle A)
6,905.61 = 9,120.25 + 19,054.39946... - 2×138.037674...×95.5×cos(angle A)
6,905.61 = 28,174.64946... - 26,365.19574...×cos(angle A)
-21,269.03946... = -26,365.19574...×cos(angle A)
cos(angle A) = -21,269.03946.../-26,365.19574...
= 0.806708953...
angle A = 36.22437773...°
therefore, the bearing from A to B is
146 - 36.22437773... = 109.7756223...°
Find the miing number
A number increaed by 25%. It i decreaed by __? But after decreaing it, it i the ame tarting number
When a number is first increased by 25% then if it is decreased by 25% , we will get the same starting number. hence the net increased or decreased value is zero.
What is net decrease?A decline in net income is a change from one period to the next in the amount of money you have after deducting your expenses from your revenues.
How do you calculate the net?There are two possible outcomes for net income. Your business has a positive net income when revenues exceed expenses. You have a negative net income, commonly referred to as a net loss, if all of your expenses exceed all of your revenues.
let the number is x
first it is increased by 25%
so,
x+(25/100)x=(125/100)x
now according to second condition,
we have to find a value by which it is decreased so we get the same number.
so, let that decreased value is y;
(125/100)x-y=x
-y=x-(125/100)x
-y=-(25/100)x
cancelation of sign;
y=25%
so this is our required value.
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After the antibiotic Streptomycin is given to a patient, the population (in million) of Mycobacterium in the body is given by the function f(t) = -0.02(t)2 + 3, where t is in hours. Find the rate at which the population of the bacteria is changing after 4 hours.
Dangerous, antibiotic resistant bacteria have been observed with increasing frequency over the past several decades.
In this review the factors that have been linked to this phenomenon are addressed. Profiles of bacterial species that are deemed to be particularly concerning at the present time are illustrated. Factors including economic impact, intrinsic and acquired drug resistance, morbidity and mortality rates, and means of infection are taken into account. Synchronously with the waxing of bacterial resistance there has been waning antibiotic development. The approaches that scientists are employing in the pursuit of new antibacterial agents are briefly described. The standings of established antibiotic classes as well as potentially emerging classes are assessed with an emphasis on molecules that have been clinically approved or are in advanced stages of development. Historical perspectives, mechanisms of action and resistance, spectrum of activity, and preeminent members of each class are discussed.
What antibiotic Streptomycin ?
Streptomycin injection is used to treat moderate to severe bacterial infections in many different parts of the body.
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true or false? about 60% of u.s. women older than 16 years are either currently employed or looking for work.
Answer: True
Step-by-step explanation:
Simple.
If f(x) = 2x² + 3x - 19, find f(-4)
Answer:
f(-4)=1
Step-by-step explanation:
f(x) = 2x² + 3x - 19
f(-4)=2(-4)² + 3(-4)-19
f(-4)=2(-16)+3(-4)-19
f(-4)=-32+3(-4)-19
f(-4)=32-12-19
f(-4)=20-19
f(-4)=1
Use the quadratic formula to solve. Express your answer in simplest form.
22d²- 35d + 12 = -3d²
Answer:
x= -22d/44 x = -48d/44 is your answer
where d =2x
Step-by-step explanation:
22d²- 35d + 12 = -3d²
22d²- 35d + 12 +3d²
25d²- 35d + 12 = a b c formula= - b-/+ / b^2 - 4 ac / 2a
= -35d -+/ 35^2 - 4 *22d *12 / 2*22d
= -35d -+/1225d-4 (22) (12) /44d
= -35d -+/1225d- (88) (12) /44d
= -35d -+/1225d- (1056) /44d
= -35d -+/169d- /44d
=-35d -/+ 13d /44 x= -22d/44 x = -48d/44
The discriminant b2−4ac>0
so, there are two real roots.
Felix invested $2,800 at a rate of 3.4%, compounded quarterly. [HINT: Use the
formula A = P(1 + 5 )nt]
26 aleged to 19dmun si of bas
a) What exponential growth function would model this situation?
b) What is the value of the investment after 5 years? (Round your response to the nearest
dollar).
23.02
The value of the investment after 5 years will be $3309.48.
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
The value of the investment after 5 years will be,
[tex]A = P[(1 + \dfrac{r}{100} )^{nt}]\\A = 2800[(1+0.034)^{5}[/tex]
A = $3309.48
Therefore, the value of the investment after 5 years will be $3309.48.
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Two water tank are hown. Tank A i a rectangular prim and Tank B i a triangular prim Tank A i filled with water to the 6-meter mark ome of the water from tank A i being tranferred to Tank B o that the water in tank a i at 2 meter. Shade the amount of water in tank B to indicate the approximate height of the water in tank bafter the tranfer alo write the height, to the nearet whole number of meter, in the pace provided
The water tank's illustrated prism will stand 8 meters tall.
What is a Prism?Prisms are significant polyhedron family members with congruent polygons at the base and top.
A prism's other faces are referred to as its lateral faces. It denotes that a prism's face is not curved.
The cross-section of a prism is constant along its length. The names of the prisms are determined by their cross-sections. The best example of a prism that best represents a real-world object is a metallic nut.
A rectangular prism that best represents a real-world object is a fish aquarium.
According to our question-
The following formula will be used to determine the triangle prism's base's area:
= 1/2 × 4 × 9
= 18m²
The rectangular tank's water will be drained of the following volume:
= (6 × 6) × 4
= 144m³
As a result, the height will be determined as follows:
18 × h = 144
18h = 144
h = 144/18
h = 8m
Hence, The water tank's illustrated prism will stand 8 meters tall.
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Let O , P , and Q be distinct collinear points with PQ=3 . Let P′ and Q′ be the images of points P and Q under dilation from point O with scale factor 4 .
What is the length of the image segment P′Q′ ?
Responses
1. 1
2. 7
3. 9
4. 12
Answer If O, P, and Q are collinear points with PQ = 3, and P' and Q' are the images of P and Q under dilation from O with a scale factor of 4, then the length of the segment P'Q' will be 4 times the length of the segment PQ. Since PQ = 3, the length of P'Q' will be 4 * 3 = $\boxed{12}$.
To see why this is the case, recall that a dilation with a scale factor of 4 expands or contracts a figure by a factor of 4 in each direction. In this case, the dilation from O with a scale factor of 4 expands the segment PQ by a factor of 4, resulting in the segment P'Q' with a length of 4 times the length of PQ. Since PQ = 3, the length of P'Q' will be 4 * 3 = 12.
Help with ixl please
The most horizontal line is straight so it equal 180°. You know that one side (lower left section) is 67° meaning the other side is 180° - 67° = 113° (lower right side).
The most vertical line is straight so it equal 180°. You know that one side (lower right side) is 113°. The entire right side you have: 113°, 42°, and f.
f = 180° - (113° + 42°)
f = 25°
Answer:25 deegrees
Step-by-step explanation:
9
Are the following equations the same line? *
y - 3 = 4(x - 2)
2)
and
and y + 2 = 4(x + 7)
no, because they are not the same in slope - intercept form
it would be impossible to tell
yes, because both equations are the same in slope - intercept form
(5 Points)
Answer: No, because they are not the same in slope - intercept form
Step-by-step explanation:
First, we will distribute and simplify into slope-intercept form.
Equation 1:
y - 3 = 4(x - 2)
y = 4(x - 2) + 3
y = 4x - 8 + 3
y = 4x - 5
Equation 2:
y + 2 = 4(x + 7)
y = 4(x + 7) - 2
y = 4x + 28 - 2
y = 4x + 26
We see that the answer to this question is "No, because they are not the same in slope - intercept form" as they have different y-intercepts, one being -5 and one being 26.
14% out of 100% equals how many people out of 10?
Answer:
1.4 people out of 10
Step-by-step explanation:
Just divide it by 10
Answer:
only 4 people
Given the following information, calculate the product cot per unit. Direct material = $28,000 Direct labor = $42,000. Overhead application rate = $15 per direct labor hour. Direct labor hour = 5,200. Unit product = 7,400. Product cot per unit = $
The product cost per unit is $53.30 along the rims and $28.29 along the posts.
What does the mean cost mean in math?The average cost price is the quantity as an arithmetic average of the average amount. Average or mean is defined as the product of the total number of data given and the total number of data given. We have the cost of the goods and the overall quantity of goods or products provided when determining average cost pricing.
How do you find the cost in math?Cost price, for instance, equals selling price plus profit. Cost is equal to Selling price plus Loss. Cost price = 100 Selling Price + 100 + Profit (when the Selling Price and Profit Percentage are given)
According to the above questions :-
Direct Materials rims $20
Direct Labour rims $12
Overhead $21.30
Total cost is $53.30
Direct Materials posts $18
Direct Labour posts $6
Overhead $4.29
Total cost is $28.29
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what does x equal????
Answer:
x=15.56
Step-by-step explanation:
You need to use pythagoras for this question.
Formula for pythagoras: a^2 + b^ =c^2
a= 11
b=11
c=?
11^2+11^2=c^2
121+121=c^2
242=c^2
[tex] \sqrt{242} [/tex]
=c
c=15.56
For the month of April, a checking account has a balance of $501 for 23 days, $2428 for 3 days, and $241 for 4 days. What is the account’s mean daily balance for April?
The account’s mean daily balance for April will be $105.7.
What is a mean?Mean is the total added values of all the data in a set divided by the number of data in the set.
The account had the following balances;
$501 for 23 days
$2428 for 3 days
$241 for 4 days.
To find the mean; add the total amount and divide by the total number of days
[tex]mean = \frac{501 + 2428 + 241}{23 + 3 + 4}[/tex]
[tex]mean = \frac{3170}{30}[/tex]
mean = $105.7
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what are some features that make highway roads safer for drivers who are driving at higher rates of speed? (select 5 correct answers)
There are the some features that make highway roads safer for drivers who are driving at higher rates of speed is :(5 correct answers)
1.Median barriers
2.Guard rails
3.Brake away signs
4.Rumble strips
5.Controlled access
Given,
In the question:
What are some features that make highway roads safer for drivers who are driving at higher rates of speed?
Now, According to the question:
There are the some features that make highway roads safer for drivers who are driving at higher rates of speed is :(5 correct answers)
1.Median barriers
2.Guard rails
3.Brake away signs
4.Rumble strips
5.Controlled access
Hence, There are above 5 highway roads safer for drivers.
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Find the sum of the terms.
The numerator of the simplified sum is
Answer:
numerator = 4x + 6
Step-by-step explanation:
x²+3x + 2
(x+2)(x+1)
x/(x+2)(x+1) + 3(x+2)/(x+2)(x+1)
(x+3x+6)/(x+2)(x+1)
(4x+6)/(x+2)(x+1)
Which graph represents the function f(x) = 5 ^ x
What is the slope of the line shown?
Answer:
Below
Step-by-step explanation:
Find two convenient integer coordinates ( 0,7) and (5,-3)
slope = (y1-y2) / (x1-x2)
it does not matter which point your assign as '1' or '2'
slope = ( 7 - - 3 ) / (0-5) = 10 /-5 = -2
Find a33 first term in the sequence is 3 and the common difference is -1
A. -29
B. 36
C. -36
D. -30
Answer:
Step-by-step explanation:
Find the value of the expression 2xy(8x - 3y), when x = 2 and y = 4
A 48
B 72
C 64
D 24
3.3. A triangle has sides of lengths (7x + 1) cm, (4x - 1) cm and (14- x) cm. If the
perimeter is 84 cm, find the dimensions of the triangle.
Answer:
7 cm.
The triangle dimensions are: 50, 27, and 7 cm
Step-by-step explanation:
The three sides of the triangle make up the entire perimeter. Add each side and set the result equal to 84cm, the perimeter.
(7x+1) + (4x-1) + (14-x) = 84 cm
10x + 14 = 84
10x = 70
x = 7 cm
Use x=7 to find the three dimensions:
1) (7x+1) = 50 cm
2) (4x-1) = 27 cm
3) (14-x) = 7 cm
Do these add to 84 cm?
(50+27+7) = 84 cm YES
Patricia run a mall event-organizing company baed in Nairobi. She ha jut received
an order to organize an SME development eminar at the Sarova Stanley Hotel hoted by
the World Bank. She i billing World Bank Kh 10,000 per participant while the hotel
charge her Kh 2,500 per participant for meal in addition to a charge of Kh 225,000
for the hall and other amenitie. Aume there i linear relationhip between the cot and
the number of participant. Required:
i. Obtain the minimum number of participant required to attend the forum for Patricia
to break even
Assuming that costs increase linearly with the number of attendees, Patricia needs at least 30 people to attend the forum in order to break even.
Patricia needs 75 attendees to attend the forum in order to make a profit of 337,500.
By dividing the fixed costs by the contribution margin per unit, we are able to determine the break-even threshold in units. Divide the fixed costs by the contribution margin ratio to get the break-even threshold in dollars.
The percentage of the contribution margin to the sales revenue is known as the contribution margin ratio. Prior to the division operation, we add
the profit to the fixed cost in order to reach the goal profit.
Billing rate per participant = 10,000
Hotel charges per participant = 2,500
Contribution per participant = 7,500 (10,000 - 2,500)
225,000 is the fixed fee for the hotel room and amenities.
Break-even point in units = Contribution per unit – Fixed cost
= 30 individuals (225,000 -7,500)
Fixed cost plus profit minus contribution per unit equals break-even point in units with target profit.
Target profit = 337,500
= (225,000 + 337,500) ÷ 7,500
= 75 participants
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Which expression is equivalent to x +11?
A. 11x
B. 11+x
C. 11-x
D. -x+11
Answer:
11x
Step-by-step explanation:
A garden contains secral diffrent types of flowers in the garden 2/3 of the flowers are roses of the roses 1/5 of the flowes are white and 3/5 of the flowers are pink. What fractin of the total flowers in the garden are white or pink?
The total flowers in the garden white or pink is 8/15.
What is fraction?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
In our garden, there are 2/3 total roses, making the total number of blooms that aren't roses 1/3
4/5 = 2/3 +1/3.
Since 3 is a division of 6, we must multiply by 6 to arrive at the solution.
4 x 6 =24
5 x 6 =30
24/30
Next, we calculate half of 30 and add it to get 3/3.
Then we find 1/2 of 30 and add this to make 3/3
Just like 1/2 of 2 = 1 and 2+1 = 3
30 / 2 = 15
15 + 30 =45
The answer is 24/45
We then reduce this fraction by 3 as 6 + 8 do not divide into 45
24/45 = 8/15
The total flower in the garden is 8/15
The proportion of white or pink flowers in the entire garden is 8/15.
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Does the given information represent a function?