Proof that the bisector of an isosceles triangle also bisects the angle.
Is bisector a midpoint?A line segment's midpoint is the point on the segment where it divides into two congruent parts. a right-angled segment bisector that crosses the segment. A line (or portion of a line) that cuts through the middle is known as a segment bisector.
Is the bisector always 90?When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized halves is known as a bisector. A line segment's perpendicular bisector implies that it intersects the segment at a 90-degree angle and splits it into two equal halves.
Let ABC be the isosceles triangle with AB=AC, B=C, and BAD=CAD as the vertical angle bisectors.
As a result, the triangles satisfy the ASA criterion.
⟹BD=DC
Thus, the base is divided by the vertical angel's bisector.
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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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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.
What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y=4
Answer: [tex]y-1=-\frac{1}{2}(x-4)[/tex]
Step-by-step explanation:
The equation of the given line can be rearranged as [tex]y=2x-4[/tex].
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is -1/2.
Using point-slope form, the equation is [tex]y-1=-\frac{1}{2}(x-4)[/tex].
surveys, if not done correctly, can lead to seriously biased samples. which is not a bias due to the sampling plan?
Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
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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.
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...°
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:
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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Which function has the least slope?
OA.
B.
y =
x +15
y = x - 12
C. y = 5x + 23
D. y =
=
7x6
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
A builder need 2,964 nail to finih a project. If the nail come in package of 52, how many package hould the builder purchae?
Number of nails to finish the project by buying are required = 2964 units
1 package of nails contains per unit = 52 units
To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.
So,
Number of package required to the builder
= Total number of nails required to buy by the builder / no. of nails provided per package
=2964/52
=57 packages
Therefore, No. of packages required by the builder to buy to complete the project
=57 packages needed.
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Answer: 57
Step-by-step explanation:
Just plug it into a calculator.
2964/52 = 57
He needs to buy 57 packages
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.
Which expression is equivalent to x +11?
A. 11x
B. 11+x
C. 11-x
D. -x+11
Answer:
11x
Step-by-step explanation:
What value of w makes the equation 3(−4w−5)=−7(5+w) true?
4 is the value of w which makes the equation true.
What is an equation?
There are many different ways to define an equation. A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.There are three main types of equations depending on the degree. More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A quadratic equation must have at least one variable with an exponent of 2.A third-order equation is a cubic equation. Cubic equations need the exponentiation of at least one variable.It is given that,
3(−4w−5)=−7(5+w)
by solving the equation,
-12w-15=-35-7w
12w-7w=35-15
5w=20
w=20/5
∴w=4
Hence, 4 is the value of w which makes the equation true.
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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
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)
(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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What will happen to the graph of the line y = -54x + 3 if you change -54 to 54?
Imagine Math
Which graph represents the function f(x) = 5 ^ x
The perimeter of a rectangle i 104m the length i 7m more than twice the width. What are the dimenion of the rectangle
Size will be 37 L x 15 W.
What is perimeter?Perimeter is the distance around the edge of a shape. Discover how to calculate a shape's perimeter by adding its side lengths.
Finding the dimension is required, if the perimeter is 104 meters and the length is 7 meters longer than twice the breadth.
Let L be the length and W be the width
L = 7 + 2*W
P = 2(L + W) ; 104 = 2(7 + 2W + W) ; 104 = 2(7 + 3W) ;
104 = 14 + 6W
6*W = 90 ;
W = 15 L = 37
Hence the dimension is 37*15
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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.
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.
If DG=FG=7, m∠DEG=u+21°, and m∠FEG=2u, what is the value of u?
The value of u is 21.
What is Congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Given:
DG=FG=7, m ∠DEG=u+21°, and m ∠FEG=2u,
As, from the Diagram
DE = FE (Given)
DG= FG ( Given)
GE= GE (Common)
So, ΔDEG ≅ ΔFEG by SSS Rule.
<DEG = <FEG (CPCT)
u + 21 = 2u
2u - u= 21
u=21
Hence, the value of u is 21.
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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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Which product is represented by the model?
A. 0.05×0.04=0.002
B. 5×0.4=2
C. 0.5×0.4=0.2
D. 0.5×0.04=0.02
The value of inserting area of an array is 0.02
What is meant by area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
The region that an object's shape defines as its area. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area.
Given:
5 column (hundred grid) = 5/100 = 0.05
4 row (hundred grid) = 4/100 = 0.04
Find:
Area equation
Computation:
Area equation = 0.05 x 0.04
0.05 x 0.04 = 0.002
Therefore the value of inserting area of an array is 0.02
The complete question is : Which product is represented by the model? A hundred grid model shows 5 columns shaded and 4 rows shaded. The intersecting area is an array that is 5 by 4. A. 0 . 05 × 0 . 04 = 0 . 002 B. 5 × 0 . 4 = 2 C. 0 . 5 × 0 . 4 = 0 . 2 D. 0 . 5 × 0 . 04 = 0 . 02
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4/5 divided by 1/3 equals?
Answer:
4/15
Step-by-step explanation:
reciprocal of 1/3 then cross multiply
Find the value of the expression 2xy(8x - 3y), when x = 2 and y = 4
A 48
B 72
C 64
D 24