Answer:
[tex]y=-\frac{2}{3}x-2[/tex]
Step-by-step explanation:
To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]2x+3y=-6 \\ \\ 3y=-2x-6 \\ \\ y=-\frac{2}{3}x-2[/tex]
The measure of two remote interior angles of a triangle are x - 10 and 4x + 4 The exterior angle of the triangle measures 3x + 54 Solve for the measure of the exterior angle .
The measure of the exterior angle of the triangle is 144 degrees.
How to solve angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore, the measure of the two remote interior angles of a triangle are x - 10 and 4x + 4. The exterior angle of the triangle measures 3x + 54 .
Let's solve for the exterior angle.
x - 10 + 4x + 4 = 3x + 54
5x - 6 = 3x + 54
5x - 3x = 54 + 6
2x = 60
x = 60 / 2
x = 30
Therefore,
exterior angle = 3x + 54 = 3(30) + 54 = 90 + 54 = 144 degrees
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aisha wants to buy apples and raspberries to make a fruit tart. apples cost $3 per pound and raspberries cost $2.75 per pound. how many pounds of fruit does she buy if she buys 3 pounds of apples and 2.5 pounds of raspberries? how many pounds of fruit does she buy if she buys xx pounds of apples and yy pounds of raspberries?
Answer:
6.4
Step-by-step explanation:
I guessed and got it right.
If f(x) = e¹/x then f(x)=
The derivative of f(x) is option A.
What is derivative?
The instantaneous pace at which one quantity changes in relation to another is referred to as a derivative in mathematics.
Main Body:
Since the derivative of [tex]e^{x}[/tex] is just [tex]e^{x}[/tex] , application of the chain rule to a composite function with [tex]e^{x}[/tex] as the outside function means that:
[tex]\frac{dy}{dx} (e^{f(x)} )= e^{f(x) }.f'(x)[/tex]
Now the derivative of 1/x = [tex]\frac{-1}{x^{2} }[/tex]
Hence derivative of f(x) = [tex]-e^{\frac{1}{x} } /x^{2}[/tex].
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A baseball is thrown from the pitcher's
mound at 40 m/s. It takes 0.46 seconds for
the ball to reach home plate. What is the
distance between the mound and home
plate?
Answer:
Step-by-step explanation:
Velocity = distance / time
In this problem, we need to calculate for distance, knowing time and velocity.
multiply time on both sides, on the right side the time will cancel out leaving time alone.
velocity * time = distance
40m/s * 0.46s = distance
distance = 18.4 meters
Hope it helped!
How much of a radioactive kind of zinc will be left after 2 hours if the half-life is 1 hour and
you start with 259,288 grams?
grams
Answer:
64822
Step-by-step explanation:
Half-life model:
[tex]P=P_o* \left(\frac{1}{2}\right)^{\frac{t}{D}}[/tex]
[tex]P_o[/tex] is the initial value, D is the time taken for the quantity to reduce half-life and t is the given time period.
[tex]\sf P_o = 259,288 \ grams\\\\D = 1 \ hour\\\\t = 2 \ hours[/tex]
[tex]P = 259,288*(\frac{1}{2})^\frac{2}{1}\\\\P = 259,288*(\frac{1}{2})^2\\\\P = 259,288*\frac{1}{4}\\\\P = 64822[/tex]
small airplane flew 104 miles in 50 minutes. At this rate, how many miles can it fly in 3 hours?
An airplane can fly 374.4 miles in 3 hours.
A small airplane flew 104 miles in 50 minutes.
So, the rate would be,
rate = distance / time
rate = 104/50
rate = 2.08 miles/minute
We need to find the distance the airplane can flay in 3 hours.
3 hours = 180 minutes
t = 180 minutes
r = d/t
2.08 = d/180
d = 2.08 * 180
d = 374.4 miles
Therefore, an airplane can fly 374.4 miles in 3 hours.
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Britney can do a job in 12 hours. if she works with jimmy, together they can get the job done in eight hours. how long would it take jimmy to do the job alone?
Jimmy will take 24 hours to do the given job alone.
What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)
Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.
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Solve using proportions: If a 4-pound roast takes 140 minutes to cook, how long should a 5-pound roast take to cook?
Step-by-step explanation:
[tex]4pound \: roast \: = 140 \: minutes \\ 5 \: pounds \: roast \: = {?} \\ then cross multiplication \\ 140 \times 5 \: divide \: by \: 4 \\ 700 \div 4 = 175 \\ 5 \: pound \: roast \: take \: 175 \: minutes[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point D is at -3, and point E is at 6. The point F lies on segment DE . The ratio of DF to FE is 2 : 3. Where does point F lie on the number line? Point F is at on the number line.
Using the section formula, point F lie on 3/5 in the number line.
In the given question,
On a number line, point D is at -3, and point E is at 6.
The point F lies on segment DE .
The ratio of DF to FE is 2 : 3.
We have to find where point F lie on the number line.
Since point D lies is at -3 at x axis so the point should be ( -3,0).
Point E lies is at 6 at x axis so the point should be ( 6,0).
F lies on segment DE. So let the point of F is (X, Y)
The ratio is 2:3.
Now firstly finding the value of X using section formula
X = [tex]\frac{mx_{2}+nx_{1}}{m+n}[/tex]
where [tex]x_{1}[/tex]= -3, [tex]x_{2}[/tex]= 6, m= 2 and n=3
Now putting the value
X = {2×6+(-3)3}/(2+3)
Simplifying
X = (12-9)/5
X = 3/5
Now firstly finding the value of Y using section formula
Y = [tex]\frac{my_{2}+ny_{1}}{m+n}[/tex]
where [tex]y_{1}[/tex]= 0, [tex]y_{2}[/tex]= 0, m= 2 and n=3
Now putting the value
Y = (2×0+3×0}/(2+3)
Y = 0/5
Y = 0
Hence, point F lie on 3/5 in the number line.
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how many different two-letter initials can people have using the upper case characters in the english alphabet?
The different two-letter initials can people have using the upper case characters in the English alphabet is 676 (if no specifications are given)
The question has not specified other conditions so we have assumed it by cases and solved it
Case 1 -
“Everything” allowed, means that we are considering solutions like “AA” and “BA, AB”
If this is the case then there are => 26 x 26 = 676 Combinations,
Case 2-
No repetition allowed
Here, we are excluding cases like “AA, BB” etc so here we have
26 x 25 = 650 as our answer
Case 3-
no repetition allowed + unique set every time, So
here we will have ²⁶C₂ (this is basic combinatorics formula )
= (26 x 25)/2
= 325 combinations possible
Case 4 -
Repetition allowed + unique set every time
here we will assume along with the uniqueness of each combination we will add Repeated combinations, Here we have “AA, BB, CC,……..ZZ” 26 new combinations along with unique ones So,
²⁶C₂+ 26 = 325 + 26 = 391 possible cases.
and I would recommend adding more detail to your question specifying the conditions in a better way, but the technically correct answer to your questions if no conditions are CASE 1.
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questions 1-4: the number of classes (x) a student takes in a given semester follows the following probability distribution: x 0 1 2 3 4 5 p(x) 0.4 0.25 0.15 0.08 0.02 ??? what is the expected number of classes a student will take in a given semester?
The expected number of classes a student will take in a given semester is 1.89
How calculate the expected value of x?Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.
Given :
x| 0 1 2 3 45
p| 0.4 0.25 0.15 0.08 0.02
where x = number of classes
p = probability
The expected value of x, E(x) =Σ xp
E(x) = (0×0.4) + (1×0.25) + (2×0.25) + (3×0.08) + (45×0.02)
E(x) = 0 + 0.25 + 0.5 + 0.24 + 0.9
E(x) = 1.89
Therefore, the expected number is 1.89.
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Which ordered pair gives a solution of the system of equations represented in
the graph below?
A. (-1.5, 2.5)
B. (-2.5, 1.5)
C. (2.5, -1.5)
D. (2.5,1.5)
Answer: The correct answer is D. (2.5,1.5)
Step-by-step explanation:
As noted in the graph, the lines intersect at the location where x=2.5 and y=1.5 in Quadrant I (both positive).
Hi I don't understand this can you please help me. Maura multiply 1. 8 by 2. 4 and write the product as 0. 432. Tom says that her product is incorrect. How could Tom know this without multiplying a two numbers
The correct multiplication of 1.8 and 2.4 will be 4.32.The product 0.432 calculated by Maura was incorrect.
Define the term multiplication of number?One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. The symbols for multiplication are cross (×), asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks.For the given question-
Maura divide 1. 8 by 2. 4 and enter 0. 432 as the result.
Tom claims her product is unreliable.
Tom is able to make this deduction without the need for multiplication because the value 0.432 is less than even 1.8, which is not conceivable.
Thus,when multiplying by a number bigger than 1, the result will always be greater than the starting numbers.
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A carpenter needs to build a box to hold his wood screws. He has a sheet of wood that measures 18 inches by 12 inches. He then cuts equal squares from each corner. (a) Write an expression for the length, width, and height for the open box. (b) Write a function for the volume (use factored form).
The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x
(a) How to determine the expression for the length, width, and heightFrom the question, we have the following parameters:
Dimension of sheet = 8 inches by 12 inches
Also from the question, we understand that:
He cuts equal squares from each corner.
The cut-out length from the sheet would represent the height of the box
Represent this cut-out length with x
So, we have
Height = x
The width and the length are then represented as
Width = Initial width - 2x
Length = Initial length - 2x
So, we have
Width = 12 - 2x
Length = 18 - 2x
(b) Write a function for the volumeThe volume of a box is the product of its dimensions
In this case, we have
Width = 12 - 2x
Length = 18 - 2x
Height = x
So, we have
Volume = Width * Length * Height
Substitute the known values in the above equation So, we have the following equation
V = (12 - 2x)(18 - 2x)x
So, the volume function is V = (12 - 2x)(18 - 2x)x
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correct answer gets brainliest!
Answer:
x = 14
Step-by-step explanation:
the inscribed angle JKL is half the measure of its intercepted arc, that is
83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction
166 = 9x + 40 ( subtract 40 from both sides )
126 = 9x ( divide both sides by 9 )
14 = x
What does x equal to??
x is equal to 125° in the triangle
How to determine the value x in the triangle?The figure given here is a triangle. And we know that the sum of the angles in a triangle is 180°. So we can apply this concept by writing the expression below:
x + 25° + 30° = 180°
x + 55° = 180°
x = 180° - 55°
x = 125°
Therefore, the value of x is 125°. So x is equal to 125°
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in order to estimate attendance at a music festival, management counts the number of people entering the admissions gate in a 30-minute sample time. management assumes that there is a steady stream of people entering the festival for the 10 hours that the admissions gate is open. at a particular music festival, 2,250 people were counted entering the gate in a 30-minute sample time. what was the estimated attendance at this festival?
Answer:
45,000
Step-by-step explanation:
Given a 30 minute sample of a constant stream shows 2250 people entered the gate, you want an estimate of the total number of people through the gate in 10 hours.
AttendanceA half-hour period is 1/20 of the 10-hour period the gate was open. The rate is assumed constant, so the 2250 people entering in that half-hour period is presumed to be 1/20 of the total attendance.
20 · 2250 = 45000
The estimated festival attendance is 45,000 people.
Write The recursive formula for the sequence 18,22,26,30?
The recursive formula is an = a(n-1) +4. A recursive formula is one that defines each term in a sequence by using the term before it (s)
What is recursive formula?A recursive formula is one that defines each term in a sequence by using the term before it (s). The following parameters are defined by the recursive formulas: The sequence's first term. The pattern rule for obtaining any term from its preceding term. A recursive formula is composed of two parts: a statement of the first term and a statement of the formula that connects successive terms. The sequence is as follows: 10, 15, 20, 25, 30, 35,... Look for a recursive formula. This is an arithmetic sequence (the same number, 5, is added to each term to get to the next term).The sequence's first term
The pattern rule for obtaining any term from its preceding term
Recursive Arithmetic Sequence Formula
To find the nth term of an arithmetic sequence, use the recursive formula:
an = an-1 + d for n ≥ 2
Where
an is the nth term of a A.P.
d is the common difference.
Given:
14, 18, 22, 26, 30, …
a1 = 14
and, d = 18-14
d = 4
a2 = a1 + 4
a2 = 14 + 4 = 18
Similarly, going this way
an = a(n-1) +4
Hence, the recursive formula is an = a(n-1) +4
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find the surface area of a rectangle prism that has the following deminsions.
length : 2ft
width : 14in
height : 11in
surface area : in 2
Answer:
SA(surface area) of the rectangular prism is 1,510 in inches
Step-by-step explanation:
SA=2(lh+lw+hw)
2inch=24ft
lh=264
lw=336
wh=154
755*2=1,510
please help! i dont knnow what to do
Answer: g= 61/5 or 12.2
Step-by-step explanation:
There are 39 students in the bike club.
All but 8 of them participated in a race.
What is the total cost if each student who entered the race paid $6?
Answer:
Total Cost = $186
Step-by-step explanation:
All but 8 means that All of them participated except for 8 of them
Since there is 39 Students in the Club
Then the Number of Students participated = 39 - 8 = 31 Students
Total Cost = (Cost per Student ) * ( Number of Students )
=$6 * 31 = $186
Glad to Help
Solve for
x
xx.
x
=
x=x, equals
Two triangles A B C and A D E. Triangle A B C is on top of Triangle A D E at point A. Side A C is smaller than A E and side A B is smaller than side A D. Side C B has a length of three. Side E D has a length of x. Side A B has a length of nine. Segment B D has a length of six. Angle A B C and A D E are both ninety degrees.
A
A
E
E
D
D
B
B
C
C
9
9
3
3
6
6
x
x
The ΔABC placed on top of ΔADE, and having angles ∠ABC and ∠BAC congruent to ∠ADE and ∠DAE in ΔADE is similar to ΔADE. The side CB is 3 indicating that the side ED, which has a length of x = 5
What are similar triangles?Similar triangles are triangles that have similar (the same shape), such that one triangles has side lengths that are a constant multiple of the other.
Please find attached a possible drawing that is based on the parameters of the question
From the question and the drawing created with MS Word, we have;
Length of AB = 9
Side CB = 3
Segment BD = 6
∠ABC = ∠ADE = 90°
∠ABC ≅ ∠ADE by definition of congruency
From the drawing, ∠BAC ≅ ∠BAC by reflexive property of equality
Triangle ΔBAC is similar to triangle ΔDAE by AA similarity postulate
Segment AD = Segment AB + Segment BD by segment addition postulate
AD = 9 + 6 = 15
The pair of corresponding sides of similar triangles are proportional, therefore;
[tex]\dfrac{\overline{AB}}{\overline{AD}} = \dfrac{\overline{BC}}{\overline{DE}}[/tex]
Which gives;
[tex]\dfrac{9}{15} = \dfrac{3}{x}[/tex]
9 × x = 15 × 3 = 45
x = 45 ÷ 9 = 5
The length of side ED, x = 5
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Answer: 12
Step-by-step explanation: Because 9 x 2 is 18, and 7 x 2 is 14, we want to multiply 6 by 2. This gives us the answer 12.
9 x 2 = 18
7 x 2 = 14
6 x 2 = 12
for a questionnaire survey of employees of a particular organisation to investigate a range of aspects of their job satisfaction, a researcher invites all 1000 employees to participate and aims for a sample of 200 men and 200 women. what method of sampling is this?
This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.
Given that,
A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.
A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata
Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.
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Please answer <3
A line passes through the points (-5,10) and (0,-10). What is its equation in slope-intercept form?
y=__x+___
Answer:
The equation for the slope-intercept form is y = 4x - 10
Hope this helps!
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] Equation = y = mx + b
The two points given are ( -5, 10 ) and ( 0, -10 ).
Putting in the values gives you [tex]\frac{-10-10}{0-(-5)} = \frac{-20}{5} =-4[/tex].
y = 4x + b, to find b, insert one of the points:
-10 = 4(0) + b -> -10 = 0 + b, b = -10
Putting it all together gives you y = 4x - 10
Write 95% as a fraction or mixed number in simplest form.
Which statement is true?
O
The letter has rotation symmetry only.
0
The letter has both reflection and rotation symmetry.
The letter has neither reflection nor rotation symmetry,
The letter has reflection symmetry only.
The letter has reflection symmetry only. When one half of an object or form reflects the other half, this is known as reflection symmetry. The line where you cut is referred to as the line of symmetry, generating the two equal portions, and the two halves are reflections of one another.
What is reflection symmetry?Mirror symmetry, line symmetry, reflection symmetry, and mirror-image symmetry are all terms used in mathematics to describe symmetry with respect to a reflection. To put it another way, a figure with reflectional symmetry is unaffected by reflection. There is a symmetry line or axis in 2D and a symmetry plane in 3D.
A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.
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Question 3(Multiple Choice Worth 6 points)
(02.07 MC)
What are the solutions of 2x² + 3x= -8?
The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.
What is a quadratic equation?
A second-degree algebraic equation is a quadratic equation in x.
[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.
To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]
Given, [tex]2x^{2} +3x=-8\\[/tex]
or, [tex]2x^{2} +3x+8=0[/tex]
Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation [tex]ax^{2} +bx+c=0[/tex] , we get
[tex]a=2, b=3, c=8[/tex]
Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]
or, [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]
Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]
Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].
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a/4 - 5/6 = -1/2
URGENT!
ACTUALLY DO THE MATH
Get it right and ill make the first person the brainiest!
Answer:
a = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a}{4}[/tex] - [tex]\frac{5}{6}[/tex] = - [tex]\frac{1}{2}[/tex]
multiply through by 12 ( the LCM of 4, 6 and 2 ) to clear the fractions
3a - 10 = - 6 ( add 10 to both sides )
3a = 4 ( divide both sides by 3 )
a = [tex]\frac{4}{3}[/tex]
Answer:
[tex]a=\frac{4}{3}[/tex]
Step-by-step explanation:
Move all terms not containing [tex]a[/tex] to the right side of the equation.
Add [tex]\frac{5}{6}[/tex] to both sides of the equation.
[tex]\frac{a}{4}=-\frac{1}{2} +\frac{5}{6}[/tex]
To write [tex]-\frac{1}{2}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex].
[tex]\frac{a}{4}=-\frac{1}{2}*\frac{3}{3} +\frac{5}{6}[/tex]
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
[tex]\frac{a}{4}=-\frac{3}{2*3} +\frac{5}{6}[/tex]
[tex]\frac{a}{4}=-\frac{3}{6} +\frac{5}{6}[/tex]
Combine the numerators over the common denominator.
[tex]\frac{a}{4}=\frac{-3+5}{6}[/tex]
Add [tex]-3[/tex] and [tex]5[/tex] .
[tex]\frac{a}{4}=\frac{2}{6}[/tex]
Cancel the common factor of [tex]2[/tex] and [tex]6[/tex].
Factor [tex]2[/tex] out of [tex]2[/tex].
[tex]\frac{a}{4}=\frac{2(1)}{6}[/tex]
[tex]\frac{a}{4}=\frac{2*1}{2*3}[/tex]
Cancel the common factor.
[tex]\frac{a}{4}=\frac{1}{3}[/tex]
Multiply both sides of the equation by [tex]4[/tex].
[tex]4\frac{a}{4} =4(\frac{1}{3})[/tex]
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of [tex]4[/tex].
[tex]a=4(\frac{1}{3})[/tex]
Simplify the right side.
Combine [tex]4[/tex] and [tex]\frac{1}{3}[/tex]
[tex]a=\frac{4}{3}[/tex]
if Richard correctly answered 52 questions on an exam that had 65 questions , what percent did he get
The percentage that Richard get is 8%
How to determine the percentage he got?The statement can be interpreted as:
He answered 52 correctly from a total of 65 questions
From the above statement, we have the following parameters
Dividend = 52
Divisor = 65
The percentage is then calculated as
Percentage = Dividend/Divisor x 100%
Substitute the known values in the above equation
So, we have
Percentage = 52/65 x 100%
Evaluate the quotient
Percentage = 0.8x 100%
Evaluate the product
Percentage = 8%
Hence, the percentage is 8%
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state how the 2 triangles are congruent? SSS AND SAS!! hello!!!
Answer:
SAS
Step-by-step explanation:
We now that 2 sides are congruent because of the congruent marker, and the bases of the triangles are the same, meaning they are congruent. And we also have a congruent pair of angles. So we can tell if they are congruent by using the SAS theorem.
-Hope this helped
