By power properties the exponential expression [tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex] is only equivalent to [tex]8^{2\cdot m-m^{2}}[/tex]. (Correct choice: A)
What expression is equivalent to a exponential function?
In this question we must apply power properties to prove if a given expression have at least one equivalent. Now we proceed to show alternative forms:
[tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex]
[tex]8^{2\cdot m-m^{2}}[/tex]
By power properties the exponential expression [tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex] is only equivalent to [tex]8^{2\cdot m-m^{2}}[/tex]. (Correct choice: A)
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Solve x2 – 6x + 9 = 0 by completing the square.
A)
x = 3
B)
x = –3
C)
x = 3 and x = –3
D)
x = 1 and x = 9
Answer:
A.) x = 3
Step-by-step explanation:
This equation is an example of a perfect square quadratic. This means that the quadratic can be simplified into two of the same factors.
How can you factor the equation? The simplest way is to ask yourself, which two numbers multiply to 9 while also adding to -6? The two numbers which satisfy this question are -3 and -3. Knowing this, you can construct your factors, simplify, and then solve for "x".
x² - 6x + 9 = 0 <----- Expanded equation
(x - 3)(x - 3) = 0 <----- Factored equation
(x - 3)² = 0 <----- Combine both factors
x - 3 = 0 <----- Take square root of both sides
x = 3 <----- Add 3 to both sides
A line has a y-intercept of 0 and a slope of 7. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=7x
Step-by-step explanation:
The equation of the with a slope of m and a y-intercept of b is y=mx+b.
If quadrilateral abcd is an isosceles trapezoid, which statements must be true? select three options bc ∥ ad bd ⊥ ac ba ≅ cd be ≅ ed ∠cba ≅ ∠bcd
The true statements among the given options are written below
bc || ad
ba ≅ cd
∠cba ≅ ∠bcd
In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.
Given that quadrilateral abcd is a isosceles trapezoid.
In the given trapezoid abcd
bc || ad ( pair of parallel sides )
So this is correct.
ba ≅ cd ( For an isosceles trapezoid legs are equal)
So this is correct
∠cba ≅ ∠bcd (According to the property of isosceles trapezoid )
So this is correct.
Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct
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is 2(x+4)=4x+3-2x+5 no solution or infinite solutions?
Answer:
This is always true so there are infinite solutions
Step-by-step explanation:
2(x+4)=4x+3-2x+5
To find the solution, the first step is to distribute
2x+8 =4x+3-2x+5
Combine like terms
2x+8= 2x+8
Subtract 2x from each side
2x+8 -2x = 2x+8-2x
8 = 8
This is always true so there are infinite solutions
What's the range of the graph? I have a menu that I could choose from and this is the option that I have.
Answer:
-∞ < x < 4
Step-by-step explanation:
→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.
I will give brainiest to who ever can copy and answer this math problem first : 12342345791 + 3214567349=
Answer:
15556913140
Step-by-step explanation:
From the triangle below, if AD = 5 and CD = 20, find the length of side BD.
Select one:
a.
10
b.
28
c.
7
d.
25
Answer: 10
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{BD}{5}=\frac{20}{BD}\\\\(BD)^2 = 100\\\\BD=10[/tex]
The length of side BD, given that AD = 5 and CD = 20 is 10 (Option A)
Data obtained from the questionLength of side AD = 5 Length of side CD = 20Length of side BD =?How to determine the length of side BDSince the triangles are similar, we can obtain the length of side BD as illustrated below:
CD / BD = BD / AD
20 / BD = BD / 5
Cross multiply
BD × BD = 20 × 5
BD² = 100
Take the square root of both sides
BD = √100
BD = 10
Thus, the length of side BD is 10
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also need help with this question
Answer:
C
Step-by-step explanation:
In option c, the first block is divided into 3 pieces where 2 parts are shaded whereas the second block is divided into 6 pieces where 3 parts are shaded
For both to be equivalent, both of them should be the same
2/3 = x/6
x = 4
4 pieces should be shaded in in the second block to be equal to the first one, in the diagram only 3 parts are shaded thus the answer is c
Find a in degrees.
√58
3
7
α
Answer:
23.20
Step-by-step explanation:
join my stream for an explanation
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Answer:
α ≈ 23.20°
Step-by-step explanation:
given all 3 sides of the triangle , then any of the trig ratios may be used, that is sine, cosine or tangent to find α
tanα = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{7}[/tex] , then
α = [tex]tan^{-1}[/tex] ( [tex]\frac{3}{7}[/tex] ) ≈ 23.20° ( to the nearest hundredth )
or
sinα = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{58} }[/tex] , then
α = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )
or
cosα = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{\sqrt{58} }[/tex] , then
α = [tex]cos^{-1}[/tex] ( [tex]\frac{7}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )
Select the correct answer. The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number? A. The equation that represents this situation is 10 − x = -18. The second number is 28. B. The equation that represents this situation is 10 + x = -18. The second number is -28. C. The equation that represents this situation is x − 10 = -18. The second number is -8. D. The equation that represents this situation is -10 + x = -18. The second number is -8.
Using a system of equations, the correct statement is given as follows:
B. The equation that represents this situation is 10 + x = -18. The second number is -28.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The numbers are x and y, and their sum is -18, hence:
x + y = -18.
The number y is 10, hence:
x + 10 = -18.
x = -18 - 10 = -28.
Which means that option B is correct.
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For what values of x will the function f(x) = 3x² + 13x - 10 equal zero?
Answer:
x = - 5 , x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the values of x that make f(x) zero are the zeros
to find the zeros let f(x) = 0 , that is
3x² + 13x - 10 = 0
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 10 = - 30 and sum = + 13
the factors are + 15 and - 2
use these factors to split the x- term
3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )
3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term
(x + 5)(3x - 2) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]
New flowers are being planted
in the school garden. There
are 45 dandelions for each row
in the 15 row garden. How
many dandelions are being
planted?
Answer:
45 dandelion × 15 rows= 675
Ted borrowed $5,600 from his bank for 4 months with interest at 9%. ted paid the note in full on its due date. how much was the check he gave to the bank for payment?
Ten gave the check of $5768 to the bank for payment.
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a borrower will never have to pay interest on the interest already accumulated because a creditor will only pay interest on the principal amount.
Formula for simple interest is;-
Simple interest = (principal amount×rate of interest×time duration in years)/100
S.I = (P×R×T)/100
Calculation of the total amount paid by Ted to the bank-
The principal amount is $5,600.
The rate of interest is 9%.
Time duration is 4 months equals 4/12 = 1/3 years.
S.I = (5,600×9×1)/(3×100)
S.I = 168
The simple interest on amount is $168.
Thus, the total amount is S.I + principal amount
Total amount = 168 + 5600
= 5768
Therefore, the total amount paid by the Ted to the bank is $5768.
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Juan, Mary, Celia, and Mark work as information specialists at a high tech company. They each spent a certain amount of time fixing a problem with the database. Out of the total number of hours all the workers spent, what percent of that time is Celia's?
A) 17%
B) 18%
C) 21%
D) 25%
Answer:
B) 18%
Step-by-step explanation:
100% - 36% - 29% - 17% = 18%
Answer:
the answer would be B) 18%
What is the midpoint of the segment shown below?
A. (-15, -15)
B. (-15,-15)
c. (-1/5, -15)
D. (-15-15)
The midpoint of the segment is (-15/2, -15/2)
How to determine the midpoint?The complete question is in the attached image
The points are given as:
(-8, -7) and (-7, -8)
The midpoint is calculated as:
(x,y) = 1/2 * (x1 + x2, y1 + y2)
So, we have:
(x,y) = 1/2 * (-8 - 7, -7 - 8)
Evaluate the difference
(x,y) = 1/2 * (-15, -15)
Evaluate the product
(x,y) = (-15/2, -15/2)
Hence, the midpoint of the segment is (-15/2, -15/2)
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Find the missing lengths in the triangle above
ER=
IE=
Step-by-step explanation:
IR = 9√3
E = 60°
I = 30°
R = 90°
• Find ER.
ER/sin(I) = IR/sin(E)
ER/sin(30°) = 9√3/sin(60°)
ER/(1/2) = 9√3/(1/2 √3)
ER/(1/2) = (9√3 . 2)/√3
ER/(1/2) = 18√3/√3
ER/(1/2) = 18 → IR/sin(E)
ER = 18 . 1/2
ER = 9 is the answer
• Find IE (There are 2 ways).
First, using a Sinus Rule.
IE/sin(R) = IR/sin(E)
IE/sin(90°) = 9√3/sin(60°)
IE/1 = 9√3/(1/2 √3)
IE = (9√3 . 2)/√3
IE = (18√3)/√3
IE = 18 is the answer
Second, using a Pythagoras Theorem.
IE = √(IR² + ER²)
IE = √((9√3)² + 9²)
IE = √(81.3 + 81)
IE = √(243 + 81)
IE = √324
IE = 18 is the answer
What is the solution to the system of equations?
Plug the second equation (the one already solved for y) into the first equation
2x - (2x + 3) = 7
2x - 2x - 3 = 7
-3 = 7
Since the 2x's canceled out and left a false statement, this system of equations has no solution.
Hope this helps!
(10 - d)^0
for d = 11
Answer:
1
Step-by-step explanation:
any number (except zero) raised to the 0th power is equal to 1.
Answer:
1
Step-by-step explanation:
(10 - 11)⁰ = ( -1)⁰ = 1
We have a⁰ = 1
simplify (x^2+2x+3)-(x^2+3x+2)
Answer:
- x + 1
Step-by-step explanation:
(x² + 2x + 3) - (x² + 3x + 2) ← multiply terms inside parenthesis by - 1
= x² + 2x + 3 - x² - 3x - 2 ← collect like terms
= - x + 1
The cube of the sum of a number and 5.
Answer:
[tex](x+5)^{3}[/tex]
Step-by-step explanation:
Hope this helps
The expression for the word problem is ( x + 5 )².
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given word problem is the cube of the sum of a number and 5. The expression will be formed as below:-
Let the unknown number be x.
E = ( x + 5 )²
Therefore, the expression for the word problem is ( x + 5 )².
The complete question is given below:-
The cube of the sum of a number and 5. Write the mathematical expression.
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The letters $A, B$ and $C$ are used to form every possible three letter ``word.'' When these ``words'' are arranged in alphabetical order and numbered so that $AAA$ is Word $1$ and $CCC$ is Word $27$, what number will correspond to the position of word $BAB$ on the list?
The number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.
What number will correspond to the position of word $BAB$ on the list?As evident in the task content, by observation, if follows that since; $AAA$ is Word $1 and $CCC$ is Word $27$.
Then, it can be inferred that A = 1 , B = 2 and C = 3.
On this note, the number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.
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An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b.
Which statements about finding the area of the equilateral triangle are true? Select three options.
The apothem can be found using the Pythagorean theorem.
The apothem can be found using the tangent ratio.
The perimeter of the equilateral triangle is 15 cm.
The length of the apothem is approximately 2.5 cm.
The area of the equilateral triangle is approximately 65 cm2.
Options A,B and D. The correction about the area of the triangle are
The apothem can be found using the Pythagorean theorem.The apothem can be found using the tangent ratio.The length of the apothem is approximately 2.5 cm.How to solve for the length of the Apothem using the Pythagoras theoremFirstly this is an equilateral triangle
3 of the sides have the length of 8.7cm
b = half of 8.7
= 4.35cm
To get A we have
a² + b² = c²
a² + 4.35² = 5²
When we solve this out we would have
a² = 25 - 18.9225
a ≈ 2.5 cm.
Hence we have proved that the first option is correct.
For B,
In an equilateral triangles, each of the angles = 60 degrees
60/2 = 30 is the angle that is made from the base
using tangent ratiosa / 4.35 = tan 30
then a = 4.35 tan 30
This would also give us an approximate of 2.5
For D
The calculations we have done based on the statements in A and B shows that D is correct as 2.5.
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Given: AB = DC, AC = DB
Prove: AABC= ADCB
Look at the proof. Name the postulate you would use to prove the two triangles are congruent.
Given: AB DC, AC = DB
Prove: AABC= ADCB
AB= DC
Given
AC DB
Given
BC BC
Reflexive Property
of Congruence
AABC ADCB
?
B
D
C
Answer:
by sss
Step-by-step explanation:
Make me a brain-list.The property of congruence:
ΔABC ≅ ΔDCB by the SSS criterion.
The correct option is the SSS postulate.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given information:
AB ≅ DC and AC ≅ DB.
The proof is given described as:
In triangle ABC and triangle DCB,
The two sides are congruent,
AB ≅ DC and AC ≅ DB ( As per the information provided).
And as per the diagram and reflexive property of congruence,
BC ≅ BC.
Therefore, ΔABC ≅ ΔDCB by the SSS criterion.
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What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (-3, 1)?
Oy-1= -(x+3)
Oy-1= -(x+3)
Oy-1= (x+3)
Oy - 1 = (x+3)
Answer:
The answer is B.
Step-by-step explanation:
I learned this last year.
Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)
Answer: < -4/5, 3/5>
This is equivalent to writing < -0.8, 0.6 >
======================================================
Explanation:
Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.
We have a right triangle with legs of 4 and 3. The hypotenuse is [tex]\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5[/tex] through use of the pythagorean theorem.
We have a 3-4-5 right triangle.
Therefore, the vector is 5 units long. This is the magnitude of the vector.
Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.
Therefore, we go from < -4, 3 > to < -4/5, 3/5 >
This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6
Side note: Unit vectors are useful in computer graphics.
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 4.20. A sample of 37 honors students is taken and is found to have a mean GPA equal to 4.30. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________.
The parameter to be tested is z.
We would set up the hypothesis test.
For the null hypothesis,
µ ≥ 4.2
For the alternative hypothesis,
µ < 4.2
It is a left tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 4.2
x = 4.3
σ = 0.4
n = 37
z = (4.3 - 4.2)/(0.4/√37) = 1.53
Looking at the normal distribution table, the probability corresponding to the z score is 0.933
The p value gotten is to the right of the normal curve. Since it is a left tailed test, we need the p value to the left of the curve. Therefore,
p = 1 - 0.933 = 0.067
Since alpha, 0.05 < than the p value, 0.067, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, there is no significant evidence that mean GPA of these graduates does not exceed 4.30
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68. REAL-WORLD APPLICATIONS
At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves n more customers during her shift?
Answer:
The linear equation for tip barista gets in a day is f(n)=0.5n+20.
Step-by-step explanation:
It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,
It is required to find how much will she have in her tip jar if she serves n more customers during her shift. m=0.5. Bases on this write the equation for n more customers.
Step 1 of 1
It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,
To solve this let f(n) is the total tip barista has in her tip jar after a day.
When n is equal to 0 , that barista has $20,
Then if barista make 0.5 from each customer, then for the linear function m=0.5,
Bases on this write the equation for n more customers,
[tex]$$f(n)=0.5 n+20 .$$[/tex]
There are 27000Ib of wheat to be transported, the transport company wants to know how many metric tonnes of wheat they would be transporting.
The quantity of wheat to be transported by the company in metric tonnes is; 1.224 metric tonnes.
How many metric tonnes of wheat is to be transported?Since it follows that 1 metric tonne is equivalent to 2205 lb. It therefore follows that the quantity which is equivalent to 2700lb to be transported is;
= 2700/2205 = 1.224
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Please answer correctly
Answer:
The answer is 6 and -6
Step-by-step explanation:
The given equation is
[tex]x^2 - kx + 9 = 0 ... (1)[/tex]
where a = 1. b = -k, c = a
since the equation (1) has equal roots
[tex]\Rightarrow b^2 - 4ac = 0 \newline\\\Rightarrow (-k)^2 - 4(1)(9) = 0\\ \newline\\\Rightarrow (k)^2 - 36 = 0 \newline\\\Rightarrow k^2 = 36 \newline\\\Rightarrow k = \pm 6[/tex]
Hence volume of k = 6, -6
In the diagram, O is the centre of the circle, BD = DC and PAB is a straight line. Prove that AD bisects the angle CAP.
Answer:
BAC=BDC(BDX)=30°
Step-by-step explanation:
We know that BD=OD.
But OD=OB= Radius of the circle.
Therefore
BD=OD=OB
BDO is equilateral triangle.
Angle DBO= 60°
Now let us take the intersecting point of CD and AB as X.
In triangle BDX,
BXD= 90°(BXD+BXC=180°, BXD+90°=180°, BXD=90°)
BXD+DBX+BDX=180°{Angle Sum Property}
90°+60°+BDX= 180°
BDX= 30°
We also know that,
BDC(BDX)= BAC (Angles lie on the same arc{BC} are equal in measure.
Therefore,
BAC=BDC(BDX)=30°