Answer:
ABCDE is a regular pentagon with congruent diagonals BE and BD. a) Justify AABE = ACBD with a test for congruent triangles. b) Name a pair of congruent quadrilaterals.
The present age of Madison is 1027 years and that of his mother is 3080 years (rounded off to nearest whole numbers), solved using the linear equation in one variable: (x + 614) + (3x + 614) = 5334, where x represents the present age of Madison.
What are linear equations in one variable?Linear equations in one variable are the linear relationship between two algebraic expressions not involving more than one variable throughout the equation.
How to solve the question?In the question, we are informed that the present age of Maison's mother is 3 times that of Madison. After 614 years, the sum of their age will be 5334 years.
We are asked to determine their present ages.
We assume the present age of Madison to be x years.
Therefore, the present age of Madison's mother = 3x years {3 times that of Madison}.
Now, after 614 years, both of their ages will increase by 614 years.
Therefore, age of Madison after 614 years = x + 614 {Present + 614}.
Age of Madison's mother = 3x + 614 {Present + 614}.
We are given that after 614 years, the sum of their ages will be 5334.
This can be represented by the linear equation in one variable:
(x + 614) + (3x + 614) = 5334
This linear equation in one variable can be simplified and solved in the following way:
or, 4x + 1228 = 5334 {Simplifying},
or, 4x + 1228 - 1228 = 5334 - 1228 {Subtracting 1228 from both sides}
or, 4x = 4106 {Simplifying}
or, 4x/4 = 4106/4 {Dividing both sides by 4},
or, x = 1026.5 {Simplifying}.
Therefore, the present age of Madison = x = 1026.5 = 1027 years (nearest whole number).
The present age of Madison's mother = 3x = 3*1026.5 = 3079.5 = 3080 years (nearest whole number).
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Which expressions are equivalent to the one below? Check all that apply.
49x
The equivalent expressions are (b) (7 * 7)^x , (c) 7^x * 7^x and (e) 7^(2x)
How to determine the equivalent expressions?The expression is given as:
49^x
Express 49 as 7 * 7
(7 * 7)^x ---- option (b)
Express 7 * 7 as an exponent
7^(2x) ---- option (e)
Express 2x as x + x
7^(x +x)
Expand
7^x * 7^x --- option (c)
Hence, the equivalent expressions are (b), (c) and (e)
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HELP
A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 56 miles north of the transmitter to a second city 58 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Given the radius of 50 miles and the line joining the cities at (0, 56) and (58, 0), the transmitter signal can be picked during 59.24 miles of the drive.
How can the duration of signal reception be found?Radius of broadcast of the transmitter = 50 miles
Location of starting point = 56 miles north of the transmitter
Location of destination city = 58 miles east of the transmitter
Therefore we have;
Slope of the line joining the two cities
= 56 ÷ (-58) = -0.966
Which gives the equation of the line as follows;
y = -0.966•x + 56
The equation of the circle is;
[tex] {x}^{2} + {y}^{2} = {50}^{2} [/tex]
[tex] {x}^{2} + { ( - 0.966x + 56)}^{2} = {50}^{2} [/tex]
1.933156•x^2 - 108.192•x + 636 = 0
Which gives;
x = 6.67 or x = 49.29Therefore;
When x = 6.67, we have;
y = -0.966 × 6.67 + 56 = 49.56When x = 49.29, we have;
y = -0.966 × 49.29 + 56 = 8.4The length of the drive, during which the driver can pick the signal, l, is therefore;
l = √((49.56-8.4)^2 + (49.29-6.67)^2) = 59.24 miles
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A student guesses randomly on a 15-question multiple-choice quiz, where each question has 6 options. What is the probability that the student answers all questions correctly?
The probability that the students gets all the questions correctly is (1/6)^15 .
What is the probability?Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability = (number of correct options/ total number of options)^number of questions
(1/6)^15
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f(x)=5x/x-25 asymptotes and state the end behavior of the function
The asymptote of the function given in the task content is the line; x = 25.
What is the asymptote of the function?It follows from the task content that the function given is a rational function and hence, the asymptote of the function is the X-value which renders the function undefined in which case, the denominator is equal to 0.
x - 25 = 0.
x = 25.
The end behaviour of the functions graph is that it approaches the line x = 25 but never touches the line.
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If n is an integer and 2^n is a factor of 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9, what is the greatest possible value of n?
A) 6
B) 7
C) 8
D) 9
Answer:
7
Step-by-step explanation:
2 = 2
4 = 2²
6 = 2 * 3
8 = 2³
adding the exponents of 2, we get 1+2+1+3 = 7
which statement is true?
12/13 < 36/30
13/17>24/28
Answer:
The first one: 12/13 > 36/30
Step-by-step explanation:
The first one would be correct as 12/13 is less than 36/30.
To explain why 13/17 is actually less than 24/28, see below:
So when comparing fractions, we must follow steps.
Step One: convert mixed numbers to a fraction, if there are any
There are not mixed numbers to compare, so we can move to the next step.
Step Two: find the least common denominator of the two fractions
Least common denominator = 476
Check out our least common denominator calculator for help on finding this.
Step Three: rewrite each fraction to an equivalent fraction using the denominator 476
To do this, start by dividing 476 by the denominator of the first fraction. Next, multiply the result by the numerator to find the new numerator. To rewrite, put the new numerator over 476. Repeat this for the second fraction
364/476 408/476
Step Four: compare the numerators
At this point, to compare the fractions, we can simply compare the numerators to see which is larger
364<408
Step Five: rewrite each fraction as the original fraction
13/17<24/28
Therefore, the first statement (12/13 > 36/30) is true.
Answer:
12/13 < 36/30
Step-by-step explanation:
There are many ways to compare numbers. One way is to compare them to some value that lies between. Another is to consider their difference from a value that does not lie between.
12/13 vs 36/30In the first fraction, 12 < 13, so the value of the fraction is less than 1:
12/13 < 1
In the second fraction, 36 > 30, so the value of the fraction is greater than 1:
1 < 36/30
Then the order of the fractions is ...
12/13 < 1 < 36/30
12/13 < 36/30 . . . . . the given order is True
13/17 vs 24/28We notice the difference between numerator and denominator is 4 in each case, so we can write each fraction as a difference from 1:
(13/17) vs (24/28)
= (1 - 4/17) vs (1 -4/28) . . . . . fractions rewritten
= -4/17 vs -4/28 . . . . . . . . . subtract 1 from both
The first fraction, 4/17, has a smaller-value denominator, so its magnitude is larger than that of the fraction 4/28. In other words, the ordering of these fractions is ...
-4/17 < -4/28
1 -4/17 < 1 -4/28 . . . . . . add 1 to both sides
13/17 < 24/28 . . . . . the given order is False
__
Additional comment
One sort of "no brainer" way to compare the fractions is to multiply them by the product of their denominators. This looks like "cross multiplication" where each numerator is multiplied by the opposite denominator. As long as you keep the numerators in the same relative places, the comparison symbol will be the correct one for the fractions.
12/13 vs 36/30 ⇒ (12·30) vs (13·36) ⇒ 360 < 468
The left fraction is smaller than the right fraction.
Similarly, ...
13/17 vs 24/28 ⇒ (13·28) vs (17·24) ⇒ 364 < 408
The left fraction is smaller than the right fraction.
__
Here, we have used the fractions "as is." In each case, the fraction on the right could be reduced, possibly making the comparison easier.
The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3.
The prime factorization of 18 is 2 x 3 x 3.
What is the prime factorization?A prime number is a number that is only divisible by 1 and itself. An example is 11. The factors of a number are numbers that divide another number without leaving any remainder. For example, a factor of 10 is 2. The prime factor of a number is the factors of a number that are prime numbers.
The factors of 18 = 1, 2, 3, 6, 9, 18
Prime factors = 1, 2, 3
Prime factorisation = 2 x 2 x 3
Here is the complete question:
The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3. What is the prime factorization of 18? 2 times 3 2 times 9 2 times 3 times 3 2 times 3 times 9
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Chloe’s Cafe bakes croissants that it sells to local restaurants and grocery stores. The average costs to bake the croissants are $0.40 for 2,000 and $0.35 for 4,000.If the total cost function for croissants is linear, what will be the average cost to bake 3,200?
Answer: First step is to determine the total cost
Total cost at 2,800
=$0.80 ×2,800
=$2,240
Total cost at 5,600
=$0.75 × 5,600
=$4,200
Second step is to determine the Variable cost per unit
Variable cost per unit=$4,200-$2,240
Variable cost per unit=$1,960
Variable cost per unit=5,600-2,800
Variable cost per unit=2,800
Variable cost per unit=$1,960/2,800
Variable cost per unit=$0.70
Now let determine the average cost
Average cost=$0.70×4,800+[($0.80×2800)-(2,800 ×$0.70)]
Average cost=$3,360+($2,240-$1,960)
Average cost=$3,360+$280
Average cost=$3,640
Average cost =$3,640/4,800
Average cost=$0.76
In conclusion What will be the average cost to bake 4,800 is $0.76
Step-by-step explanation:
Your classmate tells you the details of the great deal he got on his mortgage: 30 year 3.5% fixed rate with 10% down payment how much is he going to borrow to buy the house (assuming he only has the money to make the down payment from the previous question)
Assuming he has the money to make the down payment, my classmate will borrow 90% of the home price.
What is a down payment?A down payment is the upfront payment or an initial portion of the total purchase price of expensive property.
It is required that the buyer of a mortgaged property deposits this initial portion before taking the mortgage for the balance.
Data and Calculations:Mortgage period = 30 years
Interest rate = 3.5% fixed
Down payment = 10%
Balance (Mortgage) = 90% (1 - 10%)
Thus, assuming he has the money to make the down payment, my classmate will borrow 90% of the home price.
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The diameter of a proton is about 1.9 cross times 10 to the power of short dash 15 end exponent meters. A hydrogen atom has an overall length of 100,000 times (or 1 cross times 10 to the power of 5 times) the diameter of a proton.
What is the length of the hydrogen atom, in meters, if it were written in scientific notation?
A. 1.9 x 10 (15 exponent)
B. 1.9 x 10 (-15 exponent)
C. 1.9 x 10 (-8 exponent)
D. 1.9 x 10 (-12 exponent)
Using scientific notation, the length of the hydrogen atom is given as follows:
[tex]1.9 \times 10^{-10}[/tex]
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
The diameter of a proton is given by:
[tex]1.9 \times 10^{-15}[/tex].
The hydrogen atom has an overall length of 100,000 times the diameter of the proton, hence the length is given by:
[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]
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Choose the equation that satisfies the data in the table.
HELP!!!!
The equation of the line represented by the table in slope intercept form is; y = ²/₁₅x + 2
How to solve equation in slope intercept form?The formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The y-intercept will occur when x = 0. Thus, from the table, it is clear hat the y-intercept will be c = 2.
Let us find the slope using the first two points;
m = (2 - 0)/(0 - (-15))
m = 2/15
Thus, the equation is;
y = ²/₁₅x + 2
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Use the function below to find F(4).
Hello !
[tex]F(x) = 5 \times ( \frac{1}{3} ) {}^{x} [/tex]
[tex]F(4) = 5 \times ( \frac{1}{3}) {}^{4} = 5 \times \frac{1 {}^{4} }{3 {}^{4} } = 5 \times \frac{1}{81} = \frac{5}{81} [/tex]
Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana.
Explanation: Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.
Josiah and Chana travel at constant and different speeds.
The point F indicates that after 25 seconds Josiah is 60 meters from the starting line but behind Chana How can the what the the point F represent be known?Josiah's head start = 10 meters from the start
Josiah's speed = 2 m/s
Chana's speed = 3 m/s
Expressing the distance traveled as an equation, we have;
D = d + s × t
Where;
D = The distance covered
d = The distance from the starting line the runner starts
s = The speed of the runner
t = The time spent running
For Josiah, we have;
D = 10 + 2•t (line a)
For Chana, we have;
D = 0 + 3•t = 3•t (line b)
The above equations are straight line equations.
The point F is on line a, which shows Josiah distance after 25 seconds which is 60 meters. The corresponding point on line b, Chana's distance after 25 minutes is 75 meters.
Therefore;
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Answer:
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Step-by-step explanation:
I got it right on khan.
Which value is equivalent to 48 ÷ ((2 + 6) × 2) − 1? Group of answer choices 2 -12 3 3 1/5
The solution to the given expression is 2
Solving equationGiven the equation 48 ÷ ((2 + 6) × 2) − 1
Using PEMDAS
48 ÷ ((8) × 2) − 1
48÷(16) - 1
3 - 1
2
Hence the solution to the given expression is 2
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Solve the proportion.
2/3/4 = 10
LO
x = [?]
Answer:
x = 6
Step-by-step explanation:
We want to find x,
[tex]\frac{3}{5} = \frac{x}{10}[/tex]
to get x alone, we multiple both side by 10
[tex]\frac{3}{5} * 10 = \frac{x}{10} *10[/tex]
[tex]\frac{30}{5} = x[/tex]
30 divided by 5 is 6
Check:
We can see that 5 x ____ = 10 where ____ is 2
5 x 2 = 10
so 3 x 2 = 6
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Hi, can someone please help me? trying to graduate :(
Write an equation in slope-intercept form of the line that passes through the point (-6,-5) with slope 6
The equation of the line in slope-intercept form that passes through the point (-6, -5) with a slope of 6 is y = 6x + 31. The correct answer is option (D).
Given that the line passes through the point (-6, -5) with a slope of 6, we can plug these values into the equation to find the y-intercept (b).
Using the point-slope form of the equation:
y - y₁ = m(x - x₁)
Substitute (-6, -5) and the given slope (m = 6):
y - (-5) = 6(x - (-6))
y + 5 = 6(x + 6)
Now, let's simplify the equation:
y + 5 = 6x + 36
To get the equation in slope-intercept form (y = mx + b), isolate y:
y = 6x + 36 - 5
y = 6x + 31
Thus, the correct answer is option (D).
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{(3,-2), (4,-2),(5,-2), (6,-2)} is this a function
Answer:
{(3,-2), (4,-2),(5,-2), (6,-2)} this relation is not a function.
A manufacturing company has a machine that can make 16,200 bolts during an 8-hour shift. What is the constant of proportionality between the number of bolts and the number of hours?
A
1,620
B
2,025
C
2,314
D
2,700
The constant of proportionality between the number of bolts and the number of hours is 2025.
Option B is the correct answer.
What is the constant of proportionality between the number of bolts and the number of hours?Proportional relationships are relationships between two variables where their ratios are equivalent.
Using a ∝ b then a = kb
Where k is the proportionality constant.
Given that;
Number of bolts a = 16200Number of hours b = 8proportionality constant k = ?We substitute into our equation.
a = kb
16200 = k × 8
k = 16200 / 8
k = 2025
The constant of proportionality between the number of bolts and the number of hours is 2025.
Option B is the correct answer.
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Answer:
B
Step-by-step explanation:
A textbook store sold a combined total of 460 physics and math textbooks in a week. The number of math textbooks sold was 62 less than the number of physics textbooks sold. How many textbooks of each type were sold?
Number of physics textbooks sold was 261 & number of maths textbooks sold was 199.
Let, the number of physics textbooks sold = x
According to the question,
The number of math textbooks sold was 62 less than the number of physics textbooks sold.
So, Number of maths textbooks sold = x-62
The textbook store sold a combined total of 460 physics and math textbooks in a week.
So, the equation becomes,
(x-62)+x = 460
⇒ x-62+x = 460
⇒ 2x-62 = 460
⇒ 2x = 460+62
⇒ 2x = 522
⇒ x = 522/2
⇒ x = 261
So, 261 physics textbooks were sold
(261-62) = 199 maths textbooks were sold.
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Which formula do i use for this? it seems i used the wrong one.
The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.
How to calculate the payment?Mathematically, annuity can be calculated by using this formula:
[tex]A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }][/tex]
Given the following data:
Time, t = 11 years.Number of times compounded (quarterly), n = 4.Present value, A = $13,000.Interest rate, r = 3.6% = 0.036.Substituting the given parameters into the formula, we have;
[tex]13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P[/tex]
P = 13000/53.6932898522
P = $242.12.
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Complete Question:
The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?
Determine the units digit (ones digit) of the counting number represented by the exponential expression.
4^800
The units digit of the given exponential expression will be 6
Determining the units digit of an exponential expressionFrom the question, we are to determine the units digit of the given exponential expression
The given exponential expression is
4⁸⁰⁰
We know that
4¹ = 4
4² = 16
4³ = 64
4⁴ = 256
4⁵ = 1024
4⁶ = 4096
From above, we can observe that the units digit of the odd exponents is 4 while the units digit of the even exponents is 6.
The exponent of the given expression is 800. 800 is an even number.
Hence, the units digit of the given exponential expression will be 6
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Which one of the following situations could be represented by a linear function?
A. Number of bacteria is doubled every day.
B. Jacob drives a car and covers the same distance for every hour.
The integer having absolute value 10 are_________?
Marina paid $16.95 for a sweater on sale which is 65% of the original cost. How much did the sweater cost originally
Answer:
$26.08.
Step-by-step explanation:
[tex]1. \ \frac{16.95}{0.65} =\frac{x}{1};[/tex]
2) x=16.95/0.65≈$26.076923076923076923
Complete the following, using ordinary interest. (Use Days in a year table.) (Do not round intermediate calculations. Round the "Interest" and "Maturity value" to the nearest cent.)
principal 1,000 interest rate 8% Date borrowed March 8 Date repaid June 9
Exact time? interest? Maturity value?
The exact time is 93 days
The interest is $20.38
The maturity value is $1020.38
What is the interest and the maturity value?The interest is a function of the time, amount borrowed and the interest rate.
Interest = amount borrowed x time x interest rate
Time = June 9 - March 8 = 93 days
1000 x 0.08 x (93/365) = $20.38
Maturity value = 1000 + 20.38 = $1020.38
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A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).
Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+12πr . What is the domain of A(r) ? In other words, for which values of r is A(r) defined?
Part b: Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A . This is the inverse function to A(r) , i.e., to turn A as a function of r into r as a function of A .
r(A)=
Part c: If the surface area is 175 square inches, then what is the radius r ? In other words, evaluate r(175) . Round your answer to 2 decimal places.
The radius is ? inches if the surface area is 175 square inches
The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
A cylinder (round can) has a circular base and a circular top with vertical sides in between.
Let r be the radius of the top of the can and let h be the height.
The surface area of the cylinder (A) is given as
A=2πr² + 2πrh
Part A: Assume that the height of your cylinder is 6 inches.
Consider A as a function of r, so we can write that as
A(r) = 2πr² + 12πr
Then the domain of A(r) will be (0, ∞).
Part B: Continue to assume that the height of your cylinder is 6 inches.
Then the inverse function to A(r) will be
r = 2π[A(r)]² + 12πA(r)
Part C: If the surface area is 175 square inches.
Then the radius will be
175 = 2πr² + 12πr
r² + 6r – 27.866 = 0
r = 3.07, -9.07
Then the radius will be 3.07 inches.
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If a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'?
(1, –5)
(–4, –10)
(–3, –12)
(3, –12)
The coordinates of B' are 3 and -12. so option D is correct (3, -12)
How to find the coordinates of B'?The point P(x, y) may undergo translation to form P' by using a defined translation rule :
If given the rule T(a, b) synch that P undergoes translation on T; then we will have P'(x+a; y+b)
Therefore,
The point B has its coordinates as B(1, - 5)
Translation rule, T(2, - 7) then the coordination of B after undergoing transformation according to T2;
B(1, - 5) - - - > T(2, - 7) - - - - > B'(1+2 ; - 5+-7)
= B'(3, -12)
Hence, the coordinates of B' are 3 and -12. so option D is correct.
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Answer:
(D) (3, –12)
Step-by-step explanation:
If a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'? The answer is (3, –12).
You need a 25% alcohol solution. On hand, you have a 225 mL of a 35% alcohol mixture. How much pure water will you need to add to obtain the desired solution?
You will need____ mL of pure water to obtain___ mL of the desired 25% solution.
You will need 252 mL of pure water to obtain 0.25 mL of the desired 25% solution.
If we add X amount of water to the solution, the total amount of solution is 375+X.
And that must be 25%.
What is the amount of solute in the current solution?
The amount of solute in the current amount of solution is
0.6(375)=225.
That amount won't change by adding water.
So we set up the equation so that the amount of solute divided by the new total amount of solution equals 25%.
225/(375+X)=0.25
cross multiply and solve
225/0.25=(375+X)
900-375=X
X=525
The pure water will you need to add to obtain the desired solution is 525.
Then we check 225/(375+525)=0.25.
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what are the angles of rotation less than 360 degrees for figure. sorry dont have a picture.
Shape; perfect pentagon, sides are all equal, no uneven sides
Line of symmetry; 5
think you can help me out a bit?
Thank you
The Angle of rotation of the given regular pentagon after undergoing rotational transformation is; 72°
How to find the angle of rotation?
We are told that the image is a perfect pentagon that all its' sides are all equal with no uneven sides.
Now, A figure is said to have rotational symmetry if it looks exactly the same after rotating it some angle less than 360° which is a full rotation.
Now, a regular pentagon will have a rotational symmetry of order 5 because it will look the same after 5 turns.
Thus;
Angle of rotation = 360/5
Angle of rotation = 72°
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look at the picture
The end behaviour of the function is When x ---> ∞ , f(x) ---> -∞ , when x ---> -∞ f(x) ----> ∞ , Option D is the correct answer.
What is a Function ?A function is a mathematical statement that related the independent and the dependent variable.
The function given is
f(x) = [tex]\rm -2 \sqrt[3]{x}[/tex]
To understand the end behaviour the graph is plotted
When x ---> ∞ , f(x) ---> -∞
when x ---> -∞ f(x) ----> ∞
Therefore Option D is the correct answer.
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