To find the age of the eldest son in a family where the father is 50 and has 8 sons with a total age sum of 186, and the youngest son is 3, one can determine the age difference between siblings and use the formula for the sum of an arithmetic series.
The question is asking us to determine the age of the eldest son, given that the sum of the ages of a 50-year-old father and his 8 sons is 186 years and the youngest son is 3 years old. Let's assume that the sons are born at equal intervals; we can denote the age difference between each son as 'd' years.
The sequence of the sons' ages forms an arithmetic series where the youngest son is 3 years old (the first term of the series, or 'a1'), and the eldest son's age will be 'a1 + 7d' (since there are 8 sons).
Since the sum of an arithmetic series is given by the formula 'n/2 * (a1 + an)', where 'n' is the number of terms, 'a1' is the first term and 'an' is the last term, we can set up the equation:
8/2 * (3 + (3 + 7d)) = 186 - 50 (subtract the father's age from the total sum).
This simplifies to 4 * (3 + 3 + 7d) = 136, or '4 * (6 + 7d) = 136'. Dividing both sides by 4, we get '6 + 7d = 34', which leads to '7d = 28' and thus 'd = 4'.
Therefore, the age of the eldest son will be '3 + 7*4', which equals 31 years old.
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Based on the ideal gas law, what is the volume, in liters, of a sample that contains 1,200 moles?
A. 6,000
B. 24,000
C. 36,000
D. 60,000
i dont understand please helpp asap
Which is the equation for AD?
The area of a rug, which is shaped like a rectangle,is 4x²+4x square feet. Factor this polynomial to find expressions for the dimensions of the rug
Final answer:
The expressions for the dimensions of a rectangular rug with an area of 4x²+4x square feet are 4x feet and (x + 1) feet after factoring the polynomial.
Explanation:
To find the expressions for the dimensions of the rug with an area of 4x²+4x square feet, we need to factor the polynomial. Factoring out the greatest common factor (GCF), we get:
4x² + 4x = 4x(x + 1).
This indicates that one dimension of the rug is 4x feet and the other dimension is (x + 1) feet. The rug can be visualized as a rectangle where one side is 4 times a certain length x, and the other side is that length plus one.
Aubrey says that the product 10x10x10x10 and 10x-10x-10
Answer:
Aubrey says that the product of 104 and 10–2 is 10–8. Is she correct? If not, explain why.
Yes, she is correct.
No, the exponent should be positive 8.
No, she multiplied the exponents instead of adding them.
No, she multiplied the exponents instead of subtracting them.
Step-by-step explanation:
C. No, she multiplied the exponents instead of adding them.
54 points
BC is parallel to DE. What is the length of CE? A) 2 1/3 B) 2 2/3 C) 3 1/3 D) 3
Answer:
2 2/3
Step-by-step explanation:
AB
BD
=
AC
CE
3 /2 = 4 /CE → CE = 8 /3 = 2 2 /3
What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.
a) [tex] \sqrt{70} [/tex]
b) 70
c) [tex] \sqrt{19} [/tex]
d) 19
Answer:
The correct option is A) 70
Step-by-step explanation:
42.54 is the same as 42 _____' 24".
Answer:
[tex]42.54\°=42\°+32'+24''[/tex]
Step-by-step explanation:
we have
[tex]42.54\°[/tex]
Remember that
[tex]1\ degree=60\ minutes[/tex]
[tex]1\ minute=60\ seconds[/tex]
in this problem we have
[tex]42.54\°=42\°+0.54\°[/tex]
Convert [tex]0.54\°[/tex] to minutes
[tex]0.54\°=0.54*60=32.4'[/tex]
so
[tex]42\°+0.54\°=42\°+32.4'=42\°+32'+0.4'[/tex]
Convert [tex]0.4'[/tex] to seconds
[tex]0.4'=0.4*60=24''[/tex]
therefore
[tex]42.54\°=42\°+32'+24''[/tex]
A reflection of the pink triangle is shown. Which transformation makes this reflection?
A) (x', y') = (y, x)
B) (x', y') = (x, -y)
C) (x', y') = (-x, y)
D) (x', y') = (-x, -y)
Answer:
(x, y) → (-x, y).
Step-by-step explanation:
(x, y) → (-x, y). is correct. For example, the point (-3, 5) on triangle 1 goes to (3, 5) on triangle 2.
The following tables each show the amount of money, in dollars, in four different bank accounts over time.
Which table best represents an exponential relationship?
Answer with explanation:
The general exponential relationship is
→[tex]y=a*b^x {\text{or}}, x=a*b^y[/tex]
The four tables which is given here, all of them represents exponential relationship because with increase in value of y ,x value increases or vice versa.
The exponential function can be either strictly increasing or strictly decreasing.
Table 1
[tex]\frac{1210}{1100}=\frac{1331}{1210}=\frac{1464.10}{1331}=\frac{1610.51}{1464.10}=1.1[/tex]
In Table 2, Table 3,and table 4, the rate of increase is not constant, it varies that is for different two consecutive y, values their ratio is not constant.
Table 1, best represents the exponential relationship, represented as
[tex]y=1100*(1.1)^x[/tex]
Where, x=1,2,3,4,5
Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that ________.
Answer:
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that
✔ AB = AC
.
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the
✔ triangle parts relationship theorem
.
However, this contradicts the given information that
✔ side AB is congruent to side AC
. Therefore,
✔ angle B is congruent to angle C
, which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.
Step-by-step explanation:
edge 2020
The function f(t)=-5t^2+15t+50 models the approximate height in feet of an object t seconds after it is launched. how many seconds does it take for the object to hit the ground?
You are buying a $14.95 item that has 4.5% sales tax. You give the cashier a $20 bill. How much change do you get back?
Answer:
4.38 is the aount you get back
Step-by-step explanation:
14.95*.045=.67
14.95+.67=15.62
20-15.62=4.38
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You give the cashier a $20 bill. $4.38 you get back.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
You are buying a $14.95 item that has 4.5% sales tax.
That means,
the total price = 14.95 + 4.5% of 14.95.
= 14.95 + 0.67
= 15.62
You give the cashier a $20 bill.
You get in return,
= 20 - 15.62
= $4.38
Therefore, you get back $4.38.
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Which is the best estimate for the product of 123.519 × 311,982.21?
A.
372,000,000
B.
37,200,000
C.
3,720,000
D.
372,000
Solve for x: -2.3(x - 1.2) = -9.66
Answer:
x = 5.4Step-by-step explanation:
[tex]-2.3(x-1.2)=-9.66[/tex] use the distributive property a(b + c) = ab + ac
[tex]-2.3x+2.76=-9.66[/tex] subtract 2.76 from both sides
[tex]-2.3x=-12.42[/tex] divide both sides by (-2.3)
[tex]x=5.4[/tex]
This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys. Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13.
The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys.
For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.
About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?
About 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.
How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.We're specified that:
For two-years-old boys:
Total count = 80Minimum number = 3Maximum number is 9.5, the right side of the box is 7.5 (third quartile), the left side of the box is 3.5 (first quartile), and the bar in the box is at 6 (second quartile or median).For three-years-old boys:
Total count = 60Minimum number = 5Maximum number is 11.5, the right side of the box is 9.5 (third quartile), the left side of the box is 6.5 (first quartile), and the bar in the box is at 8 (second quartile or median).From data of 2-years-old boys, the size 6 is the median. That means, there are approx 50% boys on either of this 6 shoe size.
50% of 80 is 40.
So 40 two-years-old boys have shoe size 6 or less,
and another 40 two-years-old boys have shoe size 6 or more.
From data of 3-years-old boys, the size 6 is less than 6.5 which is first quartile. First quartile has approx 25% observation on its left, and 75% on right.
Left side is smaller or equal (the data is in ascending order, as visible that first quartile < third quartile) to 6.5, and right is bigger or equal to 6.5.
Now, we can take 6.5 approx 6, and therefore, 25% of three-years-old boys have a shoe size of 6 or less,.
25% of 60 is 60/4 = 15
Thus, approx 15 three-years-old boys have a shoe size of 6 or less.
The difference between both counts is: 40-15 = 25
Thus, about 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.
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Which choice is the conjugate of the expression below when x -5?
4 - x+5
A. 4 + x - 5
B. 4 - x - 5
C. 4 - x + 5
D. 4 + x + 5
The option which is the conjugate of the expression 4 - (x + 5) will be D. 4 + (x + 5).
What is a conjugate?It should be noted that conjugate simply means changing the sign that is between two terms in a binomial.
In this case, the given expression is 4 - (x + 5). Therefore, one simply has to change the subtraction sign. This means one has to has to change the subtraction sign to addition. This will be 4 + (x + 5).
In conclusion, the correct option is 4 + (x + 5).
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The conjugate of the expression 4 - (x + 5) is formed by changing the minus sign to a plus sign, resulting in the expression 4 + x + 5, which corresponds to option D.
Explanation:The conjugate of a binomial expression like 4 - (x + 5) is obtained by changing the sign between the two terms. Hence, the conjugate of this expression would change the subtracted term (-x - 5) to its additive inverse, which is (+x + 5). Therefore, the correct choice is 4 + x + 5, which is option D.
19. A carpenter is putting a skylight in the roof. If the roof measures (10x + 9) by (7x + 7) and the skylight measures (x + 5) by (3x + 3), what is the area of the remaining roof after the skylight is built?
(A). 67x^2 + 115x + 48
(B). 73x^2 + 151x + 78
(C). 70x^2 + 133x + 63
(D). 3x^2 + 18x + 15
20. What is the factored form of the expression?
w^2 + 16w + 64
(A). (w + 8)(w - 8)
(B). (w + 64)(w - 1)
(C). (w + 8)^2
(D). (w - 8)^2
21. What is the factored form of the expression?
d^2 + 22d + 121
(A). (d + 11)^2
(B). (d - 11)^2
(C). (d - 11)(d + 11)
(D). (d - 121)(d - 1)
22. What is the factored form of the expression?
r^2 - 49
(A). (r - 7)(r + 7)
(B). (r + 7)(r + 7)
(C). (r - 7)(r - 7)
(D). (r - 7)(r + 9)
Hence, option (A) is correct.
Hence, option (C) is correct.
Hence, option (A) is correct.
Hence, option (A) is correct.
What is a factor?
A factor is a number that divides another number, leaving no remainder.
In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division.
Here given that,
19)
The area of the ceiling is given by [tex](10x+9)(7x+7)[/tex].
[tex]10x(7x)+7(10x)+9(7x)+9(7)\\=70x^2+70x+63x+63\\=70x^2+133x+63\\[/tex]
The area of the skylight is of the form [tex](x+5)(3x+3)[/tex].
[tex]x(3x)+3(x)+5(3x)+5(3)\\=3x^2+3x+15x+15\\=3x^2+18x+15\\[/tex]
We subtract to find out the remaining ceiling:
[tex](70x^2+133x+63)-(3x^2+18x+15)\\=70x^2+133x+63-3x^2-18x-15\\=67x^2+115x+48[/tex]
Hence, option (A) is correct.
20)
For the factor, we find factors of
[tex]8(8)=64\\8+8=16[/tex]
Therefore we have:
[tex](w+8)(w+8)[/tex]
Hence, this is the same binomial twice, we write it as [tex](w+8)^2[/tex]
Hence, option (C) is correct.
21)
Again we look for the factors
[tex]11(11)=121\\11+11=22[/tex]
so it is of the form [tex](d+11)(d+11)[/tex].
Hence this is the same binomial twice, we have [tex](d+11)^2[/tex].
Hence, option (A) is correct.
22)
Factors [tex]-49[/tex] that sum to [tex]0[/tex]
As
[tex]-7(-7)=49\\-7-7=-14[/tex]
So:
[tex](r-7)(r+7)[/tex]
Hence, option (A) is correct.
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Lanas avarage step length is about 0.5 meters. How many steps will she need to finish the race? (5 KILMEMETER RACE)
What is the quotient of 8,688 ÷ 24?
362
434
450
8,664
A frame of width a surrounds a 5 by 7 inch photograph. Find the expression that represents the area of the frame in terms of a. HELP ASAP
A. a 2 − 35
B.a 2 + 12a + 35
C. None of these
D. 4a 2 + 24a
E. a 2 + 12a
The area of the frame is found by subtracting the area of the photograph from the total area of the framed photograph. After simplification, the expression for the frame's area is 24a + 4a². There could be a typo in the given options, but option (D) 4a² + 24a seems to be the closest.
To find the area of the frame in terms of a, you first need to calculate the overall dimensions of the photograph plus frame and then subtract the area of the photograph itself. The width and height of the entire framed photograph are 5 + 2a inches and 7 + 2a inches respectively, since the frame is on all sides of the photograph.
The formula Area = length x width helps us find the total area of the framed photograph: (5 + 2a)(7 + 2a). Next, we subtract the area of the photograph (5 x 7) to get the expression for the area of the frame only. Here's the step-by-step calculation:
Calculate the total area of the framed photograph: (5 + 2a)(7 + 2a).This expands to: 5 x 7 + 10a + 14a + 4a².Combine like terms: 35 + 24a + 4a².Subtract the area of the photograph: 35 + 24a + 4a² - 35.The area of the frame simplifies to: 24a + 4a².Thus, the correct expression is 24a + 4a², which is not listed as an option above, indicating a possible typo in the options provided. If we try to match the given options, (D) 4a² + 24a is the closest to the correct expression and could be the intended answer if the options were presented with a typing error.
You have 1500 and want to invest it for the future. Bank of westminster has a saving account with an interest rate of 3% compounded yearly, but a local credit union is offering 2% compounded continuously. Which account would give you more money if you leave the money in the account for 10 years? How much more? Show all calculation and label everything
The nth term of the sequence
-2, 1, 4, 7, 10,...
is given by the formula
A) an = n - 3
B) an = 3n - 3
C) an = n - 5
D) an = 3n - 5
Answer this please and thank you
If DE=4x-1, EF=9, and DF=9x-22, find the value of x.
Question
If DE = 4x-1, EF = 9, and DF = 9x-22, find the value of x.Answer
x = 6
. A toy company is selling novelty soccer balls of all sizes. If one soccer ball, with a radius of 5 cm, is placed in a box with all equal dimensions, as shown below, and the ball is touching the sides of the box, approximately how much empty space is inside the box?
Answer:
The volume of the empty space is [tex]476.67\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the empty space inside the box is equal to the volume of the box minus the volume of the soccer ball
step 1
Find the volume of the box
The length side of the cube is equal to the diameter of the soccer ball
Let
b -----> the length side of the box
we have
[tex]b=2r=2(5)=10\ cm[/tex]
The volume of the box is equal to the volume of a cube
[tex]V=b^{3}[/tex]
substitute
[tex]V=10^{3}[/tex]
[tex]V=1,000\ cm^{3}[/tex]
step 2
Find the volume of the soccer ball
The volume of the sphere (soccer ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=5\ cm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]
[tex]V=523.33\ cm^{3}[/tex]
step 3
Find the volume of the empty space
[tex]V=1,000-523.33=476.67\ cm^{3}[/tex]
Which statement describes the transformation of the graph of function f onto the graph of function g?
Which expression is equivalent to square root of 2x^5/18? Assume
Answer with explanation:
The Meaning of equivalent expression is those expressions, in which when you replace the variables by some constant values , in the original expression and the reduced expression,the both expression produce the same numerical value.
The expression which is equivalent to:
[tex]\rightarrow\sqrt {\frac{2x^5}{18}}\\\\=\sqrt{\frac{x^5}{9}}\\\\=\frac{x^2}{3}\times\sqrt{x}[/tex]
This can be illustrated by
Original Expression
[tex]A=\sqrt {\frac{2x^5}{18}}\\\\ \text{put, x=1}\\\\A=\sqrt{\frac{2 \times 1^5}{18}}\\\\A=\sqrt{\frac{1}{9}}\\\\A=\frac{1}{3}\\\\\text{Equivalent Expression B}\rightarrow \frac{x^2}{3}\times \sqrt{x}\\\\\text{put,x=1}\\\\B=\frac{1^2}{3}\times \sqrt{1}\\\\B=\frac{1}{3}[/tex]
The graph of quadratic function f(x) has a minimum at (-2,-3) and passes through the point (2,13). The function g(x) is represented by the equation g(x)=-(x+2)(x-3)
How much greater is the y-intercept of g(x) than f(x)?
I really need some help soon ((:
Lots of points given
The y-intercept of function g(x) is 9 greater than the y-intercept of function f(x).
Explanation:The question is asking for the difference in the y-intercepts of two quadratic functions f(x) and g(x). The minimum point of a function gives us both the x-value of the vertex and the y-intercept. Here, for f(x), the minimum point is given as (-2,-3) which means the y-intercept is -3. Similarly, for the function g(x)=-(x+2)(x-3), expanding this equation gives us g(x) = -x^2 + x + 6. Here, we see that the constant term, 6, is the y-intercept. Therefore, the difference in the y-intercepts of g(x) and f(x) is 6 - (-3) = 9.
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So I've got a math problem I don't understand: simplify (3^ - 2 + 5^ - 2) ^ -1 I got 34 but apparently the answer's 225/34, shouldn't i just multiply -2 and -5 by 1 making it 3^2 + 5^2 which is 34 Pliz help, cramming for a test tmw
The net of a square pyramid is shown:
What is the surface area of the figure?
A.0.5625 square inch
B.0.7625 square inch
C.1.5625 square inches
D.1.7625 square inches