Answer:
Step-by-step explanation:
Let's call the ages D for daughter and S for son.
We know that the son is twice as old as the daughter, so:
S = 2D
We also know that in 15 years, their ages add up to 100, so:
(40+15) + (S+15) + (D+15) = 100
55 + S + 15 + D + 15 = 100
85 + S + D = 100
S + D = 15
Substituting the first equation:
2D + D = 15
3D = 15
D = 5
Therefore:
S = 2D = 10
The son is 10 and the daughter is 5.
Answer:
son = 10
daughter = 5
Step-by-step explanation:
Let the daughter = d
Let the son = s
s = 2*d
there ages in 15 years
Mother = 40 + 15 = 55
Son = s + 15
daughter = d + 15
Total: s + 15 + d+15 + 55 = 100 Combine the like terms.
s + d + 85 = 100 Subtract 85 from both sides.
s + d = 100 - 85
s + d = 15
s = 2*d Substitute for son
2d + d = 15
3d = 15
d = 15/3
d = 5
son = 2*5
son = 10
Check
son = 15 = 25
daughter + 15 = 20
Mother + 15 = 55
Total 100 just as it should be.
Please help me!!!!!!!
Answer:
B(5,2)
Explanation:
AC=8 units
AB must equal 2 units.
If line AC is y=x-3, and x values are -1<x<7 in AC, then B is located in x= 5. Plug x in equation.
y=5-3
y=2
B(5,2)
why does the function k(f(x)) provide a better model for the scatter plot when 4
Answer:
It reduces the distance from the plotted points to the function curve.
Step-by-step explanation:
The goodness of fit of a model is measured by the "residuals", the differences between the given points and the modeled points. The smaller the residuals, the better the model. Any change to the model that will put it closer to the plotted points makes it a better model. The change proposed in your problem statement does that.
A bookcase has a mass of 30 kilograms. A book in the bookcase has a mass of 400 grams. How many books of the same mass would it take to equal the mass of the bookcase? A. 75 books B. 120 books C. 750 books D. 1,200 books
Answer: OPTION A
Step-by-step explanation:
You can convert 30 kilograms to grams ([tex]1\ kilogram= 1,000\ grams[/tex]), then:
[tex](30\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=30,000\ grams[/tex]
Then, if a book in the bookcase has a mass of 400 grams and you need to find the number of books of the same mass that would take to equal the mass of the bookcase, you can divide the weight of the bookcase (in grams) by the weigth of one of these books.
Therefore:
[tex]books=\frac{30,000\ grams}{400\ grams}\\\\books=75[/tex]
let f(x)=x^2-6x+13. what is the vertex form of f(x)? what is the minimum value of f(x)?
Answer:
The vertex form of a quadratic equation is:
[tex]f(x) = (x-3)^2+4[/tex]
the minimum value of f(x) is [tex]y=4[/tex]
Step-by-step explanation:
Given a quadratic equation of the form [tex]f (x) = ax ^ 2 + bx + c[/tex] then the x coordinate of the vertex is
[tex]x=-\frac{b}{2a}[/tex]
So for [tex]f(x)=x^2-6x+13[/tex]
[tex]a=1\\b=-6\\c=13\\[/tex]
Therefore
The x coordinate of the vertex is:
[tex]x=-\frac{(-6)}{2(1)}[/tex]
[tex]x=3[/tex]
The y coordinate of the vertex is:
[tex]f(3)=(3)^2-6(3)+13[/tex]
[tex]y=f(3)=4[/tex]
By definition the minimum value of the quadratic function is the same as the coordinate of y of its vertex
So the minimum value is [tex]y=4[/tex]
The vertex form of a quadratic equation is:
[tex]f(x) = a(x-h)^2+k[/tex]
Where
a is the main coefficient. [tex]a=1[/tex]
h is the x coordinate of the vertex. [tex]h=3[/tex]
k is the y coordinate of the vertex. [tex]k=4[/tex]
So the vertex form of a quadratic equation is:
[tex]f(x) = (x-3)^2+4[/tex]
Answer:
a. [tex]f(x)=(x-3)^2+4[/tex]
b. The minimum value is 4
Step-by-step explanation:
The given function is: [tex]f(x)=x^2-6x+13[/tex]
We add and subtract half the square of the coefficient of x.
[tex]f(x)=x^2-6x+3^2-3^2+13[/tex]
This becomes: [tex]f(x)=x^2-6x+9-9+13[/tex]
The first three terms form a perfect square trinomial.
[tex]f(x)=(x-3)^2+4[/tex]
The function is now in the form: [tex]f(x)=a(x-h)^2+k[/tex], where V(h,k) is the vertex.
Therefore the vertex is (3,4).
The minimum value is the y-value of the vertex, which is 4.
How many 4-digit multiples of 2 are there?
there are 4,500 of 4 digit multiples of 2
Answer:
4500
Step-by-step explanation:
The wholesale cost of a sofa is $520. Based on selling price, the original markup was 69%. Find the final sale price after the following series of price changes occurred: a markdown of 13%, a markup of 30%, and a second markdown of 36%. Round each intermediate selling price to the nearest cent.
Answer:
$1214.19
Step-by-step explanation:
Let c and p represent the cost of the sofa and the original selling price, respectively. The original markup was 0.69·p, so we have ...
c + 0.69p = p . . . . . based on selling price, the original markup was 69%
c = p(1 -0.69) = 0.31p . . . . subtract the markup
p = c/0.31 . . . . . . . . . . . . . divide by the coefficient of c
So, the original selling price was ...
520/0.31 ≈ 1677.42
The first markdown decreased the selling price to ...
1677.42 - 0.13·1677.42 = 0.87·1677.42 ≈ 1459.36
The markup increased the selling price to ...
1459.36 +0.30·1459.36 ≈ 1897.17
And the final markdown decreased the selling price to ...
1897.17 -0.36·1897.17 ≈ 1214.19
The final sale price was $1214.19.
PLZ HELP I BEG YOU 20 POINTS!!!!
Answer:
[tex]b=\frac{g}{x} + \frac{5}{x^{3} } +\frac{1}{x^{2} }[/tex]
Step-by-step explanation:
[tex]10=\frac{5}{-2}-b(-2)^{2} +1\\\\\\9=\frac{5}{-2} -b(4)\\\\-18=5-b(4)\\\\-23=-b(4)\\\\\frac{-23}{4} =-b\\\\\frac{23}{4}=b\\\\\\b=\frac{23}{4}[/tex]
Show the Standard form of this problem
the answer is C. move the decimal place to the left 4 times since it is positive to the 4th power
Use the ratio table to solve the percent problem what percent is 8 out of 40
Answer:
20%
Step-by-step explanation:
So, 40 is the dependent and 8 is the independent
40% divided by 8% equals 5%
100% divided by 20% equals 5%
Please help question about currency exchange rate....
If 55LRD=1USD and 100LRD=1CHD
how much does ?CHD=1USD?
Answer:
Step-by-step explanation:
55 LRD = 1 USD
100 LRD = 1 CHD
[tex]1 LRD = \frac{1}{55} USD\\\\100 LRD = \frac{100}{55} USD = 1\frac{45}{55} USD=1\frac{9}{11} USD\\1 CHD = \frac{100}{55} USD\\1 USD = \frac{55}{100} CHD = 0.55CHD[/tex]
If possible, could someone assist me by showing me how to get the plausible answer as I was absent while my professer went over this topic.
Answer:
[tex]7.5m^2[/tex]
Step-by-step explanation:
Divide the composite shape into two shapes, a rectangle and a triangle.
We can see that the rectangle has dimensions of 3 x 2.
We can use the area formula.
[tex]A=b*h[/tex]
[tex]A=3*2[/tex]
[tex]A=6[/tex]
We can also see that the triangle has a height of 3 and a base of 1 (3 - 2).
We can use the area formula.
[tex]A=\frac{1}{2}(b*h)[/tex]
[tex]A=\frac{1}{2}(3)[/tex]
[tex]A=1.5[/tex]
Now we can add these areas together.
[tex]1.5 +6=7.5[/tex]
-1/5(x-4) =-2 what is the answer for x
Answer: x=14
Step-by-step explanation:
1. Simplify 1/5(x−4) to (x−4)/5.
(−x−4)/5=−2
2. Multiply both sides by 5.
−x+4=−2×5
3. Simplify 2×5 to 10.
−x+4=−10
4. Regroup terms.
4−x=−10
5. Subtract 4 from both sides.
−x=−10−4
6. Simplify −10−4 to −14.
−x=−14
7. Multiply both sides by −1.
x=14
You have 6 reindeer, Rudy, Jebediah, Ezekiel, Lancer, Gloopin, and Balthazar, and you want to have 5 fly your sleigh. You always have your reindeer fly in a single-file line.
How many different ways can you arrange your reindeer?
Answer:
Step-by-step Answer:
6 reindeer, from which we fly 5, in N1 ways.
Each of the five must be arranged in N2 ways.
The total number of arrangements is therefore N1*N2 arranglements.
Note: C(n,r) = n!/((r!(n-r)!)
N1 = 6 choose 5 = C(6,5) = 6!/(5!/1!) = 6 ways
(same as number of ways to choose 1 reindeer to be left out).
N2 = 5! ways (5 choices for the first, 4 choices for the second, 3 for the third, and 2 for the fourth, and 1 for the last) = 5*4*3*2*1 = 120 ways.
So total number of arrangements
= N1 * N2 = 6 * 120 = 720 ways.
Alternatively, you can line up the 5 vacant spaces and choose the first among 6 reindeer, second among 5, third among 4, fourth among 3, and the last one among 2 for a total of
6*5*4*3*2 = 720 arrangements.
Which statements are true about the median of a data set?
Check all that apply.
The median isn’t affected much by one outlier.
The median is always affected by one outlier.
The median is the number in the middle on an ordered set of data.
To find the median, find the difference between the highest and lowest numbers.
To find the median of an even data set, find the average of the two middle numbers.
Answer: Third and fifth option
3) The median is the number in the middle on an ordered set of data.
5) To find the middle of an even data set, find the average of the two middle numbers.
Step-by-step explanation:
Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.
For example, for the following set of 7 data:
2, 3, [5], 8, 13
the median is 5.
If the data number is even, for example 10 data:
3, 5, 9, 12, [19, 21], 33, 35, 40, 69
The median is the average between the two data that are in the middle
[tex]\frac{19 +21}{2} = \frac{40}{2} = 20[/tex]
Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example
2, 4, 4.5, 4.8, 5 Median = 4.5
2, 4, 4.5, 67, 1506 Median = 4.5
The median does not represent the difference between the highest and the lowest data.
Therefore the correct affirmations are:
3) The median is the number in the middle on an ordered set of data.
5) To find the middle of an even data set, find the average of the two middle numbers.
You buy a quart of ice cream that comes in a cylindrical tub. A quart has a volume of about 58 cubic inches. The tub has a height of 5 inches. What is the radius of the ice-cream tub? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
Givens
V = 58 in^3
h = 5 inches
pi = 3.14
Formula
V = pi * r^2 * h
Solution
58 = 3.14 * r^2 * 5
58 = 15.7 * r^2
58/15.7 = r^2
3.6942 = r^2
sqrt(r^2) = sqrt(3.6942)
r = 1.922 which when rounded is
r = 1.92
Answer: r=1.92
given what we know about the equation i can determine what steps are needed to solve this :)
volume
1) V = 58 in^3
we know that h=5inches
2) h = 5 inches
heres what pi equals
3) pi = 3.14
then we use pi in the equation
4)= pi * r^2 * h
heres the solution steps
1)58 = 3.14 * r^2 * 5
2)58 = 15.7 * r^2
3)58/15.7 = r^2
4)3.6942 = r^2
5)sqrt(r^2) = sqrt(3.6942)
6)r = 1.922 then we round and get r = 1.92
so final solution is r = 1.92
×║hope this helps║×
Please help on this question
Answer:
26 terms
Step-by-step explanation:
The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...
an = -2 +5(n -1)
The sum of the first n terms is ...
(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573
n(5n -9) = 3146
5n^2 -9n -3146 = 0 . . . . . quadratic in standard form
Using the quadratic formula, we can find the positive solution for n to be ...
n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26
26 terms must be added to give the desired sum.
_____
Relevant formulas are ...
Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d
x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0
The perimeter of a quarter circle is 7.14 feet. What is the quarter circles radius
if the perimeter of 1/4 of the circle is 7.14, then the full circle is 4(7.14) = 28.56.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=28.56 \end{cases}\implies 28.56=2\pi r \\\\\\ \cfrac{28.56}{2\pi }=r\implies 4.55\approx r[/tex]
and the radius is the same on any location of the circle.
A quarter of a circle having a perimeter 7.14 feet has a radius of 4.55 feet.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
If a complete circle has a perimeter of 2πr, the quarter of a circle should have (2πr/4) = (1/2)πr.
Given, The perimeter of a quarter circle is 7.14 feet.
Therefore,
(1/2)πr = 7.14.
πr = 14.28.
r = 14.28/3.14.
r = 4.55 feet.
learn more about circles here :
https://brainly.com/question/29142813
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Water flows at a rate of 7500 cubic inches per minute into a cylindrical tank. The tank has a diameter of 196 inches and a height of 72 inches. What is the height, in inches, of the water in the tank after 10 minutes? Round your answer to the nearest tenth.
Answer:
2.5 inches in height
Step-by-step explanation:
Givens
water flowing = 7500 in^3 / minute
water flowing = 75000 in^3 / minute * 10 minutes
Tank diameter = 196 inches
Tank radius = 196 inches /2
Tank radius = 98 inches
h_10 minutes = ??
Formula
V = pi r^2 h
Solution
75000 = 3.14 * 98^2 * h
75000 = 3.14 * 9604 * h
75000 = 30156.56 * h
h = 75000 / 30156.56
h = 2.487 which rounded to the nearest 1/10 is
h = 2.5 inches. Seems awfully small doesn't it, considering the volume flowing in.
y intercept,slope,and linear equation=
ANSWER
Y-intercept: 3000
Slope:-275
Linear equation:y=-275x+3000
EXPLANATION
The straight line touches the y-axis at
(0,3000).
The y-intercept is b=3000
The line also passes through (2,2450).
The slope is calculated using the formula,
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex] = \frac{3000 - 2450}{0 - 2} [/tex]
[tex] = \frac{550}{ - 2} = - 275[/tex]
The slope is -275.
The linear equation is given by:
[tex]y = mx + b[/tex]
[tex]y = - 275x + 3000[/tex]
Find m∠1 if m∠2=73°, m∠3=107°, m∠4=92°. Justify your response!
Answer:
m∠1 = 92°
Step-by-step explanation:
∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that
m∠2 + m∠3 = 73° +107° = 180°
so, the angles are supplementary and lines a and b are parallel.
Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.
m∠1 = m∠4 = 92°
please help
Find the x-intercepts for the parabola defined by the equation below.
y = 2x2 + 2x - 4
A.
(-4, 0) and (2, 0)
B.
(-2, 0) and (1, 0)
C.
(0, -2) and (0, 1)
D.
(0, -4) and (0, 2)
Answer:
B. (-2, 0) and (1, 0)
Step-by-step explanation:
The equation can be factored as ...
y = 2(x^2 +x -2) = 2(x +2)(x -1)
The x-intercepts are the values of x where y=0, so will be the values of x that make one or the other of the binomial factors zero:
x = -2
x = 1
Then the intercept points are (-2, 0) and (1, 0). . . . . . . . . matches choice B
write the equation of the line
Answer:
y = 1/2x -8
Step-by-step explanation:
The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...
rise/run = 1/2
The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...
y = slope·x + y-intercept
y = 1/2x -8
By United States cultural standards, it has been determined that 6 people live comfortably in 1500 square feet of living space. Based on this standard, how many square feet would be needed to comfortably house 200 people? Enter the number only.
Answer:
50,000
Step-by-step explanation:
Set up a proportion:
6/1500 = 200/x
Cross multiply and solve for x:
200x1500 = 6x
300000 = 6x
50000 = x
Answer:
50000
Step-by-step explanation:
Find the "unit rate" for occupancy:
1500 ft²
------------- = 250 ft²/person
6 people
Now multiply this unit rate by 200 people. "people" drops out, and you are left with
250 ft²
--------------- * 200 people = 50,000 ft²
1 person
Enter 50000. 200 people will need 50000 ft² of housing.
What is the simplified form of 4z^2-16z+15/ 2z^2-11z+15
[tex]\frac{4z^2-16z+15}{2z^2-11z+15}[/tex] Factor the numerator and the denominator
[ax² + bx + c]
4z² - 16z + 15 Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.
(a·c) --> (4 · 15) = 60
Factors of 60:
1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10
[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z
4z² - 6z - 10z + 15 Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15
2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:
(2z - 3)(2z - 5)
Do the same for the denominator, and you should get (z - 3)(2z - 5)
Now you have:
[tex]\frac{(2z - 3)(2z-5)}{(z-3)(2z - 5)}[/tex] You can cancel out (2z - 5)
[tex]\frac{2z - 3}{z-3}[/tex]
ANSWER
[tex]\frac{(2z-3)}{(z-3)} [/tex]
EXPLANATION
The given expression is:
[tex] \frac{4z^2-16z+15}{2z^2-11z+15} [/tex]
Let us split the middle terms to get,
[tex]\frac{4z^2-6z - 10z+15}{2z^2-6z - 5z+15} [/tex]
Factor by grouping:
[tex]\frac{2z(2z-3) - 5(2z - 3)}{2z(z-3) - 5(z - 3)} [/tex]
Factor further:
[tex]\frac{(2z - 5)(2z-3)}{(2z - 5)(z-3)} [/tex]
We cancel the common factors,
[tex]\frac{(2z-3)}{(z-3)} [/tex]
where
[tex]z \ne \frac{5}{2} \: or \: z \ne3[/tex]
PLEASE! Someone help me answer this and explain it
Answer:
12.5
Step-by-step explanation:i did that problem before
ind the volume of the pyramid, if the base is a square with the side 3.5 cm and height of the pyramid is 1.5 cm
Answer:
The volume of the pyramid is [tex]6.125\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of the pyramid
h is the height of the pyramid
Find the area of the base B
[tex]B=3.5^{2}= 12.25\ cm^{2}[/tex]
we have
[tex]h=1.5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(12.25)(1.5)[/tex]
[tex]V=6.125\ cm^{3}[/tex]
If the second term of an arithmic progression is -3 and the fourth term is 5, find the ninth term
Answer:
25
Step-by-step explanation:
You can get that the common difference for all of the terms if four by finding the difference between -3 and 5, which gives us four. Using this, we can calculate the last term by doing 5+4*5 which is 25.
What is the product of 5/6 and 2/3?
Answer:
The product of [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{3}[/tex] is [tex]\frac{5}{9}[/tex] .
Step-by-step explanation:
Multiply both numerators and denominators.
[tex]\frac{5*2}{6*3}[/tex]
[tex]\frac{10}{18}[/tex]
Simplify this by dividing both the numerator and denominator by 2.
[tex]\frac{10/2}{18/2}[/tex]
[tex]\frac{5}{9}[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{The word product means multiply}[/tex]
[tex]\dfrac{5}{6}\times\dfrac{2}{3}=\ ?\\\\\\\dfrac{5(2)}{6(3)}=\dfrac{5\times2}{6\times3}\\\\\bf{5\times2=10}\\\\\bf{6\times3=18}\\\\\\=\dfrac{10}{18}\\\\\\\text{Both numbers foes into two so we can DIIVIDE it by two}\\\\\\\dfrac{10\div2}{18\div2}=?[/tex]
[tex]10\div2=5\\\\\18\div2= 9\\\\\\\boxed{\boxed{\bf{Answer:\dfrac{5}{9}}}}\checkmark[/tex]
[tex]\text{Good luck on your asignment and enjoy your day!}\\\\\\\frak{LoveYourselfFirst:)}[/tex]
Using paper folding to construct a line perpendicular to a given line through a point
Answer: upon itself
Step-by-step explanation: apex
Triangle ABC = triangle blank
Answer:
QPR
Step-by-step explanation:
It is triangle QPR because of the order of corresponding angles.