The present age of mother and her daughter respectively are; 40 and 10 years respectively.
How to Solve Algebra Word Problems?Let x and y be the present age of mother and her daughter respectively.
Therefore;
x + y = 50
x = 50 − y .....(1)
After 20 years, mother's age will be twice her daughter's age at the time. Thus;
x + 20 = 2(y + 20)
x − 2y = 20 .....(2)
Plugging eq 1 into eq 2 gives us;
50 − y − 2y = 20
3y = 30
y = 10
Thus;
x = 50 − 10
x = 40
Thus, the present age of mother and her daughter is 40 and 10 years respectively.
Translation of the question into English is;
The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at the time. Find their present ages.
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Simplify the expression -3z(1.8z-2.2).
-5.4z² + 6.6z
-5.4z²-6.6z
-1.2z²+5.2z
-1.2z²-5.2z
Mark this and return
Save and Exit
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Submit
Answer:
[tex] - 5.4z {}^{2} + 6.6z[/tex]
Step-by-step explanation:
Given:
[tex]-3z(1.8z-2.2)[/tex]
Solution:
Applying Distributive property,we obtain
[tex](−3z)(1.8z)+(−3z)(−2.2)[/tex]Simplifying using PEMDAS:
[tex] - 5.4z {}^{2} + 6.6z[/tex]Done!
Answer:A
Step-by-step explanation:
solve the system of equations for one of the variables x+4y=5 x-4y=5
Answer:
x=5 y=0
Step-by-step explanation:
cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.
Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.5 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
Answer:
6.3 *30= 189; so 4 cotton swabs
Help! I need help with this math problem
Answer:
h(-1) is -1, h(-0.5) is 0 and h(1) is 1.
Step-by-step explanation:
functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.
h(-1)In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.
h(-0.5)In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.
h(1)In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.
Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.
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Factor the binomial 9t to second power,-4 =
Using subtraction of perfect squares, it is found that the factored expression is:
9t² - 4 = (3t - 2)(3t + 2).
What is the subtraction of perfect squares factoring?It is given as follows:
a^2 - b^2 = (a - b)(a + b)
In this problem, the binomial is given as follows:
9t² - 4.
Hence:
a² = 9t² -> a = 3t.b² = 4 -> b = 2.Hence the factored expression is:
9t² - 4 = (3t - 2)(3t + 2).
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Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.) (-5, 10) and (5, -10) a. y = 2x-10 b. C. d. y = 2x y = -2x+ 20 y=-2x A
Answer:
y = -2x
Step-by-step explanation:
It passes through -5, 10 and 5, -10
gradient = Δy/Δx
gradient = -10 - 10 / 5 -- 5
gradient = -20 / 10
gradient = -2
let's use -5, 10 for y = mx + b
10 = -2(-5) + b
10 = 10 + b
b = 10 - 10
b = 0.
the equation of the line is just y = -2x
Find the slope of the line passing through the points (3,-9) and (2, -3).
Answer:
The slope of the line passing through is -6.
Suppose that
f
(
x
,
y
)
=
x
+
5
y
f
(
x
,
y
)
=
x
+
5
y
at which
−
1
≤
x
≤
1
,
−
1
≤
y
≤
1
-
1
≤
x
≤
1
,
-
1
≤
y
≤
1
.
Absolute minimum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Absolute maximum of
f
(
x
,
y
)
f
(
x
,
y
)
is
========================================================
Explanation:
The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.
Similarly the smallest y value is y = -1 and the largest is y = 1.
----------
Plug in the smallest x and y value to get
f(x,y) = x+5y
f(-1,-1) = -1+5(-1)
f(-1,-1) = -6
Therefore, the absolute min is -6
----------
Now plug in the largest x and y values
f(x,y) = x+5y
f(1,1) = 1+5(1)
f(1,1) = 6
The absolute max is 6
Can someone help me answer fast
Answer:
2x+3+9
because plyer scored 9 points and throw 2point shotand same number 3
NEED ASAP
The scatter plot below shows the amount of profit earned per month by a bagel shop over a period of 11 months.
Write an equation for the line of best fit that models the relationship between profit in thousands, p, and time in months,m. Then, use your equation to predict the profit the bagel shop will earn in month 12. Round slope and -y intercept to the nearest tenth.
The bagel shop will earn $9625 in 12 months.
What is a Scatter Plot ?Scatter plot are graphs that identifies relation between x and y variables.
The scatter points are given in the graph and we have to determine the equation that best fits the data .
the points in the scatter plot is
(3,4) and (8,6)
The slope of the equation
y = mx +c is given by
m =(y2 - y1)/(x2-x1)
m = (9-4)/(11-3)
m = 5/8 = 0.625
The equation is
y= 0.625x +2.125
for 12 months
y = 9.625 thousand = 9625 thousand in 12 months
Therefore the bagel shop will earn $9625 in 12 months.
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Answer:
$9,625 is the answer, and $9,300 is the rounded answer
Step-by-step explanation:
general formula: y=ax-b
required form: p=am-b
choose two dots: (11,9), (3,4)
find the slope: 9-4/11-3=5/8 -> p=5/8
put it into an equation: f(11)=6&7/8-b=9, f(3)=1&7/8-b=4
finding the y-intercept: -9+6&7/8=2&1/8, -4+1&7/8=2&1/8 -> b=2&1/8
forming a whole equation: p=5/8m+2&1/8
predict the profit in December: p=7&4/8+2&1/8=9&5/8
the bagel shop will earn $9,625 in December
round them to the nearest tenth: p=0.6m+2.1
predict the profit in December: p=7.2+2.1=9.3 -> $9,300
Here is the histogram of a data distribution. All class widths are
What is the median of the distribution?
The median of the distribution is 4.
What is the median?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The median is the number at the center of the data set.
Arranging the numbers in the histogram in ascending order is: 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10
Total numbers = 21 Median = 1/2 x (n + 1)1/2 x 22 = 11th number 4
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If 3x − 6 ≤ f(x) ≤ x2 − 3x + 3 for x ≥ 0, find lim x→3 f(x).
Answer:
Step-by-step explanation:
There were 582 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed.
Answer:
let the no. of students who failed the examination be X
therefore, no. of students passed = 5x
total no. of students = 582
5x + X = 582
6x = 582
x = 97
no. of students failed the examination = 97
no. of students passed = 97*5 = 485
Which number comes next in this series 1/64 1/32 1/16 1/8 1/4 1/2
Answer:
1/1
Step-by-step explanation:
As the question is halfing by 2
So
2 divide 2 equals 1
Answer:
1
Step-by-step explanation:
it's fractions of divided half. next one will be number 1
Triangle P Q R is shown. Angle P Q R is a right angle. The length of hypotenuse P R is q, the length of P Q is r, and the length of Q R is p.,
Which cosine ratios are correct for ΔPQR? Check all that apply.
cos (P) = StartFraction r Over q EndFraction
cos (P) = StartFraction p Over q EndFraction
cos (Q) = StartFraction r Over p EndFraction
cos (R) = StartFraction r Over p EndFraction
cos (R) = StartFraction p Over q EndFraction
The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.
We have,
Δ PQR,
Length of hypotenuse PR = q
The length of PQ = r,
And the length of QR = p
NOw,
We know that Trigonometric ratios of CosineΘ;
CosineΘ = Base/Hypotenuse
So,
CosineP = r/q
And,
CosineR = p/q
So, from the above find out values we can say that these values are given in option (a) and option (d).
Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.
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Each statement describes a transformation of the graph of y = log2x. Which statement correctly describes the graph of y = log2(x + 3) - 9?
The transformation of a function may involve any change in the initial function. The correct option is C.
The complete question is:
Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?
It is the graph of y = log2x translated 3 units down and 9 units to the left.It is the graph of y = log2x translated 9 units down and 3 units to the right.It is the graph of y = log2x translated 9 units down and 3 units to the left.It is the graph of y = log2x translated 3 units up and 9 units to the left.How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]Given the initial function y = log2x, now if the function is needed to be transformed to y = log2(x + 3) - 9, then the function is needed to be shifted left by 3 units and down by 9 units.
Hence, the correct option is C.
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what point is not included in the solution set for the inequality (0,6) (1,5) (2,4) (3,2)
Answer:
(3, 2)
Step-by-step explanation:
To be considered part of a solution set for the inequality provided, a given point must lie within the shaded region that is graphed. Since we want to find the point that is not included in the solution set for the inequality, we need to find the point that does not lie in the shaded region.
Let's test each point to see which doesn't lie in the region. Refer to the image below if you're having trouble graphing the points:
(0, 6): This point lies in the shaded region, so it is not our answer.(1, 5): This point lies in the shaded region, so it is not our answer.(2, 4): This point lies in the shaded region, so it is not our answer.(3, 2): This point does not lie in the shaded region, so it is our answer.Hope this helps!
Seismology In 1812, an earthquake of magnitude 7.9 shook New Madrid,
Missouri. Compare the amount of energy released by that earthquake to the
amount of energy released by each earthquake below.
magnitude 9.5 in Valdivia, Chile, in 1960
WILL GIVE THE BRAINLIEST!
If r and s are real numbers such that
r>s>0, then
(A) -s>-r> 0.
(B) 0>-r> -s.
(C) 0> -s> -r.
(D) -s>0> -r.
(E) -r> -s > 0.
Answer: Choice (C) 0> -s> -r
==========================================================
Explanation:
Let's consider an example. Pick any two positive numbers for r and s, where r is larger than s. I'll go with these:
r = 5s = 2We see that r > s is true since 5 > 2 is true
Also both are larger than 0 so we can say r > 0 and s > 0
This all combines into r > s > 0 being the case.
If we negate each number, then -r > -s would no longer be true. Use a number line to see that -5 is to the left of -2, so -5 > -2 is not true. Instead it would be -5 < -2
You can think of it like floors on a skyscraper. Positive numbers are above ground, while negative numbers are below ground in the basement levels. See the diagram below.
So -r > -s must be -r < -s instead. Both are smaller than 0
-r < 0 and -s < 0
This combines to -r < -s < 0
Flip everything and swap the outer sides to get 0 > -s > -r which leads us to choice C as the final answer
Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?
6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared
By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.
What is the area of the circle?
In this question we have a circle whose radius (r) is kwown. Besides, we know that Maria draws a circle with double the area of the prior circle. The area of the circle (A) is described by the following formula:
A = π · r² (1)
Then, we have that the area drawn by Maria is:
A = 2 · [π · 3²]
A = 18π
By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.
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Answer:
18π units squared
Step-by-step explanation:
On edge
How do you solve 32-34?
Answer:
32. {-4, 1, 2, 12}
33. {2, 6, 9, 31, 65}
34. No
Step-by-step explanation:
32. The domain of a relation is the set that contains all the x-coordinates of all the ordered pairs of the relation.
domain = {-4, 1, 2, 12}
33. The range of a relation is the set that contains all the y-coordinates of all the ordered pairs of the relation.
range = {2, 6, 9, 31, 65}
34. No since the same number, 2, appears twice as an x-coordinate. In a function, no two ordered pairs can have the same x-coordinate.
Think about all of the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and a parabola can intersect.
00
1
2
03
04
05
DONE
There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle and a parabola:
As we know the standard form of a circle:
[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]
The standard form of the parabola:
[tex]\rm y = a(x-h)^2+k[/tex]
If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)
The solution of the quartic equation will be 4.
Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
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The sum of the measures of two exterior angles of a triangle is 264. What is the
measure of the third exterior angle?
Answer: 96 degrees
Step-by-step explanation: Assuming that angle ℒ is the third measure, then angle ℒ is 96 degrees as all exterior angle measures of a triangle are 360 degrees.
360-264 = 96 degrees =
ℒ
Please give brainliest if helpful.
The Wilson family had 5 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had
at least 3 girls?
at most 3 girls?
The expression represents the probability of getting exactly 3 heads is,
[tex]C(n,r)(0.5)^3(0.5)^6[/tex]
We have given
Aron flips a penny 9 times.
We have to determine
Which expression represents the probability of getting exactly 3 heads
What is binomial distribution?The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.
The binomial probability formula shown has variables that represent:
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).
r is the number we want to find (here, we want the probability of 3 heads, so r = 3).
p is the probability of success (here, success means getting heads.
So, in a coin flip the probability of heads is always 1/2, so p = 1/2).
Therefore, The expression represents the probability of getting exactly 3 heads is;
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]
Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].
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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,
Probability (x≥3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰
= 0.5
Probability (x≤3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵
= 0.8125
Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
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find the x and y values of this graph algebra 2
x y
2,0
1,-2
0,-4
-1,-6
-2,-8
Evaluate the given function. The values of the independent variable are approximate.
f(x) = 3x² - 3x, find f(3.52) and f(-8.77)
The values of f(3.52)=26.61 and f(-8.77)=257.05
An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.
The given function is f(x) = 3x²-3x =3x(x-1)
f(3.52)=3*(3.52)(3.52-1)
=26.61
f(-8.77)=3*(-8.77)(-8.77-1)
=257.05
Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
At West Painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job will take. If they average painting of a room with of a gallon of paint, then they can paint, on average,
rooms per gallon.
Answer:
Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.
Step-by-step explanation:
Concept: Use the method of ratio and proportion.
In this method, if a relationship is given between two values, then using that relationship we can find another relationship with respect to another variable.
Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.
2/5 gallons of paint = 3/4 rooms
1 gallon of paint = [tex]\frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875[/tex] rooms
So, on an average they can paint 1.875 rooms per gallon.
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What is −7.6 − 2(2.2)
Answer:
-12
Step-by-step explanation:
Order of operations:
PEMDAS
First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12
If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5
Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x + 8 - 4x - 3 ← collect like terms
= - 3x + 5
Answer:
[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]
Step-by-step explanation:
Given functions:f(x) = x + 8g(x) = -4x - 3Solution:Add both functions
(f + g)(x) = x + 8 + (-4x - 3)
(f + g)(x) = x + 8 - 4x - 3
(f + g)(x) = x - 4x + 8 - 3
(f + g)(x) = -3x + 5
[tex]\rule[225]{225}{2}[/tex]
Which expression can be used to find the difference of the polynomials?
The expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n). D
How to find the difference
Given the expression:
(4m - 5) - (6m - 7 + 2n)
Note that - * - = +
+ * - = -
So in finding the difference, we have
(4m - 5) - ( 6m + 7 - 2n )
It could as be written as
(4m - 5) + ( -6m + 7 - 2n)
Therefore, the expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n) . D
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