If the sum of the digits of a two-digits number is 12. and when 15 is added to the number, the result is 6 times the unit digit. the number is 48
How to find the numberThis is a word problem which will be used t o form equation
Let the first digit be x and the second digit be y
so that
x + y = 12
xy + 15 = 6y
from x + y = 12, x = 12 - y
substituting x = 12 - y into xy + 15 = 6y
y(12 - y) + 15 = 6y
expanding and arranging the equation gives
y^2 - 6y - 15 = 0
solving the quadratic equation gives
y = 7.899 OR -1.899
take the positive value, y is approximately 8
plug in y = 8 and solve for x
x = 12 - y
x = 12 - 8
x = 4
Therefore the number is 48
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Audrey is driving to a concert and needs to pay for parking. There is an automatic fee
of $6 just to enter the parking lot, and when she leaves the lot, she will have to pay an
additional $2 for every hour she had her car in the lot. How much total money would
Audrey have to pay for parking if she left her car in the lot for 5 hours? How much
would Audrey have to pay if she left her car in the lot for t hours?
Answer:$16
$6 + $2(t)
Step-by-step explanation:
$6 + $2(5)
Audrey is driving to a concert and needs to pay for parking. There is an automatic fee of $6 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Audrey have to pay for parking if she left her car in the lot for 5 hours? How much would Audrey have to pay if she left her car in the lot for tt hours?
Cost of parking for 5 hours:
Cost of parking for tt hours:
A shed for holding sports equipment is 180 inches
long. There are 12 inches in 1 foot. How many feet
long is the shed?
Answer: 15 feet
Step-by-step explanation:
180 inch = 15 feet
24 feet is how many meters?
Answer:
There are 7.3152 meters in 24 feet.
Step-by-step explanation:
1 foot = 0.3048, so...
0.3048 x 24 = 7.3152 meters = 24 feet.
What is the factored form of this polynomial?
p(x) = x³ + 7x² + 4x − 12
Select the correct answer from each drop-down menu
Answer:
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3+7x2
Group 2: 4x-12
Pull out from each group separately :
Group 1: (x+7) • (x2)
Group 2: (x-3) • (4)
Answer:
from the drop down menu the answers are:
x-1
x+2
x+6
IXL Help Fast Please !
Answer:
y=-10-7
Step-by-step explanation:
3=-10(-1)+5/4
3=10+5/4
3=11 1/4
11 1/4-3=8 1/4
5/4-33/4=-28/4=-7
3=-10(-1)-7
3=10-7
3=3
Answer:
y=-10x-7
Step-by-step explanation:
3=-10(-1)+5/4
3=10+5/4
3=11 1/4
11 1/4-3=8 1/4
5/4-33/4=-28/4=-7
3=-10(-1)-7
3=10-7
3=3
Harry asked a sample of 444 people how many siblings they had. Here are their responses: 0, 0, 1, 30,0,1,30, comma, 0, comma, 1, comma, 3 The mean is \bar x =1 x ˉ =1x, with, \bar, on top, equals, 1 sibling. Which of these formulas gives the standard deviation? Choose 1 answer:
The formulas give the standard deviation will be sₓ=√(0-1)²+(0-1)²+(1-1)²+(3-1)²/4.Option C is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that, Harry asked a sample of 4 people how many siblings they had. Here are their responses:0,0,1,3 The mean is 1 sibling.
[tex]\bar x =1 \\\\ n =4[/tex]
The formulas give the standard deviation as,
[tex]\rm s_x = \sqrt{\frac{(x_1-\bar x)^2+(x_2-\bar x)^2 +(x_3- \bar x)^2 }{n-1} } \\\\ s_x = \sqrt{\frac{(0- 1)^2+(0-1)^2 +(1- 1)^2 + (3-1)^2}{3} }[/tex]
Thus, the formulas give the standard deviation will be sₓ=√(0-1)²+(0-1)²+(1-1)²+(3-1)²/4.Option C is correct.
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According to the Mini-Lesson, which of the following are TRUE regarding f(x) = a(b)? Check all that
apply. Assume a > 0.
00000
The Domain of the exponential functions is All Real Numbers.
The Domain of the exponential functions is a > 0.
The Horizontal Asymptote is the point (0, a).
The Horizontal Asymptote is the line y = 0.
The Range of the exponential functions is f(x) > 0.
The Range of the exponential functions is All Real Numbers.
The Horizontal Asymptote is the line =
= 0.
Answer:
The Horizontal Asymptote is the point (0, a).
The Horizontal Asymptote is the line =
= 0.
Step-by-step explanation:
The following statements are true regarding f(x) = aᵇ:
The Domain of the exponential functions is All Real Numbers.
The Horizontal Asymptote is the line y = 0.
The Range of the exponential functions is f(x) > 0.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The horizontal asymptote is the horizontal line that the graph of the function approaches as x approaches infinity or negative infinity. In this case, the horizontal asymptote is the line y = 0, which means that as x gets very large, the value of f(x) approaches 0.
The domain of the function is the set of all values of x that can be plugged into the function. For exponential functions, the domain is all real numbers because any real number can be raised to any power.
The range of the function is the set of all possible output values that the function can produce. For exponential functions, the range is f(x) > 0, which means that the function can produce any positive real number as output.
The following conclusions about f(x) = aᵇ are correct:
All Real Numbers are the domain of exponential functions.
The line y = 0 is the Horizontal Asymptote.
The exponential functions have a range of f(x) > 0.
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Base Number is unknown: a/?= x/100?
Answer:
A. x= .100
Step-by-step explanation:
ook at the following sum.
1 + 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64. . .
Notice that the denominator of each fraction in the sum is twice the denominator that comes before it.
If you continue adding on fractions according to this pattern, when will you reach a sum of 2?
Answer: We will never reach a sum of 2
We get closer and closer to 2, but never actually reach this exact value.
==============================================================
Explanation:
The sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
is geometric with these properties
a = 1 = first termr = 1/2 = common ratioWe multiply each term by 1/2 to get the next one.
Examples:
(1/8)*(1/2) = 1/16(1/32)*(1/2) = 1/64----------------
Notice how -1 < r < 1 is true, i.e. -1 < 1/2 < 1 is true.
Because of this fact, we can determine the sum of infinitely many terms.
That infinite sum is
S = a/(1-r)
This is our upper bound of what we can reach for S.
Calculating it gives:
S = a/(1-r)
S = 1/(1-0.5)
S = 2
Therefore, the sum of the infinitely many terms of this geometric sequence is 2.
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... = 2
We never quite reach 2 exactly due to the fact we cannot reach infinity on the number line. Infinity is not a number, but rather a concept.
Therefore, we never reach a sum of 2. We simply get closer and closer.
-------------
Using computer software, I was able to generate this:
1 + 1/2 = 1.51 + 1/2 + 1/4 = 1.751 + 1/2 + 1/4 + 1/8 = 1.8751 + 1/2 + 1/4 + 1/8 + 1/16 = 1.93751 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1.968751 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 = 1.984375The decimal values are exact without any rounding done to them. As you can see, the results of 1.5, 1.75, 1.875, etc are slowly approaching 2 but never get to that exact value itself. Visually you can think of an asymptote.
i need help asap with this question
Answer:
-8/9
Step-by-step explanation:
(-7/9) /( (-1 1/6) * (-3/4) ) make all fractions improper fractions
(-7/9) / (-7/6 * -3/4) solve brackets
(-7/9) / (7/8)
(-7/9) * (8/7)
-8/9
A29-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 38 m Find the length of the shadow. If necessary, round your answer to the nearest tenth.
The length of the shadow is 24. 56m
How to determine the lengthFrom the information given, we have that;
Height of the tree = 29mThe top of the building to the tip of the shadow is 38 m Length of the shadow = cUsing the Pythagorean theorem, we have;
a² = b² + c²
Substitute the values, we get;
38² = 29² + c²
Find the squares
1444 - 841 = c²
c² = 603
Find the square root of both sides
c = 603
c = 24. 56m
Hence, the value is 24. 56m
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A small hardware store makes a profit of $20,000 during its first year. The store owner sets a goal of increasing profits by $5,000 each year for the next 4 years. Assuming that this goal in met, find the total profit during the first 5 years of business.
profit = $ ___________
What is the distance between (4,5) and (-2, -3)?
Answer:
10 units
Step-by-step explanation:
The distance formula is as follows:
D = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-2 - 4)^2 + (-3 - 5)^2]
= √(-6)2 + (-8)2
= √100
= 10
Answer:
10 Units
Step-by-step explanation:
Distance (d) = √(-2 - 4)2 + (-3 - 5)2
= √(-6)2 + (-8)2
= √100
= 10
Hope this helps! :)
How many rows are left?
7/15 rows are left after crows ate some rows.
Total no. of rows he planted = 1 2/3
= 1 + 2/3
= (3 + 2)/3
= 5/3
No. of rows crows ate = 1 1/5
= 1 + 1/5
= (5 + 1)/5
= 6/5
No. of rows left = 5/3 - 6/5
= (25 - 18)/15
= 7/15
Hence, no. of rows left is 7/15.
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An exponential function approaches 10 as x approaches infinity. Write a possible equation for the function.
An exponential function approaching a value of 10 as x approaches infinity is given as follows:
[tex]y = (0.25)^x + 10[/tex].
What is an exponential function?The general model for an exponential function is presented as follows:
[tex]y = ab^x + c[/tex]
In which the variables of the function are listed as follows:
a is the initial value of the function.b is the rate of change of the function.c is the asymptote of the function.In this problem, the function approaches value of 10 as x approaches infinity, meaning that the asymptote is of 10, hence:
c = 10.
The above condition is also only possible if the exponential function is decreasing, that is parameter b is between 0 and 1, hence one possible function is:
[tex]y = (0.25)^x + 10[/tex]
The restriction for parameter b is because if the function was increasing, that is, b > 1, it would approach infinity as x approaches infinity.
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Needing help pleasee!!
ΔRNP and ΔSOP are congruent by the ASA rule.
What is Angle-Side-Angle (ASA) Rule?
If two angles and the included side of one triangle equal two angles and the included side of another, the triangles are congruent.
In the given figure,
For ΔRNP and ΔSOP,
∠NRP ≅ ∠OSP ----- (Alternate angles)
∠OPS ≅ ∠RPN ----- (Opposite angles)
Side PR ≅ Side PS
Hence, ΔRNP and ΔSOP are congruent by the ASA rule.
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8. Noah has a coin jar containing d dimes and 9 quarters worth a total of $5.00.
Select all the equations that represent this situation.
a. d+q=5
b. d+q=500
c. 0.1d +0.25q = 5
d. 10d+25q=500
e. d=50
f. q=20
Answer: A and C
d + q = 5 is one correct answer, not 500
0.1d + 0.25q = 5 as this is literally just the equation you are doing.
please help me with this
Model equivalent to 16 2/3 % is Option D.
Given:
The number of students at Liam's elementary school has increased 16 2/3 % in the past two weeks.
Option D is divide into six parts with one filled which is equal to 16 2/3 %.
Total parts = 6 * 16 2/3
= 6*48+2/3
= 6 * 50/3
= 300/3
= 100%
Here total parts is equal to 100% so it is the correct option.
Therefore model equivalent to 16 2/3 % is Option D.
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Michael made 22 out of 25 of his shots this basketball season. What percentage of his shots did he make?
Answer:
88%
Step-by-step explanation:
A boat is heading towards a lighthouse, where Aaden is watching from a vertical distance of 103 feet above the water. Aaden measures an angle of depression to the boat at point
A
A to be 18
∘
∘
. At some later time, Aaden takes another measurement and finds the angle of depression to the boat (now at point
B
B) to be 75
∘
∘
. Find the distance from point
A
A to point
B
B. Round your answer to the nearest tenth of a foot if necessary.
The slope concept shows that there are 335.3953 feet between points A and B.
What is a slope?The slope is calculated by dividing the vertical and horizontal changes. A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Additionally, it is the tangent to the depression angle.
The vertical change in this issue is 103 feet.
At point A, the horizontal position is represented by xA, and the angle there is 18o, so: tan 18 degree = 103/xA xA = 103/tan 18 degree xA = - 90.5653
At point B, the horizontal position is at, and the angle is at, so: tan 75degree = 103/xB xB = 103/tan 75 degree xB = - 244.83
The measurement is given by: d = xA - xB d = -90.5653 - ( - 244.83)
d = 335.3953
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Answer:
289.4
Step-by-step explanation:
One factor of the function f(x) = x3 − 7x2 + 14x − 8 is (x − 4). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.
According to the plotted graph, the x intercepts are (1,0),(2,0) and (4,0) and the y intercept is (0, -8)
Intercepts:
In the graph theory, the x-intercept is the point where a line crosses the x-axis, similarly the y-intercept is the point where a line crosses the y-axis.
Given,
One factor of the function f(x) = x³ − 7x² + 14x − 8 is (x − 4).
Here we need to identify the x and y intercept of the function through the graph of the function.
Here we have to do the following steps on the graphing calculator, to plot the function,
1) Set the x and y axis values on the graphing calculator.
2) Enter the required function on the input box.
3) Which ever the point that placed on the x axis are the points that refers the x intercept
4) Similarly, which ever the point that placed on the y axis are the points that refers the y intercept.
Now, the graph of the function is plotted and attached below.
Therefore, the x intercept are (1,0), (2,0) and (4,0) and the y intercept is (0,-8)
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HELP FAST 34 POINTS AND BRAINLIEST!!
In a bag of marbles there are 9 red marbles,6 blue marbles and 3 white marbles.Using fractions in their lowest terms,calculate the probability of drawing out:
a red marble
a white marble
a blue marble
Answer:
Red: 1/2
White: 1/6
Blue: 1/3
Step-by-step explanation:
You take and find the total number of marbles, which is 18. You then take the number of each different color and make that number your numerator, and 18 your denominator and reduce.
Red: 9/18 reduces to 1/2
White: 3/18 reduces to 1/6
Blue: 6/18 reduces to 1/3
Evaluate the following functions.
Help
The midpoint of a given line segment must lie on the given line segment.
A. Trime
OB. False
The midpoint of a given line segment must lie on the given line segment is True.
What is midpoint?
A midpoint is a location that sits in the middle of the line connecting two points and is situated between them. If a line is drawn connecting the two points, the midpoint is the place on the line that is equally distant from both points. A point B that is situated halfway between two other points, such as A and C, is said to be the midpoint. Because of this, finding the midway only requires measuring the length of the line segment and dividing it by 2.
Here the given statement is,
=> The midpoint of a given line segment must lie on the given line segment.
Here according to the given statement we know that the midpoint of the any line lies on the given line.
Hence the given statement is True.
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Use the Distributive Property to simplify (–5 – c)( –1).
5 + c
–5 + c
–5 – c
5 – c
Need Help Please! Real quick....I'll give brainliest to first correct answer!!!! ASAP.....Gotta turn it in.
Answer:
2x + y = 3 becomes y = 3 - 2x
-2x + y = -1 becomes y = -1 + 2x
2x + y = 5 becomes y = 5 - 2x
Parallel: 2x + y = 5
Perpendicular: 0.5x + 7
neither parallel nor perpendicular to line a: -2x + y = -1
Suppose there are 9 freshman, 13 sophomores, 13 juniors, and 16 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?
These people are elected in 47814 different ways to these positions.
Given, there are 9 freshman, 13 sophomores, 13 juniors and 16 seniors running for the offices of president, vice president, and secretary.
Now, the number of different ways in which these people can be elected for these positions be,
C(9 , 1)×C(13 , 1)×C(13 , 1)×3! + C(9 , 1)×C(13 , 1)×C(16 , 1)×3! + C(9 , 1)×C(13 , 1)×C(16 , 1)×3! + C(13 , 1)×C(13 , 1)×C(16 , 1)×3!
= 9×13×13×6 + 9×13×16×6 + 9×13×16×6 + 13×13×16×6
= 9126 + 11232 + 11232 + 16224
= 47814
So, these people can be elected in 47814 different ways.
Hence, these people are elected in 47814 different ways to these positions.
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3) Helen has $1.35 in her bank of nickels and dimes. There are 9 more nickels than dimes. Find the number she has of each kind.
Samantha travels 175 miles in 25 hours? How many miles does Samantha travel in 5 hours?
Answer:
THERES MUCH INFORMATION EXCLUDED!
Step-by-step explanation:
She travels 7 miles per 25 hours
If the total distance travelled was 500 miles and the time it took you was 5 hours, then your average speed was 500 / 5 = 100 miles per hour (mph).
BASED ON MY OWN CALCULATIONS:
I helped you..help me by marking me brainliest:)
Question 4 of 10
Which two correctly relate the attraction between the particles of a liquid and
the temperature at which the liquid changes state?
A. Strong attractions mean the liquid melts at a lower temperature.
B. Strong attractions mean the liquid boils at a lower temperature.
C. Strong attractions mean the liquid boils at a higher temperature.
D. Strong attractions mean the liquid melts at a higher temperature.
SUBMIT
Answer: a,c
Step-by-step explanation:
