Answer:
○ Length = 20 centimeters and Width = 5 centimeters
Step-by-step explanation:
Let the length = L
Then the width is L - 15
A = lw
100 = L(L - 15)
L² - 15L - 100 = 0
(L - 20)(L + 5) = 0
L - 20 = 0 or L + 5 = 0
L = 20 or L = -5
Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.
L = 20
width = L - 15 = 20 - 15 = 5
Answer: ○ Length = 20 centimeters and Width = 5 centimeters
Write the equation for the function graphed below.
Answer:
f(x) = (x + 1)^2 + 2
Step-by-step explanation:
A parabola function has different forms:
standard form: f(x) = ax + bx + c^2
vertex form: f(x) = a (x − h)^2 + k
Our equation that includes a horizontal translation is h
- negative h shifts right
- positive h shifts left
this graph shows a shift to the left by 1 so h = 1
Our equation that includes a vertical translation is k
- negative k shifts down
- positive k shifts up
this graph shows a shift to the up by 2 so k = 2
- a represents a compression / stretch which seems not to be in this graph
combine, f(x) = (x + 1)^2 + 2
A carpenter wants to cut an 84 inches long board into two-pieces such that one piece is twice as long as the other piece. Set up an equation and find the length of each piece.
Answer:
small piece = 28 inches
large piece = 56 inches
Step-by-step explanation:
The carpenter has one piece of wood 84 inches long. He wants to cut that piece of wood into two pieces. One piece will be 2 times as long as the other. Let's let x = the small piece of wood
2x + x = 84
In this equation, the longer piece is 2 times the shorter piece and the shorter piece is added, which equals 84 inches. Lets solve:
2x + x = 84
3x = 84
3x/3 = 84/3
x = 28
This means that the shorter piece is 28 inches. To find the longer piece, multiply 28 by 2 because the longer piece is twice the shorter piece. Therefore the longer piece is
28 × 2 = 56
Finally, we figured out that the short piece is 28 inches and the longer piece is 56 inches
We can double check this by doing 56 + 28 and making sure it equals 84
What is the equation for the following word problem: Hayden is selling snacks for $1.50 each. If he made $15, how many snacks did he sell?
Answer:
10
Step-by-step explanation:
15 ÷ 1.5 = 10
can someone please help me
Answer: C
Step-by-step explanation:
The slope is positive, so m>0.
The y-intercept is negative, so b<0.
Chad has a rope that is 24 yards long. How many pieces of rope measuring of a yard can he divide his rope into1/4
The pieces of rope measuring a yard can he divide his rope into1/4 would be 96.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Chad has a rope that is 24 yards long. He wants to divide the rope so each piece will be 1/4 yards
= 24÷1/4
= 24× 4
= 96
Hence he can divide the rope into 96 pieces.
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100 adults were asked how they keep fit.
Each adult goes to the gym, runs or cycles.
45 of these adults are female.
30 of the 52 adults who go to the gym are female.
35 adults run.
9 males cycle.
One of the females is chosen at random.
Write down the probability that she runs.
The probability that a female chosen runs = 0.24
How to find the probability?We are given;
Number of adults surveyed = 100
Total number of females = 45
Total Number of Males = 55
Number of female adults that go to gym = 30
Number of adults that run = 35
Number of males that cycle = 9
Thus;
From the probability table attached, we can say that;
Number of females that can run = 11
Probability that she runs = 11/45
Probability that she runs = 0.24
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A banner is in the shape of a rectangle. It is 15 feet long and 12 feet wide. What is the perimeter?
Here....
The length is given 15 feet and the width is 12 feet...Now let's find the Perimeter..
The formula to calculate Perimeter of rectangle is 2 ( l + b )Perimeter = 2 ( l + b )
= 2 ( 15 + 12 )
= 2 × 27
= 54 feet
[tex]...[/tex]
:)...
Determine whether it is a function
Answer:
Relation 1: FunctionRelation 2: FunctionStep-by-step explanation:
A function is defined so that for each input, there is no more than one output.
Rohan had (-4x – 12y + 6z) rupees. He spent (7x – 3y + 8z )to buy new clothes. How much is left with him now?
Construct a linear equation for the linear data presented in the table
Answer:
y = -7x
Explanation:
Take two points from table: (-4, 28), (-3, 21)
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope\ (m): \dfrac{21-28}{-3-(-4)} = -7[/tex]
Now find equation:
[tex]\sf y - y_1 = m (x - x_1)[/tex]
[tex]\rightarrow \sf y - 21 = -7(x - (-3))[/tex]
[tex]\rightarrow \sf y = -7(x +3) + 21[/tex]
[tex]\rightarrow \sf y = -7x -21 + 21[/tex]
[tex]\rightarrow \sf y = -7x[/tex]
Slope
m=y/xm=14/-2m=-7Equation of line
y=mx+0y=-7xHello what is the next number in the sequence 7, 11, 2, 18, -7, ?
The next number in the sequence 7, 11, 2, 18, -7, would be -11.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
Given sequence;
7, 11, 2, 18, -7,
We can see that the fifth term is similar to the first term, except for the negative.
So, we can conclude that the integers start from the fifth term and leads to the next term as a negative of the second one.
Therefore, The next number in the sequence 7, 11, 2, 18, -7, would be -11.
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7/8 yard of material is needed to make a blanket, how many blankets can be made from 21 yards of material?
Answer:
24
Step-by-step explanation:
the question translates to asking how many times does 7/8 fit in 21, so 21 divided by 7/8.
when we divide by a fraction, we can multiply by it's inverse, so 21 divided by 7/8, is 21 multiplied by 8/7. so:
21×8/7 = (21×8)/7 = (21/7)×8 = 3×8 = 24
3x2+14x=−11 solve for x
x= -.55
6x+14x=11
20x=-11
x=-11/20
Help me with this question please!! :)
ANSWERS ARE AT THE BOTTOM.
To find the probability of 2 events happening in a row, we need to multiply their probabilities.
For example, if a friend bet: "If you roll a six on a dice and filp and coin and get heads, then I'll give you 500 bucks. However, if you don't roll a six and flip and coin and get heads in a row, then you have to give me 500 bucks."
You want to know the probability of you winning this bet.
So, we need to multiply the probability of rolling a six, and the probability of flipping a coin and landing heads.
This is 1/6 * 1/2
That is 1/12
You probably should't take this bet, because you only have a 1/12 chance of winning.
Lets go back to your problem. The jar contains 16 red marbles and 28 blue marbles. The probability of picking a red marble right now is 16/28, or 4/7. Assume we picked a red marble on our first try. Now, there are only 15 red marbles. The probability of picking a red marble right now is 15/28.
Probability of picking a red marble on your first try: 4/7
Probability of picking a red marble on your second try: 15/28
Now, we need to multiply the probabilities.
4/7 * 15/28
60/196
15/49
ANSWER:
15/49
Standard Form
Instructions: Rewrite the equation in proper Standard Form.
Equation: x - y = −3
Standard Form:
Check
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
In this graph, the number of containers is plotted along the x-axis and the amount of water in the containers is along the y-axis.
The proportionality constant of the graph (y to x) is
The constant of the proportional relationship graphed in this problem is of 10.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the points on the graph are: (0,0), (2,20), (4,40), ..., hence the constant is:
k = 40/4 = 20/2 = 10.
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A. Find the slope of the lines through the pairs of points, (1,-8) and (1,-9) the slope is m=
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: slope = not \:\: defined [/tex]
with closest value = [tex] \sf{\infin} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: slope = \cfrac{rise}{run}[/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ - 8 - ( - 9)}{1 - 1} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ - 8 + 9}{0} [/tex]
[tex]\qquad \tt \rightarrow \: m \: \: is \: \: not \: \: defined[/tex]
[ Any real number divided by 0 is not defined ]
You can also assume it's closest value if possible, that is infinity ([tex]\sf{\infin}[/tex])
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Which of the following represents a geometric sequence with a common ratio r = 6?
1, 6, 36, 216, 1,296
3, 18, 24, 144, 864
7, 13, 19, 25, 31
648, 108, 18, 3, 0.5
Answer:
The first sequence is correct being (6)^k
Step-by-step explanation:
To find a ratio divide a term by its previous member such as 36/6 to give you r=6.
urgent help needed algebra 2
The missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
[tex]\rm F = \dfrac{9}{5}C + 32[/tex]
Make subject C and solve:
[tex]\rm \dfrac{5}{9}(F-32) = \dfrac{5}{9}\times\dfrac{9}{5}C[/tex]
[tex]\rm \dfrac{5}{9}(F-32) = C[/tex]
Plug F = 41
[tex]\rm \dfrac{5}{9}(41-32) = C[/tex]
[tex]\rm \dfrac{5}{9}(9) = C[/tex]
41 degrees F = 5 degrees C
Thus, the missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.
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The function f(x) = ex-3 when evaluated for f(4) is equivalent to?
Answer:
[tex]f(4)=e^{4}-3[/tex] or [tex]f(4)\approx51.5981500331...[/tex]
Step-by-step explanation:
The following is a general explanation of functions, what they mean, and how to evaluate them. The simplifications and calculations at the end are based on the clarification from your comments that [tex]f(x)=e^{x}-3[/tex] . If [tex]f(x)[/tex] is equal to something else, the simplifications/calculation will obviously be a little different, and the answer will likely be different, but the general process will be the same.
Understanding function notation
In the equation [tex]f(x)=e^{x}-3[/tex] , the left side of the equation is saying several things at once.
Names
The first character, "f", is the name of the function.
The name of a function tells you which set of directions you should look for to apply to an input. Some functions have names that are more than one letter, and even might give a hint as to what they do, for instance I might name a certain function [tex]squareroot[/tex], and based on the name, you might guess what the equation for [tex]squareroot(x)[/tex] might look like.
Mathematicians often use "f" as a function name between different problems over and over and over again, unless they come up with a special function that is worth giving a special name to.
Input
The rest of the characters after the name of the function, are "(x)" which is a pair of parentheses to contain the input, and the input itself.
Again, mathematicians often use "x" as a generic input over and over and over again, until we actually know which number we want to put into the function.
Output
Even though we've already discussed every character in the notation on the left, there is actually one more thing that the left side of the equation is saying: Altogether, "f(x)" is the output of the function, when the input "x" is put in. I feel it's worth stating, because it's often glossed over.
The equation itself
Next in the equation is the equals sign, which means that the left side of the equation, which is the output "f(x)", is equal to the stuff on the right.
The right side of the equation is the rule to follow describing what f(x) does to an input, and can help you calculate the output.
For instance, if I asked what p(4) was, it is clear that there is an input of 4, but without knowing what the function "p" does, there's no way to know what the function will give as an output when one inputs "4". This is why the right-hand side of the equation for a function is important.
Evaluating functions
To evaluate any function, we take an input, apply the function, and simplify/calculate the output.
In this case, the question asks for [tex]f(4)[/tex], meaning that the "input" is "4".
In this case, the question gives an explanation of what the function does through a rule given in equation form.
Given your clarification of the given function, [tex]f(x)=e^{x}-3[/tex] , meaning a generic input (in this case "x") is put into the function "f" and the output is found by doing the arithmetic on the right side of the equation (exponentiating the number by "e", and then subtracting 4)
Notice that in the expression [tex]f(4)[/tex], the "x" was replaced with "4". So, we need to substitute "4" where we see an "x" in the rule on the right hand side of the equation rule, and simplify and/or calculate (calculate, like with a calculator)
So, to evaluate the expression [tex]f(4)[/tex], simply substitute, and simplify/calculate.
Simplifying (no calculator)
To simplify without a calculator, we substitute "4". Any time you make a substitution, use parentheses. Then, try to simplify.
[tex]f(4)=e^{(4)}-3[/tex]
[tex]f(4)=e^{4}-3[/tex]
As it turns out, this is as much as we could simplify things here (without a calculator). So, if an exact answer is needed, this would be it.
Calculating (with a calculator)
To calculate with a calculator, we substitute "4". Any time you make a substitution, use parentheses. Then, try to simplify.
[tex]f(4)=e^{(4)}-3[/tex]
[tex]f(4)=e^{4}-3[/tex]
[tex]f(4)=54.5981500331...-3[/tex]
[tex]f(4)=51.5981500331...[/tex]
So calculating with a calculator, the output of the function "f", for an input of "4", is approximately 51.598.
Sasha's bank account earns 4% simple interest. How much must she deposit in the account today if she wants it to be worth $1,000 in 5 years?
If Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Sasha's bank account earns 4% simple interest. Therefore, if she wants it to be worth $1,000 in 5 years then the principal amount must be,
Account balance = PRT + P
$1,000 = P[(0.04×5)+1]
$1,000 = 1.2 P
P = $833.34
Hence, if Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.
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Question 1
The total length of a hiking trail in the mountains is 8 miles. If Dale and his son completed 4/5 of the trail yesterday, how many feet did they hike?
42,240 feet
22,528 feet
11,264 feet
33,792 feet
Answer:
33, 792
Step-by-step explanation:
first convert the 8 miles to feet because our answers are in feet.
1 mile= 5280 feet
therefore 8 miles= 5280×8
= 42240
Dale and son covered 4/5 of the 42240 feet
= 4/5×42240
= 33,782 feet
Which statements are true from the graph ? Check all that apply:
the line is horizontal the line is vertical
The statements that are true from the graph are:
The line is horizontalThe line goes through (4, 4 )The y- values are all 4Calculations and ParametersGiven the graph, we can note some things:
There is a line with a slope of zero.This is a horizontal line parallel to the x-axis.The equation of the line is y = cc is the value of the y- coordinates the line passes through.
The line passes through (0, 4 ) with a y- coordinate of 4
Therefore, the equation of the line of y= 4
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unrjdjxbzbwnf c and f f
Answer:
.
Step-by-step explanation:
.
A shop advertises a 24% off sale. The coat sold for $258 fins the decrease in price and the sale price
Answer:
339.47
Step-by-step explanation:
100 - 24 = 76
258 = 76 percent
3.39473684211 = 1 percent
339.47 = 100 percent
Answer:
The decrease in price is $61.92
The sale price is $196.08
Step-by-step explanation:
24% × 258 = 61.92
258 decrease 24% =
258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08
Which shows the first step in the solution to the
equation log₂x + log₂(x - 6) = 4?
log was used calculate big numbers before calculators
log is a re-arranged way to show a number with an exponent
example
log₂ 16 = 4 means 2^4 = 16
logx(Z) = y means x^y=Z
log(x-6)/log(2) + log(x)/log(2) = 4
(log(x-6)+ log(x))/log(2) = 4
(log(x-6)+ log(x)) = 4log(2)
(log(x-6)x) = log(16)
x=8
Please help me solve this
A function assigns the values. The value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given p(x)= x²+5x, therefore, the value of (p·p)(x) can be written as,
(p·p)(x) = p(p(x))
= (x²+5x)²+5(x²+5x)
= x⁴ + 25x² + 10x³ + 5x² + 25x
= x⁴ + 10x³ + 30x² + 25x
Hence, the value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.
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How do you do this?
a) The ratio of the perimeters is the same as the scale factor, so the ratio is the perimeters is 2/3.
b) The perimeter of triangle ABC is [tex]36\left(\frac{3}{2} \right)=\boxed{54 \text{ ft}}[/tex]
c) The ratio of the areas is the scale of the scale factor. In this case, the ratio is [tex](2/3)^{2}=\boxed{4/9}[/tex]
d) The area of FDE is [tex]36(4/9)=\boxed{16 \text{ ft}^{2}}[/tex]
Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
[tex]\sqrt{1}[/tex]
Step-by-step explanation:
We know that a rational number cannot have roots. All of the answer choices cannot be simplified except for [tex]\sqrt{1}[/tex], which can become 1. Therefore, our answer is [tex]\sqrt{1}[/tex].
Solve x: 60 pts if u can figure it out and the first one gets brainiest answer
3x+99x=1188
Is this even possible to work out????
Answer:
11.65
Step-by-step explanation:
3x+99x=102x
1188/102=11.65
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3x + 99x = 1,188}[/tex]
[tex]\large\textbf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(3x + 99x) = 1,188}\\\mathsf{3x + 99x = 1,188}\\\mathsf{\bold{102x} = 1,188}[/tex]
[tex]\large\textbf{DIVIDE 102 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{102x}{102} = \dfrac{1,188}{102}}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{1,188}{102}}[/tex]
[tex]\mathsf{x = 11.64705882}[/tex]
[tex]\large\textbf{AND IF YOU'RE ROUNDING}[/tex]
[tex]\mathsf{x \approx 12}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x \approx 12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]