The simplified expression is x² + 2x - 15.
We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.
E = (x + 5)(x - 3)
We will use the distributive property.
E = x*(x - 3) + 5*(x - 3)
E = x*x - x*3 + 5*x - 5*3
E = x² - 3x + 5x - 15
E = x² + 2x - 15
Hence, the expanded and simplified form of the given expression is x² + 2x - 15.
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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
18, 14, 10, .
Answer: The sequence has a common difference between consecutive terms
14 - 18 = 10 - 14 = - 4
This indicates it is an arithmetic sequence with a common difference - 4
Step-by-step explanation:
(b) Bill removed 70 fish from his pond over a period of 7 days. He removed the same number of
fish each day. What was the change in the number of fish in the pond each day?
-70 fish
Answer:
ROC=10/1
Step-by-step explanation:
ROC=change in y-change in x
We can first write out a few more points.
(7,70), (14,140), (21,210)
210-140=70
140-70=70
21-14=7
14-7=7
So the ROC is 70/7 or 10/1
71. Coffee and Muffins On Monday the office staff paid a total of
$7.77 including tax for 3 coffees and 7 muffins. On Tuesday
the bill was $14.80 including tax for 6 coffees and 14 muffins.
If the sales tax rate is 7%, then what is the price of a coffee
and what is the price of a muffin?
Answer:
Step-by-step explanation:
if i help you with this can yu do this
1. Describe, in detail, the way Jews were treated by the Nazi Party between 1933 and 1944. Be sure to address the restrictions on the Jews and their movement as well as discussing the creation and impact of the Nuremberg Laws.
2.explain how literature can help us understand the past. How can reading literature sometimes be more effective than studying an informational/historical document or simply studying "facts" from the past.
120 or more for both questions!!!
please hurry need asap
Find the area of this triangle.
155
175
260
Answer:
13170.421 -> rounded to nearest whole number is 13170
Step-by-step explanation:
u = a + b + c
area = √(u/2 * (u/2-a) * (u/2-b) * (u/2-c))
You have 14 pens and markers. You have six more markers than pens. How many of each item do you have?
Answer: 13 markers and one pen
Step-by-step explanation:
14/2 = 7
7+6=13 markers
Which means there is only one pen left
From the obtained equation, there are 4 pens and 10 markers.
Given that, there are 14 pens and markers.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of pens be p.
Then, the number of markers will be p+6
Now, the equation is p+p+6=14
⇒ 2p+6=14
⇒ 2p=8
⇒ p=4
Thus, p+6=10
Therefore, from the obtained equation, there are 4 pens and 10 markers.
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19x=y
in standerds form
Answer:
19x − y = 0
__
Find the circumference of a circular swimming pool with a diameter of 22 feet. Use 3.14 as an approximation for pie. Round your answer to the nearest whole foot. Enter only the number.
Answer:
380 ft²
Step-by-step explanation:
diameter = 22 ft
radius = diameter/2 = 22 ft/2 = 11 ft
area = πr²
area = 3.14 × (11 ft)²
area = 379.94 ft²
Answer: 380 ft²
an article in a medical journal suggested that approximately 18% of such operations result in complications. using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.06?
The needed Sample size is 32.2 so that the confidence interval will have a margin of error of 0.06.
We have provided that , An article in a medical journal approx. 18% of operation results complications.
Using the estimate formula, for standard margin of error
Margin of error (E) = Z x √p(1-p)/n
where , E---> margin of error
Z---> estimate value
p----> sample proportion
n -----> Sample size
we have the value of E = 0.06 , p = 18% = 0.18
put all the values in above formula we get,
0.06 = Z × √0.18× 0.82/n
critical value or Z-value for sample proportion 0.18 is 0.91
Now, 0.06 = 0.91 × √0.18×0.82/n
=> √0.14/n= 0.065 => 0.14/n = 0.0043
=> n= 32.2
So, sample size is 32.2
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Please I need help please
Answer:
m∠T = 60°
m∠U = 60°
TS = 13 cm
SU = 13 cm
Step-by-step explanation:
The diagram shows that 2 sides, UT and TS, are equal, so it is an isosceles triangle. Since it is an isosceles triangle, the two angles opposite the equal sides are also congruent to each other, so m∠S = m∠U = 60°.
Now we know the measure of 2 angles, we can find the measure of the third angle, by subtracting the 2 known angles from 180°.
m∠T = 180° - m∠S - m∠U
m∠T = 180° - 60° - 60°
m∠T = 60°
Since all 3 angles are congruent, it is an equilateral triangle, therefore all the sides must be congruent too. So UT = TS = SU = 13 cm.
PLEASE ANSWER QUESTIONS IN IMAGE GIVING BRAINLIEST!!!!
The function of Car A is an exponential function.
The function that describes the value is g(x) = [tex]18,000(0.94^{x})[/tex].
The value of f(x) in 9 years is $10,313.91.
The function of Car B is a linear function.
The function that describes the value is g(x) = 18,500 -750x.
The value of f(x) in 9 years is $11,750.
What is the value of the cars in 9 years?The value of the car declines with the passage of time. Thus, the value of the car depreciates with the passage of time.
A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value.
The general form of a linear function is f(x) = a + bx
Where:
a = initial value b = rate of change x = number of yearsRate of change = value of the car B in year 2 - value of the car B in year 1
17,000 - 17,750 = - 750
g(x) = 18,500 -750x
Value of g(x) when x is 9:
g(x) = 18,500 -750(9)
g(x) = 18,500 - 6,750
g(x) = $11,750
An exponential function can be described as an equation with exponents. The exponent is usually a variable.
The general form of exponential function is f(x) = [tex]e^{x}[/tex]
Where:
• x = the variable
• e = constant
Constant = (Value of the car in year 2 / value of the car in year 1) - 1
Constant = (16,346.60 / 17,390) - 1 = -0.06 = -6%
g(x) = [tex]18,000(0.94^{x})[/tex]
Value of the car in 9 years = [tex]18,000(0.94^{9})[/tex] = $10,313.91
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question is at the bottom !! anyone know the answer ??
PLS DONT ANSWER IF YOU DONT KNOW IT, i will report u if you do this.
ONLY ANSWER IF U KNOW!
12 is the marginal cost at the production level of 1000 units.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The marginal cost represents the additional cost if 1 more unit is produced. So, we can find the marginal cost by computing C(1,001) and subtracting (1,000)
First, let's evaluate the cost at both x= 1,001 and x=1,000
C(1000)=0.002(1000)^2+8(1000)+6000
=0.002(1000000)+8000+6000
=2000+8000+6000
=16000
C(1001)=0.002(1001)^2+8(1001)+6000
=2004.002+8008+6000
=16012
The difference between these costs is $12.002. Rounding to the nearest cent, we find a marginal cost of $12 per unit. Let's see if we get a similar result from the derivative.
Hence 12 is the marginal cost at the production level of 1000 units.
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the anser answer are A(250 feet)-(b)150 feet)-c)100 feet)-d(200 feet)
Answer:
(b) 150 feet
Step-by-step explanation:
You want to know the height of a kite at the end of 225 feet of string, flying at an angle of elevation of 45°.
Right triangleThe 45° angle in the given right triangle tells you this is one of the "special" right triangles. Its side lengths have the ratios ...
1 : 1 : √2
where √2 is the hypotenuse.
That means the other two legs of this right triangle are ...
(225 ft)/√2 ≈ 159.099 ft
Rounded to the nearest 50 feet, this is about 150 feet.
__
Additional comment
The sine function relates the angle value to the opposite side:
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse · Sin
height = (225 ft)·sin(45°) = 225 ft/√2 ≈ 159.099 ft
For what values of the variable does each of the following expressions make sense; square root of -3(1-5x)
Answer: x is greater than or equal to 1/5
Step-by-step explanation:
The value of -3( 1 - 5x) CANNOT be negative.
Using this information we know that 1-5x is negative.
We can write:
1-5x >= 0
1>=5x
x>=1/5
A hat that normally cost $20 is on sale for $14. What percent of the regular price is the
sale price?
Answer:
70
Step-by-step explanation:
(14/20)*100=70
can you substitute y=2x+4 y=2
Answer: x = -1
Step-by-step explanation:
Since, you know y = 2, substitute that y-value into the other function:
[tex]2=2x+4\\\\2x=2-4=-2\\\\x=\frac{-2}{2} =-1[/tex]
Solve the simultaneous equations
Answer:
(x = -0.90, y = 2.31) and (x = 1.40, y = 9.19)
Step-by-step explanation:
See the attached image
23. A group of friends is collecting aluminum for a recycling drive. Each person
who donates at least 4.25 pounds of aluminum receives a free movie coupon.
The weight of each person's donation is shown in the table.
Brenda
4.3
Claire
5.5
Jim
61/10
Micah
15
4
Weight
(lb)
a. Order the weights of the donations from greatest to least.
Peter
43
b. Which of the friends will receive a free movie coupon? Which will not?
c. What If? Would the person with the smallest donation win a movie
coupon if he or she had collected pound more of aluminum? Explain. Which of the friends will receive a free movie coupon?which will not
Answer:
Step-by-step explanation:
a. 6.17 , 5.5 , 4.375 , 4.3 , 3.75
b. Everyone except Micah.
C. Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have; 3.75+0.5=3.75 pounds. Then he would have got the coupon as a minimum of 4.25 pounds is required.
Please fill in the missing blanks! I will give brainly to the best!
The required missing terms are sequential as 3, -8, -10, 1, -9, -7, 5, 10, 6, -9, 1, -1, 1, and -7.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
What we do is, lets fill the blank space be x,
Now for 1,
[-1] + [-1] + x = 1
-2 + x = 1
x = 1 + 2
x = 3
Similarly, all the blank spaces can be determined as, -8, -10, 1, -9, -7, 5, 10, 6, -9, 1, -1, 1, and -7.
Thus, the required missing terms are sequential as 3, -8, -10, 1, -9, -7, 5, 10, 6, -9, 1, -1, 1, and -7.
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Does a multi-step equation always, sometimes, or never have a solution? Explain your reasoning.
What value of a makes lines m and n parallel?
Answer:
20
Step-by-step explanation:
3x + 5 should be equal to 65
3x + 5 = 65
3x = 65 - 5
3x = 60
x = 60/3
x = 20
what 27 over 54 in lowest terms
Answer: 1/2
Step-by-step explanation: Divide both the numerator and denominator by the GCD (Greatest Common Denominator)
27 ÷ 27
54 ÷ 27 (its 27/54 divided by 27/27
Reduced fraction:
1/2
Therefore, 27/54 simplified to lowest terms is 1/2.
enter a quadratic polynomial which has zeros at -7 and 7
The required quadratic polynomial whose roots are -7 and 7 is
[tex]x^{2} - 49[/tex]
As the zeroes are given, i.e., 7 and -7.
∴ Sum of roots = 7+(−7) = 7− 7 = 0
Product of roots = 7×(−7) = −49
As we know, a quadratic polynomial whose zeroes are given can be represented as-
[tex]x^{2}[/tex] - (Sum of roots)x + (product of roots) = 0
[tex]x^{2} -0*x +(-49) = 0\\\\x^{2} - 49 = 0[/tex]
Hence, the required quadratic polynomial whose roots are -7 and 7 is
[tex]x^{2} - 49[/tex]
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What’s the IQR for jacobs data set
The IQR for Jacob's data set is determined as: 2 seconds.
What is the Interquartile Range of a Data Set?To find the interquartile range (IQR) of a Data set, find the third quartile value and the first quartile value. Their difference is the Interquartile Range (IQR) of the data.
Interquartile Range (IQR) = third quartile - first quartile.
In the box plot given, we can deduce that:
Third quartile = 15.5
First quartile = 13.5
Interquartile Range (IQR) = 15.5 - 13.5
Interquartile Range (IQR) = 2 seconds
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Answer: 2 seconds
Step-by-step explanation:
write and solve a system of linear equations to find the values of $x$ and $y$ . a quadrilateral. the angles of the quadrilateral are 5x degrees, (4y minus 2 )degrees, (13x plus 10 )degrees, and 10y degrees.
As per the angle sum property of quadrilateral, then values of x is 245 and the value of y is 341
Angle sum property of quadrilateral:
The angle sum property states that the sum of all the angles of the quadrilateral is 360 degree.
Given,
The angles of the quadrilateral are 5x degrees, (4y minus 2 )degrees, (13x plus 10 )degrees, and 10y degrees.
Now we have to write and solve a system of linear equations to find the values of x and y.
While we looking into the given angles, then we get the values
=> 5x°
=> (4y - 2)°
=> (13x + 10)°
=> 10y°
We know that, the sum of all the angles of the quadrilateral is 360°.
So, it ca be written as,
=> 5x° + (4y - 2)° + (13x+ 10)° + 10y° = 360°
=> 18x° + 14y° - 8° = 360°
=> 18x° + 14y° = 354°
When we divide all of them by 2, then we get the equation as,
=> 9x° + 7y° = 177°
Now we have to rewrite the given equation as,
=> 9x° = 177° - 7y°
=> x° = (177° - 7y°)/9
Apply these value on the angles, then we get,
=> 13(177 - 7y)/9 = -10
=> 13(177 - 7y) = 90
=> -7y = -90 - 2301
=> 7y = 2391
=> 341
Then the value of x is
=> 245
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What is the slope of a line parallel to the line whose equation is x + y = 6
Answer:
-1
Step-by-step explanation:
put this equation in slope intercept form : y=mx+b
x+y=6
-x. -x
y=-1x+6
The slope of this line is -1 and for it to be parallel they both have to have the same slope
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1. Stanley's cat weighs 5 pounds. Stanley's dog weighs 3 3/5 times as much as his cat.
How much does Stanley's dog weigh?
Answer:
18
Step-by-step explanation:
Answer:
18 pounds
Step-by-step explanation:
5x 3 3/5= 18
Find both unit rates.
: An object traveled 691.12 feet in 21.2 seconds.
Question 1 options:
A: 32.6 s/ft and approximately 0.03 s/ft
B: 32.6 ft/s and approximately 0.03 s/ft
C: 32.6 ft/s and approximately 0.03 ft/s
D: 32.6 s/ft and approximately 0.03 ft/s Warning: Whoever Answers this wrong will be reported. :l
The unit rate is 32.6 ft/s and approximately 0.03 s/ft.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
An object traveled 691.12 feet in 21.2 seconds.
So, the unit rate as feet per second.
= 691.12/ 21.2
= 32.6 ft/s
and, the unit rate as second per feet
= 21.2/ 691.12
= 0.03 s/ ft
Hence, the unit rate is 32.6 ft/s and approximately 0.03 s/ft
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A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in: 8 ft. How tall is the model of the lighthouse in inches?.
The height of the model of the lighthouse in inches is 20 inches
The real height of the lighthouse = 160 feet
The scale model of the light house has scale of
1 inch : 8 feet
Consider the height of the model of the lighthouse is x
Then the proportion of the scale model of the lighthouse and the actual height will be
1 inch / 8 feet = x inches / 160 feet
Cross multiply the terms
1 × 160 = 8x
Multiply the terms
8x = 160
Divide both side of the equation by 8
8x / 8 = 160 / 8
x = 20 inches
Hence, the height of the model of the lighthouse in inches is 20 inches
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50 POINTS TO WHOEVER ANSWER THIS QUESTION!! THANKS SO MUCH!!!
The value of side x is given by (C) 14.7 units approximately.
Given the triangle is a right angled triangle.
Now given also that, Height of triangle is = x units
Base of triangle is = 15 units
Hypotenuse of triangle is = 21 units
So by Pythagoras theorem, we get the sum of squares of base and height is equal to the square of hypotenuse. So,
[tex]x^2+15^2=21^2\\\Rightarrow x^2+225=441\\\Rightarrow x^2=441-225\\\Rightarrow x^2=216\\\Rightarrow x\approx14.7[/tex]
So the value of x is 14.7 units approximately.
Hence the correct option is (C).
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A z-test with a z observed of 2.56 (two-tailed) would have a p-value of ______, which would lead a research to _______ the null hypothesis if alpha is .05.
A z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.
Given:
z - score = 2.56
p value at z = 2.56 is:
p = 0.010467
The result is statistically significant: you can reject the null hypothesis and accept the alternative.
This decision is made at significance level α = 0.05.
Therefore a z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.
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