Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.
How to determine the speed of this plane?In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:
Let d₁ represent the distance covered by Mattie.Let v₁ represent the speed of Mattie's car.Let d₂ represent the distance covered by the turbopropeller plane.Let v₂ represent the speed of the turbopropeller plane.Translating the word problem into an algebraic equation, we have;
v₂ = v₁ + 200
Since Mattie and the turbopropeller plane travled at the same time, we have:
Time = distance/speed
Time = d₁/v₁ = d₂/v₂
Time = 140/v₁ = 540/v₁ + 200
Cross-multiplying, we have:
140(v₁ + 200) = 540v₁
140v₁ + 28,000 = 540v₁
Next, we would rearrange the equation by collecting like terms as follows:
540v₁ - 140v₁ = 28,000
400v₁ = 28,000
Speed of plane, v₁ = 28,000/400
Speed of plane, v₁ = 70 mph.
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PLEASE HELP ILL GIVE BRAINLIST ANYTHING PLEASE
n -3/8> -2/5
Answer:
n>-1/40
Step-by-step explanation:
Hope this helps!! (I promise...it's the right one)
Answer:
b) n > (-1/40)
Step-by-step explanation:
Given equation,
→ n - (3/8) > (-2/5)
Now the value of n will be,
→ n - (3/8) > (-2/5)
→ n > (-2/5) + (3/8)
→ n > (-16/40) + (15/40)
→ n > (-16 + 15)/40
→ [ n > (-1/40) ]
Hence, value of n is -1/40.
When the remainder is zero, which statement is NOT true?
A. The quotient is a factor
B. The divisor is a factor
C. The solution of the divisor is a zero
D. The dividend is a factor
(right answer only!)
When the remainder is zero, the statement that isn't true is that C. The solution of the divisor is a zero.
What is a dividend?A dividend simply means the value that is divided by another value in order to far the result. It is the base of the division problem.
For example, 12 divided by 6 is 2. In this case, 6 is the dividend. 6 is a factor of 12.
Therefore, the correct option is C
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I baked a cake for my siblings. My brother ate \large \frac{1}{8} of the cake and my sister ate \large \frac{3}{4}. How much of the cake is left for me?
In a case whereby I baked a cake for my siblings ad My brother ate large fraction 1/8 of the cake and my sister ate \large frac 3/4 , the amount of cake is left for me is 1/8.
How can the amount of the cake remaining can be calculated?In this question , we are dealing with fraction, which implies that the number of the cake that i am having is 1.
And we are told that 1/8 of the cake is been eaten by my brother, where 3/4 of the cake is been eaten by my sister, then to know the amount of cake that was left for me, we will need to perform some simplification as:
1-(1/8) - (3/4) =1/8.
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If a cake is baked, In which her brother ate 1/8 and sister ate 3/4. Then 1/8 of cake is left me.
What is Fraction?A fraction represents a part of a whole
Given that a cake was baked for her siblings.
Her big brother ate large part of the cake that is 1/8.
Her sister ate 3/4 of the cake.
We need to find the left out cake for her.
To do that we have to remove 1/8 and 3/4 from 1.
1-(1/8)-(3/4)
(8-1-6)/8
1/8
Hence she has 1/8 of cake which is left.
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For f(x) = 2x + 1 and g(x) = 2
7, find (f- g)(x)
The value of (f- g)(x) is 2x - 26.
This is a question of subtraction of functions.
Subtraction of functions
The subtraction of function involves the creation of a new function through the addition of two other functions.
Subtraction of one real-valued function from another.
Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.
Given that:-
f(x) = 2x + 1
g(x) = 27
We have to find the value of (f- g)(x)
We know that,
(f- g)(x) = f(x) - g(x)
Hence, we can write,
(f- g)(x) = 2x + 1 - 27 = 2x - 26
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Under her cell phone plan, Paisley pays a flat cost of $60 per month and $3 per
gigabyte. She wants to keep her bill under $75 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Paisley can use
while staying within her budget.
V
9
VI
Inequality:
Submit Answer
IV
The inequality used to represent Paisley budget and the number of gigabytes Paisley can use while staying within her budget is 5 gigabyte
How to determine the inequality used to represent Paisley's budgetInformation gotten from the question include
Paisley pays a flat cost of $60 per month and $3 per gigabyte
bill under $75 per month
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variables to suit the problem to be solved
y = Total cost
m = cost per gigabyte
x = number of gigabyte
c = flat cost
The inequality equation as described in the problem is represented using linear function as as follows
3x + 60 < 75
3x < 75 - 60
3x < 15
x < 5
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11th term of the arithmetic sequence with the rule an= - 2 + 6(n - 1)?
⇒Given that the general rule to find the nth term is
[tex]T_{n} =-2+6(n-1)[/tex]
⇒To find the 11th term this means that they need a term which is in the position 11
⇒To get the number we plug in the 11 which is the position in the place of n and simplify.
[tex]T_{11} =-2+6(11-1)\\T_{11} =-2+6(10)\\T_{11} =-2+60\\T_{11} =58[/tex]
The 11th term is 58
Goodluck!!!
Marty invested $7000 in treasury notes and stocks. The stocks paid 7% in the notes paid 8%, giving an annual income of $535. How much is invested into the treasury notes?
Answer:
3500
Step-by-step explanation:
split 7000 in half for stocks and treasury= 3500 each.
7 percent on 3500 is 3724, 7 percent of 3500 is 245 dollors. 535 x 7 is 3745 = 3500 invested in treasury.
Y-4x is equal to or less than -6
Answer:
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star, like.
this is the correct solution.
Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
The area to the left of z = 0.54 is
.
Area under the standard normal curve of z - score :
P(z < 0.54) = 0.7054
Given:
The area under the standard normal curve left is z = 0.54.
and, also sketch the area of normal curve and allocate the area left to the z - score .
What do z-scores mean?
Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.
Now,
The area under the curve represents the probability, therefore, the total area under the curve is equal to 1.
The Area under the standard normal curve of z - score :
P(z < 0.54) = 0.7054
Here, The sketch the under the standard normal curve over the indicated interval.
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Which polynomial represents the difference below?2x^2 + 7x+6(3x^2 - x)O A. 2x^2 + 5x + 6B. 2x^2 + 4x + 6c. - x^2 + 6x + 6D. - x^2 + 8x+ 6
The given polynomials are as ,
[tex]\begin{gathered} 2x^2+7x+6\text{ and} \\ 3x^2-x \end{gathered}[/tex]We have to subtracrt these given polynomials,
[tex]\begin{gathered} =2x^2+7x+6-3x^2-(-x) \\ =2x^2+7x+6-3x^2+x \\ =-3x^2+2x^2+7x+x+6 \\ =-x^2+8x+6 \end{gathered}[/tex]Option D is correct.
Can someone help me i will give brainlest :) 12, 13, 14, only do those one's
Plotted Answers:
12.) See attached for my work
13.) See attached for my work
14.) See attached for my work
Simplified Answers:
12.) y > –24
13.) x ≥ –12
14.) x > –7
Hope that helps! Have an amazing rest of your day! Please consider giving me the Brainliest! :)
Identify the following scatter plots as having a positive correlation,
negative correlation, or no correlation. Explain your reasoning.
Need help ASAP!!!
The given scatterplot has no correlation. This is because there is no pattern among the dots on the scatterplot.
What is correlation?Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables. Correlation can either be positive, negative or zero. The closer the correlation coefficient is to one, the higher the correlation.
Positive correlation is when two variables move in the same direction. When drawn on a scatterplot, the line of best fit is upward sloping. The coeffect of correlation for positive correlation is always positive.
Negative correlation is when two variables move in different directions. When drawn on a scatterplot, the line of best fit is downward sloping. The coeffect of correlation for negative correlation is always negative.
Zero correlation or no correlation is when there is no relationship between the variables. When drawn on a scatterplot, there is no discernible patterns among the variables.
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This is Evaluating Functions.Replace the X values with the number in the question ("Find f( )" )
Given the following function:
f(x) = 3x - 3
Let's determine the value at f(-3),
This means that we will be replacing all x variables of f(x) by -3.
We get,
f(x) = 3x - 3
f(-3) = 3(-3) - 3
= -9 - 3
f(-3) = -12
Therefore, f(-3) = -12
Given the following function:
f(x) = 3x - 3
Let's determine the value at f(-3),
This means that we will be replacing all x variables of f(x) by -3.
We get,
f(x) = 3x - 3
f(-3) = 3(-3) - 3
= -9 - 3
f(-3) = -12
Therefore, f(-3) = -12
simplify 20:15
simplify 35:49
simplify 81:36
simplify 27:45
simplify 21:36
pls help me i’m crying rn bro
Answer:
1. 4:3
2. 5:7
3. 9:4
4. 3:5
5. 7:12
Step-by-step explanation:
I'm sure you don't care how to get the answers, you just want them :)
A retailer purchases some merchandise with an invoice price of $19,500 and terms of sale of 5/15, n/45. What is the net amount due (in $) on the order if a partial payment of $10,800 is made on the 15th day? (Round your answer to the nearest cent.)
The net amount due on the order after partial payment done is $8700
Given,
A retailer purchases some merchandise;
The invoice price for the merchandise = $19,500
Terms of sale for the merchandise = 5/15, n/45
On 15th day partial payment done = $10,800
We have to find the net amount due on the order after partial payment is done.
Here,
Net amount due = Invoice price - Partial payment
Net amount due = 19,500 - 10,800
Net amount due = 8700
That is,
The net amount due on the order after partial payment done is $8700
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Which of these is a perfect square? Responses 29/ 78/ 144/ -6/
Here, 144=12×12=12². Therefore, 144 is a perfect square.
The given numbers are 29, 78, 144 and -6.
What is a perfect square?A perfect square is a positive integer that is obtained by multiplying an integer by itself. In simple words, we can say that perfect squares are numbers that are the products of integers by themselves.
By perfect square definition
29=29×1
78=2×2×17
144=2×2×2×2×3×3=12×12
-6=-2×3
So, from the above factors it is clear that, 144 is a perfect square.
Here, 144=12×12=12². Therefore, 144 is a perfect square.
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study questions from digital text book page 2.03 : Picture's down below
Question #1 : What is m∠SVT?
Question #2: What is the m∡BEC?
Disclaimer!! these are not from a Test, Quiz, or Assignment. these are from a practice page and i wanted to know how do these questions for a Future assignment with questions like these. I am just informing you guys because i didn't know the guidelines until now and i will no longer put test questions up because I am now aware its not ok to do so. So This Is not from a Test, Quiz, or Assignment. Thank you
The angle measures in this problem are given as follows:
1. Angle SVT: 79º.
2. Angle BEC: 65º.
Angle SVTAngles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:
8y - 33 = 5y + 9
3y = 42
y = 42/3
y = 14.
Hence the measure of the angle SVT is of:
m<SVT = 5y + 9 = 5(14) + 9 = 79º.
Angle BECThe two angles given in this problem are also vertical, meaning that we can solve for x as follows:
5x - 10 = 3x + 40
2x = 50
x = 50/2
x = 25º.
Then the bottom angle is:
3 x 25 + 40 = 115º.
The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:
115 + m<BEC = 180
m<BEC = 180 - 115
m<BEC = 65º.
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Write an equation of the line passing through the point (2, -9) that is perpendicular to the line V=x+6.
The equation of the line that is perpendicular to y = x + 6 is expressed as: y = -x - 7
How to Write the Equation of a Line?The equation of a line can be written as y = mx + 1. The value of m is the slope while the value of b is the y-intercept.
The slopes of two lines that are perpendicular to each other are negative reciprocals. This means, if we multiply their slope values together, we will get -1.
Given the line, y = x + 6, the slope of the line is 1. The slope of the line it is perpendicular to is -1, because -1 is the negative reciprocal of 1.
Substitute m = -1 and (x, y) = (2, -9) onto y = mx + b to find the value of b:
-9 = -1(2) + b
-9 = -2 + b
-9 + 2 = b
-7 = b
b = -7
To write the equation of the perpendicular line, substitute m = -1 and b = -7 into y = mx + b:
y = -x - 7
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Write the quadratic equation that has roots -1-rt2/3 and -1+rt2/3 if its coefficient with x^2 is equal to 1
[tex]\frac{-1-\sqrt{2}}{3}[/tex] [tex]\frac{-1+\sqrt{2} }{3}[/tex]
The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9
How to determine the quadratic equation?From the question, the given parameters are:
Roots = (-1 - √2)/3 and (-1 + √2)/3
The quadratic equation is then calculated as
f(x) = The products of (x - roots)
Substitute the known values in the above equation
So, we have the following equation
[tex]f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})[/tex]
This gives
[tex]f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})[/tex]
Evaluate the products
[tex]f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})[/tex]
Evaluate the like terms
[tex]f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}[/tex]
So, we have
f(x) = x²+ 2/3x - 1/9
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multiplicative inverse of 7^-2
Answer:
[tex] 7^2[/tex]
Step-by-step explanation:
multiplicative inverse of[tex] \:\:7^{-2} =7^2[/tex]Answer:
7²
Step-by-step explanation:
the product of a number and its multiplicative inverse is equal to 1 , that is
a ×[tex]\frac{1}{a}[/tex] = 1
given
[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and
[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1
72.1232 rounded to the nearest thousandth
72.1232 rounded to the nearest thousandth is 72.123.
What does it mean to round to the nearest thousandth?The term "rounding to the nearest thousandth" refers to the practice of rounding any decimal number to the next thousandth value. Thousandth in the decimal system signifies (1/1000) or 0.001. 3.125, for example, is the number 3.1249 rounded to the closest thousandth.
To round it to the closest thousandth, we must focus on the number following this spot - tens of thousandths. This figure will determine whether we round up or round down. "Five and above go up like a bird," as the phrase goes. Therefore, this will give a value of 72.123.
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x + 3y = 1 ; 7x + 8y = 11 solve by substitution.
Step-by-step explanation:
x + 3y = 1
x = 1 - 3y-(i)
7x + 8y = 11
x= 11-8y/7-(ii)
substituting eqn (i) in eqn (ii)
11-8y/7= 1-3y
11-8y=7-21y
13y=-4
y=-4/13
putting the value of y in eqn (i)
x=1-(-12/13)
x=25/13
63 > 7y solve the inequality for y and simplify your answer as much as possible
Answer:
y < 9
Step-by-step explanation:
Hello!
We can solve the inequality for y by dividing both sides by 7.
Remember, when dividing or multiplying both sides of an inequality with a negative number, make sure to flip the sign. Since 7 is positive, we don't have to flip the sign.
Solve the Inequality63 > 7y63/7 = 7y/79 > ySo the inequality is true for all y values less than 9.
Hey there!
63 > 7y
7y < 63
DIVIDE 7 to BOTH SIDES
7y/7 < 63/7
SIMPLIFY IT
y < 63/7
y < 9
You have an open circle starting at 9 and going down to left side of the number line.
Therefore, your answer should beD
y < 9
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which one is it because i thought it was 32g+26
The equivalent expression of 4(8g + 5) + 6 is 4(5 + 8g) + 6
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Therefore, let's find the equivalent expression of 4(8g + 5) + 6.
Hence,
4(8g + 5) + 6
32g + 20 + 6
32g + 26
Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6
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Use the factor theorem to find all real zeros and one factor.
f(x) = 2x³-9x² + 13x - 6; x - 1
Answer:
x = {1, 1.5, 2}Step-by-step explanation:
GivenPolynomial f(x) = 2x³ - 9x² + 13x - 6, One of the factors x - 1.Factorize the polynomial using the given details.
Since one of the factors known, try to factor it out and futher:
2x³ - 9x² + 13x - 6 = 2x³ - 2x² - 7x² + 7x + 6x - 6 = 2x²(x - 1) - 7x(x - 1) + 6(x - 1) = (x - 1)(2x² - 7x + 6) = (x - 1)(2x² - 3x - 4x + 6) = (x - 1)[x(2x - 3) - 2(2x - 3)] =(x - 1)(x - 2)(2x - 3)Find its zero's:
x - 1 = 0 or x - 2 = 0 or 2x - 3 = 0x = 1 or x = 2 or x = 1.5Answer:
[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.
Given polynomial function:
[tex]f(x)=2x^3-9x^2+13x-6[/tex]
Sum the coefficients:
[tex]\implies 2-9+13-6=0[/tex]
As the sum of the coefficients is zero, (x - 1) is a factor.
Therefore:
[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]
[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]
Compare the coefficients with the given polynomial.
As the coefficient of the leading term of the polynomial is 2:
[tex]\implies a=2[/tex]
As the coefficient of the term in x² is -9:
[tex]\implies b-a=-9[/tex]
[tex]\implies b-2=-9[/tex]
[tex]\implies b=-7[/tex]
As the constant of the given polynomial is -6:
[tex]\implies c=6[/tex]
Substitute the found values of a, b and c into the factored form of the polynomial:
[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]
Factor the quadratic:
[tex]\implies 2x^2-7x+6[/tex]
[tex]\implies 2x^2-4x-3x+6[/tex]
[tex]\implies 2x(x-2)-3(x-2)[/tex]
[tex]\implies (2x-3)(x-2)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]
To find the zeros, set the function to zero:
[tex]\implies f(x)=0[/tex]
[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]
Apply the zero-product property:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.
Solve for x? Please help me with this asap! Show your work if you want the extra points and Brainiest!
The value of x is 10
How to determine the valueFrom the diagram shown, we can see that it takes the shape of a parallelogram
The properties of a parallelogram includes;
Opposite sides are described as parallel to each otherOpposite sides are equal or congruentThe same-sided interior angles are said to be supplementary, that is, they add up 180 degreesEvery diagonal of the parallelogram divides it into two equal triangleThe diagonals of a parallelogram bisect each other at right anglesWe can see that the diagonal bisects the parallelogram into equal halves and then the parallel and opposite sides are equal.
If the opposite sides of x = 10
Then, x = 10
Hence, the value is 10
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what are the coordinates of the image P for a dilation with center (0,0) and a scale factor 2? answer choices :• (2,0) • (0,6)• (-4, 2)• (0,5)
Rule for a dilation with center (0,0)
[tex](x,y)\rightarrow(kx,ky)[/tex]k is the scale factor.
For point P (0,3):
[tex]\begin{gathered} P(0,3)\rightarrow P^{\prime}(2(0),2(3)) \\ P(0,3)\rightarrow P^{\prime}(0,6) \end{gathered}[/tex]Then the coordiantes of point P after the dilation are (0,6)reid took seven tests. on the first five tests that he took, he averaged $86$ points. on the last three tests, he averaged $95$ points. if he averaged $88$ points on all seven tests, how many points did he average on the last two tests?
The points that he average on the last two tests will be 93 points.
What is mean?A mean is the average of the set of numbers that are given.
On the first five tests that he took, he averaged 86 points. The total points will be:
= 86 × 5
= 430 points
He averaged 88 points on all seven tests. The total will be:
= (88 × 7)
= 616 points
The point average on the last two tests will be:
= (616 - 430)/2
= 186/2
= 93 points
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Question 7 013 points Redo Which theorem is depicted by the figure and information shown below? R S Theorem? ZRAZT 2Qazs A) Opposite sides of parallelograms are congruent (Tm 16-A) B) Opposte angles in a parallelogram are congruent. (Tm 16-B) C) The sum of any consecutive angles within a parallelogram equals 180 (Tm 16-C) D) The diagonals of a parallelogram bisect each other (Tm 16-D) E) The diagonal of a parallelogram separates it into two congruent triangles (Tm 16-E)
Answer:
B. Opposite angles in a parallelogram are congruent.
Explanation:
The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.
Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.
So, the answer is B. Opposite angles in a parallelogram are congruent.
For the rhombus below, find the measures