Answer:
5Step-by-step explanation:
Given the expression (8x² −15x)−(x² −27x) = ax² +bx, we are to determine the value of b-a. Before we determine the vwlue of b-a, we need to first calculate for the value of a and b from the given expression.
On expanding the left hand side of the expression we have;
= (8x² −15x)−(x² −27x)
Open the paranthesis
= 8x² −15x−x²+27x
collect the like terms
= 8x²−x²+27x −15x
= 7x²+12x
Comparing the resulting expression with ax²+bx
7x²+12x = ax²+bx
7x² = ax²
a = 7
Also;
12x = bx
b =12
The value of b - a = 12 - 7
b -a = 5
Hence the value of b-a is equivalent to 5
The value of b minus a is 5
Calculation of the value:Since the expression is
[tex](8x^2 -15x)-(x^2 -27x) = ax^2 +bx[/tex]
Here we have to expand the left-hand side of the expression so it should be like
[tex]= (8x^2 -15x)-(x^2 -27x)\\\\= 8x^2 -15x-x^2+27x\\\\= 8x^2-x^2+27x -15x\\\\= 7x^2+12x[/tex]
Now
[tex]7x^2+12x = ax^2+bx\\\\7x^2 = ax^2[/tex]
a = 7
Also;
12x = bx
b =12
So,
The value of b - a = 12 - 7
b -a = 5
Hence the value of b-a should be 5
Learn more about equation here: https://brainly.com/question/24540444
In which row and column will the number 83 appear?
Answer:
Row 10 and in column F
Step-by-step explanation:
rows 1 and 3 are decreasing and we are looking for an increase so we can cross those out immediately.
However we do see a pattern in rows 2 to 4 (add 8) so if we add 8 for 3 more rows than we get 37 but add 8 more and we get 45.
from 37 to 43 is 6 more than 37 so we have 4 columns but if we add 3 more we get the 6 columns also column f.
Hope this helps!
If the ratio of two supplementary angles is 10 to 47, calculate the measure of the larger of the two angles.
Answer:
a) 148.52
Step-by-step explanation:
If sum of two angles is 180, then they are supplementary
Ratio = 10 : 47
Smaller angle = 10x
Larger angle = 47x
10x + 47x = 180
57x = 180
Divide both sides by 57
x = 180/57
x = 3.16
Larger angle = 47x = 47 * 3.16 = 148.52
what's 10*4/19+2=
use pemdas to get the answers .
Answer:
4.10526315789
Step-by-step explanation:
Answer: 4.10526315789
Step-by-step explanation:
Please help.. I'm really stuck
Answer:
C. C only
Step-by-step explanation:
Well to determine if the given graphs are functions we need to do the vertical line test to all the graphs,
A. This fails the vertical line test because the vertical line could pass through 2 points on the lines.
B. this also fails because a vertical line could pass through 2 points.
C. This passes because the vertical line doesn’t touch 2 points.
Rose likes to water ski using her sister's boat. The boat takes 3 gallons of gas each hour to run. Gas costs $5 per gallon, how much money will she spend on gas to ski for 4 hours?
Answer:
$60
Step-by-step explanation:
Answer:
60$
Step-by-step explanation:
3 gallons per hr
multiply by 4
12gl per 4hrs
5 dl per gl
multiply by 12
60 dl per 12 gl
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
What is the simplified sum of 3x/x-4 + x-3/2x
━━━━━━━☆☆━━━━━━━
▹ Answer
-1 - 1/2x
▹ Step-by-Step Explanation
3x ÷ x - 4 + x - 3 ÷ 2x
Divide and Rewrite:
3 * 1 - 4 + x - 3 ÷ 2 * x
Calculate:
3 - 4 + x - 3/2x
-1 + x - 3/2x
= -1 - 1/2x
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
Step-by-step explanation:
[tex]\frac{3x}{x-4}+\frac{x-3}{2x}[/tex]
Make them into common denominators. To do so, multiply by the LCM of the denominators. The LCM of the denominators is (x-4)(2x). Thus, we multiply 2x to the first term and (x-4) to the second:
[tex](\frac{2x}{2x}) \frac{3x}{x-4}+(\frac{x-4}{x-4}) \frac{x-3}{2x}[/tex]
Simplify:
[tex]\frac{6x^2}{2x(x-4)}+\frac{x^2-7x+12}{2x(x-4)} \\=\frac{7x^2-7x+12}{2x(x-4)}[/tex]
And this cannot be simplified further (you can also distribute the denominator if preferred).
Enter a counterexample for the conclusion. If x is a prime number, then x + 1 is not a prime number. A counterexample is x = .
Answer:
x = 2
Step-by-step explanation:
If x is a prime number, then x + 1 is not a prime number.
A counterexample is x = 2.
x = 2
2 is prime
x + 1 = 2 + 1 = 3
3 is also prime
I NEED IN THE NEXT 10 MIN PLS. GRAPH ATTACHED WILL GIVE BRAINLIEST Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis at five that ends at the open point 2, 5, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3 and continues to the right. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
Answer:
Step-by-step explanation:
You gave very clear instructions on how to draw this graph, so that's what I did. What you need to remember in particular with limits is that you do not care in the least what happens AT the x value of 2, only what happens as it is being approached. Because we are asked the limit as x is approaching from the left and the right, this is a one-sided limit question. In order for the limit to exist as x approaches 2 (NOT from the left or the right), the limit would have to agree from the left and the right, and this one doesn't. Having said that there is "a horizontal line crossing the y-axis at 5 that ends at the open point (2, 5)..." is a limit approaching x from the left. Therefore,
[tex]\lim_{x \to 2^-} f(x)=5[/tex]
Having also said there is "...another horizontal line starting at the open point (2, -3) and continues to the right..." is a limit approaching x from the right. Therefore,
[tex]\lim_{x \to 2^+} f(x)= -3[/tex]
The closed point at (2, 1) is where x IS, and remember that we don't care about what happens AT x. So disregard this point in limits.
In the figure below, if x = 80° and z =
36°, find y.
Step-by-step explanation:
theanswer is 64 degrees
A machine fills 680 bottles in 5hours how many bottles will it fill in three hours?
Answer:
408 bottles
Step-by-step explanation:
the machine can fill 136 bottles in 1 hour, 136×3=408
Answer:
408
Step-by-step explanation:
680 bottles in 5 hours
in three hours:
1 hour =680/5=136
in three hours:it will be 136*3=408
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking Last weekwalked 18 miles in 6 hours This week d = 2.5h Which statement must be true?
THIS IS THE COMPLETE QUESTION BELOW;
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.
Last week: walked 18 miles in 6 hours
This week: d = 2.5h
Which statement must be true?
A.This week, she walked a greater distance.
B. Last week, she walked a greater distance
C. This week, she walked at a faster pace.
D. Last week, she walked at a faster pace
Answer
OPTION B is correct
B)Last week, she walked a greater distance
Step-by-step explanation:
We were told Rosemary walks each week for exercise.
From the question,
✓d represented the distance walked
✓h represent the number of hours spent walking.
A)Last week: she walked 18 miles in 6 hours
Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)
= 3 miles per hour
B)This week: d = 2.5h
This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.
So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.
Therefore, OPTION B is correct, (Last week, she walked a greater distance)
Answer:
It's b
Step-by-step explanation:
Help need work shown ASAP
Answer:
y = 2x + 1
Step-by-step explanation:
From the table attached,
x y Difference [tex][d=(y_2-y_1)][/tex]
-1 -1 -
0 1 1 - (-1) = 2
1 3 3 - 1 = 2
2 5 5 - 3 = 2
Since,there is a common difference 'd' = 2
Therefore, this table represents a linear equation.
Let the equation is,
y = mx + b
where 'm' is the slope and 'b' is the y-intercept.
Two points lying on the linear equation are (-1, -1) and (0, 1)
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{1+1}{0+1}[/tex]
m = 2
And y-intercept 'b' = 1 unit
Therefore, equation of the line will be,
y = 2x + 1
Use the discriminant to determine the number of real solutions to the equation. −4x^2=−8−10x
Answer:
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.
The discriminant is part of the quadratic formula. It is:
[tex]b^2-4ac[/tex]. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:
[tex]-4x^2=-8-10x[/tex] but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:
[tex]-4x^2+10x+8=0[/tex]
From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:
[tex]10^2-4(-4)(8)[/tex] which gives us a value of
100 - [4(-4)(8)] (don't forget orders of operation here!)
100 - (-128) = 100 + 128 = 228
This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.
Which expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign? A sign labeled 2x-1 on one side. A: 4x^2 - 1 B:4x^2 + 1 C: 4x^2 + 4x - 1 D: 4x^2 - 4x + 1
Answer:
D: 4x² - 4x + 1
Step-by-step explanation:
(2x - 1) ( 2x - 1)
4x² - 2x - 2x + 1
4x² - 4x + 1
The correct answer is d) 4x2 - 4x + 1.
The area of a square is found by squaring the side length:
(2x-1)? = (2x-1)(2x-1) = 2x*2x - 2x*1 - 2x*1 - = 1(-1) = 4 x 2 - 2x - 2x + 1 = 4x2-4x+1
Find the area of the shape shown below.
9.0
3.5
2
5
2.
units
Answer:
[tex] \boxed{42.5 \: {units}^{2} }[/tex]Step-by-step explanation:
The shape could be divided into a rectangle and a trapezoid ( bottom part )
Let's find the area of the given shape:
Area of the given shape = [tex] \mathsf{ (l \times b) + \frac{1}{2} (b1 + b2)h}[/tex]
plug the values
[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 +9 - (5 + 2) \times 2}[/tex]
[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 + 2)(2)}[/tex]
[tex] \mathsf{ = 31.5 + \frac{1}{2} \times 11 \times 2}[/tex]
[tex] \mathsf{ = 31.5 + 11}[/tex]
[tex] \mathsf{ = 42.5 \: {units}^{2} }[/tex]
Hope I helped!
Best regards!
Help !!! Thank you a lot!!
Answer:
E) 45
Step-by-step explanation:
Since b is 90 degrees, and lines CB and BA are equal (as seeen with the 2 lines across them) we can assume that this angle is 45 degrees, half or 90 degrees.
Angle C is also equal to angle A
Answer:
E
Step-by-step explanation:
Using the fact that the sum of angles in a triangle is 180 degrees, we can write the following equation to solve for 3x:
3x + 3x + 90 = 180
3x + 3x = 90
2 * 3x = 90
3x = 45°
BRAINLIEST, THANKS AND 5 STARS IF ANSWERED BOTH CORRECTLY. What is the 7th term in this geometric sequence? 3, 12, 48, 192.. ---------- What is the ratio (multiplier) of the following geometric sequence? 4, 2, 1, 0.5
Answer:
see below
Step-by-step explanation:
3, 12, 48, 192
We are multiplying by 4 each time (12/3 =4)
The 5th term
192 *4 =768
The 6th term
768 *4 =3072
The th term
3072 *4 =12288
To find the common ratio, take the second term and divide by the first
2/4 = 1/2
The common ratio is 1/2
Problem 1
Answer: 12288---------------------------
Explanation:
The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is
a(n) = a*(r)^(n-1)
a(n) = 3*(4)^(n-1)
Plug in n = 7 to get the seventh term
a(7) = 3*(4)^(7-1)
a(7) = 3*(4)^6
a(7) = 3*4096
a(7) = 12288
====================================================
Problem 2
Answer: 1/2 or 0.5----------------------
Explanation:
To find the common ratio, we pick any term but the first one and divide it over its previous term
r = common ratio
r = (second term)/(first term) = 2/4 = 1/2 = 0.5
r = (third term)/(second term) = 1/2 = 0.5
r = (fourth term)/(third term) = 0.5/1 = 0.5
Each term is cut in half to get the next one.
Solve for b.
ab+c=d
b=a+c/d
b= a/(c-d)
b = (d - c)/a
Answer:
[tex]b = \frac{(d-c)}{a}[/tex]
Step-by-step explanation:
ab + c = d
Subtract c from both sides
ab + c - c = d -c
ab = d - c
Divide both sides by 'a'
[tex]\frac{ab}{a}=\frac{d-c}{a}\\\\b = \frac{(d-c)}{a}[/tex]
Answer:
b = (d - c)/a
Step-by-step explanation:
just took this test
How to do this question plz answer me step by step plzz
Answer:
4 cm
Step-by-step explanation:
At 12 cm depth, the depth is 12/15 = 4/5 of the height of the container.
When the container is tipped on its side, so its height is 5 cm, the depth will still be 4/5 of the height.
(4/5)(5 cm) = 4 cm
The depth will be 4 cm.
A rectangle has a length of 12 m and a width of 400 cm. What is the perimeter of the rectangle?
Answer:
Perimeter = 32 meters
Step-by-step explanation:
1 meter = 1m = 100 cm = 100 centimeters
400cm = 400/100 = 4 meters
Rectangle Perimeter = 2(legth + width)
= 2(12 + 4)
= 2*16
= 32 meters
-5y+6>26 does the inequality sign flip?
Answer:
Yes
Step-by-step explanation:
Answer:
y < -4
Step-by-step explanation:
-5y+6>26
subtract 6 from each side
-5y+6-6>26-6
-5y > 20
Divide each side by -5. remembering to flip the inequality
-5y/-5 < 20/-5
y < -4
Help pls need work shown
Answer:
1.) P = 8g + 50
2.) Find the attached file for the graph.
Step-by-step explanation:
Let the profit = P
And g = good sold.
Given that each yo-yo sells for $8.00
The rate or the slope of the equation will be 8
Also, it is given that they must pay a clerk $50.00 a day to sell them. A flat rate of 50 dollars is an intercept of the equation.
Using the general linear equation of
Y = mX + C
The equation for the profit the store will make in a day will be.
P = 8g + 50
Please find the attached file for the graph
how do you work out 28.4 x 1.92
Answer:
54.528
Step-by-step explanation:
0. A submarine was at sea level and
then dove 752 ft. It then rose at a rate
of 12 ft. per minute. What was the
depth of the submarine after 8
minutes?
Also idk the equation so if u could help me out with that id be grateful
One equation you can use is y = -12x+752 and you plug in x = 8 to find y.
=================================================
Explanation:
x = number of minutes
y = depth of the submarine
Being at sea level means the depth is y = 0. Diving 752 ft below sea level means the depth is y = 752. It's tempting to make this negative since we're below sea level, but depth values are always positive. They are simply distances you are from the surface of the water. Negative distances are never possible. So this concept might be a bit tricky to get used to.
Possibly equally confusing is the fact that the "12 ft per minute" means the slope is -12. This is because the depth is getting smaller as the submarine gets closer to the surface (aka the sub is rising).
The equation is y = -12x+752. The equation is in the form y = mx+b with m = -12 as the slope and b = 752 as the y intercept. Note how the y intercept is the starting depth value.
From here, we plug in x = 8 to find where the sub is
y = -12x+752
y = -12*8+752
y = -96+752
y = 656
The submarine's depth after eight minutes is 656 feet
----------------------
An alternative equation to use is
y = 12x-752
which is very similar to the other one used earlier. All I did was flip the sign of each term. Now y represents the height of the sub. Negative y values indicate we're below the surface of the water. The slope being positive means the submarine is going upward. The negative y intercept indicates we're starting 752 feet below sea level. Plugging in x = 8 will lead to y = -656, which you'll need to make positive (since all depth values are positive).
As you can probably guess, the change from y = -12x+752 and y = 12x-752 is simply multiplying the right hand side by -1, which explains why the signs flip (and explains how the y value sign flips as well)
how many are 6 raised to 3 ???
Answer:
216
Step-by-step explanation:
When you say "6 raised to 3", it means you multiply 6, 3 times. Meaning:
6✖️6✖️6=216
Hope this helped!
Have a nice day:)
Find the area of the shaded region
Answer:
5x^2 +24x +1
Step-by-step explanation:
First you'll want to find the area of the larger rectangle, and then you'll subtract the area of the smaller rectangle (which is not shaded) to get your answer.
Larger Rectangle:
A = length * width
A = (2x + 3)(4x - 5) = (8x^2 - 10x + 12x - 15) = 8x^2 + 2x - 15
Smaller Rectangle:
A = length * width
A = (x - 8)(3x + 2) = (3x^2 + 2x - 24x - 16) = 3x^2 - 22x - 16
Larger Rectangle minus Smaller Rectangle:
(8x^2 + 2x - 15) - (3x^2 - 22x - 16)
5x^2 +24x +1
Question 9(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x - 9)?
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
una
Answer:
The graph will shift 9 units to the right
Sorry about my hand writing
Answer: It moves 9 units to the right
Step-by-step explanation:
It moves 9 units to the right is because if it's inside parentheses it moves right/left instead of up/down. I also talked to my Algebra Teacher about it and got it right in the final test.
a passenger train takes 2 hours less for a journey of 300 kilometre if its speed is increased by 5 kilometre per hour from its usual speed find its usual speed
Answer:
Its usual speed is 25 kilometre/hour
Step-by-step explanation:
Let the usual time duration for a journey of 300 km. = t
Let the usual speed = v
The parameters given are;
The time duration for the 300 km. journey at increased speed = t - 2
The increased speed of the passenger train = v + 5
Distance, d = Speed, v × Time, t
Therefore, we have;
v × t = 300
∴ t = 300/v
Also (v + 5)×(t - 2) = 300
Substituting the value of t = 300/v, we have;
(v + 5)×(300/v - 2) = 300
[tex]- \dfrac{2 \cdot v^2 - 290 \cdot v - 1500}{v} = 300[/tex]
Which gives;
2·v² + 10·v - 1500 = 0
Which is equivalent to v² + 5·v - 750 = 0
Therefore we have;
(v + 30)·(v - 25) = 0 whereby v = -35 or 25 km/h
v = Natural number = 25 km/hour
Therefore its usual speed is 25 kilometre/hour.
The table shows the relationship between time spent running and distance traveled. A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 1, 2, 3, 4, 5. The second column is labeled distance (feet) with entries 530; 1,050; 1,600; 2,110; 2,650. Which type of model best describes the relationship?
linear, because the r value for the linear model is closest to 1
exponential, because the r value for the exponential model is closest to 0
linear, because the rate of change between each pair of points is exactly 520
exponential, because the rate of change between each pair of points is 1.98
Answer:
Step-by-step explanation:
It is not perfectly linear because the difference between the y values is not constant. However, when you use the regression function on your calculator and enter the L1 values as your x's and the L2 values as your y's and use the LinReg equation, you get an r-squared value of .999900 and an r value of .999950. So it linear, with your answer being "linear, because the r value for the linear model is closest to 1".
In this question, we have two columns, you giving the time and the other the distance. We have to identify it the relationship is linear or exponential.
First, I am going to explain when we have a linear relation and when we have an exponential relation, then we observe the data and solve this question, getting the following correct answer:
linear, because the r value for the linear model is closest to 1
Linear and exponential data:
If the absolute value of the change assume close values, it is linear.
If the rates are, it is exponential.
Data:
t = 1 -> d = 530
t = 2 -> d = 1050
t = 3 -> d = 1600
t = 4 -> d = 2110
t = 5 -> d = 2650
Subtractions:
2650 - 2110 = 540
2110 - 1600 = 510
1600 - 1050 = 550
1050 - 530 = 520
Divisions(rates):
2650/2110 = 1.25
2110/1600 = 1.32
1600/1050 = 1.52
1050/530 = 1.98
The rates change considerably more than the subtractions, so it is linear relationship, and the correct option is:
linear, because the r value for the linear model is closest to 1.
For more on linear/exponential growths, you can check https://brainly.com/question/24282972
Find the area of the shaded region . RQ= 71.5 inches and PO=93.4 inches . Use 3.14 as necessary
Answer:
25,886.01 in²
Step-by-step explanation:
The area of shaded region = Area of the outter circle (the larger circle) - area of the inner circle (the smaller circle)
Area of a circle = πr²
Radius of larger circle = PO = 93.4 in
Area of the larger circle = 3.14*93.4² = 27,391.98 in²
Radius of smaller circle = PO - RQ = 93.4 - 71.5 = 21.9
Area of smaller circle = 3.14*21.9² = 1,505.97 in²
Area of shaded region = 27,391.98 - 1,505.97 = 25,886.01 in²
