Answer:
x = 3
Step-by-step explanation:
Given
7x - 4 = 2x + 11 ( subtract 2x from both sides )
5x - 4 = 11 ( add 4 to both sides )
5x = 15 ( divide both sides by 5 )
x = 3
What is the remainder when 58 is divided by 7?
Answer:2
Step-by-step explanation:
If you devide 58 by 7,you will get 8 as quotient..so 7×8=56..
So you will find (58-56)=2 as remainder..
Answer:
The Remainder of 58÷7 is 2
Step-by-step explanation:
The Remainder of a Division Operation is calculated by finding how many times the denominator goes into the numerator without going over and then subtracting that from the numerator.
For Example : [tex]58/7 = 8.28[/tex] ......which means 7 goes into 58 , 8 times.
Next we multiply 7*8 to give us 56.
Lastly, we subtract 58-56 to give us a remainder of 2.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
What is the product?
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}6&18\end{array}\right]}[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}4&2\end{array}\right] \times\left[\begin{array}{ccc}-2&5\\7&-1\end{array}\right] =\left[\begin{array}{ccc}(4)(-2)+(2)(7)&(4)(5)+(2)(-1)\end{array}\right] \\\\=\left[\begin{array}{ccc}-8+14&20-2\end{array}\right] =\left[\begin{array}{ccc}6&18\end{array}\right][/tex]
A is the point with coordinates (3,8) b is the point with coordinates (x,13) the gradient of an is 2.5 .work out the value of x
Answer:
x = 5
Step-by-step explanation:
The formula for the gradient is given by:
m = (y2 - y1)/(x2 - x1), where two points (x1, y1) and (x2, y2) are given.
Thus if we have a gradient of 2.5 and two points (3, 8) and (x, 13), we can substitute this into the above formula for the gradient to get:
2.5 = (13 - 8)/(x - 3)
2.5(x - 3) = 5 (Multiply both sides by (x - 3))
x - 3 = 2 (Divide both sides by 2.5)
x = 5 (Add 3 to both sides)
Thus, the value of x is 5.
Solve for x.
2x^2 − 4x = 0
Answer:
First, find a constant that can help you solve the equation. Note the equal sign, what you do to one side, you do to the other.
Remember, you are trying to do the following, changing: (note that y = constant)
x² - xy + y = (x - y)(x - y)
First, solve for the obvious answer. Plug in 0 to x:
2(0²) - 4(0) = 0
2(0) - 0 = 0
0 - 0 = 0
x = 0 is one of your answer choices.
Solve for the more complicated answer by doing what I put on the top:
2x² - 4x + 0 (+2) = 0 (+2)
2x² - 4x + 2 = 2
Divide 2 from both sides & all terms:
2(x² - 2x + 1) = 2(1)
x² - 2x + 1 = 1
Solve. Remember to set the equation = 0. Subtract 1 from both sides:
x² - 2x + 1 = 1
x² - 2x + 1 (-1) = 1 (-1)
x² - 2x + 0 = 0
x² - 2x = 0
Isolate the -2x. Add 2x to both sides.
x² - 2x (+2x) = 0 (+2x)
x² = 2x
Isolate the variable x. Divide x from both sides.
(x²)/x = (2x)/x
x = 2x/x
x = 2
x = 2 is your other answer choice.
x = 0, 2 is your answer.
~
Answer:
(0,2)
Step-by-step explanation:
x² - xy + y = (x - y)(x - y)
2(0²) - 4(0) = 0
2(0) - 0 = 0
0 - 0 = 0
2x² - 4x + 0 (+2) = 0 (+2)
2x² - 4x + 2 = 2
2(x² - 2x + 1) = 2(1)
x² - 2x + 1 = 1
x² - 2x + 1 = 1
x² - 2x + 1 (-1) = 1 (-1)
x² - 2x + 0 = 0
x² - 2x = 0
x² - 2x (+2x) = 0 (+2x)
x² = 2x
(x²)/x = (2x)/x
x = 2x/x
x = 2
x = 0, 2 is your answer.
Noemi strings together x green beads at $0.75 each with 3 blue beads at $0.30 each. She makes a bracelet that averages $0.60 per bead. Write an equation to model the situation
Given that Noemi makes a bracelet that averages $0.60 per bead, we need to write an equation that models this average bead cost. This can be found by taking the total cost of the beads and dividing it by the number of beads used.
1. The total cost of the beads may be found by multiplying the price of each type of bead by the number used, and then adding these values together. Thus:
Total Cost = 0.75x + 3*0.3
= 0.75x + 0.9
2. Total number of beads = x + 3
3. Thus, the average cost is:
(0.75x + 0.9)/(x + 3)
4. Using the value of the average cost per bead given to us ($0.60), we can now write up the full equation:
0.6 = (0.75x + 0.9)/(x + 3)
The equation that represents Noemi's situation with the beads is [(0.75x) + (3*0.30)] / (x + 3) = 0.60, where x is the number of green beads. This equates the average cost per bead to the total cost of all the beads divided by the total number of beads.
Explanation:Noemi strings together x green beads at $0.75 each with 3 blue beads at $0.30 each and she makes a bracelet that averages $0.60 per bead. We can therefore write the situation as an equation where the total cost of the beads is equal to the average cost per bead times the total number of beads.
That is,[tex][(0.75x) + (3*0.30)] / (x + 3) = 0.60[/tex]
This equation represents the total cost of the green and blue beads (0.75x + 0.90), divided by the total number of beads (x + 3), is equal to the average cost per bead ($0.60). You can solve this equation for x to find the number of green beads Noemi used in her bracelet.
Learn more about Algebra here:https://brainly.com/question/32436021
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A cylindrical rainwater tank is 1.5 m tall with a diameter of 1.4 m. What is the maximum volume of rainwater it can hold??
I need answer.. please help me.... please
To work out the volume of a prism, you multiply the area of cross-section by the height (or length).
So for a cylinder, you work out the area of the circle and then multiply it by the height.
Area of circle (or cross-section) = π × radius²
= π × 0.7²
= 0.49π m²
Now to get the volume of the cylinder, you times this area of the cross-section by the height of the cylinder:
Volume = 0.49π × 1.5
= 2.3 m³ (accurate to 2 decimal places)
---------------------------------------------------------------
Answer:
The maximum volume of rainwater the cylinder can hold is:
2.3 m³
The maximum volume of rainwater will be "2.3 m³".
Volume of Cylinder:Given values are:
Height = 1.5 m
Diameter = 1.4 m
The Area of circle will be:
= [tex]\pi\times radius^2[/tex]
= [tex]\pi\times 0.7^2[/tex]
= [tex]0.49 \pi \ m^2[/tex]
hence,
The volume of cylinder be:
= [tex]0.49 \pi\times 1.5[/tex]
= [tex]2.3 \ m^3[/tex]
Thus the answer above is correct.
Find out more information about volume here:
https://brainly.com/question/9554871
Line JK passes through points J(-4,-5) and K(-6,3). If the equation of the line is written in slope-intercept form, y = mx + b
what is the value of b?
-21
4
11
27
[tex]\bf J(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})\qquad K(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-5)}{-6-(-4)}\implies \cfrac{3+5}{-6+4}\implies \cfrac{8}{-2}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-4[x-(-4)]\implies y+5=-4(x+4)[/tex]
[tex]\bf y+5=-4x-16\implies y=-4x\stackrel{b}{\boxed{-21}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
use the substitution method to solve the system of equations. y=7x +8 y=x +20
Answer:
x = 2, y = 22 → (2, 22)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=7x+8&(1)\\y=x+20&(2)\end{array}\right\qquad\text{substitute (1) to (2):}\\\\7x+8=x+20\qquad\text{subtract 8 from both sides}\\7x=x+12\qquad\text{subtract x from both sides}\\6x=12\qquad\text{divide both sides by 6}\\x=2\\\\\text{put the value of x to (2):}\\\\y=2+22\\y=22[/tex]
find the perimeter of the following.
Answer:
24.997 = 25.00 (rounded off to 2 decimal figures)
Step-by-step explanation:
By observation, we can see that both straight lines are of equal length and that the angle between the lines is 90°. Hence we can conclude that this is a quadrant of a circle with radius, r = 7 cm.
length of the curved section
= 1/4 x circumference of the circle
= 1/4 x 2πr
= 1/4 x 2 x 3.142 x 7
= 10.997 cm²
HEnce circumference = 10.997 + 7 + 7 = 24.997 = 25.00 (rounded off to 2 decimal figures)
Can someone Help me please
Answer:
mean=1.6
Step-by-step explanation:
The mean is the average of numbers so it is 0+1+2+2+3=8/5
Answer:
1.6
Step-by-step explanation:
To find the mean we divide the jokers by the decks of cards. There are 8 jokers and 5 decks of cards. 8/5=1.6. The mean is 1.6
Use the information given below, to compare the cost of operating two different vehicles for one month (4 weeks) You
are considering two different cars. You drive to work, a 20 mile round trip, five days a week. Gasoline costs you $1.50
per gallon
Car Agets 28 miles per gallon, would have $300 a year in maintenance costs, and would cost you $1,500 per year to
insure
Car B gets 19 miles per gallon, would have $500 a year in maintenance costs, and would cost you $1,000 per year to
insure
Costs
Car A
Car B
Gas cost per month
Insurance cost per month
Maintenance cost per month $
Total cost per month
Answer:
Gas Cost Per Month: Car A $21.43, Car B $31.58
Insurance Cost Per Month: Car A $125, Car B $83.33
Maintenance Cost Per Month: Car A $25, Car B $41.67
Total Cost Per Month: Car A $171.43, Car B $156.58
Step-by-step explanation:
Gas Cost Per Month:
It is a 20 mile round trip per day, so five days a week would be 100 miles. This means that you drive 400 miles to work in one month. So for Car A, 400/28 = 14.29 gallons. 14.29 gallons times $1.50 = $21.43 per month. For Car B, 400/19 = 21.05 gallons. 21.05 Gallons times $1.50 = $31.58 per month.
Insurance Cost Per Month:
Car A costs $1,500 to insure for one year. So if we take 1,500 and divide it by 12 we get $125 per month. Car B costs $1,000 to insure for one year. So taking 1,000 and dividing by 12 gives us roughly $83.33.
Maintenance Cost Per Month:
Car A costs $300 per year, so taking 300 and dividing by 12 gives us $25 per month. Car B costs $500 per year, so taking 500 and dividing by 12 gives us roughly $41.67 per month.
Total Cost Per Month:
Now all we need to do is add everything together. For Car A, we have $21.43 in gas, $125 in insurance, and $25 in maintenance. This gives a grand total of $171.43 per month. For Car B, we have $31.58 in gas, $83.33 in insurance, and $41.67 in maintenance, leaving a grand total of $156.58.
Hope this helps!
To compare the monthly operating costs of Car A and Car B, calculate and sum up the gas, insurance, and maintenance costs for each car. Car B, with a total monthly cost of $156.58, is less expensive to operate than Car A, which costs $171.43 per month.
To compare the cost of operating two different vehicles for one month, we need to calculate the monthly gas, insurance, and maintenance costs for each vehicle and then add them up to get the total monthly cost.
Calculating Costs for Car A
Gas Cost per Month: You drive 20 miles a day for 5 days a week, that's 100 miles a week or 400 miles for 4 weeks (1 month). At 28 miles per gallon, you would need roughly 14.29 gallons (400/28) per month. At $1.50 per gallon, the monthly gas cost is 14.29 gallons * $1.50/gallon = $21.43.Insurance Cost per Month: $1,500 per year translates to $125 per month ($1,500/12 months).Maintenance Cost per Month: $300 a year equates to $25 per month ($300/12 months).Total Cost for Car A per Month = Gas + Insurance + Maintenance = $21.43 + $125 + $25 = $171.43.Calculating Costs for Car B
Gas Cost per Month: With the same driving pattern, you would need roughly 21.05 gallons (400/19) per month. At $1.50 per gallon, the monthly gas cost is 21.05 gallons * $1.50/gallon = $31.58.Insurance Cost per Month: $1,000 per year is about $83.33 per month ($1,000/12 months).Maintenance Cost per Month: $500 a year is about $41.67 per month ($500/12 months).Total Cost for Car B per Month = Gas + Insurance + Maintenance = $31.58 + $83.33 + $41.67 = $156.58.Comparing the total monthly costs, Car B is less expensive to operate than Car A.
Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.
Which of Jubal’s equations has no solution hurry please
Answer:
3x+2=3x-2
Step-by-step explanation:
The second equation has no solution, because is not true
so
3x+2=3x-2 ------> is not true
therefore
The equation has no solutions
Answer:
[tex]3x+2=3x-2[/tex]
Step-by-step explanation:
When an equation has no solution there's no true value for x. What we have is a Contradiction, a false answer.
1)The first and the last equation has a true solution in the form:
[tex]0x=0[/tex]
True
2)The third one has a solution:
[tex]x=7[/tex]
True
3) The second one
[tex]3x+2=3x-2\\0x=-4[/tex]
FALSE
A Contradiction. Then, this one has no solution.
Which is the equivalent to 641/4
Answer:
32 1/2
2
or
160.25
Step-by-step explanation:
the equivalent to 641/4
is 160.25 in decimal
32 1/2
2
32 whole number 1/2 over or divided by 2
For this case we must indicate an expression equivalent to the following:
[tex]\frac {641} {4}[/tex]
It is observed that the fraction can not be simplified, so, its decimal form is given by:
[tex]\frac {641} {4} = 160.25[/tex]
We can convert to a mixed number, for this, We convert the decimal number to a fraction by placing it on a power of ten. Since there are 2 numbers to the right of the decimal point, we place the decimal on [tex]10 ^ 2 = 100[/tex]. So:
[tex]160 \frac {25} {100}[/tex]
We simplify:
[tex]160 \frac {1} {4}[/tex]
Answer:
[tex]160.25\\160 \frac {1} {4}[/tex]
triangle JLK be a right triangle with right angle L. If JM=3 and and MK equals 6 find LM show work
Answer:
The length of LM is 4.24
Step-by-step explanation:
* Lets revise the rules in the right angle triangle when we draw the
perpendicular from the right angle to the hypotenuse
- In triangle ABC
# Angle B is a right angle
# The hypotenuse is AC
# BD ⊥ AC
∴ (AB)² = AD × AC
∴ (BC)² = CD × AC
∴ (BD)² = AD × CD
∴ BD × AC = AB × BC
* Lets use one of these rules to solve the problem
∵ Δ JLK is a right triangle
∵ ∠L is a right angle
∵ LM ⊥ JK
- We can find LM by one of the rule above
∵ JM = 3
∵ MK = 6
∵ (LM)² = JM × KM
∴ (LM)² = 3 × 6 = 18 ⇒ take a square root for both sides
∴ LM = √18 = 3√2 ≅ 4.24
* The length of LM is 4.24
What are the units of the volume of the figure? Please help
Answer: Cubic Inches
Step-by-step explanation: Because its measured in inches, that would eliminate the choice of centimeters. Its a cube so you use inches cubed. Square inches are for a 2-dimensional object. Such as square feet of a house, as the floor is technically 2-dimensional.
Answer:
Ello mate !
The answer would be cubic inches !
The sum of 5 consecutive even numbers is 310.
What is the third number in this sequence?
Answer:62
Step-by-step explanation:
The differance between 2 consecutive even number is 2...so if the first consecutive even number is x, then the next 4 consecutive even number will(x+2),(x+4),(x+6),(x+8)
So
X+(x+2)+(x+4)+(x+6)+(x+8)=310
5x+20=310
So,x=58
As the third number is (x+4)
Putting the value of x the final result comes(58+4)=62.
2,2n+2,2n+4,2n+6,2n+8 - 5 consecutive even integers
2n+4 - 3rd number
[tex]2n+2n+2+2n+4+2n+6+2n+8=310\\10n+20=310\\10n=290\\n=29\\\\2n+4=2\cdot29+4=62[/tex]
Find the product
x^5•x^4•x^3
If you are multiply, and all of the numbers are the same, then you add the powers. And if you divide, you subtract the powers.
Since all of the base numbers are the same (there are all x), then you add the powers:
x⁵ * x⁴ * x³ = x¹² ( 5 + 4 + 3 = 12)
--------------------------------------------------------
Answer:
x¹²
Which statement is true regarding the parallel and
perpendicular lines in the diagram?
Answer:
W is parallel to N and N is perpendicular to M
Step-by-step explanation:
Solve the system of equations y=2x-3 y=x^2-2x-8
Answer:
[tex]\boxed{x = -1; \, x = 5}[/tex]
Step-by-step explanation:
(a) Set the two functions equal to each other
[tex]\begin{array}{rcl}y & = & 2x - 3\\y & = & x^{2} - 2x - 8\\2x - 3 & = & x^{2} - 2x - 8\\2x & = & x^{2} -2x - 5\\x^{2} - 4x - 5 & = & 0\\\end{array}[/tex]
(b) Factor the quadratic equation
Find two numbers that multiply to give -5 and add to give ₄9.
Possible pairs are 1, -5; -1, 5;
By trial and error, you will find that 1 and -5 work:
1 × (-5) = -5 and 1 - 5= -4
x² - 4x - 8 = (x + 1)(x - 5)
(c) Solve the quadratic
[tex]\begin{array}{rlcrl}x+ 1 & =0 & \qquad & x - 5 & =0\\x & = -1 & \qquad & x & = 5\\\end{array}\\\text{The solution to the system of equations is }\boxed{\mathbf{x = -1; x = 5}}[/tex]
the solutions to the equations is (-1, -5) and (5, 7)
Franco scored 9 3/5 in a gymnastics cam petition. Which point on the number line represents his score.
Answer:
K
Step-by-step explanation:
They scored a 9.35 and K is between 9.25 and 9.5.
Which of the following is a key property of the linear parent function? A-it does not go through the origin. B-it is a curved line. C- it is in quadrants ll and lV. D- it has a slope of 1.
Answer:
c
Step-by-step explanation:
Select the correct answer
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could
possibly receive the tickets?
•
A.13
B.40
C.56
D.64
Answer:
The correct answer option is C. 56.
Step-by-step explanation:
We are given that a group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets.
We are to find the number of combinations these 5 friends could
possibly receive the tickets.
Here, we will use the concept of combination as the order of the friends is not specific.
[tex]5C5+ (5C4 * 3C1) + (5C3*3C2) + (5C2*3C3)[/tex]
[tex]=1+5*3 + 10*3 +10*1 = 1+15+30+10=[/tex] 56
Answer:
Answer is C.
Step-by-step explanation:
The general formula for calculating combinations is:
[tex]\frac{n!}{k!(n-k)!}[/tex]
Where n is the total number of options and k is the number of options in the combination.
In this case, sub in the numbers given in the question:
[tex]\frac{8!}{5!(8-5)!}[/tex]
[tex]=\frac{8\times 7 \times 6 }{3 \times 2}[/tex]
[tex]=8 \times 7[/tex]
[tex]=56[/tex]
what is the value of y
Answer:
B y=40
Step-by-step explanation:
60-3y+60=180-60
3y=120/3
y=40
Answer this question thanks:)
First multiply 2 to both sides to isolate q. Since 2 is being divided by q, multiplication (the opposite of division) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.
[tex]\frac{q}{2}[/tex] × 2 < 2 × 2
q < 4
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
q < 4
aka q is less then four
This means that the graph will have an empty circle and the arrow will go to the left of 4. (look at image below)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Look at the picture
Step-by-step explanation:
[tex]<,\ >-\text{op}\text{en circle}\\\\\leq,\ \geq-\text{closed circle}\\\\<,\ \leq-\text{draw a ray to the left}\\\\>,\ \geq-\text{draw a ray to the right}[/tex]
[tex]\dfrac{q}{2}<2\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{q}{2\!\!\!\!\diagup_1}<2\cdot2\\\\q<4[/tex]
[tex]\text{op}\text{en circle on number 4}\\\\\text{draw a ray to the left}[/tex]
Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form
Answer:
[tex]y = 5x - 11[/tex]
Step-by-step explanation:
1) Find slope
2) Substitute 1 point back into formula to find y-intercept, aka c
ANSWER
[tex]y = 5x - 11[/tex]
EXPLANATION
The given line passes through:
(3,4) and (2,-1).
The slope is given by:
[tex]m = \frac{ - 1 - 4}{2 - 3} [/tex]
[tex]m = \frac{ - 5}{ - 1} = 5[/tex]
The equation can be found using
[tex]y-y_1=m(x-x_1)[/tex]
We plug in the point and slope to get:
[tex]y - 4 = 5(x - 3)[/tex]
[tex]y - 4 = 5x - 15[/tex]
[tex]y = 5x - 15 + 4[/tex]
[tex]y = 5x - 11[/tex]
This is the slope-intercept form
which point on the number line best represents 22
Answer:
Where is the point?
Step-by-step explanation:
Answer:
B at 4.7
Step-by-step explanation:
Solve the formula c = pie d for d
Answer:
[tex]\large\boxed{d=\dfrac{C}{\pi}}[/tex]
Step-by-step explanation:
It's the formula of a circumference:
[tex]C=\pi d[/tex]
d - diameter
Solve for d:
[tex]\pi d=C[/tex] divide both sides by π
[tex]d=\dfrac{C}{\pi}[/tex]
Answer:
he is right. you need to divide both sides by pie which is 3.14
Step-by-step explanation:
can someone please help me with equating coefficients?
(x+4)(ax^2 + bx + c) = -2x^3 -7x^2 + 3x -4
ANSWER
a=-2,v=1,c=-1
EXPLANATION
[tex](x + 4)(a {x}^{2} + bx + c) = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]
We expand the left hand side to get,
[tex]a {x}^{3} + b {x}^{2} + cx + 4ax^{2} + 4bx + 4c = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]
Simplify further to get:
[tex]a {x}^{3} +(4a + b) {x}^{2} +( 4b + c)x + 4c = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]
Comparing the coefficients of the cubic terms , we have
[tex]a {x}^{3}=-2{x}^{3} [/tex]
[tex]a =- 2[/tex]
Comparing the quadratic terms,
[tex](4a + b) {x}^{2} = - 7 {x}^{2} [/tex]
[tex]4a + b = - 7[/tex]
[tex]4( - 2) + b = - 7[/tex]
[tex] - 8 + b = - 7[/tex]
[tex]b = - 7 + 8 = 1[/tex]
Comparing the constant terms,
[tex]4c = - 4[/tex]
[tex]c = - 1[/tex]
Answer:
[tex]\large\boxed{a=-2,\ b=1,\ c=-1}[/tex]
Step-by-step explanation:
[tex](x+4)(ax^2+bx+c)\qquad\text{Use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(ax^2)+(x)(bx)+(x)(c)+(4)(ax^2)+(4)(bx)+(4)(c)\\\\=ax^3+bx^2+cx+4ax^2+4bx+4c\qquad\text{combine like terms}\\\\=ax^3+(b+4a)x^2+(c+4b)x+4c\\\\ax^3+(b+4a)x^2+(c+4b)x+4c=-2x^3-7x^2+3x-4\\\\\text{Comparing coefficients of terms with the same exponents:}[/tex]
[tex]\left\{\begin{array}{ccc}a=-2&(1)\\b+4a=-7&(2)\\c+4b=3&(3)\\4c=-4&(4)\end{array}\right\\\\(4)\\4c=-4\qquad\text{divide both sides by 4}\\c=-1\\---------------------\\(2)\\\text{From (1) put}\ a=-2\\b+4(-2)=-7\\b-8=-7\qquad\text{add 8 to both sides}\\b=1\\---------------------\\(3)\\\text{From (4) put}\ c=-1\\-1+4b=3\qquad\text{add 1 to both sides}\\4b=4\qquad\text{divide both sides by 4}\\b=1[/tex]
What is the value of y in the solution to the system of equations 1/3x+1/4y=1, 2x-3y=-30
Answer:
x = -3 and y = 8
Step-by-step explanation:
1/3 (-3) + 1/4 (8) = 1
-1+2=1
2(-3)-3(8)=-30
-6 - 28=-3
Answer:
The value of y in the solution to the system of equations is:
[tex]y=8[/tex]
Step-by-step explanation:
We have the following system of equations
[tex]\frac{1}{3}x+\frac{1}{4}y=1\\2x-3y=-30[/tex]
To solve the system multiply the first equation by -6 and add it to the second equation
[tex]-6*\frac{1}{3}x-6*\frac{1}{4}y=-6[/tex]
[tex]-2x-\frac{3}{2}y=-6[/tex]
+
[tex]2x-3y=-30[/tex]
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[tex]0 - 4.5y=-36[/tex]
[tex]y=\frac{-36}{-4,5}[/tex]
[tex]y=8[/tex]
Solve log base 2 of one eighth
Answer:
-3
Step-by-step explanation:
[tex]log_{2}[/tex] (1/8)
= [tex]log_{2}[/tex] 1 - [tex]log_{2}[/tex] 8 ( recall [tex]log_{2}[/tex]1 = 0)
= 0 - [tex]log_{2}[/tex] 8
= - [tex]log_{2}[/tex] 8 (change base to base 10)
= - (log 8) / (log 2) (now you can use a calculator)
= - 3
The log base 2 of [tex]\frac{1}{8}[/tex], i.e., [tex]\log_2 \frac{1}{8}[/tex] is -3.
In mathematics, the logarithm, denoted as "log," is an important mathematical function that represents the exponent to which a fixed base must be raised to obtain a given number. It is the inverse operation of exponentiation.
The logarithm function is typically written as [tex]log_b(x)[/tex], where x is the number for which we want to find the logarithm and b is the base. The base can be any positive number greater than 1, commonly used bases include 10 (logarithm to the base 10, often written as log(x)) and the mathematical constant e (natural logarithm, often written as ln(x)).
[tex]\log_2 \frac{1}{8}[/tex] = [tex]\log_2 2^-^3[/tex]
= -3.
So, [tex]\log_2 \frac{1}{8}[/tex] is -3.
Learn more about log here:
https://brainly.com/question/32621120
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