Answers
4x + 8 + 5x - 8 = 90
9x = 90
x = 90/9
x=10
4x + 8 = 5x - 8
Do the math, Add 8 to both sides
4x +8 +8 = 5x - 8 + 8
4x + 16 = 5x
Subtract 4x from both sides
4x - 4x + 16 = 5x - 4x
16 = x or x = 16
Related Questions
How do you completely factor 2x^3 + 16y^3
Answers
2x³+16y³= 2(x³+8y³)
You have a gift card for your favorite clothing store for the amount of $60. You have found a shirt you want for $15. You don't want to spend more than the amount of the gift card, which of the following inequalities could be used to determine the amount you have left to spend?
x+15 is greater than or equal to 60
x-15 is greater than or equal to 60
x+15 is less than or equal to 60
x-15 is less than or equal to 60
Answers
Let
x--------> the amount you have left to spend
y--------> the cost of a shirt you want
z------> the amount of the gift card
we know that
[tex] x+y \leq z [/tex] --------> equation [tex] 1 [/tex]
[tex] y=\$ 15 [/tex] --------> equation [tex] 2 [/tex]
[tex] z=\$ 60 [/tex] --------> equation [tex] 3 [/tex]
Substitute the equation [tex] 2 [/tex] and equation [tex] 3 in the equation [tex] 1 [/tex] [/tex]
[tex] x+y \leq z [/tex]
[tex] x+15 \leq 60 [/tex]
therefore
the answer is the option
x+15 is less than or equal to 60
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.
5x+2y=21
-2x+6y=-34
...?
Answers
sub into second equation
-2(21-2y)/5+6y=-34(-42+4y)/5+6y=-34solve for yy=-64/17plug into equation and solve for x=(97/17)
Answer:
The y-coordinate of the solution would be [tex]-\frac{64}{17}[/tex]
Step-by-step explanation:
Given system of equations,
5x+2y = 21 ----------(1)
-2x+6y = -34 ---------(2),
2 × Equation (1) + 5 × Equation (1),
We get,
4y + 30y = 42 - 170
34y = -128
[tex]\implies y = -\frac{128}{34}=-\frac{64}{17}[/tex]
Find angle A if mDE is equal to 53° and mBC is equal to 8°
Answers
Remember that if two secants intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs. So, our equation would be A = (1/2)(mDE-mBC). Now let us plug in the values.
A= 1/2(53-8)
a= 1/2(45)
A = 22.5
Therefore, the measure of angle A is 22.5 degrees.
Hope this is the answer that you are looking for.
A 5 ft woman is standing next to a tree. her shadow is 10 ft long the trees casts a shadow that is 116 ft long. how tall is the tree? worksheet
Answers
tree's height tree's shadow height
5 = 10
x 116
580 = 10x
x = 58 ft
What's 44/8 as a mixed number
Answers
Just simply find the GCF of 44 and 8 then divide them 44 by 4 over 44 over 8 and u get 11/2. Now divide 11 and 2 and u get 5 with the remainder of 1, now simplify and u get 5 1/2. 5 from the sentence before this one and convert 1 to one half.
44/8 = 5 with a remainder of 4. Your remainder goes over your original denominator. Your quotient is your whole number. So in this instance, the quotient is 5 and the remainder is 4, so that means the answer is ..
5 [tex] \frac{4}{8} [/tex]
Which can be reduced to..
5 [tex] \frac{1}{2} [/tex]
There you are!
Hope this helps! :)
how to integrate arctan 3x.dx ...?
Answers
arctan(3x) = 1*arctan(3x)
ill take
u = arctan(3x)
dv = 1
-so you know
du = 3/(1+9x^2) ...... derivative of tangent inverse
v = x
∫ u dv = uv - ∫ v du
∫ (arctan(3x) * 1) dx = x*arctan(3x) - ∫ (x * (3/(1+9x^2))) dx
= x*arctan(3x) - ∫ (3x / (1 + 9x^2)) dx
take w = 1 + 9x^2
dw = w' dx
dw = 18x dx
dx = dw / 18x
so now you have
= x*arctan(3x) - ∫ (3x)/w * dw/18x
the x's cancel and you end up with
= x*arctan(3x) - (1/6)*∫(1/w)dw
= x*arctan(3x) - (1/6) * ln|w|
= x*arctan(3x) - (ln(1 + 9x^2))/6.......1 + 9x^2 is always positive
your answer:
x*arctan(3x) - (ln(1 + 9x^2))/6
What is the minimum number of colors required to color in the following map if no two adjacent regions can have the same color? In a complete sentence, explain how you got your answer
Answers
Write an equation to solve the problem.
Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 45 mi/h. When will they be 400 mi apart? ...?
Answers
ok guys this is for connexus introduction to solving equations: practice
1. B, h=2A/b 2. C, v=h+5t^2/t 3. D, 23 4. D, -81 5. A, 17/7 6. D, 8 7. A, 4 hours 8. C, width is 4.5; length is 7.5 9. C, never true 10. B, sometimes true
-hope this helps you guys out :3 your welcome
When making a statistical inference about the mean of a normally distributed population based on a sample drawn from that population, which of the following statements is correct, all else being equal?
The 68% confidence interval is wider than the 90% confidence interval.
The 90% confidence interval is narrower than the 95% confidence interval.
The 90% confidence interval is wider than the 99% confidence interval.
The 99% confidence interval is narrower than the 68% confidence interval
Answers
Then, an interval of 68% is narrower than 90%, which is narrower than 95%, which is narrower than 98%.
The only option of the list that is right is the second one.
Answer: the 90% confidence interval is narrower than the 95% confidence interval.
Which expressions are equivalent to the one below? Check all that apply.
3^x
Answers
First one isn't answer because 3^x is exponetial while x^3 is cubic function. If you draw them you will see that they are very different.
B is correct because we can divide both numerator and denominator by 6 and we get 3^x
C is not correct because x is not powering 3 so we cannot devide both by 6
D is correct because 3^(x-1) is same as 3^x*3^(-1) = 3^x/3 and when multiplied by 3 we get 3^x
E is not correct. will understand after explanation in D
F is correct. x is powering both numbers so it can be outside parethasis.
Answer:
All of the answers in the picture provided are correct
Step-by-step explanation:
A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?
Answers
Answer:
[tex]\boxed{\boxed{a = 240, b = 1.16}}[/tex]
Step-by-step explanation:
General exponential function for growth or decay is,
[tex]y=a(1\pm r)^{x}[/tex]
Where,
a = initial value,
r = rate of change
+ is used for growth and - is used for decay.
As here, the number of birds increasing so, the exponential function is,
[tex]y=a(1+r)^{x}[/tex]
And initial value a = 240, r = rate of change = 16% = 0.16
Putting the values,
[tex]y=240(1+0.16)^{x}\\\\y=240(1.16)^{x}[/tex]
Comparing this with the given equation [tex]y=ab^{x}[/tex]
Hence, a = 240, b = 1.16
Answer:
The value of a is 240 and b is 1.16.
Step-by-step explanation:
Given,
The initial population of the birds = 240,
Annual rate of increasing = 16 %,
Hence, the population of birds after x years
[tex]P=240(1+\frac{16}{100})^x[/tex]
[tex]=240(1+0.16)^x[/tex]
[tex]=240(1.16)^x[/tex]
We can put P = f(x), ( because, f(x) also shows the population of birds after x years )
[tex]\implies f(x) = 240(1.16)^x[/tex] --------(1)
According to the question,
[tex]f(x) =ab^x[/tex] --------(2),
From equation (1) and (2),
a = 240 and b = 1.16
Pete wants to make turkey sandwiches for two friends and himself. He wants each sandwich to contain 3.5 ounces of turkey.how many ounces of Turkey does he need?
Answers
Hope this helps
Write the following comparison as a ratio reduced to lowest terms.
10 nickels to 11 dimes
Answers
10 nickels to 11*2 nickels
10 nickels to 22 nickels
10 nickels: 22 nickels
10:22
5:11
[tex]\frac{5}{11}[/tex]
To find the simplified ratio of 10 nickels to 11 dimes, convert the counts into their monetary values, create a ratio, and reduce it. The end result is a simplified ratio of 5:11, as 10 nickels are worth 50 cents and 11 dimes are worth 110 cents.
The question asks for a ratio to be written and reduced to its lowest terms. This involves dividing both quantities by the same number until they cannot be divided further without resulting in a fraction. To write the comparison of 10 nickels to 11 dimes as a ratio reduced to lowest terms, we consider the value of each coin type. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, 10 nickels have a value of 10 x 5 = 50 cents, and 11 dimes have a value of 11 x 10 = 110 cents.
Creating a ratio of these values, we get 50:110. Since both numbers are divisible by 10, we can simplify the ratio by dividing each side by 10, which gives us 5:11. This ratio is already in its simplest form, as 5 and 11 have no common divisor other than 1.
The simplified ratio of the value of 10 nickels to 11 dimes is 5:11.
In ΔABC shown below, ∠BAC is congruent to ∠BCA:
Triangle ABC, where angles A and C are congruent
Given: Base ∠BAC and ∠ACB are congruent.
Prove: ΔABC is an isosceles triangle.
When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle.
Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D:
m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.
∠BDA is congruent to ∠BDC by the definition of congruent angles.
Line segment AD is congruent to Line segment DC of a perpendicular bisector.
ΔBAD is congruent to ΔBCD by_____1_______.
Line segment AB is congruent to Line segment BC because____2_____.
Consequently, ΔABC is isosceles by definition of an isosceles triangle.
Answers
Refer to the image attached.
Given: [tex]\angle BAC[/tex] and [tex]\angle ACB[/tex] are congruent.
To Prove: [tex]\Delta[/tex]ABC is an isosceles triangle.
Construction: Construct a perpendicular bisector from point B to Line segment AC.
Consider triangle BAD and BCD,
[tex]\angle BAC = \angle ACB[/tex] (given)
[tex]\angle BDA = \angle BDC = 90^\circ[/tex]
(By the definition of a perpendicular bisector)
[tex]AD=DC[/tex] (By the definition of a perpendicular bisector)
Therefore, [tex]\Delta ABD \cong \Delta BDC[/tex] by Angle Side Angle(ASA) Postulate.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent.(CPCTC)
Final answer:
By constructing a perpendicular bisector from B to AC in triangle ABC, we use the RHS Congruence rule and CPCTC to prove that AB is congruent to BC, thus showing that triangle ABC is isosceles.
Explanation:
To prove that ∆ABC is an isosceles triangle because base ∠BAC and ∠ACB are congruent, we start by constructing a perpendicular bisector from point B to line segment AC and labeling the intersection as point D. By definition, m∠BDA and m∠BDC are 90°, and ∠BDA is congruent to ∠BDC. Also, AD is congruent to DC because D is the midpoint of AC. Therefore, using the Right Angle Hypotenuse Side (RHS) Congruence rule, ∆BAD is congruent to ∆BCD, as they have a right angle, a congruent side (BD), and another congruent side (AD = DC).
Since the triangles ∆BAD and ∆BCD are congruent, it follows that line segment AB is congruent to line segment BC, by Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Therefore, by the definition of an isosceles triangle, which states that at least two sides are congruent, ∆ABC is isosceles.
please help!! Choose the equation below that represents the line passing through the point (−5, 1) with a slope of 3/2
A: y − 5 = 3/2 (x + 1) B: y + 1 =3/2 (x − 5) C: y + 5 = 3/2 (x − 1) D: y − 1 = 3/2 (x + 5)
Answers
Write 0.4375 as a fraction in simplest form.
Answers
= 7/16
Answer: 7/16
Step-by-step explanation:
because if you do long division your answer is
16 ) 7.0000 ( 0.4375
-64
60
-48
120
-112
80
-80
0
wich is is = 0.4375
I'll upvote everything
Which expression represents "3 more than twice a number"?
3−2n3−2n
2n−32n−3
2n+32n+3
2+n+3
Answers
So, for this problem, I don't really see an answer choice that fits along with this description?? The last one is the closest to the answer I believe it is, but still doesn't fit exactly:
Twice a number = 2n
Three more than = +3
Final equation = 2n+3
Perhaps you have a typo either in your question or your answer problem, or I'm just way too tired. Either way, I hope this helped you out, and feel free to ask me any additional questions you may have.
–Lamb :-)
You have 17 coins in pennies, nickels, and dimes in your pocket. The value of the coins is $0.47. There are four times the number of pennies as nickels. How many of each type of coin do you have? Set up the system and solve.
Answers
p = number of pennies
n = number of nickles
d = number of dimes
p(1) + n(5) + d(10) = 47
that is, the number of pennies x 1 cent + number nickles x 5 cents
+ number of dimes x ten cents equals 47 cents
p = 4n
p + n + d = 17
Substituting 4n for p in the above
4n + n + d = 17
5n + d = 17
Subtract 5n from each side
d = 17 - 5n
We will now substitute 4n for p and ( 17-5n ) for d in
the equation
p(1) + n(5) + d(10) = 47
4n(1) +n(5) + (17-5n)(10) = 47
9n + 170 - 50n = 47
-41n + 170 = 47
Subtract 170 from each side
-41n = 47 - 170
-41n = -123
Divide each side by -41
n = 3
Since p = 4n
p = 4(3)
p = 12
Since p + n + d = 17
12 + 3 + d = 17
15 + d = 17
d = 2
So we have 12 pennies, 3 nickles and 2 dimes
12 + 3(5) + 2(10) ?= 47
12 + 15 + 20 ?= 47
Final answer:
By setting up a system of equations and using the elimination method, we concluded that there are 12 pennies, 3 nickels, and 2 dimes to make up the 17 coins totaling $0.47.
Explanation:
The question asks us to determine how many pennies, nickels, and dimes we have, given that there are a total of 17 coins worth $0.47, with four times as many pennies as nickels. To solve this problem, we can set up a system of equations based on the information given.
Let p be the number of pennies, n be the number of nickels, and d be the number of dimes. Therefore, we have three equations:
p + n + d = 17 (total number of coins)
1p + 5n + 10d = 47 (total value of coins in cents)
p = 4n (four times as many pennies as nickels)
Substituting the third equation into the first and second equations, we get:
4n + n + d = 17
4n + 5n + 10d = 47
Simplify the equations:
5n + d = 17
9n + 10d = 47
Now, we solve this system of equations using substitution or elimination. Let's use the elimination method:
Multiply the first equation by 10 so that when subtracted from the second equation, the d variable will be eliminated: 50n + 10d = 170
Now subtract this from the second equation: (9n + 10d) - (50n + 10d) = 47 - 170
This results in -41n = -123, and after dividing both sides by -41, we get n = 3
Substitute n = 3 into the first simplified equation: 5(3) + d = 17, resulting in d = 17 - 15, so d = 2
Substitute n = 3 into the original third equation to find the number of pennies: p = 4(3), so p = 12
Therefore, we have 12 pennies, 3 nickels, and 2 dimes.
An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 degrees north of west, then 50 steps due south.Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut. ...?
Answers
Setting the coordinate system: positive x points to the east and positive y points to the north. This can be solved by vector addition.
A = <40cos(45), 40sin(45)>
B = <-60cos(60), 60sin(60)>
C = <0, -50>
R = A + B + C = <-1.72, 80.25>
The displacement that needs to return him is by the vector -R.
Therefore, <1.72, -80.25>
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Set up a proportion and use cross multiplication to solve.
15 is ________% of 60.
Answers
So, your final answer is 25%
Hope this helps!
Answer:
25% Hope It Help's :)
Step-by-step explanation:
the principal will randomly choose 6 students from a large school to represent the school in a newspaper photograph. the probability that a chose student is an athlete is 30%. (assume that this doesn't change) What is the probability that 4 athletes are chosen? ...?
Answers
This is a binomial distribution. The probability of a binomial distribution is given by
P = nCr * p^r * q^(n-r)
For this problem,
n = 6
r = 4
p = 0.30
q = 0.70
P = 6C4 * 0.30^4 * 0.70^(6-4)
P = 5.95%
To find the probability of choosing exactly 4 athletes from 6 students when the chance of any student being an athlete is 30%, we use the binomial probability formula considering a fixed number of trials, a binary outcome, a constant probability, and independent trials.
Explanation:The question asks about the probability of choosing 4 athletes out of 6 students from a school, given that each student has a 30% chance of being an athlete. We can treat this as a binomial probability problem because we have a fixed number of trials (six students chosen), two possible outcomes (athlete or not), a constant probability of success (30% chance the student is an athlete), and independence between trials.
To calculate the probability of exactly 4 athletes being chosen, we use the binomial probability formula:
P(X = k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]
Where:
n is the number of trials (6 students)k is the number of successful trials (4 athletes)p is the probability of success on a single trial (30% or 0.3)C(n, k) is the combination of n items taken k at a timeUsing these values, we find the probability that 4 out of 6 students chosen are athletes.
Which quadratic function has a leading coefficient of 2 and a constant term of –3?
f(x) = 2x3 – 3
f(x) = –3x2 – 3x + 2
f(x) = –3x3 + 2
f(x) = 2x2 + 3x – 3
Answers
f(x) = ax² + bx + c
a - the leading coefficient
c - the constant term
We are looking for a = 2, c = -3
Through the process of elimination:
The first (f(x) = 2x3 – 3) and the third choice (f(x) = –3x3 + 2) have x³ so these are not quadratic function.
In the function: f(x) = –3x2 – 3x + 2
a = -3
c = 2
In the function: f(x) = 2x2 + 3x – 3
a = 2
c = -3
Subtract the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
Subtract 2x^2 - 6x - 4
from 4x^2 - 4x + 3. ...?
Answers
The correct answer is: 2x^2+2x+7
The point (-3,11) is a solution of which of the following systems?
y≥x-2
2x+y≤5
y>x+8
3x+y>2
y>-x+8
2x+3y≥7
y≤-3x+1
x-y≥-15
Answers
A ballplayer catches a ball 3.0s after throwing it vertically upward. With what speed did he throw it, and what height did it reach?
Answers
Answer:
d=11, vo=15m/s
Step-by-step explanation:
use first and second kinematic equation, plug in T as 1.5 since that is when it reaches the top. G=-9.8 m/s^2, thats gravity or acceleration in this case.
why wouldn't the man stand in line to step on the scale ?
answer ?
Answers
The man wouldn't stand in line to step on the scale because the scale measures weight, not mass. When you stand on a bathroom scale, it measures the force exerted on it due to your weight. Weight is the force of gravity acting on an object, while mass is the amount of matter in an object.
Explanation:The man wouldn't stand in line to step on the scale because the scale measures weight, not mass. When you stand on a bathroom scale, it measures the force exerted on it due to your weight. Weight is the force of gravity acting on an object, while mass is the amount of matter in an object. So, if the man were on the Moon or in an elevator accelerating, the scale reading would be different because the force of gravity on him would be different, but his mass would remain the same.
Sandy walks 26 miles in a month. how many miles will she have walked in 2 years
Answers
Final answer:
Sandy walks 312 miles in a year, so over 2 years, she would walk 624 miles. As a reference point, a marathon runner with an average speed of 9.5 mi/h would take approximately 2.76 hours to run a 26.22 mi marathon.
Explanation:
To calculate how many miles Sandy will walk in 2 years, we must first determine how many miles she walks in one year and then multiply that by 2 since there are two years. Sandy walks 26 miles in a month. Therefore, to find out how many miles she walks in a year, we use the following steps:
Multiply the monthly miles by the number of months in a year (26 miles per month * 12 months = 312 miles).
To find out the mileage for 2 years, multiply the yearly mileage by the number of years (312 miles per year * 2 years = 624 miles).
Therefore, Sandy will have walked 624 miles in 2 years.
If a marathon runner averages 9.5 mi/h, the calculation to determine how long it takes him or her to run a 26.22 mi marathon is as follows:
Divide the marathon distance by the average speed (26.22 mi / 9.5 mi/h).
The result gives us approximately 2.76 hours, which is the time it takes to complete the marathon
Add.
(3x4 – 2x3 + 1) + (12x4 + x2 – 11)
Answer
15x4 – 2x3 + x2 + 10
15x4 – x3 – 10
15x4 – x2 – 10
15x4 – 2x3 + x2 – 10
...?
Answers
3x^4 - 2x^3 -11
12x^4 +x^2 +1 <<< Add these using the normal addition process
----------------------------------
15x^4 - 2x^3 +x^2 -10
Therefore, the answer would be the last option: 15x4 – 2x3 + x2 – 10
Hope this is the answer that you are looking for. Thanks for posting!
freddy is searching for a shirt and discovers that he has 12 shirts for every 6 pair of jeans. If he has 18 shirts, how many pairs of jeans does he have?
Answers
Answer:
9 pairs of jeans
Step-by-step explanation:
there are 2 times as many shirts as jeans, and 18 divided by 2=9