Answer:
[tex]8\ units< x < 18\ units[/tex]
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the Theorem
case 1) [tex]42+4x > 2x-6[/tex]
[tex]4x-2x > -6-42[/tex]
[tex]2x > -48[/tex]
[tex]x > -24\ units[/tex]
case 2) [tex]42+(2x-6) >4x[/tex]
[tex]42-6 >4x-2x[/tex]
[tex]36 >2x[/tex]
[tex]18 >x[/tex] -----> rewrite
[tex]x<18\ units[/tex]
case 3) [tex]4x+(2x-6) > 42[/tex]
[tex]4x+2x > 42+6[/tex]
[tex]6x > 48[/tex]
[tex]x > 8\ units[/tex]
therefore
[tex]8\ units< x < 18\ units[/tex]
which of the following is an equvilant form of the compound inequality -44> -2x -8 greater or equal to -8
-44>-2x-8
Add 8 on both sides
-36>-2x
Divide by -2 dice your x can't be negative
18<x
The sign flips when you divide by a negative. Therefore if the question is a true or false question, the answer would be false
Answer: 18 ≤ x < 0
Step-by-step explanation:
-44 > -2x - 8 ≥ -8
-36 > -2x ≥ 0 added 8 to all three sides
18 < x ≤ 0 divided all three sides by -2 (which flips the inequality signs)
Hello! I would appreciate the help, and please write step by step solutions. Will mark brainliest. Thanks!
QUESTION 5
The side length of the first tra-pezoid and the second tra-pezoid are in the ratio [tex]5:7[/tex].
To find the corresponding ratio of their area, we square each term in the ratio.
The ratio of the area of the first figure, to the ratio of the area of the second is
[tex]5^2:7^2=25:49[/tex]
QUESTION 6
The side length of the first figure and the second figure are in the ratio [tex]12:7[/tex].
To find the corresponding ratio of their area, we square each term in the ratio.
The ratio of the area of the first figure, to the ratio of the area of the second figure is
[tex]12^2:7^2=144:49[/tex]
QUESTION 7
Let [tex]h[/tex] represent the height of this triangle.
[tex]\sin 30\degree=\frac{h}{6}[/tex]
This implies that;
[tex]h=6\sin 30\degree[/tex]
[tex]h=3ft[/tex]
The area of the triangle is [tex]=\frac{1}{2}bh[/tex]
The base is 9 ft and the height is 3 ft.
We substitute these values to obtain;
[tex]A=\frac{1}{2}(9)(3)[/tex]
[tex]A=13.5ft^2[/tex] to the nearest tenth.
QUESTION 8
The area of a parallelogram is [tex]base\times\:height[/tex]
Let h represent the height of this parallelogram.
[tex]\sin60\degree=\frac{h}{6}[/tex]
[tex]h=6\sin60\degree[/tex]
[tex]h=3\sqrt{3}m[/tex]
The area of the parallelogram is [tex]=10\times3\sqrt{3}m^2[/tex]
[tex]=30\sqrt{3}m^2[/tex]
[tex]=52.0m^2[/tex] to the nearest tenth.
A 100-point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and the short response questions are worth 8 points each.
Write a system of Linear Equations that represent this situation. Solve the system.
I REALLY NEED HElP WITH THE TOP PART BUT IF YOU HAVE TIME CAN YOU ANSWER THIS TWO!
How many multible choice questions are on the test?
How many short response questions are on the test?
Answer: 3x+8y=100
x+y=20
x=12
y=8
Step-by-step explanation: x would represent the number of multiple choice questions and y would represent the number of short response questions. the multiple choice questions were 3 points meaning that you need to find x. the short answer response questions were 8 points meaning you need to find y. altogether you need to get 100 points. for the second equation you have 20 questions that need to be both multiple choice and short response. therefore the second equation would be x+y=20. if you solved this, the answer would be that x equals 12 and y equals 8. hope this helped! :))
What is the total cost of a $704 tablet computer that is on a sale at 11% off the local sales tax rate is 4%
Answer: $654.72
Step-by-step explanation:
11 percent of $704 is $77.44 - (11*704/100)
You do $704-$77.44 because it is on sale.
Equalling $626.56
4 percent of $704 is $28.16 - (4*704/100)
Add $28.16 to 626.56 because your being taxed.
Equalling $654.72 your answer
The total cost of the $704 tablet computer, after an 11% discount and 4% sales tax, is $651.62.
Explanation:To find the total cost of the $704 tablet computer, we first need to calculate the sale price after the 11% discount. The discount amount can be found by multiplying the original price by 11% (or 0.11). So, the discount amount is $704 * 0.11 = $77.44. The sale price is then $704 - $77.44 = $626.56.
Next, we need to calculate the sales tax amount. The sales tax rate is 4%, so the tax amount is $626.56 * 0.04 = $25.06.
Finally, to find the total cost, we need to add the sale price and the sales tax amount together. Therefore, the total cost of the $704 tablet computer, including the discount and sales tax, is $626.56 + $25.06 = $651.62.
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Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1? (1, –1) (0, 0) and (0, –1) (0, 0) and (2, 0) no solutions Mark this and return
ANSWER
No solution
EXPLANATION
The first equation is
[tex]y = {x}^{2} - 2x[/tex]
and the second equation is
[tex]y = - 2x - 1[/tex]
We equate the two equations to obtain;
[tex] {x}^{2} - 2x = - 2x - 1[/tex]
This implies that
[tex] {x}^{2} = - 2x + 2x - 1[/tex]
[tex] {x}^{2} = - 1[/tex]
There is no real number whose square is -1.
Therefore, the equation has no solution.
Answer: no solution
Step-by-step explanation: no cap
Two way table on given data help. I don’t understand how to place it on table.
Answer:
I don't know either. I'd help if i knew the answer.
Step-by-step explanation:
The area of a small square patio is 42 square feet. The length of each side of the patio is √42 feet. Between what two whole-number measurements does √42 feet lie?
A) 4 feet and 5 feet
B) 11 feet and 12 feet
C) 22 feet and 24 feet
D) 528 feet and 530 feet
Answer:
The answer is A.
Step-by-step explanation:
Because the square root of 42 is about 6 and those two numbers are close to 6.
Hope this helps!
Please mark brainliest!! thanks!
A) 4 feet and 5 feet
What is the area of square ?
The space occupied by a square is called area of the square.
Let, length of each side of the square = a unit
Then, Area of the square = [tex]a^{2}[/tex] sq.unit
What is the required result ?Given, area of a small square patio = 42 sq. feet
Also the length of each side of the patio = [tex]\sqrt{42}[/tex] feet
The value of [tex]\sqrt{42}[/tex] = 6.48 (approx)
The required value is 6.48 feet, which is close to 4feet & 5feet.
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Jacob’s cell phone service costs $5 each month plus $0.35 for each minute he uses. Every fraction of a minute is rounded up to the next minute.
a. Draw a graph to represent the cost of using the cell phone.
b. What is Jacob’s monthly bill if he uses 124.8 minutes?
Answer:
B. Jacobs monthly bill shall be $48.75
Step-by-step explanation:
On this specific mont, Jacob used 124.8 minutes.
Considering that every fraction of a minute is rounded off to the next minute,
Jacob used 125 minutes.
Each minute goes for $0.35
Now multiply total nomber of minutes by $0.35 rate
0.35 * 125 = 43.75
This is bill for the minutes used.
The bill for service is $5 per month.
To get the total bill, we add $5 to $43.75
Which gives us $48.75
HELP I WILL GIVE BRAINLIEST I MEED THIS ASAP
johnny bought 5 movie tickets and spent $44. Of the tickets he bought, 3/5 were children's tickets that cost $8 each. The other tickets were adult tickets. How much does one adult ticket cost?
Answer:
Adult tickets cost 10$
Step-by-step explanation:
You would have to multiple the cost of child ticket by the number purchased, subtract that number from the total amount spent, and then divide it by 2 to get the cost of an adult ticket.
if angle A and B are alternate interior angles, what is the measure of angle B if angle A measures 105°
Answer:
75 degrees
Step-by-step explanation:
both the angles must add up to 18.
180 - 105 = 75
105 + 75 = 180
Answer:
105
Step-by-step explanation:
alternate angles are equal
You are applying for an 80/20 mortgage to buy a house costing $145,000. The first (80%) mortgage has an interest rate of 4.75%, and the second (20%) mortgage has an interest rate of 7.525%. Both the first mortgage and the second mortgage are 30-year fixed-rate mortgages. What will the total amount of the mortgage be?
Answer:
$291,016.80
A is correct.
Step-by-step explanation:
You are applying for an 80/20 mortgage to buy a house costing $145,000.
Loan Formula:
[tex]EMI=\dfrac{P\cdot r}{1-(1+r)^{-n}}[/tex]
Case 1:
Loan amount, P = 80% of 145000 = $ 116,000
Rate of interest, r = 4.75% = 0.0475
Time of loan, n = 30 years = 360 months
Substitute the values into formula.
[tex]EMI=\dfrac{116000\cdot \frac{0.0475}{12}}{1-(1+\frac{0.0475}{12})^{-360}}[/tex]
[tex]EMI=605.11[/tex]
Total payment for case 1: 605.11 x 360 = $217,839.60
Case 2:
Loan amount, P = 20% of 145000 = $ 29,000
Rate of interest, r = 4.75% = 0.07525
Time of loan, n = 30 years = 360 months
Substitute the values into formula.
[tex]EMI=\dfrac{29000\cdot \frac{0.07525}{12}}{1-(1+\frac{0.07525}{12})^{-360}}[/tex]
[tex]EMI=203.27[/tex]
Total payment for case 1: 203.27 x 360 = $73,177.20
Total amount of the mortgage = $217,839.60 + $73,177.20
= $291,016.80
Hence, The total amount of the mortgage is $291,016.80
Plz help me!!!!!!!!!
Answer:
Step-by-step explanation:
3a-4=a(a-3)
3a-4=a²-3a
3a=a²-3a+4
0=a²-6a+4
a=(6±√[36-4(1)(4)])/2(1)
a=(6±√(36-16))/2
=(6±√20)/2
=3±(2√5)/2
=3±√5
a=3+√5
a=3-√5
Answer: 3 ± √5
Step-by-step explanation:
[tex]3a-4=a(a-3)\\\\3a-4=a^2-3a\qquad distributed\ "a"\ on\ the\ right\ side\\\\0=a^2-6a+4\qquad subtracted\ 3a-4\ from\ both\ sides\\\\a=1,\ b=-6,\ c=4\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4(1)(4)}}{2(1)}\\\\\\.\ =\dfrac{6\pm \sqrt{36-16}}{2}\\\\\\.\ =\dfrac{6\pm \sqrt{20}}{2}\\\\\\,\ =\dfrac{6\pm 2\sqrt5}{2}\\\\\\.\ =3\pm\sqrt5[/tex]
Simplify 12-(6x+4)/2
Answer:
10 - 3x
Step-by-step explanation:
given
12 - [tex]\frac{6x+4}{2}[/tex]
= 12 - [tex]\frac{6x}{2}[/tex] - [tex]\frac{4}{2}[/tex]
= 12 - 3x - 2 ← collect like terms
= 10 - 3x
A number when divided by 899 gives a remainder 63. If the same number is divided by 29, then the remainder will be :
[A]2
[B]4
[C]5
[D]10
x = 899xy + 63
29x31xy + 29x^2+5
29(31y+2)+85
=29
63-58=5
The remainder will be 5.
Answer:
Your answer would be C. 5
Step-by-step explanation:
In 2005 there were 14000 students at college A, with a projected enrollment increase of 750 students per year. In the same year there were 35000 students at college B with a projected enrollment decline of 1000 students per year. According to these projectors when will the colleges have the same enrollment? What will be the enrollment in each college at that time
Answer: in 12 years (2017)
23,000 students enrolled
Step-by-step explanation:
Let x represent the number of years since 2005.
Let y represent the number of students enrolled.
College A: y = 14,000 + 750x
College B: y = 35,000 - 1000x
Solve the system using the Substitution Method:
14,000 + 750x = 35,000 - 1000x
+1000x +1000x
14,000 + 1750x = 35,000
-14,000 -14,000
1750x = 21,000
x = 12
Input x = 12 into one of the equations to solve for y.
y = 35,000 - 1000x
= 35,000 - 1000(12)
= 35,000 - 12,000
= 23,000
Explanation on when two colleges will have the same enrollment and what the enrollment will be at that time.
Explanation:Step 1: Set up equations for the enrollment at each college over time. Let x be the number of years since 2005:
College A enrollment = 14000 + 750x
College B enrollment = 35000 - 1000x
Step 2: Set the two equations equal to each other:
14000 + 750x = 35000 - 1000x
Step 3: Solve for x to find when the colleges will have the same enrollment:
x = 10 years
Step 4: Substitute x back into the equations to find the enrollment at each college after 10 years:
College A enrollment = 14000 + 750(10) = 21500 students
College B enrollment = 35000 - 1000(10) = 25000 students
What is the value of s to the nearest whole number? HELP!
Answer:
14
Step-by-step explanation:
Using the law of cosines on ΔRST, then
s² = 9² + 8² - (2 × 9 × 8 × cos111° )
= 81 + 64 - ( 144 × cos111° )
= 145 - (- 51.6)
= 145 + 51 . 6 = 196.6 ( take the square root of both sides )
s = [tex]\sqrt{196.6}[/tex] ≈ 14
The answer is: 14
Why?Using the law of cosines and the given information, we can find the value of s.
Law of cosines is:
[tex]a^{2}=b^{2}+c^{2}-2abcos(A)[/tex]
Where,
[tex]a=s\\b=9\\c=8\\A=111(degrees)[/tex]
By substituting we have:
[tex]s=\sqrt{9^{2}+8^{2}-2*9*8*cos(111)}\\\\s=\sqrt{81+64-(144)*(-0.35)}=\sqrt{145+50.4}=\sqrt{195.4}=13.98=14[/tex]
So, the correct answer is:
[tex]s=14[/tex]
Have a nice day!
given f(x) =2x^2 - 3x+ 7, find (2.5)
Final answer:
To find f(x) at x = 2.5 in the given function, substitute the value of x into the function and simplify the expression, giving us f(2.5) = 12.
Explanation:
To find the value of f(x) at x = 2.5, we substitute the value of x into the given function: f(2.5) = [tex]2(2.5)^2[/tex] + 7.
Simplifying this expression, we get f(2.5) = 2(6.25) - 7.5 + 7 = 12.5 - 7.5 + 7 = 12.5 - 0.5 = 12.
Therefore, f(2.5) = 12.
if a projectile is fired straight upward from the ground with an intial speed of 64ft per second, then its height in feet after seconds is give by the function h(t)=-16t
Answer:
64 ft
Step-by-step explanation:
if a projectile is fired straight upward from the ground with an initial speed of 64 feet per second, then its height in feet after seconds is given by the function h(t)=-16t^2 + 64t. find the maximum height of the projectile.
***
h(t)=-16t^2 + 64t
complete the square
h(t)=-16(t^2 -4t+4)+64
h(t)=-16(t-2)^2+64
This is an equation of a parabola that opens upward with vertex at (2,64)
maximum height of the projectile=64 ft (2 sec after it is fired)
The cylinders shown below are similar
A 3cm
B 6cm
C 9cm
D 18cm
Im pretty sure that the answer would be 3 cm, answer letter A
A store has apples on sale for $28.00 for 8 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $168.00? Complete the explanation.
The cost per pound of the apples on sale is $
.
You can buy
pounds of apples for $168.00.
Since 1 pound = 16 ounces, so there are about
apples in each pound.
You can buy approximately
apples for $168.00.
To determine how many apples you can buy for $168.00, you first calculate the cost per pound to be $3.50. Then, calculate that you can buy 48 pounds of apples, and since there are about 3.2 apples per pound, you can purchase approximately 153 apples for $168.00.
To determine how many apples you can buy for $168.00, let's start by calculating the cost per pound of the apples on sale, which is $28.00 for 8 pounds. This yields a cost per pound of $3.50.
Next, we'll find out how many pounds of apples you can buy for $168.00. By dividing $168.00 by the cost per pound ($3.50), we get 48 pounds of apples.
Since 1 pound equals 16 ounces, and each apple is approximately 5 ounces, we can calculate how many apples are in each pound by dividing 16 by 5, which gives us about 3.2 apples per pound.
Lastly, to find out the total number of apples you can buy for $168.00, we multiply the total pounds of apples (48) by the number of apples per pound (3.2), resulting in a total of approximately 153.6, which we can round down to 153 apples.
Help with this question plz
Your answer would be 200ft I believe. 20 times 5 times 2 :)
There are six girls and seven boys in the class a team of 10 players is to be selected from the class how many different combinations of players it is possible
Answer:
In 286 different ways 10 players can be selected.
Step-by-step explanation:
There are 6 girls and 7 boys in a class. So in total there are 6+7 = 13 number of students in the class.
A team of 10 players is to be selected from the class.
As there is no other conditions are given, we can pick any 10 students from 13 students.
The way we can select 10 players from 13 students is;
= (13 10)
= 13!/10!(13-10)!
= 13!/10! 3!
= (13 × 12 × 11 × 10!)/ 10! 3!
= ( 13 × 12 × 11)/6
= 286
Abdul invests $5,000 at an interest
rate of 4%, compounded quarterly.
How much is the investment worth
at the end of 3 years?
Answer:
about $5,203.02
Step-by-step explanation:
5000(1+(.04/4))^4
The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 4% per year compounded 1 times per year over 3 years is $5,624.32.
Given Data
Principal = $5000Rate = 4%Time = 3 yearsA = P + I where
P (principal) = $5,000.00
I (interest) = $624.32
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,000.00(1 + 0.04/1)^(1)(3)
A = 5,000.00(1 + 0.04)^(3)
A = $5,624.32
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10 points!! Please show work!!
Answer:
Smaller x -10
Larger x -2
Step-by-step explanation:
f(x) = (x+6) ^2 - 16
To find the zero's, we set the function equal to zero
0 = (x+6) ^2 - 16
Add 16 to each side
16 = (x+6) ^2 - 16 + 16
16 = (x+6)^2
Take the square root of each side
±sqrt(16) = sqrt((x+6)^2))
±4 = x+6
Subtract 6 from each side
-6±4 = x+6-6
-6±4 = x
-6 -4 = x -6+4 =x
-10 =x -2 =x
Smaller x -10
Larger x -2
Answer:
Smaller x: -10
Larger x: -2
Step-by-step explanation:
You are looking for where the function equals 0. So, you can set f(x) equal to 0:
f(x) = [tex]0=(x+6)^{2} -16[/tex]
Now add 16 to both sides:
[tex]16=(x+6)^{2}[/tex]
Now that you have a perfect square on both sides, you can take the square root of both sides. On the right, this would simply remove the exponent. On the left, you have the square root of 16, or 4. It is important to remember that this can be positive or negative (since -4 squared also equals 16).
±4 = x + 6
To find your two solutions, you have to then evaluate the equation for 4 and -4. First, with -4:
-4 = x + 6 subtract 6 from both sides
-10 = x
Now, with 4:
4 = x + 6 subtract 6 from both sides
-2 = x
And there are your two solutions. Since -10 < -2, -10 is the smaller x and -2 is the larger one.
A toy box has a volume of 60 cubic feet. The box is 5 feet long and 4 feet wide. What is the height of the toy box?
The height is 3 feet long
you multiply 5 by 4 and get 20 and 20x3=60 therefore 3 is your answer
Answer:
height = 3
Step-by-step explanation:
length X width X height = volume
5 X 4 X 3 = 60
an easy way if you have two of them and volume is putting random numbers till it equals the correct volume
Point O is the center of the circle. What is the value of x?
A.) 57
B.) 66
C.) 26
D.) 114
B.) 66
arc PN is 114 degrees bc it’s congruent to the central angle. therefore, the rest of the circle is 246 degrees bc 360-114=246. divide the difference of intercepted arcs (246 and 114) by 2 to get the angle formed by the tangents. (246-114)/2=66
If Point O is the center of the circle then value of x is 66 degrees
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that Point O is the center of the circle
We have to find the value of x
arc PN is 114 degrees because it’s congruent to the central angle.
We know that the total measure of triangle is 360 degrees
By removing arc PN the remaining circle has 246 degrees of measure
Divide the difference of intercepted arcs (246 and 114) by 2 to get the angle formed by the tangents.
(246-114)/2
=66 degrees
Hence, if Point O is the center of the circle then value of x is 66 degrees
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5. Which third-party wants little to no government interference?
6. Which u.s. parties would likely approve of a plan to help unemployed workers?
7. Which u.s. parties with disapprove of a tax on businesses to clean up the environment?
8. Which u.s. political parties would likely approve of a plan to provide cheaper Healthcare?
Answer:
Which U.S. political parties would likely approve of a plan to help unemployed workers?
Step-by-step explanation:
1. Communists
2. Democrats
3. Libertarians
4. Republicans
5. Socialists
the answer is 5,3,1
Final answer:
The Libertarian Party wants little to no government interference. The Democratic and Republican parties have different stances on helping unemployed workers, taxing businesses for environmental cleanup, and providing cheaper healthcare.
Explanation:
In the United States, the Libertarian Party is a third-party that wants little to no government interference. They advocate for limited government intervention in both social and economic areas. For example, they support lower taxes, less regulation, and individual freedom.
The Democratic and Republican parties would likely approve of a plan to help unemployed workers. The Democrats often propose policies such as extending unemployment benefits and increasing job training programs, while the Republicans tend to support tax cuts and reducing government regulations to stimulate job growth.
The Democratic party is more likely to approve of a tax on businesses to clean up the environment. They generally advocate for stricter environmental regulations and support policies aimed at reducing pollution. The Republican party, on the other hand, often opposes new taxes and regulations on businesses.
The Democratic party and the Progressive wing of the Democratic party would likely approve of a plan to provide cheaper healthcare. They have been pushing for measures such as expanding Medicaid, implementing a public health insurance option, and decreasing prescription drug prices. The Republican party, however, tends to advocate for free-market solutions and reducing government involvement in healthcare.
What is the next term in the pattern? 1,-1,2,-2,3...
Answer:
Step-by-step explanation: the pattern is going positive to negative and going further away from zero so the next term would be -3
In the equation 6x-2 = -4x + 2, Spencer claims that the
first step is to add 4x to both sides. Jeremiah claims that
the first step is to subtract 6x from both sides. Who is
correct? Explain.
Both Spencer and Jeremiah are correct
The given equation;
6x - 2 = -4x + 2
The solution to the equationThe first step is obtaining the solution to the given equation is to collect similar terms together.
Add 4x to both sides of the equation;
6x + 4x - 2 = -4x + 4x + 2
10x - 2 = 2
Or
Subtract 6x from both sides of the equation;
6x - 6x - 2 = -4x - 6x
-2 = -10x + 2
Thus, both Spencer and Jeremiah are correct.
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