Answer:
(-5;-8)
Step-by-step explanation:
-6y-63-7y=41
-13y=104
y=-8
x=-2*-8-21=-5
The solution is
The value of x = -5
The value of y = -8
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the equation A is
3x - 7y = 41 be equation (1)
x = -2y - 21 be equation (2)
Now , substitute the value of equation (2) in equation (1) , we get
3x - 7y = 41
3 ( -2y - 21 ) - 7y = 41
On simplifying the equation , we get
-6y - 63 - 7y = 41
Adding 63 on both sides of the equation , we get
-13y = 104
Divide by -13 on both sides of the equation , we get
y = -8
So , the value of y = -8
Substitute the value of y in equation (2) , we get
x = -2y - 21
x = - 2 ( -8 ) - 21
x = 16 - 21
x = -5
So , the value of x = -5
Therefore , the value of x is -5 and y is -8
Hence ,
The value of x = -5
The value of y = -8
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What is the number of possible outcomes if two marbles are picked out of a bag that contains three red marbles and three blue marbles? A) 2 B) 3 C) 4 D) 6
Answer:
2
Step-by-step explanation:
Answer:
its 3
Step-by-step explanation:
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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y is directly proportional to X
When y = 30, x = 6
a) work out an equation connecting y and x.
b) Work out the value of y when x = 12
Answer:
a. y÷x=5 , b. y=60 because x is increased by 2 times so y should be increased by 2 times
Step-by-step explanation:
HELP I WILL GIVE BRAINLIEST I MEED THIS ASAP
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
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.
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
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)
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.
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]
What’s the area of the triangle?
Answer:
A=75 cm
Step-by-step explanation:
The formula of the area of a triangle is A=bh/2.
A=(15)(10)/2.
A=150/2
A=75 cm is your answer.
Answer:
A=75 cm
Step-by-step explanation:
A=bh/2 is the formula for the area of a triangle
1) Multiply 15 the base and the height 10 first
A=(15)(10)
A= 150 cm
2) divide 150cm by 2
A=150/2
A=75 cm is your answer.
Hopes this helps My friend!
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.
Which inequality is shown in this graph
ANSWER
[tex]y \leqslant - 2x - 2[/tex]
EXPLANATION
The boundary line passes through (-2,2) and (0,-2).
The slope of this line is
[tex]m = \frac{ - 2 - 2}{0 - - 2} [/tex]
[tex]m = \frac{ - 4}{2} = - 2[/tex]
The y-intercept is , c=-2.
The slope-intercept form of this line is given by;
[tex]y = mx + c[/tex]
We substitute values to obtain;
[tex]y = - 2x - 2[/tex]
Since the lower half-plane is shaded the required inequality is
[tex]y \leqslant - 2x - 2[/tex]
how are expressions and equations different.
Answer:
Equations are composed for many expressions.
Expressions can indicate variables, constants, etc.
Best regards
Answer:
Step-by-step explanation:
Expressions generally contain literals and may be "evaluated" by subbing the given values of the literal into them. Expressions may be simplified, including being rewritten in alternative forms.
Equations, on the other hand, involve the " = " symbol. If a literal, such as x or y, is included in the equation, we can usually solve the equation for that literal, thereby creating a function.
Help I’m not sure how to answer this
Answer:
option A is the correct choice
Step-by-step explanation:
The trigonometric equation you are using has a general form
y = A* tan w*(x - r)
Where
A is the amplitude of the function
w is the frequency rad/s
r is the phase shift
In your case
A = 2
B = w = 3
r = pi/2
y = 2* tan 3*(x - pi/2)
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:
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
Owen and Ethan have $175 together. How much money does each of them have if Ethan has $33 more than Owen?
write 8.54x10^3 in standard notation
Answer: The real number is 8540
Step-by-step explanation: 85.4 1000
PLEASE HELP AS FAST AS POSSIBLE (35 POINTS)
2 QUESTIONS
Answer:
36 and 32
Step-by-step explanation:
So what you do is look at the radius which is 18. The radius is half the distance. So all you have to do is do 18*2=36.
Same with the other one 16*2=32.
Those are your answers.
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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What is the area of this trapezoid? Please help me.
Step-by-step explanation:
Area of a trapezoid is 1/2h(b1+b2)
So let's substitute.
1/2*17*(15+27)
1/2*17*42
Answer is 357 cm squared
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
Solve by factoring: X^3+7x^2-x-7=0
Answer:
[tex]\boxed{\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}}[/tex]
Step-by-step explanation:
Factor [tex]\bold{x^3+7x^2-x-7}[/tex]
[tex]\bold{\left(x+7\right)\left(x^2-1\right)}[/tex]
Factor [tex]\bold{0}[/tex]
[tex]\bold{0}[/tex]
Rewrite Equation
[tex]\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}[/tex]
[tex] {x}^{3} + 7 {x}^{2} - x - 7 = 0 \\ \Leftrightarrow {x}^{2} (x + 7) - (x + 7) = 0 \\ \Leftrightarrow ( {x}^{2} - 1)(x + 7) = 0 \\ \Leftrightarrow (x - 1)(x + 1)(x + 7) = 0 \\ \Leftrightarrow x = - 7 \: \vee \: x = - 1 \: \vee \: x = 1[/tex]
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!
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
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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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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What is the value of n in the equation below?
Answer:
12
Step-by-step explanation:
We can use the property of exponents [tex]\frac{a^b}{a^c}=a^{b-c}[/tex] over here.
Let's use this property to write:
[tex]\frac{a^n}{a^3}\\=a^{n-3}[/tex]
This is equal to a^9, hence, n - 3 = 9. Let's solve for n:
[tex]n-3=9\\n=9+3\\n=12[/tex]
n = 12
Answer:
option C
12
Step-by-step explanation:
Given in the question an expression
[tex]\frac{a^{n} }{a^{3} }=a^{9}[/tex]
To solve for n we will use rules of exponent
cross multiply
[tex]a^{n}=a^{9}a^{3}[/tex]
apply product rule
[tex]a^{n}=a^{9+3}[/tex]
[tex]a^{n}=a^{12}[/tex]
Apply logarithm on both sides of equation
[tex]lna^{n}=lna^{12}[/tex]
apply power rule of logarithm
nln(a) = 12ln(a)
ln(a) will cancel out on each side so we are left with
n= 12