Answers
-x - 2y = - 9
multiply the (1st) equation by 3
-3x - 6y = -27
now you have
-3x - 6y = -27
3x - 6y = -15
-----------------------add
-12y = -42
y = 3.5
2(3.5) = -x + 9
7 = - x + 9
x = 2
answer
(2 , 3.5)
Related Questions
What is the simplest form of ^4 sqrt 81x^8y^5
Answers
ANSWER
[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]
EXPLANATION
We want to simplify:
[tex] \sqrt[4]{81 {x}^{8} {y}^{5} } [/tex]
We can split the radical sign to obtain:
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} } [/tex]
Or
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y} [/tex]
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]
[tex]\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]
Recall that:
[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]
[tex]{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y} [/tex]
[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]
Answer:
B!!!!!!!!!
Step-by-step explanation:
What is the quotient in simplest form? State any restrictions on the variable.
(z^2 - 4)/(z - 3) divided by (z+2)/(z^2+z -12),
Answers
The first step to solve this problem is to completely factor the expressions first.
(z^2 - 4)/(z - 3) / (z+2)/(z^2+z -12)(z + 2)(z – 2)/(z – 3) / (z + 2)/(z +4)(z – 3)
When dividing two fractions, you have to reciprocate the denominator and do the multiplication:
(z + 2)(z – 2)/(z – 3) / (z +4)(z – 3)/(z + 2)
The expressions (z + 2) and (z – 3) will be cancelled. So the expression would become: (z – 2)(z + 4) = z^2 + 2z - 8
Final Answer:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
Explanation:
To find the quotient in simplest form when dividing two rational expressions, you need to multiply the first expression by the reciprocal of the second. The given expressions are:
Expression 1: [tex]\(\frac{z^2 - 4}{z - 3}\)[/tex]
Expression 2: [tex]\(\frac{z + 2}{z^2 + z - 12}\)[/tex]
Firstly, let's take the reciprocal of Expression 2, which is:
Reciprocal of Expression 2: [tex]\(\frac{z^2 + z - 12}{z + 2}\)[/tex]
Now, to find the quotient, multiply Expression 1 by the reciprocal of Expression 2:
Quotient: [tex]\(\frac{z^2 - 4}{z - 3} \cdot \frac{z^2 + z - 12}{z + 2}\)[/tex]
Before multiplying, it's helpful to factor where possible to simplify. Let's factor both the numerator and the denominator where applicable:
For the expression [tex]\(z^2 - 4\)[/tex] (the difference of squares), it factors into:
[tex]\(z^2 - 4 = (z - 2)(z + 2)\)[/tex]
For the quadratic expression [tex]\(z^2 + z - 12\)[/tex], we look for two numbers that multiply to -12 and add to +1. These numbers are +4 and -3.
So this expression factors into:
[tex]\(z^2 + z - 12 = (z - 3)(z + 4)\)[/tex]
Now substitute in these factorizations:
[tex]\(\frac{(z - 2)(z + 2)}{z - 3} \cdot \frac{(z - 3)(z + 4)}{z + 2}\)[/tex]
Next, we cancel out the common terms in the numerator and the denominator:
The z + 2 term in the numerator of the first fraction cancels with the z + 2 term in the denominator of the second fraction.
Similarly, the z - 3 term in the denominator of the first fraction cancels with the z - 3 term in the numerator of the second fraction.
What remains is:
Quotient: (z - 2)(z + 4)
Finally, you can expand this to get the simplest form of the quotient:
[tex]\(z^2 + 4z - 2z - 8\)[/tex]
Combine like terms:
[tex]\(z^2 + 2z - 8\)[/tex]
So the simplest form of the quotient is:
[tex]\(\frac{z^2 + 2z - 8}{1}\)[/tex]
or simply:
[tex]\(z^2 + 2z - 8\)[/tex]
Now let's consider the restrictions on the variable z. Before we canceled terms, the original expression had denominators of z - 3 and [tex]\(z^2 + z - 12\)[/tex]. Division by zero is undefined, which means we have restrictions where these denominators equal zero:
For z - 3 = 0, the restriction is [tex]\(z \neq 3\)[/tex].
For [tex]\(z^2 + z - 12 = 0\)[/tex], we had already factored this into (z - 3)(z + 4). From the factored form, we can find the restrictions by setting each factor equal to zero:
z - 3 = 0 gives z = 3 (which we already noted) and z + 4 = 0 gives z = -4.
Therefore, the restrictions on the variable z are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
To summarize:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
The polygons below are similar. Find the value of y.
12
16
Guess: 16
Answers
Answer:
4.5
Step-by-step explanation:
In similar polygons, the ratios of corresponding sides is equal.
The only two corresponding sides we have measurements for are BC, with a measure of 8, and FG, with a measure of 6. This makes their ratio 8/6.
The other half of the proportion will be comparing AB, with a measure of 6, to EF, with a measure of y:
8/6= 6/y
Cross multiply:
8(y) = 6(6)
8y = 36
Divide both sides by 8:
8y/8 = 36/8
y = 4.5
The value of y will be 4.5.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The polygons are similar.
Now,
Since, The polygons are similar.
Hence, The proportional of corresponding sides are equal.
So, We can formulate;
⇒ 6 / y = 8 / 6
⇒ 6×6 / 8 = y
⇒ y = 36 / 8
⇒ y = 4.5
Thus, The value of y will be 4.5.
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PLEASE HELP!
Fine Line Trucks rents an 18-ft truck for $42 per day plus 35¢ per mile. Judy needs a truck for one day to deliver a shipment of plants. However, she only has a budget of $70.
a) Set up an equation that models this information.
b) How many miles can Judy drive to stay within her budget?
Answers
She wants the truck for one day, which will cost $45. We don't know how far the truck is traveling so that is the variable. She cannot spend more than $70, since that is her budget.
b.) Solve for x using the above equation:
0.35x + 42 ≤ 70
0.35x ≤ 28
x ≤ 80
Judy can drive 80 miles
One of the sides of a parallelogram has the length of 5 in. can the lengths of the diagonals be: c 6 in and 7 in?
Answers
In a parallelogram, only the opposite sides of the parallelogram are congruent. All the sides don't have to be congruent. Therefore we can have different measurement for the diagonals.
In a square, all of the diagonals would have to be the same.
The dimensions of 5 inches for a side and diagonals of 6 inches and 7 inches for a parallelogram violate the Pythagorean theorem and therefore are not possible for any right-angled triangle, suggesting an error if considered for a parallelogram.
Explanation:The question is whether parallelogram sides can correspond to the dimensions given, with one side being 5 inches and the possible diagonals being 6 inches and 7 inches respectively. By applying the Pythagorean theorem, we can deduce that a parallelogram with such dimensions may not be possible due to the constraints of the theorem.
Given the Pythagorean theorem, expressed as a² + b² = c², the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. If we consider the diagonals and the side as parts of a right triangle, then 6² + 5² does not equal 7² (36 + 25 = 61, which is not equal to 49).
Therefore, it is not possible for a parallelogram to have side lengths and diagonal lengths as described in the question because the mathematically described conditions violate the rules of the Pythagorean theorem.
Stephanie is 20 years old and has a base annual premium of $930 and a rating factor of $1.30. What is her total premium?
A) $1,209
B) $100.75
C) $604.50
D) $1,032.65
Answers
Hope I help
Answer:
Her total premium would be $1,209.00
Other answer is incorrect.
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.
Answers
p - pounds of peanuts
c - pounds of cashews
therefore the total pounds should be equal to 10 pounds
p + c = 10 -----> 1)
the cost for ;
peanuts - 4.00 per pound * p pounds = 4p
cashews - 6.50 per pound * c pounds = 6.5c
the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5
4p+6.5c = 47.5 ---> 2)
to solve for p and c lets use simultaneous equations
p + c = 10 -----> 1)
4p+6.5c = 47.5 ---> 2)
multiply 1st equation by 4
4p + 4c = 40 ---> 3)
subtract 3rd equation from the 2nd
2.5c = 7.5
c = 3
substituting c= 3 in 1st equation
p+c = 10
p+3 = 10
p = 7
therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture
Picture included!
Can someone help me with these 2 questions please?
Answers
Solve for x
2/(7x) = 6/5
5/21
-21/5
21/5
I don't know
- 5/21
Answers
________________________________________
Given:
2/ (7x) = 6/5;
→ (6/5) * (7x) = 2 ;
42x / 5 = 2 ;
42x = 2*5 ;
42x = 10 ;
42x /42 = 10/42 ;
x = 10/42 = (10÷2) / (42÷2) = 5/21 ;
x = [tex] \frac{5}{21} [/tex] ;
→ which is: Answer choice: [A]: " [tex] \frac{5}{21} [/tex] " .
__________________________________________________
Which polynomial is in standard form
Answers
What is the specific name for a regular quadrilateral?
Answers
The specific name for a regular quadrilateral is a polygon
~cutie
Zero is a solution of (-1 < x < 1).
A. True
B. False
Answers
In order to convert from radians to degrees multiply the radians by...
Answers
What is the measure of angle A?
Answers
180 - 43 = 137
So angle A is 137 degrees
Tickets for a concert sold for $8 for floor seats and $6 for balcony seats. For one performance, 400 tickets were sold, bringing in $2,888. How many of each ticket were sold?
Answers
What is 65% written as a fraction in its simplest form?
Answers
(divide by 5 on both sides)
Hope this helped!
In the year 1997 d takahashi and y kanada calculated pi to 51,539,600,000 decimal places. what type of computer did they use? where did they do the calculations
Answers
They used a computer called the HITACHI SR2201 which has 1024 processors. As an example most desktops in use now (by individuals such as you and I -- not by computer scientists doing research) have 1-2 processors with 2 cores each.
You are knitting a blanket. You want the area of the planet to be 24ft^2. You want the length of the blanket to be 2ft longer than it's worth. What should the dimensions of the blanket be?
Answers
length being longer than the width means that blanket is a rectangle
width of the blanket = x
length of blanket = x +2
area = length * width
area = x * (x+2)
= x² + 2x
since area = 24
x² + 2x = 24
x² + 2x - 24 = 0
we have a quadratic equation and we need to now solve for x
x² + 6x - 4x - 24 = 0
x (x + 6) - 4(x + 6) = 0
(x-4) (x+6) = 0
x-4 = 0 or x + 6 = 0
x = 4 or x = -6
x could be either 4 or -6. since dimensions cannot have negative values,
x ≠ -6
therefore x = 4
width = 4 ft
length = 6 ft
4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
(1 point)
The statement is not reversible.
Yes; if two lines intersect at right angles, then they are perpendicular.
Yes; if two lines are perpendicular, then they intersect at right angles.
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
(1 point)
The statement is not reversible.
Yes; if two lines intersect at right angles, then they are perpendicular.
Yes; if two lines are perpendicular, then they intersect at right angles.
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
@Mathematics
Answers
Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
A. The statement is not reversible.
B. Yes; if two lines intersect at right angles, then they are perpendicular.
C. Yes; if two lines are perpendicular, then they intersect at right angles.
D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.
Your Answer would be (D)
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
REF: 2-3 Biconditionals and Definitions
Answer:
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
Step-by-step explanation:
In a biconditional statement, both parts have to be true. In this case, if the two lines intersect at a right angle then they are perpendicular, and if they are perpendicular then they intersect at a right angle
The management of the unico department store has decided to enclose an 833 ft2 area outside the building for displaying potted plants and flowers. one side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. if the pine board fencing costs $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)
Answers
To maximize area and minimize perimeter, you want a figure that is as close to equilateral as you can get. Therefore we take the square root of our area:
√833 = 28.9.
Dividing 833/28.9 we get 28.8.
We want to use the shorter side, 28.8, for the pine boards, as they cost more. 28.8*2*6 = 345.60.
The cost of the steel side is given by 28.9*2 = 57.80.
Together it costs 345.60+57.80 = 403.40.
What is the solution to the system of equations?
{x + 3y + 2z = 8
{3x + y + 3z = -10
{-2x -2y - z = 10
A: (-10, -2, 6)
B: (10, 2, 6)
C: (-10, 2, 6)
D: (-10, 2, -6)
Answers
Convert the angle \theta=\dfrac{23\pi}{20}θ= 20 23π theta, equals, start fraction, 23, pi, divided by, 20, end fraction radians to degrees
Answers
For this case we have the following angle in radians:
[tex] theta = \frac{23\pi}{20} [/tex]
The first thing you should know to answer the question is the following conversion:
π radians = 180 degrees
Applying the conversion to the given angle we have:
[tex] theta = \frac{23\pi}{20}*\frac{180}{\pi} [/tex]
Rewriting we have:
[tex] theta = 207 [/tex]
Answer:
the angle measured in degrees, it is given by:
[tex] theta = 207 [/tex]
what is the slope of the line that contains the points (-1,2) and (3,3)?
A. -1/4
B. 1/4
C. 4
D. -4
Answers
the slope of the line is letter B) 1/4....
The slope of the line that contains the points (-1,2) and (3,3) is calculated using a specific formula. After performing the calculation, the result is 1/4.
Explanation:The slope of a line is calculated using a specific formula based on line's points: (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of two distinct points on the line. In this case, the points given are (-1,2) and (3,3).
Let's substitute into the formula:
(3 - 2) / (3 - (-1)) = 1 / 4.
Therefore, the slope of the line that contains the points (-1,2) and (3,3) is 1/4, which corresponds to answer choice B.
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what is the image of g for a 240° counterclockwise rotation about the center of the regular hexagon
A. A
B. N
C. H
D. X
Answers
This would move G to the point H
C. H
State the property that justifies the statement:
If 3x = 6, then x = 2
a. Subtraction Property of Equality
b. Addition Property of Equality
c. Division Property of Equality
d. Multiplication Property of Equality
Given that AD and BC are parallel, find the value of x.
a. 15
b. 5
c. 12.5
d. 17.5
Answers
If tan theta= 15/8, then:
A. sec theta = 17/8
B. cos theta = 15/17
C. cot theta = 8/15
D. csc theta = 17/15
There's potentially more than one answer.,
Answers
The only thing we have to do here is remember our trigonometric functions!
sin=y/r
cos=x/r
tan=y/x
sec=r/x
csc=r/y
cot=x/y
Knowing that tanᎾ=15/8, we know that y=15 and x=8
Now we need to look at the answer choices and see if they are correct.
A. secᎾ=17/8
Since secᎾ=r/x and r=17 and x=8, this is correct.
B. cosᎾ=15/17
Since cosᎾ=x/r and x=8 and r=17, this is wrong.
C. cotᎾ=8/15
Since cotᎾ=x/y and x=8 and y=15, this is also correct!
D. cscᎾ=17/15
Since cscᎾ=r/y and r=17 and y=15, this is right too.
I really hope this helps!
Best wishes :)
Answer:
secᎾ=17/8
cotᎾ=8/15
cscᎾ=17/15
Step-by-step explanation:
what is the value of x will mark brain list 20 extra points
Answers
2x + 5 = 4x - 1
5 = 2x - 1
6 = 2x
3 = x
Do you get it?
Rewrite the slope intercept equation of the line y=1/3x-2 in standard form
Answers
3y = x - 6
x - 3y = 6 ...this is standard form
The standard form of the given equation is x - 3y = 6.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, y = 1/3 x - 2
The given equation is in slope intercept form, i.e. y = mx+ c, where m is slope and c is constant,
Here, slope (m) = 1/3 and constant (c) = -2
Converting the equation in standard form,
y = 1/3 x - 2
3y = x - 6
x - 3y = 6
Hence, the standard form of the equation is x - 3y = 6
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PLEASE HELP ASAP!!! WILL GIVE BRAINLIEST FOR BEST/RIGHT ANSWER!!!!!!!!
Answers
How can categorical data for two categories be summarized?
Answers
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Hope this answer has helped you...