Answers
Explanation:
The first determinant is that of the matrix of coefficients:
[tex]|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19[/tex]
The second determinant is the same as the above but with the constants substituted for the x-coefficients.
[tex]|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76[/tex]
The third determinant is the same as the first but with the constants substituted for the y-coefficients.
[tex]|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57[/tex]
_____
The solution to the system of equations is then ...
[tex]x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3[/tex]
Related Questions
Read the statement.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Check all that apply.
p → q represents the original conditional statement.
~p → ~q represents the inverse of the original conditional statement.
q → p represents the original conditional statement.
~q → ~p represents the converse of the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
Answers
Answer:
True, True , False , False , False
Step-by-step explanation:
Let us see the correction for the rest of the three False Statements
3) p→q represent the original conditional statement.
4) ~q → ~p represents the contrapositive of the original conditional statement
5) contrapositive of the original conditional statement will be ~q → ~p
There is one more implication called Converse of the original conditional statement . It is represented as q→p
Simply 6^-1(4^-2) plz help
Answers
Answer:
1/96
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
Then ...
[tex]6^{-1}\cdot 4^{-2}=\dfrac{1}{6}\cdot\dfrac{1}{4^{2}}=\dfrac{1}{6\cdot 16}=\dfrac{1}{96}[/tex]
Shavon has $23 to spend on school supplies. She buys a set of colored pencils for $5 and wants to spend the rest on notebooks. Each notebook costs $3.25. Circle symbols to create an inequity that models the the number of notebooks, n. Shavon can buy
Answers
Answer:
23-5≥3.25n
18≥3.25n
nancy made a table runner that has an area of 80 square inches. the length and width are whole numbers. the length is 5 times greater than the width. what are the dimensions
Answers
Answer : The dimensions of table runner will be, 20 inch length and 4 inch width.
Step-by-step explanation :
Let the width of table runner be, x
and, the length of table runner will be, 5x
Given:
Area of table runner = [tex]80inch^2[/tex]
As we know that:
Area of rectangle = Length × Width
[tex]80inch^2=(5x)\times (x)[/tex]
[tex]80inch^2=5x^2[/tex]
[tex]x=4inch[/tex]
The width of table runner = x = 4 inch
The length of table runner = 5x = 5(4) inch = 20 inch
Therefore, the dimensions of table runner will be, 20 inch length and 4 inch width.
Can someone please help me on this problem? I don’t know how to do it!!!
Answers
Answer:
(x^(11/4))(y^(5/9))
Step-by-step explanation:
The applicable rules of exponents are ...
(x^a)(x^b) = x^(a+b)
(x^a)/(x^b) = x^(a-b) . . . . . no surprise, since 1/x^b = x^-b
_____
Your expression simplifies to ...
x^((5/4) -(-5/4) -(-1/4)) · y^((1/18) -(-1/2))
= x^(5/4 +5/4 +1/4) · y^(1/18 +1/2)
= x^(11/4) · y^(1/18 +9/18)
= x^(11/4) · y^(5/9)
Genise is making cookies. She needs 1 1/2 cups of flour for one batch, but she wants to make 2 1/2 batches. Write an equation that can be used to find how many cups of flour genise will need.
Answers
To calculate how many cups of flour Genise will need for 2 1/2 batches, multiply the amount of flour for one batch (1 1/2 cups) by the number of batches (2 1/2). This results in 3 3/4 cups of flour needed.
To find how many cups of flour Genise will need, we start by writing an equation that reflects the amount of flour needed for one batch times the number of batches she plans to make. Since she needs 1 1/2 cups of flour for one batch and she wants to make 2 1/2 batches, we set up the multiplication:
flour_needed = (cups of flour per batch) * (number of batches)
So the equation will be:
flour_needed = 1 1/2 * 2 1/2
Converting mixed numbers to improper fractions for easier multiplication, we have:
flour_needed = 3/2 * 5/2 = 15/4 cups
Then, we convert the improper fraction back to a mixed number, which is:
flour_needed = 3 3/4 cups of flour
Maria is 7 years older than her brother Robert and in 2 years her age will be four times what Robert’s age was three years ago. Find their present ages.
Answers
Answer:
Robert is 7 years old and Maria is 14 years old.
Step-by-step explanation:
You can use 2 variables: m and r and write 2 equations:
m = r +7
m + 2 = 4( r -3)
So 3 * r = 21 or r= 7
Maria and Robert are currently with present ages as 14 and 7 years old, respectively.
What do you mean by an equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It demonstrates that the expressions on the left and right sides are connected in the same way.
An equation has components like as coefficients, variables, operators, constants, terms, expressions, and the equal to sign. The "=" sign and terms on both sides are required when generating an equation.
The information is ,
Let's say the equation looks like this: A
Right now, A is valued at
Let Maria's age be x.
Let Robert's age be y.
Maria now has a 7-year age gap with Robert.
Hence, the equation x = 7 plus y (1)
Also, in two years she will be four times Robert's age from the previous three years.
The equation is (x + 2) = 4 (y - 3). (2)
We obtain (7 + y + 2) = 4y - 12 y + 9 = 4y - 12 after simplifying.
We obtain 3y = 21 by subtracting y and adding 12 on both sides.
We obtain y = 7 years old by dividing both sides by 3.
Robert is therefore 7 years old.
And , x = 14 years old
And , the age of Maria is 14 years old
As a result, Maria and Robert are currently 14 and 7 years old, respectively.
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Ben is 12 years older than Ishaan. Ben and ishaan first met two years ago. Three years ago, Ben was 4 times as old as Ishaan.
Answers
Answer:
ok what is tthe question
Step-by-step explanation:
HELP!!! I NEED AN ANSWER SOON!!!!! FIRST TO ANSWER WILL GET BRAINLIEST!!!!!!!!!!! THANKS IN ADVANCE!!!!!!!!!
Answers
Answer:
a= 84.83
Step-by-step explanation:
so remember this: my teacher taught me this amazing strategy to remember the formulas
C=πd : cherry pie delicious
a=πr² : apple pie are too
and to find the area of the saded area, we need to find the area of the big circle and subtract that by the smaller circle area.
so, area of the big circle:
fill in the variables for a=πr²
you get: a=π6²
follow the pemdas, the order of operations. now on the state test don't write pemdas as your answer because people are stupid and they dont take that answer
you do the exponent first then multiply by pie.
you get: 6²=36
36xπ=113.09733552923255658465516179806
round that answer to the nearest tenths and get: 113.1
now time to find the area of the smaller circle!!!
fill in a=πr² and get: a=π3²
its not 6 this time because that was the radius for the bigger circle. the smaller circles radius is half the size as the bigger circle so divide that by two and get 3.
now solve:
a=π3²
a=π9
a=28.274333882308139146163790449516
round and get: 28.27
now subtract the the bigger circles area and the smaller circles area:
113.1 is the bigger circles area
28.27 is the smaller circles area.
113.1 - 28.27 = 84.83
a=84.83
plz give me brainliesttt
Decide if the answer to 5/7×6 is less than, greater than or equal to 6
less than
equal to
greater than
Answers
Answer:
less than
Step-by-step explanation:
The multiplying fraction (5/7) is less than 1 so its product with 6 will be less than 6.
___
5/7·6 = 30/7 = 4 2/7 < 6
The expression 5/7×6 results in a value that is less than 6. This is because the value of 5/7 is less than 1, and multiplying it by 6 gives a result that is consequently less than 6.
Explanation:To determine whether 5/7×6 is less than, greater than, or equal to 6, we perform the multiplication. Multiplying 5/7 by 6 can be viewed as 5 multiplied by 6, which equals 30, and then that result divided by 7. So the calculation is 30÷7, which equals approximately 4.29. Since 4.29 is less than 6, we can conclude that 5/7×6 is less than 6.
When solving mathematical problems involving multiplication and fractions, it's important to eliminate terms wherever possible to simplify the algebra and to check the answer to see if it is reasonable. Comparing the original fraction to 1 before the multiplication can help us understand whether the result will be greater or less than the number we're multiplying. In this case, since 5/7 is less than 1, multiplying it by 6 will give a result that is less than the original number, which is 6.
Find all pairs of natural numbers which can be the solution to the equation: x+y=11
Answers
Answer:
How many solution does ++=11
x
+
y
+
z
=
11
have where ,,
x
,
y
,
z
are non-negative integers. In light of the restrictions, its clear that ,,∈{0,1,2,..11}
x
,
y
,
z
∈
{
0
,
1
,
2
,
.
.11
}
. So, at face value I would assign a value for
x
and determine the different combinations that
y
and
z
can hold. For example,
For =0
x
=
0
, we have +=11
y
+
z
=
11
. With writing them out I found that there are 12
12
different assigned combinations for
y
and
z
that satisfy the equation. For =1
x
=
1
, I got 11
11
. Consequently, the pattern becomes clear whereby each one takes a value less by one. Hence, the number of solutions is 1+2+3+4+5+6+7..+12=78
1
+
2
+
3
+
4
+
5
+
6
+
7..
+
12
=
78
. I was wondering if there is an easier method perhaps with combinations equation (,)
C
(
a
,
b
)
..?
Step-by-step explanation:
(x,y)
1,10
2,9
3,8
4,7
5,6
6,5
7,4
8,3
9,2
10,1
Find the equation of the perpendicular bisector of the given segment by following these steps. 1. Determine the slope of the given segment.
Answers
Answer:
The equation of the perpendicular bisector is 2x + 3y - 3 = 0
Step-by-step explanation:
* How to find the equation of a line from two points (x1 , y1)
and (x2 , y2) lie on it
- Find the slope of the line using the rule
The slope (m) = (y2 - y1)/(x2 - x1)
- Use the rule of the equation y - y1 = m (x - x1), where m is
the slope of the line and (x1 , y1) is a point on the line
* Remember if two line are perpendicular, then the product of
their slopes = -1, that means one of them is an additive inverse
and multiplicative inverse to the other
# Ex: if the slope of a line is a/b, then the slope of the
perpendicular to it is -b/a
* Now lets read the problem, we need the equation of the
perpendicular bisector to the line that passes through the
points (2 , 4) and (-2 , -2)
- Find the slope of the line in the graph by using the given points
# m = (-2 - 4)/(-2 - 2) = -6/-4 = 3/2
∴ The slope of the perpendicular line = -2/3 ⇒ multiplicative
inverse and additive inverse of it
* Bisector means intersect it in the mid-point of the given line
- The rule of the mid-point is [(x1 + x2)/2 , (y1 + y2)/2]
∴ The mid-point of the line is [(2 + -2)/2 , (4 + -2)/2] = (0 , 1)
* Now we have the slope and a point on the line, to find the
equation of the perpendicular bisector its slope is -2/3 and
a point (0 , 1)
∴ The equation: y - 1 = -2/3 (x - 0)
The equation : y - 1 = -2/3 x ⇒ Multiply both sides by 3
The equation : 3y - 3 = -2x ⇒ collect x , y in the same side
The equation : 2x + 3y - 3 = 0
* The equation of the perpendicular bisector is 2x + 3y - 3 = 0
Answer:3/2
Step-by-step explanation:
whats the difference between range and interquartile range?
Answers
Answer:
Step-by-step explanation:
The range is the difference between the highest and the lowest values in a set of data. The interquartile range, the IQR, is what's "inside" the box in a box plot, which consists of the difference between the central measures, which are the first and the third quartiles.
Range is the difference between the maximum and minimum values in a dataset, while the Interquartile Range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3), representing the spread of the middle 50% of the data.
Range is the simplest measure of variability in a dataset.It is calculated by subtracting the minimum value from the maximum value.
For example, if the highest score in a test is 95 and the lowest score is 55,
the range is 95 - 55 = 40.
Interquartile Range (IQR) is a more sophisticated measure of variability that focuses on the middle 50% of the data.To find the IQR, we first need to determine the first quartile (Q1) and the third quartile (Q3).
Q1 is the median of the lower half of the data, while Q3 is the median of the upper half.
The IQR is then calculated by subtracting Q1 from Q3.
For example, in a dataset:
If Q1 = 70 and Q3 = 90, then
IQR = 90 - 70 = 20.
The IQR is useful in identifying potential outliers and understanding the spread of the central data.
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c?
Answers
Answer:
10$ an hour
Step-by-step explanation:
1/2c=6-1
c=2(6-1)
c=10
Answer:
Carey's hourly rate to babysit is $10.
Step-by-step explanation:
Given is -
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate.
Let Carey's hourly rate to babysit be represented by 'c'
So, Anderson's hourly rate will be = [tex]\frac{c}{2}+1[/tex]
Also given that Anderson earns $6 per hour.
So, equaling both, we get;
[tex]6=\frac{c}{2}+1[/tex]
[tex]6=\frac{c+2}{2}[/tex]
[tex]c+2=12[/tex]
[tex]c=10[/tex]
Hence, Carey's hourly rate to babysit is $10.
2. Quan plans to spend less than $80 for buying groceries. He plans to spend $68.25 on food and spend the rest on juice. Each juice carton costs $3. He is curious how many juice cartons he can purchase before he runs out of money.
(a) Use x to represent the number of juice cartons Quan can purchase and write an inequality that can be used to solve for x.
(b) Solve the inequality. Use the solution to determine the number of juice cartons Quan can purchase.
Check your answers if needed
Answers
He should have 27.5 left I'm 100% sure
given that a^b=x, evaluate the following: a^2b
Answers
Answer:
[tex]a^{2b}=x^{2}[/tex]
Step-by-step explanation:
we know that
[tex]a^{b}=x[/tex] ----> equation A
Find the value of [tex]a^{2b}[/tex]
Remember that
[tex]a^{2b}=(a^{b})^{2}[/tex]
[tex](a^{b})^{2}[/tex] ----> equation B
substitute equation A in the equation B
[tex](a^{b})^{2}=x^{2}[/tex]
therefore
[tex]a^{2b}=x^{2}[/tex]
Please help someone..
Answers
Answer: [tex]\bold{\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\dfrac{DF}{AK}=\dfrac{4}{20}=\large\boxed{\dfrac{1}{5}}[/tex]
Can someone help with 2.6
Answers
Answer:
B
Step-by-step explanation:
Theta is found using the sin-1 function. Start off with the sin of theta.
sin(theta) = opposite over hypotenuse.
sin(theta) = 3/8 = 0.375
Theta = Sin-1 (0.375)
Theta = 22.02 degrees.
Answer: B
Given: circle k(O), DC ∥ AB , AC ∩ DB =0, m AD =124°Find: m∠C, m∠AOB.
Answers
Answer:
Part 1) The measure of angle C is [tex]62\°[/tex]
Part 2) The measure of angle AOB is [tex]56\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<C=\frac{1}{2}(arc\ AD)[/tex]
we have
[tex]arc\ AD=124\°[/tex]
substitute
[tex]m<C=\frac{1}{2}(124\°)=62\°[/tex]
step 2
Find the measure of angle AOB
we know that
In the isosceles triangle ODC
∠D=∠C=62°
Remember that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
∠D+∠C+∠DOC=180°
substitute the values
62°+62°+∠DOC=180°
∠DOC=180°-124°=56°
we have that
∠AOB=∠DOC -----> by vertical angles
so
∠AOB=56°
Solve the triangle given two side lengths and one angle measure.
Answers
Answer:
B ≈ 64.9°C ≈ 45.1°c ≈ 82.2Step-by-step explanation:
The Law of Sines is helpful when you know one side and its opposite angle.
a/sin(A) = b/sin(B) = c/sin(C)
Rearranging gives you ...
B = arcsin(b/a·sin(A)) = arcsin(105/109·sin(70°)) ≈ 64.85138°
C = 180° -B -A = 45.14862°
c = a·sin(C)/sin(A) ≈ 82.23360
_____
Comment on the solution method
You can use the Law of Cosines if you like. The formulation would be ...
a² = b² + c² -2bc·cos(A) . . . . where a, b, and A are known
This gives a quadratic in c, the positive solution being the answer you're looking for. Then, either the law of sines or the law of cosines can be used to find one of the other two angles.
c = 105·cos[70°] + √[856 + 11025·cos[70°]²]
c ≈ 82.2336
How do i solve this?
Answers
Answer:
see below
Step-by-step explanation:
If the left-side tiles are numbered 1–7 from top to bottom, their order on the right is ...
7 — denominators factored
6 — common factors canceled
5 — make the left side have the same denominator as the right
3 — express the sum over the common denominator
2 — collect numerator terms
40 points... Please help.
I am doing a project for geometry and need the ratio for both figures. The figure is a bird house and I am doubling the size. What would the ratio be?
Answers
Answer:
The ratio would be 1:2 my guy,if you're trying to triple the size, 1:3 if your trying to quadruple the size, it'd be 1:4, etc, etc
A machine can make 5 miles of ribbon in an hour. Graph the length of the ribbon the machine will make in eight hours. Another machine can make 8 miles of ribbon in an hour. Graph the length of the ribbon the machine will make in 8 hours. What is the difference in length for a 8 hour period between the two machines? Write an Equation in slope intercept for each machine.
Answers
The equations for the two machines are y = 5x and y = 8x, which represent their respective production rates. Over an 8 hour period, the first machine produces 40 miles of ribbon and the second produces 64 miles, resulting in a difference of 24 miles.
Explanation:The two machines described in the question produce ribbon at different rates, which can be represented with two linear equations in slope-intercept form (y = mx + b) where m is the rate of production (slope) and b is the initial amount of ribbon (y-intercept, in this case 0 as the machine starts with no ribbon).
The first machine can produce 5 miles of ribbon in an hour, so its rate is 5 miles/hour. This gives the equation y = 5x.
The second machine can produce 8 miles of ribbon in an hour, leading to the equation y = 8x.
In an 8 hour period, the first machine will produce y = 5*8 = 40 miles of ribbon, while the second machine will produce y = 8*8 = 64 miles of ribbon. The difference is 64 - 40 = 24 miles.
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The first machine will make 40 miles of ribbon in 8 hours, and the second machine will make 64 miles of ribbon. The difference in length for an 8-hour period between the two machines is 24 miles.
Explanation:To graph the length of ribbon each machine will make in 8 hours, we can start by determining the length each machine can make in one hour.
The first machine can make 5 miles of ribbon in an hour, so in 8 hours, it will make 8 times 5 = 40 miles of ribbon.
The second machine can make 8 miles of ribbon in an hour, so in 8 hours, it will make 8 times 8 = 64 miles of ribbon.
The slope-intercept form of an equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept. For the first machine, the equation would be y = 5x + 0, and for the second machine, the equation would be y = 8x + 0.
The difference in length between the two machines for an 8-hour period is 64 - 40 = 24 miles.
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x-y-4z=-9
4x-3y-2z=-9
-x-3y-6z=-7
solve
Answers
Answer:
(x, y, z) = (-2, -1, 2)
Step-by-step explanation:
Your graphing calculator can usually solve systems of linear equations easily.
What series of transformations from △ABC to △DEF shows that △ABC ≌ △DEF?
a). a reflection across the y-axis followed by a translation of 1 unit right and 2 units up
b). a clockwise rotation of 90º about the origin followed by a translation of 4 units right and 4 units up
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
d). a reflection across the line y=x followed by a positive rotation of 270º about the center
Answers
Answer:
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
Step-by-step explanation:
You want to know the transformations that map ΔABC onto ΔDEF.
TransformationsThe answer choices would ask us to consider some combination of the following transformations:
reflection across the y-axis: (x, y) ⇒ (-x, y)reflection across the x-axis: (x, y) ⇒ (x, -y)reflection across the line y=x: (x, y) ⇒ (y, x)clockwise rotation 90°: (x, y) ⇒ (y, -x)positive rotation 270°: (x, y) ⇒ (y, -x) . . . same as 90° CWtranslation by (h, k): (x, y) ⇒ (x+h, y+k) . . . h units right, k units upApplicationWe can apply these relations to the answer choices to see if they provide the desired mapping ...
A(-4, 1) ⇒ D(-3, -2)B(-6, 5) ⇒ E(-5, -6)C(-1, 2) ⇒ F(0, -3)a) Reflection across the y-axis, translation (1, 2)
A(-4, 1) ⇒ A'(4, 1) . . . reflection
A'(4, 1) ⇒ D(4+1, 1+2) = D(5, 3) . . . . not the correct point
b) Rotation CW 90°, translation (4, 4)
A(-4, 1) ⇒ A'(1, 4) . . . rotation 90° CW
A'(1, 4) ⇒ D(1+4, 4+4) = D(5, 8) . . . . not the correct point
c) Reflection across the x-axis, translation (1, -1)
A(-4, 1) ⇒ A'(-4, -1) . . . reflection
A'(-4, -1) ⇒ D(-4+1, -1+(-1)) = D(-3, -2) . . . . the correct location of D
d) Reflection across y=x, rotation CCW 270°
A(-4, 1) ⇒ A'(1, -4) . . . reflection
A'(1, -4) ⇒ D(-4, -1) . . . . not the correct point
The correct series of transformations is reflection across the x-axis followed by translation 1 right and 1 down.
a) One of the roots of the equation 10x^2−33x+c=0 is 5.3. Find the other root and the coefficient c.
b)The difference between the roots of the quadratic equation x^2−12x+q=0 is 2. Find q.
c)The difference between the roots of the quadratic equation x^2+x+c=0 is 6. Find c.
Answers
Answer:
a) The other root is -2
The coefficient c = -106
b) q = 35
c) c = -8.75
Step-by-step explanation:
* Lets study the general form of the quadratic equation
* ax² + bx + c = 0
- Their roots are x1 and and x2
- The sum of them = -b/a ⇒ x1 + x2 = -b/a
- The product of them = c/a ⇒ (x1)(x2) = c/a
a) * Assume that the roots of the equation 10x² - 33x + c = 0
are m and n
∵ m + n = -b/a
∵ a = 10 and b = -33
∴ m + n = -(-33)/10 = 3.3
∵ m = 5.3
∴ 5.3 + n = 3.3 ⇒ n = 3.3 - 5.5 = -2
∴ n = -2
* The other root is -2
∵ m × n = c/a
∵ m = 5.3 , n = -2 , a = 10
∴ (5.3)(-2) = c/10
∴ -10.6 = c/10 ⇒ Multiply both sides by 10
∴ c = -106
* The coefficient c = -106
b) * Assume that the roots of the equation x² - 12x + q = 0
are m and n
∵ The difference between the roots is 2
∴ m - n = 2 ⇒ (1)
∵ From the equation m + n = -b/a
∵ a = 1 , b = -12
∴ m + n = -(-12)/1 = 12
∴ m + n = 12 ⇒ (2)
* Lets solve the two equation
- Add the two equation to eliminate n
∴ 2m = 14 ⇒ divide both sides by 2
∴ m = 7
* Substitute the value of m in (1) or (2)
∴ 7 - n = 2 ⇒ 7 - 2 = n ⇒ 5 = n
∴ n = 5
∵ mn = c/a
∵ c = q , a = 1
∴ mn = q/1 = q
∴ q = 7 × 5 = 35
* q = 35
c) * Assume that the roots of the equation x² + x + c = 0
are m and n
∵ The difference between the roots is 6
∴ m - n = 6 ⇒ (1)
∵ From the equation m + n = -b/a
∵ a = 1 , b = 1
∴ m + n = -(1)/1 = -1
∴ m + n = -1 ⇒ (2)
* Lets solve the two equation
- Add the two equation to eliminate n
∴ 2m = 5 ⇒ divide both sides by 2
∴ m = 2.5
* Substitute the value of m in (1) or (2)
∴ 2.5 + n = -1 ⇒ n = -1 - 2.5 = -3.5
∴ n = -3.5
∵ mn = c/a
∵ c = c , a = 1
∴ mn = c/1 = c
∴ c = 2.5 × (-3.5) = -8.75
* c = -8.75
Find the range of y=4sin2x+3
Answers
Answer:
[-1, 7]
Step-by-step explanation:
If you mean ...
y = 4sin(2x) +3
then you can substitute the range of the sine function into the equation and evaluate it to find the range of y.
The range of sin( ) is [-1, 1], so the range of y is ...
4[-1, 1] +3 = [4(-1)+3, 4(1)+3] = [-1, 7]
_____
Comment on the problem statement
The range of y = 4sin²(x)+3 will be different, and the range of 4sin(2x+3) will be different yet. It is usually a good idea to use parentheses around function arguments.
Answer:
-1,7
Step-by-step explanation:
got it right on odessyware
What is another way to describe an equilateral triangle?
A) acute
B) obtuse
C) right
D) scalene
Answers
I think it a but I sorry if it wrong
Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.
Answers
Answer:
The two consecutive positive integers are 7 and 8
Step-by-step explanation:
Let
x ----> the first positive integer
x+1 ----> the second consecutive positive integer
we know that
[tex]x^{2} -17=4(x+1)[/tex]
Solve for x
[tex]x^{2} -17=4x+4\\ \\x^{2}-4x-21=0[/tex]
Solve the quadratic equation by graphing
The solution is x=7
see the attached figure
Find the value of x+1
x+1=7+1=8
therefore
The two consecutive positive integers are 7 and 8
To find two consecutive positive integers, we can set up an equation and solve for the values of x and x + 1.
Let's assume the first positive integer is x. Since we need to find two consecutive positive integers, the second positive integer would be x + 1. According to the given condition, the square of the first decreased by 17 should be equal to 4 times the second. This can be written as:
x^2 - 17 = 4(x + 1)
Now, we can solve this equation to find the values of x and x + 1.
x^2 - 17 = 4x + 4
x^2 - 4x - 21 = 0
By factoring or using the quadratic formula, we can find the solutions for x. Once we have the values of x, we can calculate x + 1 to find the two consecutive positive integers.
Learn more about Consecutive positive integers here:https://brainly.com/question/29767409
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I'd appreciate an answer to this.
Here are the 30 best lifetime baseball batting averages of all time, arranged in order from lowest to highest.
Answers
Answer:
C. 0.366
Step-by-step explanation:
In this stemplot, it is apparent that the number on the right is the least-significant digit (thousandths digit) of the batting average. The two most-significant digits are to the left of the vertical line.
Hence the value 0.36 | 6 represents an average that is 36 hundredths plus 6 thousandths: 0.366.