Answer:
5
Step-by-step explanation:
Find the number in the whole number place
5
and look one place to the right for the rounding digit on the right side of the decimal point
3
.Round up if this number is greater than or equal to
5
and round down if it is less than
5
.
Solve the system of equations.
5x−4y=−10
−4x+5y=8
Answer:
(- 2, 0 )
Step-by-step explanation:
5x - 4y = - 10 → (1)
- 4x + 5y = 8 → (2)
multiplying (1) by 4 and (2) by 5 and adding result will eliminate x
20x - 16y = - 40 → (3)
- 20x + 25y = 40 → (4)
add (3) and (4) term by term to eliminate x
9y = 0 , thus
y = 0
substitute y = 0 into either of the 2 equations and solve for x
substituting into (1)
5x - 4(0) = - 10
5x - 0 = - 10
5x = - 10 ( divide both sides by 5 )
x = - 2
solution is (- 2, 0 )
Choose the equation for the relationship shown in the graph.
A) y = x + 50
B) y = x – 50
C) y = 50 - x
D) x = 50 - y
Answer:
B) y = x - 50
Step-by-step explanation:
It is B because the graph's y-intercept lies on the point (0, -50), hence the equation, y = x - 50. In addition, you can verify that B is the correct answer because the slope of the graph is positive, and so the x-value also must be positive.
Find (qor)(x).
q(x) = 3x
r(x) = 6x + 5
Write your answer as a polynomial in simplest form.
Answer: 18x + 15
Step-by-step explanation:
(qor)(x)
q(r(x))
q(6x+5)
3(6x+5)
⇒18x + 15 This is your answer I believe
if we were solving for x then..
⇒x = [tex]-\frac{15}{18}[/tex]
if you were asked to convert the complex number, -6 + 8i, into polar form, what values of “r” and “0” would be in polar form?
Answer:
10∠126.87°
r = 10; θ = 126.87°
Step-by-step explanation:
The coordinate conversion from (x, y) or (x +yi) to (r; θ) can be done using the relations ...
r = √(x² +y²)
θ = arctan(y/x) . . . . paying attention to quadrant
__
For the given complex number, we have ...
r = √((-6)² +8²) = √(36 +64) = √100 = 10
θ = arctan(8/(-6)) = arctan(-4/3) . . . . in the 2nd quadrant
θ ≈ -53.13° +180° = 126.87°
The equivalence is ...
-6 +8i ⇔ 10∠126.87° . . . . . in the form r∠θ
_____
Additional comment
Many scientific and graphing calculators are equipped to work with complex numbers, including their conversion to or from polar form.
Find sin(b) in the triangle.
A.4/3
B.3/5
C.3/4
D.4/5
The value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.
What are the trigonometric ratios?Trigonometric ratios are the ratio of sides of a right angled triangle. There are 6 types of trigonometric ratios: sin, cos, tan, cosec, sec, and cot.
Sine trigonometric ratio is the ratio of perpendicular (side opposite to the angle) to the hypotenuse.
In the given figure, the side opposite to the angle [tex]\beta[/tex] is AC = 4 and the hypotenuse is AB = 5.
So, the sine ratio will be equal to,
[tex]\sin \beta=\dfrac{4}{5}[/tex]
Therefore, the value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.
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Which of the following graphs could be the graph of the function f(x)=0.003x^2(x^2-25)?
Answer:
See below
Step-by-step explanation:
You don't give any options, but here's the information you can get from just the equation itself:
Since your polynomial is a 4th-degree polynomial, I would expect to see 3 turning points at most. I would also expect to see zeroes at x=0, x=5, and x=-5Look for these characteristics and find the appropriate graph.
What transformations would result in the image shown?
Δ ABC is reflected over the x-axis and translated right 1 unit.
Δ ABC is reflected over the y-axis and translated up 1 unit.
Δ ABC is reflected over both axes.
Δ ABC is translated right 4 units and up 1 unit.
Dialtion, reduction or enlargment. Explain and show work. Homework is due today!!
Answer the questions and show work please!
Answer:
A)Reduction
B)0.5
Step-by-step explanation:
A)It gets smaller
B)A-D=12
A'-d'=6
6/12=0.5
how would I solve y=9(x+3)(x-1) I need to find the vertex and the X intercepts
Answer:
See below ~
Step-by-step explanation:
Finding the x-intercepts :
The x-intercept's y-value is always 00 = 9(x + 3)(x - 1)x + 3 = 0 ⇒ x = -3x - 1 = 0 ⇒ x = 1So, hence the x-intercepts are : (-3, 0) and (1, 0)Finding the vertex :
Expand the polynomial from factorized formy = 9(x + 3)(x - 1)y = 9(x² + 3x - x - 3)y = 9(x² + 2x - 3)y = 9x² + 18x - 27Vertex = (h, k)h = -b/2a = -18/2(9) = -1k = 9(-1 + 3)(-1 - 1)k = 9(2)(-2)k = 9(-4) = -36Vertex = (-1, -36)Answer:
x-intercepts: x = 1 and x = -3
vertex: (-1, -36)
Step-by-step explanation:
x-interceptsx-intercepts are when y = 0
⇒ 9(x + 3)(x - 1) = 0
Divide both sides by 9:
⇒ (x + 3)(x - 1) = 0
Therefore:
⇒ (x + 3) = 0 ⇒ x = -3
⇒ (x - 1) = 0 ⇒ x = 1
Therefore the x-intercepts are x = 1 and x = -3
VertexVertex form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex
Completing the square
[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]
Therefore:
[tex]y=9(x+3)(x-1)[/tex]
[tex]\implies y=9x^2+18x-27[/tex]
Completing the square to rewrite the equation in vertex form:
[tex]\begin{aligned}y & =9x^2+18x-27\\& =9\left(x^2+\dfrac{18}{9}x\right)-27\\\\& =a\left(x^2+\dfrac{18}{9}x+\left(\dfrac{18}{2(9)}\right)^2\right)-27-9\left(\dfrac{18}{2(9)}\right)^2\\\\& =9\left(x-\left(-\dfrac{18}{2(9)}\right)\right)^2-27-\dfrac{18^2}{4(9)}\\\\& =9(x+1)^2-36\end{aligned}[/tex]
Therefore, the vertex is (-1, -36)
please help !!!!!!!!!
Answer:
a) 1
b) 0
c) hundreths
d) .8
Step-by-step explanation:
The order, for this problem, is:
hundreds, tens, ones,
then after the decimal
tenths, hundredths, thousandths, ten thousandths, etc.
as for step d, imagine .08 as 8/100, and 8/10. Would you rather have 8 slices of pizza out of 100 slices, or 8 out of 10 slices of the whole?
I hope I helped!
Angles around a point
Grade 8
Answer:
x=45, y=45, z= 131
Step-by-step explanation:
x and y makes up a right angle (90). You can even;y split them in half, which is 45 degrees. Therefore, x= 45 and y also = 45.
Now that there are 2 right angles, that makes up 180. 180+49=229
A full rotation is 360, so you subtract that. 360-229=131
z=131.
Answer:
x = 41°y = 49°z = 131°Step-by-step explanation:
The relevant relations are ...
a straight angle measures 180°a right angle measures 90°vertical angles have the same measure__
The angle marked 49° and the one marked "y" are vertical angles, so have the same measure.
y = 49°
The angle marked "x" and the angle marked "y" together make up a right angle, so total 90°.
x + y = 90°
x + 49° = 90°
x = 41° . . . . . . . . . subtract 49°
The angle marked z and the one marked 49° together make up a straight angle, so total 180°. (They are a "linear pair.")
49° +z = 180°
z = 131° . . . . . . . subtract 49°
The measures of the marked angles are ...
x = 41°
y = 49°
z = 131°
This is hard pls help
The length of the SM parallelogram when the length of the rectangle is 15 cm and width is 8 cm is 8/5 units.
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
The length of the rectangle is 15 cm and width is 8 cm. Thus, the area of it is,
[tex]A=15\times8\\A=120\rm\; cm^2[/tex]
All three parts has equal area. Thus, the area of parallelogram NCMA is,
[tex]A_p=\dfrac{120}{3}\\A_p=40\rm\; cm^2[/tex]
MN is the height of the parallelogram. Thus,
[tex]A_p=h\times AS\\40=h\times15\\h=\dfrac{40}{15}\\h=\dfrac{8}{5}[/tex]
Thus, the length of the Sm parallelogram when the length of the rectangle is 15 cm and width is 8 cm is 8/5 units.
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True or False: A sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.
O True
O False
Question 1 True or False: A sector of a circle with a measure of 72 and radius of 12 cm has an arc length of about 15cm. True O False
Step-by-step explanation:
its false
The given statement about the sector of the circle is true.
What is a circle?A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the centre. A circle is also the set of all points that are equidistant from the centre.
Given that we need to check whether a sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm, or not,
Arc length = central angle / 360° × 2π × radius
= 72/ 360° × 2(3.14) × 12
= 0.2 × 6.28 × 12
= 15.072
≈ 15
Therefore, yes the sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.
Hence, the given statement about the sector of the circle is true.
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Need help asap, will give brainliest
A triangle has sides with lengths of 31 feet, 72 feet, and 78 feet. Is it a right triangle?
yes
no
=========================================================
Explanation:
We have a triangle with these side lengths
a = 31b = 72c = 78The order of 'a' and b doesn't matter, but we must have c as the largest value. Usually a,b,c are in ascending order.
Plug those values into the formula for the pythagorean theorem. If we get the same thing on both sides, then we have a right triangle.
[tex]a^2 + b^2 = c^2\\\\31^2 + 72^2 = 78^2\\\\961+5184 = 6084\\\\6145 = 6084\\\\[/tex]
We have a false statement at the end, which means the original equation is false for those a,b,c values.
Therefore, we do not have a right triangle.
Instead, this triangle is acute since the [tex]a^2+b^2[/tex] side is larger than the [tex]c^2[/tex] side
---------------
Rules to have in your notebook or on a reference sheet:
[tex]\text{If }a^2 + b^2 = c^2 \text{ then it is a right triangle}\\\\\text{If }a^2 + b^2 > c^2 \text{ then the triangle is acute}\\\\\text{If }a^2 + b^2 < c^2 \text{ then the triangle is obtuse}\\\\[/tex]
For more information, check out the converse of the pythagorean theorem.
write an inequality to represent the situation:the temperature stayed above -15
Answer:
temperature > -15
The base of a ladder is 2.8m placed away from a tree that is 4.5m tall. The end of the ladder touches the top of the tree. Calculate the length of the ladder.
Step-by-step explanation:
Hello all beautiful your day
Combine the like terms to create an equivalent expression. 8k−5k
Answer:
3k
Step-by-step explanation:
8k and 5k are "like terms" because they have the same variable to the same degree. So because the are like terms they can be subtracted. Similarly to how 8-5 is 3,
8k - 5k is 3k
I need help answering this question please!
Answer:
p(x) = x⁴ -7x³ +59x² -343x +490
Step-by-step explanation:
Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.
__
The given roots mean the polynomial can be written in factored form as ...
p(x) = (x -2)(x -5)(x -7i)(x -(-7i))
We can combine multiply these factors together to simplify the polynomial.
p(x) = (x² -7x +10)(x² +49)
p(x) = x⁴ -7x³ +59x² -343x +490
_____
Additional comment
Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.
a² -b² = (a -b)(a +b)
(x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)
Ailsa is twice as old as Barbara. Ailsa is 5 years younger the candy. the average age of candy ailsa and Barbara is 15. determine candys age
Answer:
Candy is 21 years old
Step-by-step explanation:
If Alisa is 16 years old, that would mean that Barbara would be 8, since she is half of Alisa's age.
If we add 5 to Alisa's age, we get 21. To find the average of their ages, we add them all up, and divide by how many people there are (3).
16+8+21=45
45÷3=15
Hope this helps!
Age of Ailsa is 20 years. Then Candy's age will be 15 years.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Ailsa is twice as old as Barbara. Ailsa is 5 years younger than Candy. The average age of Candy, Ailsa, and Barbara is 15.
Let 'x' be the age of Ailsa, 'y' be the age of Barbara, and 'z' be the age of Candy. Then the equations are given as,
x = 2y ...(1)
x - 5 = z ...(2)
(x + y + z) / 3 = 15 ...(3)
From equations (1), (2), and (3), then
x + x / 2 + x - 5 = 45
(5/2) x = 50
x = 20
Then the age Candy is calculated as,
z = 20 - 5
z = 15
Age of Ailsa is 20 years. Then Candy's age will be 15 years.
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what is the probability tho computer will select a point in the shaded region?
A prism has a volume of 125 cubic inches. The base measures 5 in x 5 in What is the height? a. 10 inches b. 25 inches c. 5 inches d. 125 inches
Answer:C
Step-by-step explanation:First multiply 5*5=25 then divide 125/5 = 5
A rectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 x)(9 x) = 88. what does the value of x in her solutions represent? one possible length and one possible width two possible amounts for the widths two possible amounts for the lengths two possible amounts by which the dimensions were changed
The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft
How to determine the value of x?The equation is given as:
(6 + x) * (9 + x) = 88
Express 88 as a product of two factors
(6 + x) * (9 + x) = 8 * 11
Express 8 and 11 as a sum
(6 + x) * (9 + x) = (6 + 2) * (9 + 2)
By comparison, we have:
6 + x = 6 + 2
9 + x = 9 + 2
This means that
x = 2
So, we have:
The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft
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Answer: D) two possible amounts by which the dimensions were changed
Step-by-step explanation:
Edg 2022
Let’s say you’re building a mini city, each apartment complex costs $10 each enough to supply 100 people, how many do I need to supply 50,000 people?
What is the best estimate of the area of the figure on the grid if each square has an area of 1 square inch?
O3 square inches
O 5 square inches
O 7 square inches
O9 square inches
Answer: 3 square inches
Step-by-step explanation:
See attached for how I broke the shape up. Since each square is equal to 1 square inch, and the shape is about 3 squares, the answer should be;
O 3 square inches
Please note that different people may estimate differently.
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Please Help if you can.
Answer:
6.28 meters
Step-by-step explanation:
Circumference is D[tex]\pi[/tex]
D=2 meters
2*3.14 = 6.28
Which of the following best describes how to use of the addition property of equality to isolate the variable x
below?
5=x-2
A. add 5 to both sides of the equation
B. subtract 5 from both sides of the equation
C. add 2 to both sides of the equation
D.
subtract 2 from both sides of the equation
I need help with this asap pleaseee
Answer:
Form: (x+5)^2 = 2
Solution: -6.41, -3.59
What is the rage of the data?
Answer
the range is the spread of your data from the lowest to the highest value in the distribution
Answer:
9
Step-by-step explanation:
To find the range, subtract the biggest number (here it's 9) and the smallest number (here it's 0).
9 - 0 = 9
Jonah is attending a school orchestra concert. He sees his math teacher seated 6 meters ahead of him and his science teacher seated 7 meters to his right. How far apart are the two teachers? If necessary, round to the nearest tenth.
Answer:
42 meters
Step-by-step explanation:
if his math teacher is 6 meters ahead of him and his science teacher is 7 meters to the right of him than you multiply to get the area of distance from each other.
6 x 7 = 42
the teachers are 42 area meters away from each other