Answer:
[tex]5\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\boxed{a^{2} -b^{2} = (a +b)(a -b)}[/tex]
9x² -9y²= 72
Factorise:
9(x² -y²)= 72
Divide both sides by 9:
x² -y²= 8
(x +y)(x -y)= 8
Given that x -y= 1.5,
(x +y)(1.5)= 8
Divide both sides by 1.5:
x +y= [tex]5\frac{1}{3}[/tex]
Tim will buy a pair of shoes that cost $120.He received a 35% discount coupon. Luckily his friend Mario gets an additional 15% discount being an employee of the store. If Mario buys the shoes for Tim, how much will Mario pay if the tax is 8%? Round your answer to the nearest centavo
Answer:
$69.60
Step-by-step explanation:
In the polynomial below, what number should replace the question mark to produce a difference of squares?
x^2 + ?x - 36
A. 12
B. 36
C. 6
D. 0
Answer:
Step-by-step explanation:
c
What is a number greater then 0.6 but less than 0.7
Answer:
0.65 is a number greater than 0.6 but less than 0.7
Yolanda cut 2 2/3 yards of fishing line from a new reel. How much is this in inches?
Answer:
1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.
Step-by-step explanation:
1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.
What the value of q?
Answer:
50°
Step-by-step explanation:
because angles on straight line add up to 180°,
180-130=50 :)
Find the missing factor._____ x 5 = 3,000
A) 6
B) 60
C) 600
D) 6,000
Answer:
a = 600
Step-by-step explanation:
Algebraically:
[tex]a*5 = 3000\\a = \frac{3000}{5}\\ a = 600[/tex]
can you please help me
Answer:
42
Step-by-step explanation:
G-14
O-14
O-14
so 14•3=42
Find the measure of x
Answer:
x=23
Step-by-step explanation:
An inscribed angle is half of the intercepted arc.
-
Angle A and B are vertical angles. If Angle A = (5x – 3)° and Angle B = (4x + 21)°,
then find the measure of Angle A.
Answer:
Angle A=87°
Step-by-step explanation:
(5x-3)°+(4x+21)°=180°
9x°+18°=180°
9x°+18°-18°=180°-18°
9x°=162°
9x°/9°=162°/9°
x=18°
Angle A=(5x18-3)°
(90-3)°
Angle A=87°
Enter in the missing numbers to create equivalent ratios. NO LINKS pls.
Answer:
Step-by-step explanation:
2 triangles. One triangle has side lengths x, 3 units, 4 units. The other triangle has side lengths 11 units, y, 8 units. The two figures are the image and pre–image of a dilation. Find the lengths of the missing sides. x = units, y = units
Answer:
5.5 and 6
Step-by-step explanation:
i got it wrong and it told me this was the correct answer
Answer:
5.5 and 6
Step-by-step explanation:
Which of the following is NOT the same for both sets of data?
MEAN?
MEDIAN?
MODE?
RANGE?
Answer:
Mode
Step-by-step explanation:
As you can see, the mode on the first data set is 10, the mode on the other is 30.
What type of function is f(x) = 2x3 – 4x2 + 5?
it's a cubic function
The given function f(x) = 2x³ – 4x² + 5 is a cubic function.
What is a cubic polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3.
It is observed that the given function is a cubic function as its highest power of the variable is three.
Therefore, the given function f(x) = 2x³ – 4x² + 5 is a cubic function.
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The piecewise function h(x) is shown on the graph.
What is the value of h(3)?
-2
ch
0-1
0 1
02
2.
-5 4 -3 -2 -14
2 3 4 5 x
-2
2
-3
-5
Answer:
1
Step-by-step explanation:
Let's say we have y=f (x)
It denotes the y value that corresponds to x.
When x=3, we can see from the graph that
The matching y value for x=3 =1
As a result, h(3)=1
The value of h(3) can be estimated from the piecewise function curve is 1. so option c is correct.
What is piecewise function?A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.
Given that,
The graph of the piecewise function
The function is divided into two piece
Interval-1 x ∈ [-4, -1)
Interval-2 x ∈ [-1, 4]
The value of the function when x is equal to 3,
In the graph it is clearly mention that for x =3
the output value of the function is 1
Hence, the output value is 1
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Use the graph of triangle JKL to answer A and B
a. Reflect JKL over the x-axis. Record the coordinates of
the original and new image below.
b. Describe what happened to the x and y coordinates
once they were reflected.
2 Use the coordinates of triangle QRS to answer a-b.
Answer:
a) J':(-7,7) K':(-5,2) L':(-2,3)
b) The x coordinates remained the same, the y coordinates swapped from negative to positive.
Step-by-step explanation:
Aside: I'm using J', K', and L' to denote the new locations of J,K,L after the reflection.
When an object is reflected over the x-axis, it means it's positive points will flip to negative y space, and negative points will flip to positive y space.
That said, J, for instance, will have the same X-coordinate, but its Y-coordinate will flip from negative to positive. Doing this with every vertex mirrors the triangle over the X-axis.
Therefore, J:(-7,-7) will become J':(-7,7), and likewise with K and L becoming K':(-5,2) and L':(-2,3).
Answer:
Step-by-step explanation:
In the diagram below, what kind of line is BF relative to ABC?
Line BF is one of the three angle bisectors that meet at point F (incenter), hence, line BF as it relates to ABC is called the: interior angle bisector.
What is an Interior Angle Bisector?An interior angle bisector can be described as the line segment that divides an interior angle into two halves.
When the three interior angle bisector of a triangle meet at a point, the point is referred to a the incenter.
The diagram guven shows the incenter where the three interior angle bisectors meet.
Therefore, line BF as it relates to ABc is called the: interior angle bisector.
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The perimeter of the rectangle below is 168 units. Find the length of side AB.
Write your answer without variables.
D
С
AB
0
4z + 1
SZ+2
Answer:
47
Step-by-step explanation:
10z + 4 + 8z + 2 = 168
first we find z
z = 9
5×9 +2 is 47
ANSWER IS 47
I don’t get it because I don’t have a calculator
Algebra: Right answer pls
Which statement about the graph of y = 4 (1.25)× is true?
The coordinates of the x-intercept are (4, 0)
The coordinates of the y- internet are (0, 4) (ʀɤɢʜʈ Åɴswɛɾ)
The equation of the asymptote is x = 4
The graph includes the point (0, 1.25)
Answer: B
Step-by-step explanation:
HELP 50pts!!!!!!!!!!
Answer:
2.5, which would be 2:30 hours
Step-by-step explanation:
time/distance:
22.5/9 = 2.5
9 x 2.5 = 22.5
so the answer is 2.5
Answer:
2.5 hours
Step-by-step explanation:
[tex]\sf time \ taken = \dfrac{distance}{speed}[/tex]
Here:
distance : 22.5 kmspeed : 9 km/hr[tex]\hookrightarrow \sf \dfrac{22.5}{9}[/tex]
[tex]\hookrightarrow \sf 2.5[/tex]
Solve for x. -14 - x = 14
Answer:
x= -28
Step-by-step explanation:
1. First you have to add 14 to both sides to get the x by itself. That's always the first thing you have to do. Get x by itself.
2. After that, you should have -x= 28. You can't leave it like that because it is still not simplified. It's basically saying 28 is the opposite of x. What's the opposite of positive? Negative.
3. Therefore, your final answer should be -28
Answer:
x = -28
Step-by-step explanation:
Hey! First, lets establish our equation :)
-14 -x = 14
Now, we are going to get our x alone on a single side, to do this, we are going to add 14 to both sides to be able to cut out -14 on the left side!
-14 -x = 14
+14 +14
-x = 28
The last thing we have to do is divide both sides by -1 to get x by itself without it being negative!
-x = 28
÷-1 ÷-1
x = -28
So, x, is equal to -28 (negative 28!) :)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
15 Mary needs to work out the size of angle x in this diagram.
DO NOT WRITE IN THIS AREA
63°
X
B
С
She writes
x = 63° because base angles of an isosceles triangle are equal.
Mary is wrong.
(a) Explain why.
Mary is wrong because ∠A = ∠B = 63°, while ∠C = x ≠ 63°
What is a triangle?
A triangle is a polygon with three sides and three angles. Types of triangles are equilateral, isosceles and right angled.
An isosceles triangle is a triangle in which two sides and two angles are equal.
From the diagram:
∠A = ∠B (base angles)
Mary is wrong because ∠A = ∠B = 63°, while ∠C = x ≠ 63°
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Help anyonee?? 100 points!!
Answer:
D
Step-by-step explanation:
[tex]4\sqrt{x2[/tex] means [tex](x^{2})^{\frac{1}{4} }[/tex] so then according to indices rule, the powers will be multiplied. Do the same thing for y and z as well, and you will get the answer
Find the domain for each expression. (1/x)+5
1/x
X+5/x+5
X^2/x
7/(x-2)
Using it's concept, it is found that the domain for the expressions is, respectively, given by:
[tex]x \neq 0, x \neq 0, (-\infty, \infty), (-\infty, \infty), x \neq 2[/tex]
What is the domain of a function?It is the set that contains all possible input values.
In a fraction, the denominator cannot be zero, hence:
The domain of the first two expressions is of [tex]x \neq 0[/tex].The domain of the last expression is of [tex]x \neq 2[/tex].The third expression can be simplified, as:
(x + 5)/(x + 5) = 1.
The same is true for the fourth, as:
x²/x = 1.
Neither has any restriction, hence their domain is all real numbers, represented by [tex](-\infty, \infty)[/tex].
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Factor completely 2x2 – X – 4.
(3x - 1)(x + 4)
(3x + 4)(x - 1)
(3x − 2)(x + 2)
-
(3x – 4)(x + 1)
-
[tex]2x {}^{2} - x - 4[/tex]
[tex]x = \frac{ - ( - 1) + \sqrt{1 - 4(2)( - 4)} }{2(2)} = \frac{1 + \sqrt{33} }{4} [/tex]
[tex]x = \frac{1 - \sqrt{33} }{4} [/tex]
[tex](x - \frac{1 + \sqrt{33} }{4} )(x - \frac{1 - \sqrt{33} }{4} )[/tex]
[tex](4x - 1 - \sqrt{33} )(4x - 1 + \sqrt{33} )[/tex]
42. A triangle has an area of 14 square inches. The height of the triangle is three inches more than the
base. What are the base and height of the triangle?
43. Jill has a small treasure box that is 6 inches long. It can hold a volume of 72 inches cubed, and the
width of the box is 5 inches less than twice the height of the box. What are the dimensions of the box?
44. Jessie is mowing her back yard that is in the shape of a right triangle. The shortest side is 7 meters
shorter than the second side, and the hypotenuse is 13 meters long. What are the lengths of the two
sides?
Answer:
Question 42
area of a triangle = 1/2 × base × height
Given:
area = 14 in²height = x + 3base = xSubstituting given values into the formula:
⇒ 14 = 1/2 × x × (x + 3)
⇒ 28 = (x + 3)x
⇒ 28 = x² + 3x
⇒ x² + 3x - 28 = 0
⇒ (x - 4)(x + 7) = 0
⇒ x = 4, x = -7
As length is positive, x = 4 only.
⇒ height = 4 + 3 = 7 in
⇒ base = 4 in
-----------------------------------------------------------------------------------------
Question 43
volume of a cuboid = length x width x height
Given:
volume = 72 in³length = 6 inheight = xwidth = 2x - 5Substituting given values into the formula:
⇒ 72 = 6 × (2x - 5) × x
⇒ 12 = (2x - 5)x
⇒ 12 = 2x² - 5x
⇒ 2x² - 5x - 12 = 0
⇒ (x - 4)(2x + 3) = 0
⇒ x = 4, x = -1.5
As length is positive, x = 4 only.
⇒ height = 4 in
⇒ width = 2(4) - 5 = 3 in
-----------------------------------------------------------------------------------------
Question 44
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = x - 7b = xc = 13 mSubstituting given values into the formula:
⇒ (x - 7)² + x² = 13²
⇒ x² - 14x + 49 + x² = 169
⇒ 2x² - 14x - 120 = 0
⇒ x² - 7x - 60 = 0
⇒ (x - 12)(x + 5) = 0
⇒ x = 12, x = -5
As length is positive, x = 12 only.
⇒ one leg = 12 m
⇒ other leg = 12 - 7 = 5 m
Which of the following statements about area is not true?
A. Area is the total space within the outside edges of a two-dimensional object.
B. Area can be found by counting the number of unit squares that fill a space.
C. Area is the total distance around the outside of a shape.
D. Area is used to help describe the dimensions of a shape.
Answer:
C. Area is the total distance around the outside of a shape.
Step-by-step explanation:
Answer:
Area is the total distance around the outside of a shape, Would be correct.
Step-by-step explanation:
proof for the extreme value theorem
Teddy has two sisters. One of them is 3 years older than Teddy, the other one is 7 years younger than her only brother. How old was the older sisters when the younger sister was born
Lets let Teddy be x.
Sister 1: x+3
Sister 2: x-7
If we subtract the younger sister (sister 2) from the older sister (sister 1), we get:
x+3 - (x-7) = x+3 - x + 7 = 10
The older sister was 10 years old when the younger sister was born.
Find the point P on the line y = 5x that is closest to the point (52,0)
Answer:
(2,10)
Step-by-step explanation:
Whenever you want to find the point that is closest, it will always be perpendicular to the line
This is because the perpendicular line is the shortest distance to a point (it will make 90 degrees with the line)
So
In order to find the slope of the perpendicular line, you take the slop and you do the negative reciprocal of it.
In this case:
the slope is 5
So:
the negative reciprocal is -1/5
Now we know the slope of the line that will be made by point P to intersect with y=5x
Then, you use the equation:
y=mx+b
and plug in the numbers that you know which is the y coordinate, x coordinate, and slope to find the y-intercept:
0 = -1/5(52) + b
b = 52/5
Finally, set the equations equal to each other to find the point that the perpendicular line intersects y=5x
5x = -1/5x + 52/5
x = 2
then to find the y coordinate you plug the x back into the equation:
y = 5(2)
y = 10
So the answer is (2,10)