The simplified form of the expression is [tex]7c^2d - 7c + 4d - 10[/tex].
To simplify the expression, we first combine like terms:
[tex]5c^2d - 4c + 3d - 3 + 2c^2d - 3c + d - 7[/tex]
Grouping similar terms:
[tex](5c^2d + 2c^2d) + (-4c - 3c) + (3d + d) + (-3 - 7)[/tex]
Simplifying each group:
[tex]7c^2d - 7c + 4d - 10[/tex]
Thus, the simplified form of the expression is [tex]7c^2d - 7c + 4d - 10[/tex]. This result arises from combining the coefficients of like terms. The coefficients of [tex]c^2d[/tex] add up to 7, those of c add up to -7, those of d add up to 4, and the constants add up to -10.
Complete Question:
What is the simplified form of the expression?
[tex]$$5 c^2 d-4 c+3 d-3+2 c^2 d-3 c+d-7$$[/tex]
[tex]a. 3 c^2 d-7 c+2 d-10\\\\b. 3 c^2 d-7 c+4 d-10\\\\c. 7 c^2 d-7 c+2 d-10\\\\d. 7 c^2 d-7 c+4 d-10[/tex]
Which of the following measurements could be the side lengths of a right triangle?
A.
54 in, 72 in, 108 in
B.
54 in, 81 in, 90 in
C.
45 in, 72 in, 90 in
D.
54 in, 72 in, 90 in
Answer:
Step-by-step explanation:
To determine the side lengths of a right triangle, use the converse of the Pythagorean Theorem, where c is the longest side, as shown below.
If c2 < a2 + b2, the triangle is acute.
If c2 = a2 + b2, the triangle is right.
If c2 > a2 + b2, the triangle is obtuse.
Check each answer choice, according to the rules above.
This is an acute triangle.
This is an obtuse triangle.
This is an obtuse triangle.
This is a right triangle.
Therefore, 54 in, 72 in, and 90 in are the side lengths of a right triangle.
Correct option is (D) 54 in, 72 in, 90 in
Using the converse of the Pythagorean Theorem, we can determine whether the given sides form a right angled triangle or not
Thus if '[tex]c^2 < a^2 + b^2[/tex]' then the triangle is acute angled triangle
Similarly if ' [tex]c^2 = a^2 + b^2[/tex] ' then the triangle is right angled triangle
Similarly if ' [tex]c^2 > a^2 + b^2[/tex] ' then the triangle is obtuse angled triangle
Thus we would be checking for each options
Option(A) :
Given that the sides are 54 in, 72 in, 108 in
[tex]108^{2} =11664[/tex]
[tex]54^2+72^2=2916+5184\\54^2+72^2=8100[/tex]
Thus it can be seen that
[tex]108^2 > 54^2 + 72^2[/tex]
We can say that the given sides form an acute angled triangle
Option(B) :
Given that the sides are 54 in, 81 in, 90 in
[tex]90^{2} =8100[/tex]
[tex]54^2+81^2=2916+6561\\54^2+81^2=9,477[/tex]
Thus it can be seen that,
[tex]90^2 > 54^2 + 81^2[/tex]
We can say that the given sides form an obtuse angled triangle
Option(C) :
Given that the sides are 45 in, 72 in, 90 in
[tex]90^{2} =8100\\45^2+72^2=2025+5184\\45^2+72^2=7209[/tex]
Thus it can be seen that,
[tex]90^2 > 45^2 + 72^2[/tex]
We can say that the given sides form an obtuse angled triangle
Option(D) :
Given that the sides are 54 in, 72 in, 90 in
[tex]90^{2} =8100\\54^2+72^2=2916+5184\\54^2+72^2=8100[/tex]
Thus it can be seen that,
[tex]90^2 =54^2 + 72^2[/tex]
We can say that the given sides form an right angled triangle
Thus, 54 in, 72 in, and 90 in are the side lengths of a right triangle.
Hector needs to buy a window shade in his house. He measured the width of the window as 37 inches. The actual measurement is 40 inches. What is the percent error
Answer:
3/40 = 7.5%
Step-by-step explanation:
3/40 percent error.
3/40 = 7.5%
List parallelograms, polygons, quadrilaterals, and rectangles in order from the least specific group to the most specific one.
A) parallelograms, polygons, quadrilaterals, rectangles
Answer:
(B)
Step-by-step explanation:
Option (B) is in correct order when talking about the specific ones.
Polygon is the least specific as it can be of many sides.
example: A polygon with 3 sides is a triangle. and the polygon with 4 sides is a quadrilateral.
Hence, quadrilateral is on the second number in least specific group.
Quadrilaterals with 2 sides parallel and equal are known as parallelogram.
Therefore, they are on the 3rd number in specific group.
Parallelograms with opposite sides parallel and equal and all the vertex angles at right angles are known as rectangles.
Therefore, rectangles are the most specific one in the group. The list is given by (option (B):
1) polygons
2) quadrilaterals
3) parallelograms
4) rectangles.
mark brainliest :)
Answer:
The answer is B!!!!
Step-by-step explanation:
I not that good at explain but i'll try to explain :).Ummmmmmm....I took the same test so thats how I know
A: Line n was translated up 8 units.
B: Line m was translated down 4 units.
C: Line l was translated down 8 units.
D: Line m was translated up 4 units.
Answer:
4
Step-by-step explanation:
move up a units then take a line and move that down 4 units then down four more then back up 8 and you get your answer of
a box shaped like a rectangular prism has a height of 17 in and a volume of 2720 in^3. the length is 4 inches greater than twice the width. what is the width of the box
Answer:
8 inches
Step-by-step explanation:
You want to find the width (w) in inches such that ...
V = LWH
2720 = (2w+4)·w·17 . . . . . . . . . . fill in the given values
80 = (w+2)(w) = w^2 + 2w . . . . . divide by 34
81 = (w +1)^2 . . . . . . . . . . . . . . . . complete the square
9 = w+1 . . . . . . square root (we only care about the positive solution)
8 = w . . . . . . . . subtract 1
The width of the box is 8 inches.
Answer:
8 inches
Step-by-step explanation:
The solids are similar. Find the volume V of the red solid.
Answer:
196 mm³
Step-by-step explanation:
The ratio of volumes the the cube of the ratio of linear dimensions. Hence the volume of the red solid is ...
(7/21)³×(5292 mm³) = 196 mm³
Solve the quadratic equation. (x + 1)^2 = 16
A) x = 3 or -5 B) x = -3 or 5 C) x = ±5 D) x = ±1
If the square of a certain quantity must be 16, that quantity must be either 4 or -4.
In fact, in both cases we have [tex]4^2=(-4)^2=16[/tex]
So, we have two possible solutions:
[tex]x+1=4 \iff x=3[/tex]
[tex]x+1=-4 \iff x=-5[/tex]
Answer:
A. x= 3 or -5
Step-by-step explanation:
The solution is x = 3 or -5. The steps for solving the equation are shown.
(x + 1)2 = 16
(x + 1)2
= ±
16
x + 1 = ± 4
x + 1 = 4 or x + 1 = -4
x = 3 or -5
I will rate brainliest help
Answer:
The correct answer is A) x does not equal 8
Step-by-step explanation:
In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.
x - 8 = 0
x = 8
Given two functions j(x)=−3x+2 and k(x)=3+4x , what is the function rule for (kj) (x) ?
Answer:
(k·j)(x) = -12x^2 -x +6
Step-by-step explanation:
(k·j)(x) = k(x)·j(x) = (4x+3)(-3x+2) . . . . . substitute function definitions
= 4·(-3)x^2 +(4·2+3(-3))x +3·2 . . . . . multiply using the distributive property
= -12x^2 -x +6
Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16. How many seconds after being thrown will the ball hit the ground?
Answer:
Step-by-step explanation:
H(x)=0
-2x^2 +4x+16=0
X^2 - 2x - 8 = 0
(X + 2) (x-4) = 0
X + 2 = 0 or x -4 = 0
X= -2 or x=4
Since -2 doesn’t make sense use 4
The ball will hit ground in 4 seconds
Answer:
4 seconds
Step-by-step explanation:
Given : The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by: [tex]h(x)=-2x^2+4x+16.[/tex]
To Find: How many seconds after being thrown will the ball hit the ground?
Solution:
We are supposed to find after how much time the ball hits the ground.
So, we are required to substitute h = 0 because when ball hits the ground the height will be 0
So, [tex]0=-2x^2+4x+16[/tex]
[tex]2x^2-4x-16=0[/tex]
[tex]x^2-2x-8=0[/tex]
[tex]x^2-4x+2x-8=0[/tex]
[tex]x(x-4)+2(x-4)=0[/tex]
[tex](x-4)(x+2)=0[/tex]
[tex]x=4,-2[/tex]
Since time cannot be negative .So, neglect -2
Hence A ball will take 4 seconds to hit the ground after being thrown.