Answer:
w = 22 in, h = 8 in.
Step-by-step explanation:
Reading the problem, I immediately see two equations. This hints me towards a system of equations problem.
Statement 1 is The width of a triangle is six more than twice the height.
The width (w) of a triangle is (=) six (6) more (+) than twice (2) the height (h).
Equation 1: w = 6 + 2h
Statement 2 is The area of the triangle is 88 in2.
The formula for the area of a triangle is [tex]\frac{wh}{2}[/tex]. So, we get our second equation.
Equation 2: wh/2 = 88
We see that we have the same number of equations as unknowns, two. This is important as it lets us know that we can find two unknowns in the two equations. If there are more unknowns than equations, then we cannot find the values of all the variables. Look for another equation in the problem. However, if the # equations greater than or equal to number of unknowns, then we are ready to start solving! So, we can now move to solving.
Equation 1 isolates one of the unknowns (w). So, we can replace w in the second equation with the right side of eq 1. Then, we simplify for h.
[tex]\frac{wh}{2} = 88[/tex]
[tex]\frac{(6 + 2h)h}{2} = 88[/tex]
[tex]\frac{6h + 2h^2}{2} = 88[/tex]
[tex]6h + 2h^2 = 176[/tex]
[tex]2h^2 + 6h - 176 = 0[/tex]
[tex]h = -11, 8[/tex] (assuming you know how to solve quadratics)
Since we know that heights of triangles cannot be negative, we find that [tex]h = 8[/tex] in.
For the final step, we plug [tex]h[/tex] into our first equation to find [tex]w[/tex].
[tex]w = 6 + 2h[/tex]
[tex]w = 6 + 2(8)[/tex]
[tex]w = 6 + 16[/tex]
[tex]w = 22[/tex]
So, the answer is w = 22 in, h = 8 in.
To check if we were right, we can plug the values into both equations to see if they are equal. I will skip equation 1 since we used that equation "as-is" to find w.
[tex]\frac{wh}{2} = 88[/tex]
[tex]\frac{22 * 8}{2} = 88[/tex]
[tex]11 * 8 = 88[/tex]
[tex]88 = 88[/tex]
The solution checks out!
Which triangles are similar?
Triangle A
34/
A
30
37
12
15
h
53
9
62
16
Triangle C
Triangle B
A. Triangles A and C
B. Triangles A, B, and C
C. Triangles A and B
D. Triangles B and C
Triangle A and C are same because the angles formed by all three sides are same in both triangles.
Hope it helps you....
Please mark as brainlliest!!!
the length of a rectangle is 4 less than 3 times its width.if its width is 5 cm what will be its perimeter
Answer:
32cm
Step-by-step explanation:
Answer:
Given that: The length of a rectangle is 4 less than 3 times its width. The perimeter of a rectangle is 32 cm.
Simplify the expression using trigonometric identities: sec (–θ) – cos θ.
Answer:
sin θ . tan θ
Step-by-step explanation:
Note : -
sec ( - θ ) = sec θ
Formula / Identity : -
sec θ = 1 / cos θ
sec ( - θ ) - cos θ
= [ 1 / cos θ ] - cos θ
{ LCM = cos θ }
= [ 1 / cos θ ] - [ cos²θ / cos θ ]
= [ 1 - cos²θ ] / cos θ
{ 1 - cos²θ = sin²θ }
= sin²θ / cos θ
{ sin²θ = sin θ . sin θ }
= sin θ . sin θ / cos θ
{ sin θ / cos θ = tan θ }
= sin θ . tan θ
Hence, simplified.
Solve for x, please help, thank you
Answer:x=6
Step-by-step explanation:
x+5x=36
Step 1: Simplify both sides of the equation.
x+5x=36
(x+5x)=36(Combine Like Terms)
6x=36
6x=36
Step 2: Divide both sides by 6.
[tex]\frac{6x}{6} =\frac{36}{6}[/tex]
x=6
Answer:
x=6
A farmer wants to increase the area of His rectangular pen but keep the pen a rectangular shape. He decides to a 5.7 yards of fencing
to the width of the pen but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Which can be used to determine the original width of the pen?
5.7 (W+9.5) = 77.9
S95219
9.5 (W + 5.7) = 77.9
Using the equation for the area of a rectangle, the original width of the pen is determined by:
9.5 (W + 5.7) = 77.9
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
In this problem:
Increases the width by 5.7 yards, hence [tex]w = w + 5.7[/tex], in which w is the original width.The length remains at 9.5 yards, hence [tex]l = 9.5[/tex].The area is of 77.9 square yards, hence [tex]A = 77.9[/tex]Then:
[tex]A = lw[/tex]
[tex]9.5(w + 5.7) = 77.9[/tex]
For a similar problem, also involving the area of a rectangle, you can check https://brainly.com/question/10489198
8m – 5 for m = 9 answer please
Answer:
= 67
Step-by-step explanation:
8m – 5 for m = 9
~Substitute
8(9) - 5
~Simplify
72 - 5
~Subtract
67
Best of Luck!
i'll mark brainliest, thanks in advance!
Answer:
SSS
Step-by-step explanation:
are 2 isosceles right triangles congruent, have both sides and angles equal, so the answers are all valid, the simplest is SSS, 2 sides are the same and marked on the drawing, the third is the same accordingly
Victor drives a distance of 21.45 miles everyday from home to his office. He moves into a new apartment that is just 3.65 miles away from his office. Determine the distance by which Victor has lessened his drive to the office.
Answer:
17.8 miles
Step-by-step explanation:
His old house was 21.45 miles from the office. He moves to a new apartment which is just 3.65 miles from the office.
Since it asks for the distance he reduced to the office, we would do
21.45 - 3.65 = 17.8 miles
Im so confused- please help
Step-by-step explanation:
a/q
x + x - 3 + 2x - 9 = 36
4x - 12 = 36
4x = 36 + 12 = 48
x = 48/4 = 12
x = 12
so,
x = 12
x - 3 = 12 - 3 = 9
2x - 9 = 2(12) - 9 = 15
we know,
area = 1/2 × base × height
so,
→ 1/2 × 12 × 9
→ 1 × 6 × 9
→ 54 inches.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
Simplify the expression w²y³ ÷ wy⁴ please help me thank you for you kindness
Answer:
W/y
Step-by-step explanation:
Find the following limit without using a graphing calculator or making a table.
Answer:
Step-by-step explanation:
Tell whether the fractions are equivalent. Write = or
2/3 ______ 4/6
[tex]\dfrac 23 = \dfrac{2 \times 2 }{3 \times 2} = \dfrac 46[/tex]
Yamuna is getting ready to attend Wittenberg University in the fall. She needs 6 notebooks
at $2.19 each and a chromebook at $529.00. If she has $575 to spend, how much does
she have left for lunch?
Answer:
she has $32.86 left for lunch
Step-by-step explanation:
6 books at $2.19 each equals $13.14. plus the chrome book at 529. 529+13.14= $542.14
$575-542.14 equals $32.86
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than One-fifth? Select three options. choosing 1 blue marble choosing 1 red marble choosing 1 red marble, not replacing it, and then choosing a blue marble choosing 1 white marble, replacing it, and choosing another white marble choosing 1 white marble
hi i know i'm late but might as well add my answer!
here's your answer: B D E or
B.choosing 1 red marble
D.choosing 1 white marble, replacing it, and choosing another white marble
E.choosing 1 white marble
hope i helped
Answer:
b d and e
Step-by-step explanation:
ya
the current population of earth is estimated to be about 7,440,000,000. express number in scientific notation
Answer:
7.44x10^9
Step-by-step explanation:
A local animal shelter has many cats and dogs. The shaded part represents the percent of animals that are dogs. If there are 82 dogs, how many animals are there in total?
Answer:
weel if you divide 82 by 2 then it you will get the number of cats which is 41 then add 82 + 41 =123
Step-by-step explanation:
mark me brainliest
What’s the solution to 2x - 2 > 2x + 4 ?
Answer:
This inequality isn't correct.
Step-by-step explanation:
2x - 2 > 2x + 4
Substituting any value for x, the result will be incorrect.
Actually,
2x - 2 < 2x + 4 is correct.
2x - 2x < 4 + 2
0 < 6
f(3) if f(x) = 2x+2 helpppppppppppppppppp
Answer:
= 8
Step-by-step explanation:
2x = 2 × 3 is 6 because f(3) then + 2 is 8
3 x 2 = 6
6 + 2 = 8
The correct answer is 8
(Hope this helps can I pls have brainlist (crown)☺️)
Which situation involves permutations? A. choosing 5 people out of 15 to participate in a survey B. choosing 3 flavors of ice cream out of 15 for an ice-cream sundae C. choosing a dozen flowers out of 30 to create a bouquet D. choosing first second-, and third-place winners in a cooking contest
9514 1404 393
Answer:
D. choosing first second-, and third-place winners in a cooking contest
Step-by-step explanation:
Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.
Cooking contest winners involve permutations.
Please help!!
Choose the definition for the function.
9514 1404 393
Answer:
A. {2x, x<1; (x+5)/2, x≥1}
Step-by-step explanation:
The left side of the graph (x<1) has positive slope and a y-intercept of 0. Only one answer choice matches: choice A.
In this problem, I did part a) correctly, but I got 7 points off in part b) but I don’t know why?
Answer: You need to prove that ABCD is a rhombus because it's diagonals are always perpendicular, no matter what.
A rhombus is a quadrilateral and:
- its opposite angles have equal measure.
- The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.
- Its diagonals bisect opposite angles.
i'll mark brainliest, thanks in advance!
Answer:
not enough information.
Step-by-step explanation:
We know one side and the vertical angle. We do not have enough information to determine if the triangles are congruent.
Consider the graph of the of the quadratic function g(x). See below
Answer:
I believe the correct answers would be...
32.) B
33.) C
Step-by-step explanation:
32.)
Since the function is shifted downward 1 unit from the x-axis, "q" would be -1
33.)
If the function is shifted upward 4 units, the "+4" would be on the outside of the parentheses.
Use synthetic division to find the result when 3x^3 + 4x^2 - 5x - 2 is divided by x + 2
Check the picture below.
Solve the inequality -3/4(12x+16)<9-5x.
Answer:
x > -21/4
Step-by-step explanation:
Answer:
x > -24/4
Step-by-step explanation:
-3/4 (12x + 16) < 9 - 5x
-3/4 * 12x - 3/4 * 16 < 9-5x
-9x - 3/4 * 16 < 9 - 5x
-9x - 12 < 9 - 5x
-4x - 12 < 9
-4x < 21
Please help!!!
A. (-4,2)
B. (-4,-2)
C. (2,-4)
D. (2,4)
Answer:
A
Step-by-step explanation:
Have a nice day
thanks i'll mark brainliest
Answer:
1.
Step-by-step explanation:
Please take a look at the picture
Answer:
D) The number that is 5 to the right of -6 on the number line
Hope this helps :)
A) y = 5x
B) y = 10x
C) y = 7.5x
D) y = 30x
What is the value of the expression?
(323+1715)−(1135+213)
Enter your answer as a mixed number in simplest form by filling in the boxe
Answer:
690
Step-by-step explanation:
(323+1715)-(1135+213)
(2038)-(1348)
=690
The value of the expression is 690
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (323+1715)−(1135+213)
We have to find the value of expression
By using PEMDAS rule we solve the expression
Let us find the value in parenthesis
2038 -1348
We get 690
Hence, the value of the expression is 690
To learn more on Expressions click:
https://brainly.com/question/14083225
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