The height of a triangle is 12 centimeters more than its base. The area of the triangle is 189 square centimeters Find the base and height of the tiangle?
Answers
Answer:
C
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
so, we know in our case
b(b+12) = 189 cm²
b² + 12b - 189 = 0
let's try to solve this by completing the square.
that means we try to find the expression
(b + k)² + c
that is equal to
b² + 12b - 189
(b + k)² + c = b² + 2kb + k² + c = b² + 12b - 189
so,
2k = 12
k = 6
and then
k² + c = -189
6² + c = -189
36 + c = -189
c = -225
(b + 6)² - 225 = 0
(b + 6)² = 225
b + 6 = 15
b = 9
so, the baseline b = 9 cm.
the height b+12 = 9+12 = 21 cm.
Related Questions
A line that passes through the points (x, 4) and (6, -1) has a slope of 56. what value of x will yield the given slope?
Answers
The value of x that yields a slope of 56 is 6.09
How to determine the value of x?The given parameters are:
Slope = 56Points: (x,4) and (6,-1)The slope of two points is:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]\frac{-1 -4}{6 -x} = 56[/tex]
Evaluate the difference
[tex]\frac{-5}{6 -x} = 56[/tex]
Cross multiply
56(6 - x) = -5
Divide both sides by 56
6 - x = -0.09
Make x the subject
x = 6 + 0.09
Evaluate
x = 6.09
Hence, the value of x that yields a slope of 56 is 6.09
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Consider the function f(x) = log x. Which two transformations can be used to move
the graph of f(x) to the graph of -f(x+4)?
Select all that apply
Answers
The parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = log x
First transformation:
Replace x → (x+4)
The parent function will shift left side by 4 units.
Second transformation:
Multiply the function with -1
The function will reflect over x-axis
The function becomes:
g(x) = -log(x+4)
Thus, the parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
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Which of these shapes is an obtuse isosceles triangle? Help me A, B, C, Or D?
Answers
Answer:
A
Step-by-step explanation:
A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
i added the graph
Answers
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
What is the greatest common factor (GCF) of 40 and 56?
Answers
Answer:
8
Step-by-step explanation:
Factors of 40: 1 2 4 5 8 10 20 40
Factors of 56: 1 2 4 8 14 28 56
Common factors: 1 2 4 8
Greatest common factor: 8
Answer:
8
Step-by-step explanation:
Prime factorization
40 = 2 x 2 x 2 x 5
56 = 2 x 2 x 2 x 7 common factor 2 x 2 x 2 = 8
PLEASE HELP QUICKLY!
Part A: Abe rented a bike at $36 for 5 days. If he rents the same bike for 8 days, he has to pay a total rent of $48.
Write an equation in the standard form to represent the total rent (y) that Abe has to pay for renting the bike for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
(10 points)
Answers
Answer:
(5,36)(8,48)slope = (48 - 36) / (8 - 5)
Step-by-step explanation:
Answer: Equation of the system is y = 4x + 16 and in function form is f(x) = 4x + 16.
Explanation
◄) There were 60 dogs at the dog park last Saturday, and 30 of them were purebreds.
Considering this data, how many of the next 18 dogs to arrive at the park next Saturday
should you expect to be purebreds?
purebreds
Submit
Answers
30!outcof 60 were purebreds 30/60 = 1/2
1/2 of the dogs were purebreds.
18 x 1/2 = 9
Answer: 9 dogs
Answer:9 points
Step-by-step explanation:in the hyperproberbillity of things it’s this answer.
Which equation represents the solution of x^3 = 72?
Answers
Noemi decide hacer una cadena de solidaridad. Para esto
ella pide $500 a tres amigos, al día siguiente cada uno de los
amigos pide $500 a otros tres amigos y así sucesivamente.
A) ¿Cuánto dinero se habrá recaudado al 5° día?
B) ¿Cuántas personas colaboraron durante los primeros 5
días?.
Answers
The amount of money collected after 5 days is $181,500
The number of people that collaborated during the first 5
days is 363 people
Calculations and Parameters:To solve this problem, we would use the Geometric Progression with the formula:
[tex]\frac{a(r^n -1)}{r-1} \\[/tex]
Where:
r= 3
a= 3
n= 5
[tex]\frac{3(3^5 - 1)}{3-1} \\[/tex]
= [tex]\frac{3(243 -1)}{2}[/tex]
121 * 3 = 363 people.
Therefore, the amount contributed is $500 * 363= $181,500
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100 PTS AND WILL GIVE BRAINLY!!!
THE SCENARIO
The Tortoise and the Hare finally have their long awaited rematch. The Tortoise gets a
300 m lead and runs at 0.2 m/s. The Hare begins at the starting line and runs at a rate of 2 m/s. There is also a rat in this race. The Rat starts 350 m ahead of the Hare and runs back towards the starting line at a rate of 0.6 m/s.
THE CALCULATIONS
Create a table of values for each runner in the race. The domain for the race will be 0 ≤ t ≤ 200 seconds. You can decide on 5 time intervals for your table.
Answers
Answer:
Tortoise:
Hare:
Rat:
All will be shown later
Step-by-step explanation:
Equation for Torotise: f(x)=0.2(x)+300
Equation for the Hare: f(x)=2(x)
I hope it helps! I will show you screenshots in the comments
4m=6m-2/5
First answer get to be brainliest!
Answers
Answer:
m = 1/5Step-by-step explanation:
4m = 6m - 2/5
-2m = -2/5
m = 2/5 : 2
m = 1/5Select the correct answer.
Courtney constructed this figure using a compass with its width set equal to PR, the radius of the circle.
She claims triangle PRS is equilateral because all three sides of the triangle are equal to PR. She also claims that applying the same argument to prove each triangle in the figure is equilateral proves that the inscribed hexagon is also equilateral.
Which statement is true?
A.
Courtney's reasoning about triangle PRS is correct, but the hexagon is not equilateral.
B.
Courtney's reasoning about triangle PRS is correct, and the hexagon is equilateral.
C.
Courtney's reasoning about triangle PRS is incorrect, and the hexagon is not equilateral.
D.
Courtney's reasoning about triangle PRS is incorrect, but the hexagon is equilateral.
Answers
Answer:
B.Courtney’s reasoning about triangle PRS is correct, and the hexagon is equilateral.
Step-by-step explanation:
What is the area of the painting shown ?
Answers
Area = length x width
Length = x + 6 + x + 2 = 2x + 8
Width = x + 4 + x = 2x + 4
area = 2x + 8 * 2x + 4
multiply each term by each term
Area = 4x^2 + 24x + 32
Answer: I think this is correct but i'm not sure! the answer should be 48 im not sure though
Step-by-step explanation:
6 x 2 = 12 x 4 = 48
URGENT I NEED HELP ASAP Which of the following steps were applied to AABC obtain AA'B'C'?
B
12
10
-6
8-
64
4
2-
-2
-2
र
8
10
A. Shifted 4 units right and 3 units up
B. Shifted 3 units right and 2 units up
C. Shifted 3 units right and 3 units up
D. Shifted 2 units right and 3 units up
T
B
2
C
C'
Answers
Hope this helped
The steps to translate the triangle ABC to A'B'C' are Shifted 3 units right and 2 units up.
The correct option is (B).
What is Coordinate Geometry?By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given diagram:
We are given the diagram of two triangles drawn on a graph.
With the help of the graph, we can easily figure out the coordinates of each point of the triangle.
The steps to translate the triangle will be the same as that to translate any vertices of the triangle.
Let us consider A:
Coordinates of A = (2, 5)
Coordinates of A' = (5, 7)
For translating A to A':
3 units in +ve x direction. {right}
2 units in +ve y direction. {up}
Hence, The steps to translate the triangle ABC to A'B'C' are Shifted 3 units right and 2 units up.
To learn more about Coordinate Geometry, click:
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The kinetic energy (K) that an object has varies jointly with its mass (m) and the square of its velocity (v). The equation that represents this relationship is given by [tex]K=kmv^2[/tex] where k is the kinetic energy constant. If a bowling ball of mass 5 kilograms is traveling at 2 meters per second, its kinetic energy is 10 Joules. What is the kinetic energy of a bowling ball of mass 3 kilograms traveling at 2.6 meters per second?
Answers
The kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.
What is Kinetic Energy?Kinetic energy is simply a form of energy a particle or object possesses due to its motion.
It is expressed as;
K = (1/2)mv²
Where m is mass of the object and v is its velocity.
Given that;
Mass of the bowling ball m = 3kgVelocity of the bowling ball v = 2.6m/sKinetic energy K = ?We substitute the given values into the above equation.
K = (1/2)mv²
K = 0.5 × 3kg × (2.6m/s)²
K = 0.5 × 3kg × 6.76m²/s²
K = 10.14kgm²/s²
K = 10.14J
Therefore, the kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.
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WILL MARK BRAINLIEST! WILL GIVE 57 POINTSSSS! NO FUNNY ANSWERS I WILL REPORT YOU UNTIL YOU GET BANNED.
Complete the function table. then write a rule for the function.
Pls Help Quickly! :)
Answers
Answer:
-5
-3
-2
Rule: Subtract 2 from the input value
Step-by-step explanation:
Examine the pattern of the input and the corresponding output for the two given ordered pairs:
Input -2 → Output -4
Output - Input = -4 - (-2) = -2
Input 1 → Output -1
Output - Input = -1 - 1 = -2
Therefore to get the output value (y-value), we subtract 2 from the input value (x-value).
[tex]\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} -3 & -5 \\\cline{1-2} -2 & -4 \\\cline{1-2} -1 & -3 \\\cline{1-2} 0 & -2\\\cline{1-2} 1 & -1 \\\cline{1-2}\end{array}[/tex]
As the rule for the function is the subtract 2 from the input value to get the output value, we can write this as:
Output = Input - 2
or as an equation: [tex]y=x-2[/tex]
Having a hard time finding the Surface Area, help?
(Formula is SA=hp+2B)
Answers
Answer:
89.3 cm. sq.
Step-by-step explanation:
Just find the area of each face and then add those areas together.
hope this helps
have a good day
The figures below are similar. What is v?
Answers
Answer:
v = 16 mm
Step-by-step explanation:
since the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{v}{20}[/tex] = [tex]\frac{28}{35}[/tex] ( cross- multiply )
35v = 560 ( divide both sides by 35 )
v = 16
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
-7
1) 1/7. 3). 1. 5). 49. yes this is right answer
Whoever answers first i will mark brainlist
Answers
what is the approximate of this cone
Answers
Answer:
so the volume of our cone is exactly π ! As we all know, this can be approximated as volume ≈3.14159
WILL MARK BRAINLESS IF YOU'RE RIGHT!!! "a field in the shape of a right triangle is bordered on one side by a lake on another side by a street and on a third side by a tree line what angle does this lake make the street."
Answers
Answer:
b≈26.46
Step-by-step explanation:
see image attached
Using the net below, find the surface area of the triangular prism 5 cm 5 cm 4 cm 4 cm 3 cm 3 cm 3 cm 5 cm
Answers
Answer:
54000
Step-by-step explanation:
use multiplication
do ur own work if you want to see if I'm wrong
Here are two rectangles. the area of the shaded rectangle is 1/4 the area of the large rectangle. work out the value of x
Answers
The area of the rectangle is the product of length and width. The value of the variable x is 3.6 cm
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
The diagram is given below.
Let A₁ be the area of the small rectangle and A be the area of the large rectangle.
A₁ = 1/4 A
4A₁ = A
4 × 2× (12 - x) = 12 × (x + 2)
8(12 - x ) = 12x + 24
96 - 8x = 12x + 24
72 = 20x
x = 3.6
Then the value of the variable x is 3.6 cm
More about the area of the rectangle link is given below.
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Will mark brainlist to whoever answers first
(5).
Answers
Answer:
Step-by-step explanation:
US=26
SV=UV=[tex]\frac{26}{2}[/tex] (diagonals of parallelogram bisect each other)
UV=13
12. Solve the following inequality.
Answers
Answer:
C. The solution set is {x|x < 6}.
Step-by-step explanation:
Given :
7x + 4 < 46Subtract 4 from both sides.
7x + 4 - 4 < 46 - 47x < 42Divide 7 from both sides.
7x/7 < 42/7x < 6C. The solution set is {x|x < 6}.
Hi everyone i hope you can help with this exercise
Answers
s = area = 11.76
p = perimeter = 16.8
r=2*11.76/16.8=23.52/16.8=1.4
r=1.4
a= 90 degrees
b=36.87 degrees
c=53.13 degrees
triangle is in a circle
Circumradius: R = 3.5
You toss a nickel a penny and a dime what is the probability that the nickel comes up heads
Answers
The penny can land two ways. The nickel can land two ways. The dime can land two ways. The quarter can land two ways. The total number of ways that all of them can land is (2x2x2x2)= 16 possibilities. Only ONE result shows no heads . . . TAIL-TAIL- TAIL-TAIL. All of the other 15 possibilities include at least one HEAD. So the probability is 15/16 = 93.25% .
A solid glass sphere is cast with a diameter of 30 cm. find the volume of the sphere. please leave in terms of pi.
a. v = 20pie cm^3
b. v = 40pie cm^3
c. v = 4,500pie cm^3
d. v=14,137pie cm^3
Answers
Answer:
C
Step-by-step explanation:
Recall that the volume of a sphere is given by:
[tex]\displaystyle V = \frac{4}{3}\pi r^3[/tex]
Because the sphere has a diameter of 30 cm, its radius is 15 cm. Therefore, its volume is:
[tex]\displaystyle \begin{aligned} V & =\frac{4}{3}\pi(15\text{ cm})^3 \\ \\ & = \frac{4}{3}\pi(3375\text{ cm}^3) \\ \\ & = 4500\pi\text{ cm}^3 \end{aligned}[/tex]
In conclusion, our answer is C.
In a recent survey, 8 people were each asked the number of times they have been on an airplane. Here is a list of the responses.
9, 21, 7, 11, 13, 21, 5, 14
Find the range of the data set.
Answers
Explanation: Range is the difference between the highest and lowest number.
21 - 5 = 16.
Answer: The range of the data set is: " 16 " .
______
Explanation:
The range is calculated by subtracting the lowest value in the given data set from the highest value in the data set.
______
Given: The data set: 9, 21, 7, 11, 13, 21, 5, 14 ;
Let us organize these numbers from lowest value to highest value:
" 5, 7, 9, 11, 13, 14, 21, 21 " ;
Note: This is done by inspection. Note that all eight (8) values are accounted for.
So, we subtract the lowest value in our given data set: "5" ;
from the highest value in our given data set: "21" ; to get the "range":
→ " 21 − 5 = 16 " ;
______
The range is: " 16 " .
______
Hope this is helpful! Best wishes!