Answer:
A(7,5)
Step-by-step explanation:
This is correct because the area of a triangle is b × h = a.
Answer:
The measure of ∠ABC is 45°.
Step-by-step explanation:
Given : The vertices of a triangle are A(7,5) B(4,2) and C(9,2).
To find : What is ∠ABC ?
Solution :
First we side the length of the sides,
Using Distance formula,
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Length of side AB, A(7,5) and B(4,2)
[tex]c= \sqrt{(7-4)^2 + (5-2)^2} \\c= \sqrt{(3)^2 + (3)^2} \\c= \sqrt{9+9} \\c= \sqrt{18}[/tex]
Length of side BC, B(4,2) and C(9,2)
[tex]a= \sqrt{(4-9)^2 +(2-2)^2} \\a= \sqrt{(-5)^2 + 0} \\a= \sqrt{25} \\a= 5[/tex]
Length of the side AC, A(7,5) and C(9,2)
[tex]b = \sqrt{(7-9)^2 +(5-2)^2}\\ b= \sqrt{(-2)^2 + (3)^2} \\b= \sqrt{4+ 9}\\b=\sqrt{13}[/tex]
By the Law of Cosines,
[tex]\cos B=\frac{a^2 + c^2 -b^2}{2ac}[/tex]
Substitute the values,
[tex]\cos B=\frac{(5)^2 + (\sqrt{18})^2 - (\sqrt{13})^2}{2\times 5\times \sqrt{18}}[/tex]
[tex]\cos B =\frac{25+18-13}{10\sqrt{18}}[/tex]
[tex]\cos B=\frac{30}{10\sqrt{18}}[/tex]
[tex]\cos B =\frac{3}{\sqrt{18}}[/tex]
[tex]\cos B= \frac{3}{3\sqrt{2}}[/tex]
[tex]\cos B= \frac{1}{\sqrt{2}}[/tex]
Taking Inverse Cosine function,
[tex]B= \cos^{-1}( \frac{1}{\sqrt{2}})[/tex]
[tex]B=45^\circ[/tex]
Therefore, The measure of ∠ABC is 45°.
a shirt was originally $35 and is now 25% off.What is the sale price
100% - 25% = 75%
$35 x 75/100 = $26.25
The sale price should be $26.25.
Given information:
a shirt was original $35 and is now 25% off.
Calculation of the sale price:Since it is 25% off
So, it should be
= 100% - 25%
= 75%
Now the 75% of $35 should be $26.25.
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What are the factors of x2 − 25?
(x − 5)(x − 5)
(x + 5)(x − 5)
(x − 1)(x + 25)
Prime
Answer:
)x + 5)(x - 5)
Step-by-step explanation:
x² - 25 ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b), thus
x² - 25 = x² - 5² = (x + 5)(x - 5)
This set of 3 number are measured of a right triangle 91 41 40
Answer:
False
Step-by-step explanation:
The measures of a right-angle are;
45°,45°,90° (45° right triangle)30°, 60°, 90° (30°- 60° right triangle)A right triangle has a 90° angle and two acute angles and the sum of angles should add up to 180°. The leg angles could be 45 to form an °isosceles triangle.
Rachel has an 80:1 scale drawing of the floor plan of her house. On the floor plan, the dimensions of her rectangular living room are 1 7/8 by 2 1/2 inches. What is the area of her actual living room in square feet?
Answer:
208⅓ ft²
Step-by-step explanation:
The dimensions of Rachel's living room are 80 times the measurements on the scale drawing.
Calculate the width:
w = 80 × 1⅞
Convert the mixed number to an improper fraction = 80 × 15/8
Cancel the 8s = 10 × 15
= 150 in
Convert inches to feet = 150/12
Convert the improper fraction to a mixed number = (144 + 6)/12
= 12⁶/₁₂
Reduce the fraction to lowest terms = 12½ ft
Calculate the length
l = 80 × 2½ = 80 × 5/2 = 40 × 5 = 200 in = 200/12 = (192 + 8)/12
l = 16⁸/₁₂ = 16⅔ ft
Calculate the area
A = lw
A = 16⅔ × 12½
Convert the mixed numbers to improper fractions
A = 50/3× 25/2
Cancel the 2s
= 25/3 × 25
Multiply numerators and denominators
= 625/3
Convert the improper fraction to a mixed number
= (624 + 1)/3
= 208⅓ ft²
The area of Rachel's living room is 208⅓ ft².
A population of 550 rabbits is increasing by 7.5% each year. In about how many years will the population be over 1000?
A.) 9 years
B.) 5 years
C.)7 years
D.)15 years
Answer:
D.) 15 years
Step-by-step explanation:
7.5% of 550 rabbits would be 41.25
if you are increasing till you get over 1,000
it would take 10.9 almost 11 years to get to 1,000
meaning it would be 15 years when your over 1,000 giving you 1,168.75
Which of the following equations represents a line that is parallel
Answer:
B
Step-by-step explanation:
A parallel line means equal m values, so the slope of the equation has to be 3.
Then, we can plug in the (1,6) to each of the equations with 3 as a slope and see if they are equal to each other.
B. 6 = 3 + 3
B. 6 = 6
So B is the correct equation.
39 POINTS!! I NEED HELP ASAP!!!!!!! 2 QUESTIONS!!!!!
1) the area of a rectangle is 8w + 18. Use your width expression to find the width of the rectangle when w = 1.25 feet. Show your work.
2) The sixth grade band students are selling magazines to raise money for new instruments. As a reward for selling, the students earn points to spend on prizes. Each student gets 25 points to start with, and then they earn an additional 5 points for each magazine they sell. If m represents the number of magazines a student sells, write an expression to represent the total number of points the student has. Determine how many points a student has if they sell 6 magazines. Show your work.
Note: the width expression is just the way how you yourself does it, no specific way is required))
Thank you.
Answer: 1) [tex]A = 28ft^{2}[/tex]
2) 55 points
Step-by-step explanation:
1) A= 8w + 18, w=1.25
A = 8(1.25) + 18
A = 10 + 18
A = 28ft^2
2) 25 points to start with, additional 5 points per magazine they sell, m = number of magazines they sell
total points = 25 + 5m
How many if they sell 6?
total = 25 + 5(6)
= 25 + 30
total = 55
The area of a rectangle is 48 square feet. The length is 8 feet longer than the width. 1) Which picture corresponds to the problem? 2) What are the dimensions of the rectangle?
Answer:
1) The picture whose width = x and Length = (x + 8) feet
2) Width = 4 feet
Length = 12 feet
Step-by-step explanation:
A rectangle has one side longer than the other.
Area of a rectangle = product of its sides.
= length × width
Width = x feet
Length = (x + 8) feet
Area = 48
∴ x × (x + 8) = 48
x² + 8x = 48
x² + 8x + 4² = 48 + 4²
(x + 4)² = 64
x + 4 = √64
x = ±8 - 4
x = - 12 or x = 4
Since length can not be negative, x = 4
∴ Width = 4 feet
Length =4 + 8 = 12 feet
The dimensions of the rectangle where its area is 48 square feet and length is 8 feet more than width is 4 feet (width) and 12 feet (length). The question is set on algebra, calculation of area and understanding of shapes.
Explanation:This problem falls under the category of algebra and involves understanding the concept of shapes, particularly rectangles, and calculation of their area.
We know, the area of a rectangle is calculated as the product of its length and width. Given that the area is 48 square feet and the length is 8 feet more than the width. Let's denote the width as 'w' and the length as 'w + 8'.
So, we can set up the equation as: w * (w + 8) = 48. Solving this quadratic equation will give us the values for 'w' and 'w + 8' or the dimensions of the rectangle.
If you factor the quadratic equation, you get (w - 4)(w + 12) = 0. Setting these factors to zero, we find that w = 4 or w = -12. Since width cannot be negative, the width is 4 feet. And the length, which is 8 feet more than the width, will be 4 + 8 = 12 feet.
For the picture representation, simply imagine or draw a rectangle. Label the shorter side as 4 feet (width) and longer side (length) as 12 feet.
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Can someone help me please
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Which statement above is true about the value of x
➷ Angles in a triangle equal 180 degrees
180 - (38 + 39) = 103
Angles on a straight line equal 180 degrees
180 - 103 = 77
The correct statement would be the first one as x is greater than 38
✽➶ Hope This Helps You!
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➶ Have A Great Day ^-^
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I REALLY NEED HELP!! PLEASE DO IT FAST!!
8,000÷(28x+4)−15=25
Answer:
x = 7
Step-by-step explanation:
Order of operations rules require that we do multiplication and division BEFORE addition and subtraction.
Let's start by simplifying the expression. Adding 15 to both sides results in:
8,000÷(28x+4) = 40.
Multiplying both sides by (28x + 4) results in the simpler:
8000 = 40(28x + 4).
Dividing both sides by 40 results in:
200 = 28x + 4, or
196 = 28x
Solve for x by dividing both sides by 28:
x = 7
A bag contains 6 red balls, 4 green balls, and 3 blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?
Answer:
2/13
Step-by-step explanation:
There are 6 + 4 + 3 = 13 balls all together.
If the first one is green, this will happen with a probability of 4/13. Now there are 12 balls left
There are 6 red balls. 6/12 = 1/2
The probability of the way this happens is 1/2 * 4/13 = 2/13
The gym teacher wants to know how many students play a sport. She asks 20 students throughout the day. What is the population?
Final Answer:
The population is the total number of students in the school.
Explanation:
The gym teacher's inquiry regarding the number of students playing a sport pertains to a subset of the larger student body. In statistical terms, the 20 students she questioned represent a sample.
The population, in this context, encapsulates the entirety of students attending the school, irrespective of whether they were asked about their sports participation or not.
When the gym teacher approached 20 students throughout the day, she was essentially drawing information from a limited group within the school. The population, however, extends beyond these 20 individuals to encompass every student enrolled in the institution.
This broader set includes students who might not have been present that day or were not approached by the teacher for their input. Determining the population aids in understanding the context and scale of the sampled data.
For instance, if the gym teacher's goal is to ascertain the percentage of students engaged in sports activities, the population figure (total number of students) becomes crucial for accurate statistical inference.
Consequently, the teacher can use this information to make informed decisions or implement strategies that cater to the entire student body, considering the interests and involvement in sports across the school.
What is the slope of the line show below?
Algebra form: y1 - y2, and x1 - x2.
( 2 - 1 ) ( 6 - 3 ).
= 1/3.
slope = 1/3.
which table represents a linear function
Answer:
option C
Step-by-step explanation:
Given table is a linear function when the change in y to change is x is a constant.
From the tables, difference of x is a constant 1
Lets look at the difference of y values
First table
We find the change in y values
[tex]-6+2=-4[/tex]
[tex]-2+6=+4[/tex]
the difference is not a constant. So it is not a linear
Second table
[tex]-5+2=3[/tex]
[tex]-9+5= 4[/tex]
the difference is not a constant. So it is not a linear
Third table
[tex]-10+2= -8[/tex]
[tex]-18+10=-8[/tex]
[tex]-26+18= -8[/tex]
the difference is a constant. So it is a linear function.
Find the value of x. The diagram is not to scale.
Answer:
x = 33
Step-by-step explanation:
There are 180 degrees in a triangle.
There are also 180 degrees in a straight line.
180 - 105 = 75.
Thus, 75+72+x=180.
x=33
Answer:
x=33
Step-by-step explanation:
Step one :
From the screen shot
The sum of angles on a straight line is 180° hence 180°-105°=75°
The unknown angle is 75°
Step two :
To find the angle x° the sum of angles in a triangle is 180°
Therefore
x°+72°+75°=180°
x+147=180
x=180-147
x=33°
each squuare on the grid paper is 1 square in find the area of the figure
Answer:
Count up however many squares are in the grip paper, and if it's not all the way full call it 1/2. Then add your half squares together, then add your whole squares to your half squares
Step-by-step explanation:
HELP PLSSSS ASAP!!!
The tenth in 149.95 is 9. To round it to the nearest tenth, use the hundredth. The hundredth is 5. When rounding, always round up when it is a 5. 95 should be rounded to 100, but it is a decimal. 100 as a decimal is equal to 1. 149 + 1 = 150.
Answer:
149.95 becomes 150 when rounded to the nearest tenth because 149.95 is only .5 away from 150. If it was something like 149.4 it would be rounded to 149.
Evaluate b^2 c^-1 for b = -4 and c = 2.
Answer:
8
Step-by-step explanation:
b^2 c^-1
Let b=-4 and c =2
(-4)^2 * (2)^-1
The negative exponent means it is in the denominator
(-4)^2 / (2)^1
16/2
8
Find the geometric mean of 12 and 27. Write
Answer:
The geometric mean is 18
Step-by-step explanation:
To find the geometric mean of two numbers, start by multiplying them together.
12 * 27 = 324
Now take the square root of that number
√324 = 18
The graph of f(x) is shown. What is the value of f (x) when x= -2?
Please explain this question to me because i really dont understand it and id like to learn.
What is the distance between -13 and 13 on a number line
Answer:
26 units
Step-by-step explanation:
Due to:
in the rect line, left to zero = 13 (absolute value)
in the rect line, right to zero = 13 (absolute value)
So the sum of each absolute value is the distance.
Best regards
need help with this...
Answer:
asfvbrgterwgwertbewgrq3geqgrewrgergergfergewrg
Step-by-step explanation:
What is the solution to the equation 4x-6=10x-3?
x=-2
x=-1/2
x=1/2
x=2
Answer:
x=-1/2
Step-by-step explanation:
4x-6=10x-3
Subtract 4x from each side
4x-4x-6=10x-4x-3
-6 =6x-3
Add 3 to each side
-6+3 =6x-3+3
-3 = 6x
Divide each side by 6
-3/6 = 6x/6
-1/2 =x
➷ 4x - 6 = 10x - 3
Add 3 to both sides:
4x - 3 = 10x
Subtract 4x from both sides:
- 3 = 6x
Divide both sides by 6:
x = -1/2
The correct answer would be B. x = -1/2
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➶ Good Luck (:
➶ Have A Great Day ^-^
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If AD equals 3X +3 CD equals X +9, what is the value of X?
Answer:
x=3
Step-by-step explanation:
2x+3=9
2x=6
x=3
What is the vertex of the quadratic function with a negative a value?
A) (2, 3)
B) (3, 2)
C) (-4, -4)
D) (-1, -0.5)
Answer:
C) (-4, -4)Step-by-step explanation:
If y = ax² + bx + c has negative value of a, then a parabola is open down.
Look at the picture.
Vertex = (-4, -4)
Answer:
C) (-4, -4)
Step-by-step explanation:
Write the following as algebraic expressions:
On each of n plates there are k apples and m pears. What is the total number of fruit are there on these plates?
PLEASE HELP!
50 points!
The average number of accidents is 3 per month, what is the probability of 1 accident?
The answer is: 33.33%
Why?Since we have the average number of accidents that occurs in 1 month, and it's equal to 3, we can calculate the probability of 1 accident occurs by dividing it into the average number of accidents, using the following formula:
[tex]Probability=\frac{FavorableOutcomes}{Outcomes}*100[/tex]
Where,
Favorable outcomes are the occurrence of the event, for this case, it's equal to 1.
Outcomes are the possible occurrence of the event, for this case, it's equal to 3.
So, by substituting we have:
[tex]Probability=\frac{1}{3}*100[/tex]
[tex]Probability=0.3333*100=33.33[/tex]
So, the probability will be equal to 33.33%
Have a nice day!
can someone explain please
Answer:
[tex]\large\boxed{B.\ \dfrac{7}{4}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\Delta y}{\Delta x}=\dfrac{14}{8}=\dfrac{14:2}{8:2}=\dfrac{7}{4}[/tex]
x+2y=6 how do I solve this ?
Answer:
The answer is 4y
Step-by-step explanation:
This is because when you have a variable and 2 numbers you work backwards to find the number of the x so you do the opposite of adding you subtract, 2 - 6 remember you are working backwards but now you have the answer 4 but there is a variable next to the two so you so you add that to the four.