Answer: OPTION D
Step-by-step explanation:
Given the functions [tex]f(x) = x^2 - 2x + 9[/tex] and [tex]g(x) = 8 - x[/tex], you need to substitute the function g(x) into the function f(x), then:
[tex](fog)(x)=(8-x)^2 - 2(8-x) + 9[/tex]
Now, you need substitute the input value [tex]x=-4[/tex] into [tex](fog)(x)[/tex], then you get the following output value:
[tex](fog)(-4)=(8-(-4))^2 - 2(8-(-4)) + 9[/tex]
[tex](fog)(x)=(8+4)^2 - 2(8+4) + 9[/tex]
[tex](fog)(x)=(12)^2 - 2(12) + 9[/tex]
[tex](fog)(x)=129[/tex]
This matchis with the option D
Find the 18th term of the sequence 5, 8, 11, 14, 17...
Answer:
The answer would be 56.
Answer:
56 will be your answer
Step-by-step explanation:
20 23 26 29 32 35 38 41 44 47 50 53 56
Please mark Brainiest.
Find the angles of a rhombus if the ratio of the angles that the diagonals form with a side is 6:9.
Answer:
The measures of the angles of the rhombus are 72° , 108° , 72° , 108°
Step-by-step explanation:
* Lets revise the properties of the rhombus
- It has 4 equal sides
- Each two opposite angles are equal
- Each two adjacent angles are supplementary (their sum = 180°)
- The diagonals are perpendicular to each other
- The diagonals bisect the vertices angles (divide each vertex into two
equal parts)
* Now lets solve the problem
- Let the name of the rhombus is ABCD
- The two diagonals are AC and BD
- Let the diagonals AC and BD make the angles BAC and ABD with
side AB
∵ The diagonals of the rhombus bisect the vertex angles
∴ m∠BAC is half m∠A
∴ m∠ABD is half m∠B
- There is a ratio between the measures of the angles BAC and ABD
∵ m∠BAC : m∠ABD = 6 : 9
∵ m∠A + m∠B = 180° ⇒ consecutive angles
∴ m∠BAC + m∠ABD = 1/2 × 180° = 90°
∵ m∠BAC : m∠ABD : their sum
6 : 9 : 15⇒(6 + 9)
? : ? : 90° ⇒(the sum of the angles)
∴ m∠BAC = 6/15 × 90° = 36°
∴ m∠ABD = 9/15 × 90° = 54°
∵ m∠BAC is half m∠A
∴ m∠A = 36° × 2 = 72°
∵ m∠ABD is half m∠B
∴ m∠B = 54° × 2 = 108°
* The measures of the angles of the rhombus are 72° , 108° , 72° , 108°
Answer:
72°, 108°, 72°, and 108°
Notes:
You should probably give the other person Brainliest, the answered first and they have a better explanation.
A bowl contains 24 marbles consisting of 6 white marbles, 8 blue marbles, 7 black marbles, 3 red marbles. What is the probability of drawing a black marble?
6/24
5/24
17/24
7/24
Answer:
D 7/24
Step-by-step explanation:
Because on the first choice, there is a total of 24 marbles
if theres 7 black marbles the chance of pulling a black marble is 7/24
How many of those 100 customers would likely want the store to stay open late.
Answer:
Step-by-step explanation:
find the percentage of the people who want the store open longer. of the 40 customers that were surveyed, 12 would want that. 12 divided by 40 is .30, so 30 percent of the customers want it open.
100 more customers are surveyed, so you take 30 percent of 100, which is 30. your answer is "B"
Which sequence is generated by the function f(n 1) = f(n) – 2 for f(1) = 10? (a) –10, –12, –14, –16, –18, ... (b) –2, 8, 18, 28, 38, ... (c) 8, 18, 28, 38, 48, ... (d) 10, 8, 6, 4, 2, ...
Answer:
d
Step-by-step explanation:
Given
f(n + 1) = f(n) - 2 with f(1) = 10
To generate the sequence substitute values for n into the recursive formula.
f(1) = 10
f(2) = f(1) - 2 = 10 - 2 = 8
f(3) = f(2) - 2 = 8 - 2 = 6
f(4) = f(3) - 2 = 6 - 2 = 4
f(5) = f(4) - 2 = 4 - 2 = 2
The first 5 terms are 10, 8, 6, 4, 2
Answer:
D,10,8,6,4,2
Step-by-step explanation:
If a line with a slope of -2 crosses the y-axis at (0, 3), what is the equation of the line in slope intercept form
Answer:
y=-2x+3
Step-by-step explanation:
Slope intercept form is y = mx + b where m is the slope, b is the y-intercept, and y and x are their respective coordinates.
The questions gives us a coordinate pair and a slope so all we need to find is the y-intercept to find the equation.
Begin by plugging in what we know.
(3) = (-2)(0) + b
3 = 0 + b
3 = b
Plug in the y-intercept (b) and slope (m)
y=-2x+3
Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle rob will be three times Tonyas age
Answer:
i believe Tonya will be at least 26 years old or 34 years old.
Step-by-step explanation:
17+17=34
How many revolutions does a go kart with a wheel circumference of 62.8318 inches make in a 1609 m race? Please answer as quickly as possible!
Answer: 1008 revolutions
Step-by-step explanation:
1 revolution is equal to [tex]2\pi r[/tex]
To find how many revolutions the wheel makes, you must divide the distance traveled in the race between the circumference of the wheel
You must first convert 62.8318 in to meters.
We know that 1 inch is 0.0254 meters
Then
[tex]62.8318\ in*\frac{0.0254\ m}{1\ in}= 1.5959\ m[/tex]
[tex]revolutions = \frac{1609}{1.5959}\\\\revolutions=1008.21\\[/tex]
Finally The wheel made 1008.21 revolutions
Please help me
Show your work
Answer:
No, the ladder will not be save at the height 16.5 feet from the ground
She must to buy 9 rolls to have enough crepe papers to decorate her ceiling
Step-by-step explanation:
* Lets change the story problem to mathematics information
- The ladder , the wall and the ground formed together a right
angle triangle
- The wall and the ground are perpendicular to each other
- The length of the ladder is the hypotenuse of the triangle
- The vertical height of the ladder is the vertical leg of the triangle
- The horizontal distance between the ladder and the vertical wall
on the ground is the horizontal leg of the triangle
* Lets revise the trigonometry functions
- In any right angle triangle:
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
- For angle A
# sin(A) = opposite/hypotenuse
∵ The opposite to ∠A is BC
∵ The hypotenuse is AC
∴ sin(A) = BC/AC
# cos(A) = adjacent/hypotenuse
∵ The adjacent to ∠A is AB
∵ The hypotenuse is AC
∴ cos(A) = AB/AC
# tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB
* Lets solve the problem
- We need to calculate the measure of the angle between the
ladder and the ground, let it called Ф
- The vertical height is the opposite to this angle Ф
- The hypotenuse is the length of the ladder
∵ We have the opposite and the hypotenuse, we can use
the sin function
∵ sin(Ф) = opposite/hypotenuse
∵ The opposite is the vertical height = 16.5 feet
∵ The hypotenuse is the length of the ladder = 17 feet
∴ sin(Ф) = 16.5/17
∴ Ф = [tex]sin^{-1}\frac{16.5}{17}=76.1[/tex] dgree
- The ladder will be save if the angle between the ladder and
the ground is no more than 70°
∵ The angle between the ladder and the ground is 76.1°
∴ Its measure is greater than 70°
* The ladder will not be save at the height 16.5 feet from the ground
* Lets study the information in the problem
- Katie wants to put the crepe paper around the perimeter of the
ceiling which shaped a square of side length 12 feet
- And also from each corner to the opposite corner
- She needs the length of the 4 sides of the square and the length
of its 2 diagonals
* Lets find the length of the diagonal of the square
∵ The two adjacent sides of the square formed two legs of a right
angle triangle and the diagonal joining the endpoints of the legs
is the hypotenuse of the triangle
- Use Pythagoras theorem to find the length of the diagonal
∴ The length of the diagonal = √(s² + s²) √(2s²) = s√2
∵ The length of the side of the square = 12 feet
∴ The length of the diagonal = 12√2
* Now lets find the length of the crepe papers she needs
∵ She needs the length of the 4 sides of the square and the length
of its 2 diagonals
∴ The length of crepe papers = 12 + 12 + 12 + 12 + 12√2 + 12√2 = 81.94 feet
∵ Each roll of the crepe papers contain 10 feet
- To find the number of rolls divide the length of the crepe papers by 10
∴ The number of rolls = 81.94 ÷ 10 = 8.194
* She must to buy 9 rolls to have enough crepe papers to decorate
her ceiling
* V.I.N:
- If she decide to buy 8 rolls, some part of ceiling will not decorate
because the 8 rolls have 80 feet only and she needs 81.94 feet
Answer;
NO!!!!!!!!!!
Step-by-step explanation:
a^2 + b^2 =c^2
17^2 + b^2=16.5^2
289 + b = 272.25
-289 -289
b=[16.75
b=4.09
The two prisms below are similar. What is the value of x?
A. 30
B. 1
C. 9
D. 3
Answer:
D. 3
Step-by-step explanation:
If the prisms are said to the similar, that means that the ratio/relation between their corresponding sides have to equal, so
[tex]\frac{x}{1} = \frac{9}{3} = \frac{30}{10}[/tex]
We can easily use the part x/1 = 9/3 to make a cross-multiplication that would give us:
x = (1 * 9) / 3 = 9/3 = 3
So, the green prism is a dilated version of the blue one by a dilation/scale factor of 3.
As a math teacher, I would guide you through solving the problem of finding the value of \( x \) for two similar prisms. However, without specific information about the measurements of the prisms, we can't calculate this value. Similarity in prisms implies that corresponding lengths are proportional, but without knowing these lengths or their ratios, we can't determine \( x \).
However, let's assume you have provided the dimensions for both prisms. For similar prisms, the ratio of any two corresponding linear measurements (such as the height, width, or depth) is the same. If we were given that the ratio of a pair of corresponding dimensions is 1:3, for example, then all other pairs of corresponding dimensions would also have a 1:3 ratio.
Here's a typical process to follow if you had the dimenions:
1. Determine the ratio of corresponding lengths:
Suppose for the smaller prism, a certain length is given as 'a', and for the corresponding length on the larger prism, the length is given as '3a' (implying a 1:3 ratio for the sides).
2. Apply the ratio to unknown lengths:
If 'x' is an unknown length on the larger prism and its corresponding length on the smaller prism is given as some value 'b', then we set up the proportion \( \frac{b}{x} = \frac{1}{3} \).
3. Solve for 'x':
To find 'x', you would solve the proportion by cross-multiplying and dividing as necessary, \( x = 3b \).
However, since we don't have actual numbers here, we can't follow these steps. To answer this question, I would need specific lengths for the corresponding sides of the prisms. Once provided, I can demonstrate the mathematical process to find \( x \). For now, there is not enough information to solve for \( x \), and none of the options A, B, C, or D can be verified as correct.
what is the period of the parent cosine function, y = cos(x)
Answer:
2π
Step-by-step explanation:
This is a little something you have to memorize, but you could derive it from the equation pb = 2π. In the parent function, the b value is 1, so the period, p, is equal to 2π/1 or just 2π.
What is the period of the parent cosine function, y = cos(x)?
360 degrees
What is the period of the cosine function shown in the graph?
1080 degrees
Which type of transformation of the parent function is shown by the graph?
horizontal stretch
10 points. The diameters of two circles are in the ratio of 2:3. Find the area of the smaller circle if the area of the larger is 63π square meters.
[tex]63 \times \frac{2}{3} = \frac{63 \times 2}{3} = \frac{126}{3} = 42 \\ [/tex]
The area of the smaller circle is
[tex]42\pi \: square \: meters[/tex]
Find the value of x, rounded to the nearest tenth.
Answer:
x= 36.2
Step-by-step explanation:
Because that's a right triangle and the reference angle and adjacent side measures are given to us, we can use the trig ratio for cosine. Cosine relates the side adjacent to (next to...NOT ever the hypotenuse!) the angle to the hypotenuse. Therefore, our equation will look like this:
[tex]cos(28)=\frac{32}{x}[/tex]
Solving for x we have
[tex]x=\frac{32}{cos(28)}[/tex]
Perform that operation on your calculator in degree mode and you'll get that the length of the hypotenuse is 36.2. If for some reason, your math gave you the length of the hypotenuse and it was shorter than one of the other sides, you did something wrong. The hypotenuse will ALWAYS be the longest side in a right triangle.
A plane flying against the wind flew 270 miles in 3 hours. Flying with the wind, the plane traveled 260 miles in 2 hours. Find the rate of the plane in calm air and the rate of the wind. I want to know the answer for this pleasee
Answer:
The plane would have been going the amount as it supposed to g.
Step-by-step explanation:
The plane flying against the wind is going 90 mph and the plane flying with the wind is traveling at 130 mph. Your welcome
Which expressions are perfect cubes? –1,000,27r21,343p, g3h30 , 1
Answer:
Step-by-step explanation:
1000 = 10³ is a perfect cube.
27r^21 can be re-written as (3r^7)³ and is a perfect cube.
343p can be rewritten as (7)³·∛p. (7)³ is a perfect cube, but ∛p is not.
g³h^30 can be rewritten as (g·h^10)³ and is a perfect cube.
1 is a perfect cube: 1³ = 1
Answer:
A, B, D, E
Step-by-step explanation:
A = 1,000
B = [tex]27r^{21}[/tex]
D= [tex]g^{3}h^{30}[/tex]
E = 1
(just took it on edge)
Consider the two equations, y=5(x-2)^2-6 and (y+2)^2=9
How many solutions are there to this system? Without solving, give a convincing argument explain why there are that many solutions to the system.
Answer:
One solution. A system of linear equations has one solution when the graphs intersect at a point.
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
yy
y
xx
x
No solution. A system of linear equations has no solution when the graphs are parallel.
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
yy
y
xx
x
Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.
Step-by-step explanation:
A bag contains blue and green marbles. The probability of drawing a green marble and then a blue marble, P(G, then B), without replacement is 14⋅1. How many green and blue marbles are in the bag at the beginning?
A. 1 green and 4 blue
B. 4 green and 1 blue
C. 1 green and 3 blue
D. 3 green and 1 blue
Answer:
the answer is C
Step-by-step explanation:
I THOUGHT IT WAS B BUT I WAS WRONG
1 green and 3 blue are in the bag at the beginning.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
The sum has been solved using a tree diagram.
To know more about probability refer to :
https://brainly.com/question/24756209
#SPJ2
Does each situation describe a survey, an experiment, or an observational study?
Select Survey, Experiment, or Observational Study for each situation.
Answer:
Observational study, survey, experiment
Step-by-step explanation:
The first is an observational study. The children make the choices and the choices are observed.
The second one is a survey. The employees are given questionnaires to answer.
The third one is an experiment. The nurse selects random samples to compare the effects of different ointments.
Charlene's swimming pool is rectangular. It has an area of 120 ft2. Charlene drew a scale drawing of the pool using the scale LaTeX: 1\frac{1}{2} 1 1 2 centimeters = 2 feet. What was the area of the scale drawing?
Answer:
The area of the scale drawing is [tex]67.5\ cm^{2}[/tex]
Step-by-step explanation:
The scale drawing is
[tex](1\frac{1}{2})/2\ \frac{cm}{ft}[/tex]
Convert to an improper fraction
[tex](1\frac{1}{2})=3/2[/tex]
substitute
[tex](1\frac{1}{2})/2=(3/4)=0.75\ \frac{cm}{ft}[/tex]
The area is equal to
[tex]120\ ft^{2}[/tex]
substitute
[tex]120*(0.75)^{2}=67.5\ cm^{2}[/tex]
The area of the scale drawing of Charlene's swimming pool is [tex]\( 67.5} \)[/tex] square feet.
To find the area of the scale drawing of Charlene's swimming pool, we need to understand the scale given and how it applies to the dimensions and area.
Given:
Actual area of the swimming pool: [tex]\( 120 \) ft\(^2\)[/tex]
Scale of the drawing: [tex]\( 1 \frac{1}{2} \) centimeters = 2 feet[/tex]
First, convert the scale to centimeters:
[tex]\[ 1 \frac{1}{2} \text{ centimeters} = 1.5 \text{ centimeters} \][/tex]
Now, determine the scale factor for the dimensions:
[tex]\[ \text{Scale factor} = \frac{1.5 \text{ cm}}{2 \text{ ft}} \][/tex]
To find the area of the scale drawing, we need to square the scale factor, because area is two-dimensional:
[tex]\[ \text{Area scale factor} = \left(\frac{1.5}{2}\right)^2 \][/tex]
[tex]\[ \text{Area scale factor} = \left(0.75\right)^2 \][/tex]
[tex]\[ \text{Area scale factor} = 0.5625 \][/tex]
Now, calculate the area of the scale drawing:
[tex]\[ \text{Area of scale drawing} = 0.5625 \times 120 \text{ ft}^2 \][/tex]
[tex]\[ \text{Area of scale drawing} = 67.5 \text{ ft}^2 \][/tex]
Please help me out with this
Answer:
48
Step-by-step explanation:
central angle with arc of <y is 96
so circumference angle 48
Answer:
y = 48°
Step-by-step explanation:
The angle on the circle ( the inscribed angle ) y is half of the central angle subtended by the same arc on the circle, hence
y = 0.5 × 96° = 48°
Garvey’s Electronics store is having a storewide sale. For a television set with a regular price of x dollars, a 15 percent discount is equal to $30. Which of the following equations could NOT be used to determine x?
0.15x = 30
0.85x = x – 30
0.15x = x – 30
x – 0.15x = x – 30
Answer:
0.15x=x-30
Step-by-step explanation:
Let
x-----> the regular price
we know that
15%=15/100=0.15
so
0.15x=30
x=30/0.15=$200
Verify each case
case a) 0.15x=30
x=30/0.15=$200
therefore
The equation could be used to determine x
case b) 0.85x=x-30
x-0.85x=30
0.15x=30
x=30/0.15=$200
therefore
The equation could be used to determine x
case c) 0.15x=x-30
x-0.15x=30
0.85x=30
x=30/0.85=$35.29
therefore
The equation could not be used to determine x
case d) x-0.15x=x-30
-0.15x=-30
0.15x=30
x=30/0.15=$200
therefore
The equation could be used to determine x
What are the domain and range of f(x) = (1/6)x + 2? domain: ; range: {y | y > 0} domain: ; range: {y | y > 2} domain: {x | x is a real number}; range: {y | y > 2} domain: {x | x is a real number}; range: {y | y > –2}
Final answer:
The domain of f(x) = (1/6)x + 2 is all real numbers and the range is y > 2.
Explanation:
The domain of the function f(x) = (1/6)x + 2 is {x | x is a real number} because there are no restrictions on the input values. The range of the function is {y | y > 2} because any value of x will give a y-value greater than 2. To find the range, you can consider that the slope of the function is positive, meaning that as x increases, y will also increase, but it will never go below 2.
What is the standard deviation for the data set?
359, 320, 365, 310, 349, 351, 310, 314, 364
Express your answer as a decimal to the nearest tenth
Answer:
The standard deviation is 22.6 to the nearest tenth
Step-by-step explanation:
* Lets study how to find the standard deviation (σ) for data set
- First step find the mean of the data
∵ The mean = the sum of the data ÷ the number of the data
# The sum of the data is
359 + 320 + 365 + 310 + 349 + 351 + 310 + 314 + 364 = 3042
# The number of the data is 9
∴ The mean = 3042 ÷ 9 = 338
- Second step find the difference between each data and the mean
and square the difference
# 359 - 338 = 21 ⇒ (21)² = 441
# 320 - 338 = -18 ⇒ (-18)² = 324
# 365 - 338 = 27 ⇒ (27)² = 729
# 310 - 338 = -28 ⇒ (-28)² = 784
# 349 - 338 = 11 ⇒ (11)² = 121
# 351 - 338 = 13 ⇒ (13)² = 169
# 310 - 338 = -28 ⇒ (-28)² = 784
# 314 - 338 = -24 ⇒ (-24)² = 576
# 364 - 338 = 26 ⇒ (26)² = 676
- Third step find the variance (σ²)
# Add all the square difference and divide the sum by the
number of data
∴ σ² = (441 + 324 + 729 + 784 + 121 + 169 + 784 + 576 + 676) ÷ 9
∴ σ² = 4604 ÷ 9 = 511.5555556
- Fourth step find the standard deviation σ it is the square root of
the variance
∴ σ = 22.6 to the nearest tenth
* The standard deviation is 22.6 to the nearest tenth
Answer:
24.0
Step-by-step explanation:
i took the test on k12
Cadence is substituting t=4 and t=6 to determine if the two expressions are equivalent.
2(7t-3)
15t(-12)
Which statement is true?
a. Both expressions are equivalent to 78 when t=6.
b. Both expressions are equivalent to 81 when t=6.
c. Both expressions are equivalent to 48 when t=4.
d. The expressions are equivalent.
Answer:
Both expressions are equivalent to 78 when t = 6 ⇒ answer A
Step-by-step explanation:
* To solve this problem substitute the value of t and then check
the answer
∵ The first expression is 2(7t - 3) ⇒ simplify it
# 2(7t) = 14t
# 2(3) = 6
∴ 2(7t - 3) = 14t - 6
- Substitute t by 4
∴ 14t - 6 = 14(4) - 6 = 56 - 6 = 50
- Substitute t by 6
∴ 14t - 6 = 14(6) - 6 = 84 - 6 = 78
∵ The second expression is 15t - 12
- Substitute t by 4
∴ 15t - 12 = 15(4) - 12 = 60 - 12 = 48
- Substitute t by 6
∴ 15t - 12 = 15(6) - 12 = 90 - 12 = 78
- The first expression has two values
# 50 when t = 4
# 78 when t = 6
- The second expression has two values
# 48 when t = 4
# 78 when t = 6
- From these information
# The two expressions have the same value 78 when t = 6
∴ Both expressions are equivalent to 78 when t = 6
given any triangle ABC labeled as shown, the law of sines states that:
Answer:
A. The ratios of the sine of the angle to the opposite side are the same.
Step-by-step explanation:
The law of sines is ...
sin(A)/a = sin(B)/b = sin(C)/c
Answer:
Option A is correct that is the ratio of the sine of an angle to the length of the opposite side is the same for all part of the triangle.
Step-by-step explanation:
Given:
Three angles of the triangles = ∠A , ∠B and ∠C
Three Sides of the triangle = a , b , c
We need to find statement which states the Law of Sines.
We know that Law of Sines is given by,
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]
or
[tex]\frac{sin\,A}{a}=\frac{sin\,B}{b}=\frac{sin\,C}{c}[/tex]
Therefore, Option A is correct that is the ratio of the sine of an angle to the length of the opposite side is the same for all part of the triangle.
A clothing store sells T-shirts, t, for $8 a shirt; shorts, s, for $12; and hats, h, for $10 each. The store earned $406 in revenue last month. The store sold three times as many T-shirts than hats, and twice as many shorts as hats. Using the substitution method, how many T-shirts, shorts, and hats did the store sell?
Step-by-step explanation:
From the total revenue, we know that:
8t + 12s + 10h = 406
We're also told:
t = 3h
s = 2h
If we substitute these for t and s:
8 (3h) + 12 (2h) + 10h = 406
24h + 24h + 10h = 406
58h = 406
h = 7
Now we can find t and s:
t = 3h = 21
s = 2h = 14
The store sold 21 T-shirts, 14 shorts, and 7 hats.
The clothing store has sold a total of 21 t-shirts, 7 hats, and 14 shorts.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given,
T-shirts, t, for $8 a shirt; shorts, s, for $12; and hats, h, for $10 each and stored earn $406
So,
8t + 12s + 10h = 406
And
the store sold three times as many T-shirts than hats
So,
t = 3h
And
twice as many shorts as hats.
s = 2h
By substituting t and s into the equation first
8(3h) + 12(2h) + 10h = 406
h = 7
Now
t = 21 and s = 14.
Hence, The clothing store has sold a total of 21 t-shirts, 7 hats, and 14 shorts.
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What is the measure of
Answer:
91
Step-by-step explanation:
The lines that are parallel are parallel and because of that 89+91=180 for two angles of the square on the same side.
Which pairs of polygons are congruent?
A. pairs 1, 2, and 3
B. pairs 1, 2, 3, and 4
O c. pairs 2 and 3
OD. pairs 1 and 3
the volume of rectangular prism that measures 7 meters long, 9 meters wide, and 6 meters high is 378m^3
True or False
Answer:
Step-by-step explanation:
True
7 X 9 X 6 = 378
Answer:
First option: True.
Step-by-step explanation:
To know if the volume of this rectangular prism is 378 m³, you need to use the formula for calculate the volume of a rectangular prism:
[tex]V=lwh[/tex]
Where "l" is the lenght, "w" is the width and "h" is the height.
You know that that this rectangular prism measures 7 meters long, 9 meters wide, and 6 meters high, then you can substitute these values into the formula.
Therefore, the volume of the rectangular prism is:
[tex]V=(7m)(9m)(6m)\\V=378m^3[/tex]
Then the answer is: True.
Please show all work
Answer:
I. 336 ft²Step-by-step explanation:
We have
two right triangle with legs 6ft and 8ft
one rectangle 8ft × 12ft
one rectangle 6ft × 12ft
one rectangle 10ft × 12ft
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
a,b - legs
Substitute:
[tex]A_1=\dfrac{(6)(8)}{2}=(3)(8)=24\ ft^2[/tex]
The formula of an area of a rectangle:
[tex]A=lw[/tex]
l,w - length, width (dimensions of rectangle)
Substitute:
[tex]A_2=(6)(12)=72\ ft^2\\\\A_3=(8)(12)=96\ ft^2\\\\A_4=(10)(12)=120\ ft^2[/tex]
The Surface Area:
[tex]S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=(2)(24)+72+96+120=336\ ft^2[/tex]