Answer:
120 degrees
Step-by-step explanation:
The angles in a pentagon add up to 540 degrees. This means that we can set up an equation to find this. We'll call the measure of the angle that we want to find x.
112+68+3x=540
Solving this, we get 180+3x=540, and 3x=360. That means that x is 120 degrees.
The interior angles of the pentagon is A = { 112° , 68° , 120° , 120° , 120° }
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the polygon be represented as A = pentagon
The number of sides n = 5
So , the sum of interior angles of A = nθ = 180 ( n - 2 )
nθ = 180 ( 5 - 2 ) = 540°
The 2 angles of the pentagon = 112° , 68°
And , let the remaining angles = x + x + x
So , x + x + x + 112° + 68° = 540°
On simplifying , we get
3x + 180° = 540°
3x = 360°
x = 120°
Hence , the angles are 120° each
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15-3 as a numerical expression
Answer:
12
Step-by-step explanation:
simplify: 15 + -3
combine: 15 + -3 = 12
The numerical expression 15-3 is equal to 12.
Explanation:A numerical expression is a mathematical phrase containing only numbers and operational symbols (such as +, -, *, /) without any variables. It represents a specific value when the numbers are replaced with actual values. For example, "3 + 5 * 2" is a numerical expression that evaluates to 13.
The numerical expression 15-3 can be solved by subtracting 3 from 15. You can start with the number 15 and subtract 3 to get the result.
15 - 3 = 12
So, the numerical expression 15-3 is equal to 12.
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MP2 Reasoning Joel is 23 inches
shorter than Carlos Carlos is 12 inches
taller than Dan. If Dan is 587 inches ta
how many inches tall is Joel?
Answer: 576 inches
Step-by-step explanation:
Carlos’ height :587+12=599
Joel’s height: 599-23=576
:)
Answer:
Step-by-step explanation:
Height of Dan = 587 inches
Height of Carlos = 587 + 12 = 599 inches
Height of Joel = 599 - 23 = 576 inches
factory workers make $15 per hour and work 40 hours per week. how much should the Radcliff Company budget for salary each week if they have 250 workers?
Answer:
123,000
Step-by-step explanation: 40×15=600
For 1 worker
600×250=123,000
For all 250 workers
Which of the following shows the expression −3t2−2t(4s−9t)+7st in simplest form
Answer:
15t^2-ts
Step-by-step explanation:
-3t^2-2t(4s-9t)+7ts
-3t^2-8ts+18t^2+7ts
-3t^2+18t^2-8ts+7ts
15t^2-ts
The expression −3t^2−2t(4s−9t)+7st can be simplified to 15t^2-st.
Explanation:This expression is a quadratic equation in the form of −3t^2−2t(4s−9t)+7st. To simplify, we can start by distributing the -2t across the terms inside the parentheses:
−3t^2−8st+18t^2+7st
Combining like terms, we get:
15t^2-st
So, the expression −3t^2−2t(4s−9t)+7st in simplest form is 15t^2-st.
Two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. Which Sedona transformation will result in a image that is similar to, but not congruent to, the original figure?
A. A clockwise rotation of 90 degrees about the center
B. A clockwise rotation of 180 degrees about the center
C. A dilation by a scale factor of 1 with the origin as the center of a dilation
D. A dilation by a scale factor of 1/2 with the origin as the center of dilation
Answer:
Only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
Step-by-step explanation:
When we transform a certain shape, we normally associate the original shape as 'object', while the transformed shape is associated as "image',
If any shape like triangle, parallelogram or any other certain quadrilateral is rotated, reflected or translated, it wold preserve the same size. Hence, the resulting transformed image would be similar and also called 'congruent' to the original object.
But, if any shape like triangle, parallelogram or any other certain quadrilateral is enlarged or resized, it would certainly change in size. Therefore, the resulting transformed image would still be considered as similar, but it would no longer congruent to the original object.
Hence, when two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. A dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
In all other cases, like a clockwise rotation of 90 degrees about the center, A clockwise rotation of 180 degrees about the center and a dilation by a scale factor of 1 with the origin as the center of a dilation would not not alter the size of the shape, and the resulting transformed image would be similar as well as called 'congruent' to the original object.
Hence, only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
Therefore, only option D is correct.
Keywords: dilation, transformation
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The Sedona transformation that will result in an image that is similar to, but not congruent to the original figure is D. A dilation by a scale factor of 1/2 with the origin as the center of dilation.
How to get an image that is similar but not congruent to the original figure?To get an image that is similar but not congruent to the original figure, we shall perform a transformation that changes the size of the figure while keeping the same shape.
This is because when a figure is translated 8 units to the left, its position changes, but its size and shape remain the same.
A dilation by a scale factor of 1/2 with the origin as the center of dilation means the image would be reduced to half of its original size while maintaining the same shape.
This transformation results in a figure that is similar but not congruent to the original figure, as it has the same shape but a different size.
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Jim went to a carnival with $25.00. He bought some food for $3.75. Jim wants to spend the rest of his money on tickets for rides, r, which cost $1.25 each. Which represents, r, the number of tickets Jim can purchase?
(A) r is < than equal to 17
(B) r is > greater than equal to 17
(C) r is < less than equal to 20
(D) r is > greater than equal to 20
Answer:
(A) [tex]r[/tex] is < than equal to 17
Step-by-step explanation:
Total amount Jim had for the carnival =$25.00
Amount spent on food = $3.75
Amount left with him = [tex]\$25.00-\$3.75=\$21.25[/tex]
Jim plans to sped rest on tickets for rides.
Cost of each ride ticket = $1.25
Given: [tex]r[/tex] represents the number of ride tickets bought.
Using unitary method
If 1 ride ticket cost = $1.25
Cost of [tex]r[/tex] ride tickets in dollars will be = [tex]1.25r[/tex]
Amount spent on rides must be less than or equal to the total amount left with Jim which is =$21.25.
So, we have:
⇒ [tex]1.25r\leq 21.25[/tex]
Dividing both sides by 1.25.
⇒ [tex]\frac{1.25r}{1.25}\leq \frac{21.25}{1.25}[/tex]
∴ [tex]r\leq 17[/tex]
Thus, the inequality representing te number of tickets Jim can purchase is given by:
[tex]r\leq 17[/tex]
Solve the linear system of equations using the linear combination method
4x +5y=7
y=3x+9
Enter your answers in the boxes.
x=
y=
Answer:
x = -2
y = 3
Step-by-step explanation:
Write the system the following way:
4x + 5y = 7
-3x +y = 9
we need to eliminate one unknown by multiplying one equation for a suitable number in such a way that when we add the equations one unknown is eliminated.
If we multiply the second eq. by -5 the y is eliminated
4x + 5y = 7
15x -5y = -45
add the equations
19x = -38 ===> x = -38/19 ===> x = -2
Now replace this value in any equation to get y. For example, in 1st one.
4(-2) + 5y = 7 ===> -8 +5y = 7 ===> 5y = 7+8 ===> 5y = 15 ===> y = 15/5 ===>
y=3
Let $x=(0.\overline{6})(0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?
Answer:
32
Step-by-step explanation:
The sum of the first $15$ digits is 32.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Let $x = 0.666666.....
$x = = 6/9 = 2/3
And .606060..... = 60/99
⇒(2/3) (60/99)
⇒ (2/99)(60/3)
⇒(2/99)(20)
⇒ 40/99
⇒ .040404.........
So, the sum of the first 15 digits = 8(4) + 7(0) + 0 = 32
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Let a = x2 + 4. Use a to find the solutions for the following equation:
(x2 + 4)2 + 32 = 12x2 + 48
Which of the following are solutions for x?
The solutions for x are -2, 0, 2
Solution:
Given that,
[tex]\text { Let } a = x^2 + 4[/tex]
Given equation is:
[tex](x^2 + 4)^2 + 32 = 12x^2 + 48[/tex]
[tex](x^2 + 4)^2 + 32 = 12(x^2 + 4)[/tex]
[tex]\text { Subtsitute } a = x^2 + 4 \text{ in above equation }[/tex]
[tex]a^2 + 32 = 12a\\\\a^2 -12a + 32 = 0[/tex]
[tex]\text{ Let us factorize the above equation }\\\\\text{ Splitting the middle term -12a as -4a - 8a we get, }[/tex]
[tex]a^2 -4a - 8a + 32 = 0[/tex]
Taking "a" as common term from first two terms and taking "-8" as common from last two terms
[tex]a(a-4)-8(a - 4) = 0[/tex]
[tex]\text{Taking (a - 4) as common term, }\\\\(a - 4)(a - 8) = 0[/tex]
[tex]\text{Equating to zero we get, }\\\\(a - 4) = 0 \text{ or } (a - 8) = 0\\\\a = 4 \text{ or } a = 8[/tex]
[tex]\text{Now substitute the value of a = 8 and a = 4 in: }\\\\a = x^2 + 4[/tex]
[tex]\text{ For a = 8: }\\\\a = x^2 + 4\\\\8 = x^2 + 4\\\\x^2 = 4\\\\x = \pm2\\\\x = +2 \text{ or } -2[/tex]
[tex]\text{For a = 4: }\\\\a = x^2 + 4\\\\4 = x^2 + 4\\\\x = 0[/tex]
[tex]\text{Thus solutions of } x \text{ are: }\\\\x = 0 \text{ or } x = 2 \text{ or } x = -2[/tex]
20 points
The graphs of functions f and g are shown below.
a) Find all values of x for which f(x)=g(x).
b) Find all values of x for which f(x)
c) Find all values of x for which f(x)>g(x).
Answer:
a) x=-10,0,11
b) x<-10, 0<x<11
c) x>11, -10<x<0
Step-by-step explanation:
a) Find all the intersecting points of the two graphs.
b) Find all the x values when g(x) (the curving one) is higher than f(x). g(x) or f(x) is kind of like the y coordinate in these graphs. There for to find when f(x)<g(x), you have to find when g(x) is above f(x). Any part of g(x) above the intersecting points is your answer. So we can see that at -10, the curving line is above the straight one, f(x). There for that would be when x<-10, g(x)>f(x). Use these intersection points to figure out the rest.
c) Find all the x values of when the curving line, g(x) is below f(x), the straight line. Use the points where the two lines intersect t start off your answer. For example, we can see the curved line is below the straight one between -10 and 0. Therefore, f(x)>(g) when -10<x<0. x>11 is the only other moment when g(x), the curving line is also below f(x).
I also struggled with this question and I tried my best to explain.
A drill team is raising money by holding a car wash. The team earns $6.00 for each car washed. The team's expenses include $50.00 for advertising plus $0.50 in materials for each car washed. Let f(x) represent the team's total earning for washing x cars and g(x) represent the team's total expenses for washing x cars. Describe how you can use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars. Then write a rule for p(x)
The function p(x) is obtained by subtracting g(x) from f(x)
The rule of p(x) is p(x) = 5.5 x - 50
Step-by-step explanation:
A drill team is raising money by holding a car wash
The team earns $6.00 for each car washedThe team's expenses include $50.00 for advertising plus $0.50 in materials for each car washedf(x) represent the team's total earning for washing x carsg(x) represent the team's total expenses for washing x carsp(x) that gives the team's profit for washing x carsWe need to describe how can you use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars, and then write a rule for p(x)
∵ The team earns $6.00 for each car washed
∵ f(x) represent the team's total earning for washing x cars
- Equate f(x) by the product of x and 6
∴ f(x) = 6 x
∵ The team's expenses include $50.00 for advertising plus $0.50
in materials for each car washed
∵ g(x) represent the team's total expenses for washing x cars
- Equate g(x) by the sum of 50 and the product of 0.5 and x
∴ g(x) = 50 + 0.5 x
The profit = total earning - total expenses
∵ f(x) is the total earning for washing x cars
∵ g(x) is the total expenses for washing x cars
∵ p(x) represents the team's profit for washing x cars
- Subtract g(x) from f(x) and equate the difference by p(x)
∴ p(x) = f(x) - g(x)
The function p(x) is obtained by subtracting g(x) from f(x)
∵ f(x) = 6 x
∵ g(x) = 50 + 0.5 x
∴ p(x) = 6 x - (50 + 0.5 x)
- Simplify the right hand side
∴ p(x) = 6 x - 50 - 0.5 x
- Add the like term
∴ p(x) = 5.5 x - 50
The rule of p(x) is p(x) = 5.5 x - 50
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What is 20% as an whole number
Final answer:
20% does not directly convert into a whole number; it represents a fractional part of a whole. If you look at the percent as a part of some quantity, you calculate 20% of that quantity to find the represented part. However, 20% by itself is 0.20 in decimal form, not a whole number.
Explanation:
What is 20% as a whole number?
When talking about percentages, it's important to understand that a percent is a way of expressing a fractional amount as part of a whole divided into 100 parts. For example, 5% means 5 out of 100.
In the case of 20%, you are looking at 20 out of 100. As a whole number, however, percentages less than 100% do not directly convert since they represent a part of a whole, not the whole itself. 20% can be represented as 0.20 in decimal form, which still does not constitute a whole number. The closest concept related to whole numbers would be if you had some quantity that you wish to find 20% of; you would then calculate 20% of that number to find the part it represents. But the 20% by itself remains a fraction, not a whole number.
Which terms complete the factorization of x2+27x+162
represented by the model?
27, 9x, 18%
9, 9x, 18x
27, 9x, 27x
9, 9x, 27x
Answer:
B. 9, 9x, 18x
Step-by-step explanation:
The value in each box is the product of the row heading and column heading. You can find the missing column heading by dividing the box value (162) by the row heading (18).
The correct terms are 9, 9x, and 18x. Hence, option B is correct.
To factorize the quadratic expression x² + 27x + 162, we need to find two numbers that multiply to 162 (the constant term) and add up to 27 (the coefficient of x). These numbers are 9 and 18.
Identify the constant term (162) and the coefficient of the linear term (27).
Find two numbers that multiply to 162 and add to 27. These numbers are 9 and 18.
Rewrite the middle term using these numbers: x² + 9x + 18x + 162.
Factor by grouping: (x² + 9x) + (18x + 162).
Factor out the greatest common factor from each group: x(x + 9) + 18(x + 9).
Factor out the common binomial factor: (x + 9)(x + 18).
Therefore, the factorization of x² + 27x + 162 is (x + 9)(x + 18).
Based on this factorization, the correct terms from the choices provided are (B) 9, 9x, and 18x.
What percent of time does marissa spend playing basketball ? Show or explain how you got your answer?
Walking 45percent
Jogging 15 percent
Swimming 10 percent
Bowling 10 percent
Answer:
20% of the time
Step-by-step explanation:
Marissa spends 20% of the time playing basketball. I figured this out my subtracting all of the other sports from 100% , (the whole), to get 20%.
Hope this helps :)
I need help please and thank you
Answer:
10 000
Step-by-step explanation:
For each choice of the first two digits you have 10 choices for the third digit. Thus you have 10x10x10 = 1000 choices for the first three digits. Finally you have 10 choices for the fourth digit and thus there are 10x10x10x10 = 10 000 possible 4 digit combinations from 0-9.
If tan 0=11/60, what is the value of cot 0?
Answer:
Step-by-step explanation:
tan 0 = 1/ cot 0
so, tan 0=11/60,
cot 0= 1/ (11/60)
cot 0= 60/ 11
standard form of x^2 + 16x + 71
Answer:
It's (-8,7) I believe, I hope this helps!
Step-by-step explanation:
there are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter. to the nearest inch, how many meters are in 511 inches
12.9794 meters or 13 meters (rounded)
You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.
Hope this helped! (Please mark me brainliest!)
Answer:
12.9794 meters or 13 meters (rounded)
Step-by-step explanation:
You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.
Which shows a difference of squares? 10 y squared minus 4 x squared 16 y squared minus x squared 8 x squared minus 40 x + 25 64 x squared minus 48 x + 9
Answer:
16y² - x² shows a correct difference of squares.
Step-by-step explanation:
Following are the given options from which we have to chose which represents the difference of squares.
A) 10y² - 4x²
B) 16y² - x²
C) 8x² - 40x+25
D) 64x² - 48x+9
Difference of square is given by:
a² - b² = (a + b) (a - b)
If we analyze the expressions from the choices given in the question. We should figure out that option B) should be the right answer that shows a difference of squares. i.e. 16y² - x² shows a correct difference of squares. All other options do not represent the difference of perfect squares.
As in option A) 10y² - 4x²
10y² is not a complete square of any number. Hence, option A) is incorrect.
As in option C) 8x² - 40x+25
Neither of the terms in the expression as shown in option C can be a perfect square. Hence, option C) is incorrect.
As in option D) 64x² - 48x+9
The term 48x+9 in the expression as shown in option D can not be a perfect square. Hence, option D) is incorrect.
Lets take the expression 16y² - x² of option B) and solve it.
First simplify the terms separately to associate them as perfect squares as shown below:
⇒ 16y² = (4y)² Equation (1)
⇒ x² = (1x)² Equation (2)
Now, take the difference of Equation (1) and Equation (2).
⇒ 16y² - x²
⇒ (4y)² - (1x)² Equation (3)
So,
Equation (3 )shows a difference of squares. It can also be represented as factorizing the difference of two perfect squares such as (4y - x) (4y + x).
Which is
(4y - x) (4y + x) = 16y² - x²
= (4y)² - (1x)²
So, option B) i.e. 16y² - x² shows a correct difference of squares.
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Answer:
the correct answer would be
16y² - x²
Dad bought $200,000 of term life insurance at the rate of $5.40 per thousand-dollar unit. How much is the annual premium?
Answer:
It is clear that the annual premium = $1080
Explanation:
Given:
As the total term amount for life insurance is given in the question which is $200,000
rate per $1000 unit = $5.40
Simple Calculation Procedure to get the annual premium:
First step:
Let’s assume $1000 is one unit and the mentioned rate per $1000 unit is $5.40. Now, all you need is to find total number of $1000 units in total term insurance amount ($200,000).
So,
divide $200,000 by $1000 to establish the total number of
1000 units in $200,000 = $200,000/$1000 = 200
Second step:
As 200 is found to be the total number of $1000 units in $200,000.
So, just multiply 200 with $5.40 to ultimately find the annual premium
i.e. $5.40 × 200 = $1080
Hence, it is clear that the annual premium = $1080
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Evaluate the expression of 9! - 4! (5!)
Answer:
360,000.
Step-by-step explanation:
9! - 4! (5!)
= 9*8*7*6*5*4*3*2*1 - 4*3*2*1 * 5*4*3*2*1
= 5*4*3*2*1 ( 9*8*7*6 - 4*3*2*1)
= 120( 3024 - 24)
= 120 * 3000
= 360,000
BRAINLEST AND POINTS PLEASE THANK U.
Answer:
P'(7, - 8 )
Step-by-step explanation:
Given the translation rule
(x, y ) → (x + 4, y - 3 )
This means add 4 to the original x- coordinate and subtract 3 from the original y- coordinate, thus
P(3, - 5 ) → P'(3 + 4, - 5 - 3 ) → P'(7, - 8 )
Consider the following system of equations:
Equation 1: 3x + y = 5
Equation 2:5x – 4y = -3
What is the solution to this system?
(To answer this question, we need to know the value of y.)
O (1.8)
O (1,2)
O (1,1)
O (1.3)
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
3x+y=5
5x-4y=-3
---------------
4(3x+y)=4(5)
5x-4y=-3
----------------------
12x+4y=20
5x-4y=-3
---------------
17x=17
x=17/17
x=1
3(1)+y=5
y=5-3
y=2
9 - 4(7x - 8x) = x - 3
Answer:
.2 or 1/5
Step-by-step explanation:
sorry for bad picture
A 14-gram serving of mayonnaise contains
11 grams of fat. What percent of the mayonnaise,
to the nearest tenth of a percent, is fat?
Answer:
Step-by-step explanation:
the answer is 78.6%
11/14*100=78.6
The total percentage of fat in mayonnaise 78.6 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of mayonnaise be A = 14 grams
Let the total amount of fat be B = 11 garms
Now , the equation will be
The total percentage of fat in mayonnaise is =
( total amount of fat / total amount of mayonnaise ) x 100
The total percentage of fat in mayonnaise is = ( 11 / 14 ) x 100
= 0.7857 x 100
= 78.57 %
Now , on simplifying the equation we get
The total percentage of fat in mayonnaise 78.6 %
Hence , The total percentage of fat in mayonnaise 78.6 %
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how can i solve thus problem help me
Answer:
Position from point A= 383.33 meters
Step-by-step explanation:
A concept to know is that the integral of velocity will give you the distance traveled.
[tex]d=\int\limits^{t_1}_{t_0}{v(t)} \, dt[/tex]
where the interval of integration are the starting time and ending time.
I let the starting time be t₀ = 0, and the ending time t₁=10 for the 10 seconds that it traveled.
I did the integration and got 383.33m traveled in 10 seconds.
So the answer is 383.33 meters.
Ignore the final answer in the image. I misread the question.
The height ,h, in feet of a baseball that is popped up into the air is a quadratic function of the time,t, in seconds, since it was hit. An equation that may model this situation is h(t)=4+60t-16t^2. Answers the following questions accurately, rounding to two decimals places when needed. How high is the ball when it strikes the bat?
Answer: [tex]4\ feet[/tex]
Step-by-step explanation:
The exercise provides you the following Quadratic function:
[tex]h(t)=4+60t-16t^2[/tex]
Then, based on the information given in the exercise, you can conclude that, when the ball strikes the bat, the time in seconds is the following:
[tex]t=0[/tex]
Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and then evaluate.
Then, you get this result:
[tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4+0-0\\\\h(0)=4[/tex]
The value of x in the expression 2x+3=13 is
A. 8
B.5
C.4
D.3
Answer:
the anwer of youre question is B.5 .
I need help please and thank you
Answer:
15
Step-by-step explanation:
n is the number of people and k the number of chairs
here n = 6 and k = 4
note n! = n(n - 1)(n - 2).... × 3 × 2 × 1, thus
[tex]\frac{6!}{4!(6 -4)!}[/tex]
= [tex]\frac{6(5)(4)(3)(2)(1)}{4!(2!)}[/tex]
= [tex]\frac{720}{4(3)(2)(1)2(1)}[/tex]
= [tex]\frac{720}{24(2)}[/tex]
= [tex]\frac{720}{48}[/tex]
= 15
a number machine uses a rule to charge input numbers into output numbers. this number machine charged 4 into 16, 5 into 20, and 6 into 24. what number will 7 be cgarged into?
Answer:
28
Step-by-step explanation:
The function that we have in this is f(x) = 4x. We can see this in 4 * 4 = 16, 5 * 4 = 20 and 6 * 4 = 24. Therefore, following the pattern, 7 * 4 = 28.