The simplified form of the expression -2(-8x+7)-(-3x - 7) is 19x - 7.
To simplify the expression -2(-8x+7)-(-3x - 7), we can start by applying the distributive property and simplifying the terms.
First, we distribute -2 to (-8x+7):
-2*(-8x) + (-2)*7 - (-3x) - (-7)
This simplifies to:
16x - 14 + 3x + 7
Next, we combine like terms:
(16x + 3x) + (-14 + 7)
This simplifies to:
19x - 7
Therefore, the simplified form of the expression -2(-8x+7)-(-3x - 7) is 19x - 7.
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please help will give 5 stars image is attached!
Using the concept of similar triangles, the values of x is 12 units
What are similar triangles?Similar triangles are triangles that have the same shape but possibly different sizes. In other words, they have corresponding angles that are equal, and their corresponding sides are in proportion.
Two triangles are considered similar if and only if:
Their corresponding angles are congruent (equal in measure).The ratios of the lengths of their corresponding sides are equal.x/6 = (18 + 6) / x
x / 6 = 24 / x
cross multiply both sides by x;
x * x = 24 * 6
x² = 144
x = √144
x = 12
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How many cubes with edges 1/4 cm. will fit a rectangular prism with length = 7cm, width = 5 cm and height = 6cm? Show your work.
Answer:
here is your answer
Step-by-step explanation:
To find out how many cubes with edges of 1/4 cm will fit inside a rectangular prism with dimensions of length = 7 cm, width = 5 cm, and height = 6 cm, we need to calculate the volume of the rectangular prism and the volume of the individual cube.
Volume of the rectangular prism:
Volume = length × width × height
Volume = 7 cm × 5 cm × 6 cm
Volume = 210 cm³
Volume of the cube:
Volume = edge length³
Volume = (1/4 cm)³
Volume = 1/64 cm³
To determine how many cubes can fit inside the rectangular prism, we divide the volume of the rectangular prism by the volume of the cube:
Number of cubes = Volume of rectangular prism / Volume of cube
Number of cubes = 210 cm³ / (1/64 cm³)
Dividing by a fraction is equivalent to multiplying by its reciprocal:
Number of cubes = 210 cm³ * (64 cm³/1)
Number of cubes = 13440 cm³
Therefore, the rectangular prism can accommodate 13,440 cubes with edges of 1/4 cm.
we can look at this as, hmmm we have a 7x5x6 rectangular prism, whose volume is (7)(5)(6) = 210 cm³. We also have a tiny cube with all sides being ¼, meaning its volume is (¼)(¼)(¼), how many times does that volume go into the larger rectangular prism?
[tex]\stackrel{ \textit{\LARGE volumes} }{\stackrel{ \textit{rectangular prism} }{(7)(5)(6)\implies 210}\hspace{5em}\stackrel{ \textit{tiny cube} }{\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies \cfrac{1}{64}}} \\\\[-0.35em] ~\dotfill\\\\ \textit{how many times does }\frac{1}{64}\textit{ go into }210?\hspace{2em}\cfrac{210}{~~ \frac{ 1 }{ 64 } ~~}\implies 210\cdot 64\implies \text{\LARGE 13440}[/tex]
I need help with this please, The amount of money A excited at the end of t years when a certain amount P is invested at a compound annual rate r is given by A =P(1+_r)^t, if a person invests $200 in an account that pays 10% interest compounded annually find the valence after 5 years. The + is suppose to have a line under it
The value of the investment after 5 years, with an initial investment of $200 at a compound annual rate of 10%, is $322.10.
Compound annual growth rate (CAGR) is a measure of the average annual growth rate of an investment, taking into account the compounding effect over a specific period.
It provides a single percentage figure that represents the annualized growth rate of an investment over time.
The formula given is A =[tex]P(1+r)^t,[/tex] where A is the amount of money excited, P is the initial investment, r is the annual interest rate (as a decimal), and t is the number of years. So, in this case, we have P = $200, r = 0.10 (since the interest rate is 10%), and t = 5 (since we want to know the value after 5 years). We just need to plug these values into the formula and calculate:
A =$[tex]$200(1+0.10)^5[/tex]
A = $[tex]200(1.10)^5[/tex]
A = $200(1.61051)
A = $322.10
Therefore, the value of the investment after 5 years, with an initial investment of $200 at a compound annual rate of 10%, is $322.10.
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A rain gutter along the edge of a roof has the shape of a rectangular prism. It is 7 inches high and 18 feet long. It has a volume of 7560 cubic inches How wide is the gutter?
The width of prism is 5 inches.
We have,
height= 7 inch
Length of prism = 18 feet = 18 x 12 = 216 inches
and Volume of prism = 7560 cubic inches
We know the formula for Volume of Rectangular prism
7560 = l w h
7560 = 7 x 216 x width
7560 = 1512 x width
width = 7560/ 1512
width = 5 inches
Thus, the width of prism is 5 inches.
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What are prime intigers
Whole numbers that are only divisible by 1 and theirselves.
SOMEBODY PLEASE PLEASE HELP ME
ILL GIVE YOU 5 STARS, BRAINLIEST AND GIVE A HEART PLEASE HELP
(Please make sure you answer Part B of the question and show your work!!)
From the results, the mode of transportation that was faster for June is Bus.
How to determine the fastest trnasportation modeTo obtain the fastest means of transportation, the mode of the figures will provide a clue. For Bus, the figures are 16, 14, 15, 14, 31, 15 and for walking, the figures are 22, 19, 21, 20, 21, 20.
The highest nmbers in occurence for the first set of figures are 14 and 15 and for the second set of figures, the numbers that appeared most are 20, 21, and 22. So, the bus offered the fastest route for going to school.
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Rewrite using twentieths 4/5
When fraction 4/5 expressed in terms of twentieths we get 16/20.
To express fraction 4/5 in terms of twentieths, we need to find an equivalent fraction that has a denominator of 20.
To do this, we observe that 5 can be multiplied by 4 to obtain 20, which is our target denominator.
So, we multiply both the numerator and the denominator of 4/5 by 4:
(4/5)× (4/4)
= (4×4) / (5×4)
= 16/20.
By multiplying both the numerator and the denominator by 4, we obtain an equivalent fraction, 16/20, which represents the same value as 4/5.
Therefore, when expressed in terms of twentieths, 4/5 can be written as 16/20.
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suppose A and B are independent events. If P(A)=0.25 and P(B)=0.8, what is P(A B)?
If A and B are independent events with P(A) = 0.25 and P(B) = 0.8, the probability of both events occurring together, P(A B), is 0.2. I hope this helps! Let me know if you have any further questions.
Since A and B are independent events, we know that the occurrence of one event does not affect the probability of the other event happening. Therefore, we can use the formula P(A B) = P(A) * P(B).
Substituting the given probabilities, we get P(A B) = 0.25 * 0.8 = 0.2. This means that the probability of both events A and B occurring together is 0.2 or 20%.
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How many pairs of parallel sides
does this shape appear to have?
There are three pairs of parallel sides.
We have,
Parallel sides refer to two or more sides of a polygon or a shape that are always equidistant and do not intersect.
In other words, parallel sides are lines that lie in the same plane and never meet or cross each other.
In a polygon, such as a rectangle or a parallelogram, parallel sides are pairs of sides that are opposite to each other.
For example, in a rectangle, the two pairs of opposite sides are parallel to each other.
Similarly, in a parallelogram, both pairs of opposite sides are parallel.
Now,
From the figure,
There are three pairs of parallel sides:
- a and d are parallel
- b and e are parallel
- f and c are parallel
Thus,
There are three pairs of parallel sides.
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The decimal point is missing in the quotient below. 100.34/2.9=346. Write and estimate on the line and then place the decimal point in the quotient above.
The quotient with the decimal point placed correctly is 34.6.
Estimating the division of 100.34 by 2.9:
We can round 100.34 to the nearest whole number, which is 100, and round 2.9 to the nearest whole number, which is 3.
Dividing 100 by 3 gives an estimated quotient of 33.
Comparing the estimate to the given quotient:
The given quotient is 346, which is significantly larger than our estimate of 33.
To place the decimal point in the quotient, we need to determine the difference between the given quotient and our estimate. In this case, the difference is four places.
Correcting the quotient:
We can place the decimal point four places to the left in the given quotient 346 to match our estimate of 33. This gives us the corrected quotient:
100.34 ÷ 2.9 ≈ 34.6
So, the quotient with the decimal point placed correctly is 34.6.
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STATISTICS
1. The senior class president would like to host an after-graduation lock-in. There will be games, gifts, and food! In order to decide if classmates would be willing to buy tickets and aftend, she has decided to conduct a survey. She will select 25 students to meet and hear input on the prizes, food, and ticket price. There are 500 members of the senior class.
a. She selects every tenth student as they get off the bus one morning.
b. She asks her choir director to allow her to survey the choir.
c. She meets with the counselor, who selects every twentieth student on the school roster.
d. She assigns each senior a number and randomly selects 25 numbers.
e. She makes an announcement that people interested should meet in the library after school.
f. A roster of the senior class is printed, and each student's name is put into a hat. The principal selects 25 names.
Answer: Option D, she assigns each senior a number and randomly selects 25 numbers. This method would help ensure that the students selected for the survey are representative of the entire senior class.
Some of the items on a restaurant menu are vegetarian and some of them are gluten free. There are 29 items on the menu. 21 of the items are not vegetarian and 7 of these are also not gluten free. 6 of the items are vegetarian but not gluten free. a) If a randomly chosen item is gluten free, what is the probability that it is also vegetarian? b) If a randomly chosen item is vegetarian, what is the probability that it is also gluten free? Give each answer as a fraction in its simplest form.
The probability that a arbitrarily chosen thing that's gluten-free is additionally veggie lover is 6/13.
The probability that a haphazardly chosen thing that's veggie lover is additionally gluten-free is 6/19.
How to Solve the Probability?To fathom this issue, let's characterize the taking after occasions:
V = Thing is veggie lover
G = Thing is gluten-free
We are given the following data:
P(V') = 21/29 (21 things are not veggie lover out of 29)
P(V'∩G') = 7/29 (7 things are not vegan and not gluten-free out of 29)
P(V∩G') = 6/29 (6 things are veggie lover but not gluten-free out of 29)
a) We got to discover P(V|G), the likelihood that an item is vegan given that it is gluten-free. Able to utilize Bayes' hypothesis:
P(V|G) = P(V∩G) / P(G)
We know that P(V∩G) = P(G∩V) = P(V∩G') (since V and G are independent occasions), and P(G) = P(G∩V) + P(G∩V'), so:
P(V|G) = P(V∩G') / [P(G∩V) + P(G∩V')]
Substituting the given values:
P(V|G) = (6/29) / [(6/29) + (7/29)]
= 6/13
Subsequently, the probability that a arbitrarily chosen thing that's gluten-free is additionally veggie lover is 6/13.
b) We ought to discover P(G|V), the likelihood that an thing is gluten-free given that it is veggie lover. Once more, utilizing Bayes' hypothesis:
P(G|V) = P(G∩V) / P(V)
We know that P(G∩V) = P(V∩G) = P(V∩G') (since V and G are independent occasions), and P(V) = P(V∩G) + P(V∩G'), so:
P(G|V) = P(V∩G') / [P(V∩G) + P(V∩G')]
Substituting the given values:
P(G|V) = (6/29) / [(6/29) + (7/29) + (6/29)]
= 6/19
Hence, the likelihood that a haphazardly chosen thing that's veggie lover is additionally gluten-free is 6/19.
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choose the slope and y-intercept that correspond with the graph.
Answer:
First Choice: slope: -3/2 y-intercept: 2
Step-by-step explanation:
Take two plotted points, ex: (0, 2) and (2, -1)
Use slope formula: y2- y1 / x2 - x1
(0, 2) - (x1, y1)
(2, -1) - (x2, y2)
-1 - 2 / 2 - 0 = -3 / 2 (slope)
Now for the y-intercept, the line passes through the number "2" on the y-intercept. Therefore, the y-intercept must be "2".
If this was in slope-intercept form, it would look like; y = -3/2x + 2.
The answer to your question is the first choice. Hope this helps!
Mr Mbhalati has Mr Prepaid account with one of the banks in South Africa.He uses the account to pay water bills .Table 2 shows deposit fees applicable on his account in 2023
determine the minimum amount one will pay when making a deposit of notes and coins
The minimum amount one will pay making a deposit of notes and coins is R7.25.
Here, we have,
To determine the minimum amount one will pay when making a deposit of notes and coins, we need to consider the costs mentioned in Table 2.
According to Table 2, the cost for notes deposit is R2.25 per R100 (or part thereof) deposited, and the cost for coins deposit is R5 per R100 (or part thereof) deposited.
To calculate the minimum amount, we need to determine the lowest possible value for both the notes and coins deposit costs.
For notes deposit:
The minimum value would be R2.25, as it is the cost for depositing less than R100 worth of notes.
For coins deposit:
The minimum value would be R5, as it is the cost for depositing less than R100 worth of coins.
To calculate the total minimum amount, we sum up the costs for notes and coins deposits:
Minimum amount = R2.25 (notes deposit cost) + R5 (coins deposit cost)
Minimum amount = R7.25
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There are 5 purple marbles and 9 yellow marbles in a bowl. Four marbles are randomly selected from the bowl, one at a time, with replacement after each selection. What is the probability that all four marbles are purple?
Round to three decimal places.
A) 0.040
B) 0.095
C) 0.005
D) 0.016
Answer:
0.016
Step-by-step explanation:
Determine the x- and y- intercepts for the graph defined by the given equation.
y = -8
a. x-intercept is (0, -8)
b.
No y-intercept
No x-intercept
y-intercept is (0, -8)
c. x-intercept is (-8, 0)
No y-intercept
No x-intercept
y-intercept is (-8, 0)
d.
The intercepts of the function y = -8 are given as follows:
No x-intercept.y-intercept is (0,-8).What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.The function in this problem is defined as follows:
y = -8.
The function in this problem is a horizontal line at y = -8, meaning that it does not cross the x-axis, hence:
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what is the answer for
2[32-(4-1)3]
[tex] \large\sf \longrightarrow \: 2 \: [ \: 32- \: (4-1) \: 3 \: ] \\ [/tex]
[tex] \large\sf \longrightarrow \: 2 \: [ \: 32- \: (3) \: 3 \: ] \\ [/tex]
[tex]\large \sf \longrightarrow \: 2 \: [ \: 32- \: 3 \times \: 3 \: ] \\ [/tex]
[tex]\large \sf \longrightarrow \: 2 \: [ \: 32- \: 9 \: ] \\ [/tex]
[tex] \large\sf \longrightarrow \: 2 \: [ \: 23 \: ] \\ [/tex]
[tex] \large\sf \longrightarrow \: 2 \: \times 23 \\ [/tex]
[tex] \large\sf \longrightarrow \: 46 \\ [/tex]
6. What is the formula for the slope of a line passing through points (x₁, y₁) and (x2,Y₂)?
Answer: A
Slope = (difference in y) divided by (difference in x)
SOMEBODY PLEASE PLEASE HELP ME IM BEGGING YOU
ILL RATE YOU 5 STARS AND GIVE A HEART PLEASE HELP
Answer:
Step-by-step explanation:
bus / walking
mean:105/ 123
median:15/ 20
mode: 14/ 21
range: 46 /3
Answer:
Bus Walking
Mean- 17.5 Mean- 20.5
Medium- 15 Medium- 20.5
Mode- 14,15 Mode- 20,21
Range- 17 Range- 3
Step-by-step explanation:
Bus: 14, 14, 15, 15, 16, 31
Mean- 14+14+15+15+16+31= 105/6= 17.5
All the numbers combined and then divided by how many numbers were added
Medium- 15+15= 30/2= 15
Two middle numbers are added together and then divided by two
Mode- 14, 15
The most frequent number
Range- 31-14= 17
the difference between the lowest and highest values
Walking: 19, 20, 20, 21, 21, 22
Mean- 19+20+20+21+21+22= 123/6= 20.5
All the numbers combined and then divided by how many numbers were added
Medium- 20+21= 41/2= 20.5
Two middle numbers are added together and then divided by two
Mode-20,21
The most frequent number
Range- 22-19= 3
the difference between the lowest and highest values
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Mountain View School Bay Side School
0 5, 6, 8
9, 8, 2, 0 1 0, 2, 4, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 0, 0, 2, 3, 5
0 3
4 2
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Bay Side
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning. (1 point)
Part A: The measures of center in Mountain View School, mean = 4.75, median = 4.5 and Bay Side School, mean = 5.5, median = 4.5
Part B: The measures of variability: Mountain View School, Range= 9 IQR= 4, Bay Side School, Range= 10 IQR= 3
Part C: Bay Side School would be the better choice.
Part A: Measures of Center
To calculate the measures of center, we will determine the mean and median for each school.
Mountain View School:
Mean = (0 + 5 + 6 + 8 + 9 + 8 + 2 + 0) / 8 = 38 / 8 = 4.75
Median = (4 + 5) / 2 = 4.5
Bay Side School:
Mean = (10 + 2 + 4 + 5 + 6 + 8 + 8 + 7 + 6 + 5 + 5 + 4 + 4 + 3 + 1 + 0) / 16 = 88 / 16 = 5.5
Median = (4 + 5) / 2 = 4.5
Part B: Measures of Variability
To calculate the measures of variability, we will determine the range and interquartile range (IQR) for each school.
Mountain View School:
Range = 9 - 0 = 9
IQR = (6 - 2) = 4
Bay Side School:
Range = 10 - 0 = 10
IQR = (6 - 3) = 3
Part C: Choice based on Class Size
If you are interested in a larger class size, Bay Side School would be the better choice. The mean class size at Bay Side School is 5.5, while at Mountain View School it is 4.75. The range of class sizes at Bay Side School is also larger (10) compared to Mountain View School (9). This indicates that there is a greater variation in class sizes at Bay Side School, providing a higher likelihood of finding larger class sizes. However, it's important to consider other factors such as teaching quality, resources, and overall educational environment before making a final decision.
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Evaluate f (-3) for f(x) = x3 + 3x + 17
The output value of f( -3 ) in the function f(x) = x³ + 3x + 17 is -19.
What is the output value of f( -3 ) in the function?Given the function in the question:
f(x) = x³ + 3x + 17
To evaluate f(-3) for the function f(x) = x³ + 3x + 17, we simply substitute -3 for x in the expression and calculate the result.
f(x) = x³ + 3x + 17
Plug in x = -3
f(-3) = (-3)³ + 3(-3) + 17
First, let's calculate (-3)³, which means raising -3 to the power of 3:
(-3)³ = -3 × -3 × -3 = -27
Next, let's calculate 3(-3):
3(-3) = -9
Now, we can substitute these values into the expression:
f(-3) = -27 + (-9) + 17
Simplifying further:
f(-3) = -27 - 9 + 17
f(-3) = -36 + 17
f(-3) = -19
Therefore, the output value of f(-3) is -19.
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Joseph has 9 business shirts. He needs to take 4 shirts for a work conference. In how many ways can he choose 4 shirts out of 9?
Answer: 3,024
Step-by-step explanation:
This is a probability question. Here, the order does not matter, so a combination of shirts 1, 2, 3, and 4 and 4, 3, 2, and 1 count together as 1. We use the permutation calculator to get 9! / ( 9 - 4 )!. ( 9 - 4 )! is equal to 5! and 9! / 5! = 9x8x7x6, or 3,024
A triangular prism has an approximate surface area of 39.5 square feet. The sides of the equilateral triangular bases are one-third the length of the prism. What are the dimensions of the prism to the nearest foot?
Note that based on the triangular prism problem, the missing items from the blank space are:
1) 2 feet
2) 6 feet.
How is this so?Let the side of the triangular base = x ft
then the length of the prism = 3xft
The side fo the triangular base = 1/3 x the length of the prism.
Hence the surface area:
= 2 * 1/2 * x² * Sin60° + x * (3x) * 3
= √3/2x² + 9x²
The surface area = Area of two equilateral triangles + Areas of three rectangles.
Hence, (√3/2 + 9) X² = 30.5
x = 2ft
Thus, the side fo the triangular base is 2ft and the lenght of the prism is 6ft approximately.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See the attached.
someone please help with my geometry
Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.
Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.
You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.
Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.
Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.
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la 1) Juan está dando un paseo en su bicicleta por un sendero a la orilla de la playa, en donde se encuentra un faro histórico. Para llegar a este existen 2 rutas. La primera, desde donde se encuentra Juan, es de 200 yardas de distancia y la segunda es de 400 yardas. El ángulo desde el faro hacia ambas rutas es de 30°. ¿Cuál es la distancia entre ambas rutas?
La distancia entre ambas rutas es de 100yardas.Para encontrar la distancia entre ambas rutas, podemos utilizar las propiedades de los triángulos y la trigonometría.
Dado que el ángulo desde el faro hacia ambas rutas es de 30 °, podemos utilizar la función trigonométrica del seno para determinar la distancia entre las rutas. El seno de un ángulo se define como la relación entre el lado opuesto al ángulo y la hipotenusa de un triángulo rectángulo.
En este caso, el lado opuesto al ángulo de 30 ° es la distancia entre las rutas, y la hipotenusa es la distancia desde Juan hasta el faro. Tenemos dos triángulos rectángulos, uno para cada ruta.
Para la primera ruta de 200 yardas sen( 30 °) = distancia entre las rutas 200 distancia entre las rutas = sen( 30 °) * 200 Para la segunda ruta de 400 yardas sen( 30 °) = distancia entre las rutas 400 distancia entre las rutas = sen( 30 °) * 400
Simplificando las expresiones, tenemos distancia entre las rutas = (1/2) * 200 = 100 yardas distancia entre las rutas = (1/2) * 400 = 200 yardas.
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Solve by graphing. x2 + 2x – 3 = 0
By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.
We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.
1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:
0 = x^2 + 2x - 3.
This quadratic equation can be factored as (x + 3)(x - 1) = 0.
Therefore, x = -3 or x = 1.
2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.
3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).
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Help me please x^2 - 3x - 10
The factors of -10 to solve the given expression are 2 and -5. Therefore, the correct option is option C.
The given quadratic expression is x²-3x-10.
Factor of -10 sum of factors
1 and -10 1+(-10)=-9
-1 and 10 -1+10=9
2 and -5 2+(-5)=-3
-2 and 5 -2+5=3
Therefore, the correct option is option C.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Step-by-step explanation:
A. The formula for the surface area of a hemisphere is:
SA = 2πr^2
where r is the radius of the great circle. Since we are given that the radius of the great circle is 8 yd, we can substitute this value into the formula:
SA = 2π(8 yd)^2
Simplifying, we get:
SA = 2π(64 yd^2)
SA = 128π yd^2
Therefore, the surface area of the given hemisphere is 128π square yards.
B. The formula for the surface area of a sphere is:
SA = 4πr^2
where r is the radius of the sphere. Since we are given the area of the great circle, we can use the formula for the area of a circle to find the radius:
A = πr^2
r^2 = A/π
r^2 = 28.6 in²/π
r ≈ 3.4 in
Substituting this value into the formula for the surface area of a sphere, we get:
SA = 4π(3.4 in)^2
SA ≈ 146.1 in²
Therefore, the surface area of the given sphere is approximately 146.1 square inches.
Answer:
A. 603.19 yd²
B. 114.4 in²
Step-by-step explanation:
A. The surface area of a hemisphere is equal to half the surface area of a sphere plus the area of the base of the hemisphere.
The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere.
The area of the base of a hemisphere is given by the formula:
A = π r². Therefore, the surface area of a hemisphere is given by the formula:
A = 2πr^2 + πr^2 = 3πr^2
In this case, the radius of the hemisphere is 8 yards, so the surface area is:
A = 3π 8²yd² = 192π yd² approx 603.19 yd²
B. The surface area of a sphere is given by the formula A = 4πr^2,
where $r$ is the radius of the sphere.
The area of a great circle is given by the formula
A = πr^2.
Therefore, the radius of the sphere is given by the formula
[tex]r = \sqrt{A / \pi} = \sqrt{28.6 \text{ in}^2 / \pi} \approx 3.017 \text{ in}[/tex]
Therefore, the surface area of the sphere is A = 4π*3.017² in^2 approx 114.4in².
Another way.
Surface Area of sphere: 4*area of great square:4*28.6=114.4 in²
if 4x+8x=64 what is 2x
Step-by-step explanation:
4x+8x=64
or, 12x=64
or, X=64/12
X= 5.333
now, 2x= 2 multiply X= 2 multiply 5.333= 10.666
hence,2x= 10.666
A specimen of 100 mm length along the stroke of a shaper is machined with 15° rake angle tool. Determine the shear plane angle and chip thickness if uncut chip thickness is 1.5 mm and chip length obtained is 40 mm.
The shear plane angle is approximately 84.3°, and the chip thickness is approximately 15.1 mm.
What is the shear plane angle?To determine the shear plane angle and chip thickness in the given scenario, we can use the following formulas:
Shear Plane Angle (α):
tan(α) = tan(β - φ)
where β is the inclination angle of the machined surface (rake angle) and φ is the friction angle.
Chip Thickness (t):
t = tc / cos(α)
where tc is the uncut chip thickness.
Given:
Uncut chip thickness (tc) = 1.5 mm
Chip length (lc) = 40 mm
Length of the specimen (L) = 100 mm
Rake angle (β) = 15°
First, we need to calculate the shear plane angle (α):
tan(α) = tan(β - φ)
Since the friction angle (φ) is not given, we will assume a typical value of 5°.
tan(α) = tan(15° - 5°)
tan(α) = tan(10°)
α ≈ 84.3° (rounded to two decimal places)
Next, we can calculate the chip thickness (t):
t = tc / cos(α)
t = 1.5 mm / cos(84.3°)
t ≈ 15.1 mm (rounded to two decimal places)
Learn more on shear plane angle here;
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