[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{7}}} \implies \cfrac{ -6 }{ -3 }\implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{2}(x-\stackrel{x_1}{7}) \\\\\\ y-4=2x-14\implies {\Large \begin{array}{llll} y=2x-10 \end{array}}[/tex]
Determine the slope (-6,5) (3,-3)
Answer: M = -8/3
Step-by-step explanation:
When Denine went to the pizza palace to order pizza for her party her friend Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza. If there were 35 pepperoni pizzas ordered how many total pizza were ordered? While waiting on the pizza something went wrong with the oven and 2 out of every 25 pizzas were burned. How many pizzas were burned? If 360 pizzas were ordered how many cheese and how many mushroom pizzas were ordered?
Using proportions, it is found that:
If there were 35 pepperoni pizzas ordered, 150 total pizzas were ordered.12 pizzas were burned.120 cheese pizzas and 96 mushroom pizzas were ordered out of 360 pizzas.What is a proportion?A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.
One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.
Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:
Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.
If 35 pepperoni pizzas were ordered, the total number is found as follows:
7x/30 = 35
7x = 30 x 35
x = 30 x 5
x = 150 pizzas.
2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:
2/25 x 150 = 2 x 6 = 12 pizzas.
The cheese fraction is given by:
10/30.
Hence, out of 360 pizzas, the number is given by:
10/30 x 360 = 10 x 12 = 120 cheese pizzas
The mushroom fraction is given by:
8/30.
Hence, out of 360 pizzas, the number is given by:
8/30 x 360 = 8 x 12 = 96 mushroom pizzas
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A kangaroo hops 2 kilometers in 3 minutes. At this rate, how long, in minutes, does it take the kangaroo to hop 5 kilometers? Answer ________________________ minutes At this rate, how far, in kilometers, does the kangaroo travel in 2 minutes? Answer ________________________ kilometers
Answer:
It takes the kangaroo 7.5 minutes to travel 5 kilometers.
Step-by-step explanation:
It takes the kangaroo 7.5 minutes to travel 5 kilometers.
First step is to formulate
3×5/2
Second step is to determine the time by calculating the product or quotient
Time=3×5/2
Time=15/2
Time=7.5 minutes
Inconclusion how long it takes the kangaroo to travel 5 kilometers is 7.5 minutes.
50pts for this question:)
Answer: 1: 6√6 = 36
hope this helps, good luck!
n minus two dived by seven equals two
What is the measure of C in the parallelogram shown?
A. 45°
B. 35°
C. 135°
D. 145°
D
145
B
C
Given: A, B, and C are collinear, AB=BD, and BD=BC
Prove: B is the midpoint of AC
Using the definition of a midpoint and collinear points, the proof that shows that B is the midpoint of AC is explained below.
What are Collinear Points?If three points are on a straight line, they are defined as being collinear points. That is, three points, A, B, and C are collinear points if they are on a straight line, and B is in the middle of points A and b.
What is the Midpoint of a Segment?When a segment is divided into two equal halves, the point that lies in the middle of the segment where the segment is cut into halves is called the midpoint of the line segment.
The proof that shows that B is the midpoint of line segment AC is shown below:
Statements Reasons
a. A, B, and C are collinear a. Given
AB = BD, BD = BC
b. AB = BC b. Substitution
c. AB ≅ BC c. Definition of congruency
d. B is the midpoint d. AB ≅ BC
Thus, the proof above explains how point B is the midpoint of line segment AC in the image given.
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The perimeter is 70cm2. The sides are 3x-1, 3x, 4x+ 1. What is x?
The perimeter is 70[tex]cm^{2}[/tex]. and x is 7
What is perimeter ?The complete circumference of a shape is referred to as its perimeter. It is the length of any geometric shape with a two-dimensional boundary or outline. Depending on their proportions, multiple figures can have equal perimeters. Think of a triangle built of an L-length wire as an example. If the length of each side is the same, the same wire can be used to create a square. Look at the illustration below, which shows the bounds of a rectangular park.
Given that :The perimeter is 70[tex]cm^{2}[/tex]. The sides are 3x-1, 3x, 4x+ 1.
3x -1 + 3x + 4x + 1 = 70
10x = 70
x = 7
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An architect is making a scale model of an office building he wishes to construct. The model is 9 inches tall. The actual office building he plans to construct will be 75 feet tall. a. What is the scale of the model? b. What scale factor did the architect use to build his model?
Using proportions, it is found that:
a. The scale of the model is of 9:900.
b. The scale factor used was of 100.
What is a proportion, and how it is related to scale problems?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of a situation using operations such as multiplication and division to find the unit rates.
The concept of proportion is followed in scale problems, as scale is the proportion of the drawn distance by the actual distance, as follows:
Scale = Drawn distance : Actual distance.
For the building, in this problem, we have that:
The drawn height is of 9 inches.The actual height is of 75 feet = 900 inches.Applying it's formula, the scale is given by:
9 : 900
The ratio between the actual height and the drawn height is the scale factor, hence:
Scale factor = 900/9 = 100.
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Please hellllp
Determine the intercepts of the line.
Do not round your answers.
4x1= 3y + 5
x-intercept:
y-intercept:
Answer: x-intercept: 5/4
y-intercept: -5/3
Step-by-step explanation:
We can find the y-intercept by looking at the y = mx + b form, the y-intercept would be b in that form:
4x = 3y + 5
y = 4/3x - 5/3
Next, we plug x into that equation:
We can graph it, or find it mathematically:
Set 4/3x = 5/3
4/3x * 3/4 = 5/3 * 3/4
x = 5/4
7×^4 +1
The expression represents a polynomial with _terms.
The constant term is _ the leading terms_, and the leading coefficient is __
The expression represents a polynomial with two terms. The constant term is 1 ; leading terms is 7X^4 and leading coefficient is 7
What is polynomial?Algebraic expressions that are made up of variables and coefficients are called Polynomials. Variables may be called indeterminates. Arithmetic operations such as addition, subtraction, multiplication can be performed for polynomial expressions but not division. As can be noticed, Polynomial is made up of two terms that are Poly meaning “many” and nominal meaning “terms.”.
Term with the highest degree is the leading term of a polynomial therefore 7X^4
Coefficient of the leading term is the leading coefficient of a polynomial therefore 7
The expression has only two terms separated by "+" therefore two terms.
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long division synthetic division
An additional strategy for splitting polynomials is synthetic division. If you are dividing by a polynomial of degree 1, it is a shortcut for long division that only functions in that situation.
The divisor often takes the shape of (x a). Contrary to long division, you are solely concerned with the polynomials' coefficients in synthetic division.
How is lengthy synthetic division performed?Another method for dividing a polynomial by the binomial x - c, where c is a constant, is synthetic division.
Setting up the synthetic division is the first step.
Bring the leading coefficient down to the bottom row in step two.
Step 3: Divide c by the amount that was just entered in the bottom row.
Add the column you made in step 3 in step 4.
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During training, an athlete ran 250m/min. But then on the day of the race, he increased his average speed to 300m/min and finished the race one miute faster than he had during training. What distance was the race?
Answer:
6 m
Step-by-step explanation:
First I want you to understand that distance = speed × time.Consider:
speed= 250. 300.
minutes= let it be x. x-1
distance= 250× x. 300(x-1)
=250x. 300x-300
Since distance remains the same ,250x=300x-300
hence. -50x=-300.
x= 6
The length of the race was 1500 meters.
What is Speed?
Speed is defined as the rate of change of distance travelled per unit time.
Given is an athlete who ran at a speed of 250 m/min. However, on the day of the race, he increased his average speed to 300 m/min and finished the race one minute faster than he had during training.
Assume that the length of the race is (x) meters. Suppose that the runner takes (t) minutes to to complete the race in training. Therefore, we can write -
x = 250t
During the race -
x = 300(t - 1)
Equating both, we get -
250t = 300(t - 1)
250t = 300t - 300
300 = 50t
t = 6 min
Then, the length of the race will be -
x = 250 x 6 = 1500 meters
Therefore, the length of the race was 1500 meters.
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You deposit $675 in a savings account that earns 6% interest compounded
monthly.
a. Write a function that represents the balance after t years.
b. What is the balance after 3 years?
$ 807.76 is the balance after 3 years by compound interest.
What is compound interest with example?
When you earn interest on both the money you have saved and the interest you have already received, this is known as compound interest.For instance, after a year, if you deposited $1,000 in an account with 1% yearly interest, you would have received $10 in interest. Compound interest allows you to earn 1 percent on $1,010 (principal plus interest), or $10.10 in interest payments for the year, in Year Two.Given
Principal , P = $675
Rate , r = 6% = 0.06
Time = t years
n = 12 (compounded monthly)
(a)
Balance after t years is given as,
A = P(1 + r/n)nt
A = 675(1 + 0.06/12)12t
A = 675(1.005)12t
Balance after t years = 675(1.005)12t
(b)
Balance after 3 years = 675(1.005)12*3
= 675(1.005)36
= 675*1.19668
=807.7593 \approx 807.76
Balance after 3 years = $ 807.76
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b. What does the standard deviation tell you about the trees at these
farms?
From the given dot plot, it is found that:
1. Farm 1 has mean of 8 inches and standard deviation of 1.15 inches, while Farm 2 has a mean of 8 inches but a standard deviation of 2.31 inches.
2. The lower standard deviation tells that the heights of the trees in Farm 1 are more uniform than in Farm 2.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set.A dot plot shows the number of times that each observation appears in a data-set.
Hence, at farm 1, the measures are given as follows:
6, 7, 7, 8, 8, 8, 9, 9, 10.
The mean is given by:
M = (6 + 2 x 7 + 3 x 8 + 2 x 9 + 10)/9 = 8 inches.
The standard deviation is given by:
S = sqrt[((6-8)² + 2 x (7-8)² + 3 x (8-8)² + 2 x (9-8)² + (10-8)²)/9] = 1.15 inches.
For Farm 2, the measures are given as follows:
4, 6, 6, 8, 8, 8, 10, 10, 12.
Hence the mean and the standard deviation are given, respectively, by:
M = (4 + 2 x 6 + 3 x 8 + 2 x 10 + 12)/9 = 8 inches.S = sqrt[((4-8)² + 2 x (6-8)² + 3 x (8-8)² + 2 x (10-8)² + (12-8)²)/9] = 2.31 inches.Farm 1 trees' heights have a lower standard deviation than Farm 2 trees' heights, hence they have more uniform trees.
What is the missing information?The problem is missing and is given by the image at the end of the answer.
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TV
and
WY
areparallellines.
S
T
U
V
W
X
Y
Z
Which angles are adjacent angles?
Since TV and WY are parallel lines, the angles which are adjacent angles include the following: C. <VUX and <WXZ.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
In Geometry, when two (2) parallel lines are cut by a transversal, the vertical angle and its adjacent angle that are formed are supplementary angles, which makes:
<VUX and <WXZ.
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Complete Question:
TV and WY are parallel lines. Which angles are adjacent angles?
<VUX and <TUX.
<VUX and <VUX.
<VUX and <WXZ.
<VUX and <YXZ.
Which equation has the same solution as 4-(2x-5)= (x-19)/4
Algebric equations which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.
The equation given is,
4 - (2x-5) = (x - 19)/4
16 - 4(2x - 5) = (x - 19)
16 - 8x + 20 = x - 19
All terms having a variable x is taken to one side and the numerical values are kept on the other side.
16 + 20 + 19 = x + 8x
9x = 55
x = 55/9
Therefore, equation which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.
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what is a data pattern that repeats itself after a period of days, weeks, months, or quarters? part 2 a. trend b. cycle c. random variation d. seasonality
Seasonality is a data pattern that repeats itself after a period of weeks, days, months, or quarters.
The progressive upward or downward movement of the data over time is referred to as a trend. Trend movement may be explained by shifts in income, population, age distribution, or cultural perspectives.
Data patterns called cycles appear every few years. They play a significant role in short-term company analysis and planning and are typically linked to the business cycle. Because they might be influenced by worldwide unrest or political events, business cycles are challenging to predict.
Data "blips" are caused by chance and uncommon circumstances and are known as random fluctuations. They exhibit no clear pattern, making prediction impossible.
Seasonality is a recurring trend in data that occurs every few days, weeks, months, or quarters. Six typical seasonality patterns exist.
Hence, the correct option is (d) seasonality.
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Helppp
What is the factorization of the trinomial below?-x2 - 2x + 48
A.-1(x + 8)(x - 6)
B.(x + 6)(x - 8)
C.-1(x - 8)(x + 6)
D.(x - 6)(x + 8)
The factorization of the trinomial -x² - 2x + 48 gives the expression -1(x + 8)(x - 6)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Given the polynomial:
-x² - 2x + 48
Factorizing:
-1(x² + 2x - 48)
= -1[x² + 8x - 6x - 48]
= -1[x(x + 8) -6(x + 8)]
= -1(x + 8)(x - 6)
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There is a 20% sale on in Zara
The bag I want is now £60.
What was the original cost of
my bag?
please give steps for this answer!
Answer:
£72.00
Step-by-step explanation:
60*20% (0.20) = 12
60 (original price) + 12 = 72
therefore, the original price of the bag was £72.00
What is the product in simplest form?
-8/9 . 5/6
516
O-1
O
T
35
15
20
27
16
The value of the product -8/9 . 5/6 is -20/27. Option C
What is a fraction?A fraction can simply be defined as the part of a whole set or element.
The several types of fractions are listed as;
Simple fractionsComplex fractionsProper fractionsImproper fractionsMixed fractionsExamples of proper fractions: 3/4, 5/6
Examples of improper fractions: 4/3 , 8/7
Examples of mixed fractions: 2 1/2 , 3 4/5
Examples of simple fractions: 1/2 , 1/3
Given the expression:
-8/9 . 5/6
To determine the product of the fractions, we need to follow the steps
Multiply the numerators
-40/ 9 × 6
Now, multiply the denominators
-40/57
Reduce to simplest forms by using the divisor 2, we have;
-20/ 27
Hence, the value is -20/27
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the lengths of a certain species of crocodiles are normally distributed with a mean of 12.5 ft and a standard deviation of 2.1 ft. find the probability that a randomly selected crocodile is more than 12 feet long.
If the lengths of a certain species of crocodiles are normally distributed with a mean of 12.5 ft and a standard deviation of 2.1 ft. the probability that a randomly selected crocodile is more than 12 feet long is 0.5941.
ProbabilityGiven :
Mean = 12.5 ft
Standard deviation = 2 .1 ft
Randomly selected crocodile = 12 ft
Hence,
First find Z value, Z = (12 – 12.5) / 2.1
Z = - 0.5 / 2. 1
Z = - 0.238
Using Z table, we will get the probability :
Probability = 1 – 0.4059
Probability = 0.5941
Therefore we can conclude that the probability is 0.5941.
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As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
As the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.
What is sampling distribution?Regardless of the distribution of the population one samples from, is roughly normally distributed for a large sample size (we shall explain this later). The population will have a mean and standard deviation if it has a mean and one.Regardless of the distribution of the population, the central limit theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases. The CLT is frequently thought to hold for sample sizes equal to or larger than 30.The sample size and variability affect how accurate your statistics are. A tighter confidence interval with a smaller margin of error will be obtained with a bigger sample size or lower variability.Therefore, as the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.
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Find a point-slope form for the line with slope = 1/5 and passing through the point (- 1, - 9).
Answer:
[tex]y - ( - 9)) = \frac{1}{5} (x - ( - 1))[/tex]
[tex]y + 9 = \frac{1}{5} (x + 1)[/tex]
(HELP ALAAH AKBARRRR!!) 2x3=6
3x3=?
Answer:
9
Step-by-step explanation:
2x3=6 (2+2+2=6)
3x3=9 (3+3+3=9)
Answer:
ans is 9 bro
Step-by-step explanation:
2x^2 +2x+4= 0,solve for x .answers should be in decimal.
the question does not have a solution.
a) graphing - the parabola never crosses the x-axis. When y = 0, what does x equal? none.
b) cannot factor/properly solve for zeros.
Please help me with this question!
Answer:
Option 1, 4
Step-by-step explanation:
[tex]\frac{108}{8}=\frac{27}{4}=6.75 \\ \\ 169<170<196 \implies 13<\sqrt{170}<14 \\ \\ \therefore \frac{108}{8}<\sqrt{170}[/tex]
Find all values for x that will make this expression equal to 0.
(x-9)(x+1)
The values of x that will make this expression equal to 0 are -1 and 9
How to determine the valuesGiven the expression;
(x-9)(x+1)
Let's take the following steps to determine the values
First, expand the bracket, we get;
x² + x - 9x - 9
x² + x - 9x - 9
equate the expression to zero, we have;
x² + x - 9x - 9 = 0
add or subtract the like terms, we get;
x² - 8x - 9 = 0
Factorize the values
x² - 9x + x - 9 = 0
Factor out the common terms in the equation, we get;
x(x - 9) + 1(x - 9) = 0
The equation are;
x + 1 = 0 and x - 9 = 0
Then,
x + 1 = 0
x = -1
x - 9 = 0
x = 9
Thus, the values are - 1 and 9
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Calculate the slope.
Help!! I’m a little confused on how to do this do u mind explaining? thank you :)
to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}} \implies \cfrac{4 +4}{0 +3}\implies {\Large \begin{array}{llll} \cfrac{8}{3} \end{array}}[/tex]
A kite is at the end of a string that is 40 meters long. The person
is holding the end of the string 3 meters off the ground, and the
angle of elevation formed by the string is 50°. Which expression
represents how high in meters the kite is off the ground?
The expression representing height of kite from ground is Height = sin 50° × 40.
The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -
sin theta = perpendicular ÷ hypotenuse
Keep the values in mentioned trigonometric relation to find the expression -
sin 50 = height ÷ 40
Height = sin 50° × 40
Finding the height using formed equation -
Height = 0.77 × 40
Performing multiplication
Height = 30.64 meters
Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.
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